Single Molecule Kinetic and Thermodynamic Studies of
Molecular Crowding and Extreme Pressure Effects on Nucleic Acid Conformations

byHsuan-Lei Sung
B.S., National Taiwan University, 2011

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillmentof the requirements for the degree ofDoctor of Philosophy
Chemistry
2022

Committee Members:
David Nesbitt, Chair
Meredith Betterton
Joseph Falke
J. Mathias Weber
Daniel Schwartz

iiSung, Hsuan-Lei (Ph.D. Chemistry)Single-Molecule Kinetic Studies of Nucleic Acid Folding: Insights from Temperature andPressure Dependence
Thesis directed by Professor David J. Nesbitt

Biochemical activity of proteins and nucleic acids is strongly dependent on threedimensional shape. As a result, upon synthesis biomolecules often undergo a series of secondary
and tertiary folding transitions to achieve a spatial configuration crucial to biochemical function.
This dissertation describes detailed studies on the folding dynamics of small RNA/DNA nucleic
acid oligomers and RNA riboswitches at the single molecule level. In particular, our focus is on
both equilibrium and real time kinetic characterization of two physical phenomena that cangreatly impact the stability of a specific nucleic acid structure: “molecular crowding” andpressure-induced denaturation.
Nucleic acids have evolved to function inside cells. The intracellular environment ishighly concentrated (> 20% by weight) with various solutes (mono/divalent cations, anions,peptides, nucleotides, fatty acids, osmolytes, metabolites, etc.) and thus is quite different fromthe dilute buffer conditions in which biochemical studies are traditionally performed. A
predictive understanding of such spatial crowding effects on nucleic acid conformation istherefore key to unambiguous interpretation of in vitro data in terms of predicted in vivo
behavior. Single molecule Fluorescence Resonance Energy Transfer (smFRET) measurements
obtained with precise control of temperature allows us to measure equilibrium and kinetic
properties as a function of temperature, which permits deconstruction of free energy changes interms of enthalpic and entropic components. Significantly, this work reveals that stabilization of

iii
nucleic acid structure with biochemically inert polymer PEG (polyethylene glycol) is essentiallyentirely entropic, i.e., consistent with excluded volume as the primary origin of nucleic acidmolecular crowding. Furthermore, clean separation of the enthalpic and entropic chemical
contributions in such temperature studies permits the dependence of crowding on molecular size
to be revealed, with the surprising result that smaller crowders (at constant w%, percentage by
weight) promote nucleic acid folding more effectively.
Due to the rapid pressure increase as a function of ocean depth, marine life canexperience significant fluctuations in pressure. Moreover, marine organisms in deep sea regions(such as the Marianas trench) are constantly exposed to extreme pressures up to a thousand bars.
In order to better understand how deep sea organisms adapt to extreme pressures at the molecularlevel, studies of the pressure-dependent effects on biomolecular structures (both protein andnucleic acids) are thus essential. In this work, our single molecule confocal microscope iscoupled to a pressure generating system to explore the pressure response of nucleic acid folding.
The pressure dependent equilibria reveal that nucleic acids effectively take up more volume thanits unfolded conformation upon folding, which is at least initially counterintuitive to thecommonly held physical picture of a folded conformation being more compact. The studies also
demonstrated that the osmolyte trimethylamine N-oxide (TMAO), which is found to accumulate
in deep sea fish, efficiently increases the pressure stability of nucleic acids both by promoting
folding equilibrium and reducing the denaturing sensitivity to external hydrostatic pressure.

iv
Acknowledgements

First, I would like to acknowledge my advisor David Nesbitt for providing me theresearch opportunities at CU/JILA and helping me become a better scientist. David is a greatteacher, generous with both knowledge and time. He’s not only taught me things about sciencebut also encouraged me to clearly communicate my research in both speaking/writing, which has
benefitted me tremendously. I would also like to thank the current and past members of the
Nesbitt group: Andrea Menendez, David Nicholson and Abhigyan Sengupta for sharing interestin biophysics; Tim Livingston-Large, Jake Pettine and Mikhail Ryazanov for experimental
advice and assistance; Erik Holmstrom and Mario Vieweger for helping me start with the single
molecule experiment and teaching me the nucleic acid techniques; and all the rest of the groupmembers that I had the pleasure and honor to work with.
I would like to thank all the JILA staff for keeping our research going: Brian Lynch,
Jennifer Erickson, Randall Holliness, Daniel Lewis and Karen Lichtfuss in the supply office forhelping me shop lab supplies and equipment; Hans Green, Todd Asincar, Kyle Thatcher andCalvin Schwadron in the JILA instrument shop for assisting me with the high-pressure
experiment setup and fabrication of the capillary sample holders; Jim McKown and Eric
Alvarado from the computing group for taking care of our old computers in the lab; Agnieszka
Lynch of JILA human resources for hiring me and her advice on all the student and visa issues.
People from the Chemistry department need acknowledgement too: Cora Fagan, Julia Shipman
and many other graduate program managers in the past years for keeping me informed of
department and graduate school updates. I would also like to thank my classmates in the Physical
Chemistry program: Jonathan Church, Hayden Hamby and Jose Luis Falla for their friendshipv
and support. I am genuinely extremely grateful for everyone at CU who had been part of my
doctoral journey.
In the end, I would like to thank my aunts Li-Ru Fu and Hsiao-Chuan Fu for theircontinuous support for me and my family in Taiwan. I would like to acknowledge my brother
Hsing-Lei Sung for taking care of our mother and many other things at home while I am away. I
wouldn’t have the privilege to continue my study in the US without him. I would like to thankmy mother Ya-Nan Fu for everything she had done for me and the family. There are no words todescribe how grateful I am for her unconditional love and support to make me who I am today.
Last, but certainly not least I would like to thank my best friend Ross Kenneth Thomas, not only
for his friendship and company but also for motivating/encouraging me to become a better
person. Ross was always nice to everyone and genuinely care about people in need. Ross’s
friendship is the best thing to have happened to me.

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Table of Contents

Chapter 1
1.1

1.2
1.3

1.4
1.5
Chapter 2
2.1

2.2
2.3

2.4

2.5

2.6
Chapter 3

3.1
3.2
3.3

Introduction ............................................................................................................1
Nucleic acids ..................................................................................................................1
1.2.1 Nucleic acid structure and function ..................................................................2
1.2.2 Nucleic acid conformational transition ............................................................4
Single-molecule FRET kinetics .....................................................................................6
Thermodynamics of nucleic acid structural transition ...................................................8
1.3.1 Temperature as a variable.................................................................................91.3.2 Pressure as a variable .....................................................................................10
Thesis overview ...........................................................................................................12
References ....................................................................................................................14
Methods .................................................................................................................21
Single-molecule confocal microscope .........................................................................212.1.1 Laser excitation path .....................................................................................21
2.1.2 Fluorescence emission path and detection .....................................................22
Temperature control .....................................................................................................23
Sample preparation ......................................................................................................24
2.3.1 Single molecule construct ..............................................................................24
2.3.2 Sample of interest ...........................................................................................25
Single molecule FRET experiment .............................................................................27
2.4.1 Freely diffusing method .................................................................................27
2.4.2 Surface immobilization method .....................................................................28
High pressure single molecule experiment .................................................................30
2.5.1 Pressure generation and transmission.............................................................30
2.5.2 Sample preparation for high pressure measurements .....................................31
References ....................................................................................................................32
Single Molecule FRET Kinetics of the Mn2+ Riboswitch: Evidence for
Allosteric Mg2+ Control of “Induced-Fit” vs. “Conformational Selection”
Folding Pathways .................................................................................................34
Abstract ........................................................................................................................34
Introduction ..................................................................................................................35
Experiment ...................................................................................................................39
3.3.1 RNA construct design and preparation for single-molecule study.................39

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3.4

3.5

3.6
3.7
Chapter 4

4.1
4.2
4.3

4.4

4.5

4.6
4.7
Chapter 5

5.1
5.2
5.3

3.3.2 Single-molecule FRET spectroscopy and data analysis ..............................41
Results and analysis .....................................................................................................423.4.1 Manganese riboswitch folding kinetics with Mg2+ alone ...............................423.4.2 Manganese riboswitch folding kinetics with Mn2+ alone ...............................48
3.4.3 Synergistic folding in the presence of both Mn2+ and Mg2+ ..........................50
Discussion ....................................................................................................................52
3.5.1 Induced fit vs. conformational selection mechanisms: dependence on
Mn2+/Mg2+ alone ............................................................................................52
3.5.2 Mg2+ mediated manganese riboswitch folding under physiological conditions........................................................................................................................54
Summary and conclusion .............................................................................................59
References ....................................................................................................................60
Novel Heat-Promoted Folding Dynamics of the yybP-ykoY Manganese
Riboswitch: Kinetic and Thermodynamic Studies at the Single Molecule
Level ......................................................................................................................66
Abstract ........................................................................................................................66
Introduction ..................................................................................................................67
Experiment ...................................................................................................................70
4.3.1 RNA construct design and preparation for single-molecule study.................70
4.3.2 Single-molecule FRET spectroscopy .............................................................73
Results and analysis .....................................................................................................74
4.4.1 Temperature-promoted folding revealed by smFRET ...................................74
4.4.2 Mg2+ effects on the temperature dependence of folding ...............................75
4.4.3 Mn2+ effects on the temperature dependence of folding ...............................80
Discussion ....................................................................................................................82
4.5.1 Unconventional temperature response of manganese riboswitch folding .....82
4.5.2 Temperature response of RNA .......................................................................84
4.5.3 Reconstructing folding free energy landscapes from temperature-dependent
kinetics............................................................................................................86
Summary and conclusion .............................................................................................88
References ....................................................................................................................90
Sequential Folding of the Nickel/Cobalt Riboswitch is Facilitated by aConformational Intermediate: Insights from Single-Molecule Kinetics andThermodynamics..................................................................................................97
Abstract ........................................................................................................................97
Introduction ..................................................................................................................98
Experiment .................................................................................................................102

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5.4

5.5

5.6
5.7
Chapter 6

6.1
6.2
6.3

6.4

6.5
6.6
6.7
Chapter 7

7.1
7.2

5.3.1 NiCo riboswitch construct design and sample preparation ..........................102
5.3.2 Single-Molecule FRET spectroscopy and temperature control ...................105
5.3.3 Single-Molecule EFRET trajectory and data analysis .....................................106
Results and analysis ...................................................................................................109
5.4.1 Co2+-promoted NiCo riboswitch folding ......................................................109
5.4.2 Ni2+-promoted NiCo riboswitch folding ......................................................113
5.4.3 Physiological cation (Na+/Mg2+) effects on the NiCo riboswitch structure .114
5.4.4 Temperature dependent folding equilibrium: Van’t Hoff analysis ..............117
5.4.5 Temperature dependent folding kinetics: transition state theory (TST)
analysis .........................................................................................................119
Discussion ..................................................................................................................121
5.5.1 Cations facilitate formation of a prefolded NiCo riboswitch intermediate ..121
5.5.2 Folding is induced by ligand binding to the conformational intermediate...123
5.5.3 Detailed thermodynamics for folding of the NiCo riboswitch .....................125
Summary and conclusion ...........................................................................................128
References ..................................................................................................................130
Smaller Molecules Crowd Better: Crowder Size Dependence Revealed bySingle-Molecule FRET Studies and Depletion Force Modeling Analysis .....136
Abstract ......................................................................................................................136
Introduction ................................................................................................................137
Experiment .................................................................................................................142
6.3.1 RNA construct design and sample preparation ............................................142
6.3.2 Temperature controlled single-molecule FRET spectroscopy .....................143
Results ........................................................................................................................144
6.4.1 RNA tertiary folding is promoted by PEG and small molecule DME .........144
6.4.2 Predominantly entropic stabilization confirmed by temperature dependence......................................................................................................................147
6.4.3 Stabilization free energies are greater for smaller molecular crowders .......150
Discussion ..................................................................................................................152
Summary and conclusion ...........................................................................................158
References ..................................................................................................................159
Effects of Molecular Crowders on Single-Molecule Nucleic Acid Folding:Temperature-Dependent Studies Reveal True Crowding vs Enthalpic
Interactions .........................................................................................................164
Abstract ......................................................................................................................164
Introduction ................................................................................................................165

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7.3

7.4

7.5

7.6
7.7
Chapter 8

8.1
8.2
8.3

8.4

8.5

8.6
8.7

Experiment .................................................................................................................168
7.3.1 Nucleic acid constructs and sample preparation ..........................................168
7.3.2 Single-Molecule FRET spectroscopy and temperature control ...................170
7.3.3 Single molecule FRET data analysis ............................................................171
Results and analysis ...................................................................................................172
7.4.1 Crowder effects on the DNA hairpin secondary folding kinetics ................172
7.4.2 Crowder effects on the RNA TL-TLR tertiary folding kinetics ...................174
7.4.3 Crowding effects on DNA secondary structure folding thermodynamics ...176
7.4.4 Crowding effects on RNA TL-TLR tertiary folding thermodynamics ........181
Discussion ..................................................................................................................184
7.5.1 Crowder effects on nucleic acid folding kinetics .........................................184
7.5.2 Predominantly entropic effects of PEG are consistent with pure crowding 185
7.5.3 Enthalpic/entropic effects with polysaccharides suggest preferential binding......................................................................................................................187
Summary and conclusion ...........................................................................................191
References ..................................................................................................................192
Synergism in the Molecular Crowding of Ligand-Induced Riboswitch
Folding: Kinetic/Thermodynamic Insights from Single Molecule FRET
Spectroscopy .......................................................................................................197
Abstract ......................................................................................................................197
Introduction ................................................................................................................198
Experiment .................................................................................................................200
8.3.1 Lysine riboswitch construct and sample preparation ...................................200
8.3.2 Temperature-controlled single molecule experiment and data analysis ......201
Results and analysis ...................................................................................................2048.4.1 Lysine riboswitch folding promoted by PEG ...............................................2048.4.2 PEG stabilization on lysine dependent folding illustrated by kinetic modeling......................................................................................................................2058.4.3 Temperature-dependent folding reveals both enthalpic and entropic PEG
effects ...........................................................................................................209
Discussion ..................................................................................................................212
8.5.1 Kinetic vs. thermodynamic crowding data indicate conflicting soluteinteraction models ........................................................................................212
8.5.2 PEG prearranges the unfolded riboswitch to facilitate folding ....................214
Summary and conclusions .........................................................................................216
References ..................................................................................................................217

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Chapter 9

9.1
9.2
9.3

9.4

9.5

9.6
9.7

DNA Hairpin Hybridization under Extreme Pressures: A Single-Molecule
FRET Study ........................................................................................................222
Abstract ......................................................................................................................222
Introduction ................................................................................................................223
Experiment .................................................................................................................227
9.3.1 High pressure microscopy cell and pressure control ....................................227
9.3.2 Temperature Control ....................................................................................229
9.3.3 DNA 40A hairpin construct and sample preparation ...................................230
9.3.4 Single-molecule FRET spectroscopy and data analysis ...............................232
Results and analysis ...................................................................................................234
9.4.1 Pressure dependence of DNA hairpin folding ..............................................234
9.4.2 Temperature dependence of DNA hairpin Folding ......................................238
Discussion ..................................................................................................................241
9.5.1 Deconstructing free volume changes into DNA stem and loop formation ..241
9.5.2 Deconstruction of stem (ΔHstem) and loop (ΔHloop) enthalpy changes .........244
9.5.3 Deconstruction of stem (ΔSstem) and loop (ΔSloop) entropy changes ............245
Summary and conclusion ...........................................................................................249
References ..................................................................................................................250

Chapter 10

10.1
10.2
10.3

10.4

10.5

10.6

High Pressure Single-Molecule FRET Studies of the Lysine Riboswitch:
Cationic and Osmolytic Effects on Pressure Induced Denaturation.............256

Abstract ......................................................................................................................256
Introduction ................................................................................................................257
Experiment .................................................................................................................260
10.3.1 High pressure capillary sample cell and pressure control ............................260
10.3.2 RNA lysine riboswitch construct and sample preparation ...........................262
10.3.3 Single-molecule FRET spectroscopy and data analysis ...............................263
Results and analysis ...................................................................................................267
10.4.1 Pressure-induced denaturation of the lysine riboswitch ...............................267
10.4.2 Pressure-dependent effects on ligand-induced folding of the lysine riboswitch......................................................................................................................268
10.4.3 Cation effects on pressure dependent folding of the lysine riboswitch ........272
10.4.4 TMAO effects on the pressure dependent lysine riboswitch folding ...........276
Discussion ..................................................................................................................279
10.5.1 Pressure denaturation of lysine riboswitch folding ......................................279
10.5.2 Cationic effects on the lysine riboswitch ....................................................281
10.5.3 Osmolytic protection against pressure denaturation ....................................283
Summary and conclusion ...........................................................................................289

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10.7

References ..................................................................................................................290

Chapter 11

11.1
11.2
11.3

11.4

11.5

11.6
11.7

Abstract ......................................................................................................................297
Introduction ................................................................................................................298
Experiment .................................................................................................................301
11.3.1 Single molecule FRET microscopy under external hydraulic pressure .......301
11.3.2 Sample Preparation and Single Molecule Tethering ....................................302
Results and analysis ...................................................................................................304
11.4.1 Kinetic origin of DNA hairpin unfolding with increasing pressure .............304
11.4.2 Volumetric characterization of pressure-dependent DNA (un)folding ........305
11.4.3 Effects of Na+ on pressure dependent folding kinetics ................................308
Discussion ..................................................................................................................311
11.5.1 Effective volume of the DNA hairpin increases along the folding path ......311
11.5.2 Na+ decreases the activation volumes for both folding and unfolding
pathways ...................................................................................................314
11.5.3 Cation-independent volume changes at physiological salt concentrations......................................................................................................................317
11.5.4 Na+ stabilization effects on DNA secondary structure revisited ..................320
Summary and conclusion ...........................................................................................322
References ..................................................................................................................323

Chapter 12

12.1
12.2
12.3

12.4

12.5

12.6

Single-Molecule Kinetic Studies of DNA Hybridization Under Extreme
Pressures ............................................................................................................297

Ligand-Dependent Volumetric Characterization of Manganese Riboswitch
Folding: A High-Pressure Single-Molecule Kinetic Study .............................328

Abstract ......................................................................................................................328
Introduction ................................................................................................................329
Experiment .................................................................................................................332
12.3.1 Single-molecule fluorescent construct design and sample preparation ........332
12.3.2 High pressure single-molecule FRET spectroscopy ....................................334
Results and analysis ...................................................................................................335
12.4.1 Kinetic origins of manganese riboswitch unfolding at increasing pressure .335
12.4.2 Mn2+ effects on pressure dependent riboswitch folding ...............................338
12.4.3 Mg2+ effects on the pressure dependent riboswitch folding .........................340
Discussion ..................................................................................................................342
12.5.1 Mn2+ association reduces the effective volume of the riboswitch system....342
12.5.2 Insight from free volume changes along the riboswitch folding coordinate 345
Summary and conclusion ...........................................................................................348

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12.7

References ..................................................................................................................349

Chapter 13
13.1
13.2
13.3
13.4
13.5
13.6

Postmortem and Future Directions ..................................................................353

Introduction ................................................................................................................353
Label-free single molecule biosensor for TNT detection ..........................................353
Mimicking co-transcriptional folding by the truncated guanidine-II riboswitch.......356
Single molecule kinetics of surface immobilized brome mosaic virus RNA ............358
Osmolytes and crowding effects under extreme pressures ........................................360
References ..................................................................................................................361

Bibliography ...............................................................................................................................363

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List of Tables

Table 3.1 ........................................................................................................................................46
Least squares fit results of the smFRET kinetics for Mg2+ promoted folding of the Mn2+
riboswitch.
Table 3.2 ........................................................................................................................................49
Least squares fit results of the smFRET kinetics for Mn2+ promoted folding of the Mn2+
riboswitch.
Table 5.1 ......................................................................................................................................109
Rate constants obtained from HMM and traditional dwell time analysis. Error bars inparentheses represent 1 standard deviations of the mean.
Table 5.2 ......................................................................................................................................111
Fitting results from Hill analysis. (* indicates parameters fixed in the fit). Error bars inparentheses represent 1 standard deviations of the mean.
Table 5.3 ......................................................................................................................................118
Thermodynamic values obtained from a van’t Hoff analysis of the equilibrium constantdata, where ∆G0 is calculated from Keq at T = 22.5 ℃. Error bars in parentheses represent
1 standard deviations of the mean.
Table 5.4 ......................................................................................................................................121
Thermodynamic values obtained from an Eyring/TST analysis. Error bars in parentheses
represent 1 standard deviations of the mean.
Table 6.1 ......................................................................................................................................149
Thermodynamic parameters obtained from the van’t Hoff analysis. *from global fit
results.
Table 7.1 ......................................................................................................................................179
Thermodynamic parameters of DNA hairpin folding obtained from van’t Hoff and Eyring
analyses. Asterisk (*) indicates results from global fits assuming a common slope (i.e.,
enthalpy change) between no crowder and 7.5 w% PEG data.
Table 7.2 ......................................................................................................................................193
Thermodynamic parameters of RNA TL-TLR folding obtained from van’t Hoff andEyring analyses. Asterisk (*) indicates results from global fits assuming a common slope(i.e., enthalpy change) between no crowder and 7.5 w% PEG data.
Table 8.1 ......................................................................................................................................206
Least squares fit results for the lysine-induced folding equilibria.
Table 8.2 ......................................................................................................................................208
Least squares fit results for the lysine-induced folding kinetics.
Table 10.1 ....................................................................................................................................270
V0 obtained at increasing [lysine].

xiv
Table 10.2 ....................................................................................................................................272
V0 obtained at increasing monovalent (Na+)/divalent (Mg2+) cation concentrations.
Table 10.3 ....................................................................................................................................277
V0 obtained at increasing [TMAO].
Table 11.1 ....................................................................................................................................309
Na+ dependence of overall molar volume changes (ΔV0) for the single molecule DNA
hairpin construct in the absence of divalent cation (i.e., [Mg2+] = 0).
Table 11.2 ....................................................................................................................................310
Na+ dependence of ΔV‡fold and ΔV‡unfold molar volume changes for the single molecule
DNA hairpin construct in the absence of divalent cation (i.e., [Mg2+] = 0).
Table 12.1 ....................................................................................................................................340
ΔV0 and ΔV‡fold/unfold values as a function of increasing Mn2+. The reported uncertainties
represent standard deviation of the mean for triplicate studies.

xv
List of Figures

Figure 1.1 ........................................................................................................................................1
Chemical structures of deoxyribonucleotide/ribonucleotide and the corresponding
nitrogenous bases.
Figure 1.2 ........................................................................................................................................2
Example of RNA hierarchical folding: (from top to bottom) 1o, 2o and 3o structure of themanganese (Mn2+) riboswitch. (PDB 4Y1I)
Figure 1.3 ........................................................................................................................................5
Examples of nucleic acid structural transition explored in this thesis. (A) 1o → 2o DNA
hairpin formation. (B) 2o → 3o loop-bulge interaction between tetraloop and tetraloop
receptor. (C) Full manganese riboswitch aptamer folding, which involves the Mn2+facilitated loop-loop folding and the rearrangement of the four-way junction as well as
the attached stems.
Figure 1.4 ........................................................................................................................................7
Schematic of single molecule FRET kinetic measurements and sample data. (A) the
immobilized nucleic acid construct at the laser focus for extended fluorescenceobservation. (B) Sample fluorescent signal time trace (upper panel) and the resulting
FRET transfer efficiency EFRET trajectory (lower panel). (C) Dwell time analysis; thelinearity in the semi-log plots indicates the folding and unfolding processes are welldescribed by the first order kinetics.
Figure 2.1 ......................................................................................................................................22
Schematic of the confocal microscope excitation/emission paths. The temperature control
units are indicated in red.
Figure 2.2 ......................................................................................................................................25
FRET energy transfer efficiency (EFRET) as a function of distance between Cy3 and Cy5(R0 = 50 Å).
Figure 2.3 ......................................................................................................................................27
Two common strategies of the single molecule FRET experiment: A) freely diffusing and(B) surface immobilization. The construct in (B) is tethered to the glass surface throughthe biotin-streptavidin interaction.
Figure 2.4 ......................................................................................................................................29
Sample surface immobilization single molecule FRET data. (A) fluorescence signal fromCy3 (green) and Cy5 (red) as a function of time. (B) the resulting time trajectory of
EFRET, where the high and low EFRET states corresponding to the folded and unfolded
conformation, respectively. (C) dwell time distributions (plotted in reverse cumulative
distribution functions) for each state. The data are well-fit to a single exponential decayfunction to obtain the first order folding and unfolding rate constants kfold and kunfold,respectively. Typically, each set of data contains 20 to 50 molecules throughout thisthesis.

xvi
Figure 2.5 ......................................................................................................................................30
Images of the high pressure generating system. (A) The manually operated piston screw
pump and the pressure gauge mounted on the extended surface outside the laser curtain.
(B) The three-way control valve mounted to the optical breadboard that allows verticaltranslation of the sample holder. The blue lines/arrows indicate the direction of pressuretransmitting through the high pressure tubing.
Figure 2.6 ......................................................................................................................................31
Capillary sample holder for the high pressure single molecule experiments. (A) the crosssection of the square capillary. (B) the capillary end glued into the metal plug forcoupling to the high pressure system.
Figure 3.1 ......................................................................................................................................36
Structure of L. lactis yybP-ykoY manganese riboswitch (A) Overall crystal structurereconstructed from X-ray diffraction data (PDB 4Y1I) (B) Structure of M2+ binding sites
with adjacent nucleotides (C) RNA construct design for smFRET experiment.
Figure 3.2 ......................................................................................................................................37
Schematic illustration of induced-fit (IF) and conformational selection (CS) pathways in
the context of a four-state kinetic model.
Figure 3.3 ......................................................................................................................................38
Sample smFRET experimental data; both with background 0.5 mM MgCl2 and total 125
mM monovalent cation (A) Visual representation of manganese riboswitch folding
changing the distance between Cy3 and Cy5 (B) (from top to bottom) Fluorescence time
traces of signals from Cy3 and Cy5, the corresponding EFRET trajectories, cumulative
distribution function of dwell time analysis.
Figure 3.4 ......................................................................................................................................44
Mg2+ dependence of manganese riboswitch folding (A) equilibrium fraction folded as afunction of [Mg2+] (B) Mg2+ dependence of rate constants at [Mn2+] = 0 mM (C) A fourstate model for Mg2+ facilitated manganese riboswitch folding kinetics.
Figure 3.5 ......................................................................................................................................47
Kinetics of Mn2+ promoted manganese riboswitch folding (A) Mn2+ dependent kfold andkunfold (B) Scheme of extended Hill model into six-state kinetic model (least squares fit
results summarized Table 3.2).
Figure 3.6 ......................................................................................................................................51
Equilibrium Mn2+-dependent fraction folded studied at different [Mg2+] (A) [Mg2+] = 0mM (B) 0.5 mM (C) 2 mM.
Figure 3.7 ......................................................................................................................................55
The dominant folding pathways and equilibriums in the extended kinetic model with both
Mg2+ and Mn2+ present.
Figure 3.8 ......................................................................................................................................58
Manganese riboswitch folding under near physiological condition with both Mg2+ andMn2+ (A) Decay of normalized kunfold from [Mn2+] = 0 to saturation condition suggests
Mg2+ enhances the ligand (Mn2+) affinity. (B) Schematic of dominant folding pathway

xvii
indicating that Mg2+ pre-folds the RNA via an induced-fit (IF) mechanism and then Mn2+stabilizes the folded conformation by a conformational selection (CS) mechanism.
Figure 4.1 ......................................................................................................................................71
Structure of L. lactis yybP-ykoY manganese riboswitch: (A) Overall crystal structure(PDB 4Y1I); (B) Close-up details on the cation M2+ binding sites with adjacentnucleotides; (C) Manganese riboswitch sequence in a secondary structure representation.
Figure 4.2 ......................................................................................................................................72
Sample smFRET experiment data: (A) Cartoon depiction of how manganese riboswitch
folding changes the distance between Cy3 and Cy5; (B) Sample time trace of Cy3 and Cy5
fluorescence (22.2 C, top left), the corresponding EFRET trajectory (lower left), and a seriesof EFRET trajectories (lower left) and dwell time distributions (lower right) as a function ofincreasing temperature (22.2 C-28.0C). Note that a small increase in temperature
dramatically increases the folded time distributions, consistent with strongly endothermic
folding (H > 0).
Figure 4.3 ......................................................................................................................................76
Mg2+ dependence of the manganese riboswitch folding under equilibrium conditions: (A)Folded fraction as a function of [Mg2+]; (B) van’t Hoff plot for the temperature dependent
behavior of the manganese riboswitch equilibrium constant (Keq = kfold/kunfold) at [Mn2+] =0.
Figure 4.4 ......................................................................................................................................78
Kinetic effects of Mg2+ in an activated complex/transition state theory analysis of (A)kfold and (B) kunfold.
Figure 4.5 ......................................................................................................................................80
Mn2+ effects on manganese riboswitch folding under equilibrium conditions: (A) Folded
fraction as a function of [Mn2+]; (B) van’t Hoff plot of temperature dependent manganeseriboswitch folding at [Mg2+] = 0.5 mM.
Figure 4.6 ......................................................................................................................................81
Kinetic dependence of Mn2+ in an activated complex/transition state theory analysis of(A) kfold and (B) kunfold.
Figure 4.7 ......................................................................................................................................83
Folding free energy landscapes of the manganese riboswitch: (A) Mg2+ effects on
enthalpic and entropy contributions (left) and the overall free energy (right); (B) Mn2+
effects on enthalpic and entropy contributions (left) and the overall free energy (right).
Note that although there is no information on change in absolute free energies with cation
conditions, the unfolded state (U) is conventionally referenced to zero free energy in bothplots.
Figure 5.1 ....................................................................................................................................102
Structure of E. bacterium NiCo riboswitch. (A) Overall crystal structure (PDB: 4RUM).
(B) Riboswitch sequence in secondary structure representation. The oligomers forming
the ternary smFRET construct are indicated in red, green and blue, respectively.
Figure 5.2 ....................................................................................................................................105

xviii
Schematic of the single-molecule confocal fluorescence microscope. Inset: Cartoon
representation of a doubly fluorophore labeled smFRET construct tethered on the surface
of a glass coverslip for the single-molecule fluorescence observation.
Figure 5.3 ....................................................................................................................................106
Sample fluorescence time traces of Cy3 and Cy5 signal (upper panel) and corresponding
EFRET time trajectories (lower panel) obtained with (A) [Co2+] = 0.3 µmol/L, (B) [Ni2+]= 0.3 µmol/L and (C) neat buffer (background [Mg2+] = 0.5 mmol/L and [Na+] = 100
mmol/L).
Figure 5.4 ....................................................................................................................................107
Sample data analysis of the 3-state folding system. (A) EFRET histogram fit to 3 Gaussianfunctions corresponding to unfolded (U), intermediate (I) and folded (F) subpopulationsof the NiCo riboswitch. (B) Exponential decays of the dwell time distributions presented
in a semi-logarithm plot, indicating that folding and unfolding of the NiCo riboswitch
follow first order kinetics. (C) Schematic representation of detailed NiCo riboswitch
smFRET construct folding and unfolding. Note that the cartoon representation of theunfolded state (U) suggests a more relaxed/less structured state, which does notnecessarily represent the average configuration.
Figure 5.5 ....................................................................................................................................110
Co2+ dependence of NiCo riboswitch folding. (A) Rate constants kU→I (red empty
diamonds), kI→U (green empty diamonds), kI→F (red solid circles) and kF→I (green solid
circles) as a function of [Co2+]. (B) Equilibrium fraction as a function of [Co2+] (green: U,
blue: I, red: F). Solid lines represent fits to the Hill equation (Eq. 5.1). Error bars represent
1 standard deviations of the mean.
Figure 5.6 ....................................................................................................................................112
Ni2+ dependence of NiCo riboswitch folding. (A) Rate constants kU→I (red empty
diamonds), kI→U (green empty diamonds), kI→F (red solid circles) and kF→I (green solid
circles) as a function of [Ni2+]; (B) equilibrium fraction as a function of [Ni2+] (green: U,
blue: I, red: F). Solid lines represent fits to the Hill equation (Eq. 5.1). Error bars represent
1 standard deviations of the mean.
Figure 5.7 ....................................................................................................................................115
General monovalent/divalent background cation dependence of NiCo riboswitch folding.
Rate constants kU→I (red empty diamonds), kI→U (green empty diamonds), kI→F (red solid
circles) and kF→I (green solid circles) are studied as a function of (A) [Na+] and (B)[Mg2+] concentration. Dashed lines are added to highlight the change in k (or lackthereof) as a function of cation concentration. Error bars represent 1 standard deviationof the mean.
Figure 5.8 ....................................................................................................................................116
Temperature dependence of equilibrium constants presented in van’t Hoff plots at (A)[Co2+] = 0 µmol/LM and (B) [Co2+] = 0.5 µmol/L (blue empty diamonds: KU↔I, pinksolid circles: KI↔F). Data fits with linear regression yield detailed thermodynamic
information (i.e. ∆H0 and ∆S0) by Eq. 5.2. Error bars represent 1 standard deviations of
the mean.

xix
Figure 5.9 ....................................................................................................................................119
Temperature dependence of rate constants presented in Eyring plots: kU→I (red empty
diamonds) and kI→U (green empty diamonds) at (A) [Co2+] = 0 µmol/L and (B) [Co2+] =0.5 µmol/L; kI→F (red solid circles) and kF→I (green solid circles) at (C) [Co2+] = 0µmol/L and (D) [Co2+] = 0.5 µmol/L. Data fits with linear regression yield detailed
thermodynamic information (i.e. ∆H‡ and ∆S‡) by Eq. 5.3. Error bars represent 1
standard deviation of the mean.
Figure 5.10 ..................................................................................................................................125
Detailed energy diagram of NiCo riboswitch folding at (A) [Co2+] = 0 µmol/L and (B)[Co2+] = 0.5 µmol/L, with the unfolded state (U) as reference zero (blue: ∆G, red: ∆H,green: −T(∆S) at T = 22.5 ℃).
Figure 6.1 ....................................................................................................................................140
Schematic representation of RNA TL-TLR docking/undocking in the presence of large(PEG) or small (DME) crowders. The RNA sequences color coded in green/red indicate
the tetraloop/tetraloop receptor folding motifs.
Figure 6.2 ....................................................................................................................................142
Sample data of single molecule time-dependent EFRET trajectories (left panel) and EFRET
distributions (right panel) under different crowding conditions: (A) no crowder, (B) 7.5
w% PEG 3k, and (C) 7.5 w% DME.
Figure 6.3 ....................................................................................................................................145
Crowder effects on the TL-TLR docking kinetics. (A) Cumulative distribution functions(CDFs) of docked and undocked dwell time well-characterized by single exponential
decays (B) Crowder concentration dependence of rate constants kdock and kundock withoverall trends highlighted in red dashed and green dotted lines, respectively (C)Crowding effects on rate constants illustrated in unequal free energy shifts in U
(undocked), TS (transition) and D (docked) states. Error bars represent 1σ standard
deviation of the mean.
Figure 6.4 ....................................................................................................................................148
Temperature dependence of TL-TLR docking presented in van’t Hoff plots at elevating(A) PEG 3k and (B) DME concentrations. Error bars represent 1σ standard deviation of
the mean.
Figure 6.5 ....................................................................................................................................152
Crowder size dependence well described by the depletion force model. (A) Crowdingstabilization effects as a function of crowder size at a series of w% concentrations. (B)Schematic representation of depletion force promoting TL-TLR folding. Error bars
represent 1σ standard deviation of the mean. Solid lines represent fits to the depletion
force model (see text for details).
Figure 7.1 ....................................................................................................................................167
smFRET experiment data. (A) Cartoon depiction of DNA hairpin secondary structure
folding and (B) the resulting time-resolved single-molecule fluorescent signal from thedonor, Cy3 (green) and acceptor, Cy5 (red). (C) Sample time-dependent EFRET
trajectories (blue) and the simulated time trace by the simple thresholding method

xx(orange); (D) The corresponding dwell time distribution functions of the folded andunfolded conformations with (from top to bottom) 0 w% crowder, 7.5 w% dextran, and7.5 w% PEG. Data are fit to a single exponential decay function to obtain the rate
constants kfold/kunfold, with uncertainties evaluated from the fits.
Figure 7.2 ....................................................................................................................................169
Sample smFRET experiment data. (A) Cartoon depiction of TL-TLR tertiary structure
folding and (B) the resulting time-resolved single-molecule fluorescent signal from thedonor, Cy3 (green) and acceptor, Cy5 (red). (C) Sample time-dependent EFRET
trajectories (blue) and the simulated time trace by the simple thresholding method(orange); (D) The corresponding dwell time distribution functions of the folded andunfolded conformations with (from top to bottom) 0 w% crowder, 7.5 w% dextran, and7.5 w% PEG. Data are fit to a single exponential decay function to obtain the rate
constants kfold/kunfold, with uncertainties evaluated from the fits.
Figure 7.3 ....................................................................................................................................172
Crowder effects on DNA hairpin folding at constant room temperature (21 ℃). Crowder
concentration dependence of (A) Keq, (B) kfold, and (C) kunfold. Error bars represent
standard deviation of the mean (N = 3). Data are fit to a single exponential function basedon the empirical observation of solute effects on the free energy change upon folding (seetext for more details).
Figure 7.4 ....................................................................................................................................174
Crowder effects on RNA TL-TLR folding at constant room temperature (21 ℃). Crowder
concentration dependence of (A) Keq, (B) kfold and (C) kunfold. Error bars represent
standard deviation of the mean (N = 3). Data are fit to a single exponential function basedon the empirical observation of solute effects on the free energy change upon folding (seetext for details).
Figure 7.5 ....................................................................................................................................177
van’t Hoff plot for the temperature dependent Keq of the DNA hairpin construct atconstant crowder concentrations (0 or 7.5 w%). Least squares fits of the data to Eq. 7.1
yield changes in overall enthalpies (∆H0) and entropies (∆S0).
Figure 7.6 ....................................................................................................................................178
Eyring plot for the temperature dependent (A) kfold and (B) kunfold of the DNA hairpin
construct at constant crowder concentrations (0 or 7.5 w%). Least squares fits of the data
to Eq. 7.2 yield forward/reverse activation enthalpies (∆H‡) and entropies (∆S‡) for
kfold/kunfold.
Figure 7.7 ....................................................................................................................................181
van’t Hoff plot for the temperature dependent Keq of the RNA -TL-TLR construct atconstant crowder concentrations (0 or 7.5 w%). Least squares fits of the data to Eq. 7.1
yield changes in overall enthalpies (∆H0) and entropies (∆S0).
Figure 7.8 ....................................................................................................................................182
Eyring plots for the temperature dependent (A) kfold and (B) kunfold of the RNA TL-TLR
construct at constant crowder concentrations (0 or 7.5 w%). Least squares fits of the data

xxi
to Eq. 7.2 yield forward/reverse activation enthalpies (∆H‡) and entropies (∆S‡) for
kfold/kunfold.
Figure 7.9 ....................................................................................................................................185
Folding free energy landscapes of the DNA hairpin construct. (A) Enthalpic and (B)entropic contributions along the folding coordinate, with the relative enthalpy/entropy ofthe unfold state, U conventionally referenced to zero. The corresponding (C) enthalpic
and (D) entropic changes by the three crowders at 7.5 w%. Note that entropic
contributions (-T∆S) to the free energies are estimated for room temperature conditions(21.0 ℃).
Figure 7.10 ..................................................................................................................................186
Folding free energy landscapes of the RNA TL-TLR construct. (A) Enthalpic and (B)entropic contributions along the folding coordinate with the relative enthalpy/entropy ofthe unfold state, U conventionally referenced to zero. The corresponding (C) enthalpic and(D) entropic changes by the three crowders at 7.5 w%. Note that entropic contributions (T∆S) to the free energies are estimated for room temperature conditions (21.0 ℃).
Figure 7.11 ..................................................................................................................................189
Schematic model for the effects of (A) PEG or (B) dextran on folding of the RNA TLTLR, highlighting the differential entropic (S > 0) and enthalpic contributions (H >0) due to binding of polysaccharide to the greater solvent accessible surface area (SASA)of the unfolded nucleic acid.
Figure 8.1 ....................................................................................................................................200
Schematic presentation of lysine riboswitch single molecule FRET construct folding. (A)The induced-fit mechanism of lysine riboswitch folding where I. lysine binding isfollowed by II. the riboswitch conformational change (U = unfolded riboswitch, F =folded riboswitch, and L = lysine). Note that folding brings Cy3 and Cy5 closer andthereby increases the FRET energy transfer efficiency (EFRET). (B) Sample timedependent fluorescent signal. The conformational change is visualized by the
anticorrelation between the Cy3 and Cy5 signal, which results in EFRET changes.
Figure 8.2 ....................................................................................................................................202
Sample EFRET trajectories and dwell time analysis. (A) EFRET trajectories without PEG. (B)EFRET trajectories with 8 w% PEG. Note that the construct spends significantly more timein the high EFRET state corresponding to the folded conformation. (C) Dwell time analysis
without PEG. (D) Dwell time analysis with 8 w% PEG. The cumulative distributionfunction of the unfolded dwell time decays much more rapidly, corresponding toaccelerated kfold.
Figure 8.3 ....................................................................................................................................203
PEG-dependent lysine riboswitch folding at a constant lysine concentration (1 mM). (A)folding equilibrium and (B) kinetics as a function of PEG concentration. Data are fit to asingle exponential function to highlight the rapid rise of Kfold and kfold with increasing
PEG concentration.
Figure 8.4 ....................................................................................................................................205

xxii
Lysine-dependent folding curves at a series of PEG concentrations. Folded fraction Ffold asa function of lysine with (A) 0 w%, (B) 4 w%, and (C) 8 w% PEG. Data are nonlinear leastsquares fit to the Hill equation (Eq. 8.1).
Figure 8.5 ....................................................................................................................................207
Lysine-dependent folding and unfolding rates at a series of PEG concentrations. Folding
rate constants kfold/kunfold as a function of lysine with (A) 0 w%, (B) 4 w%, and (C) 8 w%
PEG. The kfold data are fit to the Hill-like kinetic equation (Eq. 8.2), while the lysineindependent kunfold data are fit with a horizontal line.
Figure 8.6 ....................................................................................................................................209
van’t Hoff plots for the temperature dependent lysine riboswitch folding at (A) 0 w%
PEG and (B) 6 w% PEG. [lysine] = 1 mM.
Figure 8.7 ....................................................................................................................................210
Eyring plots for the temperature dependent lysine riboswitch folding at (A) 0 w% PEG
and (B) 6 w% PEG. [lysine] = 1 mM.
Figure 8.8 ....................................................................................................................................212
Free energy landscapes for lysine riboswitch folding. PEG effects on the (A) free energy,(B) enthalpic, and (C) entropic contributions along the folding coordinate (U = unfolded
state, TS = transition state, and F = folded state). Values are arbitrarily referenced to zerofor the folded state F.
Figure 8.9 ....................................................................................................................................214
Normalized EFRET distribution of the low EFRET population with 0 w% PEG (blue) and 8
w% PEG (red). Bin size = 0.05.
Figure 9.1 ....................................................................................................................................227
High pressure smFRET experiment setup: (A) High pressure generating system coupled tothe confocal microscope for smFRET freely diffusing study; (B) Top view of the squarecapillary alignment to the microscope objective and the high pressure mechanical sealing
strategy.
Figure 9.2 ....................................................................................................................................230
Details of the DNA hairpin smFRET constructs: (A) Schematic representation of DNA
hairpin folding; (B) The structural details of the complementary strand, with systematic
variations in the duplexing sequence beyond 7-bp denoted in red (A) and green (G). The
location of Cy3 labeling with respective to the duplexing sequence at 3’ end is highlighted
in green, and Cy5 is chemically attached to the 5’ end.

Figure 9.3 ....................................................................................................................................231
Sample data and analysis from the freely diffusing smFRET studies: (A) Sample time
resolved fluorescent signals from 532 nm laser excitation, with upward green and red
traces corresponding to Cy3 and Cy5 fluorescence channels, respectively. The pink trace
due to 633 nm alternating laser excitation (ALEX) of the diffusing constructs is plotted
downward for direct comparison with the 532 nm excitation signals, confirming thepresence (or absence) of the Cy5 fluor. (B) Single events in the fluorescence traces,

xxiiiwhere arrows point at the fluorescent bursts corresponding to (1) an unfolded doublylabeled hairpin, (2) a Cy3-only, (3) Cy5-only and (4) folded doubly-labeled construct. (C)Sample EFRET histogram of the 9-bp (AT) hairpin folding at ambient pressure, fit to asuperposition of two Gaussians. (D) Sample EFRET histogram of the 9-bp hairpin folding
at a series of external pressures, revealing a reversible propensity for unfolding withincreasing Pext (1-2500 bar).
Figure 9.4 ....................................................................................................................................236
Pressure dependence of folding for a systematic series of DNA hairpins: (A) Pressure
effects presented in a van’t Hoff plot of ln[Kfold] versus Pext, for which the slope yields thefree volume change due to DNA stem hybridization (∆V0 = V0fold – V0unfold). (B) Volume
changes upon folding (∆V0) as a function of number of base pairs in the duplex stems,
which reveal a remarkable linear dependence on nstem; (C) Extrapolation of this linear
dependence on stem length to nstem = 0, thereby isolating free volume contributions(∆V0loop) to DNA hybridization from formation of the 40A loop.
Figure 9.5 ....................................................................................................................................239
Temperature dependent folding response: (A) Temperature unfolding effects for a for theseries of DNA hairpins presented as a standard van’t Hoff plot, with the slope (m = -H0
) and intercept yielding the enthalpy and entropy changes upon folding; (B) Enthalpy
change (∆H0) as a function of stem length (nstem, dark blue), as well as predictions (darkred) from nearest neighbor model parameters; (C) Entropy change (∆S0) as a function of
duplex stem length (dark blue), in comparison to the nearest neighbor model prediction
for fully bimolecular stem formation (dark red). The two additional points in (B) and (C)(light blue) correspond to data for an alternate 9-bp construct with the 3’ d(A-T) replaced
by a stronger d(G-C) base pair. Corresponding enthalpy and entropy predictions fromnearest neighbor model predictions for bimolecular stem formation are also shown (lightred), which suggest a small increase in enthalpy and entropy change under unimolecular
stem formation conditions for a hairpin construct.
Figure 9.6 ....................................................................................................................................240
Subtraction of the stem length (nstem) dependent contributions from DNA double-strand
formation resulting in single-strand DNA looping (A) enthalpy (∆H0loop), (B) entropy(∆S0loop) and (C) free volume (∆V0loop) changes. The data is consistent with a simple
linear offset for these loop contributions, indicated by pink, green and orange dashedlines for enthalpy, entropy and free volume, respectively.
Figure 9.7 ....................................................................................................................................248
Summary of our simple additive model for deconstruction of the stem length dependent(9-bp (AT)) folding thermodynamics of a 40 A DNA hairpin.
Figure 10.1 ..................................................................................................................................259
Single molecule FRET construct design for studying ligand-induced lysine riboswitch
folding. (A) Crystal structure of the lysine riboswitch. (PDB: 4ERJ) (B) Schematic
representation of lysine riboswitch folding and the energy transfer between Cy3 and Cy5
in each conformation. (Left: unfolded; right: folded)
Figure 10.2 ..................................................................................................................................261
High pressure smFRET diffusing experiment setup.

xxiv
Figure 10.3 ..................................................................................................................................264
Sample data and analysis. (A) Representative time-resolved fluorescence trajectories. The
green and red signals plotted upward correspond to Cy3 and Cy5 fluorescence channels,
respectively. The pink traces from 633 nm alternating laser excitation (ALEX) is plotted
downward for direct comparison to conform the presence (or absence) of the Cy5
labeling. (B) Detailed fluorescent traces displaying individual fluorescent events: (1)folded doubly labeled, (2) Cy3-only and (3) Cy5-only labeled construct. (C) Sample
EFRET histogram of the lysine riboswitch folding with [lysine] = 2.0 mM at increasingpressure. Each set of data is fit to a two-Gaussian function where the high and low EFRET
populations correspond to folded and unfolded conformations of the lysine riboswitch
respectively. (D) The ln(Kfold) vs P plot where the slope yields the free volume change
during folding V0.
Figure 10.4 ..................................................................................................................................266
Lysine dependent folding at the ambient pressure obtained from smFRET (A) diffusing
and (B) surface tether experiments. Data of fraction folded and kfold are fit to the Hillequation with floating Hill coefficients n = 0.93(16) and 1.12(17), respectively, consistent
with the expected ligand binding stoichiometry from crystal structure data. In smFRET
diffusing experiments, the max folded fraction is observed as 0.63(6) at saturating [lysine].
In surface tether experiments where the lysine-dependent folding and unfolding rates canbe obtained by prolonged observation of the fluorescence signals from a single construct
at a time, the kunfold is found independent of [lysine] as 0.213(14) s-1 and the kfold isdetermined as 1.51(13) s-1 at saturating [lysine], leading to the steady state folded fraction
as 0.88(9). The difference in fraction folded (29(8) %) between the diffusing and surface
tether measurements is made up by the subpopulaion of constructs that are incapable offolding (28(4) %) from the previous raster scanned image.
Figure 10.5 ..................................................................................................................................269
Pressure dependence of folding at series of ligand (lysine) concentrations. (A) ln(Kfold) vsP plot where the parallel lines indicate constant V0. (B) The insensitivity of folding V0
to lysine concentration where the error bars are visually magnified by two with thevertical break.
Figure 10.6 ..................................................................................................................................271
Pressure effects on apparent Kd of lysine binding. Kd increases exponentially withpressures, suggesting riboswitch-ligand interactions are efficiently weakened at highpressures.
Figure 10.7 ..................................................................................................................................273
Pressure dependence of folding at series of Na+ concentrations. (A) ln(Kfold) vs P plot
where folding shows negligible dependence on [Na+]. (B) [Na+] (in)dependence of V0.
Figure 10.8 ..................................................................................................................................275
dependence of folding at series of Mg2+ concentrations. (A) ln(Kfold) vs P plot where
Mg2+ greatly promotes folding, while leaving the slopes (V0) mostly unchanged. (B)[Mg2+] (in)dependence of V0.
Figure 10.9 ..................................................................................................................................278

xxv
Pressure dependence of folding at series of TMAO concentrations. (A) ln(Kfold) vs P plot
where TMAO promotes folding and effectively reduces the slope (V0). (B) [TMAO]
dependence of V0. V0 decrease linearly with [TMAO] concentration.
Figure 10.10 ................................................................................................................................285
Accessible pressure range for the lysine riboswitch as a function of [TMAO], normalized
to the corresponding pressure range at [TMAO] = 0. The grey solid line corresponds thepressure range without osmolyte effects. The red solid line represents predictions fromthe fit of the [TMAO] dependence of V0 with m = -0.0228(18) mL mol-1 mM-1. The
dashed lines indicate effects due to the uncertainty in m on the pressure range as afunction of [osmolyte]: 50% larger (dark red) and 50% smaller (pink) m values.
Figure 10.11 ................................................................................................................................286
Iso-Kd curve as a function of both pressure (depth in the ocean) and [TMAO] where Kd =0.5 mM. Kd is maintained by [TMAO] = 1250 mM with (ocean depth) > 9 km. Data fit
to a negative exponential growth function (red), indicating the TMAO effects are evenstronger at high concentrations. The dashed lines indicate the effects of changes in slope
magnitude on the iso-Kd curve: + 50% (dark red) and − 50% (pink).
Figure 11.1 ..................................................................................................................................300
Schematic presentation of the surface tethered smFRET experiment performed in apressurized capillary sample holder. The doubly dye-labeled DNA hairpin construct isimmobilized on the capillary surface through biotin-streptavidin interactions. The energy
transfer efficiency (EFRET) in the folded (left) and unfolded (right) conformations
correspond to high EFRET (≈ 0.8) and low EFRET (≈ 0.1) fluorescence states, respectively.
Prior to each experiment, a thin layer of silicon oil is introduced inside the capillary cellto prevent contamination of the aqueous sample region by the pressure transmitting fluid(ethanol).
Figure 11.2 ..................................................................................................................................303
time-resolved fluorescent signals (upper panels) and corresponding EFRET trajectories(lower panels) at (A) 1 bar and (B) 1250 bar. Background [Na+] = 50 mmol/L.
Figure 11.3 ..................................................................................................................................305
Sample cumulative distribution functions of dwell time at (A) 1 bar and (B) 1250 bar.
Background [Na+] = 50 mmol/L.
Figure 11.4 ..................................................................................................................................307
Pressure dependent van’t Hoff analysis of DNA hairpin folding. (A) Folding (kfold) and
unfolding (kunfold) rate constants, and (B) folding equilibrium constant (Keq) as a functionof increasing pressure. Note that kfold and kunfold are each scaled to 1 Hz (s-1) to permit
taking logarithms of unitless quantities. The slope of these plots can be used to inferchanges in the molar volume with uncertainties ( 1 to 2 mL/mol) at  5 to 10% of asingle H2O molecule volume (V  18 mL/mol). Background [Na+] = 50 mmol/L.
Figure 11.5 ..................................................................................................................................308
Pressure dependent folding equilibrium constants (Keq) as a function of Na+concentration, expressed as a van’t Hoff pressure analysis, whereby the slope of thesexxviplots can be used to infer changes in the molar volume with uncertainties ( 1 to 2
mL/mol) at  5 to 10% of a single H2O molecule volume (V  18 mL/mol).
Figure 11.6 ..................................................................................................................................309
dependent van’t Hoff analysis of (A) folding (kfold) and (B) unfolding (kunfold) rate
constants for a series of monovalent Na+ concentrations.
Figure 11.7 ..................................................................................................................................312
Effective volume change along the folding coordinate as a function of increasing [Na+],with volume of the unfolded state (Vunfold) arbitrarily designated as the reference zero.
Figure 11.8 ..................................................................................................................................316
Effective volume change along the folding coordinate as a function of increasing [Mg2+],
with volume of the unfolded state (Vunfold) arbitrarily designated as the reference zero.
Background [Na+] = 50 mmol/L.
Figure 11.9 ..................................................................................................................................318
Pressure dependent folding equilibrium constants (Keq) as a function of Mg2+
concentration, expressed as a van’t Hoff pressure analysis, whereby the slope of theseplots can be used to infer changes in the free volume with uncertainties (1 to 2 mL/mol)at the 5 to 10% of a single H2O molecule volume (18 ml/mol). Background [Na+] = 50mmol/L.
Figure 11.10 ................................................................................................................................319
PΔV reversible work evaluated at P = 1000 bar to highlight the magnitude of free energy
contributions (kT  0.6 kcal/mol) induced by deep sea pressures as a function ofincreasing [Na+].
Figure 11.11 ................................................................................................................................321
Na+ stabilization effects on the DNA hairpin secondary structure under ambient pressure
conditions.
Figure 12.1 ..................................................................................................................................332
Schematic of the high pressure single molecule FRET experiment showing the instrument
setup. (A) The cartoon representation of the manganese riboswitch construct in the Mn2+bound folded conformation where the loop-loop interaction between P1 and P3 stems isformed. (B) The high pressure generating system coupling to the capillary sample holderaligned with the microscope objective. The reservoirs contain ethanol as the pressuretransmitting fluid throughout the high pressure tubing manifold.
Figure 12.2 ..................................................................................................................................334
Sample fluorescence traces and the resulting time trajectories of EFRET at (A) 1 bar and(B) 500 bar. The simulated traces in orange are obtained from hidden Markov modelling.
Figure 12.3 ..................................................................................................................................335
Sample dwell time distributions at (A) 1 bar and (B) 500 bar. Data are fit to a single
exponential decay function to obtain folding and unfolding rate constants kfold and kunfold,respectively.
Figure 12.4 ..................................................................................................................................336

xxviiPressure-dependent manganese riboswitch folding (A) equilibrium constant and (B)kinetics rate constant plots, where error bars represent standard deviation of the mean. In
analogy to Eyring analysis of transition state barrier energies, the data are least squares fit
to a single exponential function to obtain quantitative volumetric change information for
ΔV0 and ΔV‡fold/unfold. [Mn2+] = 15 µM; [Mg2+] = 2mM.
Figure 12.5 ..................................................................................................................................338
Pressure-dependent equilibrium constants (Kfold) for the riboswitch folding as a functionof increasing [Mn2+] in the presence of physiological [Mg2+] = 2 mM.
Figure 12.6 ..................................................................................................................................339
Pressure-dependent rate constants (A) kfold and (B) kunfold as a function of increasing[Mn2+] in the presence of physiological [Mg2+] = 2 mM.
Figure 12.7 ..................................................................................................................................341
Pressure-dependent equilibrium constant (Kfold) data for Mn2+ independent-folding of theriboswitch at [Mg2+] = 2mM (red) and 6 mM (blue).
Figure 12.8 ..................................................................................................................................342
Pressure-dependent analysis of the kinetic rate constants for Mn2+ independent-folding of
the riboswitch: (A) kfold and (B) kunfold at [Mg2+] = 2mM (red) and 6 mM (blue).
Figure 12.9 ..................................................................................................................................343
Free volume changes (ΔV0 and ΔV‡fold/unfold) along the riboswitch folding coordinate, butplotted as a function of fractional binding of Mn2+ (f = 0.0 to 1.0). The fraction of Mn2+bound riboswitch is calculated from the Mn2+ concentrations, based on dissociation
constant (KD = 16(5) µM) and Hill coefficient (n = 1.0(3)) obtained from previous
analysis for Mn2+-promoted folding of the manganese riboswitch. The open circles
represent the predicted volume changes from linear extrapolation to f =1.0.
Figure 12.10 ................................................................................................................................345
Plot of differential free volume changes (V) along the riboswitch folding coordinate fora variety of Mn2+ conditions, with “staircase-like” structures clearly indicating amonotonic increase in volume at each folding stage. Especially noteworthy is the colorcoded parsing of these volume changes with respect to Mn2+ binding fraction, which
reveal that > 50% of this increase in riboswitch volume is achieved by the time thetransition state is formed. Differential volumes are referenced to the unfolded state U ateach f.
Figure 13.1 ..................................................................................................................................353
DFHBI fluorescence enhancement. (A) Cartoon representation of DFHBI binding to the
Spinach2 RNA. (B) Chemical structure of DFHBI.
Figure 13.2 ..................................................................................................................................354
Schematic of Spinach2-TNT aptamer construct design and the resulting fluorescenceenhancement by TNT/DFHBI binding.
Figure 13.3 ..................................................................................................................................355

xxviii
Spinach2-DFHBI fluorescence measurements. (A) DFHBI titration of Sinach2 RNA.
Data are fit to the Hill equation and KD of DFHBI is determined to be 1.3(2) µM. (B)TNT titration of Spinach2-TNT construct with saturated [DFHBI] = 20 µM. Note that
despite the fluorescence increases at [TNT] > 10 µM, the count rate is way below the
Spinach2 enhancement (105 vs 107 count per second) and the estimated KD of TNT for
the TNT aptamer is at low micromolar levels.
Figure 13.4 ..................................................................................................................................356
Secondary folding of the guanidine-II riboswitch in the translation-off state. The
sequence color-coded in blue represents the Shine–Dalgarno (SD) sequence, a ribosome
binding site.
Figure 13.5 ..................................................................................................................................356
Illustration of the single molecule FRET construct design of the guanidine-II riboswitch.
Figure 13.6 ..................................................................................................................................357
Single molecule FRET experiments of the guanidine-II riboswitch constructs. (A)illustration of the freely-diffusing experiment and data analysis. (B) EFRET distribution of
the full guanidine-II riboswitch at increasing guanidine concentrations. (C) EFRET
distribution of the truncated guanidine-II riboswitch (-2 base pairs in the SD double helix
extension) at increasing guanidine concentrations.
Figure 13.7 ..................................................................................................................................359
Sample fluorescence traces of the BMV virus RNA construct and the resulting EFRET
trajectories. (A) Chemical structure of pCp-Cy3. (B) Sample fluorescence data at [Mg2+]= 0 mM, and (C) [Mg2+] = 10 mM. The intermediate EFRET state at high [Mg2+] = 10 mM
is indistinguishable with the low EFRET state (e.g. the low EFRET state at [Mg2+] = 0 mM).

1
Chapter 1
Introduction

1.1

Nucleic acids
Nucleic acids are large biopolymers that play essential roles in all forms of life and non-living biochemical machines such as viruses. The fundamental building blocks of nucleic acids
are the nucleotides, consisting of three covalently attached components: a five-carbon sugar, aphosphate group, and a nucleobase (Figure 1.1).1 The two principal categories of naturally
occurring nucleic acids are ribonucleic acid (RNA) and deoxyribonucleic acid (DNA), formed
from ribonucleotide and deoxyribonucleotide subunits, respectively. The only major difference
between these two subunits is the presence (ribonucleotides) or absence (deoxyribonucleotides)of a hydroxyl group on the 2’ carbon of the 5-carbon sugar.2

Figure 1.1 Chemical structures of deoxyribonucleotide/ribonucleotide and the corresponding
nitrogenous bases.

2
1.1.2 Nucleic acid structure and function
There are four different nucleobases: guanine (G), cytosine (C), adenine (A), and thymine(T) for deoxyribonucleic acid (DNA), and guanine (G), cytosine (C), adenine (A), and uracil (U)for ribonucleic acid (RNA), respectively (Figure 1.1). The nucleotides are linked byphosphodiester bonds between the phosphate groups and hydroxyl groups on the 5-carbon sugars
to form a linear polymeric chain,1 where the specific sequence of nucleotides defines the primary(1o) structure of the nucleic acid strand. The genetic information encoded in the DNA nucleic
acid primary sequence (and in turn the transcribed messenger mRNA sequence) contains
instructions for synthesis of proteins that facilitate most cellular function and ultimately allow
organisms to thrive.

Figure 1.2 Example of RNA hierarchical folding: (from top to bottom) 1o, 2o and 3o structure of
the manganese (Mn2+) riboswitch. (PDB 4Y1I)

3
Although the most fundamental genetic information in DNA and RNA is contained in the
1o structure, the biochemical function of nucleic acids depends famously on the subsequentdevelopment of higher order oligomeric structures (Figure 1.2).3 Specific combinations of
nucleobases in DNA (RNA) can hydrogen bond with one another to form stable Watson–Crickpairs, with G pairing with C (for both DNA/RNA) and A pairing with T (for DNA) or U (forRNA) through hydrogen bonding, which are crucial for the secondary (2o) structure formation.
Double helix formation in double-stranded DNA (dsDNA) is arguably the best known and mostprevalent 2o nucleic acid structure,4 formed by intermolecular Watson–Crick base pairing
between two complementary DNA strands and allowing efficient storage and readout ofimportant genetic information. By way of contrast, RNA typically tends to be single-stranded,
but can also form relatively short double helix-like 2o structures (“stems”) between selfcomplimentary regions through intramolecular G-C and A-U base pairing. Most importantly, theregions of unpaired and/or mismatched sequences in single stranded RNA (ssRNA) permit theformation of a much wider variety of 2o structures, such as junctions, loops, and bulges, eachelement allowing for much higher conformational flexibility.5-6 Indeed, it is this larger library of
2o motifs that allows RNA to be more functionally “creative”, with folding interactions among
these 2o motifs allowing for formation of more complex tertiary (3o) structures essential forbiochemically competent catalytic and/or sensing RNAs:7 As one CU-centric Nobel prize
winning example, discovery in the 1980s of self-splicing activity by the group I intron8 andRNase P9 followed by the hammerhead ribozyme10 demonstrated the enormous potential ofribonucleic acids as enzymatically active species. The 3o interactions among stems, loops andbulges are each found to play important roles in forming and stabilizing such functional RNA
structures,11 the biophysics of which represents a primary goal of this thesis work.

4
1.1.2 Nucleic acid conformational transition
With the help of helicases, even the highly thermodynamically stable DNA double helix
unwinds during replication.12 This suggests that nucleic acid “structure” must or at least can behighly dynamic and thus biochemical reactions may require a series of conformationaltransitions13-14 each occurring on a characteristic time scale. A detailed knowledge of nucleic
acid conformational kinetics therefore represents a fundamental goal for any predictive
understanding of such biochemical processes.
In this thesis, we explore the kinetics of the elemental structural transition, 1o to 2o and 2o
to 3o as well as the more complicated folding of the complete RNA riboswitch (Figure 1.3). One
model transformation system we have studied in detail is 2o structure formation in the DNA
hairpin construct, which consists of two short (7 to 9 nucleotide) complimentary sequences
separated by a 40-adenine linker.15-16 for which the two complimentary strands are joined by
Watson–Crick base pairing to form a closed stem-loop configuration. Such 2o folding is not only
the primary structural interaction motif in the DNA double helix but is also essential for the
widely prevalent stem/stem-loop formation in all RNA constructs. Another common RNA
structural motif is the tertiary interaction between 2o elements such as the loop (tetraloop) andbulge (tetraloop receptor), which is ubiquitously found in RNA 3D crystal structures and canserve as a nice test construct for study of 3o folding kinetics.17-18 Indeed, the specific tetralooptetraloop receptor docking construct we have chosen to explore is one of the key structuralsequences that modulate catalytic activity for self-splicing in the group I intron.17
Riboswitches are noncoding RNA elements that sometimes appear in the 5’ advance
region of a gene which are therefore transcribed first and can undergo structural rearrangement inresponse to the presence or absence of specific ligands in the cell. Such ligand-induced

5

Figure 1.3 Examples of nucleic acid structural transition explored in this thesis. (A) 1o → 2o DNA
hairpin formation. (B) 2o → 3o loop-bulge interaction between tetraloop and tetraloop receptor.
(C) Full manganese riboswitch aptamer folding, which involves the Mn2+-facilitated loop-loop
folding and the rearrangement of the four-way junction as well as the attached stems.

rearrangements in effect permit regulation of gene expression by sensing of cell environment.1920

As a result, the thermodynamics of riboswitch folding are therefore of particular importance togene regulation.21 Of particular dynamic interest, this nascent mRNA begins to form stableaptamer sensing structures (“aptamer domain”) synchronous with transcription until the complete
riboswitch sequence is produced.22-23 Such a “fold-upon-synthesis” process, often termed “cotranscriptional folding”,24 is therefore heavily impacted by the kinetics of RNA folding.25 It istherefore a crucial evolutionary strategy for the riboswitch to fold into the correct conformationin response to ligand binding and in turn generate the desired genetic response. In this thesis, westudy the folding kinetics and thermodynamics of a variety of riboswitches. One of the mostextensively studied structures is the manganese riboswitch,26-27 which conformationally responds
to the presence/absence of Mn2+ and thereby regulate the transcription to form a protein
responsible for Mn2+ homeostasis. Although such a conformational transition in the riboswitch is6primarily regulated by a Mn2+-promoted 3o loop-loop interaction, allosteric control of Mg2+
binding, rearrangement of the junctional loop and associated stems also play an important part in
the overall folding event.28

1.2

Single molecule FRET kinetics
Traditional ensemble studies measure quantities that average over ~ 1023 molecules.

