Improved Energy Landscape Reconstruction and Imagingof Nucleic and Amino Acids via Atomic Force Microscopy
byPatrick R. Heenan
B.A., University of North Carolina, 2013 (Computer Science)
B.S., University of North Carolina, 2013 (Physics)
M.S., University of Colorado, 2017 (Physics)
M.S., University of Colorado, 2017 (Computer Science)

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
Department of Physics
2019

ProQuest Number: 27548208

All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent on the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,a note will indicate the deletion.

ProQuest 27548208
Published by ProQuest LLC ( 2019 ). Copyright of the Dissertation is held by the Author.
All Rights Reserved.
This work is protected against unauthorized copying under Title 17, United States CodeMicroform Edition © ProQuest LLC.
ProQuest LLC
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, MI 48106 - 1346

This thesis entitled:
Improved Energy Landscape Reconstruction and Imaging of Nucleic and Amino Acids via Atomic
Force Microscopy
written by Patrick R. Heenan
has been approved for the Department of Physics

Prof. Thomas Perkins

Prof. Thomas Cech

Date

The final copy of this thesis has been examined by the signatories, and we find that both thecontent and the form meet acceptable presentation standards of scholarly work in the above
mentioned discipline.

iii
Heenan, Patrick R. (Ph.D., Physics)
Improved Energy Landscape Reconstruction and Imaging of Nucleic and Amino Acids via Atomic
Force Microscopy
Thesis directed by Prof. Thomas Perkins

Atomic force microscopy (AFM) is a technique widely used to image or apply forces to surfacebound biomolecules in liquid. Traditional methods for imaging DNA and protein-DNA complexes inliquid have drawbacks: DNA conformations with an anomalous persistence length, low SNR, and/orionic conditions detrimental to preserving native protein-DNA interactions. Here, we introduce aminimally perturbative method for imaging surface-bound DNA that improves data quality andquantity. In comparison to prior protocols, an eight-fold larger fraction (90%) of 680-nm-long
DNA molecules were quantifiable, and the technique is viable for imaging DNA of many lengths
and proteins in a variety of physiological buffers. In addition to improving AFM imaging, thiswork also advances the reliability and accuracy of single-molecule force spectroscopy (SMFS) AFM
experiments. In particular, recent improvements in time resolution and data throughput of SMFS
experiments highlight the need for high-precision, automated characterization of force-induced intraand inter-molecular bond ruptures. We describe a new algorithm to automatically identify thelocations of molecular ruptures in SMFS data. In order to improve molecular energy landscapecharacterization, we also applied the inverse Weierstrass transform to SMFS data and removed
the energy associated with the AFM force probe, yielding the molecular free-energy landscape.
Combined, these improvements in AFM methodology – minimally perturbative imaging of DNAprotein complexes, automated detection of molecular rupture events, and energy deconvolution offorce probes – advance the quality and reproducibility of biophysical insights gained from AFMbased experiments.

Dedication

To Mom, my first and most important teacher.

v

Acknowledgements

I owe a vast debt of gratitude to my adviser, Tom Perkins. His ceaseless patience, constantempathy and advice when things weren’t working, infectious excitement when things were working,and dedication to the craft and communication of science dramatically improved my capacity for
research and research presentation.
In addition to Tom, other members of the Perkins lab provided camaraderie and specificcontributions. Lyle Uyetake taught me many experimental, bulk molecular biology techniques.
Matt Siewny gave me my first imaging and force spectroscopy tutorials. William ‘John’ Van Patten
and Rob Walder taught me surface- and cantilever- functionalization techniques. Devin Edwards
was a ceaseless source of advice, wetlab help, and debugging suggestions. Stephen Okoneiwski andDavid Jacobson provided constructive criticisms and sympathetic ears.
The professional staff of JILA deserve special recognition for their roles. The machine shop
and clean room provided timely and robust service. The JILA shipping and purchasing departments
ensured timely delivery and receipt of packages, and the custodial staff kept JILA clean and assisted
in a variety of unexpected emergencies.
I also wish to acknowledge my friends and family for their less technical but no less important
assistance. My partner Chase was an indispensable source of encouragement. In addition, mysiblings, Erin and Palmer, and mother, Sarah, were ceaselessly supportive.

Contents

Chapter
1 Introduction

1

1.1

Atomic force microscopy as a platform for biophysical measurements . . . . . . . . .

1

1.2

Liquid imaging of biomolecules via atomic force microscopy . . . . . . . . . . . . . .

4

1.3

Single molecule force spectroscopy and energy landscape reconstruction . . . . . . . 10
1.3.1

Equilibrium techniques for energy landscape analysis . . . . . . . . . . . . . . 12

1.3.2

Constant velocity techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.3.3

Benefits and trade-offs of techniques . . . . . . . . . . . . . . . . . . . . . . . 19

2 Experimental imaging and force spectroscopy protocols
2.1

2.2

22

Imaging via atomic force microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1.1

Sample handling and wetlab techniques . . . . . . . . . . . . . . . . . . . . . 23

2.1.2

Sample deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.1.3

Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.1.4

Data analysis and processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Force spectroscopy and landscape reconstruction via AFM . . . . . . . . . . . . . . . 40
2.2.1

Sample storage and handling . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.2.2

Sample deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.2.3

Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.2.4

Data analysis and processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

vii
3 Imaging DNA Equilibrated onto Mica in Liquid using Biochemically Relevant Deposition
Conditions

49

3.1

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.3

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.1

Rapid and biochemically relevant DNA deposition protocol . . . . . . . . . . 55

3.3.2

Improved protocol relies upon a series of refinements . . . . . . . . . . . . . . 55

3.3.3

High yield of equilibrated DNA on mica in liquid . . . . . . . . . . . . . . . . 59

3.3.4

High-precision measurements of DNA conformation

3.3.5

Depositing and imaging DNA under biochemically relevant ionic conditions . 62

3.3.6

Imaging protein-DNA complexes in liquid . . . . . . . . . . . . . . . . . . . . 64

. . . . . . . . . . . . . . 60

3.4

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.5

Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.5.1

DNA samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.5.2

DNA deposition protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.5.3

Depositing protein-DNA complexes . . . . . . . . . . . . . . . . . . . . . . . . 69

3.5.4

AFM imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.5.5

Surface roughness of bare and treated mica . . . . . . . . . . . . . . . . . . . 70

3.5.6

Imaging bacteriorhodopsin. . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

3.5.7

Image analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

3.5.8

Automated annotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.6

Author contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.7

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.8

Supporting Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.8.1

Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4 FEATHER: Automated Analysis of Force Spectroscopy Unbinding/Unfolding Data via aviii
Bayesian Algorithm

90

4.1

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3

Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.4

Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

91

4.4.1

Description of FEATHER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.4.2

Evaluating FEATHER’s performance . . . . . . . . . . . . . . . . . . . . . . . 97

4.5

Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.6Open data statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.7

Author contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.8

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.9

Supporting Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.9.1

Algorithm Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.9.2

Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.9.3

Data Acquisition and Annotation . . . . . . . . . . . . . . . . . . . . . . . . . 111

4.9.4

Simulation

4.9.5

Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

4.9.6

Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

5 Improved free-energy landscape reconstruction of bacteriorhodopsin highlights local variations in unfolding energy

127

5.1

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

5.2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.3

Free-energy landscape reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

5.4

Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5.5

Conclusion

5.6

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

ix
5.7

Supporting Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.7.1

Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

5.7.2

Methodology for comparison with coarse-grained MD simulation . . . . . . . 145

6 Conclusions and future directions

147

Bibliography149

TablesTable
1.1

Comparison of energy landscape techniques.

. . . . . . . . . . . . . . . . . . . . . .

21

2.1

Imaging cantilever comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.2

Imaging suggestions for common systems of interest. . . . . . . . . . . . . . . . . . . 35

2.3

Imaging troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.1

Performance metrics for each algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.2

Statistical information on the polyprotein data set.

4.3

Primers sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

4.4

Statistical information on the 650-nm DNA data set. . . . . . . . . . . . . . . . . . . 123

4.5

Pseudocode for FEATHER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

4.6

Variable and performance metric definitions. . . . . . . . . . . . . . . . . . . . . . . . 125

4.7

Table Title . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

4.8

Parameters for simulated force-extension curves. . . . . . . . . . . . . . . . . . . . . 125

4.9

Definition and values of physical parameters used in Equation 4.3. . . . . . . . . . . 126

5.1

Amino acid transfer energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146. . . . . . . . . . . . . . . . . . 122

Figures

Figure1.1

Illustration of AFM imaging operation.

1.2

Atomic resolution AFM images of the mica lattice are consistent with its expected
crystal structure.

. . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . .

3

5

1.3

Surface roughness of glass depends on treatment.

7

1.4

Quantification of polymeric and geometric properties using AFM imaging.

. . . . .

8

1.5

Illustrative definition of energy landscape parameters. . . . . . . . . . . . . . . . . .