Because the bulk system is often in rapid dynamic equilibrium due to both forward andbackward reaction pathways, an ensemble experiment typically permits only observation ofequilibrium properties, obscuring any detailed kinetics of the forward/backward folding
reactions. To obtain kinetic information from such ensemble studies requires “molecularsynchronization”, for example, measuring the effective unimolecular rate constant for a nonequilibrium system returning to equilibrium, where the non-equilibrium state might be caused by
rapid change in temperature/pressure (i.e., T-jump and pressure jump experiments) or bufferconditions (e.g., stopped-flow methods).29-30 Despite a rich history, widespread use, andconsiderable generality, such synchronization methods often require additionally restrictive
kinetic assumptions, for example, independent knowledge of fast vs. slow kinetic processes todeconstruct forward and reverse rate constants. Moreover, one additional assumption intrinsic toensemble measurements (and perhaps the most critical to biomolecule conformationaltransitions) is that all the molecules are exactly identical. In fact, the presence of kinetic
heterogeneity in biomolecule samples is a known issue,31 for which study of the resulting
kinetics requires observation of single molecules, one at a time.32-33
For much of the 20th century, the prospect of studying kinetics at the single molecule
level was thought to be simply a dream. In fact, the underlying physical techniques (lasers,

7

Figure 1.4 Schematic of single molecule FRET kinetic measurements and sample data. (A) the
immobilized nucleic acid construct at the laser focus for extended fluorescence observation. (B)Sample fluorescent signal time trace (upper panel) and the resulting FRET transfer efficiency EFRET
trajectory (lower panel). (C) Dwell time analysis; the linearity in the semi-log plots indicates thefolding and unfolding processes are well described by the first order kinetics.

photomultipliers, high NA microscopes, etc.) to achieve this ultimate sensitivity goal had
arguably existed since the 1960s, requiring only particularly intrepid scientists to turn this into a
reality. Indeed, such single molecule observations in early 1990s were first realized by W. E.
Moerner in cryogenic crystals,34-35 with the techniques greatly improved in the next several
decades with the help of more versatile lasers, faster detectors, and brighter fluorophores. It waslater extended to biological samples in coupling with various fluorescence methods including
Foster resonance energy transfer (FRET).36-37 FRET describes the energy transfer between two
chromophores (light-absorbing molecules), where the dipole-dipole transfer efficiency is foundto strongly depend (1/R6) on the distance. It is therefore commonly used in structural studies witha pair of fluorophores to inform on distance between the labeled folding motifs withinmolecule(s) of interest. In this thesis, we utilize FRET between Cy3 and Cy5 fluorophore pair tovisualize the folding of nucleic acids, whereby the change in distance between Cy3 and Cy5
during conformational transition results in different colors (Cy3 (green) vs Cy5 (red)) in
fluorescence. Furthermore, with the confocal microscope setup,38 the tightly focused laser allows

8
us to obtain the fluorescent signal from a single molecule at a time (Figure 1.4A). With surfaceimmobilized molecules, direct observation of folding/unfolding dynamics of nucleic acidstructures can be realized by the prolonged observation of FRET from a single fluorophorelabeled construct (Figure 1.4B). The resulting kinetic information on the folded vs unfolded
status of a single nucleic acid can therefore be obtained by analyzing the time dependent
fluorescent traces for a single molecule (Figure 1.4C).
In addition to measurements of nucleic acid folding/unfolding rate constants, we are alsointerested in the response of these rate constants to mono/divalent salts, osmolytes, andriboswitch ligands. In particular, we can apply kinetic models to ligand-induced riboswitch
folding (see Chapter 3 and 4 in this thesis), which reveal that folding in the presence ofincreasing magnesium shifts from a ligand binding-induced conformational change (i.e., “bindthen-fold” or induced fit: IF) mechanism to that of a pre-formed riboswitch structure successfullystabilized by subsequent binding of the ligand (i.e., “fold-then-bind” or conformation selection:
CS).39 Moreover, the recognition of multiple conformations (and thus FRET states) is also madepossible with single molecule study. With such smFRET tools, we have successfully resolved
three different conformational states for the Ni2+/Co2+-sensing riboswitch (see Chapter 5),40-41
and can directly monitor the folding of each step promoted by mono/divalent cations and therelevant riboswitch ligands, respectively.42

1.3

Thermodynamics of nucleic acid structural transition
In thermodynamics, the Gibbs free energy determines the spontaneity of a reaction (e.g.

conformational transition). It measures the maximum amount of work available from a reaction:∆𝐺 = ∆𝐺 0 + 𝑅𝑇𝑙𝑛𝑄,

Eq. 1.1

9
where ΔG0 is the change in free energy under standard state conditions (1 atm for ideal gases,
1M for ideal solutes), R the gas constant, and Q the reaction quotient. For a system in
equilibrium, we have ΔG = 0 and Q = Keq (equilibrium constant), which from Eq. 1.1 can be
rewritten as∆𝐺 0 = −𝑅𝑇𝑙𝑛𝐾𝑒𝑞 ,Eq. 1.2

which denotes the relation between the Gibbs free energy and the equilibrium constant.
1.3.1 Temperature as a variable
Conformational transitions in nucleic acids involve base stacking, hydrogen bondformation and disruption, as well as change in hydration including cation association and water
reorganization.43 Each of these interactions contribute to changes in enthalpy (ΔH) and entropy(ΔS) of the overall nucleic acid folding.44 According the thermodynamic definition of thestandard Gibbs free energy∆𝐺 0 = ∆𝐻 0 − 𝑇∆𝑆 0 ,Eq. 1.3

Eq. 1.2 can be rearranged into the van’t Hoff equation
𝑙𝑛𝐾𝑒𝑞 =−∆𝐺 0
𝑅𝑇

1 −∆𝐻 0= 𝑇( 𝑅 )+

∆𝑆 0
𝑅

,

Eq. 1.4

which permits the deconstruction of the free energy into enthalpy and entropy contributions bytemperature dependence of the folding equilibrium constant.
Our single molecule microscope is equipped with heating (and cooling) devices toachieve precise and tunable temperature control of the sample.45 Temperature dependent folding
experiments have revealed valuable biophysical insights:46 In particular, we are able to identify
the stabilization effects of PEG (polyethylene glycol) on nucleic acid 2o and 3o structures to be
predominantly entropic (see Chapter 6 and 7),47-49 which is entirely consistent with the crowding

10
effect originating from the pure excluded volume interaction.50-51 Therefore, the steric constraintof the crowded intracellular environment may be effectively simulated by PEG to enhance theapplicability of the in vitro studies to in vivo observations.52 This successful incorporation oftemperature control can also be extended to single molecule kinetics by Erying transition state
analysis53∆𝐻 ‡ 1∆𝑆 ‡ln(𝑘) = − 𝑅 𝑇 + 𝑅 + ln 𝜈,

Eq. 1.5

where ΔH‡ and ΔS‡ are the enthalpic and entropic difference between the transition state and thefolded/unfolded conformations, and ν is the attempt frequency for the system to cross thetransition barrier.54-55 The resulting detailed thermodynamic characterization allows us todeconstruct free energy contributions at the folding transition state into both enthalpic andentropic components, achieving even higher levels of insight into the free energy landscape
topology.
1.3.2 Pressure as a variable
Pressure is another thermodynamic variable that drives biochemical reactions, including
biomolecule folding. Although the effect of air pressure is rather negligible, hydraulic pressure
can change quite rapidly in the ocean environment, at the rate of approximately 1 bar per 10
meters in depth. Marine organisms, especially deep-sea species, thus experience quite highpressures, with values up to ≈ 1.1 kilobars at the deepest part of the ocean/Mariana Trench.56 It istherefore reasonable to speculate that conformational folding of biomolecules (e.g. proteins andnucleic acids) in deep-sea species must have evolved to adapt to such extreme pressure
environments. Although there have been several efforts to study pressure effects on biomolecularfolding in the early 1980s,57-58 it is fair to say that the understanding of pressure-induced
conformational change at the molecular level is still in its infancy.59 Specifically, while various

11
protein species are found to unfold at high pressures60-61 (i..e, pressure-induced denaturation),62
the corresponding pressure-dependent response for nucleic acid structures is much less wellunderstood, with the studies to date largely limited to 2o structure formations.63-65 Sincebiomolecular function is strongly tied to structure, the kinetic and thermodynamic
conformational response of nucleic acids to pressure would appear to be critical for evolutionary
strategies adapting to extreme ocean depths.
Recently, single molecule FRET has been incorporated with high pressure systems tocharacterize the pressure response of nucleic acid folding (see Chapter 9 and 10).66-67 In theseexperiments, the excitation laser is focused into the solution to record the fluorescent signal ofmolecules diffusing through the focal region,68 allowing direct observation of folded vs. unfolded
populations differentiated by FRET efficiency and photon color.69-70 According to thethermodynamic relation between free energy and pressure, the volume change during folding(ΔV0) can be obtained from pressure dependence of the equilibrium constant60-61(

𝜕𝑙𝑛𝐾𝑒𝑞
𝜕𝑃

)𝑇 =

−∆𝑉 0
𝑅𝑇

.

Eq. 1.6

Interestingly, according to Eq. 1.6, the fact that pressure commonly induces unfolding(denaturation) indicates that biomolecules (such as proteins, nucleic acids) effectively take up
more volume as it folds, despite ostensibly achieving a more compact folded conformation.
Although not yet completely understood, this volume increase during folding is thought to result
from nanoscopic voids/cavities formed in the folded conformation.71-73 These cavities may either
exclude the water molecules or disrupt the water network, resulting in a less compact water
structure due to spatial confinement.74 Another possible cause of the larger volume folded state
may be the change in hydration,75-76 with the less exposed charged surfaces and (cat)ion

12
recruitment result in the surrounding water molecules becoming less aligned by the charged
folded biomolecule. Clearly, the key to resolving such counterintuitive volume change is toinclude the surrounding solvent into the physical picture of folding.43, 77
In this thesis, we have extended the high pressure single molecule equilibrium studies tokinetic measurements with surface immobilized nucleic acid constructs (see Chapter 11 and
12).78 The resulting pressure dependent rate constants now inform on the volume changes
associated with the folded, unfolded, and transition state conformations,60 and thus provide
particularly novel opportunities for detailed characterization of the volume change along thenucleic acid folding coordinate. We have determined the volume of nucleic acid monotonicallyincreases along the nucleic acid folding (VU < VTS < VF).78 Moreover, we have found ΔV to behighly sensitive to cation association; the resulting detailed volumetric information of the folding
landscapes is shown to complement the kinetic modeling performed at ambient pressure,providing additional insights into cation-nucleic acid interactions.

1.4

Thesis overview
In this thesis, we use single molecule FRET spectroscopy incorporated with temperatureand pressure control to investigate several important topics in biophysics. Chapter 2 describes the
single molecule FRET measurement in detail with special focus on development of the highpressure experimental apparatus. In Chapters 3 to 5, we study metal cation (Mn2+, Ni2+, andCo2+) sensing riboswitches folding with emphasis on temperature dependent single molecule
kinetics. Specifically, in Chapter 3 and 4, kinetic modeling reveals that the presence ofmagnesium cation shifts the predominant folding pathway for the manganese (Mn2+) riboswitch
between two kinetic paradigms of an induced-fit (IF, bind-then-fold) to a conformational

13selection (CS, fold-then-bind) mechanism.28, 39 In Chapter 5, the effects of magnesium induced
pre-folding is again evidenced in the nickel/cobalt (Ni2+/Co2+) riboswitch, which now exhibits
three distinctive FRET states.42 Simply summarized, sequential folding kinetics of thenickel/cobalt riboswitch reveals that magnesium significantly promotes the formation of this prefolded intermediate, but cannot achieve the final folded conformation without obligate Ni2+ orCo2+ binding. In Chapter 6, we explore the effects of “molecular crowding” on conformational
folding with single molecule kinetic and thermodynamic studies.48 These studies reveal not onlythat stabilization of nucleic acid structure by PEG is predominantly entropic (and well describedby excluded volume models), but rather more surprisingly that this effectiveness (on a w% basis)increases with decreasing PEG size. Both of these observations are consistent with molecular
crowding effect, in which the excluded volume is the predominant interaction. Chapter 7
explores and reveals the significant additional enthalpic effects of polysaccharides (i.e., dextran
and Ficoll, common protein crowding agents) on nucleic acid folding, in strong contrast with thepredominantly entropic effects of crowding by PEG.49 The effect of molecular crowding on thelysine riboswitch has been explored in Chapter 8,79 for which kinetic analysis reveals that PEG
promotes riboswitch folding primarily by enhancement in the lysine ligand affinity. In Chapter 9
and 10, we develop and exploit high pressure single molecule FRET methods to study thepressure dependent folding equilibrium of the DNA hairpin69 and lysine riboswitch,70
respectively. Of special importance, the studies reveal that the osmolyte TMAO (trimethylamine
N-oxide), which has been found to accumulate in deep-sea fish,80 effectively protects the lysine
riboswitch from pressure-induced denaturation by not only the stabilization of the folding event
but also a reduced sensitivity to external pressure (ΔΔV0TMAO < 0). In Chapter 11 and 12, wedemonstrate the ability to extend these high pressure experiments from equilibrium studies of

14
freely diffusing molecules into the time domain by direct monitoring folding kinetics for single
molecule constructs tethered to the inside surface of a high pressure capillary. With this new
capability, we are able to achieve high pressure kinetic measurements of the folding/unfolding
kinetics for both secondary (40A DNA hairpin)78 and tertiary (manganese riboswitch) structureformation, and thereby infer the “free volume landscape” between unfolded, transition state, andfolded configurations. Indeed, our experimental methods can be taken one step further frompressure dependent folding studies of the riboswitch measured over a series of Mn2+
concentrations, from which we are able to deduce differential changes in the free volume change
for folding upon binding of the ligand Mn2+ (ΔV0bind). Interestingly, our measurements reveal
such differential volume effects to be negative (ΔV0bind < 0), which implies that ligand binding isfavored with increasing pressure. Coming full circle back to deep sea organisms, such a negative
pressure dependence for ligand binding may help mitigate the positive pressure-induced
unfolding effects on the overall riboswitch structure (ΔV0fold > 0) and thereby preserve
riboswitch function over wider extremes of pressure.

1.5

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Natl. Acad. Sci. U.S.A. 2005, 102 (30), 10505-10510.

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Sung, H.-L.; Nesbitt, D. J., Single-Molecule FRET Kinetics of the Mn2+ Riboswitch:
Evidence for Allosteric Mg2+ Control of “Induced-Fit” vs “Conformational Selection”
Folding Pathways. J. Phys. Chem. B 2019, 123 (9), 2005-2015.

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Facilitated by a Conformational Intermediate: Insights from Single-Molecule Kinetics
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with Ligands. Q. Rev. Biophys. 2000, 33 (3), 255-306.

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Dupuis, N. F.; Holmstrom, E. D.; Nesbitt, D. J., Molecular-Crowding Effects on SingleMolecule RNA Folding/Unfolding Thermodynamics and Kinetics. Proc. Natl. Acad. Sci.
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Sung, H.-L.; Sengupta, A.; Nesbitt, D., Smaller Molecules Crowd Better: Crowder Size
Dependence Revealed by Single-Molecule FRET Studies and Depletion Force Modeling
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Sung, H.-L.; Nesbitt, D. J., Effects of Molecular Crowders on Single-Molecule Nucleic
Acid Folding: Temperature-Dependent Studies Reveal True Crowding vs Enthalpic
Interactions. J. Phys. Chem. B 2021, 125 (48), 13147-13157.

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20
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21
Chapter 2
Methods

2.1

Single molecule confocal microscope
Observation of single molecule fluorescence is facilitated by a home-built confocal

microscope.1 The microscope system was first set up by a former postdoctoral researcher, Dr.
Jose Hodak, with assistance from a former graduate student, Dr. Julie Fiore, and later modified
by Dr. Erik Holmstrom. In addition to the microscope setup described in this section, both thesesof Dr. Julie Fiore and Dr. Erik Holmstrom are great resources.
2.1.1 Laser excitation path
The excitation source of the single molecule experiment is a 532 nm frequency-doubled
Nd:YAG laser pulsed at 20 MHz. The wavelength is chosen to efficiently excite the FRET donor
Cy3 (absorption λmax = 555 nm) and facilitate the spectral filtering of the resulting Cy3/Cy5
fluorescence (emission λmax = 570/670 nm). The laser output is first polarized by a half wave
plate and a polarizing beam splitter. The 1 mm diameter (1/e2) beam is then expanded by a
Keplerian telescope consisting a pair of lenses with focal lengths 25 mm and 300 mm,
respectively. Before being directed to the back port of the inverted microscope (Olympus IX70),
the beam is attenuated by an array of neutral density filters in adjustment of the optical power for
single molecule fluorescence experiments. Inside the microscope (Figure 2.1), the beam isreflected upward by a custom two-color dichroic mirror to a 1.2 N.A. water immersion objective.
With the back aperture (daperture = 9.25 mm) overfilled by the collimated beam, the objective caneffectively focus the laser into a diffraction-limited spot (dx-y = 260 nm) for excitation andcollection of the single molecule fluorescence.

22

Figure 2.1 Schematic of the confocal microscope excitation/emission paths. The temperature
control units are indicated in red.

2.1.2 Fluorescence emission path and detection
During single molecule fluorescence experiments, the emitted photons within the laser
focus are collected by the same objective, directed through a dichroic mirror, and focused by atube lens (f = 80 mm) before exiting the microscope side port (Figure 2.1). The resulting focused
beam is subsequently filtered by a 50 µm pinhole to reject out-of-focus photons and directed tothe detection unit, which contains a tree of four avalanche photodiodes (APDs, SPCM-ARQ-14,
Excelitas). The photons are first spatially separated by polarization with a polarizing beam cube,
and then by color with dichroic mirrors (645DCXR, Chroma Technology). Prior to detection,
photons are filtered by band pass (long pass) filters to reject the photons from excitation sourceand ensure only Cy3 (Cy5) fluorescence reaches the green (red) APDs.

23
2.2

Temperature Control
Temperature as an experimental variable enables the deconstruction of the free energy

into enthalpy and entropy contributions (e.g., via the van’t Hoff analysis).2 Moreover, inconjunction with the kinetic information obtained from the single molecule measurements,
temperature dependence helps characterize the thermodynamic property of the transition state,
and in turn construct the energy landscape in both enthalpic and entropic components. Suchabundance of thermodynamic information allows us to readily identify physical phenomena suchas ligand binding and the molecular crowding effect as described later in the thesis.
The temperature control is achieved by sample heating (Figure 2.1). In temperaturedependent experiments, the sample is placed in the chamber of the enclosed heating stage(Instec) with vacuum grease to increase thermal contact. Moreover, the resistively heated wirebased collar heater (Bioptechs) is used to warm up the microscope objective to minimize the heatflow across the sample. With simultaneous heating both the sample and objective, the sample
temperature can be precisely controlled with minimal thermal fluctuation (± 0.1 ℃). It is
important to note due to the delicate nature of optical elements inside the microscope objective,
the maximum heating temperature is limited to 50 ℃ with a relatively slow temperature ramp of
1 ℃/min. The system is allowed to equilibrate for 10 minutes prior to each temperaturecontrolled experiment. Although the 20 to 50 ℃ heating range is sufficient to explore most of thethermodynamic properties of our interest (i.e., nucleic acid folding), it’s worth noting that an
infrared-based laser heating method is developed by a former graduate student, Dr. Erik
Holmstrom to expand the heading capability (up to 90 ℃) in our lab.3 For more experimentdetails, please refer to his thesis.

24
2.3

Sample preparation
We use FRET (Forster resonance energy transfer) to visualize the conformation changesof biomolecules. To enable FRET observation, biomolecules of interest are doubly labeled with
the Cy3-Cy5 FRET pair, and often with biotin modification to allow surface immobilization
measurements (2.4.2).
2.3.1 Single molecule construct
The doubly fluorophore-labeled construct design is perhaps the most important step forthe single molecule FRET experiment. The goal is to generate a biologically-relevant structurethat i) undergoes conformational transition and ii) generate sufficient contrast in FRET
efficiency, EFRET. The selection of the fluorophore-labeling positions is therefore particularly
crucial in construct design. Fortunately, it can be efficiently assisted by known structural data,
especially the crystal structure of the protein/nucleic acid of interest in its native folded state.
Since the characteristic length R0 of the Cy3-Cy5 FRET pair is ≈ 50 Å, EFRET is extremely
sensitive to the change in distance between Cy3 and Cy5 (~ r6) when r ≈ R0 (Figure 2.2).
Therefore, the general approach is to label Cy3 and Cy5 on each of the stems that are most likely
to undergo conformational transition at a distance that is roughly 5 to 10 Å below R0 according
to the structural data of the folded conformation. In that case, we usually obtain a folded/native
conformation with a mid to high EFRET value, and would expect a sharp decrease in EFRET when
the construct unfolds and brings Cy3 and Cy5 further apart. However, the structure andconsequently the EFRET of the unfolded conformation is much less predictable due to lack ofstructural characterization. The unsuccessful design may result from insufficient EFRET change
upon unfolding or simply the fact that the targeted interaction might not be sensitive to the soluteof interest (e.g., salts, osmolytes, and related ligands) at the physiologically relevant range.

25
In the surface immobilization experiments (2.4.2), the construct is tethered to the surface
through biotin-streptavidin interaction, and therefore also needs to be biotin-labeled. Due to theconstraint from the labeling site, we often apply the “flagpole” method to reduce the synthetic
complexity of the oligomers, and provide reliable tethering without significant perturbation fromthe surface. Specifically, we attach a biotinylated DNA/RNA flagpole to the dangling extension
strand of the readily fluorophore-labeled construct.1 The rigid double-stranded flagpole ensure
the minimal interaction between the construct and the protein-passivated surface.

Figure 2.2 FRET energy transfer efficiency (EFRET) as a function of distance between Cy3 andCy5 (R0 = 50 Å).
With extensive use of the flagpole strategy, our nucleic acid constructs are often
assemblies of two or more oligomers. To prepare the multicomponent construct, the oligomers
are first heat annealed, followed by high performance liquid chromatography (HPLC)
purification. The purified product is stored at -70 ℃ in 50 mM HEPES buffer with 0.1 mM
EDTA to prevent cleavage of the nucleic acid catalyzed by the divalent cation, e.g. Mg2+. For use
in day to day experiments, aliquot of the stock is dilute to 25 nM and may be stored at -20 ℃.
2.3.2 Sample of interest

26
Both the feely diffusing (2.4.1) and the surface immobilization (2.4.2) single molecule
FRET measurements can be performed directly on the glass coverslip under the open-air
condition. However, the data collection often required a extended experiment time. Therefore,
the sandwich style sample holder is preferred in order to minimize the sample evaporation. To
prepare the sandwich style sample holder, two stripes of double-sided sticky tape (3M) are apply
parallelly across the glass slide with a ≈ 5 mm spacing. The space between the double-sided
sticky tapes is subsequently topped with a coverslip to create a channel with the height of ≈ 80
µm, which allows us to flush through the desired solution via the capillary effect. In the single
molecule experiment, the sandwich style sample holder can be directly supported by the
microscope stage with the coverslip side down. In the temperature dependent experiment, theglass slide support is trimmed down to 25 mm × 25 mm in size by a diamond glass scriber pen inorder to fit in the enclosed chamber of the heating stage (2.2).
For the feely diffusing (see 2.4.1 for more details) experiment, the nucleic acid stock isdiluted in the imaging buffer to obtain the sample solution with 100 pM nucleic acid. The
resulting sample solution can be directly flowed into the sandwich style sample holder for feely
diffusing single molecule study. The imaging buffer contains buffer and background salts,
solute(s) of interest, and the enzymatic oxygen scavenging system (PCA/PCD/TROLOX)4 to
catalytically remove oxygen and increase the photostability of the fluorophores.
Sample for the surface immobilization (2.4.2) single molecule measurement requires
additional steps to decorate the surface of the coverslip with nucleic acid constructs via the biotin
streptavidin interaction. First the surface of the coverslip is passivated by flushing the channel ofthe sandwich sample holder by a 10% biotinylated BSA (bovine serum albumin) solution (10mg/mL). The BSA surface is negatively charged and therefore efficiently repels the nucleic acid27
construct to prevent nonspecific surface attachment. The sample holder is then consecutively
incubated with the streptavidin (200 µg/mL) and the biotinylated construct (≈ 25 pM) solutions
with a 10-minute incubation time for each. Prior to each experiment, the sample holder is flushed
by the imaging buffer with the desired experiment condition.

Figure 2.3 Two common strategies of the single molecule FRET experiment: A) freely diffusing
and (B) surface immobilization. The construct in (B) is tethered to the glass surface through thebiotin-streptavidin interaction.
2.4

Single molecule FRET experiment
The two strategies of the single molecule experiment are illustrated in Figure 2.3. The

freely diffusing method offers a simple way to directly observe the FRET efficiency EFRET froma doubly fluorophore-labeled construct diffusing though the confocal volume, and the results arefree of surface perturbation. The surface immobilization method, on the other hand allows
monitoring the single molecule EFRET as a function of time and therefore generate valuablekinetic information.
2.4.1 Freely diffusing method
To perform the single molecule experiment, the nucleic acid construct is allowed to freely
diffuse in the solution (Figure 2.3A). The excitation laser is focused into the solution and record
the fluorescence signal each time a fluorophore-labeled construct passing through. To ensure

28
each fluorescent event comes from a single nucleic acid construct, its concentration needs to be
sufficiently low so only one construct is in the focus at a time. With the present microscope
setup, the 1/e2 focus region (termed as confocal volume) is measured as ≈ 0.20 fL. The
concentration to have approximately 1 construct per 0.20 fL is calculated to be ≈ 10 nM. We
therefore work with lower construct concentrations ≈100 pM to ensure majority of thefluorescence events coming from a single construct, while being able to acquire sufficient
statistics of fluorescence events within reasonable experiment time.
In practice, the source of Cy3 emission event (EFRET ≈ 0) can be complex, including the
doubly fluorophore-labeled construct in the low EFRET conformation, construct withphotobleached Cy5, incomplete construct with Cy3 only, and free Cy3 molecule. Therefore, a635 nm laser is incorporated into the freely diffusing experiment to selectively excite Cy5 (λmax =650 nm) via the alternating laser excitation scheme (ALEX).5 The intervening excitation of Cy3
and Cy5 allows us to confirm the fluorescent event comes from a doubly fluorophore-labeledconstruct by examining the signal correlation between the 532 nm and 635 nm excitation
channels.
2.4.2 Surface immobilization method
Surface immobilization permits prolonged observation of the fluorescent signal from asingle nucleic acid construct (Figure 2.3B). To achieve that, a surface scan of the excitation laser
is performed to locate the fluorophore-labeled construct. With extended laser illumination, thetime-dependent fluorescence of the located molecule can be used to calculate the time trajectoryof EFRET for further kinetic analysis (Figure 2.4). With the in-house analysis software written by
Dr. Vasiliy Fomenko, the bin time of the resulting trajectory can be adjusted post-acquisition to
improve the signal-to-noise level in trade of the temporal resolution. A simple thresholding

29
method can be used to determine the dwell time for each EFRET state when the two EFRET
populations are widely separated with respected to their spread (Figure 2.4B). Specifically, an
EFRET threshold between two EFRET populations is applied to distinguish the state of the nucleic
acid construct at each bin. From that, a collection of dwell time—time spent in a particularstate—can be obtained and further used to acquire the kinetic information (Figure 2.4C). In cases
when the cumulative distribution of dwell time can be well-fit to a single exponential decayfunction, the process can be sufficiently described by a first order kinetic constant.

Figure 2.4 Sample surface immobilization single molecule FRET data. (A) fluorescence signal
from Cy3 (green) and Cy5 (red) as a function of time. (B) the resulting time trajectory of EFRET,
where the high and low EFRET states corresponding to the folded and unfolded conformation,
respectively. (C) dwell time distributions (plotted in reverse cumulative distribution functions) for
each state. The data are well-fit to a single exponential decay function to obtain the first orderfolding and unfolding rate constants kfold and kunfold, respectively. Typically, each set of datacontains 20 to 50 molecules throughout this thesis.

30

Figure 2.5 Images of the high pressure generating system. (A) The manually operated piston screw
pump and the pressure gauge mounted on the extended surface outside the laser curtain. (B) The
three-way control valve mounted to the optical breadboard that allows vertical translation of thesample holder. The blue lines/arrows indicate the direction of pressure transmitting through thehigh pressure tubing.

2.5

High pressure single molecule experiment
Besides temperature, pressure is another thermodynamic variable that plays an importantrole in biomolecule conformational change.6 The single molecule experiment is herein
incorporated with a pressure generating system to facilitate the exploration of the pressure
dependent nucleic acid folding.
2.5.1 Pressure generation and transmission
The source of high pressure is a manually operated piston screw pump (Figure 2.5A,
High Pressure Equipment), which is connected through high-pressure stainless-steel tubing to abourdon tube pressure gauge for pressure measurements (accuracy ≈ 25 bar).7-8 The liquid
reservoirs contain ethanol as pressure transmitting fluid in use to remove air bubbles in thestainless-steel tubing manifold to increase the pressuring efficiency. The pressure is directed to athree-way control valve for coupling with the high pressure sample cell (Figure 2.5B). Note that31
the control valve is mounted onto an optical breadboard with an adjustable post clamp to allow
the vertical translation along the metal post for sample alignment with the microscope.

Figure 2.6 Capillary sample holder for the high pressure single molecule experiments. (A) thecross section of the square capillary. (B) the capillary end glued into the metal plug for coupling
to the high pressure system.

2.5.2 Sample preparation for high pressure measurements
The high pressure sample holder is made from a glass capillary with a square crosssection (Polymicro) while the inner and outer dimensions are measured as 50 µm and 360 µm,
respectively (Figure 2.6A). The small surface area permits the capillary cell to sustain pressure
up to ≈ 4 kilobars. Moreover, the flat surfaces and wall thickness (155 µm) allow it to behave
like a regular coverslip in standard microscope imaging. To prepare the sample holder, one endof the capillary is first glue to a metal plug with a 450 µm diameter hole for further coupling to
the high pressure system (Figure 2.6B). To create an optical window for fluorescenceobservation, about 1 to 2 inches of the nontransparent polyimide coating is burned away with apropane torch. Note that the location of the exposed capillary has to align with the objective afterplugged into the control valve, about 17.5 cm away from the metal plug end in current
instrument configuration.

32
In high pressure freely diffusing experiments, the capillary is filled with the imaging
buffer containing the doubly fluorophore-labeled construct through the capillary effect simply bydipping the metal plug-attached open end into the sample solution. The same end of the capillary
is then dipped into the low-viscosity silicon oil to create a thin film (≈ 25 to 50 µm) inside thecapillary to prevent the sample contamination from the pressure transmitting fluid ethanol.
Before high pressure experiment, the distal end (from the metal plug) of the capillary is sealedwith an oxy-propane torch.
For high pressure surface immobilization experiments,9 the sample is prepared byconsecutively flushing the capillary cell with the following solutions: i) 10% biotinylated BSA(10 mg/mL), ii) streptavidin (200 µg/mL), iii) nucleic acid construct (≈ 25 pM), and iv) the
imaging buffer (2.3.2). With a mechanical micropipette (Eppendorf) to continuously push thesolutions through the capillary at the flow rate measured as ≈ 2 µL/min, the exposure time foreach solution is approximately 2 minutes. After the interior surface of the capillary is decorated
with nucleic acid in the desired buffer solution, the metal-plug end is then dipped into the siliconoil, followed by sealing the distal end with an oxy-propane torch prior to coupling to the highpressure system.

2.6

References

1.

Fiore, J. L.; Hodak, J. H.; Piestert, O.; Downey, C. D.; Nesbitt, D. J., Monovalent andDivalent Promoted GAAA Tetraloop-Receptor Tertiary Interactions from Freely
Diffusing Single-Molecule Studies. Biophys. J. 2008, 95 (8), 3892-3905.

2.

Holmstrom, E. D.; Nesbitt, D. J., Biophysical Insights from Temperature-Dependent
Single-Molecule Förster Resonance Energy Transfer. Annu. Rev. Phys. Chem. 2016, 67(1), 441-465.

33
3.

Holmstrom, E. D.; Nesbitt, D. J., Localized Heating of Single Oligonucleotides using
Infrared Light. Biophys. J. 2012, 102 (3), 180a.

4.

Aitken, C. E.; Marshall, R. A.; Puglisi, J. D., An Oxygen Scavenging System for
Improvement of Dye Stability in Single-Molecule Fluorescence Experiments. Biophys. J.
2008, 94 (5), 1826-1835.

5.

Lee, N. K.; Kapanidis, A. N.; Wang, Y.; Michalet, X.; Mukhopadhyay, J.; Ebright, R. H.;
Weiss, S., Accurate FRET Measurements within Single Diffusing Biomolecules Using
Alternating-Laser Excitation. Biophys. J. 2005, 88 (4), 2939-2953.

6.

Mozhaev, V. V.; Heremans, K.; Frank, J.; Masson, P.; Balny, C., High Pressure Effects
on Protein Structure and Function. Proteins 1996, 24 (1), 81-91.

7.

Patra, S.; Anders, C.; Erwin, N.; Winter, R., Osmolyte Effects on the Conformational
Dynamics of a DNA Hairpin at Ambient and Extreme Environmental Conditions. Angew.
Chem. 2017, 56 (18), 5045-5049.

8.

Sung, H.-L.; Nesbitt, D. J., DNA Hairpin Hybridization under Extreme Pressures: A
Single-Molecule FRET Study. J. Phys. Chem. B 2020, 124 (1), 110-120.

9.

Sung, H.-L.; Nesbitt, D. J., Single-Molecule Kinetic Studies of DNA Hybridization under
Extreme Pressures. Phys. Chem. Chem. Phys. 2020, 22 (41), 23491-23501.

34
Chapter 3
Single Molecule FRET Kinetics of the Mn2+ Riboswitch: Evidence for Allosteric Mn2+
Control of “Induced-Fit” vs. “Conformational Selection” Folding Pathways

3.1

Abstract
Gene expression in bacteria is often regulated dynamically by conformational changes ina riboswitch upon ligand binding, a detailed understanding of which is very much in its infancy.
For example, the manganese riboswitch is a widespread RNA motif that conformationallyresponds in regulating bacterial gene expression to M levels of its eponymous ligand, Mn2+, but
the mechanistic pathways are poorly understood. In this work, we quantitatively explore thedynamic folding behavior of the manganese riboswitch by single molecule FRET spectroscopy(smFRET) as function of cation/ligand conditions. From detailed analysis of the kinetics, theMn2+ is shown to fold the riboswitch by a “bind-then-fold” (i.e., “induced-fit,” IF) mechanism,
whereby the ligand binds first and then promotes folding. On the other hand, the data also clearly
reveal the presence of a folded yet ligand free structure predominating due to addition ofphysiological Mg2+ to a non-selective metal ion binding site. Of particular kinetic interest, such a
Mg2+ “pre-folded” conformation of the riboswitch is shown to exhibit a significantly increased
affinity for Mn2+ and further stabilization by subsequent binding of the ligand, thereby promoting
efficient riboswitch folding by a “fold-then-bind” (i.e., “conformational selection,” CS)mechanism. Our results not only demonstrate Mg2+ controlled switching between IF and CS
riboswitch folding pathways, but also suggest a novel heterotropic allosteric control in the
manganese riboswitch activity co-regulated by Mg2+ binding.
*This chapter is adapted from: Sung, H.-L.; Nesbitt, D. J. Single Molecule FRET Kinetics of the Mn2+
Riboswitch: Evidence for Allosteric Mg2+ Control of “Induced Fit” vs. “Conformational Selection” Folding
Pathways. J. Phys. Chem. B 2019, 123, 2005-2015.

35
3.2

Introduction
Riboswitches are cis-acting regulatory RNA strands typically encoded in the 5’ upstream

untranslated regions of the genes which they regulate1-4. These structured RNA elements consistof i) an aptamer domain and ii) an expression platform, whereby the aptamer structurally binds a
cognate ligand, inducing the expression platform to undergo conformational change in response56. This conformational shift, in turn, achieves a desired biochemical goal, such as blocked

initiation of the translational event, premature termination of gene transcription, or controlledcleavage of the mRNA4-5. Such regulatory mechanisms of ligand responsive riboswitches arewidely adopted by the bacterial kingdom. Many classes of both translational and transcriptional
riboswitches have been identified and structurally characterized to date, responding to variety ofmolecular ligands, including enzymatic cofactors7-11, nucleotide derivatives12-13, and aminoacids14-16, but also simple atomic ions such as F- 17-18, Mg2+ 19, Ni2+/Co2+ 20 and Mn2+ 21-22.
The manganese (Mn2+) responsive riboswitch (commonly denoted as the yybP-ykoY
riboswitch) is now known to be extensively distributed among many bacterial phyla. However,even simple confirmation of the ligand identity was obtained only recently21-22, due primarily tolack of characterization of the associated genes (yybP and ykoY) in Bacillus subtilis where theRNA motif was first discovered23. The aptamer domain of the manganese riboswitch comprises afour-way junction connecting four helices, which in the ligand-bound crystal structure (Figure
3.1A)21 coaxially align in pairs to generate a tight hairpin-like conformation. The two helices (P1and P3) then dock into highly conserved internal loop regions (L1 and L3), forming an elaborate
interface stabilized by two coordinated divalent metal ion sites evident in the crystal structure(Figure 3.1B). Of these two metal binding sites, the first exhibits a very high specificity for Mn2+
over Mg2+, whereas the second shows little cation selectivity and is largely occupied by Mg2+

36

Figure 3.1 Structure of L. lactis yybP-ykoY manganese riboswitch (A) Overall crystal structurereconstructed from X-ray diffraction data (PDB 4Y1I) (B) Structure of M2+ binding sites withadjacent nucleotides (C) RNA construct design for smFRET experiment.

under physiological conditions. In fact, it is rather remarkable that this RNA riboswitch responds
so preferentially to Mn2+ over Mg2+, as both cations are similar in size, charge and coordination
complex geometry24, particularly with cellular Mg2+ concentrations25 10-100 fold higher thanMn2+26. From previous mutational studies, it has been demonstrated that the origin of this highMn2+ selectivity is preferential coordination between manganese and nitrogen (N7) in A41(Figure 3.1B)21, 24, 27 as Mg2+ is only known directly coordinated in RNA to oxygen.
Despite detailed crystallographic knowledge of the ligand-bound (i.e. fully-folded)
riboswitch conformation, the dynamics and mechanisms for ligand-aptamer recognition andfolding processes has remained elusive. By way of introduction, ligand promoted folding
mechanisms can generally be classified into two categories, either i) induced-fit (IF) or ii)

37

Figure 3.2 Schematic illustration of induced-fit (IF) and conformational selection (CS) pathways
in the context of a four-state kinetic model.
conformational selection (CS)28-32 (See Figure 3.2). In the induced-fit (IF) mechanism, the ligand
binds to the unfolded conformation and triggers the folding event (“bind-then-fold”), whereas via
conformational selection (CS), the structure dynamically rearranges into a “pre-folded” state thatis subsequently further stabilized by the ligand (“fold-then-bind”). Despite obvious physicaldifferences between these two kinetic pathways, it has proven quite challenging to distinguishbetween them in equilibrium ensemble experiments. With single-molecule methods, by way ofcontrast, conformational changes in response to the ligand can be probed at the single constructlevel, which in recent studies has enabled the identification of these two distinct IF and CS
folding pathways for both proteins33-34 and nucleic acids35-40.
In this present work, the folding dynamics of the manganese riboswitch are monitored
directly by single-molecule FRET (smFRET) spectroscopy, for which energy transfer (EFRET)
between covalently attached Cy3 and Cy5 dyes provides a probe of RNA conformationalchanges in real time at the single molecule level (Figure 3.1C). The resulting time dependent
EFRET trajectories provide direct kinetic information on the folding (kfold) and unfolding (kunfold)kinetic rate constants, as well as the overall folding equilibrium behavior (Keq = kfold/kunfold). Of
particular relevance to the present study, the ligand dependence of the folding/unfolding rate

38

Figure 3.3 Sample smFRET experimental data; both with background 0.5 mM MgCl2 and total
125 mM monovalent cation (A) Visual representation of manganese riboswitch folding changing
the distance between Cy3 and Cy5 (B) (from top to bottom) Fluorescence time traces of signals
from Cy3 and Cy5, the corresponding EFRET trajectories, cumulative distribution function of dwell
time analysis.

constants allows the aptamer recognition and folding mechanisms to be kinetically isolated andcharacterized individually.
In this investigation of manganese riboswitch folding, we build kinetic models and fit thesmFRET data as a function of [Mn2+] and [Mg2+] to explicitly demonstrate which of the two (IFor CS) folding pathways is chosen under a specific cation environment. Interestingly, the work

39
reveals that manganese riboswitch folding can be impacted by either [Mn2+] or [Mg2+]. On the
one hand, detailed kinetic analysis of the smFRET data reveals a 100-fold greater binding
affinity for Mn2+ vs Mg2+, which lends support to the simple Mn2+ ligand-promoted “induced-fit”
folding mechanism. However, a parallel Mg2+ mediated folding process has also been identified,
specifically in which Mg2+ promotes formation of a transient Mn2+ ligand-free (apo) pre-folded
state, which then provides a subsequent binding platform for Mn2+ to further stabilize theconformation. We note that such Mg2+ control of the kinetic mechanism is strongly reminiscentof allostery commonly seen in enzymes, whereby binding of an “effector” species can alter theoverall conformation and thereby regulate ligand affinity at a remote binding site.41-43. As
explicitly shown in the current smFRET data, the ability of Mg2+ to facilitate riboswitch
sampling states of more fold-like character provides an intriguing example of “RNAallostery.”44-46 Simply stated, the presence or absence of physiological Mg2+ is able to modulate
the Mn+2 riboswitch folding pathway from that of induced-fit (“bind-then-fold”) to
conformational selection (“fold-then-bind”).

3.3

Experiment3.3.1 RNA construct design and preparation for single-molecule study
The aptamer domain of manganese riboswitch is a hairpin-like structure rearranged withfour helices joined by a four-way junction (see Figure 3.1A). As shown in this crystal structure21, folding between loops L1 and L3 can be stabilized by one Mn2+ and one Mg2+ (or a secondMn2+) through metal coordination. The smFRET RNA construct (Figure 3.1C) is designed toprobe the interaction between L1 and L3 that are not only considered as the major structural

40change during riboswitch folding but also have been identified as crucial elements for ligand
recognition and binding21-22.
The manganese riboswitch in this work is constructed from the sequence of Lactococcus
lactis that has been structurally characterized in previous studies.21 To achieve surface
immobilization and dye labeling, the riboswitch construct is formed by annealing threechemically modified RNA oligos from Integrated DNA Technologies (IDT, Coralville, IA): (i)Biotinylated strand 1, 5’-biotin- GUG UGU GUG UGU GUG GCA AAG GGG AGU AGC
GUC GGG AAA CCG AAA CAA AGU CGU CAA UUC GUG AGC GCA CUC GUC UGA
G-3’; (ii) Cy3 labeled strand 2, 5’-GGU ACG CAC GUA CGG UAU GUU UAG CAA GAC
CU-Cy3- UUG CCA CAC ACA CAC ACA C-3’; and (iii) Cy5 labeled strand 3, 5’-Cy5-CUC
AGA CGA GUG CGC UCA CCG GCU UUG UUG ACA UAC CGU ACG UGC GUA CC-3’(Figure 3.1C). Each end of the open helix is extended from its native sequence by 14 base pairs
to stabilize the RNA trimer construct under all experimental cation conditions of interest. The
FRET pair Cy3 and Cy5 are labeled at the end of P1 and P3 respectively with distance between
them estimated from crystal structure plots to be ~45 Å21. For the characteristic Forster length of
the Cy3 and Cy5 FRET pair (R0 ~50 Å), we expect an intermediate EFRET (~ 0.5) state for thefolded conformation, which will drop to FRET values near zero in the unfolded state due to therapid ~1/R6 dependence on distance. (Figure 3.3).
The RNA molecules for smFRET studies are tethered on the surface of glass coverslip bybiotin-streptavidin interactions. Sample preparation is accomplished by successively flushing thesample holder in the following solution order to obtain ~ RNAs per 100 m2 surface coverage:(i) 10 mg/mL bovine serum albumin (BSA) with 10% biotinylated BSA, (ii) 200 µg/mL
streptavidin solution, (iii) ~ 25 pM of the biotin/dye labeled and annealed RNA riboswitch

41
construct, with the samples allowed to incubate for 10 mins between each step. Immediately
prior to a specific smFRET data run, the sample holder is then flushed by a buffer containing (i)50 mM hemisodium HEPES buffer (pH 7.5), (ii) enzymatic oxygen scavenger cocktail(PCD/PCA/Trolox) to catalytically remove oxygen, (iii) 100 mM NaCl to provide backgroundmonovalent salt, and (iv) sufficient MgCl2 and/or MnCl2 to tune the divalent cation
concentrations over the desired dynamic range.

3.3.2 Single-molecule FRET spectroscopy and data analysis
A 532 nm beam from a pulsed Nd:YAG laser (10 ps pulses at a 20 MHz repetition rate) is
directed onto a sample through an inverted confocal microscope with a 1.2 N.A. water
immersion objective. The beam is collimated with lenses in the backplane to overfill the limiting
microscope aperture, resulting in a diffraction limited laser excitation/collection spot (rx-y ~250nm). For the smFRET experiments, the laser illuminates the surface of coverslip with subfemtoliter confocal volume control to allow observation of single fluorophore-labeled RNA
constructs. The resulting fluorescence signal is then collected through the same objective andsplit by i) color (green/red) and ii) polarization (horizontal/vertical) before detection on four
single photon avalanche photodiodes (APDs). For each photon detection event, 4 bits of
information (color, polarization, wall clock time ( 50 ns) and microtime with respect to the laser
pulse ( 50 ps)) are recorded with a time-correlated single-photon counting (TCSPC) module.
The donor/acceptor fluoresence photon arrivals as a function of wall clock time are
analyzed with in-house software to generate background and cross talk corrected EFRET =I(red)/(I(green) + I(red)) trajectories with 20-ms bin time resolution (Figure 3.3B). Since
populations for the two distinct riboswitch conformations are quite separated in EFRET value, a42
simple thresholding routine can be used to obtain dwell time distributions for the ensemble oftime durations spent in the folded (docked) vs. unfolded (undocked) state between transitions.
The folding (docking) equilibrium constant (Keq  [fold]/[unfold]) can be accurately measured byi) ratios of total dwell times for folded and unfolded states, but with far more detailed
information on the folding/unfolding kinetic rate constants obtained from ii) analyzing
cumulative distribution functions (CDFs) for the individual dwell times (P(𝞽)/P(0))47. The
resulting plots of ln [P(𝞽)/P(0)] vs. low FRET and high FRET dwell times are linear (see Figure
3.3B, lower panel), corresponding to single exponential decays that yield first order docking andundocking rate constants (kdock and kundock), respectively.

3.4

Results and analysis

3.4.1 Manganese riboswitch folding kinetics with Mg2+ alone
Structural changes in the manganese riboswitch construct are signaled by the labeled
Cy3/Cy5 FRET dye pair, with FRET energy transfer clearly evident in the anti-correlated red
and green fluorescent signals as function of time (Figure 3.3B upper panel). The resulting EFRET
time trajectories indicate that the manganese riboswitch oscillates between two states with
distinct EFRET values ~ 0.5 and 0, consistent with predictions based on the construct geometry.
The high EFRET state corresponds to a fully folded conformation with the two L1 and L3 loops
mutually docked onto each other, while the low EFRET state corresponds to an unfolded
conformation with the two loops substantially further apart.
In these smFRET experiments, the presence of either Mg2+ or Mn2+ divalent metal cationis required for folding of the manganese riboswitch. Specifically, no folding events are seen at
background (125 mM) monovalent salt levels. However, as evident in the trajectories in Figure

43
3.3B, transitions between high and low EFRET states are readily observed already at 0.5 mM
Mg2+, with the low EFRET state more dominant and the RNA mostly unfolded. On the other hand,with addition of only 100 𝞵M Mn2+ (right panels of Figure 3.3B), the high EFRET population
becomes significantly more prominent, indicating that the overall stability of the folded
manganese riboswitch is promoted by its eponymous ligand Mn2+. Note that from EFRET values,
the folded states promoted by Mn2+ and Mg2+ alone are indistinguishable, consistent with Mg2+
alone being capable of facilitating L1 and L3 docking and promoting transcriptional readthroughin previous in vitro transcription assay at relatively high concentration (> 10 mM)21.
We first explore the Mg2+ concentration dependence of manganese riboswitch folding in
absence of ligand ([Mn2+] = 0), explicitly probing the equilibrium folded fraction as a function of[Mg2+]. The sample data in Figure 3.4A make it clear that Mg2+ promotes folding and the data
exhibit minimal cooperativity, as evidenced by a nearly linear increase in folded fraction at low[Mg2+]. The results can be fit to a modified Hill equation48-53:n[M2+ ]

fraction folded = F0 + (1 − F0 ) × Fs (K n +[M2+]n ),D

Eq. 3.1

where F0 and Fs are attributed to folding under [Mg2+] = 0 and saturation conditions respectively.
The effective binding constant KD is determined as 1.1(2) mM for Mg2+ with a Hill coefficient ofn 1.3(2). In general, the Hill coefficient n indicates the number of associated ligands (Mg2+)
during folding. As a result, n could moderately depend on [Mg2+] since, as [Mg2+] increases,
more Mg2+ ions may preferentially surround the negatively charged RNA to facilitate folding.54
However, within the limited range of [Mg2+] explored, as well as with sufficient backgroundmonovalent cations (> 100 mM), n can be treated as a constant in our study.54-56 The n = 1.3(2)indicates a negligible level of cooperativity in Mg2+-mediated folding. Despite n is not always
equivalent to the binding stoichiometry, one nearly fully (5-fold) coordinated Mg2+ has been

44

Figure 3.4 Mg2+ dependence of manganese riboswitch folding (A) equilibrium fraction folded asa function of [Mg2+] (B) Mg2+ dependence of rate constants at [Mn2+] = 0 mM (C) A four-statemodel for Mg2+ facilitated manganese riboswitch folding kinetics.

found crucial to stabilize the L1 and L3 folding interface of the manganese riboswitch inprevious structural study (consistent with n = 1).21 We therefore simplify our kinetic analysis
with a model of single Mg2+ binding. The deviation of n = 1.3(2) from 1 may indicate the weakassociation of the divalent cation Mg2+ accumulated around the negatively charged RNA. As we45shall see, this non-cooperativity (n = 1) of Mg2+ raises the intriguing possibility that occupancyof the non-selective site by Mg2+ can promote conformational changes in manganese riboswitch,in particular shifting the mechanistic folding pathway from an induced fit (IF) kinetic paradigm
to one of conformational selection (CS).
In addition to the above equilibrium results, the smFRET time traces also permit direct
measurement of the folding/unfolding rate constants kfold and kunfold as a function of [Mg2+](Figure 3.4B). The near-linear dependence of kfold at low [Mg2+] again suggests the folding
process to be non-cooperative with effectively only single Mg2+ binding. We thus restrict ouranalysis of the kinetic data to a single binding site (n = 1), which, assuming rapid equilibration
between Mg2+ associated/dissociated species, is equivalent to the well-known four-state model(folded vs. unfolded and Mg2+ bound vs. unbound), used in previous studies47, 57-58 and shown
schematically in Figure 3.4C. In such a four-state model, the apparent single exponential
folding/unfolding rate constants can be analytically derived to be:
𝑘𝑓𝑜𝑙𝑑/𝑢𝑛𝑓𝑜𝑙𝑑 =𝑘1/−1 +𝑘2/−2 𝐾𝑎/𝑏 [𝑀𝑔2+ ]1+𝐾𝑎/𝑏 [𝑀𝑔2+ ]Eq. 3.2(where subscripts designate folding and unfolding pathways, respectively) and used to leastsquares fit the folding/unfolding kinetic data in Figure 3.4B. First of all, kfold at [Mg2+] = 0(Figure 3.4C, Table 3.1) is indistinguishable from zero and indeed yields zero folding events inthe absence of any divalent cations. To limit the number of free parameters and parametercorrelation, we set k1  0, though the results are in fact insensitive to whether k1 is left freely
floating in the least squares fits. Physically this would imply that all riboswitch folding eventsoccur from the Mg2+ bound construct (i.e., k2), which also explains the kinetic saturation
behavior achieved at high Mg2+ >> 1/Ka = 4.7(8) mM.

46

2+

Table 3.1 Least squares fit results of the smFRET kinetics for Mg promoted folding of the Mnriboswitch.

2+

In dramatic contrast, the unfolding rate constant, kunfold  2.7 s-1, shows essentially no
dependence on [Mg2+] over nearly two orders of magnitude (300 M to 15 mM). In the context
of a 4 state-kinetic model, this would be consistent with either (i) Kb strongly favoring Mg2+
binding to the folded riboswitch (F) and thus only the rate constant kunfold  k1 is measured evenat the lowest Mg2+ levels, or (ii) kunfold  k-1  k-2 and the unfolding results are therefore perfectly
insensitive to Mg2+. Furthermore, no smFRET transitions are observed at [Mg2+] = 0, which
again implies that k1  0 within experimental uncertainty. Since k1/k-1= [F]/[U] requires [F] <<[U], the kinetic analysis for kunfold becomes completely insensitive to k-1 due to [F] << [FMg] [U]. Simply stated, the effective unfolding rate constant kunfold ~ 2.7 s-1 can be ascribed entirely
to k-2, with FMg as the dominant folded species at our lowest possible [Mg2+]  300 M andunimolecular unfolding from FMg to UMg as the predominant unfolding channel. In essence, theindependence of kunfold on Mg2+ signals facile Mg2+ binding to the folded riboswitch (1/Kb <<300 M), which prevents probing smFRET kinetics at sufficiently low Mg2+ to accurately
sample the [Mg2+] = 0 unfolding rate pathway.
As a unifying theme, we return to characterizing the Mg2+ promoted folding/unfolding pathways
in terms of the “induced fit” vs “conformational selection” kinetic limits, which can be visually
distinguished by either counterclockwise (blue arrow) vs clockwise (orange arrow) pathways
around the 4-state kinetic model (see Figure 3.4C). The purely Mg2+ promoted folding/unfolding

47
kinetics for the Mn2+ riboswitch clearly follows the “induced-fit” paradigm, i.e., whereby Mg2+
binding to the riboswitch is a prerequisite for folding. (Indeed, the dramatic insensitivity of kunfold
to Mg2+ follows directly from an induced-fit mechanism.) Specifically, this implies for our
riboswitch a predominantly clockwise kinetic pathway (Figure 3.4C, orange) from the unfolded(U) to the Mg2+-bound and folded (FMg) state, without corresponding evidence for acounterclockwise pathway (Figure 3.4C, blue) involving a Mg2+-free folded (F) riboswitch
state.32, 40

Figure 3.5 Kinetics of Mn2+ promoted manganese riboswitch folding (A) Mn2+ dependent kfold andkunfold (B) Scheme of extended Hill model into six-state kinetic model (least squares fit resultssummarized Table 3.2).

48
3.4.2 Manganese riboswitch folding kinetics with Mn2+ alone
As a next step up in kinetic complexity, we have similarly investigated the smFRET
kinetics of Mn2+ mediated folding of the riboswitch in absence of Mg2+, with the kinetic datasummarized in Figure 3.5A. Note that such conditions now allow the cognate ligand Mn2+ to
occupy both highly selective and non-selective binding sites on the riboswitch, from which wemight anticipate strong cooperativity in a Hill kinetic analysis at sufficiently low Mn2+.
Fortunately, the effective folding rate constant kfold is clearly measurable by smFRET methods
even at [Mn2+] > 30 M, which is sufficient for multiple folding events to be observed within theexperimental photobleaching time window. As expected, the rate constant kfold increases
supralinearly at low [Mn2+] and eventually approaches an asymptotic value, consistent withsigmoidal growth kinetics and a positive cooperativity (i.e., Hill coefficient n > 1). Conversely,
kunfold decreases rapidly with increasing Mn2+, also gradually reaching an asymptotic rate
constant at saturating Mn2+ conditions.
From a least squares fit analysis of kfold (Figure 3.5A) and the fraction folded (Figure
3.6A), the Hill cooperativity is found to be n  2.0(3) and 2.1(2), respectively. This is consistent
with the presence of two Mn2+ ions associated with the riboswitch during the folding process andas confirmed by x-ray crystallography.21 To appropriately include the effects of these twodivalent cations, we therefore must expand our previous 4-state model into a more detailed
kinetic model with n = 2 (see Figure 3.5B). Such a 6-state kinetic treatment incorporates folding
and unfolding processes between each of the RNA conformations associated with zero, one andtwo Mn2+ cations, which requires a large number of model kinetic parameters. To limit
parameter correlation and make such a multistate treatment mathematically tractable, therefore,
we have assumed that the Mn2+ association/dissociation processes for the unfolded (Ke) and49
folded (Kf ) states are both rapid and insensitive to number of Mn2+ (i.e., Ke  Kf). In this kinetic
limit, the apparent kfold and kunfold rate constants can be analytically expressed in terms of rate andequilibrium constants as:
𝑘𝑓𝑜𝑙𝑑/𝑢𝑛𝑓𝑜𝑙𝑑 =2
𝑘1/−1 +𝑘3/−3 𝐾𝑒/𝑓 [𝑀𝑛2+ ]+𝑘4/−4 𝐾𝑒/𝑓
[𝑀𝑛2+ ]2
2 [𝑀𝑛2+ ]2
1+𝐾𝑒/𝑓 [𝑀𝑛2+ ]+𝐾𝑒/𝑓,

Eq. 3.3

which can be least squares fit to the smFRET kinetic dwell times. Sample kinetic data are shownin Figure 3.5A, with least square fitted results from the Mn2+ dependent studies summarized inTable 3.2, where the docking rate constant in the absence of Mn2+ (k1  0) is fixed at zero as per
experimental observation. Interestingly, the binding constant [(Ke/f)-1] is found to be  2-foldsmaller for the folded vs. unfolded state, reflecting a higher ligand affinity riboswitch
conformation when the binding site is pre-organized by docking of L1 and L3. In addition, thedata reveals a systematic speed up of the folding rate processes (e.g. k4 > k3 > k1), as well as acorresponding slowing down of the unfolding rate processes (k-1 > k-3 ~ k-4) with incremental
Mn2+ association.

2+

Table 3.2 Least squares fit results of the smFRET kinetics for Mn promoted folding of the Mnriboswitch.
Once again, the prerequisite of one or both Mn2+ ligands for folding of the manganeseriboswitch is consistent with a predominantly “induced-fit” (IF) mechanism. Indeed, the leastsquares fit indicates that the overall folding rate for the riboswitch is dominated by the doubly2+50
Mn2+ associated unfolded state (k4). However, the data are agnostic whether or not folding canbe achieved with only a single Mn2+, due to residual uncertainty in k3 = 0.1(5). If k3 is finite,
folding could be induced by a single Mn2+ occupying one of the two metal binding sites, with thefolded conformation further stabilized by sequential binding of a second Mn2+. Indeed, thisproves to be the case for tandem Mg+2 and Mn+2 promoted folding, as explored in detail below.

3.4.3

Synergistic folding in the presence of both Mn2+ and Mg2+

Armed with this information on individual Mg2+ and Mn2+ promoted folding pathways, we can
now tackle the more complex yet biologically relevant “multi-cation” kinetic nature of thisriboswitch. As mentioned in the introduction, previous structural studies have demonstrated thatthe manganese riboswitch contains two highly coordinated divalent metal binding sites: one witha more than 200-fold selectivity for Mn2+ over Mg2+ and the other with essentially no preference
between the two cations21. Consequently, manganese riboswitch folding is therefore dependent
on the simultaneous occupancy of both selective and non-selective binding sites. To address therole of such heterogeneous binding sites, we have studied the equilibrium folding behavior andits dependence on [Mn2+] for a series of different Mg2+ concentrations.
The resulting equilibrium folding fractions are fit to the modified Hill equation (Eq. 3.1),
with the results summarized in Figure 3.6A, B, and C. In the absence of Mg2+ (Figure 3.6A), thepresence of Mn2+ promotes efficient fractional folding from 0.0 to ~ 0.9 with an effective KD =111(4) 𝞵M. The clear, sigmoidal nature of this curve is again indicative of a strong positive
cooperativity, which can be least squares fit with a Hill coefficient of n = 2.1(2). Interestingly,
the Hill coefficient for Mn2+ systematically drops from n = 2.1(2) to 1.0(3) as [Mg2+] increases
from 0 to 2 mM (Figure 3.6A to 3.6C). This would be consistent with a simple kinetic picture

51
whereby, of the two metal binding sites, one is exclusively reserved for Mn2+ binding, while theother could be equally well occupied by Mn2+ or Mg2+ under near physiological conditions.
Moreover, it also suggests that the occupancy of the non-Mn2+ selective site by Mg2+ is
responsible for “pre-folding” conformational kinetics promoted by Mg2+ alone, as previously
described in Section 3.4.1.

Figure 3.6 Equilibrium Mn2+-dependent fraction folded studied at different [Mg2+] (A) [Mg2+] =0 mM (B) 0.5 mM (C) 2 mM.

52
Besides providing a source of cation competition for the non-selective binding site,another clear effect of Mg2+ in Figure 3.6A, 3.6B, 3.6C is that it dramatically lowers theeffective KD for Mn2+ facilitated folding from 111(4) to 16(5) 𝞵M. Similar synergistic effects
have been observed in other riboswitches, where the presence of Mg2+ is shown to significantly
enhance ligand affinity 50, 59-61. Since the ligand-free “pre-folded” conformation of themanganese riboswitch is promoted solely by Mg2+, it is likely that such a structure has higher
Mn2+ ligand affinity due to formation of a new binding site.

3.5

Discussion

3.5.1

Induced fit vs. conformational selection mechanisms: dependence on Mn 2+/Mg2+

alone
We have presented extensive smFRET kinetic data for folding and unfolding of themanganese riboswitch, which has two binding sites (on Mn2+ and Mg2+) and therefore generates
a complex parameter space of concentrations to explore. In this discussion, we present evidence
that even in such complex kinetic folding landscapes, we can be guided by simple considerationsof a few limiting kinetic mechanisms and pathways. There are two commonly proposed (and
often debated) biophysical mechanisms (see Figure 3.2) for ligand-promoted folding of abiomolecule, either by “induced-fit” or “conformational selection” processes.28-32 In the inducedfit (“bind-then-fold”) mechanism, the ligand (L) binds tightly to an initially unfolded structure(U), changes some folding transition state barrier/rate constant, which in turn kineticallyfacilitates formation of a ligand bound folded state (FL). In the simplifying kinetic framework
pictured in Figure 3.2, this would be represented by the clockwise, orange path. Conversely, inthe conformational selection paradigm (“fold-then-bind”), the unfolded state dynamically53
searches over a large ensemble of folded/unfolded conformations (Ui), with the ligand
preferentially binding to states with more fold-like character (Fj) and thus driving the equilibrium
towards the folded state (FL). In the context of Figure 3.2, this would be represented by thecounterclockwise, blue path. As shown in previous smFRET kinetic studies of riboswitch
folding40, the dependence of kunfold on ligand concentration can clearly distinguish between these
two mechanisms. For a conformational selection (CS) process, kunfold should depend strongly on
ligand concentration due to rapid equilibration between ligand-free (fold-like) and ligand-bound(folded) states. For the induced-fit (IF) mechanism, on the other hand, kunfold will be relatively
insensitive to ligand concentration, since the dominant pathway is unfolding of the ligand-boundstate. On the other hand, the requirement of ligand binding prior to folding and the linear
response of kfold on ligand concentration both support the IF mechanism. However, there could
be potential ambiguity about whether or not the lifetime of the “pre-folded” state (which could
be quite dynamic) is long enough to be detected under experimental conditions. The actual
folding mechanism is therefore not determined by kfold alone but more by the integrated kinetic
picture.
We first consider the folding kinetics in the absence of the Mn2+ ligand, i.e., pure Mg2+
controlled folding. From Figure 3.4B, kunfold is clearly independent of [Mg2+]. Moreover, the factthat kfold vanishes at [Mg2+]  0 indicates that binding of the Mg2+ ligand is crucial for folding.
Both of the above statements strongly support an induced-fit mechanism for riboswitch folding
with respect to a single Mg2+. Thus, despite the fact that Mg2+ is not cognate for the manganeseriboswitch, it can still act as a ligand to promote folding through an induced-fit mechanism. This
folding pathway is already illustrated in the upper half diagonal subset of the 4 state kinetic
model presented in Figure 3.2 and Figure 3.4C, by which Mg2+ predominantly associates with

54
the unfolded riboswitch (UMg), which then folds to form FMg (“bind-then-fold”). Conversely,
exponential decay of the folded conformation occurs simply via unimolecular unfolding from thecation bound FMg state, which would explain why kunfold is kinetically independent of Mg2+
concentration.
Similarly, for riboswitch folding kinetics observed solely in the presence of Mn2+ (i.e.,[Mg2+] = 0, see Figure 3.5A), the folding rate constant i) vanishes in the limit of [Mn2+] = 0 andii) exhibits a strong positive cooperativity (n = 2.0(3)). Both of these observations signal an
induced-fit mechanism for ligand promoted folding of the manganese riboswitch, as explicitly
demonstrated by fitting rate constants to the six-state kinetic model (Figure 3.5B, upper half
diagonal and Table 3.2). However, in contrast to Mg2+ dependent folding, kunfold now depends
significantly on Mn2+, decreasing rapidly at low concentration to a saturation value. As shown inthe kinetic model, the folded species can associate up to two Mn2+ and each state may exhibit a
distinct unfolding rate. Since we are able to probe manganese riboswitch folding at sufficiently
low [Mn2+] ( 30 M), the rapid equilibrium between the three folded conformations withdifferent numbers of bound Mn2+ cations can explain the Mn2+ dependence in kunfold.

3.5.2

Mg2+ mediated manganese riboswitch folding under physiological conditions
The folding of the manganese riboswitch in the presence of Mn2+ and Mg2+ alone havebeen determined by the above kinetic analysis to proceed by an induced-fit mechanism.
However, under more physiologically relevant cation conditions, the presence of both Mn2+ andMg2+ need to be considered. Indeed, typical Mg2+ concentrations inside bacterial cells are alreadyat the few millimolar level, while Mn2+ concentrations range from only ten to hundreds ofmicromolar25-26. Furthermore, Mg2+ is known to be a particularly relevant cation for formation

55
and maintenance of RNA tertiary structure, as well as to promote pre-folded structures relevantto the conformational selection mechanism. In fact, it has been suggested in previous studies that
conformational selection is the preferred pathway for Mg2+ promoted riboswitch folding and that
[Mg2+] may be responsible for shifting the folding mechanism from induced-fit toconformational selection36, 38, 40, 50.
In the current smFRET experiments, the ligand-free “pre-folded” riboswitch structure isdirectly observable in the presence of Mg2+ alone and, according to EFRET value, is structurally
indistinguishable from the ligand-bound folded state. It has also been shown that magnesium
effectively promotes formation of a ligand-free folded species under physiologically relevant
concentrations of Mg2+ (KD  1.1 mM). It is worth remembering that ligand (Mn2+) facilitatedfolding of the manganese riboswitch in the absence of Mg2+ proceeds via an induced-fit (IF)mechanism. The ligand-free folded structure achieved with single site Mg2+ binding cantherefore results in a “kinetic shift” toward the conformational selection (CS) folding pathway,
due to a selectively available Mn2+ vacant site as well as increased cognate ligand affinity in the
pre-folded state. In the presence of Mn2+, this pre-folded structure can be stabilized by ligand

Figure 3.7 The dominant folding pathways and equilibriums in the extended kinetic model withboth Mg2+ and Mn2+ present.