11

1.6

Demonstration of deconvolution of a force probe’s point spread function.

1.7

Model-based reconstruction of equilibrium single molecule force spectroscopy data.

1.8

Model-based reconstruction of force ramp (constant velocity) single molecule force. . . . . . 1315spectroscopy data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.9

Reconstruction of force ramp experiment using Jarzynski’s equality. . . . . . . . . . 20

2.1

Deposition of DNA onto NiCl2 -treated mica in a dithiothreitol (DTT)-containing
buffer.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2

Nanoscopic precipitates adhere to mica surfaces after many hours of imaging.

2.3

Flowchart for AFM imaging operation. . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.4

Imaging drive frequency should be chosen near the first thermal resonance of thecantilever.

. . . 29

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.5

Background correction of AFM images. . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.6

Verifying surface functionalization via fluorescence imaging.

. . . . . . . . . . . . . 42

xii
2.7

Flowchart for AFM SMFS operation.

. . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.8

Processing AFM force-extension curves (FECs).

3.1

Configuration of DNA on mica depends on the details of the deposition process.

3.2

Rapid three-step protocol for preparing DNA for imaging on mica in liquid. . . . . . 56

3.3

Improved DNA deposition required a sequence of refinements. . . . . . . . . . . . . . 58

3.4

Images of individual DNA molecules highlight the resulting high signal-to-noise ratio. 61

3.5

Equilibrated DNA deposited across a broad range of monovalent ionic conditions.

3.6

High signal-to-noise ratio images of protein-nucleic acid complexes deposited at bio-

. . . . . . . . . . . . . . . . . . . . 46
. . 52. 63

chemically relevant conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.7

Determining persistence length from AFM images. . . . . . . . . . . . . . . . . . . . 74

3.8

Drying method after NiCl2 treatment influences data quality. . . . . . . . . . . . . . 75

3.9Higher concentration of NiCl2 during pre-treatment improves subsequent imaging. . 76

3.10 Proof-of-principle image resolves a void in the 2D-trimer lattice of bacteriorhodopsin. 77
3.11 Depositing and imaging DNA at biologically relevant ionic conditions. . . . . . . . . 78
3.12 Partial dewetting of the sample decreases data quality. . . . . . . . . . . . . . . . . . 79
3.13 Concurrence between the number of experimentally observed looped configurations
and a simulation of a 2D WLC equilibrated on a surface.

. . . . . . . . . . . . . . . 80

3.14 End-to-end distance of DNA is consistent with 2D WLC equilibrated on a surface. .

81

3.15 Contour and persistence lengths obtained from human and computationally annotated data are consistent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.16 Measured height of the DNA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.17 Characterizing the surface roughness of mica in liquid for different mica treatment
protocols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.18 High-resolution imaging reveals the right-handed helical structure of DNA. . . . . . 85
3.19 Measured contour length agrees within 1% of the expected contour length for B-form
DNA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

xiii
3.20 Images of short (300-bp) DNA deposited using our protocol. . . . . . . . . . . . . . . 86
3.21 Dependence of persistence length on ionic strength is consistent with 2D equilibrated
DNA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.22 Efficient deposition and imaging is possible with little or no divalent cations in solution. 87
3.23 Replacing NiCl2 for MgCl2 during deposition leads to kinetically trapped configurations even when using our final protocol that includes extensive but gentle rinsing. . 88
3.24 Age of NiCl2 powder appeared to influence data quality. . . . . . . . . . . . . . . . . 89
4.1

An overview of force spectroscopy analysis. . . . . . . . . . . . . . . . . . . . . . . . 93

4.2

FEATHER’s analysis scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.3

Evaluating FEATHER’s performance. . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.4

Runtime of each algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

4.5

Representative examples of 650-nm DNA force-extension curves with one event (A–C), two events (D), and three events (E). . . . . . . . . . . . . . . . . . . . . . . . . 115

4.6

Effect of smoothing on BCC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

4.7

Overview of the FEATHER algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.8

The sensitivity of the Bhattacharya coefficient’s complement (BCC) . . . . . . . . . 117

4.9

Additional metrics for comparing algorithm performance between FEATHER, OpenFovea, and Scientific Python. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

4.10 FEATHER outperforms the reference algorithms in analyzing a 650-nm DNA dataset
acquired at a high-retraction velocity (1,000 nm/s).

. . . . . . . . . . . . . . . . . . 119

4.11 FEATHER generalizes well to force spectroscopy of 650-nm DNA data set containing
multiple attachments over three different retraction velocities (100, 500, and 1,000nm/s).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

4.12 FEATHER generalizes well to a wide range of simulated data.

. . . . . . . . . . . . 120

4.13 Typical failure mode for FEATHER. . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.1

High-resolution studies of bacteriorhodopsin (BR). . . . . . . . . . . . . . . . . . . 129

xiv
5.2

Process for free-energy landscape reconstruction of BR using an inverse Weierstrasstransform (IWT). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

5.3

Local unfolding free energies as a function of extension vary broadly between andwithin BR’s major structural elements (the ED, CB and A helices, respectively). . . 139

5.4

Work-weighted statistics are necessary for accurate landscape reconstruction. . . . . 142

5.5

Filtering choice balances fitting and derivative error with spatial resolution. . . . . . 143

5.6

The mean landscape curvature (or stiffness) plotted versus extension relative to thestart of the ED helix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

Chapter 1
Introduction

1.1

Atomic force microscopy as a platform for biophysical measurements

The complexity of biological systems necessitates simplification in order to develop scientificinsight. Since biological processes often bridge multiple scales – from atoms and single molecules tosingle cells and beyond – the combinatorial complexity of biological interaction confounds simple
explanation. Biophysics, or the physics of living systems, leverages the power of physics-basedmodels to develop useful simplifications of complex biological systems. Biophysical approximations
provide insight but require trade-offs between model accuracy and generalization. In particular,
physics-based models take a reductionist approach, ignoring difficult-to-model behavior and providing insight only for a particular subset of problems. In single molecule biophysics, the physicalproperties of biological molecules are measured on a per-molecule basis. Due to experimental constraints, single molecule studies are often limited to simpler systems than studies which investigate
ensembles of molecules or living cells. In other words, in single-molecule biophysics, the trade-off
between reducing complexity and increasing model applicability often results in precisely studying
a molecule or set of molecules, but measuring the system in relative isolation, compared to a more
complex, native environment.
Despite the simplifications necessitated by single-molecule methods, well-established techniques have yielded decades of impactful research. Fluorescence microscopy excites fluorophore-2labeled molecules, measures emitted light by the fluorophore, and tracks the motion of labeled
single molecules[1, 2]. A more complicated technique called fluorescence resonance energy transfer(FRET) microscopy leverages multiple different fluorophores and enables the measurement of interor intra-molecular distances [3, 4]. In contrast to passive observation of emitted fluorescent light,
single molecule force spectroscopy (SMFS) measures the molecular response to applied force via
molecular tethering to a force probe [5–7]. Combinations of SMFS and light microscopy techniques
provide additional measurement power at the cost of added experimental complexity. Ultimately,some experimental techniques are more appropriate for certain systems due to trade-offs in sample
preparation (e.g. necessity for labels) or measurement constraints (e.g. instrumental time response)[5].
Atomic force microscopy (AFM, [8]) is a technique widely used to apply forces or image
surface-bound biomolecules. AFM-based imaging characterizes the properties of DNA and diverse
proteins bound to DNA, including RNA polymerase, restriction enzymes, and nucleosomes [9–24].
In addition to imaging, AFM-based single molecule force spectroscopy (AFM-SMFS) has emerged
as an important tool in determining the energetics underlying the folding and unfolding of individual
proteins [25–28], protein-ligand bond strength [29, 30], and other mechanically robust biologicalsystems [31–35]. This thesis leverages both AFM-SMFS and AFM-based imaging and is motivatedby a desire to improve the insights gained from applying energy landscape reconstruction techniques
to SMFS data (see Chapters 4 and 5) or physical models to topographs obtained by AFM imaging(see Chapter 3).
A variety of techniques reconstruct energy landscapes or estimate energy landscape parameters by leveraging AFM-SMFS. In Section 1.3, several energy landscape reconstruction techniques
are reviewed, and their practical use is demonstrated using simulated data. The equilibrium techniques reviewed are the inverse Boltzmann technique [36] and the so-called ‘rate-map’ (unfolding
rate versus rupture force) approach [37]. Non-equilibrium techniques for energy landscape reconstruction are demonstrated by the Jarzynski equality [38] and the rate map transformation [37].

3Figure 1.1: Illustration of AFM imaging operation.
(A) A cartoon of a cantileverpoised above a surface, where the surface is color-coded according to its height above an arbitrary
zero point. A laser (green) reflects off of the cantilever onto a quadrant photodiode. Diagram is
simplified and not to scale. (B) As the cantilever moves across the surface, the relative change
in cantilever angle is recorded over time as height. (C) Controlling the x and y position of thecantilever (blue line) assigns the height at each particular time (B) to a height (color-coded as inA) at a particular (x,y) position.

B
Height

A

C

Time

4
The rate map technique relies on the correct determination of event locations, motivating theautomated event detection algorithm of Chapter 4. In addition, the energy associated with themeasurement probe convolves with the biomolecular energy of interest and leads to a corrupted
energy landscape estimation. Chapter 5 demonstrates the first AFM-based validation of the inverse
Weierstrass probe deconvolution algorithm [39]. The goal of automated event detection or probe
deconvolution in AFM-SMFS are identical: to obtain biological insights from AFM-SMFS in an
unbiased and reliable manner.
In addition to enabling energy landscape reconstruction by SMFS, AFM is a powerful imaging platform for measuring the mechanical properties of surface-bound molecules. AFM requires
surface-bound samples for reliable imaging, but adhering a molecule to a surface necessarily reduces
molecular degrees of freedom and may perturb native behaviors or structures from their expectedvalues. One well-known surface-induced perturbation of native structure is DNA’s distributionof bending angles (e.g. Figure 1.4 B). In particular, air-based AFM imaging gives the expecteddistribution of DNA bend angles [40], but liquid-based AFM imaging historically observes a wider
distribution of bending angles [23]. In other words, AFM imaging of DNA in liquid has historicallymeasured excessively bendy or flexible DNA, as compared to other bulk or single-molecule methods. Chapter 3 demonstrates that the spuriously high apparent flexiblity of DNA is due to thedetails of the surface-DNA binding, and Chapter 3 provides a simple method for liquid imaging of
surface-bound DNA while obtaining the correct DNA bending angle distribution. In addition, theimaging and deposition method is compatible with many protein systems and therefore provides ahigh signal-to-noise method of imaging protein-DNA interactions in liquid.

1.2

Liquid imaging of biomolecules via atomic force microscopy

In AFM-based imaging, light is reflected off of a microscopic cantilever onto a detector (Figure
1.1 A). Nanoscopic movements of the cantilever are recorded as changes in the position of the5

Figure 1.2: Atomic resolution AFM images of the mica lattice are consistent with its
expected crystal structure.
(A) AFM images of the mica lattice. From left to right, eachsuccessive image is twice as large as the first, which is 5 nm by 5 nm. (B) Simplified diagram of themica lattice, with the two canonical lattice vectors denoted by a and b. (C) The Fourier transformof the AFM images in the a direction (â) yields a strong signal near the expected lattice spacing
based on the crystal structure [41]. (D) As panel C, but for the b̂ direction.

A

1.0 Å

2x

2x

0.5

2x

0.0
-0.5

4 nm

8 nm

C

1

b
a
Symmetry axis

0.5 nmFFT Power (au)

B

2 nm

16 nm

D

a
axtal

0.75

-1.0

b
bxtal

0.5
0.25
00

0.5

1

1.5

Lattice spacing (nm)

20

0.5

1

1.5

Lattice spacing (nm)2

6reflected light (Figure 1.1 B). Height topography, or assignment of a particular height over a twodimensional matrix of positions, is measured by controlling the position of the cantilever in thexy-plane of the surface (Figure 1.1 C). For imaging discussed in this work (except Figure 1.2),‘tapping mode’ imaging will be used, in which the cantilever is transiently in contact with thesurface [42]. Tapping mode is generally more gentle than contact mode imaging, in which the AFM
cantilever is in constant, high-force contact with a surface.
High signal-to-noise images of surface-bound biomolecules require low surface roughness anda surface binding strong enough to withstand typical imaging forces. Muscovite mica and glass
are two common substrates for AFM imaging of biomolecules due to their relative flatness andversatility in binding mechanisms. Glass can be etched to achieve nanoscopic smoothness (Figure1.3) and functionalized with various groups, as described in Chapter 4. Mica is a common substrate
for AFM imaging due to the ease of cleaving mica along its 001 plane and obtaining an atomicallyflat surface (Figure 1.2) [9, 10, 43–47]. In addition, cleaved mica has a slight negative charge[41], which enhances adsorption of positively charged molecules, and the method of Chapter 3
describes how mica’s surface charge can be flipped and thereby enables adsorption of negatively
charged molecules. Reversing the surface charge polarity of mica typically relies on ion-exchanging
mica’s K+ ions with a divalent cation [47] or coating the mica in positively charged polymers [48].
Since many biomolecules of interest are negatively charged at physiological pH (e.g. DNA, many
proteins), the ability to switch the polarity of mica’s surface charge is critical for strongly binding
a diverse set of molecules to the surface and obtaining high-quality images.
The application of mechanical or polymeric models to AFM images yields biophysical insight.
For extended polymers made up of N approximately straight segments of length li , the contour
length, L0 , is L0 =∑N

i=1 li (Figure 1.4 A). Segment bending is quantified by measuring the change

in tangent vectors along the chain, θ(s), as a function of arc distance s =∑j lj , where ‘j’ runs

over the segments of interest (Figure 1.4 B). For a two-dimensional worm-like chain with segment
length l, the quantity σl2 is known as the persistence length p, where σθ is the standard deviation ofθ7

Figure 1.3: Surface roughness of glass depends on treatment.
The surface roughness,
defined as the standard deviation in surface height, is plotted for (from left to right) untreated glass,glass subjected to a potassium hydroxide (KOH) treatment, and KOH-treated glass immersed ina solution of silane-PEG (poly-ethylene glycol) for the indicated time, as described in Chapter 4.
Images above the plot are representative of their respective conditions. The approximate roughnessof mica is plotted as a horizontal line (see Figures 1.2 and 3.17).

PEG incubation time

100

KO

H-t

0m
20

m
32

8m

2m

s
30

rea

ted

Mica
ate
d

10 1

Un
tre

surface (nm)

10 m

8
θ(s) (Figure 1.4 B, inset) [40]. The persistence length can also be estimated by the average squared
end-to-end distance, < R2 >, as a function of the arc length s between the points (Figure 1.4 C)[40].
Volumetric and areal measurements complement the polymeric measurements of L0 , p, andR2 . The width of a polymer, w(s), may vary along the arc and provide evidence of morphology
changes in the sample (e.g. binding partners, polymer isoform changes, polymer movement) (Figure
1.4 D). The width along the contour is quantified by establishing a direction perpendicular to thecontour, s⊥ . For s⊥ of length 2L⊥ , given a position ps = [x, y] along the arc and angle θ(s), we
define s⊥ (s) = ps + ds · [cos( π2 + θ(s)), sin( π2 + θ(s))] for ds which varies from -L⊥ to L⊥ . In otherwords, s⊥ at a particular point ps at an arc length of s is a line perpendicular to the arc tangent at ps(Figure 1.4 E, colored lines). The height along this direction, h(s⊥ ), defines the cross section along
the contour (Figure 1.4 E, inset), and the maximum height also provides a useful measurement forpolymers with known diameters, such as DNA (Figure 1.4 F).
Figure 1.4 (following page): Quantification of polymeric and geometric properties
using AFM imaging. (A) (Top) Cartoon of a simulated 650-nm DNA molecule with a twodimensional persistence length, p, of 50 nm. (Bottom) Dotted blue line represents the segments
which sum to the contour length, L0 . (B) (Top) The angle between two tangents separated bycontour (arc) length, s, is defined as θ(s). (Bottom, left) The distributions of bending angles
for values of s as indicated. (Bottom, right) Despite the changing variance of the bending angle
distribution, the ratio of the arc length s to the variance in the angle at a constant s remains
constant. (C) (Top) Illustrative definition of the end to end distance, R, between two points A
and B. (Bottom) The average value of R2 (blue circles) follows the expected distribution for a
two-dimensional worm-like chain (green line, see [40]). (D) A heatmap-style topograph, wherecolor is proportional to height, of a polymer with an apparent bulge (bright area). Green arrows
illustrate the dependence of the width of the polymer on arc length. (Inset) Width of the polymer
as a function of arc. (E) As (D), except three colored lines perpendicular to the contour, s⊥ ,illustrate the variability in cross-section. (Inset) The height along each colored line demonstrates
that the cross-sectional area changes as a function of arc length. (F) Three-dimensional image ofthe region near bulge, with magenta line overlayed at the maximum height along the contour, h(s),as indicated by the pink arrow. (Inset) The height as a function of arc length quantifies the increasein height of the bulge relative to the rest of the polymer.

9

A

B

C
A
R( s ) A B

(s )

30

E
w(s)

15
00

400

s (nm)0015

s (nm)

F

30

3
1.5
0

-25

0

s (nm)

25

s 3

s 2

s 1
200 nm1

0.5

0 -80 0 80 10
0 1 101s (nm)(s) (deg.)h(s ) (nm)w(s) (nm)D

p2D=50 nm

200 nmh(s) (nm)

200 nm

200 nm60

s=3 nms=6 nms=13 nms=26 nm

1.5

L0

200 nms/ 2 (nm)Prob. (10 2/deg.)