56
association, further shifting the equilibrium towards a fully folded riboswitch conformation(Figure 3.7).
To provide further experimental validation for such a Mg2+ induced switch between
induced fit (IF) and conformational selection (CS) mechanisms, we must include additional
pathways in our kinetic model (Figure 3.7), whereby the Mg2+ associated yet ligand-free prefolded state can further accommodate a Mn2+ cation. In Section 3.4.1, we demonstrated that the
Mg2+-bound pre-folded structure FMg is the dominant folded species in presence ofphysiological magnesium. With Kb = [FMg]/[F] >>1 largely favoring the FMg state, it is clear
under physiological [Mg2+] (~2 mM) that the dominant folded species are in rapid equilibrium
between FMg and FMgMn. This makes Kc the key driver of the pre-folded (FMg) structure
towards a ligand-bound fully folded state (FMgMn) through conformational selection. Since
there are only two species differing by absence or presence of Mn2+, the apparent kunfold can be
written as:
𝑘𝑢𝑛𝑓𝑜𝑙𝑑 =𝑘−2 +𝑘−5 𝐾𝑐 [𝑀𝑛2+ ]1+𝐾𝑐 [𝑀𝑛2+ ],Eq. 3.4

which of course closely parallels the kinetics of unfolding with single Mn2+ association in thefour-state model. (djn) The model is then applied to the [Mn2+] dependence of kunfold (Figure
3.8A, kunfold decay from [Mn2+] = 0 to saturation [Mn2+]), revealing that the effective Mn2+
binding constant KD (= (Kc)-1) is reduced to 14(2) M from 84 M, approximately 6 times
enhancement in Mn2+ affinity for the Mg2+-bound ligand-free folded state. Therefore, we not
only isolate the ligand-free pre-folded manganese riboswitch with Mg2+-mediated folding but
also demonstrate such pre-folded structure can effectively associate one Mn2+ into its fully
folded state with even higher ligand affinity, indicating Mg2+ is the key to shifting the folding
mechanism from induced-fit to conformational selection.

57
It is worth noting that such binding-promoted change in conformation and ligand affinity by
Mg2+ resembles the allosteric control strategy widely adopted in the regulation of enzymes41-43.
In allosteric regulation, a specific molecule (“effector”) binds to a site removed from the active
site to induce conformational changes that either promote or inhibit enzymatic activity. In the
manganese riboswitch, Mg2+ binding facilitates the sampling of states with more fold-likecharacter (e.g. L1-L3 docking), which enhances Mn2+ affinity and thus biochemical competence
for promoting gene expression. It is worth noting that one of the gene products of this riboswitch
is the manganese efflux pump62-64, a transporter protein that actively removes Mn2+. Thus, one
control loop for Mn2+ transport would be that physiological [Mg2+] conditions lead to greater
activation of the manganese riboswitch, resulting in more efflux pump proteins produced, which
in turn promote removal of excess Mn2+. Conversely, under reduced [Mg2+] conditions, fewer
Mn2+ transporters are synthesized and thus more Mn2+ remains to maintain cellular function.
Though the actual metal homeostasis pathways may be more complicated, the data suggest that
allosteric modulation of the manganese riboswitch by Mg2+ is designed to confer evolutionary
advantage.
The concept of “RNA allostery” has been discussed previously in the literature, thoughsome could argue that all riboswitches are modulated by ligand-induced conformational changes
and thus operate allosterically.65-66 If we focus on cases where riboswitch functionality is
activated by multiple copies of the same ligand43, several systems (e.g., Ni2+/Co2+ 20 andtetrahydrofolate riboswitches67) may be regarded as examples of homotropic RNA allostery, withbehavior often identified by cooperativity in Hill plots.43 The more distinctive case ofheterotropic allostery (i.e., conformational activation of ligand binding by a different ligand), on

58

Figure 3.8 Manganese riboswitch folding under near physiological condition with both Mg2+ andMn2+ (A) Decay of normalized kunfold from [Mn2+] = 0 to saturation condition suggests Mg2+
enhances the ligand (Mn2+) affinity. (B) Schematic of dominant folding pathway indicating that
Mg2+ pre-folds the RNA via an induced-fit (IF) mechanism and then Mn2+ stabilizes the folded
conformation by a conformational selection (CS) mechanism.

the other hand, would appear to be far less common in RNA. Indeed, to date, the c-di-GMP-II
riboswitch-ribozyme is the only known system with well-characterized heterotropic RNA
allostery. In this system, cyclic-di-GMP binds to a pseudo knot to stabilize the folded aptamer
structure in the riboswitch, exposing a downstream ribozyme core domain which then binds with
GTP to promote self-splicing activity.68-69 In this work, we report another example ofheterotropic allostery in the RNA world, where the conformation of the manganese riboswitch
responds to the presence of Mg2+, which in turn enhances riboswitch activity by increased
affinity for a remote, highly selective cognate Mn2+ ligand. Considering that cations are known
to in general promote RNA structure formation, one might speculate whether or not Mg2+
facilitates manganese riboswitch folding through some more universal cation effect. However,

59
the distinct 5-fold coordination of the Mg2+ binding site and the correlation between [Mg2+] andmanganese riboswitch function suggests a designated allosteric control loop that could play arole in metal ion homeostasis inside cells. Finally, the smFRET data explicitly reveals that Mg2+
promotes a dynamical sampling of more fold-like configurations of the manganese riboswitch,which suggests a case where allostery kinetically observed under ensemble conditions may
reflect a more dynamic rather than fully stabilized structural effect.44-46

3.6

Summary and Conclusion

The equilibrium and kinetics of manganese riboswitch folding have been studied with smFRET
microscopy as a function of divalent Mn2+ and Mg2+ concentrations. It has been shown that thefolded riboswitch structure is promoted by the presence of Mn2+ and Mg2+, alone as well as intandem. In single molecule studies of the folded fraction (FF) under equilibrium conditions, Hill
analysis suggests that two Mn2+ ions are cooperatively associated with folding of the riboswitch,
consistent with the presence of two different M2+ binding sites with a 200 fold difference inselectivity to the cognate Mn2+ ligand.21 Magnesium concentration dependent studies indicatethat Mg2+ does not occupy the Mn2+ specific binding site, with Hill analysis of the kinetics
confirming that only a single Mg2+ associates with the riboswitch during folding. Both the Mg2+
and Mn2+ kinetic results can be well fit to 4- and 6-state kinetic models, respectively, with rate
constants indicating that prior binding of the cations is a prerequisite to subsequent folding of themanganese riboswitch, as per an induced-fit (“bind-then-fold”) mechanism. By way of contrast,
our analysis of riboswitch folding kinetics in the presence of both Mn2+ and Mg2+ indicates thatthe most relevant equilibrium is between a Mn+2 ligand-free “pre-folded” structure (containing
one Mg2+) and the corresponding Mn2+ ligand-bound folded structure, where Mn2+ binding to the60ligand-free pre-folded structure represents the rate limiting pathway for stabilization of thefolded riboswitch. Such a kinetic process corresponds to a conformational selection (“fold-thenbind”) mechanism, with the shift between induced fit (IF) and conformational selection (CS)pathways mediated by cellular levels of Mg2+. Moreover, the ability to directly observe andisolate such Mg2+ induced structures in a smFRET experiment provides support for thewidespread notion that Mg2+ promotes formation of ligand-free “pre-folded” structures in a
conformational selection pathway. In fact, such Mg2+ induced changes in riboswitch
conformation and subsequent cognate ligand affinity is analogous to the allosteric regulation
behavior commonly noted in protein enzymes, suggesting that a similar regulatory strategy may
be adopted by both RNAs and proteins.

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66
Chapter 4
Novel Heat-Promoted Folding Dynamics of the yybP-ykoY Manganese Riboswitch:
Kinetic and Thermodynamic Studies at the Single Molecule Level

4.1

Abstract
Riboswitches are highly structured RNA elements that regulate gene expressions byundergoing conformational changes in response to their cognate ligands. Such regulatory
strategies are particularly prevalent among bacteria, which need to be evolutionarily responsive
to thermal fluctuations in the surrounding environment, for example, generating extremophiles
evolved to survive anomalously high or low temperatures. As a consequence, the response ofsuch riboswitches to thermal stress becomes of considerable interest. In this study, thetemperature-dependent folding kinetics and thermodynamics of the manganese riboswitch (yybPykoY) is studied by single-molecule FRET spectroscopy under external thermal control.
Surprisingly, the folding of the manganese riboswitch is found to be strongly promoted bytemperature. Detailed thermodynamic analysis of the equilibrium and forward/reverse kinetic
rate constants reveal folding to be a strongly endothermic process (H > 0) made feasible by an
overall entropic lowering (-TS< 0) in free energy. This is in contrast to a more typical picture of
RNA folding achieving a more compact, highly ordered state (S < 0) and clearly speaks to thesignificant role of solvent/cation reorganization in the folding thermodynamics. With the help oftransition state theory, free energy landscapes for the manganese riboswitch are constructed fromthe temperature-dependent kinetic data, revealing two distinctive folding mechanisms promoted*This chapter is adapted from: Sung, H.-L.; Nesbitt, D. J. Novel Heat-Promoted Folding Dynamics of the
yybP-ykoY Manganese Riboswitch: Kinetic and Thermodynamic Studies at the Single Molecule Level. J.
Phys. Chem. B 2019, 123, 5412-5422.

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dependence for folding of the manganese riboswitch may reflect evolution of bacterial gene
regulation strategies to survive environments with large temperature variations.

4.2

Introduction
Riboswitches are noncoding mRNA elements that regulate gene expression by

undergoing conformational change upon ligand binding1-3. These riboswitches are particularly
widely exploited in bacterial gene regulation, responding to a wide variety of ligands including
small molecule metabolites and atomic ions4-5. The structure of a riboswitch is typicallycomprised of an aptamer domain and an expression platform5-6. The aptamer domain of ariboswitch structurally conforms to selectively capture its cognate ligand, while the expression
platform adopts a distinctive folding structure in response to the aptamer. Such complex
conformational transitions result in clear “on” and “off” states of a riboswitch 6, which canstructurally regulate downstream gene expression. Common regulatory strategies include
premature transcriptional termination and blocked translation initiation4-5.
Temperature is known to significantly influence biomolecular structure and,
consequently, biochemical function. Folding into a more ordered RNA structure typically results
in a state of lower entropy7-8 (-TΔS > 0) with the net folding enthalpically driven (H < 0) by
interactions such as hydrogen bonding and charge neutralization9-10. By Le Chatelier’s principle,
such enthalpically driven processes give rise to strongly temperature dependent equilibrium andkinetic behavior. The requisite exothermicity for such structure formation, in turn, is routinely
observed and confirmed in many examples of thermal denaturation, whereby biomolecules
unfold from their native structures with elevated temperature11-12. However, in contrast to thesemore conventional pictures of folding, some biomolecules are found to unfold with decreasing

68
temperature, i.e., so called “heat-promoted folding” or, equivalently, “cold denaturation”13-14.
Such reversal in the normal paradigmatic behavior can arise, for example, from changes in thesolvent configurations dominated by hydrophobic and hydrophilic interactions, which also
contribute significantly to the overall free energy and thereby influence the thermal sensitivity of
biomolecular folding7, 15-16. In the case of cold denaturation, it is the entropic gain in solvent
configuration which overcomes any entropic penalty associated with a more compact structure,thus providing a predominantly entropic driving force for biomolecular folding.
Unlike many proteins which function from a native folded state, riboswitches regulate
gene expression dynamically by switching between on and off configurations in response tocellular environment and ligand association. As the two different conformational states result in
opposite biochemical outcomes, it is reasonable to expect gene regulation by riboswitches to bemodulated by temperature. However, exactly how a riboswitch reacts to thermal stress remains
unclear, due to the fact that both on and off state conformations each contain complex secondary
and tertiary structural motifs. This provides important motivation for exploring temperaturedependent dynamics of riboswitch folding as well as consideration of any potential evolutionary
advantages. Given that bacteria can experience significant temperature fluctuations in theirenvironment and indeed some may even endure high or low extremes17-19, it is not surprising thatthey may have evolved to incorporate thermal stress as an important element in gene regulation
strategies20-23. In fact, some temperature-responsive RNA motifs commonly referred to as “RNAthermometers” have been discovered22-23. Similar to riboswitches, they often regulate genes
related to heat shock response by a thermally responsive conformational change. The results ofthe present study take this concept one step further, suggesting that temperature modulation

69
might be a common feature of riboswitch gene regulation and thus potentially a more generalprotective mechanism for bacteria under thermal fluctuations and/or biochemical distress.
As the particular focus of this work, the manganese riboswitch is found extensively
distributed in the noncoding regions of bacterial mRNA24-26. It responds to micromolar ofcellular Mn2+ and regulates the expression of genes responsible for metal homeostasis, including
the manganese efflux pump, a transport protein that removes excessive Mn2+ from the cell27-29.
The aptamer domain of manganese riboswitch consists of four helices tethered by a four-way
junction (Figure 4.1A and 4.1C). In the ligand-bound folded state identified in previous x-ray
studies25 (Figure 4.1A), the four helices coaxially align into a tight hairpin-like structure withdocking between two highly conserved loops L1 and L3. The docking interface formed by L1
and L3 contains one Mn2+ specific binding site and one non-selective divalent cation M2+ (M =Mn or Mg) binding site that is predominantly occupied by Mg2+ due to natural physiologicalabundance (Figure 4.1B). Regulation of gene expression can therefore be activated by single
metal ion (M2+) binding, followed by L1 and L3 docking.
In this study, thermal response of the manganese riboswitch is studied by single-molecule
FRET (smFRET) spectroscopy and kinetics under external temperature control (± 0.1 oC), where
conformational folding of a single RNA molecule is monitored by FRET energy transfer
efficiency (EFRET) as a function of time. The resulting EFRET time trajectories not only explicitly
recapitulate the equilibrium folding behavior but also contain detailed information on single
molecule kinetics for further analysis of the unimolecular folding/unfolding rate processes.
Indeed, it has long been recognized that “co-transcriptional formation” of the natively folded
riboswitch structure is a crucial strategic element in real time gene regulation1, 30-31. Thus, thekinetic time scales for both manganese riboswitch folding and unfolding become particularly

70
important to ensuring an adequate temporal window for both i) metabolite recognition and ii)
conformational change with respect to the gene transcription regulated event.
In our investigation of such temperature-dependent manganese riboswitch dynamics, wefind that the folding kinetics is strongly sensitive to and increases dramatically with temperature.
Thermodynamic analysis of the single molecule data as a function of temperature allows us todecompose the folding free energy into entropic and enthalpic contributions, revealing thatmanganese riboswitch folding is surprisingly endothermic and compensated by favorable
entropic gain. With the help of such thermodynamic and kinetic data, a detailed energy
landscapes of manganese riboswitch folding can be reconstructed from transition state theory,
highlighting several intriguing observations consistent with our previous kinetic study ofmanganese riboswitch folding mechanisms32. Specifically, the manganese riboswitch is found torespond to Mg2+ primarily during the early stages of folding and prior to surmounting thetransition state barrier. This is in agreement with a “bind-then-fold” (i.e., induced fit or IF)
mechanism, whereby folding is directly promoted by Mg2+ association. Mn2+, on the other hand,changes free energies in both early and late stages of folding, implying different M2+ (M = Mn orMg) occupancies can be adopted in the folded manganese riboswitch. This is in support of the“fold-then-bind” (i.e. conformation selection or CS) mechanism, whereby the ligand binds to andthermodynamically stabilizes an already preorganized fold-like structure30, 32-33.

4.3

Experiment

4.3.1

RNA construct design and preparation for single-molecule study
The ligand-bound folded state of manganese riboswitch has been determined in previous

x-ray studies to be a hairpin-like structure formed from four jointed helices (Figure 4.1A)25. The

71

Figure 4.1 Structure of L. lactis yybP-ykoY manganese riboswitch: (A) Overall crystal structure(PDB 4Y1I); (B) Close-up details on the cation M2+ binding sites with adjacent nucleotides; (C)Manganese riboswitch sequence in a secondary structure representation.
major docking interaction between L1 and L3 directly responds to M2+ ligand binding, which is
crucial to stabilizing the folded conformation. Therefore, we have designed a smFRET RNA
construct sensitive to the distance between L1 and L3 as a proxy for conformational change32. In
this smFRET construct design, the cyanine dyes Cy3 and Cy5 are covalently labeled on P1 andP3 stems respectively to achieve two distinct distance-dependent energy transfer statesdistinguished by RNA folding/unfolding (Figure 4.2A). A biotin modification is introduced to
the P1 end so that the RNA construct can be tethered on a coverslip surface by biotinstreptavidin interactions for study at the single molecule level. The Mn2+ aptamer domain is

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Figure 4.2 Sample smFRET experiment data: (A) Cartoon depiction of how manganese riboswitch
folding changes the distance between Cy3 and Cy5; (B) Sample time trace of Cy3 and Cy5
fluorescence (22.2 C, top left), the corresponding EFRET trajectory (lower left), and a series of EFRET
trajectories (lower left) and dwell time distributions (lower right) as a function of increasing
temperature (22.2 C-28.0C). Note that a small increase in temperature dramatically increases thefolded time distributions, consistent with strongly endothermic folding (H > 0).

reconstructed from the RNA sequence in Lactococcus lactis, as structurally characterized inprevious studies25, 32. The final smFRET manganese riboswitch construct is synthesized byannealing three chemically modified RNA oligos purchased from Integrated DNA Technologies(IDT, Coralville, IA), followed by HPLC purification. Detailed construct design and explicit
oligo sequences can be found in our previous work32.

73
By way of sample preparation for these smFRET experiments, the sample holder isflushed in sequential order with: (i) 10 mg/mL BSA (bovine serum albumin) with 10%
biotinylation for surface pacification, (ii) 200 µg/mL streptavidin for surface tethering, and (iii) ~25 pM of the biotinylated RNA construct. Each flushing step is followed by a 10-minuteincubation period, which yields a consistent, reliable surface coverage of ~ RNAs per 100 m2.
In addition to the specified Mn2+ (MnCl2) and Mg2+ (MgCl2) divalent cation concentrations, thesmFRET buffer solution also contains (i) 50 mM hemisodium HEPES (pH 7.5), (ii) an enzymatic
oxygen scavenger system (PCD/PCA/TROLOX), and (iii) 100 mM NaCl background salt.
4.3.2

Single-molecule FRET spectroscopy
Single-molecule fluorescence imaging capabilities are achieved in a homebuilt confocal

microscope system described in previous papers 34-35. In short, a 532 nm pulsed Nd:YAG laser iscollimated by a Keplerian beam expander before being directed into an inverted microscopewater immersion objective (1.2 N.A), resulting in a diffraction limited laser excitation spot of~250 nm lateral dimension. In smFRET experiments, the dye-labeled RNA molecules are locatedby scanning the coverslip surface under conditions where RNA coverage is sufficiently low toensure observation of one RNA molecule at a time in the sub-femtoliter confocal volume. The
fluorescence photon from a single dye-labeled RNA is collected for each pulse through the same
microscope objective and split into color (green/red) and polarization (horizontal/vertical)
channels before detection by four single photon avalanche photodiodes (APDs). For each photon
event, the color, polarization, wall clock time ( 50 ns) and time respect to the laser pulse ( 50
ps) are recorded by a time-correlated single-photon counting (TCSPC) module35-36. For
temperature controlled studies, thermal equilibrium at a desired temperature (± 0.1 oC) isachieved by heating both sample and microscope objective simultaneously, with details of the74commercial stage and objective heater setup presented in previous work34-36. Before eachexperimental temperature run, samples remain in contact with the objective for > 15 mins toensure complete thermal equilibrium.

4.4

Results and analysis

4.4.1 Temperature-promoted folding revealed by smFRET
The smFRET RNA construct is doubly labeled with fluorophores Cy3 and Cy5 so that theconformational change can be visualized by distance-dependent FRET energy transfer (EFRET)32.
In the sample fluorescence signal time trace (Figure 4.2B upper panel), the clearly anti-correlated
switching between the donor (green) and acceptor (red) signals unambiguously reflects
folding/unfolding events and energy transfer between Cy3 and Cy5, from which thecorresponding time dependent EFRET trajectory can be calculated. The resulting time trace for
EFRET (see Figure 4.2B) reveals that the RNA construct switches between two distinct states withwell separated EFRET values of ~ 0.55 and ~ 0. As expected from the construct geometry32 andcrystal structure data25, the high EFRET state (EFRET ~ 0.55) corresponds to a compact folded
conformation of the manganese riboswitch with loops L1 and L3 docking onto each other.
Conversely, the low EFRET is consistent with the two loops much further apart, corresponding to a
non-compact, unfolded conformation.
From the EFRET trajectory, the folding equilibrium constant (Keq) can be readily obtained
from the ratio of total time spent in the high EFRET (folded) versus low EFRET (unfolded) state.
More revealingly, however, direct observation of the dynamic folding/unfolding behavior also
permits the rate constants (kfold and kunfold) to be determined by analysis of the corresponding
dwell time distributions (Figure 4.2B right panels)32, 35. Specifically, semi-logarithmic plots of

75
the resulting cumulative distribution functions (P(𝞽)/P(0)) vs. dwell times are quite linear, andthus appropriately fit to a single exponential decay function to extract the first orderfolding/unfolding rate constants (kfold and kunfold).
In the temperature dependent studies, the temperature is controlled (± 0.1 oC) by
simultaneously heating the sample and the optical objective. A representative temperature
response of the manganese riboswitch is illustrated in the series of EFRET trajectories obtained atincreasing thermal stress (Figure 4.2B from top to bottom), for which the RNA clearly spends
more time in the high EFRET (i.e., folded) state. Indeed, the approximately 5-fold increase in Keq
for T = + 5.8 oC indicates that folding of the manganese riboswitch is both highly sensitive totemperature and favored by heat. In addition, the dwell time analysis (Figure 4.2B right) reveals
the kinetic origin of such “heat-promoted folding” behavior arising from a temperaturedependent increase in kfold and decrease in kunfold, respectively.

4.4.2 Mg2+ effects on the temperature dependence of folding
Previous studies have shown that docking between the loops L1 and L3 of the manganeseriboswitch requires binding of at least one divalent cation M2+ (Mg2+ or Mn2+)25, 32. It has also
been shown that Mg2+ alone promotes manganese riboswitch folding by only occupying the nonselective binding site, leaving the Mn2+-specific site open for further ligand association (Figure4.1). According to previous detailed kinetic analysis32, the fold-like structure achieved with
Mg2+-binding plays a crucial role in opening a conformational selection (“fold-then-bind”)
pathway by enhancing the Mn2+ ligand affinity. It is therefore useful to further explore theformation of the this Mn2+ ligand-free folded state with single molecule thermodynamic
techniques.

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Figure 4.3 Mg2+ dependence of the manganese riboswitch folding under equilibrium conditions:(A) Folded fraction as a function of [Mg2+]; (B) van’t Hoff plot for the temperature dependent
behavior of the manganese riboswitch equilibrium constant (Keq = kfold/kunfold) at [Mn2+] = 0.
From the [Mg2+] dependent studies, folding of the manganese riboswitch is known to beeffectively promoted by millimolar levels of Mg2+ (Figure 4.3A). By visual inspection, thefraction folded increases monotonically with [Mg2+], gradually reaching a saturation value. The
nearly linear increase of fraction folded at low [Mg2+] indicates only a minimal Hill cooperativity(n ~ 1). More quantitatively, the data can be fit to the normalized Hill equation in the form of32,37-39
n[M2+ ]

fraction folded = F0 + (1 − F0 ) × Fs (K n +[M2+]n ),D

Eq. 4.1

where F0 and Fs are fractions of the riboswitch folded at 0 and saturation [M2+] (M = Mg or Mn),
respectively. The Hill coefficient n is readily determined to be 1.3(2), suggesting that folding iseffectively promoted by a singly occupied 5-fold coordination Mg2+ binding site, in agreement

77
with characterization in previous structural studies25. It is worth noting that the Hill coefficientindicates the number of ligands (Mg2+) that become associated during the folding event and need
not necessarily equal the binding stoichiometry40. Indeed, the minor deviation of n from unity
could reflect increased number of Mg2+ ions surrounding the riboswitch during folding, forwhich the effective Mg2+ binding constant is found to be KD = 1.1(2) mM. To explore thethermodynamics of subsequent Mn2+ binding, we therefore choose to study the temperaturedependence of manganese riboswitch folding at two representative [Mg2+] concentrations of i)relatively low ([Mg2+] = 0.5 mM < KD) and ii) near saturation ([Mg2+] = 2 mM > KD) levels.
The results are summarized in a van’t Hoff analysis (see Figure 4.3B), where Keq isplotted logarithmically vs. reciprocal temperature (1/T, T in Kelvin). The negative slopes in thedata immediately reveal that folding of the manganese riboswitch is promoted by increasing
temperature. In particular, the data indicate approximately 20- and 10-fold increase in theequilibrium folding constant (Keq) over a temperature change of only 10 oC, at 0.5 and 2 mM
Mg2+, respectively, signaling an unusually strong dependence of riboswitch conformation ontemperature. More quantitatively, linear least squares fit of such van’t Hoff data to:
∆H0 1

∆S0

ln(K eq ) = − R T + R ,Eq. 4.2

allows one to deconstruct overall free energies into enthalpic and entropic contributions;corresponding to -ΔH0/R and ΔS0/R, respectively. The negative slope is consistent with ΔH0 > 0,
meaning the folding is endothermic process and thus promoted by heat; whereas the positive
intercept suggests a strong increase in entropy (S0 > 0) upon folding. Such heat promotedfolding (or “cold-denaturation”) behavior is relatively unusual, as we more conventionally expect
the folding into a more order compact state to be entropically unfavored (ΔS0 < 0) andenthalpically driven (ΔH0 < 0) by interactions such as hydrogen bonding and metal coordination.

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Figure 4.4 Kinetic effects of Mg2+ in an activated complex/transition state theory analysis of (A)kfold and (B) kunfold.
Furthermore, the [Mg2+] dependence of this van’t Hoff plot shows moderate changes in slope
and intercept, indicating that the Mg2+ dependence of folding occurs by mildly lowering theenthalpic cost (H0  0) while increasing the overall entropic gain (S0 > 0) (Figure 4.3B).
At the kinetic level, we can trace the impact of temperature on equilibrium constantsfrom the corresponding folding and unfolding rate constants. If we associate purely single
exponential kinetic behavior with a single rate limiting transition state, the detailed
thermodynamic properties of this transition state can be obtained from an activated transition
state/Eyring analysis of ln(kfold) or ln(kunfold) vs 1/T (see Figure 4.4):∆𝐻 ‡ 1∆𝑆 ‡ln(𝑘) = − 𝑅 𝑇 + 𝑅 + ln 𝜈 .

Eq. 4.3

In Eq. 4.3, ΔH‡ and ΔS‡ represent differences in enthalpy and entropy between the transition
state and the folded (or unfolded) state, while 𝜈 is the so called “attempt frequency” to access the79transition barrier along the reaction coordinate 34-35, 41-43. One challenge of such an activatedtransition state analysis is that  is generally not known a priori and often simply estimated to beof order 1012 -1014 s-1, though the inferred entropy of the transition state (ΔS‡) depends only
logarithmically on . However, it is worth noting that any cation induced changes in this entropic
barrier (i.e., -Δ[TS‡]) exactly cancel even this weak logarithmic sensitivity and become
rigorously independent of the choice of 𝜈34-35.
The results of such an Eyring analysis immediately reveal several interesting features.
First of all, a temperature rise promotes folding of the manganese riboswitch by both increasing
kfold and decreasing kunfold, as clearly evident from the negative and positive slopes in Figure
4.4A and 4.4B, respectively. Secondly, the negative slopes for kfold implies that overall folding of
the manganese riboswitch is an endothermic process, in contrast with the more usual exothermic
folding behavior due to formation of additional stabilizing hydrogen bonding networks. Thirdly,
increasing Mg2+ from 0.5 to 2 mM increases the riboswitch stability (Keq) significantly, butalmost entirely by dramatic enhancement in kfold (Figure 4.4A) with relatively little change on
kunfold (Figure 4.4B). However, even though kfold is uniformly larger under high [Mg2+]
conditions, it is also much less temperature sensitive than at low [Mg2+]. Conversely, thetemperature dependence of kunfold is almost completely insensitive to [Mg2+], which echoes asimilar lack of [Mg2+] dependence to unfolding rate constants observed from previous study atroom temperature 32. Simply summarized, these results suggest that Mg2+ promotes the stabilityof the folded riboswitch structure predominantly by lowering both the folded and transition state
free energies by equivalent amounts, thereby permitting kfold and kunfold to be strongly increased
and largely unaffected, respectively.

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Figure 4.5 Mn2+ effects on manganese riboswitch folding under equilibrium conditions: (A)Folded fraction as a function of [Mn2+]; (B) van’t Hoff plot of temperature dependent manganeseriboswitch folding at [Mg2+] = 0.5 mM.
4.4.3 Mn2+ effects on the temperature dependence of folding
The [Mn2+] dependent folding data suggests a positive cooperativity of Mn2+, whereby
the fraction folded increases nearly quadratically at low [Mn2+] and gradually reaches saturation(Figure 4.5A). By Hill analysis, the cooperativity is found to be n = 1.7(2), consistent with thepresence of two M2+ binding sites determined by x-ray structural studies25. Deviation of the Hillcoefficient from 2 can be understood as arising from the non-selective cation site already being
partially occupied by Mg2+ under near physiological conditions ([Mg2+]  0.5 mM)32. More
importantly, the effective binding constant KD for Mn2+ is determined to achieve a much tighter
value of 56(4) 𝞵M. We thus choose to explore the temperature dependent rate processes at three
representative [Mn2+] conditions corresponding to folding at i) far below (0 M), ii) comparablewith (50 M), and iii) above (100 M) the value of KD, respectively.

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Figure 4.6 Kinetic dependence of Mn2+ in an activated complex/transition state theory analysis of(A) kfold and (B) kunfold.
From van’t Hoff analyses summarized in Figure 4.5B, the folding equilibria under all
three cation conditions are clearly shown to be endothermic (negative slopes) and thereby
promoted by increasing temperature. Furthermore, the positive intercepts indicate that folding
increases the overall entropy (S0 > 0) of the system. However, the manganese riboswitch
reveals an unconventional heat-promoted folding behavior with a surprising sensitivity to[Mn2+]. Specifically as [Mn2+] increases, the magnitudes of both the van’t Hoff slopes andintercepts decrease. The net effect of Mn2+ on manganese riboswitch folding would therefore
appear to be a simultaneous reduction in ΔH0 and ΔS0. Though more work need to be done, thiswould at least be consistent with a more common physical scenario of cation binding resulting inenthalpic stabilization (ΔH0 < 0) and yet added entropic cost ([-TΔS0] > 0), largely caused byloss in translational entropy of the ligand44-46.

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From the corresponding temperature dependent folding/unfolding kinetics summarized in
Figure 4.6, a rise in temperature promotes the overall manganese riboswitch folding once again
by increasing kfold and decreasing kunfold. From the Eyring plots, kfold (Figure 4.6A) becomes lesssensitive to temperature, with the overall rate constant increasing but slope magnitudes
decreasing dramatically with increasing [Mn2+]. This would be consistent with any enthalpic
barrier between the unfolded state and transition state being lowered by increasing Mn2+. Theintercept, on the other hand, also decreases ([-TS0] > 0) with increasing Mn2+, suggesting thatany entropy gain achieved during folding is mitigated by Mn2+. Finally, both Eyring analysis
slopes and intercepts for kunfold are observed to decrease with increasing [Mn2+] conditions. In
summary, the effect of Mn2+ on the kinetics would appear to lower the enthalpic barrier tofolding and yet also contribute to entropically destabilizing the folded configuration.

4.5

Discussion

4.5.1 Unconventional temperature response of manganese riboswitch folding
The combination of hydrogen bonding, coulombic interactions (both attractive andrepulsive), and water hydration often cause nucleic acid biomolecules to spontaneously rearrange
into a more ordered and compact conformation7-8. As a result, the conventional thermodynamic
paradigm for RNA folding is an enthalpically driven process (H0 < 0) but with appreciable
increase in free energy due to entropic penalty in the final state (-TS0 > 0). In the current
studies, folding of the manganese riboswitch has been shown to be strongly promoted byincreasing temperature. The negative slopes and positive intercepts in the van’t Hoff plots under
all Mg2+ and Mn2+ conditions indicate that folding occurs spontaneously, made possible byentropic gain competing against an unfavorable enthalpic penalty. Though such temperature-

83
promoted folding (“cold denaturation”) seems at first counterintuitive, such behavior has
nonetheless been discovered in many proteins, with the phenomenon often linked to change insolvent exposed area during folding47-49, for which largely entropically driven hydrophobic andhydrophilic interactions play the dominant role.
The thermodynamic analysis of Section 4.4.2 and 4.4.3 clearly reveals that both enthalpy
and entropy of the system (i.e., RNA construct plus surrounding solvent environment) increase
with folding of the manganese riboswitch, with a large entropic contribution (–TΔS)
compensating and even dominating free energy stabilization of the more structured
conformation. Previous studies indicate that variation in solvent exposure along the folding

Figure 4.7 Folding free energy landscapes of the manganese riboswitch: (A) Mg2+ effects on
enthalpic and entropy contributions (left) and the overall free energy (right); (B) Mn2+ effects on
enthalpic and entropy contributions (left) and the overall free energy (right). Note that although
there is no information on change in absolute free energies with cation conditions, the unfolded
state (U) is conventionally referenced to zero free energy in both plots.

84
coordinate plays an important role in cold denaturation47-49, which in turn results in significant
solvent impact on the equilibrium behavior. In the manganese riboswitch, the two M2+ bindingsites are rich in phosphate groups and highly negatively charged (Figure 4.1B). When such acharged species is placed in aqueous solution, the water molecules orient to lower the enthalpy(ΔH0 < 0), with water ordering resulting in a large entropy decrease for the solvent system (ΔS0 >0), a process known as hydration50-51. When the manganese riboswitch folds, the highly charged
regions of RNA become less accessible to water due to partial neutralization by counterions.
Thus, the reverse “dehydration” process can occur during the folding event due to water
expulsion around the highly charged binding sites. If such dehydration effects predominate overintramolecular hydrogen bonding in the RNA construct, this could thereby result in i) a large
enthalpic cost (ΔH0 > 0) balanced by ii) entropically driven folding (ΔS0 < 0). Since themanganese riboswitch folds into a more order state upon metal binding, we would expect both
ΔH0 and ΔS0 for the construct to be less than zero. However, it is the total enthalpies andentropies of the system (RNA plus buffer solution) that is observed, likely dominated by thehydration process and solvent reorganization. For Mn2+ binding to the Mn2+-specific site25, 32, theprocess can therefore quite understandably result in lowering both the enthalpic cost and entropic
gain (Δ(ΔH0) < 0, Δ(ΔS0) < 0), consistent with our observations in Figure 4.7B.
4.5.2 Temperature response of RNA
Although cold denaturation (or heat-promoted folding) has been widely explored inproteins, it is a much less commonly observed in RNA. One such RNA system known to exhibit
heat-promoted folding is the hammerhead ribozyme47-48, for which temperature-dependent
folding of the three way junction has been investigated with circular dichroism (CD) over a wide
range of temperature. Interestingly, the studies reveal that the three way junction folded structure

85
is stabilized with increasing temperature at relatively low temperature, but that this thermal
stabilization of folding reverses at a critical temperature. In another recent study of the adeninesensing riboswitch, it was shown by NMR spectroscopy that achievement of the ligand-freefolded conformation is also promoted by temperature increase52. Despite only relatively few
direct measurements of temperature responsive RNA folding, the thermodynamic parameters forligand-mediated riboswitch folding can be estimated from isothermal titration calorimetry (ITC)
as well as other temperature-dependent binding studies, since ligand binding is always
accompanied by conformational change in the RNA riboswitch. From literature search over 17classes of riboswitches/ribozymes that responding to various ligands and substrates38, 53-77, nine
appear to exhibit entropically favored binding (ΔS0 > 0) 53-62, indicating that configurational
entropy of the solvent can dominate the folding entropy of the riboswitch construct. Furthermore,
four out of these nine are also found to be endothermic (ΔH0 > 0)53-58, similar to the manganeseriboswitch behavior. Thus, one is led to speculate that cold denaturation might not actually be so
uncommon for a tertiary binding/folding strategy in RNA. In fact, RNAs are structurally
polyanion electrolytes that interact strongly with water; as a result, thermodynamic free energies
for RNA folding might reflect even greater sensitivity to the solvent and buffer system than forproteins7, 15-16. This would appear likely to have evolutionary consequences. Bacteria in the wild
experience significant temperature fluctuations, with some thriving under extreme temperature
conditions17-19. It is thus perhaps not surprising that temperature sensitivity may have been
evolutionarily integrated into riboswitch function.
It is also possible to take this analysis further toward understanding the biochemical roleof temperature in gene regulation. For example, Mn2+ is known to catalyze formation of reactive
oxidative species (ROS) that are particularly damaging to cells78-79. In this study, we have seen

86
that the manganese riboswitch at higher temperatures transcriptionally promotes gene expressionof a Mn2+ efflux protein, essentially by folding into “on” conformation. Due to more active
production and higher reactivity of ROS at high temperature80-82, such a temperature dependence
could be advantageous for bacteria survival as a protective mechanism reducing cellular [Mn2+].
Indeed, bacteria have been shown to exploit temperature control in gene regulation, as evident inso called “RNA thermometers,” 22-23 i.e., small mRNA elements that structurally respond totemperature in regulation of translational efficiency. Since RNA structures are highly responsive
to temperature, it is interesting to speculate that cation plus environmental temperature
modulation of a specific RNA conformation could reflect a more general strategic example ofmulticomponent sensitivity in riboswitch gene regulation.
4.5.3 Reconstructing folding free energy landscapes from temperature-dependent kinetics
The thermodynamic/kinetic parameters obtained from the current van’t Hoff and Eyring
analyses can provide particularly invaluable information on pieces of the overall free energy
landscape for folding of the manganese riboswitch. For example, Figure 4.7A immediately
reveals that the enthalpic (H) and entropic (-TS) contributions to the free energy (G) for boththe transition (TS) and folded (F) state confirmations move synchronously up/down withincreasing Mg2+ in a clearly anticorrelated fashion. This notable level of synchrony suggests thatthe impact of Mg2+ is primarily on the enthalpy/entropy of the unfolded state (U), as shifts inonly U would maintain all relative free energy spacings between the TS and F conformations.
Such a strong dependence of unfolded structure free energies on [Mg2+] can be rationalized asarising from differential Mg2+ occupancy at the non-selective M2+ binding site, as theseexperiments are performed at Mg2+ concentrations appreciably below (0.5 mM) and above (2mM) the effective binding affinity (KD =1.1 mM). Simply stated, since M2+ binding is essential

87
for riboswitch folding32, the free energy differences between the anticorrelated TS and F states
are insensitive to [Mg2+] due to the fact that they are both associated with one Mg2+. Thus, theMg2+-mediated manganese riboswitch folding thermodynamics plots in Figure 4.7A reveal that
Mg2+ binding must occur while the construct is still mostly unfolded. In agreement with theprevious kinetic studies, therefore, this is consistent with an induced-fit (i.e., “bind-then-fold”)
mechanism30, 32-33, whereby prior binding of the ligand is required to achieve the correct folding
behavior. We note that such information can be gleaned from the plots even in the absence ofany knowledge about absolute free energies (e.g., the free energy for the U state is kept at zeroby convention)
Similarly, for [Mn2+] dependent riboswitch folding (Figure 4.7B), the entropy andenthalpy of the TS and F states are both significantly shifted with increasing Mn2+ concentration.
Overall, as [Mn2+] increases, the enthalpic (H) and entropic (-TS) contributions bifurcate
systematically. Such effects are in agreement with ligand binding models, where the enthalpic
gain (from Mn2+ coordination) is accompanied by entropic loss (largely translational entropy ofligand and higher degree of ordering at the binding site44-46. Interestingly, however, there is also
a strongly non-linear saturation dependence of these effect on [Mn2+]. For example, the transition
state (TS) free energy changes significantly between 0 and 50 𝞵M of Mn2+ and yet remains
essentially constant with an additional aliquot of 50 𝞵M Mn2+ (100 𝞵M in total). This behavior is
likely due to the fact that Mn2+ promotes achievement of the TS state via different occupanciesof the two M2+ binding sites. Indeed, the largest free energy effects between conditions of 50 and
100 𝞵M Mn2+ appear in the folded (F) state, but now with negligible changes in the TS and U
conformations. Much as invoked above for Mg2+ dependence, this can be simply rationalized by
the folded state existing with two different metal occupancies of the two binding sites: one M2+

88(M = Mn or Mg) binding or two M2+ binding with at least one Mn2+. The Mn2+ effect of Δ(ΔH0)< 0 and Δ(ΔS0) < 0 is again consistent with increased Mn2+ binding. Although the manganeseriboswitch is known to fold via an induced-fit (IF, bind-then-fold) mechanism with at least one
M2+ binding in the unfolded state32, the ability of Mn2+ to directly bind to a (pre-)folded
conformation and thereby stabilize the folding equilibrium is consistent with a conformational
selection (CS, fold-then-bind) mechanism30, 32-33, whereby the RNA dynamically samples manydifferent configurations while the ligand binds only to those constructs with a preformed Mn2+
binding site. To summarize, the thermodynamic analysis of the rate and equilibrium data reveals
that the manganese riboswitch folds through an induced-fit mechanism via early Mg2+
association with U. Conversely, Mn2+ binds to a pre-folded ligand-free riboswitch structure tostabilize the folding equilibrium (i.e., in support of a conformation selection mechanism), as
evidenced by selective effects of Mn2+ > 50 M on the free energy of the folded (F)configuration. Finally it is worth emphasizing that such Mn2+ and Mg2+ ligand binding shifts inthe enthalpic and entropic contributions are all anticorrelated and very finely balanced to yield
only relatively small differences (or order 1 kcal/mol) in the overall free energies for the folded
vs unfolded states of the riboswitch. This allows for strong environmental regulation of the
kinetic rates and time constants for riboswitch folding, with only relatively small changes in theoverall folding stability. Such a cationic modulation of the folding time constant behavior could
be relevant in co-transcriptional folding dynamics and gene regulation strategies.30-31

4.6

Summary and conclusion
The temperature dependence of manganese riboswitch folding has been explored in detailby confocal smFRET experiments. The folded manganese riboswitch conformation is found to

89
be strongly stabilized by temperature, which from a kinetic perspective occurs via simultaneous
increase (decrease) in the folding (kfold) (unfolding) (kunfold) unimolecular rate constants,
respectively. A thermal Van’t Hoff analysis of the equilibrium constant reveals that folding isstrongly disfavored enthalpically (H > 0), while favored with significant and closely balanced
entropic contributions (-TS < 0) to yield an overall G < 0. This is in clear contrast with themore conventional behavior of ligand-promoted folding behavior of entropically disfavoredfolding into a compact state driven by enthalpic energy release9-10. Such temperature-promoted
folding (or equivalently, cold denaturation) can result from change in ionic
hydration/dehydration and hydrophilic/hydrophobic interactions, highlighting the crucial
importance of solvent contributions to the overall free energy change in an RNA folding event.
Moreover, we speculate that such a less conventional thermophilic response of the manganeseriboswitch may provide an additionally useful survival mechanism for successful bacterial
proliferation in a fluctuating temperature environment, suggesting a mechanism by which
temperature may be more widely incorporated into riboswitch gene regulation. In Mg2+-mediatedfolding, Mg2+ is found to mainly affect the free energy of the unfolded (U) state, consistent withthe unfolded structure having 0 or 1 Mg2+ occupancy and yet with the ones binding to a single
Mg2+ able to access the transition state and thereby achieve a fully folded structure. Such bindingof a single Mg2+ prior to the transition state supports the predominant existence of an induced-fit(“bind-then-fold”) mechanism for Mg2+-promoted folding. For Mn2+ mediated folding, by way ofcontrast, Mn2+ is found to significantly shift the relative free energies of both the transition (TS)and folded (F) states. This sensitivity to [Mn2+] is consistent with the folded state of theriboswitch associating different numbers of Mn2+ into its two (selective and non-selective)
binding sites, which would provide support for a conformational selection (“fold-then-bind”)

90
pathway. Such a combined thermal and cation sensitivity to modulation of the riboswitch folding
pathway offers a distinctly new opportunities for evolutionary adaptation and flexibility of themanganese riboswitch to variable environmental conditions.

4.7

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Chapter 5
Sequential Folding of the Nickel/Cobalt Riboswitch is Facilitated by a Conformational
Intermediate: Insights from Single-Molecule Kinetics and Thermodynamics

5.1

Abstract
The present work presents first single molecule Fluorescence Resonant Energy Transfer(smFRET) studies of the nickel/cobalt (NiCo) riboswitch, with temperature dependent, single
molecule confocal microscopy to provide comprehensive kinetic and thermodynamic
information on folding into a biochemically competent structure. The results indicate that the
NiCo riboswitch first folds into a more compact “prefolded” conformation, with a preorganizedbinding pocket partially stabilized under physiological conditions by non-cognatemonovalent/divalent cations. Such a prefolded intermediate then has opportunity to fold further
into a tightly ligand-bound structure, in response to the cognate ligands, Ni2+ or Co2+, with submicromolar affinities. Such stepwise ligand-induced folding represents a particularly clean
example of a conformational selection (“fold-then-bind”) mechanism, whereby a configuration
dynamically accessible by thermal fluctuation is stabilized into the final folded state by ligand
association. In addition, we observe a strong positive cooperativity in the ligand-induced folding
kinetics with respect to both Ni2+ and Co2+ ligands. This provides maximal sensitivity inriboswitch conformational response near [Ni2+] or [Co2+]  Kd, which facilitates more accurate
biochemical probing of the cell environment and therefore bioregulation of gene expression.
Temperature dependent kinetics at the single molecule level have also been explored, which*This chapter is adapted from: Sung, H.-L.; Nesbitt, D. J. Sequential Folding of the Nickel/Cobalt Riboswitch
is Facilitated by a Conformational Intermediate: Insights from Single-Molecule Kinetics andThermodynamics. J. Phys. Chem. B 2020, 124, 7348–7360.

98
permit free energies to be deconstructed into enthalpic and entropic components along thefolding coordinate. In the absence of the cognate ligand, a predominantly enthalpic barrier
between the unfolded riboswitch (U) and the prefolded intermediate (I) suggests a rearrangementof the hydrogen bonding network, whereas in the presence of the cognate ligand, a large entropic
penalty (-TS0 > 0) in forming the folded riboswitch conformation (F) is almost perfectly
counterbalanced by equivalent enthalpic gain (H  ) to yield G  0. The thermodynamic
results are therefore consistent with a simple physical picture of RNA folding, whereby
association of the cognate ligand is strongly stabilized by Coulombic attraction, while forming an
entropically more ordered structure around the binding site.

5.2

Introduction
Riboswitches are highly structured cis-regulatory elements commonly found in the 5’

untranslated region of mRNA.1-2 Part of the highly conserved structure, known as the aptamer
domain, functions as a metabolite sensor that folds to selectively capture the cognate ligand
molecule. The rest of the riboswitch sequence comprises the expression platform which
undergoes conformational transitions in response to the aptamer.2 As a result, the overallriboswitch construct often adopts two mutually exclusive conformations corresponding to “on”
and “off” states that structurally regulate expression of the downstream gene.2-3 Such aregulatory mechanism has been widely exploited in bacteria3-4, with riboswitches found torespond to a variety of ligands including small-molecule metabolites and even simple atomic
ions.5

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Heavy metals can be highly cytotoxic, forming complexes with proteins and catalyzing
the production of reactive oxidative species damaging to cells.6-7 However, heavy metals are alsoessential to cellular function, as they often serve a crucial role in enzymes and enzyme
cofactors.8-9 Ni2+, for example, is a common component of almost all hydrogenases, while Co2+
is an essential constituent of vitamin B12. As a result, tight control over intracellular metal ion
concentrations is clearly desirable, with sensing and regulatory feedback mechanisms highly
evolved to maintain ions at just the right level to support biochemical function while minimizing
toxic side effects. In bacteria, for example, genetic expression of membrane transporters andtraffic proteins for heavy metals are known to be predominantly controlled by a suite ofmetalloregulatory proteins.10-11 The exact role of RNA in maintaining this heavy metal
homeostasis is not entirely clear but changing rapidly. Indeed, the possibility of RNA selectively
responding to heavy metal ions might at first have been dismissed as unlikely due to the limited
types of functional groups available for metal coordination and the well-known association of
RNA with physiological Mg2+, the predominant divalent cation in cells.12-13 By way of contrast,
however, riboswitches have recently been identified that respond with remarkably highspecificity to manganese (Mn2+)14-15 and nickel/cobalt (Ni2+/Co2+)16, which in turn regulate thegenetic expression of the corresponding protein transporters for these cations. This strongly
suggests that metalloregulation is not the exclusive domain of proteins but also cooperatively
involves some form of RNA-based sensor of the cellular metal ion environment.
The NiCo riboswitch has been previously referred to as the czcD motif,16 which resides
upstream of czcD genes encoding a subfamily of metal export and resistance proteins.17-19 The
capability of this riboswitch motif for atomic cation Ni2+/Co2+ sensing has been recently
validated,16 and furthermore confirmed by detection of an explicitly Co2+-bound crystal structure

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in companion high resolution x-ray diffraction studies (PDB: 4RUM, Figure 5.1A). The
Ni2+/Co2+ sensing aptamer domain in this riboswitch consists of a four-way junction, with four
helices coaxially-stacked in pairs to form a twisted H conformation. As a point of particular
relevance to the present study, the NiCo riboswitch construct lacks the long-range tertiary
interactions commonly found in other known riboswitches.16 As a result, the conformation of thejunctional loop responds directly to ligand binding, in turn signaling the on- vs off- state of thegene expression mechanism. Moreover, among the four Co2+ ions resolved in the crystal
structure (Figure 5.1A), three form a strong coordination network primarily between the highly
conserved guanines at the junction. It is believed that the coordination between Co2+ and theguanine nitrogen (N7) provides the source of metal ion selectivity, since Mg2+ prefers tocoordinate with oxygens in the RNA phosphate backbone rather than nitrogens in the
nucleobases.13, 16 In terms of the gene regulation mechanism, the NiCo riboswitch controls RNA
polymerase activity by termination of the transcription event.16 Upon ligand binding, the fourway junction, particularly the stem P1, is stabilized by the Ni2+/Co2+ coordination network toprevent the expression platform from forming a self-annealed terminator hairpin that in turndisrupts the RNA polymerase transcription complex. As a result, in the presence of excess
Ni2+/Co2+, the polymerase complex proceeds to transcribe the mRNA which encodes for the
metal transporter protein.
Riboswitches are highly dynamic in structure with the ability to switch between different
conformations in response to ligand to achieve gene regulation.1 Moreover, upon transcription,
the nascent mRNA must fold in real time (t  1/kfold) and thereby participate in conformational
search over the downstream DNA, a competitive kinetic process known as cotranscriptional
folding.20-21 During transcription, only a limited time window is therefore allowed for the

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riboswitch to dynamically sample the on- vs. off-configurations and thereby achieve the desired
ligand response.22 Consequently, both ligand recognition and conformational folding rates are
crucially important to achieving the requisite regulatory effect.23-25 Over the past decade, singlemolecule techniques have been applied to study biomolecular folding and unfolding kinetics. In
particular, single-molecule Fluorescence Resonance Energy Transfer (smFRET) microscopy has
been extensively utilized,26-27 whereby the conformational change can be visualized in real timeby monitoring energy transfer efficiency (EFRET) between the fluorophore pair. Moreover, incontrast to bulk fluorescence measurements where the observed EFRET is averaged over many
trillions of replicates, smFRET at the single molecule level is in principle able to identify
multiple conformations from distinct EFRET values to elucidate a more comprehensive folding
mechanism.28-30 Furthermore, precise thermal control is incorporated into the smFRET
measurements to facilitate study of the kinetics as a function of temperature. Monitoring thethermal dependence of the NiCo riboswitch kinetics allows us to deconstruct the folding freeenergies into enthalpic and entropic contributions,31-32 from which we can generate detailedenergy diagrams explicitly demonstrating changes in each of the thermodynamic variables along
the folding coordinate.33-34
The organization of this paper is as follows. First, the experimental design including thesample preparation and smFRET experimental setup is presented in Section 5.3. Folding of the
NiCo riboswitch is then systematically explored at the single molecule level as a function of (i)monovalent (Na+), (ii) divalent (Mg2+), (iii) target ligand (Ni2+ and Co2+) cation concentrations,and (iv) sample temperature, with results presented in Section 5.4.1 to 5.4.5. Of particularinterest, we find that the NiCo riboswitch exhibits three distinct EFRET states, with a “prefolded”

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Figure 5.1 Structure of E. bacterium NiCo riboswitch. (A) Overall crystal structure (PDB:
4RUM). (B) Riboswitch sequence in secondary structure representation. The oligomers forming
the ternary smFRET construct are indicated in red, green and blue, respectively.

intermediate structure identified to play a crucial role in ligand recognition and riboswitch
folding. Such behavior is consistent with a conformational selection (“fold-then-bind”)
mechanism,35-37 where the biomolecule spontaneously samples a prefolded structure prior toligand association and stabilization. This novel combination of i) stepwise folding and ii) unique
cation response of a riboswitch observed at the single molecule level is noteworthy and provides
material for further discussion in Section 5.5.1 and 5.5.2, respectively. In addition, thethermodynamic variables obtained from our temperature dependent studies are utilized in
Section 5.5.3 to reconstruct a detailed free energy diagram of the NiCo riboswitch folding
pathway. Finally, Section 5.6 summarizes the work and points to directions for future
exploration.

5.3

Experiment5.3.1 NiCo riboswitch construct design and sample preparation
The aptamer domain of the NiCo riboswitch consists of four helices joined by a four-way
junctional loop (see Figure 5.1).16 In the cobalt-bound crystal structure (Figure 5.1A), the two

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sets of coaxially-stacked helices adopt a twisted H conformation with three out of the four
resolved Co2+ ions in direct contact with the junctional loop. The fourth Co2+ ion peripheral to
the junction (indicated by * in Figure 5.1A) shows only relatively low anomalous density in the
X-ray diffraction data and appears to make fewer contacts with any of the conserved
nucleotides.16 It is therefore presumed that this final Co2+ ion does not play a critical role in NiCo
riboswitch folding and might be substitutable by other cations such as physiological Mg2+.
Although not the first example of conformational change in a riboswitch induced byligand-binding to a junctional loop,38-40 the NiCo riboswitch is of particular interest in its own
right due to two unique structural features:16 First of all, the suite of 3-4 Co2+ ions occupying thejunction loop region and located by anomalous X-ray dispersion data forms an stronglyinteracting network and suggests that the ligand binding kinetics might be highly cooperative.
Secondly, the NiCo riboswitch lacks the long-range tertiary interaction motifs and close helicalpacking which are relatively common features found in other riboswitches. In combination, thisprovides a relatively novel opportunity for probing cooperative ligand induced conformational
response in a riboswitch, but probed by the relative orientation between minimally interacting
helices.
The NiCo riboswitch in this work is constructed from the Erysipelotrichaceae bacterium(E. Bacterium) sequence that has been well characterized in previous study.16 To achieve surface
immobilization and fluorophore labeling, the ternary smFRET construct is assembled byannealing three chemically modified RNA oligomers (Integrated DNA Technologies, Coralville,IA), followed by high-performance liquid chromatography (HPLC) purification, with detailed
oligomer sequences and fluorophore-labeled positions illustrated in Figure 5.1B. (Note:companies are mentioned for explicit information and not by way of commercial product104
support) In particular, the P1 stem has been extended by 8 base pairs and modified with aterminal biotin to tether the single molecule RNA construct onto the biotin-BSA surface throughbiotin-streptavidin interactions. The Cy3 and Cy5 FRET fluorophores are labeled at the distal
ends of P2 and P4 (Figure 5.1B), respectively, corresponding to loops L2 and L4 in the native
structure. According to previous structural characterization,16 L2 and L4 do not respond to ligand
binding and are not part of the conserved sequence essential for ligand sensing and riboswitch
function. Thus, we reasonably do not expect our choice of dye labelling sites to interfere with theoverall riboswitch conformation. Finally, the distance between Cy3 and Cy5 of the folded NiCo
riboswitch is estimated to be R ≈ 45 Å,16 which is close to the characteristic Forster length for the
Cy3 and Cy5 FRET pair (R0 ≈ 50 Å). Due to the extremely rapid (1/R6) dependence of Forster
energy transfer, we therefore expect high sensitivity in EFRET values to any changes in the Cy3Cy5 distance upon conformational unfolding.
To achieve prolonged observation of fluorescent signals from a single RNA molecule, thesmFRET NiCo riboswitch constructs are immobilized on the surface of a glass coverslip throughbiotin-streptavidin interaction. The sample is prepared by successively flushing the sample
holder with the following solutions to obtain a typical ≈ 50 RNA molecules per 100 μm2 surface
coverage:37, 41 (i) 10 mg/mL bovine serum albumin (BSA) with 10% biotinylated BSA, (ii) 200
μg/mL streptavidin solution, (iii) ≈ 25 pM of the smFRET NiCo riboswitch construct, with a 10minute incubation time between each step. Prior to each smFRET experiment, the sample isflushed with an imaging buffer containing (i) 50 mmol/L hemipotassium HEPES buffer (pH 7.5),(ii) Trolox/PCA/PCD enzymatic oxygen scavenger system to catalytically remove oxygen, (iii)
100 mmol/L NaCl and 0.5 mmol/L MgCl2 to provide background salt (unless otherwise

105
specified), and (iv) sufficient NiCl2 and CoCl2 to achieve desired cation concentration
conditions.

Figure 5.2 Schematic of the single-molecule confocal fluorescence microscope. Inset: Cartoon
representation of a doubly fluorophore labeled smFRET construct tethered on the surface of a glass
coverslip for the single-molecule fluorescence observation.

5.3.2 Single-molecule FRET spectroscopy and temperature control
The single-molecule FRET experiment in this work is based on a homebuilt confocal
microscope system adapted for additional temperature control (Figure 5.2).34, 41-42 In brief, a 532
nm collimated beam from a high repetition rate (50 MHz) pulsed Nd:YAG laser is directed onto
the sample through an inverted confocal microscope. The beam is tightly focused by a 1.2 N.A.
water immersion objective into a diffraction limited laser excitation/collection spot (1/e2 radius ≈310(30) nm), allowing for diffraction limited observation of one fluorophore-labeled RNA at atime. The resulting fluorescence photons are collected through the same objective and thenseparated with dichroics by (i) color (green/red) and (ii) polarization (horizontal/vertical) before
detection on single-photon avalanche photodiodes. For each photon detection event, four bits of
information (color, polarization, “wall clock” time (sorted into 50 ns bins), and microtime withrespect to the laser pulse (50 ps resolution)) are recorded with a fast router, time to amplitude

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converter (TAC), and a time-correlated single-photon counting modules. In this work, we focus
primarily on the photon color and arrival time information, with which we can calculate a timedependent EFRET trajectory.

Figure 5.3 Sample fluorescence time traces of Cy3 and Cy5 signal (upper panel) andcorresponding EFRET time trajectories (lower panel) obtained with (A) [Co2+] = 0.3 µmol/L, (B)[Ni2+] = 0.3 µmol/L and (C) neat buffer (background [Mg2+] = 0.5 mmol/L and [Na+] = 100
mmol/L).

For temperature-controlled experiments, the temperature is precisely servo loop stabilized
by heating the sample and the microscope objective simultaneously.31, 43 Specifically, the sample
holder is mounted to a thermal stage (Instec, Boulder, CO) that regulates the sample temperatureby responsive heating and cooling. In addition, a resistive collar (Bioptechs, Butler, PA) is used
to simultaneously heat the objective to the desired temperature, minimizing thermal gradients
throughout the sample and thereby increasing the servo loop bandwidth and temperaturestability. Prior to each experiment, the system is allowed to equilibrate for > 15 minutes toachieve steady sample temperatures with ± 0.1 ℃ precision and accuracy.
5.3.3 Single-molecule EFRET trajectory and data analysis
The donor/acceptor fluorescent signals are analyzed with in-house software to generate
background and cross talk corrected EFRET = I(red)/(I(green) + I(red)) trajectories with 20-ms bin

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Figure 5.4 Sample data analysis of the 3-state folding system. (A) EFRET histogram fit to 3
Gaussian functions corresponding to unfolded (U), intermediate (I) and folded (F) subpopulationsof the NiCo riboswitch. (B) Exponential decays of the dwell time distributions presented in a semilogarithm plot, indicating that folding and unfolding of the NiCo riboswitch follow first orderkinetics. (C) Schematic representation of detailed NiCo riboswitch smFRET construct folding andunfolding. Note that the cartoon representation of the unfolded state (U) suggests a morerelaxed/less structured state, which does not necessarily represent the average configuration.
time resolution (Figure 5.3).31 From visual inspection of sample data in Figure 5.3, the resulting
EFRET trajectories indicate that the NiCo riboswitch exists in three states with distinct EFRET
values, which are also clearly evident in the corresponding EFRET histograms (Figure 5.4A). Dueto the fact that the three EFRET distributions are partially overlapping, the traditional methods of
dwell time analysis with thresholding prove challenging to implement due to shot noise
fluctuations in the fluorescence signals.31, 44 To facilitate the data analysis and improve thereliability of the extracted rate constant information, we have implemented Hidden Markov
modeling (HMM) methods based on maximum likelihood estimation, which have been widely
applied to study time-dependent single-molecule data.45-48 Simply summarized, HMM presumes
a given kinetic model and optimizes (by changing these model parameters) the likelihood ofpredicting EFRET values/distributions that correctly match the actual EFRET time trajectory data.48

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Such an approach proves extremely useful in obtaining estimates of EFRET values, number ofstates, and kinetic rate constants. As one of many powerful attributes, HMM analysis provides
access to explicit time trajectory predictions with which to compare to experimental EFRET data
(e.g., the dark blue line in Figure 5.3) .
As yet another advantage, HMM analysis allows one to include and rigorously examine
the statistical possibility that the system is better described by more than three EFRET
distributions48. Interestingly, HMM analysis rejects this and consistently predicts three states inthe EFRET trajectories (Figure 5.3, lower panels), corresponding to EFRET ≈ 0.35, 0.60 and 0.75.
The high EFRET state (EFRET ≈ 0.75) agrees well with our prediction of the folded NiCo
riboswitch from the crystal structure.16 Furthermore, we find virtually all transitions (> 98 %)between the lowest (EFRET ≈ 0.35) and highest (EFRET ≈ 0.75) states exhibit a “pause” at theintermediate EFRET ≈ 0.60 value, strongly suggesting that the subpopulation with EFRET ≈ 0.60
corresponds to a folding intermediate (denoted herein as I) that represents a stable transition
point between fully folded (F) and unfolded (U) conformations (more details in Section 5.4). We
therefore assign the three EFRET populations to be the folded (F, EFRET = 0.75), intermediate (I,
EFRET = 0.6) and unfolded (U, EFRET = 0.35) conformations of the NiCo riboswitch, described bya simple kinetic model with 4 corresponding unimolecular rate constants (kU→I, kI→U, kI→F, kF→I)
illustrated schematically in Figure 5.4C. In Figure 5.4B, the conventional dwell time analysis of
the predicted EFRET trace supports that each folding process is effectively described by a firstorder rate constant, with the cumulative dwell time distributions well fit to exponential decayfunctions, and yielding HMM predictions of the rate constants summarized in Table 5.1. We canalso extend these kinetic results in a few ways. For example, according to the kinetic model, the109

Table 5.1 Rate constants obtained from HMM and traditional dwell time analysis. Error bars inparentheses represent 1 standard deviations of the mean.
decay rate constant of the dwell time distribution for state I should be the sum of kI→U and kI→F
due to parallel I → U and I → F pathways. The individual values of kI→U and kI→F can thus be
extracted by multiplying the total decay rate constant by the branching ratio for each transition.
For instance, the decay rate constant for I is determined to be k = 6.40(12) s-1 (Figure 5.4B, blueline), with numbers of independently observed I → U and I → F transitions as NI → U = 64 andNI→ U = 21, from which kI→U and kI→F can be readily calculated to be 4.82 s-1 and 1.58 s-1,
respectively. Finally, due to limited statistics on sampling of all three states with limited
observation times due to photobleaching, the dwell time data for the HMM analyses arecollectively analyzed for each experimental sample run consisting of N ≈ 30 single molecules
separated into n = 3 separate samples. This parsing of the data allows us to obtain HMM rate
constants independently for each of the three samples, yielding meaningful statistical averages
and standard deviations of the mean.

5.4

Results and analysis

5.4.1 Co2+-promoted NiCo riboswitch folding
From previous study of the NiCo riboswitch surveying a wide range of metal cations,16 the Ni2+
and Co2+ were alone found to influence the structure of the four-way junction, which in turncorrelates with the relative orientation between the 4 helices. As a result, we can hope to monitor

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the effects of Ni2+ and Co2+ binding to the 4-way junction loop via time-dependent EFRET
trajectories (Figure 5.3). Since the Co2+ ion positions are most clearly resolved from X-ray
crystal structures,16 we first systematically explore the folding kinetics of the NiCo riboswitch asa function of [Co2+]. Specifically, HMM methods are used to analyze EFRET trajectories for astatistically significant sample (three independent sets of N  10 molecules) of NiCo riboswitch
constructs, to obtain the 4 kinetic rate constants (kU→I, kI→U, kI→F, kF→I) connecting the unfolded(U), intermediate (I), and folded (F) conformational manifolds. The results from such an analysis
are summarized in a plot of rate constants (Figure 5.5A) as a function of Co2+, with theequilibrium fraction of U, I, F states at each ion concentration depicted in Figure 5.5B. From thebottom panel, it is clear that the overall complex equilibrium shifts systematically from unfolded

Figure 5.5 Co2+ dependence of NiCo riboswitch folding. (A) Rate constants kU→I (red empty
diamonds), kI→U (green empty diamonds), kI→F (red solid circles) and kF→I (green solid circles) as
a function of [Co2+]. (B) Equilibrium fraction as a function of [Co2+] (green: U, blue: I, red: F).
Solid lines represent fits to the Hill equation (Eq. 5.1). Error bars represent 1 standard deviationsof the mean.

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Table 5.2 Fitting results from Hill analysis. (* indicates parameters fixed in the fit).
Error bars in parentheses represent 1 standard deviations of the mean.
( (U + I)) to predominantly folded ( F) at increasing [Co2+] with sub-micromolar affinities.
However, parsed in terms of individual rate constant contributions, the kinetics become evenmore interesting, as displayed in Figure 5.5A. For example, the major contributor to suchconformational transformation appears to be the forward/reverse rate processes between I and F(solid circles), with the successful folding of the NiCo riboswitch (U → F) promoted by asimultaneous [Co2+]-dependent increase in kI→F (I → F transition) and decrease in kF→I (F → I
transition), respectively. Of particular relevance, the rate of increase in kI→F for low [Co2+] issupralinear, which suggests that conformational change from I to F is driven by the cooperative
presence of multiple Co2+.49 This can be further quantified by least squares fits of the rate
constants to a Hill equation37, 50-51n[M2+ ]

𝑘I→F = 𝑘0 +(𝑘1 − 𝑘0 ) (𝐾 n +[M2+]n ),dEq. 5.1

where k0 represents the value of kI→F at [Co2+] = 0, k1 represents the saturated value of kI→F athigh [Co2+], Kd is the apparent dissociation constant, and n is the Hill coefficient. The fits yield aHill coefficient of n = 3.1(11) for Co2+-promoted folding (Table 5.2), again indicating a strong
positive cooperativity and in good agreement with previous in-line probing assays.16 Conversely,

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the unfolding rate constant kF→I decreases as a function of increasing [Co2+]. Since the range of[Co2+] explored (0-1.2 µM) is 2-3 orders of magnitude lower than the background [Mg2+] ( 0.5
mmol/L), this monotonic decrease in kF→I cannot result from purely cationic stabilization of theaptamer domain by Co2+. Indeed, kF→I has already been shown (Section 5.4.3) to be insensitive
to [Na+] and [Mg2+] in the absence of Ni2+ or Co2+, which indicates that kF→I primarily depends
on ligand association. Thus, the strong dependence of kF→I on [Co2+] suggests that the NiCo
riboswitch unfolds at distinctive rates from each sub-population (Fi) with different numbers of
Co2+ ions, and with the equilibrium between each state Fi=1,2,3 modulated by [Co2+],37 thus
naturally leading to a strongly [Co2+]-dependent unfolding. In order to model the decrease in

Figure 5.6 Ni2+ dependence of NiCo riboswitch folding. (A) Rate constants kU→I (red empty
diamonds), kI→U (green empty diamonds), kI→F (red solid circles) and kF→I (green solid circles) as
a function of [Ni2+]; (B) equilibrium fraction as a function of [Ni2+] (green: U, blue: I, red: F).
Solid lines represent fits to the Hill equation (Eq. 5.1). Error bars represent 1 standard deviationsof the mean.

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kF→I with Co2+, the kinetic data in Figure 5.5A are similarly fit to the Hill equation (Eq. 5.1) withn fixed at 3.1 value from analysis of kI→F (Table 5.2).
By way of contrast, the conformational kinetics sampling transitions between theunfolded (U) and intermediate (I) states is insensitive to [Co2+] (Figure 5.5A, empty diamonds),
with kU→I ≈ 13 s-1 and kI→U ≈ 4 s-1, respectively. This implies that the NiCo riboswitch isactively sampling the “prefolded” intermediate state with a similar rate constant under all bufferconditions here. As these “prefolding” rate constants are on the order of or larger than thesubsequent (I → F) folding rate constants, the fractional split between [U] and [I] (see Figure
5.5B) remains relatively constant over the full dynamic range of [Co2+] explored. However, since
I folds efficiently upon Co2+ binding, the overall concentration [U + I] is significantly depletedwith increasing [Co2+] as the overall equilibrium is driven towards [F] (Figure 5.5B).
5.4.2 Ni2+-promoted NiCo riboswitch folding
The NiCo riboswitch has been shown to respond to Ni2+ as well as Co2+ in previous
structural studies and in vitro transcription assays.16 Although the x-ray crystal structure of theNi2+-bound NiCo riboswitch is currently unavailable, previous in-line probing studies haverevealed similar cleavage patterns in response to Ni2+ and Co2+ ions, suggesting that both ligands
induce a similar conformational change. Experimentally (see Figure 5.3 and 5.6), the present
studies show remarkably similar single molecule folding kinetics as a function of either [Ni2+] or[Co2+]. For example, time dependent EFRET trajectories for the NiCo riboswitch construct in thepresence of Ni2+ (Figure 5.3) also exhibit three distinct states (U, I, and F), indeed with the same
EFRET values (0.35, 0.6, 0.75) seen in the presence of Co2+. Also consistent with the [Co2+]
dependence, the rate constants for folding (kU→I) and unfolding (kI→U) from U to the “prefolded”
intermediate I remain relatively constant over the range of [Ni2+] studied (Figure 5.6A, empty

114
diamonds), with the equilibrium driven toward the F conformation by a simultaneous increase
and decrease in kI→F and kF→I, respectively (Figure 5.6A, solid circles). The only quantitative
differences in the rate analyses can be seen in the Ni2+ vs. Co2+ dependence of kI→F. Specifically,kI→F increases less superlinearly with [Ni2+] than [Co2+], which is consistent with a lower (albeit
finite) Hill cooperativity and a significantly lower saturation rate constant in kI→F. Indeed, leastsquares Hill fits of k0, k1, Kd, and n to Eq. 5.1 yield k0 = 0.9(2) s-1, k1 = 2.6(2) s-1, Kd = 0.26(7)µM and n = 1.8(10), respectively (Table 5.2). Note that Ni2+-promoted folding of the NiCo
riboswitch construct still exhibits positive cooperativity (n > 1), though with lower levels thanCo2+.16
5.4.3 Physiological cation (Na+/Mg2+) effects on the NiCo riboswitch structure
Counterions (cations) are essential for RNA folding due to charge neutralization andelectrostatic screening.52-53 Cations in the cellular environment are quite abundant, withmonovalent (Na+ and K+) and divalent (Mg2+) cation concentrations at the 100 mmol/L andfew-mmol/L levels, respectively. It is thus useful to probe NiCo riboswitch conformational
kinetics and dynamics under physiological cation conditions in the complete absence of Ni2+ orCo2+ cognate ligand. We first explore the NiCo riboswitch as a function of [Na+] without
divalent cations, i.e. [Mg2+] = 0 (Figure 5.7A). It is important to note that we still see clear
evidence in the EFRET trajectories for the three conformational states (U, I and F) even in theabsence of ligands (see Figure 5.3C), which indicates the robustness of the prefoldedintermediate and motivates a similar HMM analysis of the rate constants (see Figure 5.7A and
5.7B). Interestingly, three of the four rate constants show little dependence on monovalent [Na+],with the only significant response that the rate constant for unfolding of the intermediate (kI→U)

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Figure 5.7 General monovalent/divalent background cation dependence of NiCo riboswitch
folding. Rate constants kU→I (red empty diamonds), kI→U (green empty diamonds), kI→F (red solid
circles) and kF→I (green solid circles) are studied as a function of (A) [Na+] and (B) [Mg2+]
concentration. Dashed lines are added to highlight the change in k (or lack thereof) as a functionof cation concentration. Error bars represent 1 standard deviation of the mean.

is reduced by Na+ (Figure 5.7A). Stated alternatively, increase in [Na+] primarily enhances thefractional concentration of the prefolded intermediate [I]/[U] by decelerating the rate of I → U
unfolding. This is in dramatic contrast to the behavior noted previously for the cognate ligand
cations, which impact only the rate constants for final folding from I to F (kI→F) or vice versa(kF→I) with negligible impact on the corresponding U to I initial folding/unfolding steps (k I→Uand kU→I). Also surprisingly, the high EFRET folded state (F) is observable over the entire range of[Na+] explored, though formed with a much lower rate constant (i.e., kI→F ≈ 0.2 s-1) andequilibrium probability (KI↔F ≈ 0.05), with both kI→F and kF→I exhibiting no systematic
dependence on [Na+]. These results indicate that the NiCo riboswitch can dynamically sample
the fully folded conformation even without cognate ligand binding to stabilize the final
biochemically competent state.
Similar effects are also observed in studies of the Mg2+-dependent folding/unfolding
kinetics at a constant monovalent background [Na+] = 100 mmol/L (Figure 5.7B), except that

116
reduction in the unfolding rate constant (kI→U) is now > 100-fold more sensitive to Mg2+ andresponds at the sub-millimolar level. Therefore, both Na+ and Mg2+ background levels efficiently
promote the intermediate population (I) by decelerating the unfolding rate constant k I→U without
significant impact on unimolecular folding to the final folded state kI→F. Differential response to
the two cationic species and cognate ligands in terms of folding of the NiCo riboswitch may
therefore be sorted into two separate contributions (see Figure 5.4): (i) prefolding from U to I
promoted by universal (i.e., non-selective) counterion stabilization effects (both Na+ and Mg2+)and (ii) folding from I to F promoted by selective cognate ligand binding. Although Na+ andMg2+ do not by themselves promote the fully folded state (F), they do nevertheless facilitate
formation of the NiCo riboswitch by encouraging a “fold-like” conformation (I) and effectively
suppressing the unfolded state (U). As a result, the overall fraction of the fully folded state canstill be enhanced by background [Na+] and [Mg2+]. We note that such cation effects to promote a

Figure 5.8 Temperature dependence of equilibrium constants presented in van’t Hoff plots at (A)[Co2+] = 0 µmol/LM and (B) [Co2+] = 0.5 µmol/L (blue empty diamonds: KU↔I, pink solid circles:KI↔F). Data fits with linear regression yield detailed thermodynamic information (i.e. ∆H0 and∆S0) by Eq. 5.2. Error bars represent 1 standard deviations of the mean.

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fold-like state in preparation for folding have been observed in multiple riboswitch systems with
Mg2+.29, 36-37 It is also not surprising that cations like Na+ yield stabilization effects at higher
concentration, as monovalent-ion-promoted folding has been demonstrated with fundamental
RNA tertiary folding motifs such as the kink turn,54 four-way junction55 and tetraloop-receptor44,
56

commonly found in fully functional RNA.

5.4.4 Temperature dependent folding equilibrium: Van’t Hoff analysis
Temperature has significant impact on biomolecular structure, as the folding/unfolding
kinetics depend exponentially on enthalpic and/or entropic contributions to the overall freeenergy differences. Indeed, the temperature dependence of biomolecular folding contains crucial
thermodynamic information that helps provide a clearer physical picture of the folding
dynamics.33 Toward that end, NiCo riboswitch folding kinetics at the single molecule level has
been studied as a function of temperature (T ≈ 20–30 ℃), with and without the primary cognate
ligand ([Co2+] = 0.0 and 0.5 µM), and analyzed by HMM methods described in Section 5.3.3. Asa first stage of analysis, we focus on the two temperature dependent equilibrium constants,
KU↔I(T) = kU→I/kI→U = [I]eq/[U]eq and KI↔F(T) = kI→F/kF→I = [F]eq/[I]eq, which are extracted fromthe HMM modeling and displayed in a conventional van’t Hoff plot in Figure 5.8. This allows us
to deconstruct the two folding free energy differences (U → I and I → F) into changes inenthalpy (H0) and entropy (S0) via a linear fit to the standard van’t Hoff expression
∆H0 1

∆S0

ln(K eq ) = − R T + R .

Eq. 5.2

In the absence of Co2+ (Figure 5.8A), KU↔I shows only a weak dependence on the temperature(i.e., slope m ≈ 0 within experimental uncertainty), indicating therefore a negligible enthalpic
contribution (H0U→I = 1.4(13) kcal/mol ≈ 0). Conversely, we can extrapolate Eq. 5.2 in the hightemperature limit to yield a positive intercept that reveals U → I folding to be dominated by only

118
modest entropic gain (S0U→I = 7(4) cal/mol/K). The second stage (I ↔ F) folding equilibrium
constant (KI↔F) exhibits a more pronounced dependence on temperature, now with an overall
positive slope consistent with a mildly exothermic process (H0 I→F = -14(8) kcal/mol) and anegative intercept indicating an overall entropic penalty to folding (S0I→F = -52(26) cal/mol/K).
Thermodynamic data obtained from these van’t Hoff analyses are summarized in Table 5.3.

Table 5.3 Thermodynamic values obtained from a van’t Hoff analysis of the equilibrium constantdata, where ∆G0 is calculated from Keq at T = 22.5 ℃. Error bars in parentheses represent 1
standard deviations of the mean.

In the presence of 0.5 µM Co2+ (Figure 5.8B), the temperature dependence of the firststage (KU↔I) is virtually identical to that at 0.0 M. This is of course consistent with our previous
room temperature observations, whereby “prefolding” from U → I showed no sensitivity to thepresence or absence of the cognate ligand. However, a much more dramatic effect of Co2+ on
NiCo riboswitch folding is indicated by the rapid decrease of the second stage (K I↔F) withincreasing temperature, which now yields a strongly positive slope (m > 0) and a more negativeintercept in the van’t Hoff plot, corresponding to a substantial increase in both exothermicity(→F = −() vs -14(8) kcal/mol) and entropic loss (S0I→F = -146(21) vs -52(26)cal/mol/K) at 0.5 vs 0.0 M. As a plausible physical picture, this would be consistent with the
cognate ligand preferentially captured by a prefolded (I) vs unfolded (U) riboswitch via

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Figure 5.9 Temperature dependence of rate constants presented in Eyring plots: kU→I (red empty
diamonds) and kI→U (green empty diamonds) at (A) [Co2+] = 0 µmol/L and (B) [Co2+] = 0.5µmol/L; kI→F (red solid circles) and kF→I (green solid circles) at (C) [Co2+] = 0 µmol/L and (D)[Co2+] = 0.5 µmol/L. Data fits with linear regression yield detailed thermodynamic information(i.e. ∆H‡ and ∆S‡) by Eq. 5.3. Error bars represent 1 standard deviation of the mean.

exothermic coordination of the Co2+, resulting in a more highly ordered ligand-boundconfiguration and thus a significant loss in translational entropy.57-58
5.4.5 Temperature dependent folding kinetics: transition state theory (TST) analysis
Further information can be obtained from the corresponding temperature dependence ofthe forward/reverse kinetics, which can be deconstructed with Eyring/transition state theory(TST) analysis to yield isolated enthalpic and entropic contributions to the transition state barrier.
Specifically, the thermodynamics of the transition state can be obtained from a standard Eyring
plot of ln(k) vs 1/T:31, 34, 41∆𝐻 ‡ 1∆𝑆 ‡ln(𝑘) = − 𝑅 𝑇 + 𝑅 + ln 𝜈 .

Eq. 5.3

In Eq. 5.3, ΔH‡ and ΔS‡ represent enthalpy and entropy differences between the transition state
and the initial (or final) state, while 𝜈 represents an “attempt frequency” sampling the free energy

120barrier along the folding coordinate59-60 and often treated as a low frequency skeletal vibration
with 𝜈 ≈ 1013 s-1.61-62 It is worth noting that ΔS‡ depends only quite weakly (i.e., logarithmically)on the choice of 𝜈 and, furthermore, any differential (e.g., Co2+ induced) changes in the transition
state entropy (ΔΔS‡) are rigorously independent of 𝜈.
Eyring plots of Eq. 5.3 for the two conformational transformations U ↔ I and I ↔ F(forward and reverse) are presented in Figure 5.9 and reveal several interesting features. First ofall, by visual comparison of Figure 5.9A and 5.9B, the plots for the U ↔ I kinetics indicate Co2+
to have only quite modest effects on the forward (folding) and reverse (unfolding) rate constants
kU→I and kI→U. This insensitivity to Co2+ in both the forward/reverse rate and equilibrium
constants for this prefolding step implies negligible changes in the first transition state barrier(TSU↔I) with cognate ligand. Indeed, the negative slopes observed for both kU→I and kI→U
indicate a strong but equally endothermic process (ΔH‡U→I = 23(3) kcal/mol, ΔH‡I→U = 22(3)kcal/mol) to cross the transition barrier from either direction.
By way of contrast, the cognate ligand effects on the second stage I ↔ F conformational
kinetics are clearly much more significant. In the absence of Co2+ (Figure 5.9C), both theforward (kI→F) and reverse (kF→I) folding rate constants depend only weakly on temperature,with slopes corresponding to ΔH‡I→F = -11(8) kcal/mol and ΔH‡F→I = 3(6) kcal/mol,
respectively. Moreover, by Eq. 5.3, the entropic penalties of accessing the transition state aredetermined as ΔS‡I→F = -98(27) cal/mol/K and ΔS‡F→I = -46(22) cal/mol/K). However, in thepresence of 0.5 M Co2+, the rate constant changes dramatically (cf. Figure 5.9C vs Figure
5.9D). The first effect is an increased slope in the rate constant for folding (kI→F) with decreasing
experimental temperature, consistent with a more exothermic folding in the presence of the
cognate ligand Co2+ (ΔH‡I→F = -20(4) vs -11(8) kcal/mol). This increased slope results in a more

121
negative y-intercept, therefore predicting an even greater entropic penalty for Co2+-induced
folding (ΔS‡I→F = -123(14) vs -98(27) cal/mol/K). Simply summarized, the forward folding step
(I → F) experiences a more significant entropic penalty (-TΔΔS‡I→F > 0) which iscounterbalanced by increased enthalpic stabilization (ΔΔH‡I→F < 0) in the presence of 0.5 µM
Co2+. The reverse folding step (F → I), on the other hand (see Figure 5.9D), now becomes
noticeably more temperature sensitive. From fits to Eq. 5.3, the riboswitch needs to cross a moresignificant enthalpic barrier to fold (ΔH‡F→I = 24(4) vs 3(6) kcal/mol), with the effects strongly
mitigated by entropic gain (ΔS‡F→I = 24(13) vs -46(22) cal/mol/K) in the presence and absenceof the cognate ligand (see Table 5.4).

Table 5.4 Thermodynamic values obtained from an Eyring/TST analysis. Error bars in parentheses
represent 1 standard deviations of the mean.

5.5

Discussion

5.5.1 Cations facilitate formation of a prefolded NiCo riboswitch intermediate
The combination of FRET, time correlated single photon counting methods, and high NA
confocal microscopy have permitted monitoring of conformational kinetics of the NiCo
riboswitch construct at the single molecule level. The results indicate that folding proceeds via a
two-step process between three conformations with three distinct EFRET values (Figure 5.3),
specifically identified as unfolded (U) and folded (F) states, with a stable “prefolded”

122intermediate conformation (I) directly along the U → F folding pathway (Figure 5.4). The
cognate ligands (Co2+ and Ni2+) are found to efficiently promote the formation of F from theprefolded intermediate I with sub-micromolar affinities by simultaneously increasing anddecreasing kI→F and kF→I, respectively. In sharp contrast, however, kinetic rates and overall
equilibrium constants between the unfolded (U) and prefolded intermediate (I) conformations
show zero dependence on cognate ligand concentrations up to micromolar levels. Finally, we
find the first stage of folding/unfolding (U ↔ I) to be strongly stimulated by near physiologicallevels of monovalent (Na+) and divalent (Mg2+) cations (Figure 5.7). This collective behavior
suggests that the NiCo riboswitch intermediate (I) is a prefolded structure stabilized by cations
through charge neutralization and screening of the phosphate groups,52-53 with an intermediate
EFRET value indicating that the helices are partially aligned toward the folded conformation due
to preorganization of the junctional loop aptamer domain. Indeed, this would be consistent withprevious studies, whereby a more fold-like conformation of riboswitches can be promoted byphysiological levels of Mg2+ to increase the aptamer ligand affinity in a “fold-then-bind”
mechansim.29, 36-37 Moreover, the present work has shown that monovalent cations (Na+) exhibit
similar stabilization effects for the intermediate state, requiring higher but still physiologically
relevant concentrations. Such “fold-then-bind” behavior represents a classic example ofconformational selection, whereby a biomolecule spontaneously samples many
thermodynamically accessible configurations, but preferentially locking into an optimal “target”
structure due to enhanced binding for the cognate ligand.35 In this study, the prefolded NiCo
riboswitch intermediate (I) is sufficiently long lived to be identified by its distinct EFRET value.
As a novel result of the intermediate (I) being along the folding pathway and distinguishable
from the unfolded (U) and folded states (F), we are able to follow the folding/binding process in123
single molecule detail and thereby provide direct evidence for a “fold-then-bind” mechanism
without any underlying kinetic model assumptions.36-37
5.5.2 Folding is induced by ligand binding to the conformational intermediate
Ni2+ and Co2+ cognate ligands of the NiCo riboswitch have been shown to effectively
promote conformational transformation from a prefolded intermediate I to the fully folded state Fwith sub-micromolar affinities. Furthermore, it achieves this while maintaining a fixed [U]/[I]ratio through cationic stabilization effects dominated by physiological monovalent (Na+) anddivalent (Mg2+) salt conditions. As a function of increasing [Co2+] (Figure 5.5), the NiCo
riboswitch is stabilized in the folded state (F) both by increasing the folding (k I→F) anddecreasing the unfolding (kF→I) rate constant. The supralinear increase of kI→F at low [Co2+]
indicates the Co2+-induced folding to be highly cooperative, consistent with previous in-line
probing results.16 The cooperativity for kI→F is determined from a Hill analysis to be n = 3.1(11)(Table 5.2), in good agreement with the three bound Co2+ ions resolved in the crystal data.16 One
should stress that Hill coefficients can differ from the number of bound ligands and are notalways equivalent to the exact ligand stoichiometry.63-64 Instead, the data indicate a consistency
with complete folding (i.e. change in EFRET) of the NiCo riboswitch upon association of the three
Co2+ ions.
This cooperativity makes the NiCo riboswitch particularly sensitive to cognate ligand atconcentrations in the transition region near [Co2+]  Kd = 0.32(4) µM and thus yielding a muchsharper threshold response.65-66 Cooperative Co2+ response of the NiCo riboswitch may therefore
be advantageous by allowing cellular [Co2+] to be maintained near Kd, but where highcytotoxicity requires any additional Co2+ to be immediately removed.6-7 Note that while thepresent Kd values are in quantitative agreement with the recent studies of NiCo riboswitch-based

124
fluorescent sensors titrated in citrate buffer,67 they are roughly an order of magnitude lower (i.e.,
more sensitive) than previous in-line probing results.16 We do not know the reason for thesedifferences, but can speculate that the presence of high [Mg2+] in the in-line probing studies may
interfere with ligand recognition/binding. Indeed, since Mg2+ is the dominant divalent cation incells and is known to strongly interact with RNA, either synergy or competition between Mg2+
and the cognate ligands would be a natural possibility. This would suggest the value of futurestudies into Mg2+ cooperativity/anticooperativity effects on riboswitch response and metal ion
toxicity.
The second cognate ligand Ni2+ promotes the NiCo riboswitch folding in a way
qualitatively similar to Co2+, with kI→F and kF→I systematically increasing and decreasing,respectively as a function of [Ni2+] (Figure 5.6). There are, however, important differences
between the two ligands. Specifically, the increase in kI→F at low [Ni2+] indicates a lower
cooperativity (n = 1.8(10)) for Ni2+-promoted folding, yet which is compensated by an eventighter ligand affinity (Kd = 0.26(7) µM) (Table 5.2).67 The results suggest that the NiCo
riboswitch has evolved to trigger at lower levels of cognate ligand but more gradually towardremoval of excess Ni2+. A second difference in the NiCo riboswitch behavior can be seen in thesaturation value of kI→F, which is nearly 3 times lower for Ni2+ than Co2+ and therefore predicts
only ≈ 50 % of the folded population under saturating [Ni2+] conditions. Such incomplete folding
behavior, however, may not be characteristic of NiCo riboswitch in vivo, where more complete
folding may be aided by molecular crowding and excluded volume interactions in theintracellular environment.68-69

125

Figure 5.10 Detailed energy diagram of NiCo riboswitch folding at (A) [Co2+] = 0 µmol/L and(B) [Co2+] = 0.5 µmol/L, with the unfolded state (U) as reference zero (blue: ∆G, red: ∆H, green:−T(∆S) at T = 22.5 ℃).

5.5.3 Detailed thermodynamics for folding of the NiCo riboswitch
NiCo riboswitch folding at the single molecule level has been examined with temperature
controlled measurements to obtain detailed information on relative free energies (G0) for eachof the three conformational states (U, I and F) and two transition state barriers (TSU↔I, TSI↔F) as
well as thermodynamic deconstruction of these free energies into enthalpic (H) and entropic(−TS) contributions. These unusually rich free energy landscapes are presented in Figure 5.10,
where the single arbitrary reference energy is chosen to be zero for the unfolded state (U). First,
we focus on the limit of ligand-free folding, i.e. [Co2+] = 0 (Figure 5.10A). In the prefolding
transition (U → I), the system encounters an enthalpic barrier (ΔH‡U→I = 23(3) kcal/mol) that is
only partially mitigated by small entropic gain corresponding to a free energy contribution−T(ΔS‡U→I)  -7(3) kcal/mol at T = 22.5 ℃. Furthermore, after crossing the transition state(TSU↔I), the riboswitch reaches the intermediate prefolded state (I) with a free energy
surprisingly close to the unfolded conformation (U), despite a large 15 kcal/mol transition statebarrier. The net near zero change in both ΔH0U→I (1.4(13) kcal/mol) and –TΔS0U→I (-2.0(12)126kcal/mol) would be consistent with the absence of significant cation association in the U → I
step, which in contrast would be highly enthalpically favored and accompanied by large entropic
loss due to reduced cation mobility. This suggests that the major structural transition from U → I
instead involves modest rearrangement of the solvent (water) configuration and hydrogenbonding around the RNA junction that successively re-orientates the four helices and results inthe observed EFRET change. A predominantly enthalpic barrier would thus be consistent with thesimple physical picture that, during rearrangement, only some of the hydrogen bond structure isrestored at the transition state (TSU↔I). Furthermore, after crossing the transition barrier,hydrogen bond reformation enthalpically stabilizes the system and effectively brings down thefree energy level of the intermediate state I, as illustrated in Figure 5.10A.
The second stage of folding (I → F) is more complex. In the absence of cognate ligand(Figure 5.10A), the free energy transition state barrier (TSI→F) is dominated by entropic loss ofthe system (−T(ΔS‡I→F) = 29(8) kcal/mol) partially mitigated by a relatively small exothermicity(ΔH‡I→F = -11(8) kcal/mol). Moreover, the final folded state F is stabilized by a further decreasein enthalpy (ΔH0I→F = -14(8) kcal/mol), while destabilized by entropy loss (−T(ΔS0I→F) = 15(7)kcal/mol), with respect to the intermediate conformation (I). Such changes in thethermodynamics would be consistent with Coulomb repulsion of the phosphate groups partiallyneutralized by associated monovalent/divalent cations. We note that in the kinetic analysis,folding and unfolding between I and F conformations have been shown insensitive to Na+/Mg2+
concentrations. While the cation association and neutralization are clearly indicated in thethermodynamic analysis, we therefore suspect the cation effects may saturate at relatively low
concentrations. Alternatively stated, stabilizing cations are readily attracted to the 4-way junction

127
at relatively low concentrations. Therefore, cation stabilization effects and cation-insensitive
folding are independently observed in thermodynamic and kinetic analysis, respectively.
In the presence of cognate ligand [Co2+] = 0.5 M (Figure 5.10B), the free energychanges in the initial folding process (U → I) are quite similar to those at [Co2+] = 0 M (seealso Table 5.3 and Table 5.4). This is again consistent with our previous observation (Figure
5.5A) of an insensitivity in U → I folding pathway to Co2+. The more dramatic Co2+ effects areseen in the (I ↔ F) transition between the prefolded and fully folded state. At the second
transition state (TSI↔F), the presence of Co2+ results in an increased entropic barrier (−T(ΔS‡I→F)= 36(4) kcal/mol vs 29(8) kcal/mol at [Co2+] = 0), accompanied by a 2x greater enthalpic
stabilization (ΔH‡I→F = -20(4) kcal/mol vs -11(8) kcal/mol). Furthermore, the Co2+ effects areeven stronger for the overall I → F changes in free energy due to enthalpy (ΔH0I→F = -44(6) vs 14(8) kcal/mol) and entropic (−T(ΔS0I→F) = 43(6) vs 15(7) kcal/mol) for 0.5 m and 0.0 m,
respectively. Both this increased entropic penalty and enthalpic stabilization along the folding
coordinate are consistent with strong binding of the cognate ligand to the binding site to form amore ordered structure with loss in mobility.58 In contrast with the monovalent/divalent cation
effects at [Co2+] = 0, the greater enthalpic stabilization of Co2+ due to the metal coordination
overcomes the entropic loss, resulting an overall free energy change in slight favor of the folded(F) conformation (ΔG0I→F = -0.41 vs +1.49(7) kcal/mol at [Co2+] = 0). In fact, suchthermodynamic shifts induced by ligand association are routinely observed in both ligandbinding protein70 and nucleic acid34, 71 systems. Our results thus provide additional
thermodynamic support for cognate ligand Co2+ binding to the prefolded conformation (I)directly promoting and stabilizing the folded structure (F) in a “bind-then-fold” conformational
selection mechanism.

128
As a parting comment, it is noteworthy that the enthalpic (ΔH0) and entropic (−T(ΔS0))
contributions to the overall free energy change are large in magnitude and of opposing signs.
Such a counterbalance between the enthalpic/entropic effects is known as entropy-enthalpy
compensation.58, 72 In folding of the NiCo riboswitch, such enthalpy-entropy compensation
effects are seen to occur multiple times, as highlighted in Figure 5.10 by the relatively modest
shifts in ΔG0 values contrasting with the order of magnitude larger ΔH0 and –TΔS0 values. As
one example, the free energy ΔG0I→F for I → F folding in the presence of Co2+ is only -0.41(10)kcal/mol, despite the fact that each of the entropic penalty and enthalpic stabilization effects arelarger by 2 orders of magnitude (> 40 kcal/mol). Similarly, in the absence of Co2+, ΔG0I→F is+1.49(7) kcal/mol while the enthalpic stabilization as well as entropic destabilization
components are 10x higher (> 15 kcal/mol). Such a biological propensity to achieve nearly
equally balanced free energy contributions in −TΔS0 and ΔH0 for conformational change offers
one way to modulate the temperature sensitivity of RNA folding and conformational stability ofa biologically competent species with only small changes in the overall free energy ΔG0.

5.6

Summary and conclusion
The present work reports on the single molecule kinetics and thermodynamics of foldingof the NiCo ribowitch construct as a function of (i) cognate ligand (Ni2+, Co2+), (ii) backgroundmonovalent (Na+) and divalent (Mg2+) concentrations, and (iii) temperature (T = 20-30K).
Although the aptamer domain structure of the NiCo riboswitch is built on a 4-way junction withno long-range tertiary stem-stem or loop-loop interactions, evidence from the present single
molecule study reveals it to be more complex and kinetically interesting than a simple two-state
folder. Specifically, the NiCo riboswitch has been shown to dynamically fluctuate between three129
stable conformations (unfolded U, folded F and intermediate I) and exhibit three distinct EFRET
values. Of particular relevance, the overwhelming majority (> 98%) of all transitions between
unfolded (U) and folded (F) conformations sample this third conformation (I), which therefore
acts as a long-lived, prefolded intermediate through which overall folding proceeds by two
distinct steps (U → I and I → F). This intermediate I proves particularly crucial for selective
cognate ligand recognition and ligand-induced folding, as clearly evidenced by the fact thatNi2+/Co2+ strongly promote the I → F folding step, while Mg2+/Na+ has little effect even at 3-5
orders of magnitude higher concentrations. As a result, the first stage of this NiCo riboswitch
folding (U → I) can be facilitated by [Na+] and [Mg2+] present at physiological levels, whereas
the second stage of folding is controlled with high selectivity by submicromolar concentrationsof the cognate ligand. The overall folding pathway thus follows a classic “bind-then-fold”
conformational selection mechanism, whereby the binding site on the prefolded intermediate
captures cognate ligands with high selectivity and thereby stabilizes the overall folding event.
Furthermore, both Ni2+ and Co2+ are shown from a Hill analysis to cooperatively promote foldingof the NiCo riboswitch, with cation selective signatures in Hill cooperativity, Kd affinity, andsaturation kinetics. As a result, these unique signatures could offer the NiCo riboswitch amechanism for discriminating between Ni2+ and Co2+ to optimize gene-regulation efficiency andin vivo management of metal ion cytotoxicity. Finally, detailed free energy landscapes have beenreconstructed from van’t Hoff and Eyring analysis of the temperature dependent equilibrium andkinetic data. The results highlight a complete insensitivity of the first prefolding step (U →TSU↔I → I) to cognate ligand, with both dramatic entropy-enthalpy compensation and cognate
ligand sensitivity effects along the second step (I → TSI↔F → F) for folding the NiCo riboswitch
into biochemically competent shape.

130

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136
Chapter 6
Smaller Molecules Crowd Better: Crowder Size Dependence Revealed by Single-Molecule
FRET Studies and Depletion Force Modeling Analysis

6.1

Abstract
The cell is an extremely crowded environment which is known to have profound impact

on the thermodynamics, functionality, and conformational stability of biomolecules.
Speculations from recent theoretical molecular dynamics studies suggest an intriguing size
dependence to such purely entropic crowding effects, whereby small molecular weight crowders
under constant enthalpy conditions are more effective than larger crowders on a per volume
basis. If experimentally confirmed, this would be profoundly significant, as the cellularcytoplasm is also quite concentrated in smaller molecular weight solutes such as inorganic ions,amino acids, and various metabolites. The challenge is to perform such studies isolating entropic
effects under isoenthalpic conditions. In this work, we present first results from single molecule
FRET spectroscopy (smFRET) on the molecular size-dependent crowding stabilization of asimple RNA tertiary motif (the GAAA tetraloop-tetraloop receptor), indeed providing evidencein support of the surprising notion in the crowding literature that “smaller is better.”Specifically, systematic smFRET studies as a function of crowder solute size reveal that smallermolecules both significantly increase the RNA tertiary folding rate and yet simultaneously
decrease the unfolding rate, predicting strongly size dependent stabilization of RNA tertiary
structures under crowded cellular conditions. The size dependence of these effects has been*This chapter is adapted from: Sung, H.-L.; Sengupta, A.; Nesbitt, D. J. Smaller Molecules Crowd Better:
Crowder Size Dependence Revealed by Single-Molecule FRET Studies and Depletion Force Modeling
Analysis. J. Chem. Phys. 2021, 154, 155101.

137
explored via systematic variation of crowder size over a broad range of molecular weights (90amu to 3000 amu). Furthermore, corresponding temperature dependent studies indicate thesystematic changes in the folding equilibrium to be predominantly entropic in origin, i.e.,
consistent with a fundamental picture of entropic molecular crowding without additional
enthalpic interactions. Most importantly, all trends in the single molecule crowding data can bequantitatively recapitulated by a simple analytic depletion force model, whereby excluded
volume interactions represent the major thermodynamic driving force towards folding. Our study
thus not only provides experimental evidence and theoretical support for small molecule
crowding but also predicts further enhancement of crowding effects for even smaller molecules
on a per volume basis.

6.2

Introduction
RNA plays a crucially important role in multiple cellular processes, with particular

relevance in protein translation and gene regulation pathways.1 Due to the crucial dependence ofbiochemical competence on correct nucleic acid conformation, many studies have focused on
RNA folding,2 with experiments traditionally performed in relatively dilute buffers with typicalsolute concentrations of less than 1% by weight.3 This differs quite dramatically from the typicalintracellular environment, where cytoplasmic mass comprises approximately 20 to 30 % solute.45

Such concentrations of solute result in extremely “crowded” environments that could

significantly alter the thermodynamics, kinetics, and tertiary folding stabilities of small RNA
oligos, which in turn can directly impact biochemical activity.5-7 As a result, the deeper
understanding of such macroscopic crowding effects on the kinetics and thermodynamics ofRNA conformation remains a crucial element to establishing a predictive first principles

138
connection between in vitro experimental results and in vivo observation under physiologicalconditions.
Molecular crowding effects on biomolecular folding in nucleic acid systems have been
demonstrated by many studies.8-13 In most of those crowding studies, the common observation isthat high molecular weight crowders (i.e. polyethylene glycol (PEG) or dextran with molecularweights greater than 1000 amu) enhance thermodynamic stability of the more compact state andtherefore promote nucleic acid folding.8-13 Note that this implicitly assumes zero solute-inducedchange in enthalpic contributions to folding, which would also shift the relative free energies.
The origin of such purely entropic crowding effects is thought to arise from excluded volumeinteractions,6, 14-15 whereby a folded biomolecule takes on a more compact conformation andtherefore allows the rest of the system to (entropically) sample a larger pool of microstates. Froma simple hard sphere perspective, one might think of this additional volume as arising fromexcluded interstitial spaces between the crowder particles. One might therefore naturally
anticipate a characteristic length scale () to exist for a given biomolecular size, that allows it tofit (or not) in the unoccupied interstitial volume. For crowders with a size scale smaller than ,
there would be insufficient room to “hide” the biomolecule, which could translate into more
intense crowding effects. From this perspective, one would predict an asymptotically flat
crowding response above a certain crowder size, but with a rapid increase in crowding effects as
the crowder scale size becomes comparable to that of the biomolecule.
To date, most studies have focused on crowding effects induced by relatively large
molecular weight polymer crowders (e.g. MW > 1000 amu), often referred to as macromolecular
crowding.5-6 By way of contrast, the potential crowding effects caused by lower molecularweight species (e.g. MW < 1000 amu) has remained relatively unexplored, particularly with

139
respect to effects on RNA folding. This fundamental question of whether small molecule
crowders have significant impact on biomolecular structural stabilities remains unsettled,10, 16-18
despite the fact that all species exhibit excluded volume effects regardless of size. Recently,
small molecule crowding (and the size dependence thereof) has been studied in detail bytheoretical simulations of biomolecular folding in polypeptides and nucleic acids,19-23 withadditional size dependent predictions made based on hard sphere models.24-25 As one particularlyinteresting prediction, the stabilization due to small crowders in some of these studies wasdemonstrated to exceed that of higher molecular weight crowders under constant volume fraction
conditions.20-22, 25 Despite these theoretical predictions for small molecule crowding, theexperimental evidence to support these predictions has remained elusive: There has been somework studying small molecules such as TMAO (trimethylamine N-oxide)26 and TFE(trifluoroethanol)27 and which attributes the stabilization effects to crowding. However, thesesolutes also contain strong dipole moments and reactive functional groups, and thus, thebimolecular interaction between these small crowders and protein/nucleic acid polymers can bequite complex, with both enthalpic and entropic contributions to the overall folding
thermodynamics. This in turn makes it challenging to isolate pure entropic crowding from amore generic enthalpic steering toward/away from a specific folded configuration.
In the present work, the crowding effect on RNA tertiary folding is studied by PEG andDME crowders with various molecular weights. PEG is a class of synthetic polymer with tunable
length and well known for its inert biochemical properties. Of particular relevance, PEG has
been shown in previous studies to promote the RNA folding primarily through changes inentropy,11 consistent with a predominantly excluded volume picture of crowding.14-15 Therefore,
with PEG as a crowding agent, we can hope to isolate these entropic crowding interactions from140
the more complex enthalpic contributions such as preferential binding and hydrogen bondformation. To systematically explore potential crowding effects induced by even smaller
crowders, we then turn to 1, 2-dimethoxyethane (DME, MW = 90 amu) as the smallest repeating
unit of PEG, and its higher molecular weight analogs (MW = 134 and 222 amu), motivated by
the structural similarity to PEG (Figure 6.1).28 DME contains a polyether backbone identical to
PEG, which is considered a key reason for its low biochemical interference. Finally, the methoxy
substituted end groups in DME avoid undesired enthalpic hydrogen bonding interactions with thecrowded biomolecules, but also with other crowder molecules in solution, thus minimizing
crowding effects by clusters of poorly defined size.29-31

Figure 6.1 Schematic representation of RNA TL-TLR docking/undocking in the presence of large(PEG) or small (DME) crowders. The RNA sequences color coded in green/red indicate thetetraloop/tetraloop receptor folding motifs.

Single-molecule FRET spectroscopy (smFRET) is utilized to explore the kinetics of RNA
conformational folding as a function of crowding conditions. We exploit the RNA tetralooptetraloop receptor (TL-TLR; Figure 6.1) as a model test system to explore the influence of
crowding, since it is a ubiquitous tertiary binding motif in the 3D folding of many RNA oligos
into biocompetent structures (e.g. ribozymes, riboswitches) and has been extensively

141
characterized in biophysical studies at the single-molecule level.32-34 The TL-TLR RNA
construct is doubly labeled with fluorescent dyes to provide dynamic structural information
through FRET, with a biotin extension to allow tethering of the RNA construct to the coverslip
surface for extended single molecule fluorescence observation. The docking (folding) behavior
of TL-TLR is visualized by monitoring the FRET energy transfer efficiency (EFRET) in real time,
and thus the time-dependent EFRET trajectory contains the information on bothdocking/undocking equilibria and kinetics (Figure 6.2). Most relevantly, by supplementing thesestudies with temperature dependent kinetic and equilibrium measurements, we are able todecompose the free energy change into entropic and enthalpic contributions.33, 35 Knowledge ofthe underlying thermodynamics of crowding allows us to identify the predominantly entropic
effects of PEG/DME molecules on RNA folding and therefore provide additional quantitative
insights/interpretations into crowding phenomena from an excluded volume perspective.
As a natural extension and second major thrust of this paper, we present a simple physicalmodel based on excluded volume/depletion force to account for the size dependent PEG andDME crowding phenomena observed at the single molecule level. In such a model, the purely
entropic depletion force is generated by osmotic pressure differences arising from an uneven
distribution of solute crowders due to excluded volume effects.36-38 Based on a simplified pictureof TL-TLR docking as arising from two RNA motif surfaces drawn into intimate contact, wefind that the size dependence of PEG/DME crowding can be quantitatively well described by
predictions from a depletion force model. Of special relevance, this model predicts small
molecule crowding to be significantly more effective than larger crowders under constantvolume fraction (i.e. % weight) concentrations. The excellent agreement between our
experimental observations and theoretical studies20-22, 25 not only provides direct evidence for142“small molecule crowding” and predictions of crowder size dependence, but also highlights theimportant role of depletion forces in biomolecule folding.37

A

B

C

Figure 6.2 Sample data of single molecule time-dependent EFRET trajectories (left panel) and
EFRET distributions (right panel) under different crowding conditions: (A) no crowder, (B) 7.5
w% PEG 3k, and (C) 7.5 w% DME.

6.3

Experiment6.3.1 RNA construct design and sample preparation
A schematic of the TL-TLR folding mechanism is illustrated in Figure 6.1, where Cy3
and Cy5 indicate the positions of the labelled cyanine dyes and the colored coded sequences
correspond to the tetraloop (green) and the tetraloop receptor (red), respectively. The TL-TLR
construct consists of three nucleic acid oligomers:34 (i) a DNA surface tether strand conjugatedwith biotin, 5’-biotin-CGC ACT CGT CTG AG-3’; (ii) a Cy3 labeled RNA strand, 5’-Cy3-GGC
GAA AGC C-PEG6-CGU GUC GUC CUA AGU CGG C-3’; and (iii) a Cy5 labeled RNA
strand, 5’-Cy5-GCC GAU AUG GAC GAC ACG CCC CUC AGA CGA GUG CG-3’ (all

143purchased from Integrated DNA Technologies, Coralville, IA). Once annealed, the product isthen purified with high-performance liquid chromatography (HPLC) to isolate the full TL-TLR
ternary construct for single molecule studies.
In smFRET experiments, the TL-TLR molecules are immobilized on the coverslip
surface through biotin-streptavidin interactions for prolonged single molecule fluorescenceobservations. The imaging buffer contains: (i) 50 mM hemisodium HEPES buffer (pH 7.5) with
0.1 mM EDTA, (ii) the PCD/PCA/Trolox enzymatic oxygen scavenger system to increase thedye photostability,39 (iii) 20 mM NaCl (for temperature controlled experiments), and (iv) 0 to 10
w% PEG or DME crowder.
6.3.2 Temperature controlled single-molecule FRET spectroscopy
The smFRET experiment is performed with a home-built inverted confocal
microscope:34, 40 The collimated 532 nm pulsed laser is tightly focused by a 1.2 N.A. water
immersion objective onto a single surface-tethered TL-TLR construct. The resulting fluorescentphotons are collected by the same objective, and then sorted by colors (green/red) andpolarizations (horizontal/vertical) before detection by a series of single photon avalanche
photodiodes (APDs). The arrival time of each photon, both wall-clock “macrotime” time (50 ns
precision) and “microtime” (50 ps precision) with respect to the corresponding excitation pulse,
is recorded by the time-correlated single-photon counting (TCSPC) module and stored for later
analysis. For the temperature dependent studies, control is achieved by heating both coverslip
sample and microscope objective at the same time to minimize thermal gradients and maintainthermal equilibrium at the desired absolute temperature and precision (± 0.1 oC). Setup details
for the presently used stage and objective heater can be found in previous work.33, 40

144
6.4

Results

6.4.1 RNA tertiary folding is promoted by PEG and small molecule DME
The TL-TLR binding motif consists of non-canonical hydrogen bond formation and basestacking interactions between a loop and bulge, representing one of the most common
distinguishing features of RNA tertiary structure.33, 41 In the present smFRET study, the dockingof the TL-TLR is visualized by time-dependent EFRET trajectories, sample data from which are
shown in Figure 6.2. The data clearly indicate 2-state toggling behavior of the TL-TLR between
two distinct EFRET values, corresponding to docked (EFRET ~ 0.7) and undocked (EFRET ~ 0.35)
conformations. The docking equilibrium constant Keq is most readily extracted from the ratio of
the total time spent in the docked vs. undocked state. In the absence of crowding solute (Figure.
6.2A), the TL-TLR preferentially remains in the undocked state (Keq = 0.36(5)), while at 7.5 w%
PEG 3k (average molecular weight MWav = 3000 amu, Figure 6.2B), Keq increases by over 4fold (Keq = 1.5(2)). This confirms that crowding by PEG energetically favors the docked state of
TL-TLR, consistent with previous studies indicating PEG promotes biomolecular folding.11 Of
particular relevance to the present work, however, even stronger stabilization of the TL-TLR
tertiary folding motif is observed for the small molecule crowder DME (Figure 6.2C), which
now achieves an additional 3-fold (i.e., for an order of magnitude net) increase in Keq for theexact same 7.5 w% concentration of crowding solutes. In agreement with theoreticalpredictions,20, 25 these results provide first indications for increasingly significant stabilization
effects for RNA tertiary folding with smaller molecular crowders at constant volume fraction.
With these tethered constructs, we can obviously take this crowding analysis one stepfurther. In addition to equilibrium information, the time-dependent EFRET trajectories also report

145
on the forward/reverse kinetics of TL-TLR docking, with the rate constants obtained by analysisof the cumulative distribution functions (CDFs) of dwell times for each state.42-44 As shown in

A

B

C

Figure 6.3 Crowder effects on the TL-TLR docking kinetics. (A) Cumulative distributionfunctions (CDFs) of docked and undocked dwell time well-characterized by single exponential
decays (B) Crowder concentration dependence of rate constants kdock and kundock with overall trends
highlighted in red dashed and green dotted lines, respectively (C) Crowding effects on rate
constants illustrated in unequal free energy shifts in U (undocked), TS (transition) and D (docked)
states. Error bars represent 1σ standard deviation of the mean.

146
the sample data in Figure 6.3A, the individual CDFs clearly exhibit single exponential decay,
with the exponent yielding the first order TL-TLR docking or undocking rate constants (kdock or
kundock). The effects of PEG 3k vs. DME on the rate kinetics of TL-TLR docking/undocking are
explicitly summarized in Figure 6.3B. Both PEG and DME clearly promote formation of the TLTLR tertiary motif, predominantly by a crowding induced enhancement in kdock, but also bycommensurate decrease in kundock. Once again, the results clearly reveal significant differences atconstant w% between the 2 molecular crowding agents, with significantly stronger effects
observed for the smaller (DME) molecular crowder.
These crowding-mediated variations in docking and undocking rate constants for RNA
folding can be parsed within a simplified physical framework of activated complex or transition
state theory (TST)45-46 (Figure 6.3C). From transition state theory, the crowding dependence of
these rate constants can be quantified in terms of the free energy differences between thetransition state (TS) and either the docked or undocked state.33-34 Simply stated, crowding must
shift the free energies of the unfolded state upward (and folded state free energy downward) withrespect to the TS, in order to achieve the observed increase (decrease) in kdock (kundock),
respectively. Moreover, the transition state for RNA folding would be expected to beintermediate in size between the docked (i.e., most compact) and undocked state (i.e., most
expanded). Given that crowding decreases the system entropy by reducing the number ofaccessible microstates, the more compact state is expected to be free energetically favored in a
crowded environment. Since the undocked TL-TLR conformation is less compact than thetransition state, kdock would be predicted to increase under crowded conditions, in essence bylowering the free energy transition state barrier for docking. Conversely, the more compact
folded state experiences a greater crowding-mediated stabilization with respect to the transition

147
state, thus yielding the observed crowding induced decrease in kundock. To summarize, the rate
constant changes induced by PEG 3k and DME are in already in good qualitative agreement withtheoretical predictions of crowding on the folding kinetics. Of particular relevance, the larger
shift for both docking/undocking rate constants with DME vs PEG 3k under constant w%
conditions is consistent with the greater stabilization effects noted from equilibrium analysis,
once again indicating the presence of stronger effects for smaller molecular crowders (i.e., DME
vs PEG 3k).
6.4.2 Predominantly entropic stabilization confirmed by temperature dependence
The thermodynamic origin of PEG and DME crowding can be specified in greater detailby temperature dependent folding measurements, which permit the free energies to be broken
down into enthalpic and entropic contributions. As a first example, we probe the effects ofcrowding on the overall equilibrium Keq as a function of temperature. The free energy change for
TL-TLR docking, ΔG0 (ΔG0 = ΔG0dock – ΔG0undock) can be readily obtained from ΔG0 = -RT
ln[Keq], where R is the gas constant and T is temperature in Kelvin. These free energies can befurther deconstructed into overall entropic (-TΔS0) and enthalpic (ΔH0) contributions by
conventional van’t Hoff analysis at the single molecule level.
ln K eq = −ΔG0dock
RT

=

ΔS0
R

ΔH0

− RT .

(Eq. 6.1)

As demonstrated by sample data in Figure 6.4, a standard van’t Hoff plot of ln[Keq] vs. 1/T
yields excellent straight line fits for each set of crowding conditions, with fitted slopes andintercepts corresponding to (-ΔH0)/R and ΔS0/R, respectively. These lines are parallel within
experimental uncertainty, implying that Δ(ΔHo) ≈ 0 and therefore the overall TL-TLR docking
enthalpies are only minimally perturbed by both PEG 3k and DME molecular crowders. By way
of contrast, the vertical offsets in these linear fits are strongly concentration- and molecular

148
crowder species-dependent, which unambiguously indicate that crowding of the TL-TLR
docking event is predominantly driven by entropy (Δ(-TΔS0) < 0), though to dramaticallydifferent extents for PEG and DME crowders. These results confirm earlier observations that
PEG crowding promotes RNA folding predominantly through entropic stabilization effects, withessentially negligible enthalpic contributions.11, 15, 47 It is worth stressing that the predominanceof entropy on these free energies is entirely consistent with molecular crowding arising from
simple excluded volume (non-enthalpic) interactions,14 which would predict a purely entropic
origin.

A

B

Figure 6.4 Temperature dependence of TL-TLR docking presented in van’t Hoff plots at elevating(A) PEG 3k and (B) DME concentrations. Error bars represent 1σ standard deviation of the mean.

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Quantitative thermodynamic results from the above van’t Hoff analyses are summarizedin Table I, which indicate a strongly exothermic yet entropically penalized folding event. The
exothermicity of RNA folding arises from the non-canonical hydrogen bond formations and basestacking during the docking process33. The standard enthalpy changes (ΔHo) reported in Table I
are indistinguishable for dilute buffer vs. crowded solutions, again reinforcing the evidence forminimum differential enthalpic interactions between RNA with either PEG 3k or DME
molecular solutes. Additionally, reliable predictions of the standard entropy changes (ΔS0) canbe achieved by simply requiring a globally fit exothermicity (Δ(ΔH0) ≈ 0), as summarized in the
final column values for ΔS0. The fact that ΔSo is strongly negative in both the presence andabsence of crowders, can be readily attributed to the presence of more highly organized loop andbulge configurations in the docked state. As more clearly indicated in Table I, however, thisvalue of ΔS0 increases systematically ((ΔS0) > 0) with crowding agents, indicating that dockingof the TL-TLR is promoted by PEG and DME by a reduction in entropic penalty ((-T (ΔS0)) <0) for folding. This conclusion is made more quantitatively by the final column of constrained

ΔH0 (kcal/mol)

ΔS0 (kcal/mol/K)

ΔH0 (kcal/mol)*

No crowder-34.6 (9)-118 (3)-34.5 (5)ΔS0(kcal/mol/K)*-117.7 (17)

PEG 2.5 w%-34.4 (7)-117 (3)-34.5 (5)-116.6 (17)

PEG 5.0 w%-34.8 (20)-116 (8)-34.5 (5)-115.4 (17)

PEG 7.5 w%-34.4 (10)-114 (4)-34.5 (5)-114.1 (17)DME 2.5 w%-34.5 (14)-116 (5)-34.5 (5)-115.6 (17)DME 5.0 w%-34.3 (9)-113 (3)-34.5 (5)-113.5 (17)Table 6.1 Thermodynamic parameters obtained from the van’t Hoff analysis. *from global fit
results.

150
fits to the entropy, which reveals a systematic and indeed approximately linear dependence on
crowder w%/concentration. At least over the accessible dynamic range of 1/T probed, the results
are in excellent agreement with the assertion that the mechanism of free energy stabilization of
RNA tertiary folding events due to PEG and DME is predominantly entropic in nature, again
consistent with a simple picture of molecular crowding without significant impacts due todifferential enthalpies.
6.4.3 Stabilization free energies are greater for smaller molecular crowders
The distribution of solute sizes in cells is exceptionally broad, ranging from simple
atomic ions, to moderately sized molecular metabolites, to larger macromolecules such asproteins and nucleic acids.5 As a result, knowledge of the scaling dependence on crowder size isparticularly crucial for any predictive understanding of cellular crowding. The previous sections
have demonstrated that the effects of both i) polymer PEG 3k and its constituent subunit ii) DME
on the kinetics and thermodynamics of TL-TLR folding are consistent with a simple physicalpicture of entropic crowding. In this next section, we explore the size dependence of suchcrowding phenomena over a wide range of molecular weights (MW), with 6 species between
MW = 90 amu to MW = 3000 amu and as a function of crowder concentration. Moreover, theexperimental conditions have been carefully restricted to a dilute regime where individual
crowder molecules are diffusing independently (i.e., concentrations below which the polymer
chains start to entangle),16 and yet effects are still sufficiently pronounced to unambiguously
reflect size dependence on the crowding species. By convention, we look for changes in theoverall ΔG0 (ΔΔG0 = ΔG0crowded – ΔG0dilute) as a measure of crowding stabilization on the TLTLR tertiary structure, with size dependence of the results summarized in Figure 6.5A.

151
There are several notable features immediately visible in Figure 6.5A. First of all, foreach crowder size, the stabilization free energy increases monotonically with increasing
concentration, with a more nearly linear dependence observed at low molecular weight. Such an
approximately linear dependence on concentration is mainly due to reduction in accessible
volume and is directly proportional to the number density of crowders. We note that such a direct
proportionality between ΔΔG0 and solute concentration is also quite commonly observed inseveral RNA-solute systems with preferential interactions (i.e., nonzero ΔH0).26, 48 For the data at
hand, however, the case of such additional complicating contributions have been excluded byparallelism in the van’t Hoff slopes exhibited in the temperature dependent analyses seen in
Figure 6.4. Secondly, this free energy stabilization monotonically increases as a function of
decreasing crowder size (i.e. ΔΔG0 becomes less negative), indicating the presence of stronger
crowding effects for smaller molecular weight crowders at the same w%. Such an inverse
dependence on crowder size is in excellent qualitative agreement with theoretical predictions
from molecular dynamics simulations.20-22, 25
We can take this crowding analysis further in the context of a simple polymer model.
Specifically, the scaling between PEG radius of gyration, Rg, and molecular weight (MW) inaqueous solution has been experimentally found to be approximately Rg ~ MWν with ν = 0.58.16,
49

The fact that this exponent is higher/faster than simple hard sphere scaling (νHS = 1/3) implies

that larger PEG crowders take up more volume than smaller PEGs under constant w%
concentrations, whereas it is the smaller molecular weight crowders that promote RNA folding
more efficiently, as the above studies have surprisingly revealed. These results highlight theimportant scaling synergy between number density and crowder size in crowding phenomena,
which we will explore in greater detail in the discussion section. Furthermore, this dependence of

152
ΔΔG0 on crowder molecular weight is particularly sensitive in the low MW regime, as evident in
Figure 6.5, with such crowding effects on free energy growing less sensitive to crowder
concentration with increasing PEG molecular weight. Finally, these observations of enhanced
crowding of nucleic acid folding as a function of decreasing molecular weight is one again
qualitatively consistent with several previous theoretical predictions.20-22, 25A

B

Figure 6.5 Crowder size dependence well described by the depletion force model. (A) Crowdingstabilization effects as a function of crowder size at a series of w% concentrations. (B) Schematic
representation of depletion force promoting TL-TLR folding. Error bars represent 1σ standard
deviation of the mean. Solid lines represent fits to the depletion force model (see text for details).

6.5

Discussion
The depletion force and its intimate dependence on excluded volume is one of the mostfundamental interactions in biology, becoming especially important in studies of biomolecularfolding37-38, 50. From a hard sphere perspective, such depletion forces arise from a very simple
guiding principle: solute molecules of a given size (d) cannot intervene between two folding

153
motifs coming into contact when the separation (l) becomes less than or equal to d. This
generates a differential force pushing the two folding motifs together for l  d. A simple
thermodynamic interpretation of this depletion force is that it reflects the osmotic pressure
difference created by an uneven distribution of solutes on all sides of the folding motifs ofinterest. In the limit of a net zero enthalpic differential between solute/biomolecule andsolute/solute interactions, such free energy crowding effects are predicted to be purely entropic,
as indicated by the van’t Hoff plots in Figure 6.4.
In a solution of a single spherical solute species of radius r, the center of a solute is
excluded from the surface of any object by a distance r to avoid overlap. Such a soluteinaccessible region is sometimes known as the depletion zone51, with the volume directly
proportional to the product of the total surface area of the object and the radius of the solute.
Such depletion volume can be reduced by decreasing solvent/solute exposed surface area tomaximize the system entropy. From an osmotic pressure point of view37, 50, when two parallel
plates are placed far apart in the solution, each plate creates a depletion zone of thickness r
equivalent to the solute radius right above the surfaces. As they are brought closer toapproximately < 2r away from each other, excluded volume requires that the space between thetwo plates contain no solute molecules, creating a depletion zone with zero osmotic pressure. For
any nonzero osmotic pressure outside this depletion zone, the two plates will then be pushed into
contact due to imbalance in the force. The net result is a reduction in the depletion zone by
ΔVdepl = 2σr, where σ is the contact surface area. Since the depletion force increases the volume
available for the solute to sample, it entropically favors the contacted vs separated states, forwhich the additional free energy of stabilization can be simply evaluated as ΔΔGdepl0 = -Posm
ΔVdepl, where Posm is the osmotic pressure of the bulk solute37.

154
In the present work, folding of TL-TLR RNA forms a docking interface by bringing two
spatially separate RNA motifs (tetraloop and tetraloop receptor) into contact. Moreover,crowding conditions in this study are chosen such that crowder solute molecules are freely
diffusing in solutions and can be approximated by hydrated spheres with an isotropic monomer
distribution.16 In the framework of a depletion force model, the total reduction in depletion
volume due to TL-TLR folding is therefore ΔVdepl = 2σR, where σ is the contact area between
tetraloop and tetraloop receptor and R is the radius of crowder. For PEG and PEG-like polymer
molecules, this distance R is often approximated by the radius of gyration (Rg)51. Specifically,
there is a well-established empirical scaling relation between molecular weight (MW) and radiusof gyration given by Rg = b(MW)v, with parameters b = 0.23 Å/(g/mol) and v = 0.58
experimentally determined for aqueous PEG solutions49 to recapitulate the MW dependence of
Rg between 60 to 10k amu.16 Note that the close proximity of v  0.58 to 0.50 implies that PEG
behaves in aqueous solution approximately like a diffusive random walk (diff = 1/2), with theν − νdiff  0.08 differential reflecting contributions due to self-avoidance (νself-avoid = 0.6 for a selfavoiding walk polymer model52-53). Furthermore, the fact that v  0.58 considerably exceeds 0.33
indicates that the PEG molecules are highly hydrated and expand in size with increasing MW
faster than predicted from a simple compact hard sphere model (vhard sph = 1/3). Indeed, it isconjectured that this strong hydration sphere is what is responsible for the enthalpic inertness of
PEG with RNA ((H0) = 0)54-55 and thus prospects for primarily entropic ((S0) > 0) excluded
volume contributions to the free energy. Finally, for relatively dilute PEG solutions, we can takeosmotic pressures to be well approximated by Posm = nRT 56, where n is the crowder number
density (in # solute particles/volume). In this limit, the depletion force contribution to the TLTLR folding free energy can be expressed as

155o
ΔΔGdepl= −Posm ΔVdepl= −(𝑛RT)(2σR g )= −(w%

ρRT)(2σ𝑏(𝑀𝑊)𝜈 )𝑀𝑊= −(𝑤%)(2σρ𝑏RT)(𝑀𝑊)𝜈−1
where n =𝑤%
𝑀𝑊(Eq. 6.2)

 is the solute number density required to interconvert between mass density ()and weight percent (w%), the concentration unit most commonly used in crowding studies.11-12
In Eq. 6.2, the solutions are still dilute enough to approximate the mass density to be   1.0(g/cm3) for all crowder conditions reported in the present work.57 With b,  experimentally
determined, Eq (2) represents a simple analytic model for predicting the depletion force
contribution to crowding stabilization free energies, with the active area () as the only freeparameter.
As will become clear from fits to the data in Figure 6.5, Eq. 6.2 does not capture thecomplete story. Specifically, due to residual uncertainties in the experimentally measured ΔH0values, we cannot definitively rule out the possibility of additional small differential interactions
between the TL-TLR construct and PEG and DME crowders. However, since the solute effects
on biomolecular folding free energies are empirically found to exhibit a simple proportionality
between ΔΔG0 and solute concentration26, 48, we can therefore modify Eq. 6.2 by including an
additive linear term in our model to correct for any additional solute induced free energy shifts(G0sol) beyond that from purely entropic crowding, i.e.
o
ΔΔGsol= m(𝑤%).

(Eq. 6.3)

156
In Eq. 6.3, this multiplicative factor (m) can be readily interpreted as the m-value commonly
utilized to characterize the strength of solute interactions per unit concentration26, 48, in units ofkcal/mol/w%. To include all contributions to the PEG crowder interaction, the depletion force
model for the overall differential free energy change ((G0)) is therefore simply expressed as
the sum of the direct solute-RNA interaction free energy and depletion force contributions:oo
ΔΔGo = ΔΔGsol+ ΔΔGdepl= (𝑤%)[(𝑚 − 2σρbRT(MW)𝑣−1 )].

(Eq. 6.4)

From Eq. 6.4, the only molecular weight (MW) dependent contribution to these stabilization freeenergies arises from the depletion force entropies, with a much smaller but finite global
dependence of the solute interaction on w% of crowder. Most importantly, since the exponent ν1 = -0.42 < 0, this simple analytic expression does make the successful prediction ofprogressively stronger stabilization free energy effects for smaller molecular crowders underconstant w% conditions, as theoretically predicted from molecular dynamics simulations.20-22, 25
For further testing this simple analytical model, we have explored crowding of the TLTLR folding interaction for a systematic series of PEG molecular weight values ranging from 90
to 3000 amu with the corresponding experimentally observed differential changes in free energy
plotted versus MW in Figure 6.5A. The experimental data clearly indicate a downward curvaturein G0 as a function of lower molecular weight crowders, in excellent qualitative agreementwith Eq. 6.4. Furthermore, we have repeated these crowding studies over a systematic series of
w% values (2.5% to 10%), which indicate a systematic decrease in the G0 differential freeenergies with increasing w% over the experimentally explored range of 2.5% to 10% for each
MW crowder. In addition, we have performed global least squares fits of Eq. 6.4 to theexperimental results as a function of both w% and molecular weight (MW) of the PEG crowding

157
species. The results of these fits are shown as solid lines in Figure 6.5A and represent aquantitatively accurate characterization of the data over a remarkably wide range of molecular
crowder sizes and concentrations. By globally fitting the depletion force model to the size
dependence data with only two free parameters, σ (contact area of TL-TLR folding) and m(strength of solute interactions), it successfully captures all experimental trends in the MW and
w% dependence of the crowding effect. Finally, the surface area for TL-TLR folding isdetermined from these fit to be σ = 447(30) Å2, which is in excellent agreement with the actual
size of the TL-TLR docking site (~ 500 Å2) estimated from x-ray crystal structural studies.11, 41
Similarly, these same least squares fits also predict the G0sol dependence on w% (“mvalue”) to be m  – 0.081(5) kcal/mol per w%. This is small enough that even at the highest w%
values explored, the least squares fitted m-value would correspond to G0sol = -0.81 kcal/mol(10 w%). This is clearly non-zero and implies a relatively small but non-negligible differential
solute interaction between PEG and TL-TLR, but well within the experimental uncertainties
reported in Table 6.1. By way of establishing a more quantitative context, such small PEG solute
free energy effects on the TL-TLR construct are some 1 to 2 orders of magnitudes lower than for
urea (+4.2 kcal/mol per w%) and TMAO (Trimethylamine N-oxide; -6.4 kcal/mol per w%)26,
two well-studied osmolytes that influence RNA folding. Despite such nonzero solute effects, themodel clear demonstrates that fundamental excluded volume and crowding effects dominate thesize dependent thermodynamic stabilization of the RNA by PEG. In summary, the excellent leastsquares agreement in fits of the experimental data to our theoretical model predictions (Eq. 6.4)
drives home the two key points. Specifically, i) there is a clear molecular size dependence to theeffect of crowding on formation of a ubiquitous RNA tertiary finding motif, and ii) thesecrowding studies confirm long standing theoretical predictions20-22, 25 that under constant w%

158
conditions, smaller molecular weight crowders exert a stronger impact on free energy
stabilization for the folded species.

6.6

Summary and conclusion
The effects of size dependent molecular crowding on the folding of a model RNA tertiary

interaction have been studied in detail at the single molecule level. Crowding by the small
molecule PEG subunit such as dimethoxy ethane (DME) is found to promote TL-TLR docking
more significantly than the much larger macromolecular crowder PEG 3k. Both the observed
kinetic increase in kdock and decrease in kundock with crowder concentration are successfully
predicted from transition state theory,45-46 as well as provides simple physical pictures of thecrowding phenomena. The predominant role of entropy in the free energy stabilization of folding
is revealed by detailed temperature dependent study of the equilibrium constants, which identify
the excluded volume and depletion forces as the primary source of crowding interactions
between RNA and PEG/DME. Our results provide unambiguous evidence for the greater impact
on RNA conformational stability by smaller vs larger molecular crowders under constant w%
concentration conditions, in agreement with theoretical predictions from molecular dynamics
simulations.20-22, 25 The size dependence of these crowding effects on RNA folding has beenfurther investigated by systematic study of crowders over a wide range of molecular weights(MW) and solute concentrations (w%). Of particular importance, these stabilization free energy
effects are found to increase with decreasing crowder MW, indicating such crowding effects to
be increasingly sensitive to crowder size in the low molecular weight regime. The work
highlights the important role that relatively small solutes (e.g., inorganic ions, amino acids, and159
various metabolites) may play in intracellular crowding, whose contributions appear to havebeen largely neglected to date.