200 nm3

B<R 2(s)> (103 nm2)

s

4
2
00

250 500s (nm)

h(s)

10

1.3

Single molecule force spectroscopy and energy landscape reconstruction

This section reviews techniques for energy landscape reconstruction used in this work. The
techniques described are not comprehensive of the entire field, since it ignores some data collection
methods (e.g. force-jump techniques [49]) and data analysis methods (e.g. the Crooks fluctuation
theorem [50, 51]).
Experimental limitations of SMFS data typically require projecting free energy landscapes
to a single dimension. Since most biomolecules have many atoms (and therefore many degrees
of freedom), a one-dimensional projection is an enormous simplification but often a useful one[7, 53–55]. Figure 1.5 is an example of a one-dimensional free energy landscape as a function of
the molecular extension. Local minima in the energy landscape are sequentially numbered with astate index ‘i‘, and arrows denote energy differences or distances to adjacent transition states. As
shown in the inset in Figure 1.5, the local free energy between a state and an adjacent barrier iswell-approximated by the ‘linear-cubic’ model [52]. The free energy difference and extension change
between a state i and the barrier to state j are denoted by ∆G‡ij and ∆x‡ij , respectively.
Estimations of ∆G‡ij and ∆x‡ij are enabled by identification of transitions between states iand j in SMFS data. Applying a force F at an extension x tilts the free energy landscape by−F × x, biasing the diffusion of the molecule along the landscape in a particular direction. In
other words, the application of force in an SMFS experiment biases the frequency of transitions
kij and the states i and j. Since forward and reverse transitions are both possible (i.e. i → j
and j → i), SMFS experiments which sweep over a broad range of forces (and therefore a range ofkij (F )) more accurately measure the distances and energy differences associated with the relevanttransitions. The sections that follow detail three techniques for SMFS data acquisition and analysis
which apply forces, tilt the landscape, and thereby either reconstruct an entire energy landscapeor estimate ∆G‡ij and ∆x‡ij .

11Figure 1.5: Illustrative definition of energy landscape parameters.
A free energy
landscape is shown as a function of molecular extension (blue line), with parameters taken from[37]. From state ‘i’ to state ‘j’, color-coded arrows denote the transition energy differences, ∆G‡ij ,and the transition distances, ∆x‡ij . Note that states correspond to well minima. (Inset) A fit to
the final barrier (blue) demonstrates the general applicability of the linear-cubic model [52] forapproximating a local energy barrier.

x12

40

G21
x21
Extension (nm)30

5 kB T
1 nm

x01

20

G10

G0 (kBT)G0 (kBT)

G12

x10
10

G01

linear-cubic

0
0

1

2

Extension (nm)

3

4

5

12
1.3.1

Equilibrium techniques for energy landscape analysis

A straightforward method of energy landscape estimation applies a constant force F at atemperature T and measures the probability of a molecule to be found over a range of extensions,
P (x) (Figure 1.6 A). From elementary statistical mechanics, the energy, G(x), can be calculated
from Boltzmann statistics up to an arbitrary zero energy constant:G(x) = −kB T · log P (x)(1.1)

where kB is the Boltzmann constant. In practice, the observed extension distribution is
widened by its convolution with the point-spread function of the measurement probe, S(x) (Figure
1.6 A). However, the observed extension can be deconvolved using the following relation [36]:1
pi+1 (x) = pi (x) + r0 [1 − 2|pi (x) − |][P (x) − S(x) × pi (x)]
2

(1.2)

where r0 is a relaxation constant, the initial condition is the measured extension (i.e. p0 (x) =P (x)), and ‘×’ represents Fourier convolution. The point spread function can be approximated bymeasuring the extension distributions of the system in the absence of any transitions and modelingthe distribution as a Gaussian function with the measured width. Once the point spread function
has been measured, iteratively removing it is straightforward (Figure 1.6 B), assuming convergenceof the landscape (Figure 1.6 C). Once the probability distribution has been deconvolved, the energy landscape is obtained via Equation 1.1, and the landscape can be converted to a free energy
landscape by tilting by F · x.
In addition to Boltzmann-based reconstruction of equilibrium data, constant-force SMFS dataalso yield energy landscape barrier heights and distances (Figure 1.5) via unfolding and refolding
transition frequencies [37]. The following relationship fits the force-dependent transition rate kij (F )

13Figure 1.6: Demonstration of deconvolution of a force probe’s point spread function.
(A) Plot of the true (P (x), purple solid line) and convolved (P (x)⊗S(x), dotted blue line) extension
probability distributions. Point spread function, S(x), is given as the dashed orange line. (B)Extension probability distributions from iterative deconvolution (i.e. Equation 1.2) of the convolved
probability distribution in panel A. Distributions from earlier iterations are colored darker thandistributions from later iterations, as indicated at each order of magnitude. (C) Extension-averaged
relative error of deconvolved distributions of panel B demonstrate that the deconvolved probability
distribution converges to the correct value. The error is calculated relative to the true extension
distribution from panel A (i.e., P (x)).

Probability (1/nm)

Api(x) (1/nm)

B

20

Extension (nm)
40

60

80

P(x)
P(x) S(x)
S(x)

0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00

i=0
i = 10i = 100
i = 1000
i = 100000

1.0

Average error (au)

C

0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00

0

0.8
0.6
0.4
0.2
0.0

100

101

102

103

Iteration index i

104

105

14
from state ‘i’ to state ‘j’ to the distance between the minima of state ‘i’ and the transition barrier, x‡ ,the zero-force transition rate k0 , and the energy between the minima of state ‘i’ and the transition
barrier ∆G‡ :1log(kij ) = log(k0 ) + { − 1)c(F ) + ∆G‡ (1 − c(F )1/ν )},
ν
νκx‡
νF x‡
(1 − ν)κ(x‡ )2where c(F ) = [1 +
∓
(1
+
),
2∆G‡
∆G‡
2∆G‡

(1.3)
(1.4)

and ν is the barrier shape (either 1/2 or 2/3), κ is the spring constant of the force probe, and∓ is minus for the forward (unfolding) direction and plus for the backwards (refolding) direction.
Note that when comparing rate maps from constant force and constant velocity techniques (seeSection 1.3.2, below), the force in the constant force measurements, F , should be corrected for the′difference of measurement potentials to F as follows [37]:

′

F =

‡

F ± κ x2

‡ 2)
1 + (1−ν)κ(x2∆G‡

where the meanings are as before, except ± is a plus in the forward (unfolding) direction anda minus in the backwards (refolding) direction. The rates are straightforward to obtain by counting
the number and duration of transitions in a force-versus-time trace (Figure 1.7 A–C). The first andlast event must always be ignored, since they provide only a lower bound on the dwell time (orupper bound on the transition rate) for that particular transition. Once the rates are obtained asa function of force (Figure 1.7 D), fitting with Equation 1.4 yields the off-rate, energy difference
between the state and the transition barrier, and distance to the barrier from the state (Figure 1.7
E).

15
Figure 1.7: Model-based reconstruction of equilibrium single molecule force spectroscopy data. (A) Representative samples of 200 second, simulated traces of extension versus
time. Raw data (lighter colors) were generated at 100 kHz, and the darker data are filtered to 1
kHz using a second-order Savitsky-Golay. Data was simulated as described previously [39]. (B)Probability density of unfiltered extensions from column A. (C) Probability density of filtered extensions from column A. (D) The distributions of unfolding and refolding times, tunfold and trefold ,for 200 second, simulated extension versus time traces. (E) The average rate of unfolding (kunfold ,red downward triangles) or refolding (krefold , green upward triangles) versus the average of thefolding and unfolding forces. Fit of Bell-Evans model to unfolding data (blue dotted line) does not
capture the curvature as well as the Zhang-Dudko model [37].