6.7

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Devanand, K.; Selser, J. C., Asymptotic behavior and long-range interactions in aqueous
solutions of poly(ethylene oxide). Macromolecules 1991, 24 (22), 5943-5947.

50.

Mitchison, T. J., Colloid Osmotic Parameterization and Measurement of Subcellular
Crowding. Mol. Biol. Cell 2019, 30 (2), 173-180.

51.

Lee, H.-C.; Jiang, H.-R., Directed aggregation of carbon nanotube on curved surfaces bypolymer induced depletion attraction. AIP Adv. 2017, 7 (12), 125228.

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McKenzie, D. S., Polymers and Scaling. Phys. Rep. 1976, 27 (2), 35-88.

163
53.

Pietronero, L., Critical Dimensionality and Exponent of the "True" Self-Avoiding Walk.
Phys. Rev. B 1983, 27 (9), 5887-5889.

54.

Leung, B. O.; Yang, Z.; Wu, S. S. H.; Chou, K. C., Role of Interfacial Water on Protein
Adsorption at Cross-Linked Polyethylene Oxide Interfaces. Langmuir 2012, 28 (13),5724-5728.

55.

Leng, C.; Hung, H.-C.; Sun, S.; Wang, D.; Li, Y.; Jiang, S.; Chen, Z., Probing the Surface
Hydration of Nonfouling Zwitterionic and PEG Materials in Contact with Proteins. ACS
Appl. Mater. Interfaces 2015, 7 (30), 16881-16888.

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Money, N. P., Osmotic Pressure of Aqueous Polyethylene Glycols: Relationship between
Molecular Weight and Vapor Pressure Deficit. Plant Physiol. 1989, 91 (2), 766-769.

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Gonzalez-Tello, P.; Camacho, F.; Blazquez, G., Density and Viscosity of Concentrated
Aqueous Solutions of Polyethylene Glycol. J. Chem. Eng. Data 1994, 39 (3), 611-614.

164
Chapter 7
The Effects of Molecular Crowders on Single Molecule Nucleic Acid Folding: Temperature
Dependent Studies Reveal True Crowding vs. Enthalpic Interactions

7.1

Abstract
Biomolecular folding in cells can be strongly influenced by spatial overlap/excluded

volume interactions (i.e., “crowding”) with intracellular solute. As a result, traditional in vitro
experiments with dilute buffers may not accurately recapitulate biomolecule folding behavior invivo. In order to account for such ubiquitous excluded volume effects, biologically inert
polyethylene glycols (PEG) and polysaccharides (dextran, Ficoll) are often used as in vitro
crowding agents to mimic in vivo crowding conditions, with a common observation that highconcentrations of these polymers stabilize the more compact biomolecule conformation.
However, such an analysis can be distorted by differences in polymer interactions with thefolded vs. unfolded conformers, requiring temperature dependent analysis of thethermodynamics to reliably assess competing enthalpic vs. entropic contributions and thus the
explicit role of excluded volume. In this work, temperature-controlled single molecule
fluorescence resonance energy transfer (smFRET) is used to characterize the thermodynamic
interaction between nucleic acids and common polymer crowders PEG, dextran and Ficoll. The
results reveal that PEG promotes secondary and tertiary nucleic acid folding by simultaneously
increasing the folding rate while decreasing the unfolding rate, with temperature dependentstudies confirming that the source of PEG stabilization is predominantly entropic and consistent*This chapter is adapted from: Sung, H.-L.; Nesbitt, D. J. Effects of Molecular Crowders on Single-Molecule
Nucleic Acid Folding: Temperature-Dependent Studies Reveal True Crowding vs Enthalpic Interactions. J.
Phys. Chem. B 2021, 125, 13147-13157.

165
with a true excluded volume crowding mechanism. By way of contrast, neither dextran nor Ficoll
induce any significant concentration dependent change in nucleic acid folding stability at room
temperature, but instead, stabilization effects gradually appear with temperature increase. Such athermal response indicates that both folding enthalpies as well as entropies are impacted by
dextran and Ficoll. A detailed thermodynamic analysis of the kinetics suggests that, instead oftrue entropic molecular crowding, dextran and Ficoll associate preferentially with the unfolded
vs folded nucleic acid conformer as a result of larger solvent accessible surface area (SASA),
thereby skewing the free energy landscapes through both entropic/enthalpic contributions.

7.2

Introduction
The cell is an extremely crowded environment, with 20% of the mass taken up by variousorganic and biopolymer solutes such as proteins, nucleic acids, and small molecule metabolites.12

This raises the real likelihood that biomolecules in vivo function differently from the in vitro

behavior traditionally observed in biochemical assays under dilute buffer conditions.3-4 Correct
assessment of the impact of each solute species on biomolecular structure and function isextremely challenging to quantify, particularly under such highly concentrated, non-ideal
solution conditions. However, these solutes do share one simplifying contribution in common:
they all take up physical space in solution and therefore impose fundamental steric constraints on
the biomolecule widely known as excluded volume interactions.5-6 Simply stated, the presence ofexcess solute reduces the space available for a specific biomolecule to sample; as a result, thebiomolecule is driven into a more compact configuration to maximize the accessible microstates
for the overall biomolecule + solvent system.3 In other words, excluded volume effects are166
predicted to entropically promote biomolecule folding/compaction, with this critical yet
ubiquitous stabilization mechanism commonly referred to as “molecular crowding”.7-9
Experimentally, the effects of cellular crowding are often studied by adding polymericmacromolecules such as polyethylene glycol (PEG) or polysaccharides such as dextran and
Ficoll into the buffers.9-12 Such polymers have been shown to resist protein adhesion and are
believed to be biologically inert.13-14 They are thus often referred to as “crowders” due to thepossible predominance of these excluded volume (entropic) effects over other (enthalpic)
chemical interactions.15-17 Indeed, in the presence of these crowders, enhanced biomolecularfolding has often been observed, qualitatively consistent with predictions of excluded volume
energetically favoring the more compact state.18 Furthermore, early temperature dependentstudies of dextran stabilized lysozyme folding have revealed that the melting transition
temperatures (Tm) increase predominantly due to entropic interactions with dextran and yet withessentially negligible enthalpic contributions.16 It is this predominance of entropic stabilizationthat is a robust and distinctive feature of the excluded volume mechanism and the resulting
molecular crowding effects. Identification of crowding effects arising solely through entropic
contributions with inert polymers has since been demonstrated for both proteins and nucleic
acids, requiring detailed thermodynamic investigations as a function of variable temperature.16-17,
19-21

In intriguing contrast with these early crowding studies, more recent results havesuggested that both PEG and polysaccharide crowders may also influence the net folding
enthalpies for certain protein systems.22-25 Indeed, it is not particularly surprising that suchmolecules could exhibit differential chemical interactions with folded vs unfolded biomolecules
above and beyond simple excluded volume interactions. These studies highlight the simple fact

167
that chemical interactions can depend significantly on both structure/charge state of thebiomolecule and the presence of specific moieties on the crowding polymer species.19 It is worth
noting that most of these previous thermodynamic studies have focused on folding/unfolding inproteins, with characterization of the corresponding molecular crowding effects with nucleic
acids still very much in its infancy.26-28
To address this informational lacuna, we explore herein the effects of the most commonlyused polymeric molecular crowders (i.e., PEG, dextran, and Ficoll) on both secondary andtertiary structures of nucleic acid constructs by temperature-controlled single molecule FRET

Figure 7.1 Sample smFRET experiment data. (A) Cartoon depiction of DNA hairpin secondary
structure folding and (B) the resulting time-resolved single-molecule fluorescent signal from thedonor, Cy3 (green) and acceptor, Cy5 (red). (C) Sample time-dependent EFRET trajectories (blue)
and the simulated time trace by the simple thresholding method (orange); (D) The corresponding
dwell time distribution functions of the folded and unfolded conformations with (from top tobottom) 0 w% crowder, 7.5 w% dextran, and 7.5 w% PEG. Data are fit to a single exponential
decay function to obtain the rate constants kfold/kunfold, with uncertainties evaluated from the fits.

168
spectroscopy (smFRET).29-30 In this work, the folding/unfolding equilibria and kinetics are
revealed at the single molecule level, with deconstruction of free energies into enthalpic andentropic components extracted from temperature-dependent crowding studies. The studies indeed
reveal PEG stabilization of nucleic acid folded structures to be predominantly entropic,
consistent with the simple picture of pure crowding dynamics originating from excluded volume
effects.16-17 More surprisingly, however, we find that the commonly used polysaccharide
crowders dextran and Ficoll do not significantly impact either folding/unfolding kinetics orthermodynamic stability of nucleic acids, at least at room temperature. Interestingly, however,temperature dependent studies reveal this lack of crowding impact to be due to accidental
cancellation between folding enthalpy (H) and entropy (-TS) contributions at room
temperature, where additional changes in the enthalpy result from the preferential binding of thepolysaccharide molecules to the more solvent exposed unfolded conformation of the nucleic
acid.

7.3

Experiment7.3.1 Nucleic acid constructs and sample preparation
In order to study molecular crowding interaction on nucleic acids as a function of
secondary vs. tertiary structure, we exploit a simple DNA hairpin (Figure 7.1) and the ubiquitous
RNA tetraloop-tetraloop receptor tertiary folding domain (TL-TLR, Figure 7.2) as model
systems, respectively. The DNA hairpin (with a 7 complimentary base pair stem and a 40 dA
linker, see Figure 7.1A) is doubly dye-labeled (Cy3, Cy5), biotinylated for binding to a cover

169
slip surface, purchased in HPLC purified form (Integrated DNA technologies, Coralville, IA),and used as is.31-32 The ternary TL-TLR construct comprises three smaller oligonucleotides, eachsingly-labeled with Cy3, Cy5, or biotin (Integrated DNA technologies, Coralville, IA), as
described in detail elsewhere.33 The full ternary construct is then prepared by heat-annealing thethree oligomers together, followed by purification via high-performance liquid chromatography(HPLC).

Figure 7.2 Sample smFRET experiment data. (A) Cartoon depiction of TL-TLR tertiary structure
folding and (B) the resulting time-resolved single-molecule fluorescent signal from the donor, Cy3(green) and acceptor, Cy5 (red). (C) Sample time-dependent EFRET trajectories (blue) and thesimulated time trace by the simple thresholding method (orange); (D) The corresponding dwell
time distribution functions of the folded and unfolded conformations with (from top to bottom) 0
w% crowder, 7.5 w% dextran, and 7.5 w% PEG. Data are fit to a single exponential decay function
to obtain the rate constants kfold/kunfold, with uncertainties evaluated from the fits.

170
The smFRET sample preparation is achieved by first coating the surface of a standard
glass coverslip with an excess bovine serum albumin (BSA) and biotinylated BSA mixture,
followed by incubation with streptavidin solution to generate a streptavidin-decorated surface
with suitable surface densities. The resulting secondary and tertiary nucleic acid constructs arethen immobilized on the surface of the coverslip through the highly stable biotin-streptavidin
interactions, which permits prolonged observation of the folding/unfolding kinetics under single
molecule conditions over several minutes to fractions of an hour. The smFRET imaging bufferconsists of (i) 50 mM HEPES-KOH buffer (pH = 7.5), (ii) NaCl to provide backgroundmonovalent cation concentrations of [M+] = 100 or 150 mM for hairpin or TL-TLR construct,
respectively, (iii) an enzymatic oxygen scavenger cocktail (PCD/PCA/Trolox) to increase
fluorophore photostability,34 and (iv) polymeric crowders PEG 6k, dextran 6k (MW = 6,000amu), or Ficoll PM70 (MW = 70,000 amu), to achieve the desired concentration conditions.

7.3.2 Single-Molecule FRET spectroscopy and temperature control
The smFRET experiment in this work is performed with a home-built confocal
microscope system,35 based on a pulsed 532 nm Nd:YAG laser, collimated and directed onto thesample through an inverted confocal microscope. The beam is tightly focused into a diffraction
limited spot by a 1.2 N.A. water immersion objective, achieving /(2NA) ≈ 220 nm spatial
resolution and allowing observation of one fluorophore-labeled construct at a time. The resulting
emitted signal fluorescence is then collected through the same objective, with photons split into
four different channels corresponding to red vs. green, horizontal vs. vertical polarizations before
detection on four separate avalanche photon diodes (APD). For each detected photon, four bits of
information: color, polarization, wall-clock time (in 50 ns bins), and microtime (with respect to171the laser pulse in 50 ps resolution) are recorded with fast time to amplitude conversion and/or
time-correlated single-photon counting modules. In this work, we average over polarization
effects by simply grouping all green (donor Cy3) and red (acceptor Cy5) photons to calculate
FRET efficiency (EFRET) as a function of time and thereby obtain the resulting EFRET trajectories.
To achieve precise temperature control, the sample and the microscope objective areheated simultaneously to minimize thermal gradients.36-37 Specifically, the sample holder ismounted to a thermal stage (Instec, Boulder, CO) which regulates the sample temperature by
servo loop controlled heating and cooling. At the same time, the objective is heated by acommercially available resistive collar (Bioptechs, Butler, PA). Prior to each experiment, a 15
min incubation time is allowed to achieve steady sample temperature (± 0.1 ℃).

7.3.3 Single molecule FRET data analysis
We calculate the background and cross-talk corrected FRET energy transfer efficiency
EFRET (EFRET = IA / (ID + IA)) at 10 ms bin time resolution to generate the time dependent EFRET
trajectories. Due to widely separated EFRET values for folded (high EFRET) and unfolded (lowEFRET) conformations (Figure 7.1C and 7.2C), a simple thresholding routine is adopted todetermine the folding/unfolding states as well as the corresponding dwell time distributions.35, 38
The folding equilibrium constant Keq can be readily obtained by the ratios of total dwell times forthe folded and unfolded states. Furthermore, our kinetic analysis is achieved by generating
cumulative distribution functions of the dwell times for each state (see Figure 7.1D and 7.2D for
sample data). For both constructs, the resulting folded/unfolded dwell time distributions P(t) are
well fit to single exponential decay functions to extract rate constants kunfold/kfold, respectively,

172
confirming that the folding/unfolding processes can be satisfactorily characterized by first orderkinetics.39

Figure 7.3 Crowder effects on DNA hairpin folding at constant room temperature (21 ℃).
Crowder concentration dependence of (A) Keq, (B) kfold, and (C) kunfold. Error bars represent
standard deviation of the mean (N = 3). Data are fit to a single exponential function based on theempirical observation of solute effects on the free energy change upon folding (see text for moredetails).

7.4

Results and analysis

7.4.1 Crowder effects on the DNA hairpin secondary folding kinetics

173
Folding of the 7-base pair DNA hairpin involves formation of secondary double helix
structure essential for nucleic acid function. Its unimolecular design simplicity and easily tunable
folding/unfolding rates make this an ideal model system for exploring nucleic acid secondary
folding through single-molecule kinetic studies (Figure 7.1A).38, 40-41 Herein, we explore theeffects of three polymer crowders widely used in crowding studies: PEG, dextran, and Ficoll.
These species have been consistently shown to stabilize the folded conformation of
biomolecules,9-12 primarily proteins, although the thermodynamic origin of this stabilization still
remains debatable and probably structure-dependent.19
In the absence of crowders, the secondary folding equilibria of the DNA hairpin construct
are adjusted by NaCl in the buffer to achieve Keq ≈ 1 conditions (at room temperature 21.0 ± 0.2℃), in order to permit maximum dynamic range in Keq for shifts in either the folded or
unfolded directions (Figure 7.1). In the presence of PEG (MW = 6,000 amu), the folding
equilibrium Keq is greatly enhanced, with a nearly 20-fold increase at the maximal PEG
concentrations (10% by weight, or 10 w%) in this study (Figure 7.3A). Conversely, both
polysaccharide crowders clearly exhibit much smaller effects, with only a 20% and 50% increasein Keq for 10 w% dextran (MW = 6,000 amu) and Ficoll (MW = 70,000 amu), respectively.
Furthermore, complementary kinetic information on folding/unfolding rate constants can beobtained by dwell time analysis of the single molecule EFRET trajectories (Figure 7.1C and 7.1D).
As clearly evident in Figure 7.3, PEG promotes the DNA hairpin folding by simultaneously
increasing kfold and decreasing kunfold. Indeed, this effect is particularly significant for kfold, which
exhibits an order of magnitude increase with 10 w% PEG, with a relatively smaller but still quite
noticeable 2-fold reduction observed for kunfold. By way of contrast, similar w% concentrations of

174
the polysaccharide dextran and Ficoll increase kfold, by a relatively small amount (< 60%), with
only negligible effects on kunfold (< 10%) within experimental uncertainty.

Figure 7.4 Crowder effects on RNA TL-TLR folding at constant room temperature (21 ℃).
Crowder concentration dependence of (A) Keq, (B) kfold and (C) kunfold. Error bars represent
standard deviation of the mean (N = 3). Data are fit to a single exponential function based on theempirical observation of solute effects on the free energy change upon folding (see text for details).

7.4.2 Crowder effects on the RNA TL-TLR tertiary folding kinetics
TL-TLR is a ubiquitous folding element that is widely found in RNA tertiary structures(Figure 7.2A).42 It has been extensively studied at the single molecule level33 and its

175
kinetic/thermodynamic responses to PEG are found to be consistent with crowding effects
reported in previous studies.17, 43 Again by way of contrast, the potential crowding effects ofdextran and Ficoll on such a common tertiary RNA folding motif have remained largely
unexplored.
As a function of increasing concentration, PEG significantly promotes TL-TLR folding,with a more than 6-fold increase in Keq at 10 w%, whereas dextran and Ficoll induce only muchsmaller increases in Keq (< 50%, Figure 7.4A), very much consistent with the DNA hairpin
results. Furthermore, kinetic analysis of the smFRET trajectories indicates kfold for the TL-TLR
to increase exponentially with PEG concentration, but remain surprisingly constant (< 20%) in
response to dextran and Ficoll (Figure 7.3B). Interestingly, kunfold for the TL-TLR construct isreduced comparably by all three crowders (Figure 7.3C), although the impact of PEG crowding
is still the largest. It is also worth noting that the putative crowding dependences of Keq andkfold/kunfod are well-fit (dashed lines in Figure 7.3 and 7.4) to exponential growth/decay functions,which would be entirely consistent with empirically observed linear relationships between
folding free energy changes (∆∆G) and solute concentration.44-45 Specifically, the strength of thesolute interaction is often characterized by the so-called m-value,46-48 which corresponds toexponents in exponential growth/decay fits of the concentration-dependent Keq in Figure 7.3A
and 7.4A. In the interest of completeness, the corresponding m-values of the crowder-TL-TLR
interaction can be least squares fitted and found to be -0.115(6), -0.015(2) and -0.023(4) kcal
mol-1 w%-1 for PEG, dextran and Ficoll, respectively. The m-value from PEG concentration
dependence is therefore > 5 times larger than dextran/Ficoll, again highlighting the fact that the
TL-TLR folding free energy is much more sensitive to PEG crowding. A similar crowder

176
concentration dependence is also observed for the DNA hairpin, with m-values for PEG, dextran
and Ficoll determined to be -0.141(8), -0.005(6) and -0.027(4) kcal mol-1 w%-1, respectively.
Our results indicate that PEG promotes both nucleic acid secondary and tertiary foldingby simultaneously increasing kfold and decreasing kunfold. However, the polysaccharide crowders,
dextran and Ficoll show little to no effect on both nucleic acid folding equilibria and kinetics, i.e.
corresponding to G  0. This is already substantially different from results of several previous
protein folding studies, where the prominent stabilization effects were observed and often
attributed to crowding.5 It is worth noting that the above differential results for the impact ofdextran or Ficoll on nucleic acid folding could reflect two quite different scenarios. It could bethat there is vanishingly small differential interaction enthalpy (H0  0) between the solutes
and the folded or unfolded biomolecule, in which case the observed G0  0 would translate
into S0  0 and therefore no entropic crowding. However, G0  0 could also reflect thecoincidental balance between competing enthalpic and entropic contributions at a single
temperature. Thus, an unambiguous determination of whether dextran and Ficoll have only
minimal differential interactions with our folded/unfolded nucleic acid constructs requires
additional van’t Hoff and Arrhenius investigation of the temperature dependent equilibrium andkinetic behavior, as described below.
7.4.3 Crowding effects on DNA secondary structure folding thermodynamics
Conventional modelling of “pure” molecular crowding dynamics based on hard sphere excluded
volume considerations explicitly ignores any chemical interactions between the crowder and thecrowded species. As a result, such crowding dynamics automatically satisfy (H0)  0 (where

177

Figure 7.5 van’t Hoff plot for the temperature dependent Keq of the DNA hairpin construct atconstant crowder concentrations (0 or 7.5 w%). Least squares fits of the data to Eq. 7.1 yieldchanges in overall enthalpies (∆H0) and entropies (∆S0).
the second  reflects the differential presence/absence of crowder) and should ideally contributeonly entropically (S0 > 0) to the overall folding free energy.5, 17, 19 Herein we explore thetemperature dependent response of nucleic acid folding to identify the thermodynamics of thesolute-biomolecule crowder interactions. Specifically, van’t Hoff analysis allows deconstructionof the folding free energies into entropy and enthalpy components via:
∆G0

∆H0 1

∆S0

ln(K eq ) = − RT = − R T + R .

Eq. 7.1

From a standard ln(Keq) vs 1/T van’t Hoff plot (e.g., see Figure 7.5), the slope and intercept
permit independent quantitation of enthalpic (-∆H0/R) and entropic (∆S0/R) changes uponfolding, respectively, which can be studied in the absence/presence of crowding agents.
In the absence of crowders, the DNA hairpin becomes less stable and unfolds withincreasing temperature, consistent with temperature-induced melting/denaturation routinely
observed for nucleic acid secondary structure.49 Moreover, the linear van’t Hoff plot reveals a178

Figure 7.6 Eyring plot for the temperature dependent (A) kfold and (B) kunfold of the DNA hairpin
construct at constant crowder concentrations (0 or 7.5 w%). Least squares fits of the data to Eq.
7.2 yield forward/reverse activation enthalpies (∆H‡) and entropies (∆S‡) for kfold/kunfold.
positive slope and a negative intercept (Figure 7.5), corresponding to negative folding enthalpy(∆H0 < 0) and entropy (∆S0 < 0) changes, respectively. Such free energy behavior agrees withthe common physical picture of folding where biomolecules are enthalpically driven into themore order folded conformation.33, 50 The presence of PEG vertically translates the linear fit
upward with respect to zero-crowder conditions, suggesting a decrease in entropic penalty (∆∆S0> 0) with essentially unchanged enthalpic gain (∆∆H0 ≈ 0). Such predominantly entropic
stabilization is of course consistent with crowding effects resulting from excluded volume.5, 17, 19
By way of contrast, dextran and Ficoll clearly reveal a more complex temperature dependent

179

Table 7.1 Thermodynamic parameters of DNA hairpin folding obtained from van’t Hoff andEyring analyses. Asterisk (*) indicates results from global fits assuming a common slope (i.e.,
enthalpy change) between no crowder and 7.5 w% PEG data.

behavior, with a decrease in the slopes (∆∆H0 > 0) and increase in the intercepts (∆∆S0 > 0).
Such non-zero enthalpic contributions clearly signal additional solute-specific chemicalinteractions, as well as changes in these interactions as a function of crowding environment.
In addition to these equilibrium results for Keq, the folding rate constants kfold and kunfold
also depend on temperature and contain equally valuable thermodynamic information. For
secondary structure in the DNA hairpin, the data reveal a dramatic increase in both kfold andkunfold rate constants at elevated temperature (see Figure 7.6), signaling a significantly
endothermic approach to the transition state from both folded/unfolded sides of the barrier.
Based on results from other single molecule studies,51 such an enthalpic penalty likely arises
from competition between Coulomb repulsion of the negatively charged DNA strands and thelack of complete hydrogen bond formation in the transition state. The corresponding entropychanges can be obtained from the more sophisticated Eyring analysis of the temperaturedependent kfold/kunfold from the transition state expression:52

180∆𝐻 ‡ 1∆𝑆 ‡ln(𝑘) = − 𝑅 𝑇 + 𝑅 + ln 𝜈,

Eq. 7.2

where 𝜈 represents the attempt frequency sampling the free energy barrier along the folding
coordinate. From such a standard Eyring plot of lnk vs 1/T (see Figure 7.6), the slopes andintercepts for lnkfold or lnkunfold correspond to the activation enthalpy (-ΔH‡/R) and entropy(∆S‡/R + ln𝜈) from either the folded (F) or the unfolded (U) state, respectively. Since ΔS‡
depends only weakly (logarithmically) on 𝜈, it suffices in this work to simply estimate 𝜈 as a low
frequency skeletal vibration with 𝜈 = 1013 s-1.29, 53 However, it is also worth noting that any
reported changes in the activation entropy (i.e., ΔΔS‡) are rigorously independent of this estimate
for 𝜈.
For the DNA hairpin, the presence or absence of PEG (red vs blue solid line, Figure 7.6)
does not change the slopes in plots of both kfold and kunfold., with vertical shifts again signalingthat PEG promotes secondary nucleic acid folding predominantly through “pure” crowding (i.e.,
entropic) effects. Furthermore, both the magnitude and sign of these uniform verticaldisplacements in lnkfold vs. lnkunfold are consistent with the PEG-dependent enhancement offolding stability observed at room temperature (Figure 7.2B and 7.2C). The polysaccharide
crowders dextran and Ficoll, on the other hand, exhibit more complex behaviors, with the data
now revealing significant changes in both slopes (H‡ > 0) and intercepts (S‡ > 0) in the
Eyring plots for kfold. Interestingly, however, these slope differences are much less evident for
the unfolding step, which is consistent with polysaccharide solute effects primarily influencing
the approach to the transition state from the unfolded conformation. Thermodynamic values(H0, S0, H‡, S‡) extracted from these plots for both PEG and polysaccharide solutes arequantitatively summarized in Table 7.1.

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Figure 7.7 van’t Hoff plot for the temperature dependent Keq of the RNA -TL-TLR construct atconstant crowder concentrations (0 or 7.5 w%). Least squares fits of the data to Eq. 7.1 yieldchanges in overall enthalpies (∆H0) and entropies (∆S0).

7.4.4 Crowding effects on RNA TL-TLR tertiary folding thermodynamics
As for many compact nucleic acid conformations, the TL-TLR tertiary binding motif
weakens and unfolds with increasing temperature,33 with the positive (negative) slope (intercept)
in the van’t Hoff plot (see Figure 7.7) indicating folding to be exothermically favored (∆H0 < 0)and entropically penalized (∆S0 < 0). Once again, the presence of PEG solute at high w% shifts
the linear fits vertically upward without appreciable change in slope (∆∆H0 ≈ 0), whichcorresponds to a positive change in intercept (∆∆S0 > 0). In other words, PEG entropicallystabilizes the TL-TLR tertiary structure formation, consistent with a conventional excluded
volume mechanism for molecular crowding.17, 43 By way of contrast, the putative polysaccharide“crowders” dextran and Ficoll exhibit decreased slopes and increased intercepts in the van’t Hoffplots, indicating significant solute-dependent differential enthalpic interactions, in addition topossible entropic crowding corresponding to a less exothermic (∆∆H0 > 0) but more entropicallyfavored (∆∆S0 > 0) folding into the TL-TLR tertiary structure. It is particularly noteworthy that

182
the absence of polysaccharide “crowding” effects observed near room temperature for both the
DNA hairpin and RNA TL-TLR constructs (Figure 7.3 and 7.4) is simply due to a fortuitous
balance between entropic and enthalpic contributions. Indeed, the data in Figure 7.7 reveal thatdextran and Ficoll at 7.5 w% can and do efficiently stabilize nucleic acid folding at higher (andpresumably destabilize at lower) temperatures, but only via a temperature dependent imbalancein enthalpic and entropic contributions to the free energies. Such stabilization effects can be quite
comparable to (and indeed easily mistaken for) pure entropic crowding if the temperaturedependence is not also carefully explored and taken into account.

Figure 7.8 Eyring plots for the temperature dependent (A) kfold and (B) kunfold of the RNA TL-TLR
construct at constant crowder concentrations (0 or 7.5 w%). Least squares fits of the data to Eq.
7.2 yield forward/reverse activation enthalpies (∆H‡) and entropies (∆S‡) for kfold/kunfold.

183
The temperature dependent kinetic data for kfold and kunfold again reiterate the predominantly
entropic role of PEG stabilization on RNA tertiary folding, as indicated by parallel vertical shifts
in the Eyring plots (Figure 7.8). Again, by way of contrast, dextran and Ficoll polysaccharides
both show quite strong enthalpic and entropic effects on kfold. Indeed, the Eyring plot slopes in
Figure 7.8A for tertiary structure folding even change sign (from plus to minus), indicating thatthe presence of dextran and Ficoll transform a normally exothermic pre-folding approach into asignificantly endothermic approach to the transition state (ΔH‡ > 0). Conversely, the temperaturedependence of kunfold (Figure 7.8B) for the TL-TLR construct is much less dramatic. Similar to
the effects seen in kunfold for secondary DNA hairpin structure, the presence/absence ofpolysaccharide solute for the TL-TLR generates much more subtle changes in the unfolding
endothermicity during the U to TS transition. The list of parameters obtained fromkinetic/thermodynamic analysis of the PEG vs polysaccharide solute dependence for tertiary TLTLR folding/unfolding are summarized in Table 7.2.

Table 7.2 Thermodynamic parameters of RNA TL-TLR folding obtained from van’t Hoff andEyring analyses. Asterisk (*) indicates results from global fits assuming a common slope (i.e.,
enthalpy change) between no crowder and 7.5 w% PEG data.

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7.5

Discussion

7.5.1 Crowder effects on nucleic acid folding kinetics
Crowders (or any solute) take up physical space in solution, reducing the volume and thecorresponding number of microstates available for a nominally crowded biomolecule to sample.3
For the same crowder/solute configuration, folded biomolecules (VF) can generally sample more
space than a non-compact unfolded (VU) structure, where VU > VF;2 thus, the presence of solute
crowders entropically favors the more compact state of biomolecule.21 Furthermore, if thetransition state is considered as a partially folded conformation, we can further expect that VU >VTS > VF. The crowding effect will favor the more compact TS state over U, thereby entropicallylowering the free energy barrier for the U to TS transition and consequently increasing kfold.43
Similarly, kunfold would be expected to decrease with added solute due to the compact F state
being more efficiently stabilized by crowding with respect to the TS. In summary, molecular
crowding is predicted to promote folding entropically by simultaneously increasing kfold anddecreasing kunfold, which is entirely consistent with the PEG data for exponential enhancement of
secondary and tertiary structure formation in nucleic acids (i.e., see Figure 7.3 and 7.4). By way
of contrast, polysaccharides dextran and Ficoll at similar w% concentrations exhibit only quitemodest effects on the folding/unfolding rate constants and equilibrium constants (Keq =kfold/kunfold) for both the DNA hairpin and the RNA TL-TLR at room temperature. With respect
to impact on nucleic acid folding/unfolding dynamics, the single molecule equilibrium/kinetic
data reported herein indicate significant differential enthalpic interactions (H  0) between theputative polysaccharide “crowders” dextran and Ficoll with nucleic acid constructs. We would
argue that such behavior is inconsistent with conventional excluded volume model predictions,and thus dextran and Ficoll polysaccharides do not represent initiators of molecular crowding

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Figure 7.9 Folding free energy landscapes of the DNA hairpin construct. (A) Enthalpic and (B)entropic contributions along the folding coordinate, with the relative enthalpy/entropy of theunfold state, U conventionally referenced to zero. The corresponding (C) enthalpic and (D)entropic changes by the three crowders at 7.5 w%. Note that entropic contributions (-T∆S) to thefree energies are estimated for room temperature conditions (21.0 ℃).

phenomena for nucleic acids. Of course, this assessment depends on the nature of chemicalinteraction with the biomolecule being crowded. We cannot rule out the possibility that dextran
and Ficoll have negligible differential chemical interactions between folded vs. unfolded proteins
and therefore may act as truly entropic crowding agents.16
7.5.2 Predominantly entropic effects of PEG are consistent with pure crowding
Despite the fact that excluded volume effects are ubiquitous for all solutes, the resulting
crowding can be buried in or dominated by additional solute- and/or biomolecule-specificenthalpic chemical interactions. The chemically and biologically inactive polymer PEG provides
a valuable opportunity for us to identify and isolate pure crowding effects from these other more

186

Figure 7.10 Folding free energy landscapes of the RNA TL-TLR construct. (A) Enthalpic and (B)entropic contributions along the folding coordinate with the relative enthalpy/entropy of the unfold
state, U conventionally referenced to zero. The corresponding (C) enthalpic and (D) entropicchanges by the three crowders at 7.5 w%. Note that entropic contributions (-T∆S) to the freeenergies are estimated for room temperature conditions (21.0 ℃).

complex solute-biomolecule interactions. The literature on this important topic is still evolving.
To date, many studies have used PEG as the crowding agent and simply report the additional
stabilization to be the result of crowding.10, 40, 54-55 However, PEG has also been found to perturb
folding enthalpies of some protein systems, implying the presence of solute-specific chemicalinteractions. 24-25 This differs yet again with multiple other studies on proteins21 and nucleic
acids17, 20 claiming the effects of PEG to be primarily entropic and therefore reflect true crowding
phenomena. Such a discrepancy would seem to indicate that crowding by PEG may depend
significantly on the structure and chemical properties of the crowded biomolecules. This
provides us with additional motivation for detailed characterization of the thermodynamic
crowding effects of PEG, as applied to both secondary and tertiary structures of nucleic acids.

187
From the temperature dependent studies reported herein (Figure 7.5 to 7.8), we are able
to deconstruct the folding free energy landscape into enthalpic and entropic contributions.
Vertical shifts in the van’t Hoff plots confirm that PEG only changes the folding entropy (S0> 0) and leaves the enthalpy unchanged (H0  0) for both nucleic acid secondary (Figure 7.5)
and tertiary (Figure 7.7) folding. The predominantly entropic stabilization effects of PEG are
consistent with crowding originating from excluded volume interactions. Furthermore, fromtransition state analysis, the parallel nature of the Eyring plots for both kfold and kunfold again
signal the predominantly entropic origins of PEG stabilization effects (Figure 7.6 and 7.8). It is
worth noting that our ability to infer small enthalpic changes in these thermodynamic studies islimited by experimental uncertainties. We therefore cannot completely rule out the possibility ofsmall interactions with PEG that could either weakly stabilize or destabilize the nucleic acid.
Nevertheless, from previous work on RNA TL-TLR folding, the magnitude of such entropic
effects17 and their dependence on PEG polymer size43 were successfully predicted by hard spheremodels based purely on excluded volume interactions. Strengthened by additional confirming
evidence for both nucleic acid secondary and tertiary folding from the temperature dependent
kinetic studies, the data strongly suggest that the PEG crowding of nucleic acids can be largely
attributed to true entropic crowding effects.
7.5.3 Enthalpic/entropic effects with polysaccharides suggest preferential binding
Polysaccharide crowders such as dextran and Ficoll are also commonly used in crowding
studies, but primarily with proteins.12 One early study found that lysozyme stability isentropically enhanced by the presence of dextran,16 from which it was inferred that the effects onprotein folding arose primarily from crowding. However, some recent studies have pointed out
the additional presence of enthalpic interactions between dextran and Ficoll with certain protein

188
structures.22-23, 56-57 This raises obvious questions for the role of such polysaccharides in thecrowding of nucleic acid folding, which has received much less attention and remains poorly
understood. This further motivates us to characterize the thermodynamic free energies,
enthalpies, and entropies between model secondary and tertiary nucleic acid structure constructs
and polysaccharides widely used in protein crowding studies, i.e., dextran and Ficoll.
For both secondary (DNA hairpin) and tertiary (RNA TL-TLR) nucleic acid structures,
polysaccharide crowders dextran and Ficoll are found to significantly change enthalpic as well as
the entropic contributions to the folding free energy landscape. From standard van’t Hoffanalysis (Figure 7.5 and 7.7), an increase in dextran and Ficoll concentration (0 to 7.5 w%)
decreases the slope, indicating a reduction in overall exothermicity for folding (∆∆H0 > 0), butwith a corresponding increase in the intercept reflecting a reduction in entropic penalty (∆∆S0 >0). Moreover, from temperature dependent analysis (Figure 7.6 and 7.8), we find the effects ofthese polysaccharides on the folding kinetics to be primarily visible in the folding rate constantkfold. Specifically, dextran and Ficoll are found to increase the folding activation enthalpy (ΔΔH‡> 0), as well as the activation entropy (ΔΔS‡ > 0) during the approach from U to TS.
The overall folding free energy landscapes and the corresponding crowder-inducedchanges in the folding/activation enthalpies/entropies are conveniently summarized in Figure 7.9
and 10 for the secondary (DNA hairpin) and tertiary (RNA TL-TLR) structures, respectively. It
is worth noting that along the folding coordinate, the enthalpic penalty (ΔΔH > 0) is significant
but competing with (and indeed, at room temperature, completely compensated by) a
counterbalancing entropic stabilization (∆(-T∆S) < 0) (Figure 7.9A and 7.9B; Figure 7.10A and
7.10B), leading to a greatly reduced sensitivity in the folding kinetics and equilibrium to bothdextran and Ficoll, at least at room temperature where all three Eyring and van’t Hoff curves

189

Figure 7.11 Schematic model for the effects of (A) PEG or (B) dextran on folding of the RNA
TL-TLR, highlighting the differential entropic (S > 0) and enthalpic contributions (H > 0)due to binding of polysaccharide to the greater solvent accessible surface area (SASA) of theunfolded nucleic acid.

intersect in a single point. Such compensating tradeoffs in free energy between enthalpy andentropy58 are of course quite ubiquitous in biophysics, but may provide a partial explanation forthe mislabeling of polysaccharides as crowding agents for nucleic acids. In the present case, apotentially better qualitative interpretation for anticorrelation between enthalpic and entropicchanges may be that the more enthalpically stabilized system is also more restrictive with respect
to microstate-sampling: e.g. enthalpic binding of solute to the biomolecule diminishes the overall
translational entropy of the solution system.59
Based on the thermodynamic evidence, we propose a simple binding model to accountqualitatively for the simultaneous enthalpic destabilization (∆∆H > 0) and entropic stabilization(∆(-T∆S) < 0) effects of polysaccharides upon nucleic acid folding (Figure 7.11). First of all, we

190
expect the abundance of hydroxyl groups on the polysaccharide molecules to be overall
attractive to the nucleic acid, in order to have significant impacts on the folding free energy. As aresult, the polysaccharide solute will tend to accumulate on the accessible surface area of nucleic
acid, enthalpically stabilizing the system at the cost of entropy primarily in the translational
degrees of freedom of the bound polysaccharide and solvent reorganization. Upon folding, thissolvent accessible surface area (SASA) of the nucleic acid decreases, requiring partial expulsionof the associated polysaccharide molecules. The net effect will be a less enthalpically stabilized
folded structure (∆∆H0 > 0) with entropic gain (∆(-T∆S0) < 0) from freeing the polysaccharide
molecules, much as reflected in the thermodynamic results summarized in Figure 7.9 and 7.10.
We can take this preferential binding model one step further to interpret the influence ofpolysaccharide crowders on the folding kinetics. Specifically, the transition state for TL-TLR
folding has been previously characterized29 as a tetraloop and tetraloop receptor in close
proximity, but with unformed yet “pre-aligned” hydrogen bonds between the TL and TLR. Thisis clearly supported by the fact that the majority of the enthalpic stabilization occurs in thesecond half of the reaction coordinate as the TL-TLR evolves from the TS to the fully folded
state (see Figure 7.10A). As a result, we would expect the majority of changes in SASA to takeplace as the two folding motifs are brought into contact along the approach from U to TS. By
way of support, this would be entirely consistent with the fact that polysaccharide “crowders”
primarily influence the temperature dependence of kfold, rather than kunfold (e.g., the slopes in
Figure 7.8). Furthermore, as a result of limited changes in SASA between the TS and F states,
the model also correctly predicts the unfolding rate constant (kunfold) to be largely insensitive todifferential enthalpic contributions from dextran and Ficoll binding, which is again nicely
consistent with the temperature dependent data in Figure 7.8. Indeed, the similar impacts of all

191
three crowders revealed in Figure 7.8B signals the relatively minor role of enthalpic
contributions on kunfold. As a result, at least the unfolding kinetics for these secondary and tertiary
nucleic acid constructs appear to be dominated by more purely entropic, excluded volume effects
for both PEG and Ficoll/dextran polysaccharide polymers (Figure 7.4C).

7.6

Summary and conclusion
Temperature-controlled smFRET confocal microscopy has been used to study the

kinetics of solute-biomolecule interactions for common molecular crowding agents, PEG,
dextran and Ficoll, in order to explore/interpret the thermodynamics effects of crowding on
nucleic acid secondary (DNA hairpin) and tertiary (RNA TL-TLR) structures. Room temperaturekinetic analysis reveals that PEG promotes nucleic acid folding by simultaneously increasing
kfold and decreasing kunfold, qualitatively consistent with predictions from purely entropic
crowding effects due to excluded volume interactions. By way of contrast, polysaccharide
crowders, dextran and Ficoll do not significantly impact either the equilibria or kinetics ofnucleic acid folding at room temperature. From temperature dependent studies, thisthermodynamic stabilization at 7.5 w% PEG is found to be predominantly entropic (S > 0)with only negligible enthalpic (H  0) contributions, again perfectly consistent with excluded
volume models of crowding. Again, by way of contrast, the presence of 7.5 w% dextran and
Ficoll significantly influences both folding enthalpies as well as entropies, suggesting solutespecific chemical interactions which we attribute to preferential binding of polysaccharide withthe larger solvent accessible surface area of the unfolded nucleic acid construct. The results
indicate the presence of PEG promotes nucleic acid folding predominantly through purely

192
entropic crowding effects without enthalpic contributions. However, these studies also reveal
dextran and Ficoll to perturb the folding free energy landscape for nucleic acid folding in more
complicated ways, by differential enthalpic contributions to the folded vs unfolded
conformations (H  0) that compete with the purely entropic crowding effects (S > 0)arising from simple excluded volume models. The results highlight the power of temperaturedependent single molecule FRET microscopy studies for access to and allowing systematic
deconstruction of free energy landscapes into enthalpic and entropic contributions.

7.7

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Chapter 8
Synergism in the Molecular Crowding of Ligand-Induced Riboswitch Folding:
Kinetic/Thermodynamic Insights from Single Molecule FRET Spectroscopy

8.1

Abstract
Conformational dynamics in riboswitches involves ligand binding and folding of theRNA, each of which can be influenced by excluded volume effects under “crowded” in vivo
cellular conditions and thus incompletely characterized by in vitro studies under dilute bufferconditions. In this work, temperature-dependent single molecule FRET spectroscopy is used tocharacterize the thermodynamics of i) lysine ligand and ii) molecular crowders (PEG,
polyethylene glycol) on folding of the B. subtilis LysC lysine riboswitch. With the help of
detailed kinetic analysis, we isolate and study effects of PEG on lysine binding and riboswitch
folding individually, from which we find that PEG crowding facilitates riboswitch folding
primarily via a surprising increase in affinity for the cognate ligand. This is furthermore
confirmed by temperature dependent studies which reveal that PEG crowding is not purely
entropic and instead significantly impacts both enthalpic and entropic contributions to the freeenergy landscape for folding. The results indicate that PEG molecular crowding/stabilization of
the lysine riboswitch is more mechanistically complex and requires extension beyond theconventional picture of purely repulsive solvent-solute steric interactions arising from excluded
volume and entropy. Instead, the current experimental FRET data supports an alternative
multistep mechanism whereby PEG first entropically crowds the unfolded riboswitch into a “pre-*This chapter is adapted from: Sung, H.-L.; Nesbitt, D. J Synergism in the Molecular Crowding of LigandInduced Riboswitch Folding: Kinetic/Thermodynamic Insights from Single-Molecule Spectroscopy. J. Phys.
Chem. B 2022, 126, 6419-6427.

198
folded” conformation, which in turn greatly increases the ligand binding affinity, and thereby
enhances the overall equilibrium for riboswitch folding.

8.2

Introduction
Intracellular environments are highly concentrated with various kinds of solutes ranging

from small molecule metabolites to macromolecule proteins and nucleic acids.1 All these solutes
impose ubiquitous steric constraints (such as excluded volume) that affect both biomolecular
structure and function.2-3 Simply summarized, the presence of solute limits the space available
for the biomolecule to sample and thereby entropically favors any conformations that occupy
smaller volume.4 Such steric stabilization toward more compact biomolecule structures is often
referred to as molecular crowding.5-6
Most biochemical studies are performed in dilute buffer, which differs significantly fromthe in vivo intracellular environment where biomolecules actually function. In order to correctlyinterpret these in vitro observations, therefore, it is crucial to characterize and understand theeffects of crowding on biomolecular systems.7-9 Experimentally, polymeric crowders such as
PEG (polyethylene glycol) and dextran (polysaccharide) are often introduced into biologicalbuffers to mimic the intracellular crowding environment.10 Consistent with simple crowding
expectations, the presence of such polymers favors the more compact biomolecularconformation.11 Interestingly, many of these studies identified the origin of such polymer
stabilization12-14 to be largely entropic in nature, suggesting that the interaction between polymer
crowders and a crowded biomolecule occurs predominantly via the effective “repulsion” due topure excluded volume effects.15

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Riboswitches are RNA elements that regulate gene expression in response to ligand
concentrations in the cell.16-17 In particular, folding of the lysine riboswitch is found to be
facilitated by ligand through an induced-fit (IF, “bind-then-fold”) mechanism,18-19 whereby thepresence of the lysine binding lowers the free energy activation barrier and thereby promotes
subsequent folding of the riboswitch. As indicated in Figure 8.1A, the binding of lysine (withdissociation constant Kd) is prerequisite for the riboswitch folding; the lysine-associatedriboswitch can then fold and unfold at the rate of kfold and kunfold, respectively. Since molecular
crowding effects can in principle impact both binding and folding steps,20-24 this necessitatesfurther study into kinetic and thermodynamic mechanisms for crowding and ligand-induced
riboswitch folding, in order to deconstruct their respective influences on riboswitch function andresulting gene expression.
In this work, we explore the effects of PEG on the lysine riboswitch folding with single
molecule FRET spectroscopy. In the context of simple nucleic acid constructs, PEG has beenfound to facilitate secondary and tertiary folding via predominantly entropic effects,25 which
would be consistent with a “hard sphere” physical picture of crowding. Specifically, previous
PEG crowding studies as a function of temperature highlight the negligible role of differential
enthalpic effects in RNA/DNA conformational change. From detailed kinetic analysis of thesingle molecule data, however, one can characterize the overall riboswitch folding by twosequential mechanistic pathways: i) ligand binding and ii) subsequent conformational change ofthe lysine riboswitch,26 thereby motivating study of the impact of PEG crowding on each of theseprocesses separately. Moreover, single molecule experiments as a function of temperature enablefurther deconstruction of free energies and free energy barriers into enthalpic and entropic
contributions along the folding coordinate.27 As a result, the work potentially provides new

200
thermodynamic and kinetic insights into the effect of molecular crowding on both RNA-small
molecule binding and evolution of the lysine riboswitch from unfolded to “pre-folded” to folded
confirmations.

Figure 8.1 Schematic presentation of lysine riboswitch single molecule FRET construct folding.
(A) The induced-fit mechanism of lysine riboswitch folding where I. lysine binding is followed by
II. the riboswitch conformational change (U = unfolded riboswitch, F = folded riboswitch, and L= lysine). Note that folding brings Cy3 and Cy5 closer and thereby increases the FRET energy
transfer efficiency (EFRET). (B) Sample time dependent fluorescent signal. The conformationalchange is visualized by the anticorrelation between the Cy3 and Cy5 signal, which results in E FRET
changes.
8.3

Experiment8.3.1 Lysine riboswitch construct and sample preparation
In this work, we use a modified B. subtilis lysC lysine riboswitch28 as a model system to
explore the effect of crowding on ligand-induced RNA folding. The doubly dye-labeled andbiotinylated RNA construct is synthesized by annealing three strands of nucleic acid oligomers
together (Figure 8.1A, the biotinylated P1 extension not shown).18 The distal ends of stem P1 andP5 are labeled with the cyanine dyes Cy3 and Cy5, respectively to maximize the EFRET (FRET201
energy transfer efficiency) contrast during the conformational change in response to lysine.29
Details of the RNA sequences and synthesis methods can be found in previous work.18 We notethat the conformational change of the model construct is consistent with the wild type riboswitch
as the EFRET values can be predicted from the crystal structure.28 The ligand affinity of the model
construct is about 1 to 2 orders of magnitudes lower than the wild type riboswitch, which has thedissociation constant KD ≈ 1 µM.30 Such a discrepancy can be simply attributed to the typicallyhigher Mg2+ concentration (20 mM) used in the structural analysis (e.g., in-line probing) of thewild type RNA.30
To prepare samples for single molecule experiments, the coverslip sample holder is first
incubated with 10% biotinylated BSA (bovine serum albumin) to prevent non-specific binding.
A second incubation step results in sufficient streptavidin attachment to the coverslip, withsurface tethering of the riboswitch construct achieved by biotin-streptavidin association. Single
molecule fluorescence experiments are performed under buffer conditions with (i) 50 mM
HEPES (pH 7.5), 100 mM NaCl, 50 mM KCl and 0.5 mM MgCl2 to provide sufficient
background cations and maintain the buffer pH, (ii) Trolox/PCA/PCD oxygen scavenger system
to enhance fluorophore photostability,31 and (iii) additional lysine and PEG 3K (averagemolecular weight  3000 amu) to achieve desired experimental crowding conditions.
8.3.2 Temperature-controlled single molecule experiment and data analysis
The present single molecule FRET experiments have been performed with a throughobjective total internal reflection fluorescence (TIRF) microscope, with details described
elsewhere.32 In brief, a 532 nm laser beam is directed through a high numerical aperture oilimmersion microscope objective, with a mirror set for parallel translation of the beam withrespect to the objective axis to increase the incident angle and thereby achieve total internal

202reflection illumination of fluorescent RNA constructs immobilized at the coverslip-waterinterface. The resulting fluorescence from the sample is then collected by the same wide-fieldobjective, split by a dichroic mirror into Cy3 and Cy5 channels, and focused onto a chargecoupled device (CCD) video camera, with which data are collected in a video format at a 20 Hz
acquisition framerate (Figure 8.1B).

Figure 8.2 Sample EFRET trajectories and dwell time analysis. (A) EFRET trajectories without PEG.
(B) EFRET trajectories with 8 w% PEG. Note that the construct spends significantly more time in
the high EFRET state corresponding to the folded conformation. (C) Dwell time analysis without
PEG. (D) Dwell time analysis with 8 w% PEG. The cumulative distribution function of theunfolded dwell time decays much more rapidly, corresponding to accelerated kfold.

Single molecule fluorescent traces are obtained from the recorded movie by custom
analysis software with background correction to generate the resulting EFRET time trajectory (seesample data in Figure 8.2A and 8.2B). A standard hidden Markov modeling method is used to
identify transitions between the folded (EFRET ~ 0.7) and the unfolded (EFRET ~ 0.3 to 0.4)
conformations and thereby to acquire individual dwell times.33 The folding equilibrium constant
Kfold can be readily extracted as the ratio of total folding and unfolding dwell times (Kfold =Tfold/Tunfold), from which the folded fraction Ffold can be calculated (Ffold = Tfold/(Tfold + Tunfold)).

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The folding (kfold) and unfolding (kunfold) rate constants themselves can be obtained from analysisof the corresponding dwell time distributions for tunfold and tfold (see sample data in Figure 8.2C
and 2D), respectively.34 Cumulative distributions for both tfold and tunfold are well fit to single
exponential decay functions, consistent with folding and unfolding of the lysine riboswitch welldescribed by simple first order kinetics. Note that each cumulative distribution function (N = 3)
consists of dwell times obtained from ≈ 10 individual molecules within 1 or 2 surface scans. The
uncertainties (e.g., error bars in Figure 8.3 to 8.7) are reported as the standard deviation of themean. We believe the major source of measurement uncertainties is the sample heterogeneity,
along with minor contributions from fitting errors and temperature fluctuation.
The temperature-controlled single molecule studies are achieved with the help of
thermoelectric cooling/heating modules under servo loop control, as described in previous
work.32 Both the sample and microscope objective are cooled/heated simultaneously to minimize
any thermal gradients across the sample, with sample temperatures measured (to  0.1 ℃
accuracy) by a calibrated resistance thermometer.

Figure 8.3 PEG-dependent lysine riboswitch folding at a constant lysine concentration (1 mM).
(A) folding equilibrium and (B) kinetics as a function of PEG concentration. Data are fit to a single
exponential function to highlight the rapid rise of Kfold and kfold with increasing PEG concentration.

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8.4

Results and analysis

8.4.1 Lysine riboswitch folding promoted by PEG
Previous studies have shown that folding kinetics of the lysine riboswitch follows an
induced-fit (IF) mechanism,18-19 whereby lysine binding is an essential prerequisite for theriboswitch to fold. Under 1.0 mM lysine conditions, the riboswitch spends roughly equal averageamounts of time in the high EFRET (EFRET ~ 0.7) and low EFRET (EFRET ~ 0.3) states,
corresponding to the folded and unfolded conformations, respectively (Figure 8.2A). Additional
8 w% (percentage by weight) of PEG significantly promotes equilibrium folding of theriboswitch, as evident in the greatly enhanced time durations the fluorescent construct spends inthe high EFRET state (Figure 8.2B). Furthermore, at constant 1 millimolar lysine concentration,
Kfold increases monotonically (Figure 8.3A) with systematically increasing PEG, again consistent
with crowding promotion of the folded riboswitch conformation under equilibrium conditions.
In addition to the above equilibrium data, however, an even greater wealth of information
on single molecule biophysical kinetics is revealed in dwell time distributions for eachfluorescence trajectory. In particular, kinetic information in these single molecule fluorescence
trajectories can be obtained from logarithmic dwell time analysis of the cumulative probability
distributions,34 with sample data under low (0 w% PEG) and high (8 w% PEG) crowding
conditions displayed in Figure 8.2C and 8.2D. These data make clear that PEG dramaticallyincreases the folding rate (kfold, in red) and decreases the unfolding rate (kunfold, in green) of thelysine riboswitch (Figure 8.3B). In particular, the crowding effects are much stronger on thefolding vs. unfolding step. Specifically, there is a nearly 400% increase in kfold between 0 and 8
w% PEG concentrations, over which range kunfold is reduced by only 10%.

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8.4.2 PEG stabilization on lysine dependent folding illustrated by kinetic modeling
Here we implement a more detailed kinetic analysis to highlight the PEG effect on theligand response of the riboswitch folding.26 In previous work, folding of the lysine riboswitch
was found to be initiated by ligand association, followed by RNA conformational change in a“bind-then-fold” induced fit (IF) mechanism.18-19 The simplified IF folding pathway is illustrated
in Figure 8.1A, where Kd reflects the dissociation constant of lysine and k1/k-1 correspond tounimolecular forward/backward rate constants for overall conformational changes in theriboswitch construct.

Figure 8.4 Lysine-dependent folding curves at a series of PEG concentrations. Folded fraction
Ffold as a function of lysine with (A) 0 w%, (B) 4 w%, and (C) 8 w% PEG. Data are nonlinear leastsquares fit to the Hill equation (Eq. 8.1).

206
We first focus on the equilibrium folding behavior by studying the folded fraction Ffold =𝑇𝑓𝑜𝑙𝑑
𝑇𝑓𝑜𝑙𝑑 +𝑇𝑢𝑛𝑓𝑜𝑙𝑑

as a function of lysine at constant PEG concentration (Figure 8.4). As expected, thedata indicate linear growth in Ffold at low ligand concentration and eventual saturation at highlysine. More surprising is the dependence of these curves on crowder, with the saturation plateau
quite insensitive to PEG from 0 to 8 w%, yet with the lysine binding affinity increasing by nearly
an order of magnitude over the same range of crowding conditions. Simply summarized, themain role of PEG as molecular crowder appears to be through promotion of the lysine-riboswitch
binding interaction, which in turn facilitates subsequent folding of the riboswitch. It’s worth
noting that the enhancement of bimolecular association is expected from PEG crowding. To
highlight more quantitatively the impact of PEG on lysine-induced riboswitch folding, the data
can be fit to the Hill equation35[𝑙𝑦𝑠𝑖𝑛𝑒]𝑛1

𝐹𝑓𝑜𝑙𝑑 = 𝐹𝑚𝑎𝑥 × 𝐾 𝑛1 +[𝑙𝑦𝑠𝑖𝑛𝑒]𝑛1

Eq. 8.1

𝐷

where n1 is the Hill coefficient, KD is the effective dissociation constant for lysine binding, andFmax corresponds to the maximal Ffold value under saturated lysine conditions. Since KD
corresponds to the lysine concentration for which Ffold = Fmax/2, a smaller KD value reflects amore effective lysine promotion of riboswitch folding. The fitting results are summarized inTable 8.1 for 0 to 8 w% PEG crowder conditions, over which KD reduces from 0.68(8) mM from
0.109(5) mM, corresponding to an equivalent 7-fold efficiency increase in lysine promoted
riboswitch folding with a n1  1 (i.e., non-cooperative) Hill coefficient.

0 w% PEG
4 w% PEG
8 w% PEG

KD (mM)
0.68(8)0.36(4)
0.109(5)n10.91(9)1.02(12)1.08(6)Fmax
0.77(2)0.82(2)0.843(10)Table 8.1 Least squares fit results for the lysine-induced folding equilibria.

207

Figure 8.5 Lysine-dependent folding and unfolding rates at a series of PEG concentrations.
Folding rate constants kfold/kunfold as a function of lysine with (A) 0 w%, (B) 4 w%, and (C) 8 w%
PEG. The kfold data are fit to the Hill-like kinetic equation (Eq. 8.2), while the lysine-independent
kunfold data are fit with a horizontal line.

The kinetic promotion of lysine-induced riboswitch folding can also be investigated via
statistical analysis of the dwell time distributions (see Figure 8.5), for which the effective folding
rate constant (kfold) increases as a function of lysine and eventually reaches a saturation plateau.
By way of contrast, the unfolding rate constant kunfold is completely insensitive to lysine andremains constant over a wide range of ligand concentrations.18 Such kinetic results are in fact
entirely consistent with an induced-fit mechanism, whereby lysine promotes riboswitch folding
through a “bind-then-fold” process.18-19 Specifically for such a simplified kinetic model (seeFigure 8.1A), increase in lysine concentration simply shifts the equilibrium toward a higher

208
fraction in the ligand bound state, thereby promoting the effective unimolecular folding rate kfold
up to the limiting velocity of k1. Conversely, the effective unimolecular unfolding rate kunfold
simply reflects k-1 and remains independent of lysine concentration.26 By solving the kinetic
equations assuming rapid equilibration with respect to lysine binding, the data can be fit to anindependent Hill equation for kfold26[𝑙𝑦𝑠𝑖𝑛𝑒]𝑛2

𝑘𝑓𝑜𝑙𝑑 = 𝑘1 × 𝐾 𝑛2 +[𝑙𝑦𝑠𝑖𝑛𝑒]𝑛2

Eq. 8.2𝑑where again n2 is a Hill coefficient, Kd is the lysine dissociation constant and k1 corresponds tothe maximal kfold value under saturating ligand conditions. Similar to the results discussed above
for folding/unfolding equilibrium constant properties, we find that the addition of PEG crowder
significantly increases the efficiency for lysine binding (i.e., reduces Kd) and in turn facilitatesfolding of the lysine riboswitch. Interestingly, by way of comparison only relatively modest PEG
effects on the elemental folding/unfolding rate processes are observed, with 8 w% PEG
concentrations increasing/decreasing the unimolecular folding (k1)/unfolding (k-1) rate constantsby only 10%/40%, respectively. Such relatively modest changes in the intrinsic rates are
consistent with crowding,14 with fits of the kinetic data to Eq. 8.2 summarized in Table 8.2.
However, it is worth stressing that the predominant impact of molecular crowding from thismechanistic perspective arises from a 7x decrease in Kd (i.e., 700% enhancement of ligand
binding to the riboswitch).

0 w% PEG
4 w% PEG
8 w% PEG

Kd (mM)
3.1(9)
1.8(3)
0.58(7)n2
1.00(19)
1.12(17)1.34(17)

k1 (s-1)
1.26(13)
1.48(10)1.45(6)

Table 8.2 Least squares fit results for the lysine-induced folding kinetics.

k-1 (s-1)
0.367(8)0.317(9)0.262(11)209

Figure 8.6 van’t Hoff plots for the temperature dependent lysine riboswitch folding at (A) 0 w%
PEG and (B) 6 w% PEG. [lysine] = 1 mM.
8.4.3 Temperature-dependent folding reveals both enthalpic and entropic PEG effects
We can take such equilibrium and kinetic analyses one important step further byperforming temperature dependent smFRET folding experiments, which permit deconstructionof overall (G0) and transition state (G‡) free energies into enthalpic (H) and entropic (S)contributions as a function of PEG crowder concentrations. First of all, studies in absence of
crowder reveal that unfolding of the lysine riboswitch is strongly favored with increasing
temperature, specifically 10-fold reduction in the overall equilibrium constant Kfold over amodest 12 ℃ temperature range. Quantitative thermodynamic information for the corresponding
folding enthalpy and entropies can be extracted from a simple van’t Hoff analysis, i.e.,∆𝐻 0 1∆𝑆 0

𝑙𝑛𝐾𝑓𝑜𝑙𝑑 = − 𝑅 𝑇 + 𝑅 .

Eq. 8.3

210
As summarized in the sample data in Figure 8.6A, B, overall folding of the lysine riboswitch atboth low (0 w%) and high (6 w%) crowder conditions is found to be exothermic (ΔH0 = 32.8(18) and -15.0(14) kcal/mol, respectively) and yet entropically penalized (-TΔS0 = -111(5)and -50(3) cal/mol/K), consistent with a simple physical picture of folding whereby
biomolecules are enthalpically encouraged to fold into a more ordered (lower entropy) state.36 Of
particular interest, however, the addition of 6 w% PEG (Figure 8.6B) decreases and increases theslopes vs. intercepts, respectively, corresponding to incremental PEG-induced increase in both
ΔH0 and ΔS0 (ΔΔH0 > 0 and ΔΔS0 > 0). Simply stated, the presence of PEG crowder reduces thethermodynamic advantage of folding exothermicity and yet also lowers the entropic penalty forfolding of the lysine riboswitch. We will return to this important issue in the discussion section,
but for the moment emphasize that such changes in overall exothermicity (ΔΔH0 > 0) with PEG

Figure 8.7 Eyring plots for the temperature dependent lysine riboswitch folding at (A) 0 w% PEG
and (B) 6 w% PEG. [lysine] = 1 mM.

211
concentration are inconsistent with a purely excluded volume interpretation of crowding, forwhich the driving forces are predicted to be purely entropic (ΔΔS0 > 0).
There is of course additional thermodynamic information in the temperature-dependenceof the kinetic rate constants themselves. Specifically, if we make the plausible assumption of asingle rate-limiting transition state, we can similarly analyze the temperature-dependent kinetic
data with transition state/Eyring theory37-39∆𝐻 ‡ 1∆𝑆 ‡𝑙𝑛𝑘 = − 𝑅 𝑇 + 𝑅 + ln 𝜈

Eq. 8.4

where ΔH‡ and ΔS‡ represent enthalpic and entropic differences, respectively, between thetransition state and the folded/unfolded states of the riboswitch. In Eq 3, ν represents the attempt
frequency (set to be 1013 s-1 in our analysis) to access the transition barrier along thefolding/unfolding coordinate,40 though the extracted value of ΔS‡ is only logarithmicallydependent on such a choice. Despite the fact that any absolute entropy change associated withsurmounting the transition state barrier will depend weakly on the choice of ν, any differentialchanges in entropy (ΔΔS‡) induced by PEG crowding remain rigorously independent of any suchlogarithmic offset.
As clearly evident in Figure 8.7A, the logarithmic rate constant from such an Arrhenius
analysis for folding of the lysine riboswitch increases linearly with 1/T. The slope in Figure 8.7A
(red line) implies that folding of the riboswitch releases heat (ΔHfold‡  −17.3(16) kcal/mol) inaccessing the transition state, while the negative intercept (ΔSfold‡  −121(3) cal/mol/K)
indicates an entropic TS barrier (-TΔSfold‡ > 0) in the absence of crowding conditions. In thepresence of 6 w% PEG crowder (see Figure 8.7B), slope and intercept of the Eyring plot change
rather dramatically for kfold, corresponding to a significant differential decrease in both
exothermicity (ΔΔHfold‡ > 0) and entropic cost (-TΔΔSfold‡ < 0) for access to the folding

212
transition state. Of particular interest and in contrast with the riboswitch folding kinetics,
however, the presence of 6 w% PEG molecular crowders results in very modest effects on thetemperature dependence of kunfold, with therefore only small crowding-induced changes inenthalpy (ΔΔHunfold‡  0) and entropy ((-TΔΔSunfold‡  0) required to reach the transition statefrom the fully folded lysine riboswitch conformation.

Figure 8.8 Free energy landscapes for lysine riboswitch folding. PEG effects on the (A) freeenergy, (B) enthalpic, and (C) entropic contributions along the folding coordinate (U = unfolded
state, TS = transition state, and F = folded state). Values are arbitrarily referenced to zero for thefolded state F.