B0P (1/nm) C P (1/nm)
0.2 0

D

0.2

0

Time (s)0.08

101

P (1/s)

0.3 s

0.2

trefold
tunfold

P (1/s)Time (s)10 nm

Extension (nm)A

P (1/s)101

P (1/s)101

P (1/s)

101

101

E 104
103

kunfold
krefold
Bell EvansDudkok (Hz)

102
101
100
10 1
13

14

15

<Funfold/refold> (pN)

16

16
1.3.2

Constant velocity techniques

Constant-velocity measurements provide an alternative method of energy landscape reconstruction or energy landscape parameter estimation. In constant-velocity experiments, or ‘force
ramps’, the force probe bias (e.g. AFM cantilever stage position) is changed at a constant velocity.
The force-versus-time curves from force ramp experiments are transformed into transition rates
by noting that for any particular transition from state ‘i’ to state ‘j’ under constant force, thenumber of molecules transitioning at a particular change in force Pij (F )|dF | must be equal to thenumber of molecules transitioning over that time period Pij (t)dt. But the number of transitioning
molecules must be equal to the number of molecules in the state Ni (t) multiplied by the relevant
rate constant kij (F (t)):

Pij (F )|dF (t)| = Pij (t)dt = kij (F (t))Ni (t)dt → kij (F ((t))) =|dF (t)| Pij (F (t))
dt Ni (F (t))(1.5)

This equation is easiest to understand using several examples at different loading rates. For
each loading rate (Figure 1.8 A), we record the number of molecules (or independent force-extension
curves) in a particular state ‘i‘ at a particular time t, yielding Ni (t) or equivalently Ni (F ), where
F is the average force in a particular state (Figure 1.8 B). This requires the accurate detection of
Figure 1.8 (following page): Model-based reconstruction of force ramp (constantvelocity) single molecule force spectroscopy data. (A) A selection of simulated force versus
stage position curves at the nominal loading rates indicated in the lower right. The average force
in the folded and unfolded states (< F (t)folded > and < F (t)unfolded >) obtained from the relevant
regions of all curves are shown as red and purple dotted lines, respectively. (B) The populationof curves in the folded state, Nfolded , as a function of rupture force, FR . (C) The loading rate
as a function of rupture force. (D) The number of transitions from the folded to unfolded state,
N(F →U ) , as a function of rupture force. Note that this is equal to ∆F · PN →U in the theory parlance[37], where ∆F is the bin size. (E) The unfolding rate as a function of rupture force. (F) The
concatenation of all unfolding rate data from panel E, where the colorbar gives the nominal loadingrate. (G) Fitting the data from panel (F) to the Bell-Evans model [56] and Zhang-Dudko model[37] (blue solid line, black dotted line, respectively) to all of the data from panel (F) demonstrates
the improved fit of the Zhang-Dudko model.

17A
F (pN)z (nm)

20
15
10

200

C

0
104

dF/dt (pN/s)

foldedB

N(F U)

Dk (Hz)EFz (nm)<F(t)folded><F(t)unfolded>

60 pN/sz (nm)

240 pN/s

960 pN/sz (nm)

4 nN/s

50 nm

50 nm

50 nm

50 nm

15 FR (pN)20

15 FR (pN)20

15 FR (pN)20

15 FR (pN)20

15 nN/s

50 nm

15 FR (pN)20

103
102
100
50
0
1054
10
103
102
101
105

101

G

nN/s

105

Dudko
Bell-Evans

104

103

100
nN/s

102
101
14

16

18

F (pN)

20

kunfold (Hz)104

kunfold (Hz)z (nm)

10 1
nN/s

dF/dt

103
102
101
14

15

16

17

F (pN)

18

19

20

18
transition events for every force-versus-time curve at each loading rate tested, which is the subjectof Chapter 4. With the transition events in hand, the force-versus-time curves in a particular state
are combined to yield the average force and loading rate in that state at all times where there isa rupture (Figure 1.8 A). The state-specific average loading rates and rupture forces as a function|of time facilitate calculating the loading rate ( |dF
dt , Figure 1.8 C) and unnormalized distributionof rupture forces (Pij (F (t)), Figure 1.8 D) as a function of time or rupture force FR . Importantly,
Pij (F (t)) is the number of transitions at that particular rupture force divided by the force bin|
width. Therefore, the entire distribution will not generally sum or integrate to one. With Pij , |dF
dt i ,and Fi in hand, Equation 1.5 yields the rate map as a function of force (Figure 1.8 E–F) and fitting
equation 1.4 yields the relevant energy barrier parameters (Figure 1.8 G).
In addition to transforming non-equilibrium data using the rate map method detailed above,
there are well-established techniques for reconstructing the energy landscape as a function of molecular extension. In particular, the basis for the inverse Weierstrass transform detailed in [39] andleveraged in Chapter 5 is the Jarzynski equality [38]. This equality relates the free energy change
of a system (∆G0 ) to the measured work, W , as a function of an experimental control parameter‘z’ (e.g. AFM stage position) as follows:β
exp −β∆G0 =< exp −βW (z) >N ≈< W (z) > − σw (z),
2

(1.6)

where the average is taken over all members of an ensemble (e.g. many force-extension
curves), and the equality only holds in the limit of an infinitely large ensemble. The approximation
holds in the limit of processes happening close to equilibrium. In addition, this equality assumes
an infinitely stiff force probe; when this condition does not hold, the weighted histogram [57] orinverse Weierstrass transform [39] should be used to correct for the effect of the probe. Finally,
the landscapes obtained in this manner are still subject to the point spread function of the force
probe, and therefore should be deconvolved as described above (Figure 1.6). Table 1.1 lists common

19
tradeoffs associated with the energy landscape techniques presented in this section.

1.3.3

Benefits and trade-offs of techniques

20

Figure 1.9: Reconstruction of force ramp experiment using Jarzynski’s equality. (A)Simulated force plotted as a function of constant-velocity stage position demonstrates transitions
between unfolded and folded states. (B) Heatmap of 50 force-extension curves simulated as in panel
A. (C) The mean work (left, purple axis) and standard deviation of the work (red lines, right axis)
at each z, where the average and standard deviation are taken over the ensemble. Note that themean and standard deviation of the work approximate the free energy for high-stiffness probes (seeEquation 1.6) (D) The energy, as calculated using the Jarzynski equality (blue, solid line) or its
approximation (red, dotted line).

A
F (pN)

1 pN

Cantilever base (nm)
5 nm

B
F (pN)

1 pN

5 nm

C
1.5

80
1.0

W (kBT)< W > (kBT)

100
60
40

0.5

20

D

100

Energy (kBT)

0.0

0
80
60
40
20
0

A(z)= ln( < exp W(z) > )/A(z) < W(z) > 2 W(z)221

Table 1.1: Comparison of energy landscape techniques.
Technique
Rate map(Non-equil.)[37]

Rate map(Equilibrium)[37]

Jarzynski-based
reconstructions[38, 39, 57]

Limitations

Advantages• Large N (NFEC ∼ 100,
Ntx per v ∼ 103 )• Large v range needed (∼10104 pN/s)• Requires binning – no analytictransformation to k(F )• Samples k(F ) over large F
range• Accounts for linker• Generalizes to many states• Necessarily yields kinetics• Difficult to access k(F ) overrange of F
• Requires low drift over large
time scales• Constant force measurements
are technically difficult• Analytic solution to k(F )• Necessarily yields kinetics• Yields landscape over re• Requires high-stiffness probe
gion, not just landscape pa• Doesn’t yield kinetic or diffurameters
sive information [39]• Betterleverages
data
fromfolding/unfolding
experiments

Chapter 2
Experimental imaging and force spectroscopy protocols

This chapter describes additional details for sample preparation, data acquisition, and data
analysis for imaging and single-molecule force spectroscopy (SMFS) by AFM. The information here
is intended as a supplemental resource for the details in Chapters 3 and 4.

2.1

Imaging via atomic force microscopy

Atomic force microscopy (AFM) images of nucleic or amino acids are usually obtained byleveraging the atomic flatness and high charge of mica (see Section 1.2) and the capability of AFM
to operate in biological buffers. At physiological pH, many molecules of interest (e.g. DNA, RNA,and proteins) have the same negative charge as mica [41]. The repulsive force between such negatively charged molecules and the negatively charged mica substrate must be converted into an
attractive force to achieve stable imaging of well-bound molecules (see Chapter 3). As detailedin Section 1.2, the three-dimensional topographs obtained via AFM reveal geometric information(e.g. width, height, volume), polymeric information (bending angle distributions), and stoichiometric information (e.g. binding probabilities as a function of ligand concentration). Below, I
describe challenges and advice related to obtaining high-quality AFM images and force curves of
biomolecules.

23
2.1.1

Sample handling and wetlab techniques

Successful AFM experiments require carefully manipulating and recording many parameters(e.g. buffer condition, sample concentration, temperature). Often, dozens of individual choices
or parameters lead to a particular experimental protocol. Without sufficient foresight, individual
choices which previously seemed arbitrary or unimportant may prove critical to reliably obtaining
and interpreting high-quality data. When faced with a choice in the laboratory, answering thefollowing questions serves as a useful exercise to help guide decisions:• How can this choice improve lab safety?
• How can this choice improve reproducibility?
• How can this choice reduce contamination or potential error?
For example, when faced with the question ‘should the temperature of an organic solvent usedduring incubation of surfaces be kept at a known constant?’, the answer should be ‘yes’, since thisanswer improves lab safety by preventing a potentially hazardous and unmonitored temperaturechange, reduces experimental error due to temperature variation, and improves reproducibility byensuring a consistent temperature between subsequent experiments.
Usually, questions regarding safety, reproducibility, and error all have a consistent answer andsolution. If a choice ever conflicts (e.g. something is reproducible but dangerous), safety shouldbe placed in first priority. If considerations related to safety are at conflict with considerations oferror or contamination, a new solution should be designed to avoid this conflict. Below, I recordmy ‘best practices’ for increasing the probability of successful experiments and decreasing the riskof danger or experimental contamination.