8.5

Discussion

8.5.1 Kinetic vs. thermodynamic crowding data indicate conflicting solute interaction
modelsWe have shown the lysine riboswitch folding can be promoted by increasing PEG
concentration, which is entirely consistent with crowding effects, where the presence of PEG
favors the more compact state.13-14 From the perspective of the solute interaction model, such
PEG-enhanced structure formation can simply result from generic repulsion between PEG and
the RNA.41 Specifically, the biomolecule might tend to adopt the more compact conformation in213
order to reduce the solvent-accessible surface area (SASA) and in turn decrease overall
unfavorable solute-biomolecule contact.42-43 Taking these ideas one step further, if this repulsion
were shown to be predominantly steric (i.e. entropic) in nature, it can be unambiguously
attributed to the crowding effects originating from excluded volume.13 However, the significant
slope changes in the van’ Hoff plots in Figure 8.6 signal differential enthalpic contributions andmay suggest a more complex solute effect which we can explore further.
The thermodynamic parameters obtained from the temperature dependence aresummarized in Figure 8.8, where the relative enthalpy and entropy of each state are plotted along
the simplified folding coordinate, with the folded state F referenced to zero.35 It is shown that
PEG exerts effects (red vs blue) predominantly on the (forward) folding activation enthalpy(ΔHfold‡) and entropy (ΔSfold‡), while leaving the relative free energy contributions between thetransition state and the folded state largely unperturbed (Figure 8.8B and 8.8C). Furthermore, theshifts in Figure 8.8 suggest the unfolded conformation is enthalpically stabilized and entropicallydestabilized by PEG with respect to the transition/folded states. From the physical picture of asimple solute interaction model, such a free energy change corresponds to increase in PEG
association with the unfolded conformation of larger SASA.25 In other words, ourthermodynamic analysis reveals an overall attraction (favorable contact) between PEG and theriboswitch.
Indeed, solvent-solute interactions represent a simple yet efficient way to understandsolute-promoted biomolecule folding/unfolding. However, the thermodynamic results forpreferential PEG solvation of the unfolded state clearly contradict the general repulsion between
PEG and RNA predicted from the PEG enhanced lysine riboswitch folding. It is in fact unusual
for favorable PEG-RNA contacts to enhance folding, which requires increasing the area of the214
RNA-RNA interface. Such discrepancies suggest solute interactions alone are insufficient toaccount for our present findings, with a much more likely hybrid folding mechanism required forthe observed changes in both entropy and enthalpy with crowding conditions.
8.5.2 PEG prearranges the unfolded riboswitch to facilitate folding
Careful inspection of the EFRET trajectories in Figure 8.2 show the low EFRET state of thelysine riboswitch shifts to a slightly higher value (from ≈ 0.3 to 0.4, as illustrated in Figure 8.9)
by PEG when the riboswitch becomes more folded. Such an observation indicates PEG may not
only promote the overall riboswitch folding, but also alter the structure of the unfolded(relatively low EFRET) state. Similar behavior is also observed in previous single molecule studiesof the lysine riboswitch,18, 29, 44 where the low EFRET value increases in response to bufferconditions that promote folding. Moreover, one study is able to resolve the low EFRET populationof the same lysC riboswitch into (i) the fully unfolded, and (ii) the lysine-free pre-folded states.44
We therefore suspect that equilibrium between the unresolved low EFRET conformations may
have significant impact on our thermodynamic analysis.

Figure 8.9 Normalized EFRET distribution of the low EFRET population with 0 w% PEG (blue) and
8 w% PEG (red). Bin size = 0.05.

Although we are unable to resolve, assign, and deconvolute these low EFRET
conformations in the kinetics, we can treat the low EFRET state as an average of (1) the fully

215
unfolded and (2) the pre-folded conformations, as the simplest physical model to understand thethermodynamic consequence. The slightly elevated EFRET value indicates PEG drives theequilibrium from the unfolded to a “pre-folded” lysine riboswitch, which is consistent with thecommon observation of PEG promoting the formation of structure. Since the low EFRET state isalready partially folded by PEG, we therefore expect a lower enthalpic gain accompanied by alower entropic penalty for folding, with these predictions clearly confirmed in Figure 8.8.
Moreover, the previous study has demonstrated that this pre-folded state has stronger lysine
affinity and thus higher tendency to fold,44 which agrees completely with the rapidly decreasing
lysine dissociation constants (KD and Kd) by PEG observed in our detailed kinetic analysis(Figure 8.4). It is worth noting that a similar mechanism of solute facilitating folding by “preorganization” of the unfolded state has also been observed in several riboswitch systems.26, 34, 45
The addition of a postulated pre-folded state provides a more reasonable and plausible
mechanism with which to explain the present kinetic and thermodynamic data. Since thethermodynamics of lysine riboswitch folding is dominated by rapid equilibrium between the two
low EFRET (unfolded/prefolded) conformations, we lose the information on the PEG-RNA
interaction except for the fact that PEG increases the overall riboswitch (pre-)folding. It’s beenpreviously shown that the interactions between PEG and nucleic acid secondary/tertiary
structures are predominantly entropic and therefore consistent with crowding via fundamental
excluded volume interactions.25 In fact, it was surprising in this study to see any PEG-dependent
differential enthalpy effects for lysine riboswitch folding, as we do not expect significant
changes in thermodynamic properties between simple nucleic acid folding motifs to the more
complex structure of a riboswitch.46-47 With the partially folded state included as part of the low
EFRET population, we cannot rule out excluded volume effects as the predominant reason behind

216
any PEG-dependent changes in riboswitch conformation, despite significant enthalpic
contributions to the overall thermodynamics. In fact, the observation that the lysine-saturated
folding (k1)/unfolding (k-1) rate constants increase/decrease, respectively, as a function of PEG
concentration is entirely consistent with simple crowding predictions.14 This prompted oursuggestion of an alternative albeit simple three-state (unfolded ⇌ ”prefolded” ⇌ folded) kinetic
mechanism whereby crowding is able to manifest itself via both enthalpic and entropic changes
in the thermodynamics, in addition to recapitulating the physically correct kinetic andthermodynamic basis for PEG-promoted lysine riboswitch folding.

8.6

Summary and conclusions
We use the single molecule FRET methods to characterize the ligand-induced RNA

folding motif in response to common crowding agent PEG, for which PEG promotes the overall
RNA folding by increasing kfold and decreasing kunfold simultaneously. With detailed kinetic
analysis, we find the most prominent PEG effect is to facilitate the lysine binding and thereby
promote the overall structural change of the riboswitch. Such kinetic effects are consistent with asimple physical picture of repulsive interactions between PEG and the surface of the riboswitch
and/or lysine. However, the reduced exothermicity and entropic penalty for folding observed in
the temperature dependent studies suggests that PEG preferentially solvates the unfolded state
due to its larger surface area.48 Such a discrepancy suggests the PEG effects cannot be simply
understood by the very common physical picture of purely “repulsive” solute-biomoleculeinteractions. Further motivated by additional structural information from small EFRET shifts, wetherefore propose a simple physical model with an additional “pre-folded” low EFRET state thatnicely accounts for both the thermodynamic and kinetic findings. In the model, PEG prearranges

217
the unfolded conformation of the riboswitch and shifts the EFRET to slightly higher values, asevidence in our single molecule EFRET trajectories. From our kinetic analysis, we find the more
fold-like but ligand-free riboswitch has a much higher tendency to bind a lysine molecule andproceed to fold. On the other hand, the partially formed riboswitch structure also reduces thefolding exothermicities and entropic penalties as seen in the temperature dependent studies.
Furthermore, the proposed three-state model provides an alternative mechanism for purely
entropic crowding to induce secondary changes in the overall RNA folding enthalpy that areconsistent with experimental observation. Although this will require confirmation by additional
single molecule temperature dependent studies, the net effect is an extension of simple excluded
volume models that can correctly predict both entropic and enthalpic contributions to thecrowding process occurring in cellular environment.

8.7

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Cheung, M. S.; Klimov, D.; Thirumalai, D., Molecular Crowding Enhances Native State
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U.S.A. 2014, 111 (23), 8464-8469.

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Sung, H.-L.; Sengupta, A.; Nesbitt, D., Smaller Molecules Crowd Better: Crowder Size
Dependence Revealed by Single-Molecule FRET Studies and Depletion Force Modeling
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Chapter 9
DNA Hairpin Hybridization under Extreme Pressures:
A Single-Molecule FRET Study

9.1

Abstract
Organisms have evolved to live in a variety of complex environments, which clearly has

required cellular biology to accommodate to extreme conditions of hydraulic pressure andelevated temperature. In this work, we exploit single-molecule Forster resonance energy transfer(FRET) spectroscopy to probe structural changes in DNA hairpins as a function of pressure andtemperature, which allows us to extract detailed thermodynamic information on changes in freeenergy (G0), free volume (∆V0), enthalpy (∆H0) and entropy (∆S0) associated with DNA loop
formation and sequence dependent stem hybridization. Specifically, time correlated single
photon counting experiments on freely diffusing 40A DNA hairpin FRET constructs are
performed in a 50 m x 50 m square quartz capillary cell pressurized from ambient pressure up
to 3 kbar. By pressure-dependent van’t Hoff analysis of the equilibrium constants, ∆V0 for
hybridization of the DNA hairpin can be determined as a function of stem length (nstem = 7-10)
with single base pair resolution, which further motivates a simple linear deconstruction into
additive stem (V0stem = V0bp x nstem) and loop (V0loop) contributions. We find that increasingpressure destabilizes the DNA hairpin stem region (V0bp = +1.98(16) cm3/mol/bp), withadditional positive free volume changes (V0loop = +7.0(14) cm3/mol) we ascribe to bending and*This chapter is adapted from: Sung, H.-L.; Nesbitt, D. J. DNA Hairpin Hybridization under Extreme
Pressures: A Single-Molecule FRET Study. J. Phys. Chem. B 2020, 124, 110-120.

223
base stacking disruption of the 40A loop. From a van’t Hoff temperature dependent analysis of
the DNA 40A hairpin equilibria, the data support a similar additive loop/stem deconstruction ofenthalpic (∆H0 = ∆H0loop + ∆H0stem) and entropic (∆S0 = ∆S0loop + ∆S0stem) contributions, which
permits insightful comparison with predictions from nearest neighbor thermodynamic models for
DNA duplex formation. In particular, the stem thermodynamics is consistent with exothermicallyfavored (∆H0stem < 0) and entropically penalized (∆S0stem < 0) hydrogen bonding, but withadditional enthalpic (∆H0loop > 0) and entropic (∆S0loop > 0) contributions due to loop bending
effects and consistent with distortion of A base stacking in the 40A linker.

9.2

Introduction
Temperature and pressure are two intensive thermodynamic variables that play crucial

roles in the folding of biomolecules into biologically competent structures 1-2. Interestingly,
while the thermal dependence of biomolecular conformational change has been thoroughly
investigated, the effects of extreme hydraulic pressure have received much less attention. One
justification for such disparate attentions is that pressure is a relatively constant variable inconventional biology, while temperature fluctuations are quite common and appreciated to bemuch more important3. However, improved sampling tools in the last two decades4-5 has madeextreme biological environments increasingly available for study. As one particularly relevant
example, robotic deep sea exploration vehicles have revealed a plethora of thermophilicorganisms thriving in hydrothermal vents where extreme pressures and elevated temperatures
result from the rapid increase of hydraulic pressure with ocean depth ( 1 bar every 10 meters)
and proximity to geothermal heat sources in the ocean bed. In fact, the much of the ocean bottom
is 3500 meters below sea level (i.e., P = 350 bars), with the deepest point in the Marianas Trench

224
at 11km (i.e., P = 1.1 kbar). From such a perspective, high pressure biological environments arein fact ubiquitous, with the dynamic range of pressures spanning more than three orders ofmagnitude. This provides incentive for single molecule biophysical folding studies under
extreme (P/T) conditions, with which to explore how biology successfully adapts to (andpotentially even harnesses) such extreme variations in pressure and temperature2-3 to influence
conformational folding/unfolding and/or hybridization/dehybridization dynamics.
Pressure and temperature are particularly powerful intensive variables for suchthermodynamic exploration. According to the Gibbs free energy differential expression,d(∆G0) = -∆S0(dT) + ∆V0(dP)(Eq. 9.1)

the temperature dependence of an equilibrium process is determined by entropy change (∆S0),
while the pressure dependent response is controlled by the free volume difference (∆V0) between
folded and unfolded conformations3-4. In the past decade, spectroscopic methods have been
coupled with high pressure techniques to study local/global changes of biomolecular structure1, 3.
For example, proton exchange rates in solution phase NMR spectroscopy have been used toprobe pressure dependent structure formation in proteins6-7, while small-angle X-ray scatteringexperiments have allowed extraction of radii of gyration as a proxy for global compactness as afunction of applied pressure8-10. The single-molecule FRET spectroscopy (smFRET, Figure 9.1)
could be particularly useful in detecting conformational change of biomolecules, given theextremely rapid decrease in FRET energy transfer efficiency (EFRET ~ 1/(1+(r/r0)6)) with distance
between dye-labeled positions, which may therefore be sensitive to conformational
compactness1, 11, as well as overall folding of the biomolecule. Indeed, as external pressure cansignificantly skew the folding free energy landscape12-13, biomolecules can adopt different

225folding conformations under extreme vs. ambient conditions11, 14, which one could hope toidentify by EFRET value in high pressure smFRET studies11.
The present studies focus on pressure dependent hybridization/dehybridization of single
molecule DNA hairpins, as a simple first introduction to high pressure smFRET. DNA hairpins
play an important role in biological systems15 and have been widely used as model constructs forduplex formation, as well as probing the nucleic acid response to cosolutes such as aminoacids16, osmolytes11, 14, 17 and crowding agents18-21. The 40A DNA hairpin construct utilized in
the present studies (Figure 9.2) is ideally suitable for smFRET investigation because i) folding is
known to proceed by well-behaved, unimolecular 2-state kinetics16, 18 and yet ii) the poly(dA)linker acts as a sufficiently long spacer to provide high EFRET contrast between the folded andunfolded conformations. Free volume changes in smFRET DNA hairpin studies have been
explored recently, suggesting that the fully hybridized DNA conformation is destabilized (i.e.,
denatures) with increasing pressure11, 14, 18. While these previous studies have focused on the freevolume change (∆V0) in response to different crowding agents and cosolutes, the effects ofsequence, specifically, the dependence of free volume on stem sequence length (nstep) andchemical identity (A, T, G, C), have remained largely unexplored. Furthermore, the process of
DNA hairpin folding not only requires secondary structure formation in the stem region, but also
forces the single-stranded DNA loop domain into a more compact ring-like conformation. Sinceboth stem and loop regions represent ubiquitous structural elements in nucleic acid folding22-23,
the successful deconstruction and simple theoretical modelling of their free volume contributions
could provide intriguing, new physical insight into the thermodynamics of nucleic acid structure.
In this work, we report on the development of new high pressure smFRET capabilities in
our labs with access up to 5 kbar external pressure. We then perform “burst diffusion” smFRET

226
experiments over an extreme pressure (1-3000 bar) and a modest temperature (T  10K) range,
which permit one to extract thermodynamic properties for a series of fluorescently labelled 40A
DNA hairpin constructs. For pressure dependence studies, a manual pressure generator is
coupled to a square (50 m x 50 m) quartz capillary sample cell (Figure 9.1), which can sustain
from 1 bar up to 5000 bar in pressure without shattering. Such large dynamic ranges in pressure
enable measurement of free volume changes i) at the single molecule level and ii) withapproximately single base pair resolution. Analysis of the nucleotide sequence dependentequilibrium constants for hybridization as well as comparison to nearest neighbor predictions24-25
allow us to extract free volume (V0), enthalpy (H0), and entropy (S0) changes in stem
formation, which both isolate and highlight additional contributions to loop formation for eachthermodynamic quantity.
The organization of this paper is as follows. In Sec. 9.3, we present a detailed discussionof the smFRET apparatus, with capabilities for both extreme pressure (1-5000 bar) and modest
temperature (20–40 ℃) control, with pressure/temperature and sequence dependent results on
40A DNA hairpin constructs reported in Sec. 9.4. In Sec. 9.5A we analyze and interpret the stem
length and sequence dependence of the high pressure results and present a simple model forinterpreting these data which permits systematic deconstruction of stem (Vstem) and loop
(Vloop) free volume contributions. In Sec. 9.5B and 9.5C, we explore temperature dependenceof 40A hairpin formation, specifically deconstruction of G0 into enthalpic and entropic
contributions by van’t Hoff analysis. The resulting thermodynamic contributions proveconsistent with a simple physical picture of i) exothermic bonding (∆H0 < 0) yet ii) base stacking
in the duplex stem to achieve a more ordered (∆S0 < 0) secondary structure26. The results arethen compared to nearest neighbor (NN) model predictions (HNNstem, SNNstem) for DNA stem

227
formation24-25, which intriguingly suggest 40A loop formation to be endothermic (Hloop > 0)and yet favored by entropic gain (Sloop > 0). Finally, main conclusions and directions for further
experimental improvements are briefly summarized in Sec. 9.6.

Figure 9.1 High pressure smFRET experiment setup: (A) High pressure generating system
coupled to the confocal microscope for smFRET freely diffusing study; (B) Top view of the squarecapillary alignment to the microscope objective and the high pressure mechanical sealing strategy.

9.3

Experiment9.3.1 High pressure microscopy cell and pressure control
The current high pressure smFRET experiments (Figure 9.1) have been performed bymodification of a time correlated single photon counting confocal microscope to incorporate ahigh pressure glass capillary cell27. As one crucial design change, we use square instead of roundcapillary tubing made from fused silica, with 360 µm and 50 µm outer and inner diameter,
respectively (Polymicro, Phoenix, AZ). This is used to contain the high pressure sample formicroscope studies, with thickness and relatively flat surfaces to mimic a standard cover slip andthereby optimize collection of fluorescent photons14. Although studies have previously warned

228
that such square capillaries might fail at pressures over 2 kilobars27, we find this not to be thecase, working well beyond this limit and indeed up to nearly 5 kilobars without signs offracturing. However, we have learned that sealing the capillary end with a oxy-propane torch can
at times result in breakage at high pressure, likely due to unresolved strain in the fused silica due
to intense heating (and cooling). In our experience, such problems are mitigated by a simple
tempering of the glass capillary ends, as described below.
First of all, one end of the capillary is glued with epoxy adhesive into a modified
stainless-steel pressure plug (High Pressure Equipment, Erie, PA) with a 450 µm hole drilled
through the center (Figure 9.1B) and the opaque outer polymer coating of the capillary removed
by a low temperature propane flame to create optical access for the fluorescent measurements.
Loading of the low concentration DNA samples is then achieved by immersing one end of thecapillary into the sample hairpin solution. Once the capillary is filled by capillary action, the free
end opposite the plug is sealed with an oxy-propane torch. Since the mechanical strength of the
fused silica can be compromised by heating/cooling, we utilize an extended heating time tocreate an inner channel tapered into a needle point in the interior of the glass, thereby reducing
the contact surface area and thus the total force on the sealed end. Prior to coupling to the highpressure liquid source, the plug-attached open end of the capillary is dipped into low viscosity
silicone oil to create a thin immiscible layer, which prevents contamination of the fluorescencecapillary region by the pressure-transmitting fluid and yet still conducting the pressure
effectively. The sample is then connected to the high pressure source system by tightening thehigh pressure plug and gland nut, during which the flat surface of the square capillary is visuallyaligned with the microscope objective eyepiece. Since the capillary rotates slightly with thegland nut while being tightened, a cover slip is attached to the capillary with tape to mark the229
correct capillary orientation (Figure 9.1B). After tightening the gland nut, the cover slip is thenrotated back to the desired flat surface orientation, gently torqueing the capillary to realign its flat
surface with the microscope objective. Although this last step might seem practically equivalent
to fixing the capillary orientation before tightening the gland nut, the sudden rotation tends toloosen the tape and misalign the capillary. Indeed, strong adhesives may also work well, though
we find the tape method easier and faster to apply.
The source of high pressure is simply a manually operated piston screw pump (HighPressure Equipment) which can generate pressures up to 5 kilobars (Figure 9.1A). As adaptedfrom previous work27-28, the pressure generator is connected to the sample cell and a Bourdonpressure gauge via high pressure 1/4" stainless steel tubing (High Pressure Equipment), with theentire system filled with ethanol as the pressure-transmitting fluid. Residual air bubbles in theethanol decrease the pressuring efficiency, which are removed by repeatedly flushing the systemthrough liquid ethanol reservoirs (Figure 9.1A). The valves are then closed to isolate the fluid
reservoirs, with simple mechanical rotation of the piston achieving a desired pressure (0-5 kbar),as indicated by the Bourdon pressure gauge.
9.3.2 Temperature control
Precise temperature control (± 0.1 °C) is achieved by simultaneously heating the capillarysample and microscope objective and stabilizing the temperature with electronic feedback loop.
Prior to each temperature-controlled experiment, the sample holder is mounted on a stage heater(Instec, Boulder, CO) and stabilized via feedback control for more than 15 minutes to ensurecomplete thermal equilibrium. At the same time, the microscope objective is heated by a resistive
collar (Bioptechs, Butler, PA) to the same temperature to prevent thermal gradients due to water
immersion optics. Details of the resistive feedback heating system can be found elsewhere 29-30.

230

Figure 9.2 Details of the DNA hairpin smFRET constructs: (A) Schematic representation of DNA
hairpin folding; (B) The structural details of the complementary strand, with systematic variationsin the duplexing sequence beyond 7-bp denoted in red (A) and green (G). The location of Cy3
labeling with respective to the duplexing sequence at 3’ end is highlighted in green, and Cy5 ischemically attached to the 5’ end.

9.3.3 DNA 40A hairpin construct and sample preparation
All DNA hairpin constructs in this study contain the identical 40-nucleotide poly-adenine
linker (designated as 40A Hairpin), with the number of base pairs within the stem varying fromnstem = 7-10. The overall construct design, doubly fluorophore-labeled positions, and stem
sequences are described in Figure 9.2, with each of the DNA oligomers commercially available
in HPLC purified forms (Integrated DNA Technologies, Coralville, IA). In the “folded” state of
the hairpin, the stem is fully hybridized by complementary Watson-Crick base pairing, bringing
the two fluorescent dyes Cy3 and Cy5 in close proximity to achieve the high EFRET (~ 0.8) state.
Conversely, dissociation of the duplex stem “unfolds” hairpin, which allows the covalently
linked dye-labeled strands to diffuse to much larger (~ 80 Å) separations, resulting in a EFRET
state near zero. The observed range of EFRET values are entirely consistent with predictions based

231

Figure 9.3 Sample data and analysis from the freely diffusing smFRET studies: (A) Sample time
resolved fluorescent signals from 532 nm laser excitation, with upward green and red traces
corresponding to Cy3 and Cy5 fluorescence channels, respectively. The pink trace due to 633 nm
alternating laser excitation (ALEX) of the diffusing constructs is plotted downward for directcomparison with the 532 nm excitation signals, confirming the presence (or absence) of the Cy5
fluor. (B) Single events in the fluorescence traces, where arrows point at the fluorescent bursts
corresponding to (1) an unfolded doubly-labeled hairpin, (2) a Cy3-only, (3) Cy5-only and (4)folded doubly-labeled construct. (C) Sample EFRET histogram of the 9-bp (AT) hairpin folding at
ambient pressure, fit to a superposition of two Gaussians. (D) Sample EFRET histogram of the 9-bp
hairpin folding at a series of external pressures, revealing a reversible propensity for unfolding
with increasing Pext (1-2500 bar).

232
on the Cy3/Cy5 Forster radius (R0 = 55 Å), construct geometry, and results from previous
surface-tethered smFRET experiments16. There is a 10A-biotin oligo extension on the 3’ end
after the duplexing sequence, designed for future attachment of the 40A hairpin constructs to a
BSA surface by biotin-streptavidin interactions. For simplicity in these first high pressure
experiments, however, we have simply chosen to allow the constructs to freely diffuse insolution through the laser beam, exploiting “burst fluorescence” methods to stochastically probe
the single 40A hairpin oligos present in the confocal volume.
In preparation of the smFRET samples, the stock DNA solution has been diluted in
imaging buffer to ~ 50 pM, such that fluorescent bursts result exclusively from single doublylabeled DNA constructs diffusing through the confocal volume. The imaging buffer contains i)
50 mM hemipotassium HEPEs buffer (pH 7.5), ii) Trolox/PCA/PCD oxygen scavenger cocktail
to catalytically remove oxygen16, 30 and thereby increase Cy3/Cy5 dye photostability, with iii)
sufficient NaCl to achieve total monovalent cation concentrations of [M+] = 100 mM.
9.3.4 Single-molecule FRET spectroscopy and data analysis
Details of the confocal smFRET experimental apparatus can be found in previous work3032. In short, the output from a 532 nm Nd:YAG laser (10 ps pulses at a 20 MHz repetition rate) isbeam expanded, collimated, and directed into an inverted confocal microscope with a 1.2 N.A.
water immersion objective. The collimated beam overfills the limiting microscope aperture,
resulting in a near diffraction limited excitation and collection spot size (1/e2 radius 0 = 310(30)nm). In the current smFRET diffusion experiments (Figure 9.1A), the laser is focused into asolution of doubly dye labeled 40A DNA at sufficient dilution (~ 50 pM) to ensure that only asingle DNA molecule diffuses through the observation window at a time, thereby generating
typically an isolated  1 ms burst in fluorescent signal (Figure 9.3A and 9.3B). The resulting

233
photons are collected through the same objective, sorted by wavelength (green/red) andpolarization (horizontal/vertical) before detection on four single photon avalanche photodiodes(APDs). A 50 µm pinhole spatial filter before the APD detection unit is used to restrict out offocus photons along the (z) photon propagation direction to achieve a sub-femtoliter detection
volume. For each fluorescent burst above the 25 KHz photon/sec software adjustable count rate
threshold (i.e., 10-fold higher than background noise in an equivalent 1 ms burst window), an
EFRET value is obtained from the number of green vs. red photon counts detected, after suitablecorrection for background and cross talk contributions with in-house software31, 33. Since thedouble fluorophore labelling efficiency for the DNA constructs is high but imperfect (> 90%),
alternating laser excitation methods (ALEX) with interleaving green and red laser pulses areused to ensure only bursts from doubly-labeled DNA constructs are included in the EFRET
distributions31, 34. By way of example, the series of events flagged by arrows in Figure 9.3B andnumbered from 1 to 4 can be unambiguously sorted into fluorescent bursts corresponding to 1)
unfolded yet doubly labeled, 2) Cy3 only labeled, 3) Cy5 only labeled, and 4) folded doubly
labeled DNA constructs, respectively.
Once the EFRET value of each burst event from doubly-labeled DNA has been computed,
an EFRET histogram is generated (Figure 9.3C). Note that the EFRET value is calculated as IA/(IA +ID), where IA/D is the total acceptor/donor signal after background fluorescence and detector
crosstalk corrections. For the DNA hairpin constructs in this study, the EFRET histograms exhibit
two distinct populations with low EFRET (~0) and high EFRET (~0.8), corresponding to theunfolded and folded conformation, respectively16. The EFRET distribution is then fit to a sum of
two Gaussian functions, with the folding equilibrium constant readily calculated from the ratio ofareas under each component29, 31, 33-34. We have observed for each hairpin construct the234
maximum folded fraction to be around 80%. This actively folding fraction is consistent with oursurface-tethered smFRET experiments, for which 80% of the DNA hairpin constructs actively
fold/unfold, with the remainder are trapped in the low EFRET configuration. Quantification of thenon-folding subpopulation is thereby achieved by comparing surface-tethered results with freely
diffusing studies29, 33, with such subpopulations subtracted from the equilibrium constantcalculation, as detailed in previous work29, 33. The resulting folding equilibrium constant (Kfold) isthen obtained from this corrected data and used for further thermodynamic analyses.

9.4

Results and Analysis

9.4.1 Pressure dependence of DNA hairpin folding
The free volume taken up by a biomolecule will vary as a function of conformation,
which in turn will control the effect of external pressure on biomolecular folding3-4. By
differentiating the expression for Gibbs free energy, we can express the pressure dependence ofthe folding equilibrium constant as3(

𝜕𝑙𝑛𝐾𝑓𝑜𝑙𝑑
𝜕𝑃

)𝑇 =

−∆𝑉 0
𝑅𝑇

,

Eq. 9.2

where R is the gas constant and ∆V0 denotes the change in free volume upon folding: ∆V0 = Vfold- Vunfold. According to Eq. 9.2, folding is promoted by increasing pressure when ∆V0 < 0, andreduced by pressure when ∆V0 > 0. As expected from Le Chatelier’s principle, stress due toincreasing pressure is partially relieved by shifting the equilibrium toward the direction ofsmaller volume3. Eq. 9.2 can be integrated at constant T to predict the simple function
dependence of Kfold on external pressureln Kfold(P) =−𝑃𝑒𝑥𝑡 ∆𝑉 0
𝑅𝑇

+𝐶

or

Kfold(P) = exp(

−𝑃𝑒𝑥𝑡 ∆𝑉 0
𝑅𝑇

+ 𝐶),

Eq. 9.3

235
where C is the integration constant. Note that C can be completely decoupled from the pressuredependent term.
To explore the pressure dependence of DNA hairpin folding, smFRET experiments havebeen performed over a wide range of external pressures (Pext = 1 bar to 3000 bar) inside fusedsilica square capillaries coupled to our high pressure compression apparatus. The sample EFRET
histogram reveals two distinct populations with EFRET  0 and  0.8 (Figure 9.3C), corresponding
to unfolded and folded states of the DNA hairpin construct, respectively. As the external pressure
rises, the folded (unfolded) population decreases (increase), respectively. This implies that
increasing pressure favors the unfolded state of the DNA hairpin and thus a positive change infree volume (∆V0 > 0) (Figure 9.3D). Such pressure induced unfolding or “denaturation” hasbeen experimentally observed in previous bulk ensemble studies of nucleic acids35 and proteins3,
36. However, the physical reason behind why ∆V0 > 0 is far from obvious, since one might at first

expect nucleic acids and proteins to adopt more compact conformations upon folding. Thoughstill controversial36-39, one of the simplest interpretation would be that the folded structure
generates more hydrophobic regions which exclude the solvent shell, generating “solvent voids”
and therefore taking up greater volume; an equally plausible explanation is that the increase insolvent accessible surface area of the unfolded state facilitates solvation with a more compact
solvent structure, which translates into ∆V0 > 0 and thus correctly predicts the pressure-induced
denaturation of biomolecules36-39.
The pressure dependences of DNA hairpin folding with different stem sequences areplotted in Figure 9.4A, which display the expected linear dependence (i.e., Eq. 9.3) of ln[Kfold]vs. Pext and provides clear evidence that the 40A DNA hairpin constructs unfold with increasingpressure. Note the systematic upward shift in these curves with increasing stem sequence length,

236

Figure 9.4 Pressure dependence of folding for a systematic series of DNA hairpins: (A) Pressure
effects presented in a van’t Hoff plot of ln[Kfold] versus Pext, for which the slope yields the freevolume change due to DNA stem hybridization (∆V0 = V0fold – V0unfold). (B) Volume changes uponfolding (∆V0) as a function of number of base pairs in the duplex stems, which reveal a remarkable
linear dependence on nstem; (C) Extrapolation of this linear dependence on stem length to nstem = 0,
thereby isolating free volume contributions (∆V0loop) to DNA hybridization from formation of the
40A loop.

which is in almost all cases consistent with the exponential increase in Kfold predicted withadditional free energy release due to incremental base pairing. The only exception to this trend isevident in the nearly overlapping Kfold trendlines for the 7-bp and 8-bp constructs, which occur
because the additional stabilization due to the extra base pair (nstem = 7 vs. 8) is counteracted by
the terminal d(G-C) pair being replaced by the less stable d(A-T) (Figure 9.2B) in the 7-bp and
8-bp constructs, respectfully.
For nearly incompressible fluids, ∆V0 remains approximately constant over wide pressure
ranges36; hence the data for each stem sequence can be linearly fit to Eq. 9.3 in order to obtain

237
accurate free volume changes upon folding (∆V0) as a function of hybridization length. Although
the slopes appear quite similar for each data set, upon closer inspection, systematic differences
are visually apparent. By way of more quantitative comparison, least squares fitted slopes (∆V0)
of Figure 9.4A have been plotted against the number of base pairs in Figure 9.4B and 9.4C.
Though the slope uncertainties are appreciable, the overall trend in the data is quite clear; ∆V0increases smoothly and quasilinearly with number of base pairs within the duplex stem. This canbe rationalized by a roughly linear growth in solvent-inaccessible “voids” and hydration volume
with each additional DNA base pair in the stem sequence. Most importantly, pressure induced
measurements of ∆V0 exhibit a sensitivity to stem length that is clearly at the single base pairlevel of resolution.
If we interpret this quasilinearity as arising solely from solvent inaccessible regions in thestem, the data suggest a deconstruction of the free volume change into a simple additive sum ofstem and loop contributions with a ∆V0 resolution close to the single base pair difference, theaverage volume change per base pair ∆Vstem = Vbp*nstem is determined to be Vbp = 1.98(16)cm3/mol/bp (base pair), which is consistent with previous values (Vbp = 2.1(4) cm3/mol/bp)
obtained from high-pressure UV melting experiments on poly[d(A-T)] DNA40-42. Moreover,despite the impressively small fractional uncertainties in ∆V0 obtained from these least squares
fits, the 9-bp hairpin with a weaker terminal d(A-T) base pair is experimentally indistinguishable
from the 9-bp hairpin with a stronger terminal d(G-C). Thus, although the incremental freevolume changes due to increasing stem length are unambiguously determined in this study, thecorresponding effects due to a stronger d(G-C) or weaker d(A-T) terminal base pairing appear to
be 5 to 10 fold smaller and obscure any finer differential effects at our current sensitivities due tosingle base pair variance.

238
9.4.2 Temperature dependence of DNA hairpin Folding
Temperature plays an equally crucial role in both the kinetics and thermodynamics ofbiochemical reactions, with nucleic acid structures known to be highly sensitive to temperature43.
In general, nucleic acids fold into more ordered states driven by exothermic interactions such ashydrogen bonding and base stacking. Thus, by Le Chatelier’s principle, folding in nucleic acids
is generally but not exclusively unfavored by increasing temperature, with notable exceptions insystems where the free energy changes are dominated by solvent vs. solute contributions32, 44-45.
The temperature dependent unfolding of the DNA hairpins is shown in a van’t Hoff plot (Figure
9.5A), where ln[Kfold] is plotted as a function of reciprocal temperature (1/T). The data are well
fit to linear functions which allow us to deconstruct the full folding free energy (∆G0) into
enthalpic (∆H0) and entropic (∆S0) contributions:
1 ∆𝐻 0∆𝑆 0

𝑙𝑛𝐾𝑓𝑜𝑙𝑑 = − 𝑇 𝑅 + 𝑅 .

Eq. 9.4

Note that the fractional temperature vs. pressure changes required to see comparable effects in
Kfold differ by orders of magnitude. This is due to the large change in entropy upon folding of acomplex biomolecule, which results in much larger thermodynamic free energy contributions
arising from TS0 vs PV0 under ambient physiological conditions. In the linear least squares
fits in Figure 9.5A, the positive slopes signal folding of the 40A hairpin folding to be exothermic(∆H0 < 0) and therefore penalized by heating. Conversely, the negative intercepts from these fits
indicate a decrease in entropy (∆S0 < 0) during hairpin formation, consistent with the canonicalpicture (stated above) of folding into a more ordered structure. However, one should always be
mindful that the measured thermodynamic response is determined by free energy change for theentire system, which includes both structural effects from the biomolecules as well as thesurrounding solvent32, 46-47.

239

Figure 9.5 Temperature dependent folding response: (A) Temperature unfolding effects for a forthe series of DNA hairpins presented as a standard van’t Hoff plot, with the slope (m = -H0 ) andintercept yielding the enthalpy and entropy changes upon folding; (B) Enthalpy change (∆H0) as afunction of stem length (nstem, dark blue), as well as predictions (dark red) from nearest neighbormodel parameters; (C) Entropy change (∆S0) as a function of duplex stem length (dark blue), incomparison to the nearest neighbor model prediction for fully bimolecular stem formation (darkred). The two additional points in (B) and (C) (light blue) correspond to data for an alternate 9-bp
construct with the 3’ d(A-T) replaced by a stronger d(G-C) base pair. Corresponding enthalpy andentropy predictions from nearest neighbor model predictions for bimolecular stem formation are
also shown (light red), which suggest a small increase in enthalpy and entropy change underunimolecular stem formation conditions for a hairpin construct.
Thermodynamic results for ∆H0 and ∆S0 from van’t Hoff analysis for the nstem = 7-10-bp
and 9-bp (GC) series of constructs are summarized in Figure 9.5B and 9.5C, along withpredictions of the same quantities by nearest neighbor models24-25. Interestingly, these plots
explicitly demonstrate that ∆H0 and ∆S0 both decrease in approximately linearly fashion with thenumber of base pairs (nstem) (Figure 9.5B), consistent with a heat release and change in disorderroughly proportional to hybridization length. Also worth emphasizing, the 9-bp hairpin with a240
terminal G-C base pair exhibits a noticeably larger incremental decrease in both ∆H0 and ∆S0than for the corresponding 9-bp hairpin sequence with a terminal d(A-T) base pair. This shiftarises as a result of a stronger d(G-C) vs. d(A-T) base pairing interaction, as consistent withprevious observations24-25.

Figure 9.6 Subtraction of the stem length (nstem) dependent contributions from DNA double-strand
formation resulting in single-strand DNA looping (A) enthalpy (∆H0loop), (B) entropy (∆S0loop) and(C) free volume (∆V0loop) changes. The data is consistent with a simple linear offset for these loop
contributions, indicated by pink, green and orange dashed lines for enthalpy, entropy and freevolume, respectively.

241
9.5

Discussion

9.5.1 Deconstructing free volume changes into DNA stem and loop formation
With the present experimental combination of i) high dynamic range of pressures and ii)
quantitative smFRET measurements, we achieve single base pair resolution for the free volume
changes (∆V0) incurred upon hybridization of a 40A DNA hairpin. Furthermore, when theanalysis is repeated for a series of stem junction sequences (see Figure 9.2), the data follow anearly linear trend with a slope ∆V0bp = 1.98(16) cm3/mol/bp (Figure 9.4B), which is alreadyconsistent with a previously reported (albeit less precise) value of ∆V0bp = 2.1(4) cm3/mol/bp forpoly[d(A-T)] DNA hybridization obtained from high pressure UV melting experiments undercomparable monovalent cation concentrations40. Although the effect of swapping a single basepair (i.e., 9-bp AT to 9-bp GC) is indistinguishable for the present selection of stem sequences,results from previous high pressure UV melting studies at a relatively low monovalent cation
concentration for poly[d(A-T)], poly[d(G-C)]48, and poly[d(I-C)] (dI = 2’-deoxyinosine, a dG
like derivative) yield unit base-pair slopes of ∆V0bp = 1.42 cm3/mol/bp, 4.57 cm3/mol/bp41, and4.8(6) cm3/mol/bp48, respectively. Specifically, the predicted free volume differences for singled(A-T) and d(G-C) swaps in poly[d(A-T)] and poly[d(G-C)] would be ∆∆V0bp = 3.4 cm3/mol/bp.
This is significantly higher (20-fold) than our experimental uncertainty, yet no change is seen forsuch an d(A-T) → d(G-C) single base-pair swap in our data. In contrast, a UV melting
experiment of mixed-base pair DNA with G-C content similar to our complementary sequences
has found ∆V0bp = 1.8(2) cm3/mol/bp42, in much improved agreement with our results. We
therefore suspect that ∆Vbp may additionally depend upon interaction between neighboring basepairs, resulting in excess values of ∆V0bp for homonucleotide duplexes poly[d(G-C)] and242poly[d(I-C)], which appear to be moderated in DNA duplexes with more mixed-base-paircharacter.
If we extrapolate the linear relation between ∆V0 and the number of base pairs, thevertical intercept is clearly positive, well within experimental uncertainty (Figure 9.4C). This
indicates that there must be a free volume change ∆V0 (0 bp) > 0 even in the absence of any basepairing of the stem sequence. A simple additive model for this behavior would suggest that theoverall change in free volume is given by
V0 = V0stem + V0loop = V0bp × n + V0loop

Eq. 9.5

where ∆V0loop represents a contribution generated from loop formation of the single-strandedpoly(dA) DNA linker. Specifically, the results suggest an increase in the effective DNA volume(∆V0loop = +7.0(14) cm3/mol) when the DNA linker forms a loop structure49-50, which at first
seems counterintuitive. However, it is also well established that single stranded poly(dA) isappreciably structured due to spontaneous base stacking between adjacent adenine bases, astacking which would be disrupted upon folding of the hairpin 51-55 due to loop distortion. The
data therefore suggest that the closely stacked adenine bases occupy less volume than free bases,
and therefore when the base stacking is disrupted, the effective volume occupied by the singlestrand DNA increases, thus resulting in a positive volume change contributed from DNA linker
looping (∆V0loop > 0).
Although positive V0bp seems to imply the longer DNA double strand is more
susceptible to pressure denaturation effects, we have found the free energy stabilization per baseis more than an order of magnitude higher than the pressure-volume perturbation even at thebottom of the Marianas Trench (~ 1.1 kbar). Thus, it is true that the stability of DNA duplex isincreased with the number of base pairs at any pressure in nature (on earth). However, such

243pressure perturbation can significantly affect the local stability of a DNA double strand,
especially when the DNA needs to unzip (partially melt) to participate in biochemical reactions
such as DNA replication and transcription. Therefore, the deep sea species may alter the cellularosmolyte compositions to accommodate the high pressure environments56. It has been founddeep sea fish accumulate high level of TMAO in their muscles56-57, while TMAO is also shownto not only stabilize DNA secondary structures58, but reduce V0 to mitigate the pressure
effects11, 18. Moreover, high pressure may also destabilize RNA structures and greatly affect theirbiochemical functions. For example, the gene regulatory elements RNA riboswitches can be
extremely sensitive to pressure, due to the fact that they dynamically fold into different
conformations to control the gene expression. The deconstructed volume contributions from stem
(V0stem) and loop (V0loop) determined in this work may help to predict the more complicatedRNA folding in the future.
Although more work clearly needs to be done, our results suggest both the double-strand
stem and the single-strand loop significantly contribute for the 40A hairpin construct to thepressure dependent response for the overall folding thermodynamics. Hairpin structures are
ubiquitous in nucleic acids15, 59, the response for which may help us understand pressure effects
on more complex nucleic acid folding in extreme environments23. From our volumetric analysis,
the positive ∆V0loop is consistent with the disruption of base stacking within the poly(dA) linker,
indicating adjacent base stacking reduces the free volume of single-stranded DNA. On the other
hand, the positive ∆V0stem suggests the DNA duplex formation increase the free volume. The twomain forces that govern the structure of double-stranded DNA are inter-base-pair hydrogenbonding and base-stacking. The overall positive sign for ∆V0stem implies that inter-base-pairhydrogen bonding and perhaps higher-order structure formation (e.g., major and minor grooves)244
reduce solvent accessibility to the DNA backbone and thus lead to larger free volume60-62,
completely dominating the volume reduction by base-stacking.
9.5.2 Deconstruction of stem (Hstem) and loop (Hloop) enthalpy changes
The enthalpy (∆H0) and entropy (∆S0) changes obtained from the temperature dependent
study in Sec. 9.4B are summarized in Figure 9.5B and 9.5C, respectively. For comparison, theFigures 9.5B and 9.5C include predictions from the so-called nearest-neighbor models (NN),which take into account free energy contributions due to hydrogen bonding between single basepairs but also includes the additional base stacking and stabilization effects accrued due toneighboring base pairs. The model parameters have been significantly improved and extended
beyond Watson-Crick pairs in the past two decades, and are now thought to provide reasonably
accurate predictions of all thermodynamic parameters (∆G, ∆H and ∆S) for DNA duplexing24-25.
In Figure 9.5B, the experimental ∆H0 values for hairpin folding and the nearest-neighborpredictions for duplex stem formation from two separate DNA strands (Hduplex) clearly exhibit
the same trend, specifically an increasing exothermicity with increasing number of base pairs.
(Figure 9.5B). However, there would also appear to be an equally clear and nearly constant shift
between the two data sets, with ∆H0 - Hduplex  15 kcal/mol (Figure 9.5B and 9.6A). In a manner
similar to linear deconstruction of free volume changes (V0 = V0stem + V0loop) into stem andloop contributions, it is interesting to speculate how such an enthalpy shift could again arise by
virtue of the loop formation. Specifically, the offset between the two experimental andtheoretical enthalpy curves can be attributed to differences between i) full bimolecular formationof a stem (i.e., from separate ssDNA’s) and ii) unimolecular diffusing of the two stems together
to form a hairpin linked by the poly(dA) strand, the latter of which incurs additional enthalpic(and entropic, see Sec. 9.5C) contributions due to loop formation in the single-stranded DNA

245
linker. From this perspective, subtraction of ∆H0stem from ∆H0 (Figure 9.6A) would correspondto the additional loop formation enthalpy ∆H0loop, which from the fits in Figure 9.5B can be
estimated to be ∆H0loop  +15(2) kcal/mol. If we further assume this additional enthalpy penalty
to be proportional to linker length, the looping enthalpy per nucleotide (∆H0loop/40 nt  +0.38(5)kcal/mol/nt) would be relatively close to previously reported scaling relations (∆H0loop per nt 
+0.5 kcal/mol/nt) at comparable monovalent salt concentrations51. The source of suchendothermicity could again be attributed to disrupted base stacking and distortion in thepoly(dA) ssDNA loop51-55. Indeed, since a near-linear proportionality in incremental folding
enthalpy has been observed in previous studies for constant stem lengths with linkers varying
between 8 to 30 nucleotides51, our 20% lower per nucleotide value can be rationalized as due topartial relaxation of these looping distortions for a longer (40A) linker. Moreover, different
buffer conditions may also contribute to our low ∆H0loop; specifically, our experiments have been
performed at lower monovalent cation concentration ([M+] = 100 mM vs 250 mM). This is quite
relevant as base stacking is repressed at reduced [M+]52, thereby lowering the ∆H0loop enthalpic
penalty and as consistent with our observations. It is worth noting that such positive ∆H0loop
contributions again confirm that 40A loop formation is an endothermic process, enthalpicallydestabilizing the folded hairpin conformation.
9.5.3 Deconstruction of stem (Sstem) and loop (Sloop) entropy changes
We can take this analysis one step further and attempt to deconstruct the entropic
contributions for hairpin formation into both loop and stem components. In an analogous fashion
to the trends in ∆H0 (Figure 9.5B), the experimental dependence of ∆S0 on sequence length(Figure 9.5C) follows a similar trend to that of nearest neighbor model prediction24-25, with ∆S0systematically decreasing with increasing number of base pairs. The experimental results are246
again all shifted from model predictions by an approximately constant positive offset, which by asimilar line of reasoning as in Sec. 9.5B may be taken to represent the entropic contribution due
to poly(dA) loop formation, i.e., ∆S0loop = +25(7) cal/mol/K (Figure 9.6B). Such entropic
favoring of the looping process would again appear to be counterintuitive, since constraining theends in a random walk or worm like chain model would certainly lower the overall entropy49-50.
However, in interpreting such an entropically favored loop formation, it is important to note thatthe poly(dA) linker contribution is more than simply structural. Specifically, the poly(dA) linker
also plays a crucial role in raising the effective concentration of the one strand (S2) with respect
to its complement (S1) and vice versa. Therefore, ∆S0loop may be usefully deconstructed into two
further contributions: i) structural changes due to the biomolecule plus solvent system (∆S0struct)
and ii) unimolecular raising of the effective strand concentration (∆S0conc), with ∆S0loop = ∆S0conc+ ∆S0struct.
More quantitatively, the difference between the unimolecular folding equilibrium
constant (Kfold) from covalently linked strands, i.e., what is experimentally measured, and a fully
bimolecular duplex formation (Kbimol) from freely diffusing S1, S2 strands, i.e., what is predictedby the NN model, can be related as follows:[𝑆 𝑆 ][𝑆 𝑆 ]

1

1

1

2

2

𝐾𝑏𝑖𝑚𝑜𝑙 = [𝑆 1][𝑆2 ] = [𝑆1 2] × [𝑆 ] = 𝐾𝑓𝑜𝑙𝑑 × [𝑆 ].
1

2

Eq. 9.6

where [S1], [S2], and [S1S2] are concentrations of the two strands and the full hairpin,
respectively.
For experimental folding of the 40A hairpin, an additional term of RTln[S2]0 between
unimolecular and bimolecular folding free energies can be immediately recognized from the
Gibbs relation ∆G0 = -RTlnKfold. Such concentration effects are purely entropic, as the linker
provides a physical limit to the phase space which S2 can sample. The effective [S2]0 can be247
estimated from random walk theory, where the 40A linker is simplified into a collection of N (~9) “Kuhn segments,” with the angular orientation of a given Kuhn segment taken as completely
random and independent from adjacent units63-65. The per volume probability density of the endto-end distance for a random-walk polymer P(r) is known to be well described by a Gaussianfunction66, with P(r = 0) immediately recognized as the probability of S1 and S2 diffusing
together. Therefore, the effective concentration is simply determined by matching the encounter
probability P(0) with a bulk concentration [S2]0. With previously determined persistence lengths
and sizes of a single nucleotide base67-70, the effective concentration [S2]0 is calculated as0.74(17) mM, corresponding to an additional entropy change of ∆S0conc = +14.7(5) cal/mol/K.
The positive sign of ∆S0conc reflects the thermodynamic favoring of unimolecular overbimolecular folding due to entropic enhancement of the local strand concentration.
Consistent with our simple additive thermodynamic modeling, we can subtract thisconcentration entropy ∆S0conc from the average linker contribution (∆S0loop) to infer an overall∆S0struct = +10(7) cal/mol/K for structural change in the poly(dA) linker plus solvent system. The
positive value for ∆S0struct implies an entropy increase when linear DNA turns into a loop via
head-to-end connection. This entropy gain is at first counterintuitive, since looping structure
would be expected to restrict conformational phase space with respect to a linear configuration4950. However, looping can also disrupt the low entropy state achieved by base stacking effects inthe poly(dA) oligo. Consequently, distortion of base stacking due to loop formation could
rationalize the observed entropy increase, arising from both translation and internal degrees of
freedom such as bond rotation71. Indeed, such entropically favored unstacking between
nucleotide bases has been previously reported for poly(dA) as well as between monomer A
bases71-72. Of course, the solvent entropy is an essential component of this estimate and must also

248
be considered, since our measurements are only sensitive to entropy change of the combined
solute + solvent system. However, solvation entropy would seem unlikely to explain the S0struct> 0, as compaction of the ring structure increases the overall charge density, subsequently
stronger hydration forces, a more ordered water solvent environment, and thus ∆S0solvent < 073-74.
In short, the entropy gain from base stacking dissociation would appear to dominate the overallfavorable looping entropy, resulting in positive ∆S0struct. It is interesting to note that positive
entropy changes are also observed in detailed molecular simulation study by Mishra et al.75,
where the presence of a ssDNA linker entropically stabilizes the folded hairpin due to more
prominent base stacking upon unfolding of the hairpin75.

Figure 9.7 Summary of our simple additive model for deconstruction of the stem length dependent(9-bp (AT)) folding thermodynamics of a 40 A DNA hairpin.

In summary, the overall effect of the poly(dA) linker appears to be entropically favorable
to hairpin folding (∆S0loop > 0). Part of this contribution arises from ∆S0conc > 0 due simply to theincrease in effective strand concentration for linked polymers, which results in a larger effective
Kfold under unimolecular vs. bimolecular DNA duplexing conditions. The remainder of theentropy contribution can be attributed to conformational changes in the linker, whereby the
disruption of base stacking in the poly(dA) linker relaxes the configurational confinement intranslational and internal degrees of freedom during looping, resulting in ∆S0struct > 0. In the end,

249
subtraction of ∆V0stem = V0bp(= +1.98(16) cm3/mol/bp) × n from the overall change of the freevolume ∆V0 is also plotted in Figure 9.6C to highlight the loop contribution V0loop. In thecontext of this simple additive model, the thermodynamic properties (change in free volume,
enthalpy, and entropy) of the isolated 9-bp stem and 40 A loop are schematically summarized in
Figure 9.7.

9.6

Summary and conclusion
The thermodynamic properties (∆H0, ∆S0 and ∆V0) of DNA hairpin folding have beenstudied via smFRET spectroscopy as a function of temperature, external pressure (1-3000 bar),and base pair stem length. In the temperature dependent studies, folding of these 40A DNA
hairpin constructs is found to be exothermic (∆H0 < 0) with an entropic penalty (∆S0 < 0), withpressure-induced unfolding experiments indicating that the DNA hairpin takes up more volume
in the folded vs. unfolded state (∆V0 > 0). With such high dynamic range in external pressure
control (Pext = 1 bar to 3000 bar), changes in free volume with single base pair resolution has
been achieved, allowing ∆V0 for the DNA hairpins to be linearly deconstructed into stem (∆V0bp= +1.98(16) cm3/mol/bp) and loop (∆V0loop = +7.0(14) cm3/mol) contributions by analyzing thedependence on length and complementary sequence. Based on predictions (∆H0stem and ∆S0stem)from a nearest neighbor model, both ∆H0 and ∆S0 for the full DNA hairpin can thereby bedeconstructed into stem and loop contributions. It is found that single strand loop formation isendothermic (∆H0loop = +15(2) kcal/mol) and yet compensated by positive entropic gain (∆S0loop= +25(7) cal/mol/K), where the looping endothermicity can be attributed to the disruption of basestacking in the poly(dA) linker. In the context of a simple additive thermodynamic model, thispositive ∆S0loop can be further deconstructed into contributions due to unimolecular enhancement

250
in the effective strand concentration (∆S0conc = +14.7(5) cal/mol/K), with the remainder attributed
to structural changes in the loop (∆S0struct = +10(7) cal/mol/K) arising from the disruption of basestacking relaxing external (i.e., translational) and internal (i.e., hindered rotational) constraints.

9.7

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Chapter 10
High Pressure Single-Molecule FRET Studies of the Lysine Riboswitch:
Cationic and Osmolytic Effects on Pressure Induced Denaturation

10.1

Abstract
Deep sea biology is known to thrive at pressures up to ≈ 1 kbar, which motivates

fundamental biophysical studies of biomolecules under such extreme environments. In this work,
the conformational equilibrium of the lysine riboswitch has been systematically investigated bysingle molecule FRET (smFRET) microscopy at pressures up to 1500 bar. The lysine riboswitch
preferentially unfolds with increasing pressure, which signals an increase in free volume (∆V0 >0) upon reverse folding of the biopolymer. Indeed, the effective lysine binding constant increases
quasi-exponentially with pressure rise, which implies a significant weakening of the riboswitchligand interaction in a high-pressure environment. The effects of monovalent/divalent cations
and osmolytes on folding are also explored to acquire additional insights into cellularmechanisms for adapting to high pressures. For example, we find that although Mg2+ greatly
stabilizes folding of the lysine riboswitch (G0 < 0), there is negligible impact on changes infree volume (∆V0  ) and thus any pressure induced denaturation effects. Conversely,
osmolytes (commonly at high concentrations in deep sea marine species) such as thetrimethylamine N-oxide (TMAO) significantly reduce free volumes (∆V0  0) and thereby
diminish pressure-induced denaturation. We speculate that, besides stabilizing RNA structure,enhanced levels of TMAO in cells might increase the dynamic range for competent riboswitch*This chapter is adapted from: Sung, H.-L.; Nesbitt, D. J. High Pressure Single-Molecule FRET Studies of
the Lysine Riboswitch: Cationic and Osmolytic Effects on Pressure Induced Denaturation. Phys. Chem.
Chem. Phys. 2020, 22, 15853-15866.

257
folding by suppressing the pressure-induced denaturation response. This in turn could offer
biological advantage for vertical migration of deep-sea species, with impacts on food searchingin a resource limited environment.

10.2

Introduction
The effective free volume of a biomolecule can vary substantially upon folding, mainly

due to changes in accessibility of hydrophilic regions and compactness of the resulting water
configuration1-4. Consequently, the equilibrium between each conformation can be modulated bypressure, according to Gibbs free energy: ∆G0 = ∆U0 −T∆S0 + P∆V0.5-6 Although pressure isoften a relatively benign variable in biology, pressure dependence of folding is extremely
important to deep sea marine species, as a result of the rapid increase of hydraulic pressure withocean depth ( 1 bar every 10 meters). In fact, multiple organisms have been found thriving in
the deep sea and some even at the bottom of the Mariana Trench7, where pressure at the deepest
point is P  1.1 kbar. It is thus of considerable interest to investigate not only the biophysicalresponse of biomolecules to pressure fluctuations, but also the molecular strategies developed bydeep sea organisms to accommodate extreme pressures and changes in pressure by verticalmigration. As an explicit focus of this work, we combine single molecule fluorescencemicroscopy tools in a high pressure apparatus to explore the folding dynamics of RNA
riboswitches.
As a simple test construct for such studies, riboswitches are noncoding mRNA elementsthat can regulate their shape and gene expression in response to the specific presence of small
molecular ligands.8-10 The aptamer domain of a riboswitch structurally changes to selectively

258
capture a specific ligand molecule(s), with which the gene expression platform may toggle
between “on” and “off” conformations and thus result in disparate regulatory outcomes. In orderto optimize gene regulation, therefore, the folding equilibrium of a riboswitch must be delicately
modulated by a multitude of external variables such as external pressure, temperature, andconcentrations of monovalent/divalent cations and osmolytes. Although external pressure mightseem only a relatively small perturbation, typical free volume changes associated with DNA
hairpin formation with only 7-10 bp (say, V0  25 mL/mol) translate into free energy changesof   kcal/mol  kT at 1 kbar pressures common to deep ocean marine life11. To date,pressure-dependent studies of nucleic acid folding have been largely limited to secondary
structure formation,11-17 with studies of higher order (tertiary) interactions only for the DNA Gquadruplex18-20 and RNA tetraloop-tetraloop receptor (TL-TLR).21 This leaves the highly diverse
arena of RNA riboswitch tertiary structure motifs largely uninvestigated and ripe for further
exploration as a function of external hydrostatic pressure. In the present work, we have chosen
the lysine riboswitch22 (see Figure 10.1) as a model system to study the pressure dependent
effects on ligand binding and tertiary folding, both of which are among the most important
conformational transitions in biologically functional RNA.
To achieve these goals, we have recently converted our single molecule confocal FRET(smFRET) apparatus into a novel tool for biomolecular folding studies at high pressure (seeFigure 10.2)11, 16-17, 23. The present high pressure smFRET measurements are performed in asquare (50 m x 50 m) quartz capillary sample cell, which due to relatively small surface areaof the inner capillary can sustain pressures up to 5 kbar without shattering11. Such a large
dynamic range of pressures enables us to obtain precise measurement of free volume differences

259
upon nucleic acid folding (∆V0), as well as changes in these free volumes (∆V0) in response tovarious cationic and osmolytic buffer conditions.

Figure 10.1 Single molecule FRET construct design for studying ligand-induced lysine riboswitch
folding. (A) Crystal structure of the lysine riboswitch. (PDB: 4ERJ) (B) Schematic representationof lysine riboswitch folding and the energy transfer between Cy3 and Cy5 in each conformation.
(Left: unfolded; right: folded)

The basic organization of this paper is as follows. Key aspects of the i) high pressure
confocal experimental apparatus, ii) construct design and preparation, and iii) sample data
analysis are presented in Sec. 10.3.1-3, followed by a detailed pressure dependent studies under avariety of buffer conditions. Specifically, since both solvent and solute, in addition to thebiomolecule itself, can contribute significantly to the folding thermodynamics,24-26 the pressuredependent response of the lysine riboswitch has been systematically studied as a function of
three classes of solutes: i) ligand (lysine), ii) monovalent (Na+) and divalent (Mg2+) cations, and260iii) osmolyte (trimethylamine N-oxide, TMAO) concentrations, as presented in Sec 10.4.1-4 Firstof all, as the cognate ligand, lysine plays an obviously central role in lysine riboswitch folding,which from previous detailed kinetic analyses27 has been shown to be triggered by a single lysine
in a “induced-fit” mechanism, whereby the ligand first binds and then folds.27-28 Secondly,
nucleic acids interact strongly with cations, due to its polyanionic nature of the RNA polymer.
Thus, cationic solute species as Na+ and Mg2+ can not only result in compaction of a folded (orunfolded) nucleic acid structure, but also significantly alter the hydration shell through partial
Debye shielding of the Coulomb interactions29-30. Thirdly, TMAO is an osmolyte commonly
found in marine species31-32, with increasing accumulations in deep sea fish and amphipods.33-34
Moreover, TMAO has been shown to act as a chemical chaperone35 to stabilize protein36-37 andnucleic acids38-39 structures at ambient pressures, and to preserve enzyme activity at highpressures40-41. These suggest TMAO to be a crucial “piezolyte” with which to counteract
pressure induced denaturation effects. Indeed, in the present work, we find that an increase in
TMAO results in a novel preferential stabilization of the folded riboswitch conformation at highpressure (V0 < 0), thereby counterbalancing the above-noted tendency for RNA to bedestabilized with increasing pressure, as discussed further in Sec. 10.5. Finally, the paper
presents summary results, possible directions for future investigation, and concluding remarks in
Sec 10.6.

10.3

Experiment10.3.1 High pressure capillary sample cell and pressure control
These high pressure smFRET experiments are made possible by introduction of a highpressure glass capillary sample cell11, 17, 23 into a time correlated single photon counting confocal

261
microscope (see Figure 10.2).42 Specifically, for the sample cell we use square capillary tubing
made from fused silica, with  360 µm and  50 µm outer and inner sidewall lengths,
respectively (Polymicro, Phoenix, AZ). Due to the small surface area of the inner capillary, thecell can sustain repeated high internal pressure cycling up to 5 kbar without fracturing.
Moreover, the wall thickness ( 155 m) and relatively flat interior and exterior surfaces of thesquare capillary mimic a standard cover slip and thereby optimize the excitation/collection
photon efficiencies for fluorescence studies.

Figure 10.2 High pressure smFRET diffusing experiment setup.

To prepare a sample for high pressure smFRET study, one end of the capillary is firstglued to a modified stainless-steel pressure plug (High Pressure Equipment, Erie, PA). A small
section of the opaque hydrocarbon polymer coating of the capillary is then removed by low
temperature propane flame oxidation to create a clear optical window for fluorescence excitationand detection. We load the sample by capillary forces, simply immersing one end into the sample

262
solution; once the capillary is filled, its free end (far from the pressure plug) is sealed bymomentary heating with an oxy-propane torch. Prior to coupling the cell to the high pressure
system, the open end of the capillary is dipped into low viscosity silicone oil to create a thin,
immiscible liquid layer. This prevents any contamination of the sample from the pressuretransmitting ethanol and yet still conducts pressure effectively from the hydraulic press (videinfra) to the single molecule detection volume. More detailed description of sample cell
preparation and alignment of the excitation/fluorescence microscope can be found in ourprevious work11.
The source of high pressure is a manually operated piston screw pump (High Pressure
Equipment) which can generate and deliver pressures up to 5 kilobars. The pressure generator isconnected to the sample cell and a Bourdon pressure gauge via high pressure stainless steel
tubing with 1/4" O.D. and 1/16” I.D. (High Pressure Equipment, rated at 100,000 psi), with theentire manifold using ethanol as the pressure-transmitting fluid. Prior to high pressure
experimentation, any residual air bubbles in the manifold are removed by repeatedly venting andflushing the high pressure valves. The end-point absence of any residual air bubble isunambiguously evidenced by dramatic increase in the pressurizing efficiency with manual
displacement of the piston screw pump.
10.3.2 RNA lysine riboswitch construct and sample preparation
The crystal structure of the B. subtilis lysC riboswitch aptamer is shown in Figure
10.1A22. According to previous structural characterizations of the ligand-bound and ligand-freelysC aptamer domain22, 43-44, the lysine induced conformational change (Figure 10.1B) mostly
likely involves a change in the relative orientation of the P1 and P5 helices in response to ligand
binding at the five-way aptamer junction. Therefore, to optimize smFRET contrast in the263
construct design, the Cy3 and Cy5 dyes are attached at the distal ends of P1 and P5, respectively(Figure 10.1B).27 The three-strand lysine riboswitch smFRET construct is specifically illustrated
in Figure 10.1B, with detailed RNA oligomer designs and synthesis methods available from ourprevious lysine riboswitch studies under ambient pressure conditions.27 In anticipation of future
smFRET studies, we have also incorporated an additional biotin modification at the extended P1stem for tethering the RNA construct onto BSA-biotin/streptavidin modified surfaces, which will
restrict free diffusion and enable much longer observation times for studies of single molecule
kinetics. For maximum simplicity in these early high-pressure experiments, however, we havechosen to not tether the construct to the surface. This allows the RNA riboswitch construct tofreely diffuse in the capillary cell through the laser beam focus, for which detection/sorting
fluorescence photon “bursts” ( ~ 1 ms duration) through dichroic filters onto avalanche
photodiodes permit statistical probing of the instantaneous biomolecular conformations by
smFRET.
In preparation for smFRET sample solutions, the stock RNA solution is diluted in
imaging buffer to ~ 50 pM, i.e., sufficiently low that each fluorescence burst results exclusively
from only one doubly-labeled construct diffusing through the confocal volume. The imaging
buffer contains i) 50 mM hemipotassium HEPEs buffer (pH 7.5), ii) Trolox/PCA/PCD oxygen
scavenger cocktail to catalytically remove oxygen, iii) 25 mM KCl, 100 mM NaCl and 0.5 mM
MgCl2 to provide background salt, and iv) sufficient lysine, TMAO, additional NaCl and MgCl2
to achieve the desired experimental conditions.
10.3.3 Single-molecule FRET spectroscopy and data analysis
The high pressure smFRET experiment is based on a homebuilt inverted confocal
microscope setup with details described in previous work (Figure 10.2)42. In short, a water

264

Figure 10.3 Sample data and analysis. (A) Representative time-resolved fluorescence trajectories.
The green and red signals plotted upward correspond to Cy3 and Cy5 fluorescence channels,
respectively. The pink traces from 633 nm alternating laser excitation (ALEX) is plotted
downward for direct comparison to conform the presence (or absence) of the Cy5 labeling. (B)Detailed fluorescent traces displaying individual fluorescent events: (1) folded doubly labeled, (2)Cy3-only and (3) Cy5-only labeled construct. (C) Sample EFRET histogram of the lysine riboswitch
folding with [lysine] = 2.0 mM at increasing pressure. Each set of data is fit to a two-Gaussianfunction where the high and low EFRET populations correspond to folded and unfolded
conformations of the lysine riboswitch respectively. (D) The ln(Kfold) vs P plot where the slope
yields the free volume change during folding V0.