24
2.1.1.1

General lab hygiene

Pipettes are used for almost every aspect of work in the lab and therefore deserve special
attention. Since accurate volumes are critical for reproducing scientific results, pipettes should be
regularly (at least once per year) cleaned and calibrated. If they are contaminated by improperuse (e.g. accidentally pipetting a large volume of liquid into the internal shaft of the pipette), theyshould be disassembled; thoroughly rinsed with water, ethanol, and water again; dried; and finally
reassembled.
All glass and plastic wear for rinsing or liquid incubation should be thoroughly conditioned
in their respective solvents. If a particular piece of glass or plastic will always be dry (e.g. a teflon
holder for drying slides by N2 gas), the container should first be rinsed in a compatible solvent,typically water or isopropanol, and then dried with N2 gas. Prior to use, always check solvent
compatibility charts to reduce the risk of contamination. For example, toluene is known to dissolve
high density polyethylene, a common ingredient in many plastic containers [58].
Special care should be taken to reduce the risk of environmental contamination from the airor devices used for manipulation. For a long incubation (e.g. the three hour functionalization ofChapter 4 in toluene), reduce dust contamination of incubation chambers and solvent evaporationby covering the chambers with an inert material (e.g. a glass lid for toluene incubation chambers).
In addition, prior to their use, tweezers and other surface- or cantilever- manipulation tools should
be cleaned with isopropanol, water, then thoroughly dried by wiping in a KimWipe or applicationof N2 gas.

2.1.1.2

ProteinSample degradation is an often-confounding but easily prevented source of systematic error
or experimental failure. Protein samples should generally be stored in an ultra-low (-80 ◦ C) freezer,

25

Figure 2.1: Deposition of DNA onto NiCl2 -treated mica in a dithiothreitol (DTT)containing buffer.
Image of size 2 µm by 2 µm shows DNA bound to a surface prepared as
described in Chapter 3, except 1 mM of dithiothreitol (DTT) was added to the usual depositionbuffer (10 mM MgCl2 , 25 mM KCl, 10 mM HEPES, pH 7.5), before rinsing the surface in the same
DTT-containing buffer, and finally proceeding with the rinsing steps outline in Chapter 3. In otherwords, an extra rinsing step is necessary to prevent DTT coming into contact with and thereby
quickly reducing NiCl2 .

26
to better preserve properly folded protein [59]. Unless otherwise specified, protein should always
be subdivided or aliquotted into smaller volumes at a working concentration, then each aliquot
should be individually flash-frozen (often with 10% volume percentage glycerol). When in doubt
for how to store a protein, consult prior literature and determine consensus storage parameters. As
needed, frozen protein aliquots should be flash-thawed to room temperature and then refrigerated
at 4 ◦ C (i.e. on ice) to prevent thaw-induced misfolding [60]. For proteins with solvent-exposed
cysteine residues, keeping a disulfide-reducing agent present in the buffer is often necessary to
prevent oligomerization or misfolding of the protein via non-native disulfide bonds [61]. Note that
one common disulfide-reducing agent, dithiothreitol (DTT), also reduces Nickel [62] and therefore
is sub-optimal for use in the imaging buffers of Chapter 3. If DTT is required (instead of the Nickelcompatible TCEP), NiCl2 should be replaced by MgCl2 in equimolar amounts in the relevant buffers.
Exposing mica pre-treated with NiCl2 (see Chapter 3) to DTT does not appear to affect image
quality, as long as all DTT is rinsed before any subsequent NiCl2 is introduced into solution (Figure
2.1).

2.1.1.3

DNA

Degradation of double-stranded DNA by nicking is slowed by storing DNA samples at -20◦ C [63].

To further reduce risk of enzymatic degradation of DNA, samples are often stored ina solution of 10 mM Tris (hydroxymethyl) aminomethane hydrochloride (Tris-HCl) and 1 mM
Ethylenediaminetetraacetic acid (EDTA) at pH 8. EDTA is a chelator of divalent cations andenhances the stability of DNA, since many DNA-degrading enzymes (DNases) require divalentcations. Freezing, storage, and thawing occurs in the same manner as described above for proteins[64]. Especially for DNA substrates longer then a micron (about 3000 bp), all sample manipulation(e.g. pipetting) should be slow and gentle (less than 50 µL/s), to prevent nicking and preserve thepopulation of DNA present during storage. Wide-orifice pipettes may also be employed to reduce
the risk of shearing or nicking double-stranded DNA.

27
2.1.2

Sample deposition

High-quality AFM images require flat surfaces with well-bound samples. To prepare an
imaging substrate, a mica disk should be secured with epoxy to a metal disk and stored in a dustproof container such as a plastic wafer inside of a ParaFilm-sealed pipette box. Dozens of these
metal-epoxied mica disks can be made at a single time, and the disks can be stored for months.
Prior to this epoxying step, anything touching the mica (e.g. the metal disk or plastic wafer) should
be air-dried after rinsing thoroughly with water, isopropanol, and water again in order to reduce
potential contamination. Before deposition of any sample, imaging surfaces should be rinsed withwater and dried with a KimWipe, to reduce dust contamination.
To promote equilibrated attachment, DNA and proteins with acidic isoelectric points (i.e.
negative charges at physiological pH) are deposited onto mica treated with NiCl2 . Before deposition,
the DNA and protein (if present) must be mixed to the desired concentrations in the appropriate
buffer. For most imaging applications involving DNA, some divalent and monovalent salt will bepresent. As shown in Chapter 3, DNA is typically well-bound with 10 mM MgCl2 and 25 mM KClduring deposition, but salt concentrations more representative of cellular conditions (3 mM MgCl2
and 50 mM KCl) are also compatible with AFM imaging (Figure 3.11)
In addition to salt concentration, choosing the correct sample concentration is critical for a
successful experiment. Deposition concentrations must be chosen to promote a reasonable numberof molecules per image (and therefore reasonably high data throughput), but high concentrations
will overwhelm the surface and lead to excessive molecular crossings. As a general rule of thumb,the average distance between the center of a molecule and its closest neighbor should be larger
than twice the radius of the minimum circle enclosing the molecule, Rmin , but the average distance
between neighbors should not be more than 20 Rmin . The concentration of DNA is set by the method
at about 1.25 ng/uL (or about 1 nM for 2000 bp DNA), and the amount of protein (if present) is
determined by the binding affinity of the protein for the DNA and the relative ‘background’ affinity

28
of the protein for the substrate. Deposition protein concentrations in the range of 10-1000 nM aretypical.
Deposited DNA or protein-DNA complexes must be allowed to relax on the surface to disfavorkinetically trapped states. The imaging protocol described in Chapter 3 necessitates a series ofgentle rinses to favor an equilibrated, 2D conformation of DNA (or protein) on the surface anddisfavor the so-called ’kinetically-trapped’ conformation in which a molecule is poorly bound to
the surface and large fractions of its contour are in solution. Gently rinse surface-bound samples
and never expose them to air, since a receding meniscus is capable of exerting large forces on asurface-bound sample and disrupting binding (Figure 3.12). In the case of surface-bound DNA,
forces from partial de-wetting result in an increase in the fraction of kinetically trapped DNA andtherefore a decrease in the amount of useful data. Put another way, the rinsing should be laminarand continuous, without any abrupt, macroscopic motion of the liquid droplet off of the surface.
If there is any evidence that a surface may have been partially de-wet, the efficient thing to do isto prepare another sample, since sample preparation takes minutes and imaging a sample requires
hours or days of time investment. In other words, do not waste time (hours) slowly imaging asurface which may be ruined, since preparing a new surface is relatively fast (minutes).
Surfaces with bound samples may be stored in liquid for use as a positive control at a later
date. Care must be taken to avoid de-wetting the surface by adhesion of the water droplet onto
any surface (e.g. the top of a plastic wafer) or drying the surface by evaporation. Evaporation canbe slowed considerably, but not stopped, by placing a surface in a closed, plastic wafer inside of apipette boxed filled 50-75% with liquid, sealing with ParaFilm, and placing in a 4 ◦ C refrigerator.
Over many hours, angstrom-sized precipitates often stably bind to the mica lattice, which increases
the background noise (Figure 2.2).