265
immersion objective with 1.2 NA tightly focuses the collimated incident beam into a nearly
diffraction limited spot (1/e2 radius = 310(30) nm). The resulting fluorescent photons arecollected through the same objective, sorted into spatially distinct color/polarization channels
with dichroic filters/polarization cubes before being detected by an array of four single-photon
counting avalanche photodiodes. Since the double fluorophore labelling efficiency is < 100%,
alternating laser excitation methods (ALEX) with interleaving green and red laser pulses areused to rigorously ensure that only bursts from doubly-labeled RNA constructs are included in
the FRET energy transfer efficiency (EFRET) distributions.27, 45 Sample fluorescence traces are
exhibited in Figure 10.3A and Fig. 10.3B, with the ALEX signal plotted downward (pink) todistinguish it from the upward FRET (green/red) emission channels. By way of example, theseries of photon events flagged by arrows in Figure 10.3B and numbered from 1 to 3 can be
unambiguously sorted into fluorescent bursts corresponding to 1) doubly labeled, 2) Cy3 only
and 3) Cy5 only RNA constructs, respectively.
Integrated over the full burst diffusion time, the EFRET value (EFRET = IA/(IA + ID)) for
each event from doubly-labeled DNA is computed and used to generate a EFRET histogram(Figure 10.3C). The lysine riboswitch histogram clearly reveals two distinct populations withlow EFRET (~ 0.3) and high EFRET (~ 0.7) states, which corresponds well with predictions forunfolded and folded conformations, respectively.27 Therefore, data are fit to a two-Gaussian
distribution function with the center and width of the high EFRET peak floating globally (Figure
10.3C).27, 45 As a function of hydrostatic external pressure, the unfolded population clearly
increases while the folded population decreases (see Figure 10.3C). The relative abundance ofthe two states can be quantified by taking the ratio of the areas under the two fitted Gaussianfunctions to obtain the riboswitch equilibrium constant for folding. Note that under saturating

266
lysine/salt concentrations, the maximum fraction of free diffusing riboswitch constructs folded isonly 71(8) % of the value obtained from direct single-molecule observation of an immobilized
construct (see Figure 10.4). This fraction is in good agreement with previous reported values of67(3) % in earlier riboswitch studies restricted to a narrower range of [lysine] due to time
resolution limits.27 As shown previously, such discrepancies between the diffusing andimmobilized measurements occur because a small fraction (28(4) %) of the constructs are stuck
in long lived misfolded states, with only 72(4) % actively undergoing conformationaltransitions.27 Thus, accurate extraction of single molecule equilibrium constants (Kfold) is

Figure 10.4 Lysine dependent folding at the ambient pressure obtained from smFRET (A)diffusing and (B) surface tether experiments. Data of fraction folded and kfold are fit to the Hillequation with floating Hill coefficients n = 0.93(16) and 1.12(17), respectively, consistent with the
expected ligand binding stoichiometry from crystal structure data. In smFRET diffusing
experiments, the max folded fraction is observed as 0.63(6) at saturating [lysine]. In surface tether
experiments where the lysine-dependent folding and unfolding rates can be obtained by prolonged
observation of the fluorescence signals from a single construct at a time, the kunfold is foundindependent of [lysine] as 0.213(14) s-1 and the kfold is determined as 1.51(13) s-1 at saturating[lysine], leading to the steady state folded fraction as 0.88(9). The difference in fraction folded(29(8) %) between the diffusing and surface tether measurements is made up by the subpopulaionof constructs that are incapable of folding (28(4) %) from the previous raster scanned image.

267
obtained after correction for the inactive non-folding subpopulations,46-47 with these correctedvalues used in all further analyses.

10.4

Results and analysis

10.4.1 Pressure-induced denaturation of the lysine riboswitch
The systematic decrease in the folded (high EFRET state) construct population as afunction of increasing pressure (Figure 10.3C) clearly indicates that folding of the lysine
riboswitch is energetically disfavored at high pressure. We can quantitatively express thepressure dependence of this folding equilibrium constant from5(𝜕𝑙𝑛𝐾𝑓𝑜𝑙𝑑
𝜕𝑃

)𝑇 =

−∆𝑉 0
𝑅𝑇

,

Eq. 10.1

where R is the gas constant and ∆V0 denotes the change in effective free volume upon folding:∆V0 = Vfold - Vunfold. The pressure induced denaturation we see experimentally signifies that ∆V0> 0, e.g. the effective free volume increases upon folding. Such a free volume change can befurther quantified by a ln(Kfold) vs pressure “van’t Hoff” plot (Figure 10.3D), for which Eq. 10.1
predicts a slope of -∆V0/RT. In Figure 10.3D, the free volume change of lysine riboswitch
folding at [lysine] = 2 mM is extracted from a linear least squares fit to be ∆V0 = +75(3)mL/mol.
The positive sign of this free volume change may seem at first counterintuitive. The
folded RNA state is generally thought to be more compact in size, but such intuitions are only
valid for the solute and ignore the complete solute + solvent system. The positive ∆V0 values
therefore arise from changes not just in the biopolymer solute itself but in the effective volume ofthe surrounding solvent and solvent accessibility1-4. For example, unfolded RNA presents a lessshielded polyanionic conformation to the solvent, which therefore becomes more hydrated due to268
larger solvent-exposed surface area. This could in general result in a more highly orderedhydration shell with smaller effective volume and therefore a V0 > 0 upon refolding48-49.
Alternatively, folding with more tertiary/higher order contacts can create hydrophobic voids that
exclude water molecules, which would also contribute to the folded state occupying aneffectively larger volume with V0 > 0.2 We note that a similarly counterintuitive effects also
occur in high pressure studies of protein folding, which routinely indicate pressure induced
denaturation effects consistent with V0 > 0.4-5 One clear take home message from theanomalous sign of V0 for nucleic acid and proteins is that coupled solute + solvent dynamics
must play an exceedingly important synergistic role and cannot be ignored.
It is also worth noting that these ∆V0  75(3) mL/mol free volume changes in the lysine
riboswitch are an order of magnitude larger than the ∆V0  5 to 9 mL/mol values obtained frombulk fluorescence studies of the RNA tetraloop-tetraloop receptor (TL-TLR) at high pressuresover a series of buffer conditions.21 However, given that multiple tertiary structure formations
are involved in lysine riboswitch folding, these differences become much easier to rationalize22.
Indeed, the lysine riboswitch construct is a much more complex RNA folding motif than thesimple TL-TLR system, with a multi-helix junction connecting 5 mutually interacting stemloops. Moreover, the lysine riboswitch also has a larger molecular size (~ 6 kDa) comparable tothat of a small protein. Thus, the V0 values measured for the lysine riboswitch are in factcomparable with values measured for small proteins ( 50-150 mL/mol) over a similar range ofmolecule weights (10-20 kDa).50-51
10.4.2 Pressure-dependent effects on ligand-induced folding of the lysine riboswitch
Binding of the cognate ligand lysine to the 5-way junction promotes the folded state of
the riboswitch and thus brings stem 1 and stem 5 in close proximity (Figure 10.1B).27 The

269
association of a lysine molecule has been previously identified to be crucial for conformationalchange of the lysine riboswitch through an “induced-fit” (i.e., bind-then-fold), mechanism,27
suggesting a well-defined ligand-bound folded conformation.28 We are therefore naturallyinterested in the role of ligand in promoting or decreasing the pressure stability of the wellestablished ligand-riboswitch interaction. The pressure dependence of lysine riboswitch folding
has been studied as a function of [lysine] from 0.5 to 8 mM. Since lysine (side chain pKa = 10.5)
is already positively charged in our buffer (pH ~ 7.5), this could in principle influence theriboswitch stability due to Debye shielding effects in the Na+ and Mg2+ cation studies reported
below. To specifically isolate the ligand-aptamer interactions from the less ligand-specific effects
due to the positive charge of lysine, the dynamic range of lysine concentrations explored has

Figure 10.5 Pressure dependence of folding at series of ligand (lysine) concentrations. (A) ln(Kfold)vs P plot where the parallel lines indicate constant V0. (B) The insensitivity of folding V0 tolysine concentration where the error bars are visually magnified by two with the vertical break.

270
therefore been restricted to < 10 mM, i.e., more than an order of magnitude lower than typical[Na+] values (> 100 mM) previously shown necessary to promote nucleic acid stability.42, 52
The pressure dependence of Kfold as a function of [lysine] is displayed as a logarithmicplot in Figure 10.5A, with each set of data well fit to a linear function predicted by Eq. 10.1. By
visual inspection, the slopes remain relatively unaffected, while the intercepts all vertically shift
upwards with increasing [lysine]. Stated alternatively, the presence of lysine significantly
stabilizes the folding of the lysine riboswitch, and yet with negligible effect on any change in thefree volume (∆V0  0). The results are more quantitatively summarized in Table 10.1, where∆V0 is plotted in Figure 10.5B as a function of [lysine]. Figure 10.5B demonstrates theremarkable insensitivity of ∆V0 to lysine concentrations (note the break in the vertical axis,
visually magnifying any such lysine dependences by a factor of two).

[lysine] (mM)

0.5

1.0

2.0

4.0

8.0

ΔV0
(mL/mol)

71(4)

73(3)

75(3)

74(3)

76(3)

Table 10.1 V0 obtained at increasing [lysine]

For ligand-induced riboswitch folding, the dissociation constant is a common measure of
the ligand-RNA interaction strength,53 where Kd is equivalent to the lysine concentration at the
point of 50% folding, i.e., where [folded]  [unfolded] and thus ln(Kfold) = 0. One should notethat Kd represents an apparent dissociation constant, since the actual ligand binding andriboswitch folding event (which triggers the FRET change) could in principle be decoupled andseparated in time.28 Conveniently restated, we can therefore empirically determine the271
corresponding 50% pressures (P50%) for which [lysine] equals Kd from the data in Figure 10.5A,
obtained from the intersection of each least squares fit with ln(Kfold) = 0. For example, the xintercept for [lysine] = 0.5 mM corresponds to P50% ≈ 221 bar (see Figure 10.5A), which implies
that at 221 bar applied pressure, the lysine riboswitch is 50% unfolded and thus Kd  0.5 mM. In
this fashion, the results in Figure 10.5A can be more usefully replotted as Kd vs applied pressure(see Figure 10.6), where we have included the value (Kd = 0.31(10) mM) determined fromconcentration dependent folding at ambient pressure (see Figure 10.4). Interestingly, Figure 10.6
reveals that the dissociation constant Kd increases dramatically and indeed roughly exponentiallyas a function of increasing pressure. On the one hand, this result follows immediately from thefact that the plots in Figure 10.5A are linear and free energies scale as the logarithm ofequilibrium constants. On the other hand, our simple restatement of the data in terms of theapparent lysine Kd suggests a subtler interpretation – that external pressure weakens the apparent
binding/binding-induced folding of lysine to the riboswitch. Furthermore, this behavior predicts
that weakening of the RNA-ligand interaction becomes exponentially more significant at higher

Figure 10.6 Pressure effects on apparent Kd of lysine binding. Kd increases exponentially withpressures, suggesting riboswitch-ligand interactions are efficiently weakened at high pressures.

272
pressure. For example, at the bottom of the Mariana Trench (≈ 1.1 kbar), Figure 10.6 predicts
that Kd will be increased by 3 orders of magnitude (≈ 300 mM), signaling much higher [lysine]
required to achieve biochemically competent folding of the riboswitch. Due to such strong
denaturation influences, one anticipates the need for deep sea organisms to develop adaptive
mechanisms to counteract pressure in order to maintain correct biochemical function,31-32 a point
to which we will return and discuss further in Sec 10.5.3.
10.4.3 Cation effects on pressure dependent folding of the lysine riboswitch
Nucleic acids are highly negatively charged polymers, with one phosphate group per
nucleotide and which therefore interact strongly with solute cations. It has been well establishedthat mono- and divalent cations are crucial to stabilizing the native structure of a nucleic acidriboswitch, with tertiary interactions in the riboswitch folding particularly sensitive tophysiologically important multivalent cations such as Mg2+.29-30, 54-57 We thus are naturallyinterested in both monovalent and divalent cation effects on the pressure dependent response of
the lysine riboswitch. To explore the monovalent cation effects, the pressure dependence on
riboswitch folding is first studied as a function of [Na+] at constant divalent ([Mg2+] = 0.5 mM)
and ligand ([lysine] = 0.5 mM) concentrations (Figure 10.7A). Interestingly, over the[Na+] (mM)

125

250

500

ΔV0 (mL/mol)

71(4)

72(5)

76(6)

[Mg2+] (mM)

0.5

1.0

1.5

ΔV0 (mL/mol)

71(4)

69(6)

72(6)

Table 10.2 V0 obtained at increasing monovalent (Na+)/divalent (Mg2+) cation concentrations.

273
physiologically relevant scale of [Na+] from 100 to 500 mM, the effects are quite similar to thatof lysine, i.e., with the slopes in Figure 10.7A predicting essentially negligible dependence of
free volume change on Na+. Indeed, the slopes are indistinguishable within experimental
uncertainty, which from the above lysine analysis indicates that i) V0 is independent of Na+
over physiological range and ii) the dependence of Kfold on pressure is insensitive to [Na+] fromambient up to 1 kbar. These ∆V0 results are quantitatively summarized in Figure 10.7B and
Table 10.2, with the data confirming that both the folding equilibrium constant and its pressuredependent response remain relatively constant over the range of physiologically relevant [Na+].

Figure 10.7 Pressure dependence of folding at series of Na+ concentrations. (A) ln(Kfold) vs P plot
where folding shows negligible dependence on [Na+]. (B) [Na+] (in)dependence of V0.

We next turn to the effects of divalent Mg2+ on this pressure dependent riboswitch
folding. Once again, the slopes (see Figure 10.8) in each of the plots of ln(Kfold) vs P plots are274
equal within experimental uncertainty. This is equivalent to the statement that there is no Mg2+
dependence to free volume changes observed upon folding of the lysine riboswitch, as morequantitatively captured in the nearly horizontal data plot in Figure 10.8B. This contrasts,
however, with the monovalent Na+ results in that there are very significant effects on Kfold due tothe presence of Mg2+ even at ambient pressure (Figure 10.8A). Note that the range of [Mg2+]
studied is nearly 3 orders of magnitudes lower than [Na+], again indicating much stronger Mg2+
stabilization effects on RNA tertiary structures and consistent with many previous studies.29-30, 44,58

In the ln(Kfold) vs pressure plots in Figure 10.8A, the least squares fits reveal ∆V0 to remain

nearly constant (as echoed in Figure 10.8B, Table 10.2), while the significant upward verticalshifts in Figure 10.8A indicate that Mg2+ strongly stabilizes the folded lysine riboswitch at allpressures. We note that the independence of ∆V0 on Na+ and Mg2+ demonstrated in Figure 10.7A
and 10.8A is quite different from previous studies, where ∆V0 for DNA/RNA folding was foundto be sensitive to cations.21, 59 For instance, ∆V0 for folding of the 40A DNA hairpin is reduced
from 11.5(35) mL/mol to 5.9(10) mL/mol with [Mg2+] increasing from 0.3 mM to 1.0 mM(∆∆V0 < 0),59 while the ∆V0 of TL-TLR formation increases from 5(3) mL/mol to 9(2) mL/molwith [Mg2+] increasing from 0 mM to 1.0 mM (∆∆V0 > 0).21 Despite the fact that the pressure
denaturation is repeatedly observed (i.e., ∆V0 > 0) for each nucleic acid structure, the differential
cation response (∆∆V0) can change sign depending on the interactions involved in the folding. A
simple framework with which to understand cation effects is by charge neutralization/association
between the cations and nucleic acids, resulting in a weaker hydration structure.60 At first thiswould seem to predict a reduced ∆V0 at higher cation concentrations (∆∆V0 < 0) as the hydratingwater molecules become less ordered.48-49 However, just as for nucleic acid conformations, thesolvent configuration is also highly dynamic during nucleic acid folding; therefore, the additional

275

Figure 10.8 Pressure dependence of folding at series of Mg2+ concentrations. (A) ln(Kfold) vs P
plot where Mg2+ greatly promotes folding, while leaving the slopes (V0) mostly unchanged. (B)[Mg2+] (in)dependence of V0.

cations may preferentially interact with either the folded/unfolded state or only stay in thebulk/hydration shell during folding. As a result, the presence of cations could give rise tonegative, zero or positive values of ∆∆V0 simply due to the redistribution of hydration at
different stages of folding.21, 59 Such cationic association along the riboswitch folding coordinate
further motivates future pressure dependent analysis of the folding kinetics, which may provide
additional physical insights with which to help interpret such cation response from a structural
perspective.
Finally, the apparent lack of Na+ influence on pressure dependent folding of the fulllysine riboswitch is noteworthy, since monovalent cations have been shown to promoteformation of the isolated TL-TLR folding motif at the hundred millimolar level.30, 61 However,276
multiple tertiary contacts in the Tetrahymena thermophila ribozyme have been shown to be
unresponsive to Na+ up to [Na+] = 1.5 M in previous X-Ray footprinting studies,58 suggestingthat Mg2+ can be crucial to certain tertiary folding motifs such as bending at internal loops.58, 62 A
similar metal ion dependence can also be observed in the hairpin ribozyme63 and its four-way
junction64, where from EFRET differences it appears that monovalent Na+-induced compaction
only partially folds the RNA in the absence of divalent Mg2+. Indeed, even simpler tertiary
folding motifs (such as the RNA kink-turn) may adopt different conformations in the presence of
Na+ vs. Mg2+.65-66 Furthermore, the importance of Mg2+ in the lysine riboswitch folding can beseen in the strongly [Mg2+]-dependent Kd for lysine binding.27, 43-44 Moreover, most of themonovalent cation effects have been studied in the absence of multivalent cations.30 In our
experiments, Na+ must compete with 0.5 mM Mg2+ to interact with the lysine riboswitch andthus the results could be dominated by the more prominent Mg2+ effects.67
10.4.4 TMAO effects on the pressure dependent lysine riboswitch folding
We now return to the experimental dependence of the Kd ligand binding affinity on
external pressure. Many marine organisms accumulate small organic molecules known as
osmolytes inside cells to adjust cellular osmotic pressures against sea water.34, 68 Much of theseosmolytes are thought to have cytoprotective roles to stabilize biomolecular structures against
environmental stressors such as temperature and pressure.69 Indeed, the TMAO contents of fish
and amphipods have been recently found to correlate strongly with ocean depth, further
corroborating the protective role of TMAO against hydraulic pressure33-34. As a final focus of
this paper, we have explored the influence of TMAO osmolyte concentration on folding of thelysine riboswitch, with the hope of gaining additional molecular insight into the mechanism of277
TMAO stabilization on RNA tertiary folding of the lysine riboswitch and ligand binding under
extreme pressures.
The pressure dependent data for ln(Kfold) as a function of TMAO concentration are
exhibited in Figure 10.9A. We focus first on results at ambient pressure, P  1 bar, for which the
spread in intercepts indicates a moderate TMAO free energy enhancement in folding of thelysine riboswitch over the range of physiologically relevant concentrations sampled (100 mM to1200 mM). This modest TMAO dependent (3-4 fold) increase in Kfold is consistent withpreviously characterized stabilization effects of TMAO osmolyte on nucleic acid structures38, 7071

. However, it contrasts with the results obtained previously for lysine, Na+ and Mg2+ cosolutes.

This means that the free volume change for lysine riboswitch folding decreases significantly with
TMAO osmolyte (see Figure 10.9B and Table 10.3), indeed by nearly 50% by 1.25 M. Statedalternatively, this means that the lysine riboswitch unfolds much less effectively (i.e. is morestable) at higher [TMAO], with a difference in excess of 3-4 log units in ln(Kfold) up at thehighest pressures observed.
[TMAO]
(mM)

0

250

500

750

1000

1250

ΔV0
(mL/mol)

71(4)

63(4)

59(4)

54(4)

50(3)

40(2)

Table 10.3 V0 obtained at increasing [TMAO]

The results in Figure 10.9A, B highlight two ways in which TMAO provides a protective
mechanism against changes in external pressure, which could be crucially important in278

Figure 10.9 Pressure dependence of folding at series of TMAO concentrations. (A) ln(Kfold) vs P
plot where TMAO promotes folding and effectively reduces the slope (V0). (B) [TMAO]
dependence of V0. V0 decrease linearly with [TMAO] concentration.

maintaining accessibility of marine species to wider range of vertical depth profiles. Firstly, thecompaction of curves in Figure 10.9A near ambient pressures indicates that TMAO increases
folded lysine riboswitch stabilities only relatively modestly ( 3-4 fold), which could be crucial
to preserving biochemical function of the riboswitch.34, 69 This differs specifically from the more
dramatic dependence of riboswitch stability on Mg2+, which strongly favors riboswitch folding
and thus completely switches the gene regulation on or off. Instead, TMAO at ambient pressures
only shifts the equilibrium moderately toward the folded state. As a consequence, this allows theriboswitch to dynamically shift between two comparable free energy conformations and thereby
still efficiently regulate gene expression.

279
As an important secondary effect, however, the incorporation of TMAO into the cellsystematically decreases the slopes in Figure 10.9A and thus creates an exponential sensitivity of
Kfold on pressure. As a result, what are only modest riboswitch stabilization effects under low
pressure ambient conditions grow exponentially stronger at higher pressure. More quantitatively,
the slopes and intercepts in Figure 10.9A indicate that [TMAO] = 1250 mM achieves anequivalent lysine riboswitch folding stability at ~ 800 bar as obtained at ambient pressures in thecomplete absence of TMAO. This may signal an elegant strategy behind controlled build-up ofosmolytes such as TMAO in cells. Specifically, it promotes biomolecular folding under highpressures and yet also maintains the requisite “on-off” two-state riboswitch sensitivity to lysine
over a wider range of ocean depth profiles and external pressures.

10.5

Discussion

10.5.1 Pressure denaturation of lysine riboswitch folding
The pressure dependence of our biomolecular folding is dominated by the positive freevolume difference between the folded and unfolded conformations (∆V0 = V0fold – V0unfold  + 74
mL/mol), which according to Le Chatelier’s principle, predicts pressure-induced denaturation.5
The physical reason why ∆V0 > 0 for the lysine riboswitch is not immediately obvious, since
folded conformations of biopolymers are generally considered to be more compact. However,one must remember that measured ∆V0 values represent changes for the entire solute + solvent
system, for which the solvent can contribute significantly to the overall ∆V0.1-4 For instance,
solvent voids can be generated due to formation of hydrophobic contacts upon folding, which
can decrease the solvent accessible volume and result in a net outward displacement of thesolvent (∆V0 > 0).2 Alternatively, the unfolded RNA conformation can expose the polyanionic280
backbone to more solvent (water) and thus can form a more compact hydration shell.48-49 Since a
more highly ordered hydration structure for the unfolded conformation takes up less volume,48-49
this could translate into an increase in free volume (∆V0 > 0) as the riboswitch folds and partiallydisrupts these water contacts. The potential for competition between solute vs solvent volume
changes makes unambiguous deconstruction of the contributions to V0 challenging. However, itis the case that pressure-induced denaturation effects (which require V0 > 0) have been noted in
ensemble studies of many other protein and nucleic acid systems.4, 72
Pressure-induced denaturation of the lysine riboswitch is clearly indicated in each of theln(Kfold) vs. pressure plots in Figure 10.5-9, where negative slopes correspond to ∆V0 > 0 (Eq.
10.1). Interestingly, an increase in [lysine] stabilizes the folded conformation predominantly byparallel translation of the curves with negligible changes in the slope, consistent with ∆V0  0(Figure 10.5). What makes this particularly interesting is that it had been previously shown thatthe lysine riboswitch folding follows an “induced-fit” (bind-then-fold) mechanism and therefore
its folded state is well characterized as ligand-bound27-28. This would imply that any [lysine]changes must therefore correlate with ligand binding to the unfolded conformation. As a result,the fact that ∆V0 with respect to lysine is experimentally small could reflect that the unfolded
conformation is dominated by one of the two ligand-bound or ligand-free association states. This
looks not to be the case, however, as a dissociation constant KD = 1.7(5) mM for the unfolded
conformation has been determined from previous single molecule kinetic studies.27 which
predicts both ligand-bound and ligand-free states to be significantly present at [lysine]  0.5-8
mM. Thus, the measured independence of ∆V0 on [lysine] indicates the volumes of the ligandbound and ligand-free unfolded states to be experimentally indistinguishable. It is also worth

281
noting that the uncertainties in ∆V0 are < 5 mL/mol, i.e., less than 1/3 the volume of a single
water molecule.
From the pressure dependent folding data in Figure 10.5, we obtain the apparent
dissociation constant Kd for lysine and the corresponding 50% folding pressures (P50%) withwhich to characterize the pressure dependent riboswitch-ligand interaction. Since ∆V0 isapproximately independent of [lysine], Kd increases nearly exponentially with P (Figure 10.6),
clearly demonstrating that external pressure impedes cognate ligand-induced folding of thelysine riboswitch. This pressure-dependent binding constant for lysine decreases rapidly, with Kd
predicted at the bottom of the Mariana Trench to be 3 orders of magnitude larger (Kd  300(60)mM) than at ambient pressures (Kd  0.31(10) mM). These results demonstrate that high pressure
significantly disrupts the riboswitch-ligand interaction, which in deep sea species must therefore
be compensated by some other protective mechanism (e.g., osmotic enhancement) in order tomaintain cellular function. Finally, we note that these smFRET burst fluorescence studies only
report on the apparent dissociation constant Kd through observation of overall riboswitch
folding. More specifically, we cannot rule out whether the increase in Kd occurs by a i) pressuredependent decrease in ligand affinity or ii) pressure-dependent efficiency of the resulting ligandpromoted conformational change, although such questions should be addressed by single
molecule kinetic studies on tethered constructs.
10.5.2 Cationic effects on the lysine riboswitch
The equilibrium for lysine riboswitch folding exhibits only a quite modest dependence on[Na+] under both ambient and high-pressure conditions. Not only is the free volume change ∆V0
effectively independent of [Na+], but the riboswitch folding equilibrium constant (Kfold) is largely

282
constant over the entire physiologically relevant range ([Na+] = 100-250 mM). Since charge
neutralization and Debye shielding is an essential prerequisite for RNA forming compact
structures55, 73, this is a bit surprising. Indeed, although monovalent cations are found to be lesseffective than divalent cations in stabilizing RNA tertiary structure, they are often still able topromote RNA folding at sufficiently high concentrations.30, 46, 73 However, as discussed in Sec.
10.4.3, not all tertiary contacts in a full ribozyme can be effectively promoted by monovalentcations alone,58, 63-65 suggesting Mg2+ to be essential for RNA structure formation.62 Moreover,these Na+ dependent studies have been explored in the presence of [Mg2+] = 0.5 mM in order toeffectively promote the lysine binding.27, 43 It is unclear how Mg2+ competes with Na+ toneutralize/solvate the RNA; thus the overall monovalent cation effects may still be dominated by
Mg2+, which is known to interact strongly with RNA.67
By way of contrast, Mg2+ is known to strongly promote RNA structure formation and has
been shown in previous studies to be essential for lysine riboswitch folding,22, 27, 43 primarily inpromoting tertiary contacts and pre-organizing the ligand binding site.44 It is thus not surprisingthat Mg2+ strongly stabilizes the folded lysine riboswitch, as evidenced by strong upward
displacement of the semilogarithmic plots in Figure 10.8A. Instead, it is the parallel nature ofthese curves as a function of Mg2+ (which implies an Mg2+-independent change in ∆V0) that
becomes most noteworthy. Interestingly, although only a limited nucleic acid systems have beenstudied as a function of external pressure, ∆V0 values for nucleic acid folding have been found tobe small and [Mg2+] sensitive.21, 59 For example, ∆V0 for secondary structure formation in a DNA
40A hairpin is reduced from 11.5(35) mL/mol to 5.9(10) mL/mol between [Mg2+] = 0.3 mM 1.0 mM,59 while ∆V0 for folding of the tetraloop-receptor tertiary interaction motif is increased
from 5(3) mL/mol - 9(2) mL/mol between [Mg2+] = 0.0 - 1.0 mM.21 As described in Sec. 10.4.3,

283
such sign reversals in ∆∆V0 may result from preferential interaction of Mg2+ with folded vs.
unfolded RNA conformations. This again provides additional motivation for high pressure
kinetic studies at the single molecule level, which would permit further thermodynamic
deconstruction of these equilibrium constants into forward (folding) and reverse (unfolding) rate
constants over a transition state barrier.
Despite an RNA construct-dependent sign of ∆V0 with respect to divalent cation
concentration, the data in Figure 10.8A make clear that Mg2+ strongly stabilizes lysine
riboswitch folding. In principle, this additional stabilization could also be used to protect lysine
riboswitches from pressure-induced denaturation under deep sea conditions. However, theriboswitch gene regulatory mechanism relies on efficient, high dynamic range “switching”
between on- and off-states of comparable free energy, triggered by presence or absence of the
cognate ligand.9 Therefore, overzealous stabilization of one of the two conformations by Mg2+
would shift this equilibrium and therefore be less desirable for robust riboswitch competency.
This could represent yet another reason why marine species do not accumulate divalent salts tomodulate their cellular osmotic pressure, as these species could significantly perturb riboswitch
equilibria and therefore biomolecular function.34, 69
10.5.3 Osmolytic protection against pressure denaturation
As described in Sec. 10.4 and above, common monovalent (Na+) and divalent (Mg2+)
cations exert a negligible influence on free volume changes (V0  0) due to lysine riboswitch
folding. As a result, modulation of cation concentrations should have little impact on riboswitch
folding equilibria as a function of external pressure. Instead, marine species have evolved toaccumulate small highly polar organic molecules (“osmolytes”) to help achieve the correct

284
osmotic balance between cellular and external environments.31 Unlike inorganic cations, theseosmolytes do not significantly alter biomolecular folding equilibria and may also protect the cellfrom multiple environmental stressors such as temperature and pressure.69 Trimethyl amineoxide (TMAO) is one of the most common of these osmolytes, empirically known to be crucial
for survival of organisms at extreme deep sea pressures.33 Indeed, TMAO concentrations in fish
and amphipods increasing quasi linearly with ocean depth up to as high as [TMAO]  0.5 M.33-34
TMAO has explicitly been shown to protect proteins and DNA helices from pressure-induced
denaturation,59, 74 while effects on the stability of RNA tertiary folding under pressure haveremained largely unexplored. Although the precise biological mechanism for protection againsthigh external hydrostatic pressure in deep sea bacteria is still unclear, our current study of
TMAO pressure-induced denaturation of the lysine riboswitch highlights some useful principles
for identifying potential “piezolytes,” which can hope to counteract external pressure effects by
not only stabilizing biomolecular folding of the riboswitch but also reducing pressure sensitivity
to riboswitch folding formation by control of V0.
From pressure dependent plots of ln(Kfold) vs. [TMAO] (see Figure 10.9A), the folded
lysine riboswitch is stabilized (i.e., Kfold increases with TMAO]) all the way down to ambientpressure (1 bar). There are three closely related predictions and corollaries from Figure 10.9A
that bear emphasizing, all arising from the simple observation in Figure 10.9B of a negativeV0. 1) First and foremost is that the pressure dependence becomes weaker (i.e., the slopes
become shallower) with increasing [TMAO]. 2) The corollary is that increasing [TMAO] does
not shift folding equilibria as dramatically at low vs. high pressure conditions. As a result, theconcentration/pressure “phase space” over which ln(Kfold)  0 and thus riboswitch functionality
is maximized, which can be argued is an essential characteristic of a good osmolyte. 3) The third

285
implication is that the ln(Kfold) plots naturally fan out with increasing P, and thus by control of
TMAO levels, permit access to an exponentially larger dynamic range for osmolytic stabilizationof the riboswitch under elevated pressure conditions. The combination of these three predictions,
all fundamentally arising from V0 < 0, therefore extends the biochemically functional range ofthe lysine riboswitch for gene regulation over a greater dynamic range of pressures.

Figure 10.10 Accessible pressure range for the lysine riboswitch as a function of [TMAO],
normalized to the corresponding pressure range at [TMAO] = 0. The grey solid line corresponds
the pressure range without osmolyte effects. The red solid line represents predictions from the fitof the [TMAO] dependence of V0 with m = -0.0228(18) mL mol-1 mM-1. The dashed lines
indicate effects due to the uncertainty in m on the pressure range as a function of [osmolyte]: 50%
larger (dark red) and 50% smaller (pink) m values.

We attempt to capture this point in Figure 10.10, based on the pressure range over which
the lysine riboswitch properly functions. We can roughly estimate this range as P = Pmax-Pmin
whereby Kfold changes by some small factor , which based on elementary thermodynamics ofreversible work (P  (G0)V0), translates into P  2RTln()/V0. Next, we least squares fit
the [TMAO] dependence of (V0) in Figure 10.9B to a simple linear function V0(0) +m[osmolyte] (V0(0) = 70.6(13) mL/mol, slope m = -0.0228(18) mL/mol/mM). The explicit
influence of TMAO on pressure dependent folding can therefore be plotted as P for finite

286[TMAO] normalized to P(0) at [TMAO] = 0, which from Figure 10.10 can be seen to increasenearly 70% over [TMAO] = 0.00 M -1.25 M. Finally, it is worth noting that this normalization
process yields results conveniently independent of the arbitrary choice of . The results,
however, do indicate the correct sensitivity to the experimentally fitted slopes, which predict anenhanced pressure range (P/P(0) > 1) for negative values of m. The sensitivity of the pressure
range to the osmolyte effects (m) is also illustrated in Figure 10.10 with dark red and pink curves
corresponding to + 50% and – 50% m value of TMAO.

Figure 10.11 Iso-Kd curve as a function of both pressure (depth in the ocean) and [TMAO] where
Kd = 0.5 mM. Kd is maintained by [TMAO] = 1250 mM with (ocean depth) > 9 km. Data fit toa negative exponential growth function (red), indicating the TMAO effects are even stronger athigh concentrations. The dashed lines indicate the effects of changes in slope magnitude on the
iso-Kd curve: + 50% (dark red) and − 50% (pink).

Since the environmental factors such as temperature, salinity and dissolved oxygen
remain largely constant under deep sea conditions,75 pressure represents the major limitation fordeep sea organisms to migrate and survive at different depths. The data allow us to put thissimple model on a more rigorous mathematical footing. For example, we can determine from
Figure 10.9A the 50% pressure (P50%) at each [TMAO] for an experimentally convenient valueof the apparent dissociation constant (e.g., at Kfold  1, for which Kd  [lysine]  0.5 mM). We

287
can then use G0(P) = G0(P=0) + PV0 = -RTln(Kfold)   to plot in Figure 10.11 a constant Kd(“iso-Kd”) curve of accessible deep sea ocean pressures (P  G0(P = 0)/ V0), which reveals a
dramatic exponential increase in the accessible pressure range with increasing [TMAO].
Specifically, Figure 10.11 makes clear that a constant riboswitch-ligand affinity (Kd = 0.5 mM)
can be maintained over a 900 bar pressure increase ( 9000 m vertical migration) by control of
TMAO cellular concentrations between 0-1.25 M, with the TMAO stabilization effects
becoming exponentially more significant at higher pressures. As a result, the sensitivity to thenegative slope (m) is quite high, with the results for m and ± 50% of m indicated as dashed lines
in Figure 10.11.
It is worth noting that the maximum [TMAO] values in this study are close to thetheoretical upper bound of osmolyte concentration (~1.2 M, sea water) for marine species which
tend to achieve either isosmotic or hypoosmotic conditions. Thus, the actual [TMAO] must infact be lower due to additional salts, metabolites and other osmolytes required for cellularfunction. Our results therefore support the previous hypothesis33 that fish may be constrained
from inhabiting the deepest part of the sea below ~8500 m due to these limits on TMAO (~ 0.5
M). However, despite this crucial role in promoting biomolecule stability, the fact that fish arefound at ~7000 m with only 0.5 M TMAO indicates [TMAO] can not be the sole factor for deepsea species to survive high pressures. Indeed, genetic adaptation for deep sea organisms canfacilitate utilization of more pressure resistant protein and nucleic acid structures76 as well as
synergies between TMAO and other osmolytes/cosolutes to increase biomolecular stability. One
important example would be that of “macromolecular crowding,” which can not only stabilize
biomolecule structures but also increase the effective concentration/activity of TMAO by taking
up intracellular space.77

288
As a final comment, we can attempt a linear deconstruction of these free volume changes(∆V0) into solvent voids (∆V0void) plus solvent hydration effects (∆V0hydration).1, 3, 17 The relatively
constant values of EFRET values that we observe as a function of [TMAO] supports that TMAO
does not significantly change the lysine riboswitch conformation nor the overall compactness ofthe folded state. This in turn suggests that ∆V0void  constant, from which the linear dependence
of ln(Kfold) on [TMAO] in Figure 10.9B could be entirely ascribed to hydration contributions(∆V0hydration) linearly proportional to [TMAO]. Indeed, TMAO has been found in previous studies
to be excluded from the surfaces of proteins and RNA tertiary folding motifs78-80 and also togreatly enhance the water structure81, thereby reducing the effective volume of the bulk water.4849

It is likely that since TMAO tend to orient the water molecules in the bulk, it reduces theeffective volume difference between water molecules in the solvation shell of RNA and in thebulk, and consequently mitigate the pressure effects by reducing ∆V0hydration. The linear decreaseof ∆V0 (Figure 10.9B) which expands a wide range of [TMAO] can be simply explained by thefact that TMAO primarily affects the bulk water instead of the hydration shell surrounding theRNA.80 Indeed, it has been found in previous molecular dynamics simulations that one hydrated
TMAO is in close contact with 25 water molecules,81 suggesting the bulk water (55.5 M) could
be sufficiently ordered by the saturation [TMAO] at ~ 2.2 M. The dynamic range explored in thisstudy for [TMAO] is still far from this saturation limit and thus might expect a linear decrease in∆V0 with increasing [TMAO]. It is also worth noting that since TMAO tends to remain strongly
hydrated in the bulk water and interact only indirectly with RNA/protein,78-80 the sign of these
TMAO effects (∆∆V0 < 0) is likely to be more universal and system-independent, making it an
ideal piezolyte with which to protect biomolecular structures from pressure-induced
denaturation.

289

10.6

Summary and conclusion
The pressure dependence of lysine riboswitch folding has been investigated at the single

molecule level with smFRET spectroscopy and up to P  1500 bar pressures. The lysine
riboswitch unfolds readily at increasing pressure, with a change in free volume determined fromlinear pressure van’t Hoff plots to be ∆V0 = Vfold -Vunfold  75(3) mL/mol. These data can be
replotted as an apparent lysine riboswitch dissociation constant Kd as a function of P, which
reveals the riboswitch-ligand interaction to be weakened quasi-exponentially with increasingpressure. While monovalent Na+ effects on the free volume change are found to be negligible,
the presence of divalent Mg2+ greatly stabilizes the folded lysine riboswitch at all pressures, with
only negligible changes in ∆V0 for both Mg2+ and Na+ cations. By way of contrast, TMAO, aknown piezolyte, is found to increase pressure stability of the riboswitch by simultaneously
promoting folding (increase in Kfold) and reducing the folding-induced change in free volume(∆V0 < 0). We argue that the latter influence of TMAO on free volume can play a crucial rolein migration of deep sea species to different ocean depth layers of water in search of sparseresources. Moreover, we introduce an empirical deconstruction of the overall free volume change(V0) into solvent void formation (V0void) and changes in the hydration layer (V0hydration) uponfolding. The insensitivity of observed EFRET values suggests that TMAO does not significantly
alter the folded riboswitch conformation and thus that ∆V0void remains approximately constantover a variety of osmolyte conditions. If this is true, our deconstruction would identify the signof ∆V0 > 0 to be due to changes in hydration effects. Furthermore, since TMAO is known to be
excluded from biomolecular surfaces and to enhance the formation of ordered water, this would
be consistent with a linear reduction in ∆V0 by TMAO over a wide range of concentration due to290greater ordering of the bulk water structure and thereby lesser importance of RNA hydration
effects.

10.7

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77.

Ellis, R. J. Macromolecular Crowding: Obvious but Underappreciated. Trends in
Biochemical Sciences 2001, 26, 597-604.

78.

Canchi, D. R.; Jayasimha, P.; Rau, D. C.; Makhatadze, G. I.; Garcia, A. E. Molecular
Mechanism for the Preferential Exclusion of TMAO from Protein Surfaces. J. Phys.
Chem. B 2012, 116, 12095-12104.

79.

Ma, J.; Pazos, I. M.; Gai, F. Microscopic Insights into the Protein-Stabilizing Effect of
Trimethylamine N-Oxide (TMAO). Proc. Natl. Acad. Sci. U.S.A. 2014, 111, 8476-8481.

296
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Pincus, D. L.; Hyeon, C.; Thirumalai, D. Effects of Trimethylamine N-Oxide (TMAO)
and Crowding Agents on the Stability of RNA Hairpins. J. Am. Chem. Soc. 2008, 130,7364-7372.

81.

Zou, Q.; Bennion, B. J.; Daggett, V.; Murphy, K. P. The Molecular Mechanism of
Stabilization of Proteins by TMAO and Its Ability to Counteract the Effects of Urea. J.
Am. Chem. Soc. 2002, 124, 1192-1202.

297
Chapter 11
Single-Molecule Kinetic Studies of DNA Hybridization Under Extreme Pressures

11.1

Abstract
Pressure may perturb biomolecular function by altering equilibrium structures andfolding dynamics. Its influences are particularly important to deep sea organisms, as maximum
pressures reach up to ≈ 1100 bar at the bottom of the ocean as a result of the rapid increase in
hydraulic pressure (1 bar every 10 meters) under water. In this work, DNA hybridization kinetics
has been studied at the single molecule level under external pressure control (Pmax ≈ 1500 bar),
realized by incorporating a mechanical hydraulic capillary sample cell into a confocal
fluorescence microscope. We find that the DNA hairpin construct unfolds (“denatures”) withincreasing pressure by simultaneously decelerating and accelerating the unimolecular rate
constants for folding and unfolding, respectively. The single molecule kinetics is theninvestigated via pressure dependent van’t Hoff analysis to infer changes in the thermodynamic
molar volume, which unambiguously reveals that the effective DNA plus solvent volume
increases (V0 > 0) along the folding coordinate. Cation effects on the pressure dependent
kinetics are also explored as a function of monovalent [Na+]. In addition to stabilizing the overall
DNA secondary structure, sodium ions at low concentrations are also found to weaken anypressure dependence for the folding kinetics, but with these effects quickly saturating at
physiologically relevant levels of [Na+]. In particular, the activation volumes for the DNA*This chapter is adapted from: Sung, H.-L.; Nesbitt, D. J. Single-Molecule Kinetic Studies of DNA
Hybridization Under Extreme Pressures. Phys. Chem. Chem. Phys. 2020, 22, 23491-23501.

298
dehybridization (ΔV‡unfold) are significantly reduced with increasing [Na+], suggesting that sodium
cations help DNA adopt a more fold-like transition state configuration.

11.2

Introduction
Most biochemical studies are performed under ambient pressures (≈ 1 bar = 100,000

Pascal), though this is far from conventional conditions for marine organisms inhabiting thedeepest parts of the ocean (≈ 1100 bar).1-2 Indeed, although experimental results obtained at
atmospheric pressure are of obvious relevance to life on the surface of the earth, one could argue
that most biochemistry studies sample only a quite limited wedge of naturally occurringpressures in biology. Extreme pressure effects on biological systems turn out to be of immense
importance to marine life due to the rapid increase of hydraulic pressure (1 bar per 10 meters)
under water.3 As one particularly relevant biophysical impact, molecules such as proteins andnucleic acids may lose the thermodynamic stability of their native folded state under increasingpressure,4-7 with such pressure-induced changes in conformation known as pressure
denaturation.8-9 Marine organisms, especially those deep-sea species, therefore must evolve andadopt protective mechanisms to stabilize biomolecular structures and maintain biochemicalfunction in order to counteract extreme pressure changes due to change in depth profile.3, 10
DNA occurs in biology primarily in the form of a double helix configuration. Previous
studies have shown the pressure response of DNA secondary structures may vary, depending
heavily on the sequence and buffer condition.6 While majority of the relatively long/stable DNA
double helices are found with increasing melting temperature at higher pressure,11-12 folding of
the DNA with shorter complementary regions is constantly shown to be destabilized by elevatingpressure.13-15 Since the structure determines the biomolecular function, such a pressure

299
denaturation phenomenon of nucleic acid structures is regarded to have a potentially enormous
impact on cellular function in deep sea marine species. Moreover, nucleic acid structure is in fact
dynamic rather than static,16-17 the destabilization effects of pressure therefore may not be fully
captured by previous equilibrium observations. A predictive understanding of such pressure
induced changes in conformational structure clearly requires new tools for exploring not just theequilibria but also the kinetics of nucleic acid hybridization/dehybridization, in particular under
the impact of high hydraulic pressures relevant to deep sea life. In order to make such kinetic
studies of nucleic acid conformational dynamics possible at the single molecule level, we havecoupled together two powerful techniques, i) confocal single molecule Förster resonance energy
transfer (smFRET) with ii) a high-pressure generating system in a small quartz capillary cell.
The goal of the present study is to report first results on folding/unfolding kinetics of nucleic
acids at the single molecule level, with pressure as an external control variable up to ≈ 5kilobar.7, 15
The present work builds on previous experimental studies of pressure dependent nucleic
acid RNA and DNA folding under equilibrium conditions, made accessible via freely diffusing
smFRET methods at the single molecule level.7, 13-15 Specifically, these previous studies
investigated doubly dye-labeled nucleic acid constructs freely diffusing in solution, with FRET
energy transfer efficiencies (EFRET) sampled one molecule at a time and single molecule EFRET
distributions statistically revealing the equilibrium ratio between folded and unfolded states (Keq
= [folded]/[unfolded]) and its dependence on external pressure and temperature.7, 13-15 In thepresent work, DNA constructs are tethered onto the inner surface of a square quartz highpressure capillary cell (Figure 11.1) instead of freely diffusing in solution. By virtue of thistethering, we can locate the nucleic acid constructs by piezo scanning a focused laser beam in a300
confocal microscope and thereby interrogate single molecule fluorescence signals over an
extended temporal window.18-19 Since the photon stream changes color as a function of nucleic
acid conformation, the resulting time dependent EFRET “trajectories” contain valuable statisticalinformation on the folded and unfolded dwell time distributions19-20 which allow us to explore
nucleic acid conformational kinetics as a function of pressure.
The organization of this paper is as follows. Sec. 11.3 provides a brief description of the
combined high pressure experimental apparatus and single molecule microscope. This isfollowed by a presentation in Sec 11.4A, B of folding and unfolding kinetic results and analysis
as a function of external hydraulic pressure, for which the pressure dependent folding/unfolding
kinetics provides detailed quantitative information on the differential molar volumes (V‡fold,V‡unfold) for accessing the transition state from a pressure dependent van’t Hoff analysis. We
turn in Sec 11.4C to the impact of “ion atmosphere” on the overall (V0) and transition state(V‡) molar volume changes, which exhibit a strong sensitivity to monovalent Na+ but only a

Figure 11.1 Schematic presentation of the surface tethered smFRET experiment performed in apressurized capillary sample holder. The doubly dye-labeled DNA hairpin construct isimmobilized on the capillary surface through biotin-streptavidin interactions. The energy transfer
efficiency (EFRET) in the folded (left) and unfolded (right) conformations correspond to high EFRET(≈ 0.8) and low EFRET (≈ 0.1) fluorescence states, respectively. Prior to each experiment, a thinlayer of silicon oil is introduced inside the capillary cell to prevent contamination of the aqueous
sample region by the pressure transmitting fluid (ethanol).

301
surprisingly weak dependence on divalent Mg2+ deemed crucial for nucleic acid achievement of
the correct secondary structure. In Sec. 11.5, we discuss the reasons and simple models for suchpressure and cationic dependent behaviors, followed in Sec. 11.6 by a summary of the conclusions
and directions for further work.

11.3

Experiment11.3.1 Single molecule FRET microscopy under external hydraulic pressure
Details of our high pressure smFRET experimental apparatus can be found in previous
work;7, 15 we focus herein on modifications required for the present studies of single molecule
nucleic acid folding kinetics. In brief, a confocal microscope with a high NA objective is coupled
to a high-pressure sample cell fabricated from a fused-silica capillary with a square 50 µm × 50
µm cross section of the inner cell (Polymicro, Phoenix, AZ), where the capillary can sustainpressures up to ≈ 5 kilobar without fracturing. (Note: company names are reported forcompleteness and not intended as commercial product support) Moreover, the flat interior
surface and uniform thickness (≈ 155 µm) of the high pressure capillary cell closely
approximates that of a standard microscope coverslip configuration, therefore maximizing theexcitation/collection efficiency for a high NA (1.2) fluorescence measurement. The aqueous
sample is pressurized by a manual screw pump (High Pressure Equipment, Erie, PA) throughstainless steel tubing (High Pressure Equipment), with ethanol as pressure transmitting fluid toincrease pressurization efficiency. Before connection to the ethanol-filled pressure generating
system, one end of the capillary is sealed by a propane/oxygen torch, while the other open end isdipped into low viscosity silicon oil to create a thin liquid membrane (≈ 50 µm thickness) inside
the sample cell (Figure 11.1) to prevent diffusion of ethanol into the microscopy region. During

302
the smFRET experiment, the dye-labeled construct is excited by laser excitation through a highNA = 1.2 water immersion microscope objective, with the resulting fluorescence photons
collected through the same objective and sorted with dichroic filters before detection on singlephoton counting avalanche photodiodes. The time resolved EFRET trajectory is then calculated
from the resulting fluorescent signals (Figure 11.2) and used in the kinetics analysis described inSec. 11.4A.
11.3.2 Sample Preparation and Single Molecule Tethering
The doubly dye-labeled and biotinylated DNA hairpin construct has been purchased in
HPLC purified form (Integrated DNA Technologies, Coralville, IA) and is used as is.15, 20 The
full DNA sequence and dye labeling sites are indicated as follows: 5’-Cy5-TCTTCAGT-A40Cy3-ACTGAAGA-A10-biotin-3’. Specifically, the construct contains an 8 base paircomplimentary sequence separated by a 40-(dA) linker (Figure 11.1). The labeling of Cy3 andCy5 results in two distinct EFRET states corresponding to the folded/hybridized (EFRET ≈ 0.8) and
unfolded/dehybridized (EFRET ≈ 0.1) conformations.15, 20 To extend the observation time offluorescent signals from a single construct, the DNA hairpins are immobilized on the surface ofthe capillary cell through biotin-streptavidin interactions (Figure 11.1).18-19 We note that the
DNA hairpin is chosen in these first high pressure single molecule kinetic measurements due
mainly to the fact that not only it has been widely studied as a model system of nucleic acidsecondary structure formation, but also its folding kinetics as well as equilibrium have been
extensively characterized at the single molecule level15, 20-22. While the incorporation of thepoly(dA) linker simplifies the DNA duplexing from a bimolecular to unimolecular process, it
may also contribute to the folding kinetics and thermodynamics in addition to the duplex
formation. Despite the hairpin folding thermodynamic being previously shown to be largely

303
dominated by complementary base paring15, it is worth noting that the linker effects on the
kinetics remain uncharacterized at high pressure.
Preparation of the DNA-decorated surface is achieved by sequentially flushing thecapillary cell with the following in order: (i) 10 mg/mL bovine serum albumin (BSA) with 10%
biotinylation for surface passivation, (ii) 200 μg/mL streptavidin solution for surface
immobilization, and (iii) ≈ 25 pmol/L biotinylated DNA hairpin constructs. Prior to each
smFRET experiment, the sample holder is flushed by the imaging buffer containing (i) 50
mmol/L hemipotassium HEPES buffer (pH 7.5), (ii) Trolox/protocatechuate 3,4-dioxygenase

Figure 11.2 Sample time-resolved fluorescent signals (upper panels) and corresponding EFRET
trajectories (lower panels) at (A) 1 bar and (B) 1250 bar. Background [Na+] = 50 mmol/L.

304(PCD)/protocatechuate (PCA) oxygen scavenger cocktail to catalytically remove oxygen andthereby increase dye photostability, and (iii) sufficient NaCl and MgCl2 to achieve desired
monovalent (Na+)/divalent (Mg2+) cation concentrations. We note that 25 mmol/L of backgroundK+ from the HEPES buffer is always presented in the pressure dependent experiments.

11.4

Results and analysis

11.4.1 Kinetic origin of DNA hairpin unfolding with increasing pressure
The prolonged observation of a single DNA construct one at a time allows us to obtainthe time dependent fluorescence signals from Cy3/Cy5 and calculate the resulting EFRET
trajectory (Figure 11.2). At ambient (≈ 1 bar) pressures (Figure 11.2A), the correlation between
Cy3 and Cy5 fluorescence indicates the DNA hairpin actively switches between the folded andunfolded conformations, corresponding to EFRET ≈ 0.8 and 0.1, respectively.15, 20 As the pressure
increases to 1250 bar (Figure 11.2B), the DNA hairpin clearly spends more time in the low EFRET
conformation, indicating that the DNA hybridization equilibrium is shifted toward the denatured(i.e. unfolded) state with increasing pressure. This is completely consistent with results reported
in freely diffusing smFRET studies of the similar constructs under equilibrium conditions.13, 15
However, the present tethered studies contain much richer information on thefolding/unfolding kinetics, which can be extracted by the dwell time analysis with in-house
software and thresholding methods as previously described.18-19, 23 Specifically, the well
separated EFRET distributions for the DNA hairpin allow us to unambiguously distinguishbetween folded/unfolded conformational states with a temporal resolution of 25 ms (Figure
11.2A, B). The resulting cumulative distribution functions (CDFs) of dwell time in each of thestates are well-fit to a single exponential decay model, as clearly demonstrated by the semi-

305
logarithmic plots in Figure 11.3. Thus, both the folding and unfolding of the DNA hairpin appear
to follow simple first order kinetics,20 with the DNA hairpin folding dynamics described by firstorder rate constants kfold and kunfold, respectively. In Figure 11.3A, the CDF slope for theunfolded (red) dwell times is greater than for the folded (green) dwell times, suggesting kfold >kunfold, and therefore the DNA hairpin spends more time in the folded conformation at ambientpressure with folding equilibrium constant Keq = kfold/kunfold > 1. At the high pressure (1250 bar,
Figure 11.3B), the CDF logarithmic decays reveal a dramatic decrease in kfold accompanied by asimultaneous increase in kunfold. Thus, the kinetic origins of pressure induced denaturation of the
DNA hairpin is therefore by deceleration and acceleration of the folding and unfolding rate
constants, respectively.

Figure 11.3 Sample cumulative distribution functions of dwell time at (A) 1 bar and (B) 1250 bar.
Background [Na+] = 50 mmol/L.
11.4.2 Volumetric characterization of pressure-dependent DNA (un)folding
If we associate the purely single exponential kinetic behavior (Figure 11.3) with a single
rate limiting transition state, the rate constant k can be expressed by the Eyring equation24
Δ𝐺‡

𝑘 = 𝜈𝑒 − 𝑅𝑇 ,Eq. 11.1

where ν is the attempt frequency to reach the transition state barrier. Since the pressure
dependence of the folding/unfolding rate constants and equilibrium constants originates from306changes in molar volume along the folding path,4-5 a more quantitative evaluation can beobtained by van’t Hoff analysis of the folding/unfolding rate constants at a series of increasingpressures (Figure 11.4A).:4-5
𝜕𝑙𝑛𝑘( 𝜕𝑃 ) 𝑇 =

−∆𝑉 ‡
𝑅𝑇

,

Eq. 11.2

where ΔV‡fold (ΔV‡unfold) represents the activation volume equivalent to volume change from theunfolded (folded) conformation to the transition state: ΔV‡fold = VTS – Vunfold (ΔV‡unfold = VTS –Vfold). As shown in Figure 11.4, ln(kfold) decreases linearly as a function of increasing pressure,with the negative slope indicating an increase in volume for the DNA hairpin to reach thetransition state barrier from the unfolded state (ΔV‡fold = +22.1(16) mL/mol). Conversely,ln(kunfold) increases linearly as a function of pressure, with a slope corresponding to a negative
ΔV‡unfold = −10.3(6) mL/mol, indicating that the fully folded conformation expands further inmolar volume from the transition conformation. Simply summarized, the volumetric analysis of
the pressure dependent rate constants reveals that the molar volume of the DNA hairpin increases
monotonically along the hybridization path: Vunfold < VTS < Vfold.
Moreover, the conventional pressure-dependent folding equilibrium behavior can bereconstructed simply through the relation Keq = kfold/kunfold (Figure 11.4B). The results are
consistent with previous observations of ln(Keq) linearly decreasing as a function of increasingpressure13, 15 predicted by4-5(

𝜕𝑙𝑛𝐾𝑒𝑞
𝜕𝑃

)𝑇 =

−∆𝑉 0
𝑅𝑇

.

Eq. 11.3

The corresponding overall molar volume change upon DNA hairpin folding is found to be ΔV0 =+33.7(13) mL/mol, which is in excellent agreement with the present pressure dependent kinetic
analysis predictions of ΔV0 = ΔV‡ fold + (-ΔV‡unfold) = +32.4(17) mL/mol. It is worth noting that
this overall change in molar volume is substantially higher than found from previous high307
pressure burst fluorescence studies under equilibrium conditions (ΔV0 = +23(2) mL/mol), which
was obtained at a higher (75 vs. 50 mmol/L) sodium ion (Na+) concentration.15 Indeed, thisprovides a first indication of the substantial sensitivity to monovalent cations in the pressure
dependences of both kinetic rates and equilibrium constants for DNA hybridization. By way ofconfirmation, we have determined the overall molar volume change upon hybridization undersimilar buffer conditions ([Na+] = 75 mmol/L) to be ΔV0 = +25.9(19) mL/mol, which is now ingood agreement with previous published results. Detailed studies for the dependence of these
molar volumes on monovalent and divalent cation conditions are described below.

Figure 11.4 Pressure dependent van’t Hoff analysis of DNA hairpin folding. (A) Folding (kfold)
and unfolding (kunfold) rate constants, and (B) folding equilibrium constant (Keq) as a function ofincreasing pressure. Note that kfold and kunfold are each scaled to 1 Hz (s-1) to permit taking
logarithms of unitless quantities. The slope of these plots can be used to infer changes in the molar
volume with uncertainties ( 1 to 2 mL/mol) at  5 to 10% of a single H2O molecule volume (V 18 mL/mol). Background [Na+] = 50 mmol/L.

308
11.4.3 Effects of Na+ on pressure dependent folding kinetics
With one phosphate group per nucleotide, DNA is highly negatively charged under pH
neutral conditions; therefore cations are essential to facilitate the formation of a more compact
folded DNA configuration.25-26 Moreover, charge screening and neutralization can havesignificant impacts on the hydration structure,27 which in turn can alter the effective molar
volume of the biomolecule plus solvent system and ultimately pressure dependences for thefolding/unfolding kinetics.28-29 In this section, pressure dependent equilibrium and kinetic rate
constants of DNA hairpin folding are systematically investigated to explore the impact ofmonovalent Na+ cations.

Figure 11.5 Pressure dependent folding equilibrium constants (Keq) as a function of Na+concentration, expressed as a van’t Hoff pressure analysis, whereby the slope of these plots can beused to infer changes in the molar volume with uncertainties ( 1 to 2 mL/mol) at  5 to 10% of
a single H2O molecule volume (V  18 mL/mol).
Firstly, the pressure dependence of the equilibrium constant Keq as a function of [Na+] isdisplayed as a semi-logarithmic plot in Figure 11.5. Under all conditions explored, the overall
trend reveals linear decrease in ln(Keq) with elevated applied pressure, which by Eq. 11.3
predicts a positive ΔV0 > 0. However, there are two quite noticeable changes in Keq(P) withincreasing [Na+]: i) ln(Keq) systematically shifts upward, reflecting that sodium significantly
promotes folding of the DNA hairpin under all pressures; ii) the ln(Keq) vs P slopes become

309[Na+] (mmol/L)

25

50

75

100

ΔV0 (mL/mol)

46.4(19)33.7(13)25.9(19)26.7(17)

Table 11.1 Na+ dependence of overall molar volume changes (ΔV0) for the single molecule DNA
hairpin construct in the absence of divalent cation (i.e., [Mg2+] = 0).
shallower with increasing [Na+], indicating an overall reduction in ΔV0 and thus pressure
sensitivity for DNA hairpin folding. From linear least squares fits, the resulting [Na+] dependentchange in molar volume values are summarized in Table 11.1, which illustrate that ΔV0
decreases systematically with increasing [Na+] up to 75 mmol/L values but eventually saturates
at [Na+] ≈ 75 to 100 mmol/L. Note that ΔV0 obtained at [Na+] = 75 mmol/L is experimentally

Figure 11.6 Pressure dependent van’t Hoff analysis of (A) folding (kfold) and (B) unfolding (kunfold)rate constants for a series of monovalent Na+ concentrations.

310[Na+] (mmol/L)

25

50

75

100

ΔV‡fold (mL/mol)

26(2)22.1(16)19.6(11)20.4(10)ΔV‡unfold (mL/mol)-19(2)-10.3(6)-6.6(7)-6.2(7)

Table 11.2 Na+ dependence of ΔV‡fold and ΔV‡unfold molar volume changes for the single molecule
DNA hairpin construct in the absence of divalent cation (i.e., [Mg2+] = 0).

indistinguishable from the previous diffusion smFRET equilibrium measurements under thesame salt conditions (25.9(19) vs. 23(2) mL/mol),15 confirming that surface tethering has
negligible impact on folding equilibrium properties for the DNA hairpin construct.30-31
Secondly, access to dwell time analysis in a surface tethered smFRET experiment also
permits [Na+] dependent kinetic information to be obtained from the single-molecule EFRET
trajectories. The resulting pressure dependent rate constants kfold and kunfold from cumulative
distribution functions are presented in Figure 11.6A and Figure 11.6B, respectively, as a functionof [Na+]. In these semi-logarithmic plots, the clear upward and downward vertical shifts in kfold
and kunfold reveal that Na+ promotes DNA hairpin folding by simultaneously increasing kfold anddecreasing kunfold, respectively.20 The plots for ln(kfold) vs. pressure in Figure 11.6A are well fit toa series of nearly parallel lines with negative slopes, confirming that kfold decreases at increasingpressure and ΔV‡fold > 0 for all [Na+] conditions explored (Eq. 11.2). The steepening of slopes
for lowest [Na+] reflects a larger ΔV‡fold at [Na+] < 75 mmol/L, which then quickly decreases to asaturation value independent of increasing [Na+] (see also Table 11.2). Conversely, as evident
from the positive slopes in Figure 11.6B, ln(kunfold) increases rapidly with increasing pressure,consistent with a negative ΔV‡unfold < 0. Moreover, the sensitivity of kunfold to pressure and cation
concentration is now clearly evident in the steeper slopes at low [Na+] < 75 mmol/L, revealing a311much more significant Na+ dependence of ΔV‡unfold in the low sodium regime. Similar to ΔV‡fold,as [Na+] increases, the magnitude of ΔV‡unfold decreases and gradually reaches a saturation value
at [Na+] ≈ 75 mmol/L. By way of summary, increasing [Na+] lowers the sensitivity of both kfold
and kunfold to pressure by reduction in the magnitude of ΔV‡fold and ΔV‡unfold, respectively, withmuch stronger effects observed for the latter. However, as [Na+] increases above ≈ 75 mmol/L,
monovalent cation effects on the pressure dependent rate constants appear to saturate for both
ΔV‡fold and ΔV‡unfold.

11.5

Discussion

11.5.1 Effective volume of the DNA hairpin increases along the folding path
The surface tether smFRET experiments (Figure 11.1) performed in the high pressure
capillary sample cell allow us to probe the kinetics of DNA hairpin folding with pressure as acontrolled external variable up to ≈ 5 kilobar.7, 15 The EFRET time trajectories are calculated fromthe resulting time-dependent Cy3/Cy5 fluorescent signals (Figure 11.2) and analyzed byconventional thresholding methods to obtain dwell time distributions of the folded and unfolded
states (Figure 11.3).18-19, 23 First of all, visual inspection of the EFRET trajectories (Figure 11.2)
clearly reveals that with increasing pressure, the DNA hairpin spends more time in the unfolded(low EFRET) conformation. Such DNA unfolding at elevated pressures is commonly referred to aspressure denaturation,8-9 which had been routinely observed in multiple protein4-5 and nucleic
acid7, 32-34 systems in previous high pressure equilibrium measurements. Pressure denaturation
indicates that the thermodynamic volume of the system is larger for the folded vs unfolded
conformations (ΔV0 = Vfold – Vunfold > 0) and therefore according to Le Chatelier’s principle,
folding is disfavored at high pressures (Eq. 11.3).35 Though still a topic of intense discussion,

312

Figure 11.7 Effective volume change along the folding coordinate as a function of increasing[Na+], with volume of the unfolded state (Vunfold) arbitrarily designated as the reference zero.
such a volume increase due to folding is commonly ascribed to a corresponding change inhydration structure for the surrounding solvating water molecules.4, 35 In essence, the total system
volume can decrease with DNA unfolding, since the volume occupied by water in thistemperature range decreases with greater ordering of the solvent molecules.28-29 This greaterordering and thus decreased volume can occur upon DNA unfolding by exposing greater surface
area and thus orienting more water molecules due for example to stronger Coulombic
interactions with the phosphate anion backbone. An alternate mechanism proposed for V > 0
behavior would be the formation of water-excluding hydrophobic voids upon folding,36 which
would then effectively induce the folded DNA to displace a greater molar volume in solution.
In the kinetic analysis, Figure 11.4A explicitly reveals the origin of this pressure-induced
denaturation as a simultaneous decrease in kfold and increase in kunfold. Such kinetic response
implies that the effective transition state volume must be smaller than the fully folded state, yetlarger than the unfolded state (Vunfold < VTS < Vfold). In Figure 11.7, the volumes of each of thethree conformations are displayed with Vunfold referenced to zero, clearly revealing that thevolume of the DNA hairpin increases monotonically along the folding coordinate. Similar trends

313
have also been observed in some protein systems with pressure-jump37-38 and high pressure ZZexchange NMR39 studies. Indeed, it is not surprising that the transition state adopts anintermediate volume between the folded and unfolded configurational extremes. However, theseexperimental activation molar volumes (ΔV‡fold and ΔV‡unfold) also contain additional information
on changes in water solvation structure due to the conformational transition,29, 35 and thus may
offer insights into the influence of cations on DNA hydration as a function of thehybridization/folding coordinate,27 as discussed in Sec. 11.5B and Sec. 11.5C.
In previous pressure dependent UV melting experiments, the majority of nucleic aciddouble helices are found to be stabilized by pressure,11-12 which at first seems opposite to therecent high pressure single molecule studies with hairpins of shorter duplexing regions (< 10base-pairs).13-15, 21 However, a strong correlation between thermal stability and pressure response
also has been previously observed in UV melting experiments,6 suggesting pressure only
destabilizes the helices with low thermal stability (e.g. Tm > 50 ℃). Since the single molecule
experiments are often performed under the conditions where folded and unfolded states are bothsufficiently populated, the hairpins used in these single molecule studies are much less thermallystable with Tm close to the room temperature.13-15, 21 As a result, the pressure destabilization
effects (ΔV0 > 0) characterized at the single molecule level are in fact entirely consistent withprevious observations in UV melting studies. Although the origin of the strong correlation
between melting temperature and pressure response has not been completely understood, it canbe accounted by the complex temperature-pressure dependent interactions involved in the helixcoil transition6 such as hydration, base stacking, hydrogen bonding and Coulombic interactions,
etc.40 We note that the temperature-dependent pressure response has also been observed inprevious smFRET experiments.34

314
Besides thermodynamic properties, the kinetics of helix-coil transition can be obtained byanalysis of the hysteresis in UV melting/annealing curves.41 The results again show a negative
ΔV0 for most of the duplex sequences,42-43 while the signs of ΔV‡fold/unfold may vary.43 Moreover,the nearest neighbor parameters in ΔV0 and ΔV‡fold/unfold have been determined and the prediction
agrees will with the studied duplex systems.43 However, the same nearest neighbor analysis
predicts the ΔV0 and ΔV‡fold of the duplex sequence in our hairpin construct to be 0.0 mL/mol(+25.9 mL/mol, as the closest value measured at [Na+] = 75 mM) and -1.5 mL/mol (+19.6
mL/mol). Although the discrepancy could partially attribute to the different buffer conditions andthe poly(dA) linker, which contributes ≈ 10 mL/mol to ΔV0,15 the nearest neighbor analysis is
not expected to correctly predict our results due simply to the fact that these parameters arederived from more thermally stable duplex structures that are mostly stabilized under highpressure. Indeed, a more sophisticated high pressure smFRET experimental setup to study thebimolecular DNA duplex formation44 is needed to better understand the disparity between
pressure effects on short and long duplex sequences. The high pressure smFRET experiment
provides a powerful tool to study the pressure dependent kinetics completely free from thethermal contributions and the results obtained at low temperature may better represent the impact
of extreme pressures on deep sea organisms.
11.5.2 Na+ decreases the activation volumes for both folding and unfolding pathways
The pressure responsive DNA folding equilibrium and kinetics have been studied atincreasing [Na+] to explore the monovalent cation effects (Figure 11.6). The results arequantitatively summarized in Figure 11.7, which reveals not only an strong increase in effective
volume along the folding coordinate, but also that the presence of monovalent cation (Na+)
reduces these changes in volume and saturates above 75 mmol/L. Specifically, the most dramatic

315
effects are observed in the volume change from the transition state to the folded state (Vfold – VTS= −ΔV‡unfold), which collapses by 3-fold from +19(2) mL/mol to +6.2(7) mL/mol as [Na+]increases from 25 to 100 mmol/L. It is worth noting that the exceptionally large dynamic rangeof pressures explored in these experiments results in ΔV uncertainties down at the ≈ 1 to 2
mL/mol level. For a sense of scale, this is roughly 5 to 10% the volume of a single H2O
molecule, which in turn allows us to explore and quantify the even smaller changes in molar
volume induced by the presence of monovalent cations.
In particular, there is a quite significant Na+ dependence to the change in thermodynamic
molar volume (ΔVs, Table 11.1 and Table 11.2) which provides additional confirmation thathydration water play a crucial role in pressure induced denaturation phenomena for DNA.4, 29, 35
By way of specific physical mechanism, monovalent cation association would tend to Debye
shield the highly negatively charged DNA phosphate backbone,45-46 weakening the Coulombic
interactions that align the water molecules and therefore allowing DNA to adopt a more weakly
bound solvation shell with a larger effective volume.28-29 Furthermore, such an increase incation-induced volume changes may vary for each folding stage,7 resulting in cation dependentchanges in molar volume. In particular, since the more folded DNA hairpin has higher charge
density and smaller water-exposed surface area,47 the cations would be expected to be more
readily associated with and therefore saturate the ion atmospheres of the folded vs. unfolded
structures at progressively lower cation concentrations.48-49 Alternately stated, Vunfold increases
faster than Vfold with increasing [Na+] due to preferential cation association with the unfolded
state,50-51 resulting in an overall reduction in ΔV0 (ΔΔV0 < 0). Moreover, similar monovalentcation effects can also be expected with respect to changes in the transition state volume (VTS),316
which similarly predicts decreases in magnitudes of both ΔV‡fold and ΔV‡unfold with increasing[Na+].
In previous thermodynamic and kinetic characterizations of DNA duplex formation44,
increasing [Na+] is found to simultaneously decrease the relative entropies for both the unfolded
and transition state, indicating that Na+ may promote more organized DNA structures in bothconformations prior to folding.44 In the present work, the volumetric measurements clearly reveal
a significant decrease in the value of Vfold – Vunfold as the dominant cation response (Figure 11.7),
or, if we assume a smooth dependence on folding reaction coordinate, an increase in molar
volume between the unfolded state and the folding transition state. In this context, our highpressure volumetric analysis of the [Na+] dependence is consistent with a simple physical picturethat Na+ promotes the stability of a progressively more “folded-like” DNA structure by changes
in hydration for both the unfolded, transition state, and folded configurations, an interpretation
which is in good agreement with previous and current thermodynamic data.44

Figure 11.8 Effective volume change along the folding coordinate as a function of increasing[Mg2+], with volume of the unfolded state (Vunfold) arbitrarily designated as the reference zero.
Background [Na+] = 50 mmol/L.

317
11.5.3 Cation-independent volume changes at physiological salt concentrations
The volumetric measurements for the DNA folding kinetics support that suchmonovalent cation effects saturate at ≈ 75 mmol/L for both ΔV‡fold and ΔV‡unfold, which iscomparable to physiological monovalent cation concentration conditions ([M+] ≈ 100 mmol/L).
The results therefore predict that significant [M+] dependence in molar volume changes (ΔVs)
can only be observed under low salt conditions (i.e., [M+] < 100 mmol/L). Indeed, previous
reports for the K+-dependence of ΔV0 in DNA hairpin indicate observation of folding only in the
low monovalent cation regime ([M+] < 30 mmol/L).21 On the other hand, cesium ion (Cs+) has
been shown to reduce the volume changes at low concentration in previous high pressurepoly[d(A-T)] melting experiments, with the effects saturating at [Cs+] ≈ 100 mmol/L.11 However,
we note that in the same study that the ΔV0 dependence on Na+ does not show evidence of any
saturation up to [Na+] = 1 mol/L. We believe that sodium-promoted base stacking in the DNApoly(dA) single strand may be significantly perturbing the helix-coil transition and therefore
resulting in additional salt-induced volume changes upon melting.15, 52 Clearly more highpressure data will be needed to fully explore and understand the potential salt/structure
dependence of this saturation phenomenon.
Since magnesium (Mg2+) is the most abundant divalent cation inside cells and known tosignificantly influence nucleic acid secondary and tertiary structure,26, 53 similar volumetricanalyses have been performed as a function of increasing [Mg2+] = 0 to 0.75 mmol atbackground monovalent levels of [Na+] = 50 mmol/L and [K+] = 25 mmol/L (see SI), and theresults are summarized in Figure 11.8. The background monovalent cation mimics thephysiological environment of DNA folding and provide additional stability for the folded DNA
hairpin to increase the pressure dynamic range of the smFRET experiments. Interestingly, the318
molar volume folding landscape is only very slightly perturbed by the presence of Mg2+, with
ΔV‡fold being completely independent and with only quite modest (< 5 to 10%) changes in
ΔV‡unfold as a function of [Mg2+]. We stress that this does not mean that divalent magnesium
effects on the molar volume changes are necessarily weaker than monovalent sodium. Instead, it
could be that the overall cation effects are effectively saturated at background monovalent levelsof [M+] = 75 mmol/L and that the additional magnesium is unable to achieve any further reduce
in ΔV. We note that although the pressure response (ΔV) of the hairpin folding is only weakly
dependent on [Mg2+], magnesium still strongly stabilizes the folded hairpin structure as thevertical displacements shown in Figure 11.9. To summarize, our data suggest under sufficiently
high monovalent ([M+] ≈ 100 mmol/L and divalent ([M’2+] ≈ 1 mmol/L) salt conditions, themolar volume changes (ΔVs) for hybridization of the DNA hairpin saturate and depend only
weakly on further increase in cation concentrations. By way of additional evidence, previous
pressure dependent single molecule studies of the RNA lysine riboswitch reveal ΔV0 also to be
independent of salt under physiological conditions ([Na+] = 100 to 500 mmol/L, [Mg2+] = 0.5 to

Figure 11.9 Pressure dependent folding equilibrium constants (Keq) as a function of Mg2+
concentration, expressed as a van’t Hoff pressure analysis, whereby the slope of these plots can beused to infer changes in the free volume with uncertainties (1 to 2 mL/mol) at the 5 to 10% of asingle H2O molecule volume (18 ml/mol). Background [Na+] = 50 mmol/L.

319
1.5 mmol/L).7 Although more data are clearly needed, the results thus far encourage expectations
that cationic effects on RNA folding will exhibit a similar saturation behavior as seen in DNA.
As a final comment in this subsection, we can translate these changes in molar volume
landscapes (ΔV0 and ΔV‡fold) into corresponding change in free energy landscapes. These
reversible work contributions to free energy are specifically evaluated at a nominal P = 1 kilobar
and plotted in Figure 11.10 against [Na+] to highlight i) effects of pressure-induced denaturationin deep sea ( 10000 meter) environments, and ii) the saturation of the monovalent cation effects
under physiological relevant conditions (Figure 11.10). It is worth noting that even with ΔV0values only slightly larger than the size of a single water molecule (V ≈ 18 mL/mol), theequivalent amount of reversible PΔV work under such deep sea pressure conditions alreadycontributes at the level of +1 kcal/mol (≈ +2 kT) to the overall folding free energy, thereby
strongly shifting the equilibrium to the unfolded conformation. Furthermore, roughly half of that

Figure 11.10 PΔV reversible work evaluated at P = 1000 bar to highlight the magnitude of freeenergy contributions (kT  0.6 kcal/mol) induced by deep sea pressures as a function of increasing[Na+].

320
overall increase in free energy to folding is achieved by the transition state, which corresponds toa roughly three-fold deceleration in DNA hybridization rate constants under deep-sea environmentvs. ambient pressure conditions.
11.5.4 Na+ stabilization effects on DNA secondary structure revisited
In previous sections, we have mostly focused on the slopes in semi-logarithmic plots of
Keq or k vs P (Figure 11.5 and 11.6), whereby changes in molar volume can be directly extracted
from the pressure dependence. In addition to reducing ΔVs, sodium also promotes DNA hairpin
folding under all pressures explored by simultaneously increasing and decreasing kfold and kunfold,respectively, as shown in the vertical displacements in Figure 11.5 and Figure 11.6. For
simplicity, we first focus on monovalent Na+ effects at ambient pressure summarized in Figure
11.11, whereby the folding (ΔG0) and activation (ΔG‡) free energies for this DNA hairpin areplotted against [Na+]. In obtaining these values, we have used standard thermodynamic andtransition state expressions relating overall (ΔG0 = -kTln[Keq]) and transition state (ΔG‡ = kTln[kfold/]) free energies to the equilibrium and rate constants measured.  is an approximate
attempt frequency for achieving the transition state, whose precise value is irrelevant in Figure
11.11 for changes in free energies (G0). The monotonic decrease in ΔG0 with [Na+] confirmsthat the folded DNA hairpin is energetically favored by increasing monovalent cation
concentration. Furthermore, such a quasilinear decrease in ΔG0 with [Na+] is also consistent with
empirical observations by Pegram et al. of cation effects on DNA folding in the low
concentration regime ([M+] ≈ 100 mmol/L),47 with the slopes (∂ΔG0/∂[M+]) strongly correlatingwith strength of solute-nucleic acid interactions and the change in solvent accessible surface area
(ASA) during folding (ΔASA). Indeed, cations are known to accumulate on the surface of DNA
through Coulombic attraction,45, 54-55 and in turn facilitate the formation of a more compact

321
structure by charge neutralization and screening effects.25-26 Moreover, similar sodium
dependence is also observed in ΔG‡ but with  50% shallower slopes, most simply attributed to
fractionally smaller ΔASA‡ values or molar volume changes (V‡fold) at the transition state.

Figure 11.11 Na+ stabilization effects on the DNA hairpin secondary structure under ambientpressure conditions.
As a parting comment, we note that the empirical relation between ΔG and [Na+] may
deviate from a simple linear function at low [Na+] < 75 mmol as pressure-induced denaturation
becomes more significant at higher pressures (Figure 11.10). In other words, increased Na+ couldin principle protect the DNA structure from pressure-induced denaturation by both i) increasing
the hybridization stability and ii) suppressing the pressure-induced dehybridization response. It is
important to stress, however, that such effects would not necessarily make sodium (or othercations) suitable candidates to help deep sea organisms maintain cellular function at extreme
pressures, due to the fact that high cation concentrations can interact strongly with biomoleculesin cells and thus highly perturb their function,56 as in dynamic gene regulation by RNA
riboswitches.7 Instead of recruiting cations, therefore, deep sea organisms accumulate highconcentrations of small organic solutes (e.g. trimethylamine N-oxide, TMAO) that are much322
more compatible with biomolecule structure/function10 and can thereby counteract thesepressure-induced free energy contributions primarily by reducing the pressure sensitivity tobiomolecule conformation.7, 21, 57-58

11.6

Summary and conclusion
First high pressure kinetic studies of DNA hybridization at the single molecule level havebeen investigated by smFRET experiments on a doubly dye labelled DNA hairpin construct overa wide dynamic range of external pressures (1 to 1500 bar). The resulting EFRET time trajectories
from the prolonged observation of single tethered molecule fluorescence allows us to extract
information on the unimolecular rate of DNA hairpin folding/unfolding. The folding (kfold) and
unfolding (kunfold) rate constants are found to simultaneously decrease and increase, respectively
with increasing pressure, resulting in predictions consistent with pressure-induced denaturationof DNA secondary structure and in excellent agreement with previous equilibrium high pressurestudies on freely diffusing constructs. By way of pressure dependent van’t Hoff analysis, theeffective volume of the DNA plus solvent system is found to systematically increase along thefolding coordinate (Vunfold < VTS < Vfold), with volume sensitivities and experimental
uncertainties (1 to 2 mL/mol) on the order of 5 to 10% of a single H2O molecule. Since thecation may significantly change the hydration structure and consequently the effective volume of
the DNA plus solvent system, the change in free activation volumes for both folding andunfolding (ΔV‡fold and ΔV‡unfold) are shown to decrease at low [Na+] and gradually reachsaturation limits at [Na+] ≈ 75 mmol/L. The more significant reduction in ΔV‡unfold indicates agreater resemblance between VTS and Vfold, which in turn signifies that Na+ is able to facilitate amore folded-like transition state configuration prior to formation of the fully folded DNA

323
hairpin. Finally, both ΔV‡fold and ΔV‡unfold are approximately insensitive to monovalent (Na+)
and divalent (Mg2+) cations under near-physiological salt concentrations, suggesting cation
effects on these changes on molar volume (ΔVs) may saturate in vivo and therefore be insensitive
to moderate intracellular cation fluctuation.

11.7

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Chapter 12
Ligand-Dependent Volumetric Characterization of Manganese Riboswitch Folding:
A High-Pressure Single-Molecule Kinetic Study

12.1

Abstract
Nanoscopic differences in free volume result in pressure-dependent changes in freeenergies which can therefore impact folding/unfolding stability of biomolecules. Although such
effects are typically insignificant under ambient pressure conditions, they are crucially importantfor deep ocean marine life, where the hydraulic pressure can be on the kbar scale or higher. In
this work, single molecule FRET spectroscopy is used to study the effects of pressure on both the
kinetic rates and overall thermodynamics for folding/unfolding of the manganese riboswitch.
Detailed pressure-dependent analysis of the conformational kinetics allows one to extract
precision changes (  4 to 8 Å3) in free volumes not only between the fully folded/unfolded
conformations, but also with respect to the folding transition state of the manganese riboswitch.
This permits first extraction of a novel “reversible work” free energy (PV) landscape, which
reveals a monotonic increase in manganese riboswitch volume along the folding coordinate.
Furthermore, such a tool permits exploration of pressure-dependent effects on both Mn2+ binding
and riboswitch folding, which demonstrate that ligand attachment stabilizes the riboswitch bydecreasing the volume increase upon folding. Such competition between ligand binding andpressure induced denaturation dynamics could be of significant evolutionary advantage,*This chapter is adapted from: Sung, H.-L.; Nesbitt, D. J. Ligand-Dependent Volumetric Characterization ofManganese Riboswitch Folding: A High-Pressure Single-Molecule Kinetic Study. J. Phys. Chem. B 2022,
126, 9781-9789.

329
compensating a weakening in riboswitch tertiary structure with pressure mediated ligand binding
and promotion of folding response.

12.2

Introduction
Structural transitions in biomolecules and the associated reorganization of thesurrounding waters lead to nanoscopic changes in the overall solvent plus solute system
volume.1-2 As a result, conformational change in a biomolecule is intrinsically pressuredependent.3 Though such pressure effects are often negligible at ambient pressure (1 bar), theseeffects can become quite significant in marine biology due to rapid increase in hydraulic pressure
as a function of ocean depth (0.1 bar/meter).4 Indeed, average ocean depth already corresponds
to 350 bar pressure, with the deepest regions (e.g., the Challenger Deep) in excess of 1 kbar. As aresult, marine (micro)organisms can exhibit unique modes of biological function sculpted byevolution under high pressure conditions.5-6 It is therefore of particular biophysical interest to
explore pressure-dependent paradigms of biomolecular structure and function in order tounderstand, at the molecular level, bioadaptation of deep-sea organisms to pressure extremes.7
With a few exceptions,8-9 proteins and nucleic acids are known to thermodynamicallyunfold/dehybridize with increasing pressure.5, 10-12 Pressure-induced denaturation implies that thefolded solute + solvent system effectively occupies more space, resulting in a positive freevolume change (ΔV0 > 0) upon folding. Such an increase in volume seems initiallycounterintuitive, since one often thinks of biomolecular folding tending toward a state of greatercompaction. The reason for such anomalous behavior is that these overall volume changes arequite modest, with solvent-excluding voids13-15 and/or reorganization of the solvation shell16-18

330
thought to be major contributors to the volume increase upon folding. Interestingly, althoughpressure is known to thermodynamically destabilize the equilibrium folding behavior for nucleic
acids and proteins, the kinetics of such effects has remained far less explored.19-21 Since nucleic
acid conformations are often highly dynamic,22 with important biochemical pathways regulated
by kinetic access over a barrier to a functionally new conformation (e.g., regulation of gene
expression by co-transcriptional folding of riboswitches),23-25 it is therefore of particularimportance to also explore the effects of pressure on transition state barriers and the resulting
folding kinetics.
Recently, high pressure single-molecule Fluorescence Resonance Energy Transfer(smFRET) studies of nucleic acid folding kinetics have become experimentally accessible,
exploiting small glass capillaries as high-pressure sample cells in conjunction with confocal
single photon counting fluorescence measurements.11, 26-27 In earlier work, pulsed laser excitation
through a microscope objective into solutions at high pressure have been used to measure andrecord the FRET energy transfer efficiency (EFRET) for single RNA molecules diffusing throughthe confocal volume region. Though such studies have been limited to equilibrium conditions,they clearly demonstrated a systematic decrease in EFRET (i.e., an increase in the unfolding
fraction) with increasing pressure. In the present work, we significantly expand these equilibrium
high-pressure smFRET studies by immobilizing single RNA constructs to the inside of a highpressure capillary cell, and thereby extend observation times of the fluorescence trajectories tomonitor folding/unfolding kinetics at the single molecule level.28 The resulting pressure
dependent kinetic rate constant data now inform on the free volume changes associated with i)folded, ii) unfolded, and iii) transition state barrier conformations, and thus provide novel

331
opportunities for detailed characterization of the thermodynamic free volume along the nucleic
acid folding coordinate.29
Specifically, this work comprises detailed study of the effects of extreme pressure on thefolding/unfolding kinetics of the manganese riboswitch at the single molecule level. The folding
thermodynamics and kinetics of this riboswitch have been studied previously in both ensemble
and at the single molecule level under ambient pressure (1 bar) conditions,30-33 with the present
work exploring pressure-dependent kinetics of ligand-induced tertiary structure formation for the
first time. Of particular significance is first experimental characterization of the coupling
between i) pressure-dependent kinetic measurements and ii) the ligand binding event, whichallows us to obtain free volume changes for accessing the transition state associated withmanganese riboswitch folding. Furthermore, in the context of a simple Hill analysis,30 we areable to separate ligand Mn2+ binding from riboswitch folding events and thereby obtain novel
information on “reversible work” (PΔV) contributions to the free energy landscape along theconformational reaction path. These volume changes are revealed to be sensitive to the hydration
structure and fractional Mn2+ binding with the RNA, which offers additional insights into themechanism for ligand-induced RNA folding.
The organization of this paper is as follows. The details of sample preparation and highpressure experiment setup are illustrated in Sec. 12.3. Sec. 12.4A demonstrates high-pressure
effects on the riboswitch folding kinetics, for which increasing pressure destabilizes theriboswitch by simultaneously decreasing (increasing) the folding (unfolding) rate constants,
respectively. The effects of Mn2+ and Mg2+ cations on the pressure dependent folding are thenpresented in Sec. 12.4B and Sec. 12.4C, respectively, which reveal that cognate ligand Mn2+ (andnot Mg2+) significantly impacts changes in free volume (ΔV0bind < 0). Specifically, Mn2+ alters

332
the volumetric reversible work landscape for folding via binding of the cognate ligand to (andsubsequent compaction of) the riboswitch rather than a more generic screening of anionic
repulsion due to divalent cations. Finally, we briefly discuss in Sec. 12.5A/B the possible role ofequilibrium vs. kinetic competition between Mn2+ and pressure induced changes in riboswitch
volume on the evolutionary biology of deep-sea organisms.

Figure 12.1 Schematic of the high pressure single molecule FRET experiment showing the
instrument setup. (A) The cartoon representation of the manganese riboswitch construct in the
Mn2+-bound folded conformation where the loop-loop interaction between P1 and P3 stems isformed. (B) The high pressure generating system coupling to the capillary sample holder alignedwith the microscope objective. The reservoirs contain ethanol as the pressure transmitting fluid
throughout the high pressure tubing manifold.

12.3

Experiment12.3.1 Single-molecule fluorescent construct design and sample preparation
The ligand-bound folded structure of the manganese riboswitch consists of an RNA fourway junction with the loop-loop interaction between P1 and P3 stems stabilized by a Mn2+ cation(Figure 12.1A).33 The single-molecule FRET construct of the riboswitch is made up of three
RNA oligomers, labeled with Cy3, Cy5 and biotin, respectively. The detailed RNA sequences

333
and the labeling positions for these oligomers can be found in previous work.34 To assemble theternary RNA construct, the three oligomers are heat-annealed by temperature cycling, followedby purification via high-performance liquid chromatography (HPLC) methods. The doubly-dyelabeled and biotinylated product enables surface immobilization of the RNA construct to achieve
single-molecule fluorescence detection over a prolonged time window and thereby observe asequence of multiple folding/unfolding events. Furthermore, based on a characteristic Forster
length R0 ≈ 50 Å for the Cy3-Cy5 FRET pair, the inter-dye distances in the folded conformation
can be predicted from the manganese riboswitch crystal structure to be 45 Å,33 which is in good
agreement (EFRET (45 Å)  0.65) with the high EFRET  0.60 state observed. Conversely, when the
manganese riboswitch unfolds, the distance between Cy3 and Cy5 increases, resulting in a
reduced and easily distinguished value of EFRET  0.15 consistent with R  67 Å.
The high-pressure sample cell is made from a glass capillary with a square cross section(75 µm/360 µm inner/outer dimensions, Polymicro).27 Such small lateral dimensions permit
higher pressure (> 2000 bar) operation, while the flat interior surface and wall thickness (143µm) also allow the capillary to function as a conventional coverslip in standard microscope
imaging. To prepare the sample, one end of the capillary is first glued into a metal plug drilledwith a 450 µm diameter hole and coupled to the pressure system (Figure 12.1B). After creating
an optically transparent window by oxidizing away a small 1 cm patch of the polymer coating,
we immobilize the RNA molecules on the inner surface of the capillary through biotinstreptavidin interactions. To achieve this goal, we continuously flow the following solutions
through the capillary in succession: 1) 10 mg/mL bovine serum albumin (BSA) with 10%
biotinylation, 2) 200 µg/mL streptavidin solution, and 3) ≈ 25 pM RNA construct. The exposure
time for each solution is ≈ 2 minutes, with pressure delivered through a mechanical micropipette334(Eppendorf) to flush liquid through the capillary.29 Before any single molecule experiments, thecapillary is additionally flushed with an imaging buffer containing 1) 50 mM pH 7.5 HEPES
buffer, 2) enzymatic oxygen scavenger cocktail (PCD/PCA/Trolox) to catalytically remove
oxygen,35 3) 100 mM NaCl to provide background salt, and 4) sufficient MgCl2/MnCl2 toachieve desired divalent cation and cognate ligand concentrations. The free end of the capillary
is then sealed with an oxy-propane torch, while the metal plug end is dipped into silicon oil tocreate a thin pressure transmitting meniscus and prevent sample contamination.

Figure 12.2 Sample fluorescence traces and the resulting time trajectories of E FRET at (A) 1 barand (B) 500 bar. The simulated traces in orange are obtained from hidden Markov modelling.

12.3.2 High pressure single-molecule FRET spectroscopy
Pressure control is achieved by a manually operated piston screw pump (High Pressure
Equipment), which can deliver pressure up to 5 kilobars through high-pressure stainless steel
tubing, with the entire manifold filled with ethanol as pressure transmitting fluid (Figure
12.1B).36 We take advantage of the square cross section of the sample cell by taping it onto thesurface of a coverslip, which permits ready alignment of the optical axis of the microscope

335
objective axis with respect to the capillary wall.29 The details of the confocal single molecule
FRET spectroscopy set up can be found in previous work.37 To initiate an experiment, the laser isfocused to a diffraction limited waist (x,y ≈ 260 µm) on the inner capillary surface, with thesearch for single fluorescent molecule constructs conducted by raster scanning of the piezo stage.
Tethering of the construct to the capillary surface permits prolonged diffraction limited
observation of Cy3/Cy5 fluorescence from a single localized RNA, which in turn enables thecollection of long-lived (≈ 1 min) single molecule FRET trajectories at ≈ 4 kHz photon/sec
detection rates and limited by eventual photobleaching.

Figure 12.3 Sample dwell time distributions at (A) 1 bar and (B) 500 bar. Data are fit to a single
exponential decay function to obtain folding and unfolding rate constants kfold and kunfold,respectively.

12.4

Results and analysis

12.4.1 Kinetic origins of manganese riboswitch unfolding at increasing pressure
Time-dependent EFRET trajectories reveal that the manganese riboswitch actively switches
between low and high EFRET states (see sample FRET traces in Figure 12.2) corresponding to
unfolded and folded conformations.30 While the equilibrium constant Kfold can be readily
obtained from the total timing for folded vs. unfolded events, even more valuable information on

336
the folding kinetics can be extracted from the distribution of dwell times. As shown in Figure
12.3, this dwell time distribution is well approximated by a single exponential decay, for which
the folding/unfolding kinetics of the manganese riboswitch can be described by first order rate
constants kfold and kunfold. The resulting dwell time analysis reveals a faster decay for theunfolded state, i.e., kfold > kunfold under ambient (1 bar) conditions. As external hydrostaticpressure increases to 500 bar, however, the riboswitch spends significantly longer in the Cy3 vsCy5 low EFRET (“denatured”) conformation, as visually evident in Figure 12.2. Such pressure
dependent denaturation is consistent with previous high-pressure studies of both proteins5, 12 andFigure 12.4 Pressure-dependent manganese riboswitch folding (A) equilibrium constant and (B)kinetics rate constant plots, where error bars represent standard deviation of the mean. In analogy
to Eyring analysis of transition state barrier energies, the data are least squares fit to a single
exponential function to obtain quantitative volumetric change information for ΔV0 andΔV‡fold/unfold. [Mn2+] = 15 µM; [Mg2+] = 2mM.

337
nucleic acids.10-11 Interestingly, however, the dwell time distributions in Figure 12.3 makeevident that increasing pressure kinetically results in an equilibrium preference for the unfolded
Mn2+ riboswitch both by increase in the unfolding rate constant (kunfold) and yet also asimultaneous decrease in the folding rate constant (kfold).
The pressure effects on the manganese riboswitch folding equilibria can be summarized
in the semi-logarithm “van’t Hoff” plots of Kfold vs pressure (Figure 12.4A), which specificallyreveal a linear decrease in ln(Kfold) as a function of elevated pressure. We can further quantify
such a pressure dependence by the simple thermodynamic relation3, 5(

𝜕𝑙𝑛𝐾𝑓𝑜𝑙𝑑
𝜕𝑃

)𝑇 =

−∆𝑉 0
𝑅𝑇

,

Eq. 12.1

which allows us to relate the slope in Figure 12.4A to the change in free volume upon folding.
Least squares fits to the data yield ΔV0 = +88(4) mL/mol, with a positive sign clearlycorresponding to the manganese riboswitch occupying the greater volume upon folding. The
present high pressure single molecule kinetic capabilities permit a further interesting level ofdetail by similar volumetric analysis applied to pressure-dependence of the folding/unfolding
rate constants (Figure 12.4B). Specifically, the activation free volume ΔV‡fold/unfold for accessing
the transition state barrier from the folded/unfolded conformations can be obtained from linear
fits to an“Arrhenius-like” volumetric expression5(

𝜕𝑙𝑛𝑘𝑓𝑜𝑙𝑑/𝑢𝑛𝑓𝑜𝑙𝑑
𝜕𝑃

)𝑇 =

‡
−∆𝑉𝑓𝑜𝑙𝑑/𝑢𝑛𝑓𝑜𝑙𝑑

𝑅𝑇.

Eq. 12.2

where once again a positive volume change (ΔV‡fold = 49(4) mL/mol) and reveal that thetransition state (TS) takes up more volume than the fully unfolded state (U). Conversely, thecorresponding volume change in the unfolding direction is negative (ΔV‡unfold = -37(3) mL/mol),338
which obviously rationalizes the observed speed up in the unfolding rate constant kunfold withpressure. These results can be simply summarized as predicting a monotonic increase in the
manganese riboswitch free volume along the folding coordinate, with VU < VTS < VF, withuncertainties in these volume changes at the   4 to 8 Å3 level.

Figure 12.5 Pressure-dependent equilibrium constants (Kfold) for the riboswitch folding as afunction of increasing [Mn2+] in the presence of physiological [Mg2+] = 2 mM.

12.4.2 Mn2+ effects on pressure dependent riboswitch folding
The manganese riboswitch responds conformationally to its cognate ligand Mn2+ in theregulation of gene expression, which naturally invites study of pressure dependent folding as afunction of ligand concentration.32 As evident in Figure 12.5, increasing the cognate ligand Mn2+
concentration promotes riboswitch folding (i.e., an increase in Keq) at each pressure exploredfrom ambient to 1000 bar. Moreover, the slopes of the van’t Hoff plots are all negative (V0 >0), correctly predicting pressure induced denaturation for the manganese riboswitch at all Mn2+
concentration within a physiologically relevant range. At a higher level of quantification, thevan’t Hoff slopes in Figure 12.5 are summarized in Table 12.1, for which the ΔV0 values exhibita systematic decrease as a function of increasing Mn2+. Most importantly, this implies that all
positive free volume changes for manganese riboswitch folding/unfolding are significantly

339

Figure 12.6 Pressure-dependent rate constants (A) kfold and (B) kunfold as a function of increasing[Mn2+] in the presence of physiological [Mg2+] = 2 mM.

reduced by association with the cognate ligand/Mn2+, a point to which we will return in Sec 12.5.
Finally, we can apply a similar pressure- and Mn+2-dependent analysis to the rate constants for
manganese riboswitch folding/unfolding. As nicely summarized in Figure 12.6A/B, an increasein Mn2+ concentration systematically lowers the negative slopes in an Arrhenius-like pressure
plot for kfold, indicating a differential decrease in transition state free volume (ΔV‡fold < 0) as afunction of added Mn2+. On the other hand, the corresponding Arrhenius slopes in Figure 12.6B
for the unfolding rate constants reveal no systematic response to Mn2+ concentration, indicating
an approximately constant ΔV‡unfold independent of Mn2+ over 0 to 50 M. To further quantify
the Mn2+ effects on pressure-dependent response of the riboswitch, the folding/unfolding

340
activation volumes (ΔV‡fold/unfold) calculated by Eq. 12.2 are summarized in Table 12.1, to which
we will return as an important point of discussion in Sec. 12.5.
[Mn2+] \ ΔV

ΔV0 (mL/mol)ΔV‡fold (mL/mol)

ΔV‡unfold (mL/mol)

0 µM

110 (4)61(7)-44(4)5 µM

100(7)

56(7)-39(4)

15 µM

88(4)

49(4)

-37(3)

50 µM

79(3)

38(2)

-41(3)

Table 12.1 ΔV0 and ΔV‡fold/unfold values as a function of increasing Mn2+. The reported
uncertainties represent standard deviation of the mean for triplicate studies.

12.4.3 Mg2+ effects on the pressure dependent riboswitch folding
The manganese riboswitch has two cationic binding sites, one of which can bind with
Mg+2 at physiological levels (2 mM) and another that exclusively responds to Mn2+ but with amuch reduced affinity to Mg2+. However, it has also been shown in previous single molecule
studies that Mg2+ can promote manganese riboswitch folding with or without the cognate
ligand.30 As a parallel thrust, therefore, we have also explored Mg2+ and pressure-dependent
manganese riboswitch folding, in order to compare the effects of cognate ligand (Mn2+) vs.
divalent cation (Mg2+) under near physiological concentrations. As illustrated in the pressure
van’t Hoff plot in Figure 12.7, the presence of Mg2+ at constant Mn2+ also enhances theequilibrium stability for riboswitch folding, though requiring 1000-fold higher (i.e., mM vs M)concentrations. Interestingly, however, the slope of this van’t Hoff plot remains constant over an
additional 4000 M increase in Mg2+ concentration, consistent with changes in free volume
being insensitive to divalent Mg2+ (ΔV0  0). This contrasts with the unambiguously strong

341
effects of Mn2+ on pressure-dependent denaturation, confirming that riboswitch folding
contributions to V0  0 are clearly both site- and cation-dependent.

Figure 12.7 Pressure-dependent equilibrium constant (Kfold) data for Mn2+ independent-folding of
the riboswitch at [Mg2+] = 2mM (red) and 6 mM (blue).

Similarly, we can also deconstruct these effects by pressure-dependent investigation of
the folding/unfolding kinetics. As illustrated in Figure 12.8, Mg2+ induced folding of theriboswitch is clearly promoted at all pressures. It is interesting to note, however, that such aneffect occurs specifically by Mg2+ dependent increase in kfold, with kunfold remaining mostly
unchanged, a trend entirely consistent with Mg2+ effects found previously at ambient pressures.30,
34

Similar to the trends reported above for equilibrium stabilities (Kfold), a 4000 mM increase in

Mg2+ has no effect on slopes in Figure 12.8, indicating no significant Mg2+ effects on thetransition state activation volumes from either the folding or unfolding direction (ΔV‡fold andΔV‡unfold). Simply summarized, manganese riboswitch folding responds to much lower
concentrations of the cognate ligand Mn2+, with free volume changes (ΔV0 and ΔV‡fold)decreasing significantly with Mn2+ but insensitive to Mg2+. As a result, one concludes that Mn2+
effects on ΔV0 and ΔV‡fold result primarily from highly specific associations of the riboswitch

342
with the cognate ligand, as opposed to important but more generic divalent cation effects with
Mg2+.

Figure 12.8 Pressure-dependent analysis of the kinetic rate constants for Mn2+ independentfolding of the riboswitch: (A) kfold and (B) kunfold at [Mg2+] = 2 mM (red) and 6 mM (blue).

12.5

Discussion

12.5.1 Mn2+ association reduces the effective volume of the riboswitch system
The impact of Mn2+ on reducing both ΔV0 and ΔV‡fold has been demonstrated in Sec.
12.4B and shown to be a result of specific cognate ligand effects in Sec. 12.4C. Moreover, theMn2+ effect on the free volume changes are most efficient at low concentration and graduallysaturate with increasing concentration (see Table 12.1). These features are reminiscent of non-343
cooperative binding of Mn2+ to the riboswitch, as characterized extensively in previous works.30,
34

Specifically, the riboswitch folding equilibrium constant as a function of Mn2+ is welldescribed by a Hill equation with apparent dissociation constant KD = 16(5) µM, and near unity
Hill coefficient of n = 1.0(3). This observation motivates an intriguing analysis by which we use
these Hill parameters to convert Mn2+ concentration to the fractional occupation (f = 0.0-1.0) of
the riboswitch by Mn2+, which in turn allows us to generate free volume changes as a function ofoccupation and as illustrated in Figure 12.9. Interestingly, while ΔV0 and ΔV‡fold exhibit apronounced linear decrease as a function of Mn2+ binding, ΔV‡unfold remains approximately
constant throughout the range of Mn2+ concentrations explored. Clearly, any Mn2+ dependence inthe overall free volume change (ΔV0) must be attributed to differential changes in volume
between the unfolded and transition state conformations (ΔV‡fold), with Mn2+ association
occurring predominantly prior to the transition state barrier.

Figure 12.9 Free volume changes (ΔV0 and ΔV‡fold/unfold) along the riboswitch folding coordinate,
but plotted as a function of fractional binding of Mn2+ (f = 0.0 to 1.0). The fraction of Mn2+-boundriboswitch is calculated from the Mn2+ concentrations, based on dissociation constant (KD = 16(5)µM) and Hill coefficient (n = 1.0(3)) obtained from previous analysis for Mn2+-promoted foldingof the manganese riboswitch. The open circles represent the predicted volume changes from linear
extrapolation to f =1.0.

344
Furthermore, the linear dependence of ΔV0 on ligand binding fraction f allows us toestimate ΔV0 = 69(2) mL/mole for folding of the fully Mn2+-bound riboswitch, by simple
extrapolation to f = 1.0. Since the free volume change ΔV0 for manganese riboswitch folding in
the absence of Mn2+ is known to be 110(4) mL/mol, we thus infer a large negative change in freevolume for Mn2+ binding to the riboswitch (ΔV0bind  -41(4) mL/mol), i.e., approximately 40%
and competitive with the overall ΔV0 for riboswitch folding. Thus, one must conclude that Mn2+
association has a considerable effect on the hydration structure of the binding site.38-40
Additionally, even though the manganese riboswitch is destabilized with increasing pressure(ΔV0 > 0), association of the cognate ligand/Mn2+ is favored by pressure increase (ΔV0bind < 0),which in turn can compete directly with pressure-dependent denaturation effects on overall RNA
folding. One possibility is that such a Mn2+ dependent reduction in free volume is due to ligand
filling in “voids” formed by the folded riboswitch,13 or ion recruitment of a more compact water
structure in replacement of the loosely packed water molecules inside the confined binding
pocket.41 Although more data will be needed to deconstruct pressure dependent ligand binding
from biomolecular folding behaviors, the favorable pressure response to ligand association may
prove to be a universal feature of riboswitches, as well as other ligand-responsive biomolecules.
This Mn2+ binding-induced reduction in volume (ΔV0bind < 0) is significant and may be essential
to maintain ligand affinity as well as biochemical function for a riboswitch under pressure.
By way of specific example, the thermophilic bacterium T. maritima is found in thevicinity of hydrothermal vents at the bottom of the ocean.42 To adapt to such a high pressure andtemperature environment, the aptamer domain of the T. maritima lysine riboswitch has evolved
to contain significantly more GC interactions (38 vs 26 total GC pairs) than its B. subtiliscounterpart43-44 operating in a more ambient pressure/temperature range.35 In clear contrast,

345
however, the sequences in the aptamer binding sites themselves remain highly conserved
between these two versions of the lysine riboswitch.45 It therefore makes sense that binding
between the lysine ligand and aptamer region might be enhanced (ΔV0bind < 0) rather thanweakened by pressure destabilization (ΔV0 > 0), which in turn would help maintain appropriate
riboswitch conformation and biochemical function under high pressure conditions.

Figure 12.10 Plot of differential free volume changes (V) along the riboswitch folding coordinate
for a variety of Mn2+ conditions, with “staircase-like” structures clearly indicating a monotonic
increase in volume at each folding stage. Especially noteworthy is the color-coded parsing of thesevolume changes with respect to Mn2+ binding fraction, which reveal that > 50% of this increase inriboswitch volume is achieved by the time the transition state is formed. Differential volumes arereferenced to the unfolded state U at each f.

12.5.2 Insight from free volume changes along the riboswitch folding coordinate
To summarize the volumetric changes associated with manganese riboswitch folding, wehave plotted in Figure 12.10 the differential free volumes (V) for each of the unfolded (U),transition (TS) and folded (F) states. Even more instructively, these V values are eachdisplayed for a series of three Mn2+ occupation numbers (f = 0, 0.5, 1.0), with values for the fully
ligand-bound riboswitch obtained from linear extrapolation (see Figure 12.9) to f = 1 and all free346
volumes referenced to zero for the unfolded (U) conformation. From Figure 12.10, free volume
changes for the manganese riboswitch increase monotonically with respect to the folding
coordinate, i.e., VU < VTS < VF). Specifically, such “staircase” structure confirms asequential increase in manganese riboswitch free volume as it folds. Furthermore, such structure
is clearly responsible for the simultaneous increase (and decrease) in kunfold (and kfold) as afunction of applied hydrostatic pressure, respectively, as reported in Sec. 12.4A
Of particular relevance, however, is the fact that the free volume increase upon folding(V0 > 0) diminishes significantly (V0bind < 0) as a function of additional Mn2+, which
necessarily implies that binding of Mn2+ to the aptamer domain decreases the overall riboswitch
system volume. As mentioned above, such effects suggest that the cognate ligand replaces a lesscompact water network in the binding site of the manganese riboswitch.41 More quantitatively,
the magnitudes of the Mn2+ dependent staircase “steps” in Figure 12.10 indicate that > 50% of
this “shrinkage” is already achieved by the transition state barrier, and thus dominated by regionsof folding coordinate space where the riboswitch is less structured. By way of confirmation,
crystallographic data for the Mn2+-bound riboswitch binding pocket reveal that the majority ofphosphate ions octahedrally coordinated with Mn2+ (including the Mn2+-selective nitrogen inA41) arise from nucleotides in the P3 bulge (Figure 12.1A),.33 From this perspective, it is not
surprising that Mn2+ would bind to P3 prior to subsequent folding of the riboswitch, for which
any loop-loop tertiary interactions between P1 and P3 stems are still largely unformed. Indeed,
previous single molecule kinetic studies at Mg2+  0 explicitly reveal the folding rate constant tovanish at Mn2+  0. Stated alternatively, this implies that Mn2+ promotes folding of themanganese riboswitch through an induced fit (IF) “bind-then-fold” mechanism,30 consistent withthe binding/folding pathway postulated above and observed in this work.46

347
As a more subtle observation, however, previous single molecule kinetic studies also
provided evidence for a Mg2+ promoted switch from an induced fit (IF) to a conformational
selection (CS) “fold-then-bind” riboswitch folding mechanism.30, 34 Specifically, addition of
Mg2+ at physiological levels (2 mM) allows Mn2+ to bind with a 7-fold higher affinity, which
was attributed to “preorganization” of the P3 bulge structure prior to tertiary folding of the P1,P3 domains, i.e., consistent with a conformational selection (CS) “fold-then-bind” pathway.
Interestingly, for such an alternative CS pathway, binding of the Mn2+ ligand might be expected
to occur in later stages of folding,31 which would seem to contradict the results in the paragraphabove. By way of resolution, however, we note that IF and CS folding pathways are no longer
mutually exclusive in the presence of Mg2+.47-48 Indeed, these kinetic studies could not rule out
parallel contributions from an IF “bind-then-fold” folding pathway,30 but simply revealed thatkinetics of riboswitch folding in the presence of Mg2+ to be insensitive to prebinding of Mn2+.
Specifically, the previous kinetic investigation of kunfold in the presence of Mg2+ revealed
riboswitch unfolding to occur from both Mn2+-bound (f = 1) and Mn2+-free (f = 0) folded
conformations, with the latter now completely consistent with a parallel CS mechanism.30, 49 By
way of confirmation, one would expect the Mn2+ binding step required for an IF folding
mechanism to primarily impact the free energy landscape region between the unfolded and thetransition states, as indeed evident in Figure 12.10. Simply summarized, pressure-dependent
characterization of free volume changes complements and extends the previous work byidentifying the presence of an additional IF bind-then-fold pathway for riboswitch folding in thepresence of Mg2+. In conjunction with demonstration in these studies of remarkable sensitivity tocation association and change in hydration,29, 36, 50-51 such high pressure characterization studies
at the single molecule level (and particularly pressure-dependent single molecule kinetics) looks

348
well poised to improve our understanding of complex folding mechanisms by providing new andcomplementary information via “reversible work” PV free energy surfaces.

12.6

Summary and conclusions
In this work, we have demonstrated the ability to couple single molecule FRET kinetic

measurements with tunable high-pressure capillary cell conditions to obtain detailed
characterization of free volumes for folding of the manganese riboswitch. Based on direct
measurement of the pressure-dependent folding/unfolding rate constants, the pressure-induced
denaturation of the riboswitch has been unambiguously shown to arise from a simultaneous
decrease (increase) in kfold (kunfold), respectively, as a function of increasing pressure and further
signalling a sequential, monotonic increase in free volume for the manganese riboswitch alongfolding coordinate (VU < VTS < VF). Moreover, a series of pressure-dependent studies indicatethat increase in the cognate ligand Mn2+ lowers this free volume change upon folding (i.e.
“shrinks” the riboswitch, Vbind < 0), particularly between unfolded and transition state
conformations. Such a negative change in free volume (Vbind < 0) necessarily implies pressurepromoted binding of the cognate ligand, which would compete with pressure-induced
destabilization of riboswitch folding (ΔV0 > 0) and in turn may help mitigate pressure induced
denaturation effects in the biology of deep sea microorganisms. The study provides a novel
reversible work “volumetric” characterization of the free energy folding landscape along
riboswitch folding coordinate, which highlights the significance of pre-transition state effects due
to Mn2+. Finally, these new volumetric data provide information complementary to our previous
kinetic analysis studies under ambient pressure conditions, indicating the parallel presence of349
both induced fit (“bind-then-fold”) and conformational selection (“fold-then-bind”) components
for folding of the manganese riboswitch.

12.7

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Mitra, L.; Rouget, J.-B.; Garcia-Moreno, B.; Royer, C. A.; Winter, R., Towards a
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Mozhaev, V. V.; Heremans, K.; Frank, J.; Masson, P.; Balny, C., High Pressure Effects
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Aristides Yayanos, A., Deep-Sea Piezophilic Bacteria. In Methods in Microbiology,
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Gross, M.; Jaenicke, R., Proteins under Pressure. Eur. J. Chem. 1994, 221 (2), 617-630.

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Li, L.; Kato, C.; Horikoshi, K., Bacterial Diversity in Deep-Sea Sediments from Different
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Jannasch, H. W.; Wirsen, C. O., Variability of Pressure Adaptation in Deep sea Bacteria.
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Najaf-Zadeh, R.; Wu, J. Q.; Macgregor, R. B., Effect of Cations on the Volume of theHelix-Coil Transition of Poly[d(A-T)]. Biochim. Biophys. Acta Gene Regul. 1995, 1262
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350
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Changes Characterized by High-Pressure, Pulsed Field Gradient Diffusion NMR
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Roche, J.; Caro, J. A.; Norberto, D. R.; Barthe, P.; Roumestand, C.; Schlessman, J. L.;
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Unfolding of Proteins. Proc. Natl. Acad. Sci. U.S.A. 2012, 109 (18), 6945-6950.

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and Protein Denaturation. Biophys. J. 2010, 98 (8), 1626-1631.

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Royer, C.; Winter, R., Protein Hydration and Volumetric Properties. Curr. Opin. Colloid
Interface Sci. 2011, 16 (6), 568-571.

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Nucci, N. V.; Fuglestad, B.; Athanasoula, E. A.; Wand, A. J., Role of Cavities andHydration in the Pressure Unfolding of T4 Lysozyme. Proc. Natl. Acad. Sci. U.S.A. 2014,
111 (38), 13846-13851.

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Kinetics. Proc. Natl. Acad. Sci. U.S.A. 1999, 96 (26), 14848-14853.

20.

Woenckhaus, J.; Köhling, R.; Winter, R.; Thiyagarajan, P.; Finet, S., High Pressure-Jump
Apparatus for Kinetic Studies of Protein Folding Reactions Using the Small-Angle
Synchrotron X-Ray Scattering Technique. Rev. Sci. Instrum. 2000, 71 (10), 3895-3899.

21.

Nguyen, L. M.; Roche, J., High-Pressure NMR Techniques for the Study of Protein
Dynamics, Folding and Aggregation. J. Magn. Reson. 2017, 277, 179-185.

22.

Mustoe, A. M.; Brooks, C. L.; Al-Hashimi, H. M., Hierarchy of RNA Functional
Dynamics. Annu. Rev. Biochem. 2014, 83 (1), 441-466.

23.

Al-Hashimi, H. M.; Walter, N. G., RNA Dynamics: it is About Time. Curr. Opin. Struct.
Biol. 2008, 18 (3), 321-329.

24.

Lai, D.; Proctor, J. R.; Meyer, I. M., On the Importance of Cotranscriptional RNA
Structure Formation. RNA 2013, 19 (11), 1461-1473.

25.

Schärfen, L.; Neugebauer, K. M., Transcription Regulation Through Nascent RNA
Folding. J. Mol. Biol. 2021, 433 (14), 166975.

351
26.

Schneider, S.; Paulsen, H.; Reiter, K. C.; Hinze, E.; Schiene-Fischer, C.; Hübner, C. G.,
Single Molecule FRET Investigation of Pressure-Driven Unfolding of Cold Shock
Protein A. J. Chem. Phys. 2018, 148 (12), 123336.

27.

Sung, H.-L.; Nesbitt, D. J., DNA Hairpin Hybridization under Extreme Pressures: A
Single-Molecule FRET Study. J. Phys. Chem. B 2020, 124 (1), 110-120.

28.

Hodak, J. H.; Fiore, J. L.; Nesbitt, D. J.; Downey, C. D.; Pardi, A., Docking Kinetics andEquilibrium of a GAAA Tetraloop-Receptor Motif Probed by Single-Molecule FRET.
Proc. Natl. Acad. Sci. U.S.A. 2005, 102 (30), 10505-10510.

29.

Sung, H.-L.; Nesbitt, D. J., Single-Molecule Kinetic Studies of DNA Hybridization under
Extreme Pressures. Phys. Chem. Chem. Phys. 2020, 22 (41), 23491-23501.

30.

Sung, H.-L.; Nesbitt, D. J., Single-Molecule FRET Kinetics of the Mn2+ Riboswitch:
Evidence for Allosteric Mg2+ Control of “Induced-Fit” vs “Conformational Selection”
Folding Pathways. J. Phys. Chem. B 2019, 123 (9), 2005-2015.

31.

Suddala, K. C.; Price, I. R.; Dandpat, S. S.; Janeček, M.; Kührová, P.; Šponer, J.; Banáš,P.; Ke, A.; Walter, N. G., Local-to-Global Signal Transduction at the Core of a Mn2+
Sensing Riboswitch. Nat. Commun. 2019, 10 (1), 4304.

32.

Dambach, M.; Sandoval, M.; Updegrove, Taylor B.; Anantharaman, V.; Aravind, L.;
Waters, Lauren S.; Storz, G., The Ubiquitous yybP-ykoY Riboswitch is a ManganeseResponsive Regulatory Element. Mol. Cell 2015, 57 (6), 1099-1109.

33.

Price, Ian R.; Gaballa, A.; Ding, F.; Helmann, John D.; Ke, A., Mn2+-Sensing
Mechanisms of yybP-ykoY Orphan Riboswitches. Mol. Cell 2015, 57 (6), 1110-1123.

34.

Sung, H.-L.; Nesbitt, D. J., Novel Heat-Promoted Folding Dynamics of the yybP-ykoY
Manganese Riboswitch: Kinetic and Thermodynamic Studies at the Single-Molecule
Level. J. Phys. Chem. B 2019, 123 (26), 5412-5422.

35.

Aitken, C. E.; Marshall, R. A.; Puglisi, J. D., An Oxygen Scavenging System for
Improvement of Dye Stability in Single-Molecule Fluorescence Experiments. Biophys. J.
2008, 94 (5), 1826-1835.

36.

Sung, H.-L.; Nesbitt, D. J., High Pressure Single-Molecule FRET Studies of the Lysine
Riboswitch: Cationic and Osmolytic Effects on Pressure Induced Denaturation. Phys.
Chem. Chem. Phys. 2020, 22 (28), 15853-15866.

37.

Sung, H.-L.; Nesbitt, D. J., Sequential Folding of the Nickel/Cobalt Riboswitch Is
Facilitated by a Conformational Intermediate: Insights from Single-Molecule Kinetics
and Thermodynamics. J. Phys. Chem. B 2020, 124 (34), 7348-7360.

38.

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Biophys. J. 2019, 116 (2), 184-195.

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Ma, C. Y.; Pezzotti, S.; Schwaab, G.; Gebala, M.; Herschlag, D.; Havenith, M., Cation
Enrichment in the Ion Atmosphere is Promoted by Local Hydration of DNA. Phys.
Chem. Chem. Phys. 2021, 23 (40), 23203-23213.

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Riboswitch Regulatory mRNA Element. J. Biol. Chem. 2008, 283 (33), 22347-22351.

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the Lysine Aptamer Domain are Important for the Riboswitch Gene Regulation Control.
RNA 2007, 13 (8), 1256-1267.

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Serganov, A.; Patel, D. J., Amino Acid Recognition and Gene Regulation by
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Vogt, A. D.; Di Cera, E., Conformational Selection or Induced Fit? A Critical Appraisalof the Kinetic Mechanism. Biochemistry 2012, 51 (30), 5894-5902.

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Pavlović, R. Z.; Lalisse, R. F.; Hansen, A. L.; Waudby, C. A.; Lei, Z.; Güney, M.; Wang,X.; Hadad, C. M.; Badjić, J. D., From Selection to Instruction and Back: Competing
Conformational Selection and Induced Fit Pathways in Abiotic Hosts. Angew. Chem.
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Hammes, G. G.; Chang, Y.-C.; Oas, T. G., Conformational Selection or Induced Fit: A
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Suddala, K. C.; Wang, J.; Hou, Q.; Walter, N. G., Mg2+ Shifts Ligand-Mediated Foldingof a Riboswitch from Induced-Fit to Conformational Selection. J. Am. Chem. Soc. 2015,
137 (44), 14075-14083.

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Fan, H. Y.; Shek, Y. L.; Amiri, A.; Dubins, D. N.; Heerklotz, H.; Macgregor, R. B.;
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Patra, S.; Anders, C.; Erwin, N.; Winter, R., Osmolyte Effects on the Conformational
Dynamics of a DNA Hairpin at Ambient and Extreme Environmental Conditions. Angew.
Chem. 2017, 56 (18), 5045-5049.

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Chapter 13
Postmortem and Future Directions

13.1

Introduction
Despite extensive research and careful experiment design for each project, some may still

fail and thus never make it to the literature. This chapter documents those unsuccessful attempts
which I think were on the right track but need some modification.

Figure 13.1 DFHBI fluorescence enhancement. (A) Cartoon representation of DFHBI binding to
the Spinach2 RNA. (B) Chemical structure of DFHBI.
13.2

Label-free single molecule biosensor for TNT detection
Spinach2 is a synthetic RNA aptamer that selectively binds to DFHBI (3,5-difluoro-4-hydroxybenzylidene imidazolidinone), an analog of the GFP (green fluorescent protein)
fluorophore (Figure 13.1A).1 The benzene ring in the DFHBI can freely rotate around the single
bond. If the rotation is restricted (e.g., by aptamer binding), and the molecule is fixed in planar
conformation, the DFHBI fluorescence can be greatly enhanced (Figure 13.1B).2 As a result, theSpinach2-bound DFHBI is nearly 3 orders of magnitudes brighter than the free DFHBI.
In a collaboration with Dr. Chavez-Benavides from the Air Force Research Laboratory,
we received a TNT aptamer sequence obtained by SELEX (systematic evolution of ligands by354
exponential enrichment),3 an in vitro selection method. The structure of the TNT aptamer is a
short 48-nt stem-loop with a major internal loop and several other mismatched bases (Figure 2).
The simplicity of the aptamer structure in fact makes it difficult to generate a FRET construct tomonitor the TNT binding. We thus came up with an alternative method to generate afluorescence probe of TNT by coupling the TNT aptamer with the Spinach2 sequence (Figure 2).
The TNT binding is expected to induce conformational change in the aptamer, and thereby
stabilize the Spinach2 structure to increase DFHBI binding and thus the fluorescence.4 The
advantage is that such a Spinach2-based fluorescence probe requires no chemical modification of
the nucleotide bases and that the Spinach2 sequence can be directly integrated with the TNT
aptamer simply through in vitro transcription. Furthermore, with the common tethering strategy
described in Chapter 2, the construct can be annealed with a biotinylated flagpole strand toachieved surface immobilization for single molecule fluorescence study.

Figure 13.2 Schematic of Spinach2-TNT aptamer construct design and the resulting fluorescenceenhancement by TNT/DFHBI binding.
We have synthesized the Spinach2 and Spinach2-TNT aptamers with 1 to 3 base pairs as
spacer between the two RNA structures (Figure 2). Indeed, DFHBI titration reveals that

355
Spinach2 binds to DFHBI at the micromolar affinity level with enhanced fluorescence (Figure
13.3A). Unfortunately, however, the Spinach2-TNT aptamers never showed any significant
enhanced fluorescent activity of DFHBI over a wide range of relevant DFHBI/TNT
concentrations (Figure 13.3B). Our current thoughts are that, although the calculations conductedby the Chavez-Benavides group suggests TNT mainly interacts with the large internal loop in theaptamer, the rest of the aptamer stem may also participate in TNT binding. As the result, any
replacement of the Spinach2 sequence may interrupt the TNT aptamer structure and reduce the
TNT affinity, which is already relatively modest on the scale of riboswitches (low micromolar
levels).

Figure 13.3 Spinach2-DFHBI fluorescence measurements. (A) DFHBI titration of Sinach2 RNA.
Data are fit to the Hill equation and KD of DFHBI is determined to be 1.3(2) µM. (B) TNT titrationof Spinach2-TNT construct with saturated [DFHBI] = 20 µM. Note that despite the fluorescenceincreases at [TNT] > 10 µM, the count rate is way below the Spinach2 enhancement (105 vs 107
count per second) and the estimated KD of TNT for the TNT aptamer is at low micromolar levels.

The Spinach2-TNT probe may fail partly due to lack of structural information of the TNT
aptamer. However, the similar probe design can still be applied to other RNA riboswitches andaptamers with more detailed structural characterization (e.g., crystal data and SHAPE, selective
2'-hydroxyl acylation analyzed by primer extension). The aptamer-based sensor has great

356
potential in small molecule detection. Moreover, the rich kinetic information we could obtainfrom single molecule fluorescence studies may both motivate and facilitate future sensor design.

Figure 13.4 Secondary folding of the guanidine-II riboswitch in the translation-off state. The
sequence color-coded in blue represents the Shine–Dalgarno (SD) sequence, a ribosome binding
site.
13.3

Mimicking co-transcriptional folding by the truncated guanidine-II riboswitch
The 2o structure prediction of the guanidine-II (type II guanidine riboswitch) riboswitch

in its off state is illustrated in Figure 13.4,5 where the Shine–Dalgarno (SD) sequence (in blue)
forms double helix to prevent translation initiation by interrupting binding to the ribosome. In thepresence of guanidine (or guanidinium to properly address cationic effects), the two terminal

Figure 13.5 Illustration of the single molecule FRET construct design of the guanidine-IIriboswitch.

357
loops may form a complex with 2 guanidine molecules binding in a head to head fashion and inturn trigger the double helix dissociation to activate translation (Figure 13.5).
We first generated a single molecule FRET construct to monitor the association anddissociation of the SD double helix (Figure 13.5). In the translation-off state, the terminal Cy3
and Cy5 are close in distance, resulting in a high EFRET state. When the double helix is
dissociated by the guanidine-induced kissing loop formation, the Cy3 and Cy5 are brought
further apart. According to crystal data for the truncated kissing loop,5 the estimated > 50 Å
separation should lead to a low EFRET value (< 0.5). Unfortunately, despite the single molecule
diffusing data showing two distinct EFRET populations, the ratio between them proved to beinsensitive to guanidine concentrations (Figure 13.6).

Figure 13.6 Single molecule FRET experiments of the guanidine-II riboswitch constructs. (A)illustration of the freely-diffusing experiment and data analysis. (B) EFRET distribution of the full
guanidine-II riboswitch at increasing guanidine concentrations. (C) EFRET distribution of thetruncated guanidine-II riboswitch (-2 base pairs in the SD double helix extension) at increasing
guanidine concentrations.

358
Since the predominantly high EFRET state suggests the double helix is too stable todissociate (Figure 13.6B), we suspect the guanidine promoted kissing loop may form before theSD strand is fully extended, e.g., folding and ligand sensing during transcription. With the simple
flagpole labeling strategy, we are able to synthesize a series of guanidine riboswitches with an“adjustable” 3’ end to gradually reduce double helix interaction (-2 and -4 base pairs in the SD
double helix extension). In the sample data (Figure 13.6C), the truncated riboswitch seems to
misfold at low guanidine concentration with more prominent low EFRET population yet lessdistinctive peak structures. As guanidine concentration increases, the EFRET population becomes
nearly identical to the full riboswitch (13.6B and C). We suspect that the millimolar level ofguanidine may act more like a monovalent cation in stabilizing the shortened double helix.
Although it is unclear why guanidine does not promote double strand dissociation, further studies
on this series of truncated RNA constructs may provide a simple single molecule method toprobe more deeply into the role of RNA folding during transcription.6

13.4

Single molecule kinetics of surface immobilized brome mosaic virus RNA
The brome mosaic virus (BMV) single molecule FRET construct was designed by aprevious postdoctoral researcher Dr. Mario Vieweger.7 He extensively characterized the salt
dependent conformations of the BMV RNA construct and incorporated the single molecule
FRET results with SHAPE studies to obtain even more detailed structural information.8 In his
studies, the freely diffusing single molecule FRET measurements revealed interesting 3-statefolding behavior for the RNA virus.7 However, these observations were limited to conditions
where only equilibrium populations could be detected. To extend these efforts into the domain of

359
single molecule kinetics, therefore, I tried to re-synthesize the BMV single molecule constructwith biotin labeling to achieve surface tethering capabilities.
During the construct synthesis, the 3’ end labeling of Cy3 is particularly challenging. I
wasn’t able to achieve a reasonable labeling rate with the method of 3’ oxidation, followed by
the hydrazide-aldehyde reaction, as suggested in Mario’s work.7 After many unsuccessfulattempts, I decided to use an alternative method to label the construct. Specifically, the BMV
RNA is end-labeled with Cy3 through the enzymatic ligation with T4 RNA ligase and Cy3
modified cytidine-3',5'-bis-p (pCp-Cy3, Figure 13.7A). Such a method results in > 85% labeledRNA, as verified by HPLC analysis. Unfortunately, the resulting FRET values of the BMV RNA
proved to be significantly affected. Specifically, the labeling scheme is equivalent to extension
by one additional cytidine nucleotide, for which we lost sufficient contrast to resolve the threedifferent FRET values and conformations (Figure 13.7B and C).

Figure 13.7 Sample fluorescence traces of the BMV virus RNA construct and the resulting EFRET
trajectories. (A) Chemical structure of pCp-Cy3. (B) Sample fluorescence data at [Mg2+] = 0 mM,
and (C) [Mg2+] = 10 mM. The intermediate EFRET state at high [Mg2+] = 10 mM is indistinguishable
with the low EFRET state (e.g. the low EFRET state at [Mg2+] = 0 mM).

360
Although the original construct with the new labeling method didn’t work out, we cancertainly try to improve the FRET contrast by adjusting the length of the 3’ extension in the
BMV RNA. Moreover, I have found the ligation method consistently provides more reliable
labeling with > 85% efficiency. Hence, this would appear to be an interesting and quite feasible
direction for further progress.

13.5

Osmolytes and crowding effects under extreme pressures
The Nesbitt group has been long interested in the osmolyte effects on nucleic acidconformations. Previous graduate student Dr. Erik Holmstrom has characterized the kinetics andthermodynamics of nucleic folding at a series of TMAO (Trimethylamine N-oxide) and urea
concentrations.9 Interestingly, the content of TMAO (urea) in deep sea fish is found to increase(decrease) as a function of depth.10 The anti-correlation between the two osmolytes is speculated
to be part of the pressure adaption strategy for deep see marine life, since TMAO or urea isknown to increase or decrease biomolecular folding, respectively.11 This would appear to be an
ideal system for studying the effects of these osmolytes on pressure dependent nucleic acidfolding with our high pressure kinetic methods.
Finally, it would be a natural extension to study the effects of both crowding andosmolytes under extreme pressures, since it seems plausible that stabilization of nucleic acids by
osmolytes may compete efficiently with pressure denaturation.12 In particular, in order toconfirm or refute the entropic nature of such crowding effects at elevated pressures, we need thecapability for temperature dependent studies. Toward that end, we are therefore working on
incorporation of reliable sample heating methods to augment our high pressure single molecule361
measurements. Studies of the two-dimensional folding reaction coordinate with both temperatureand pressure as external variables would provide even richer thermodynamic information on thefree energy landscape for nucleic acid folding.

13.6

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Chapter 11

Single-Molecule Kinetic Studies of DNA Hybridization Under Extreme
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Arns, L.; Knop, J.-M.; Patra, S.; Anders, C.; Winter, R., Single-Molecule Insights into theTemperature and Pressure Dependent Conformational Dynamics of Nucleic Acids in the
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Tan, C.-Y.; Xu, C.-H.; Wong, J.; Shen, J.-R.; Sakuma, S.; Yamamoto, Y.; Lange, R.;
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Dupuis, Nicholas F.; Holmstrom, Erik D.; Nesbitt, David J., Single-Molecule Kinetics
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Das, R.; Mills, T. T.; Kwok, L. W.; Maskel, G. S.; Millett, I. S.; Doniach, S.; Finkelstein,
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Chapter 12
1.

Ligand-Dependent Volumetric Characterization of Manganese Riboswitch
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Patra, S.; Anders, C.; Schummel, P. H.; Winter, R., Antagonistic Effects of Natural
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Ramanujam, V.; Alderson, T. R.; Pritišanac, I.; Ying, J.; Bax, A., Protein Structural
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Woenckhaus, J.; Köhling, R.; Winter, R.; Thiyagarajan, P.; Finet, S., High Pressure-Jump
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Sung, H.-L.; Nesbitt, D. J., DNA Hairpin Hybridization under Extreme Pressures: A
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28.

Hodak, J. H.; Fiore, J. L.; Nesbitt, D. J.; Downey, C. D.; Pardi, A., Docking Kinetics andEquilibrium of a GAAA Tetraloop-Receptor Motif Probed by Single-Molecule FRET.
Proc. Natl. Acad. Sci. U.S.A. 2005, 102 (30), 10505-10510.

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Sung, H.-L.; Nesbitt, D. J., Single-Molecule Kinetic Studies of DNA Hybridization under
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Sung, H.-L.; Nesbitt, D. J., Single-Molecule FRET Kinetics of the Mn2+ Riboswitch:
Evidence for Allosteric Mg2+ Control of “Induced-Fit” vs “Conformational Selection”
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Suddala, K. C.; Price, I. R.; Dandpat, S. S.; Janeček, M.; Kührová, P.; Šponer, J.; Banáš,P.; Ke, A.; Walter, N. G., Local-to-Global Signal Transduction at the Core of a Mn2+
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Dambach, M.; Sandoval, M.; Updegrove, Taylor B.; Anantharaman, V.; Aravind, L.;
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Sung, H.-L.; Nesbitt, D. J., Novel Heat-Promoted Folding Dynamics of the yybP-ykoY
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Sung, H.-L.; Nesbitt, D. J., High Pressure Single-Molecule FRET Studies of the Lysine
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37.

Sung, H.-L.; Nesbitt, D. J., Sequential Folding of the Nickel/Cobalt Riboswitch Is
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