29

Figure 2.2: Nanoscopic precipitates adhere to mica surfaces after many hours ofimaging.
(A) 500 nm by 500 nm images of 300 bp DNA taken with an SNL-10A at theindicated times, where the times are relative to the leftmost image. (B) For each image in A, theprobability distribution of heights is shown. (Inset) Detailed plot for small heights shows that overtime the heights near 0.5 nm become more common, corresponding to the surface precipitates. Notethat the images were taken at different spots on the same surface.

t = 2 hrs

200 nm4
2

0 0

t = 21 hrs

200 nm

200 nm

0.25

0.25

0.25

0.25

0.2

0.2

0.2

0.2

0.15
0.1
0.05

0.15
0.1
0.05

00

0.25 0.5 0.75

12h (nm)

height, h (nm)3 0

P (1/nm)6

t = 8 hrs

200 nmP (1/nm)8
P (1/nm)Prob. density (1/nm)

B

t = 0 hrs

P (1/nm)

A

0.15
0.1
0.05

00

0.25 0.5 0.75

12h (nm)

height, h (nm)

3 0

0.15
0.1
0.05

00

0.25 0.5 0.75

12h (nm)

height, h (nm)

3 0

00

0.25 0.5 0.75

12h (nm)

height, h (nm)

3

30
2.1.3

Data acquisition

The acquisition of publication-quality AFM images requires patience and constant attention
to experimental details. Figure 2.3 is a flowchart illustrating the essential steps for running an imaging experiment, which we describe in detail below. Once a surface has been prepared as describedin Section 2.1.2, the cantilever and surface are loaded. The cantilevers I use most commonly for
imaging of DNA or DNA with bound protein are the Bruker SNL-10A and the Olympus BioLever
Mini. Each cantilever has different physical characteristics and associated tradeoffs, as detailed inTable 2.1. In particular, the tip radius of the SNL-10A is generally smaller than the BioLever Miniand therefore capable of producing sharper images, but the BioLever Mini is less prone to drift andhas a much larger range of achievable imaging amplitudes due to its much smaller size and lower
drag.
Table 2.1: Imaging cantilever comparison. Comparing the physical characteristics of thecantilevers used in imaging studies in this work.
Cantilever Tip Radius
Bruker≈ 2 nm
SNL-10A

Olympus
BioLeverMini≈ 8 nmCantilever
Length120 µm

7 µm

Benefits

Drawbacks• Better resolution• Easily dulled• High sample pressure• High drift• Less drift• Less sample pressure• Less reflective area
• Poorer resolution

Once a cantilever has been chosen, all parts of the AFM instrument which contact the sample
should be cleaned. In particular, since the AFM is not immune to contamination, the cantilever,cantilever holder, and AFM stage must be cleaned. The cantilever holder should always be secured
in a housing prior to rinsing, to prevent spilling water onto the electronics. Before securing thecantilever in the cantilever holder, the holder should be thoroughly rinsed with water, ethanol,rinsed again in water, and dried. Unless the cantilever is functionalized, the mounted cantilever can

31then be rinsed with water, ethanol, rinsed again in water, dried by application of a KimWipe, thentransferred into the final, desired imaging buffer. In addition to reducing potential contaminates
such as oil from commonly used cantilever gel packs, thoroughly rinsing the cantilever and cantilever
holder helps wash away small (< 1 mm) shards of cantilever which are commonly created whenmanipulating cantilevers. Without such rinsing, cantilever shards or contaminants will settle onto
the surface and potentially create experimental difficulties.
After mounting, rinsing, and transferring the cantilever into the desired imaging buffer, thesurface should be centered on the AFM stage, with between 150 and 300 µL of imaging buffer above
the surface, assuming a standard 15 mm-diameter metal substrate. Once the surface is mounted,
the stage should be raised to accommodate the cantilever and prevent crashing the cantilever into
the surface. After securely fixing the cantilever holder (and therefore the cantilever) onto the AFM,
the holder is slowly lowered, until the cantilever is fully immersed in the bubble of the imaging
surface.
Once the AFM-mounted cantilever is brought into contact with the sample liquid droplet,
positioning the cantilever and detection laser focus a few microns above the surface is a pre-requisite
for imaging. Any bubbles on the cantilever (observable as shadows in the live video panel) willcause drift and interfere with accurate measurement. Bubbles are removed by wetting and dewetting the cantilever using the stage motors, or by reloading the cantilever. If the cantilever isre-positioned, the rinsing protocol should be repeated. Once the cantilever lacks any observablebubbles on the live video panel, the cantilever should be positioned about 50 µm above the surface,
and the detection laser position should be adjusted to maximize the measured signal (usually byplacing the laser in the center of the cantilever). The surface position can be found by sweeping
the focus down to the metal substrate (which is highly featured and specular), and then slowly
sweeping up until the liquid-mica interface is visible as diagonal lines at the corners of the live
video panel.

32

Figure 2.3: Flowchart for AFM imaging operation. Operation starts at the text withthe diamond background, and text to the right of each edge indicates when that edge should be
followed. If there is no text, an edge should always be followed.

Load surface into AFM

Rinse, dry holder

Secure cantilever to holder
Rinse, load into AFM
visibleNo visible bubbles Bubbles
in AFM video
Position cantilever above surface

Wet/dewet
CantileverNo visible bubbles
Acquire thermal and tune
Set drive parameters
Already at surface
Not at surface

Set imaging parameters
Engage, slowly increase setopint
No contact with surface

Set free amplitude ~ 10 nm
Set setpoint ~ 5 nm
Amplitude < 10 nm
at highest z
Approach surface

Cantilever contaminatedContact with surface

Bubbles visible
in AFM video

Start new frame
No additional
drive available

Cantilever broken Image sucessfully aquired

Acquire new cantilever

Adjust parameters

Amplitude ~ 10 nm
at highest z and triggered
Acquire FEC
and determine InVOLS

Unload cantilever

33

Figure 2.4: Imaging drive frequency should be chosen near the first thermal resonanceof the cantilever. (A) The power spectral density (PSD, black) of an SNL-10A in liquid exhibits
several resonances. (B) Detailed plot of PSD from panel A (grey, left axis) and deflection amplitude(red, right axis) near the first thermal resonance. Since the cantilever in liquid and many mechanicalmodes of the AFM are excited, the amplitude has a non-trivial dependence on the drive frequency.

A

102
1.2

103

f (Hz)

104

105

106

PSD (pm/Hz1/2)

1
0.8
0.6
0.4
0.2

B

0
1.2

1

Deflection amplitude (au)

PSD (pm/Hz1/2)

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

fdrive010000 11000 12000 13000 14000

f (Hz)

034
Once the cantilever is positioned above the surface, calibration is required to ensure physically meaningful measurements. A thermal power spectral density (PSD) should be obtained todetermine the first resonance frequency of the cantilever (Figure 2.4 A). After determining thisfrequency, a ‘tune graph’ should be obtained, which is the dependence of the cantilever’s deflection
amplitude on the frequency applied to the piezo stage (Figure 2.4 B). The drive frequency, fdrive ,should usually be as close as possible to the first thermal resonance frequency of the cantilever(e.g. green line in Figure 2.4 B). Since the transfer function of the cantilever in liquid is highly
non-Gaussian, there may be more than one peak in the ‘tune graph’ near the first thermal resonance, and in this case multiple images should be taken at the peaks in the tune graph near the
first thermal resonance in order to determine the optimal frequency. In other words, if multiple
peaks in the tune graph are close to the first thermal resonance, fdrive should be chosen to obtainthe lowest instrumental background noise.
Armed with a drive frequency close to the first thermal resonance frequency of the cantilever,the cantilever is moved much closer to the surface in preparation for imaging. The surface approachshould be AC mode (i.e. tapping mode), to prevent damaging the tip by excessive force from acontact-mode approach. By setting the drive frequency close to the first thermal frequency (Figure2.4), and choosing an approach free amplitude of several nanometers, the cantilever should be
responsive during the approach and reduce the risk of damaging the tip. As the tip drops towards
the surface, the free amplitude will drop as the cantilever experiences larger drag. As a rule ofthumb for surface detection, a free amplitude of 10 nm (e.g. roughly 300 mV for an SNL-10A)
when the cantilever is positioned several microns above the surface will drop to 5 nm (about 150
mV for an SNL-10A) when the cantilever has found the surface. Therefore, a free amplitude of 10
nm and a set point (indicating the surface position to the AFM) of 5 nm is a reasonable place tostart. In general, a 50% reduction in free amplitude over a few microns is a good indicator that asurface has been found.
The surface height topographs obtained via AFM require calibration for physically meaningful

35
measurements. Once the surface has been reached, the inverse optical lever arm sensitivity (invOLS)
should be measured by pressing into the surface a few tens of nanometers (typically several hundred
millivolts of deflection). Care should be taken to avoid pressing into the surface too hard (andtherefore damaging or blunting the tip) or too soft (and therefore corrupting the invOLS calibration,
which requires a hard-contact measurement). When the invOLS is combined with the thermal PSD
measurement, the spring constant of the cantilever can be calibrated [65].
After obtaining the first thermal resonance, drive frequency, and invOLS, a cantilever poiseda few microns above a surface can be considered ‘calibrated’ and ready for data acquisition for the
purposes of biomolecular imaging. Data acquisition improves over time, especially after the firsthour or two, due to settling of the system. Therefore, for high-quality images, the cantilever shouldbe left alone and allowed to ‘settle’ before image acquisition. Without this initial settling period,
images may appear noisy, and cantilever-induced motion of surface-bound molecules may be more
pronounced. Before allowing the cantilever to settle for a lengthy period, an image with a ‘large’scan size (compared to the expected feature size) should be taken in order to verify the surface iswell-populated with the expected sample.
Table 2.2: Imaging suggestions for common systems of interest. Common parametersuggestions for AFM. Note that the mica lattice is imaged in contact mode, so it only has a set
point.
SampleScan Size(nm)

DNA (2000 bp)
DNA (800 bp)
Bacteriorhodopsin
Mica lattice

2000
1000
10000
10

Scan
speed
(Hz)
2
2
1
15-30

Set
point
(nm)
2
2
4
1-2

Free amplitude
(nm)
4
4
7
N/A

Integral
Gain
(au)
60
60
100
40

After settling, the cantilever set point (the amplitude it will have above the surface once
imaging is engaged) should be set to roughly the feature height of interest (Table 2.2). To reduce
the risk of destroying a cantilever, the free amplitude should be adjusted to be equal to the set

36point prior to imaging. When imaging is started with the free amplitude equal to the set point,
the feedback loop controlling the stage position will not lower the stage. Therefore, the drive
voltage should be slowly increased, causing the feedback loop to lower the stage and the cantileverto gently engage with the surface. Confidence that the surface has been reached is establishedby the reproducible appearance of well-defined structures on the surface. Once the surface has
been found by slowly increasing the drive amplitude, a new frame should be started to avoid an
image partially corrupted by the gentle approach to the surface. This method slowly increases
drive voltage (i.e. decreases the tip-sample distance for a fixed set point) to avoid damaging thecantilever or sample by abruptly colliding the cantilever with the surface and introducing forces on
the scale of nanonewtons.
Different imaging cantilevers and samples necessitate continuous adjustment of imaging parameters. Worse still, from an ease-of-use perspective, the properties of the same cantilever orsample may change over time for a variety of reasons. Table 2.2 lists common parameters for an
initial image of a few different samples. I emphasize again that these parameters are strongly
cantilever-dependent, and typically have to be optimized on a per-cantilever, per-sample, and perimage basis. Table 2.3 lists common tuning decisions for imaging.

2.1.4

Data analysis and processing

Tapping-mode AFM reliably measures the phase and height of a surface and its features,
assuming they are well-bound and do not appreciably move on the time scale of image acquisition(Section 1.2). Since both the height and phase are relative metrics, data analysis must choose azero point. For sparsely populated surfaces, the median value of the height (or phase) provides areasonable initial estimation of the background height or surface location.
Thorough subtraction of the image background necessitates removing an approximately polynomial instrumental artifact along each scanning line (Figure 2.5 A). For many images, particularly

37

Figure 2.5: Background correction of AFM images.
(A) AFM image of a 4000 bp-long
DNA molecule. (B) The same molecule, with a dotted line over an image row with instrumentinduced ‘shadowing’. (C) The height profile along the line shown in panel B, where the dark purple
heights are thresholded to less than two standard deviations of the entire image from the mean,
and the brown line is a third-order polynomial fit to the thresholded data. (D) The same image
as panel B, except each line has been fit as shown in panel C and the fitting polynomial has been
subtracted on a per-line basis.

38
those with large scan sizes or fast scan speeds, the AFM superimposes an approximately parabolic
function on the height of each horizontal scan line. In other words, for a given row r, the measured
height hr,meas (p) as a function of pixel number p is approximately equal to hr,true (p) + (a + px + cp2 ),where hr,true is the true height, and the coefficients {a, b, c} are related to the interference artifact
height superimposed by the AFM (Figure 2.5 B).
Once an image is properly zeroed and background corrected (Figure 2.5 C), physical parameters are extracted from the height as a function of position on the image (see Section 1.2 andFigure 1.4). For polymeric structures (e.g. dsDNA, actin) which have most of their contour along
the surface, the contour along the polymer can be measured. This yields the contour length, bend
angle, and height of the molecule as a function of distance along the polymer (see Section 1.2).
Some algorithms exist for automatically tracing molecular contours [66], but they have difficulties
tracing flexible molecules with persistence lengths much less than contour lengths or molecules withsignificant variation in height (e.g. a protein-DNA complex).
In addition to contour-dependent statistics, molecular volumes are approximated by fitting
models to the height near a feature of interest. For example, a two-dimensional elliptical Gaussianfunction with six parameters (height, center in x, center in y, variance in x, variance in y, ellipticalangle) is a reasonable model for local fits to DNA or protein-DNA complexes which are well-adhered
to a surface. Since the radius of a cantilever influences observed widths of objects on a surface [67],volumes obtained in this manner should be deconvolved [68] in order to estimate absolute volumes
or compare between different cantilevers with generally different tip radii. For samples with DNA,
one method of decovolution measures the cross-sectional area of the DNA and sets it equal to its
expected value (since the radius of DNA is about 1 nm).

39

Table 2.3: Imaging troubleshooting . Advice and suggestions for imaging via AFM
ProblemFeatures appear larger
or blurrier than expectedFeatures appear thinnerthan expected

Possible cause
Cantilever not in good
contact with sample

Action to take
Increase integral gain or drive
amplitude

Cantilever applying ex- Decrease integral gain or drive
cessive pressure to sam- amplitude
ple
Surface has unexpected, Feedback loop is caus- Decrease integral gain
small-scale periodic fea- ing ringing
tures
Surface is sticky or sam- Cantilever is engaged Decrease drive amplitude orples attach to cantilever too hard to the surface raise set point
Image appears unex- Drive frequency is excit- Choose a different tune peak
pectedly featurelessing cantilever noise
close to first thermal resonanceHigh apparent move- Cantilever applying ex- Sweep set point and drive amment of sample
cessive pressure on sam- plitude while keeping their raple
tio approximately constant
Accumulating < 1 nm Impure water used in Replace water filter or use bottall by ≈ 10 nm wide buffers
tled water for rinsing
features
Evaporation of imaging Check AFM holder seal; inbuffer
crease vapor pressure.
Unexpected > 1 nm tall Mica cleaved poorly or Deposit new sample on newby ≈ 10 nm wide fea- locally imperfectmica surfacetures
Sample appears discon- Tip is too sharp
Allow sample to settle, use
tinuousduller tip
Extreme drift or inter- failure of epoxy between re-make sample
ferencemetal and mica
Abrupt loss of surface Non-specific adhesion of De-wet/Wet cantilever a few
tracking
molecule to cantilever
times

40

2.2

Force spectroscopy and landscape reconstruction via AFM

2.2.1

Sample storage and handling

The storage of DNA and protein samples for SMFS is as described in Section 2.1.1.3. In
brief, DNA samples should be stored at -20 ◦ C and protein samples should be stored at -80 ◦ C.
Liquid samples should always be flash frozen from room temperature, and frozen samples should
be quickly thawed on a room temperature block. After thawing, samples should generally be kept
at 4 ◦ C prior to use. All experiments are performed at room temperature, which is a chilly 19 ◦ C
for the room housing the AFMs.

2.2.2

Sample deposition

The technique for covalently attaching protein or DNA to a poly-ethylene glycol (PEG)
coated surface is described elsewhere [69] and in Chapter 4. Here, I provide additional advice for
improving data throughput and quality. Briefly, the covalent attachment strategy is:• Glass is first cleaned and functionalized with a treatment in potassium hydroxide (KOH)• Cleaned glass is activated by exposure to ultraviolet light• Activated glass is incubated with a heterobifunctional PEG linker∗ One end of the linker is a silane (for covalent attachment to the glass)∗ One end of the linker is the binding partner for the intended sample (e.g. silane-PEGmaleimide for a thiol-labeled protein)• Solvent-rinsed, PEG-coated glass is incubated with the desired sample

41• Excess sample is rinsed away
The functionalization procedure for cantilevers is similar to the surface protocol listed above,
except sometimes the cantilevers use a different chemistry (e.g. maleimide for the cantilever, azide
for the surface).
The most commonly confounding phenotype of problems in a single-molecule force spectroscopy (SMFS) experiment is a lack of attachments. When this happens, there are three possible
causes: the sample, the cantilever, or the surface. Combinations of failures are also possible (e.g.
the surface and tip both fail). Below, I lay out strategies for discriminating between these sourcesof failure.
Surface functionalization is tested by using a previously-validated cantilever on a new surface, or by incubating test surfaces for an hour in a fluorescent dye labeled with the appropriate
chemistry. Figure 2.6 shows that incubating about 600 nM of DBCO-labeled AlexaFluor647 on asurface functionalized with Silane-PEG-Azide gives a strong fluorescence signal relative to a negative control. Good negative controls are an unlabeled glass surface or (better still) a PEG-coatedsurface with a ‘fluorophore-orthogonal’ labeling chemistry. For example, a silane-PEG-maleimide
surface would be an excellent negative control for a DBCO fluorophore, since there is no expectedsite-specific binding between the maleimide and the DBCO.
Cantilever functionalization is validated by testing the cantilever on a previously working
surface. Typically, DNA surfaces are active for months after successful deposition, assuming they
are kept from drying. Hence, DNA positive controls provide a way of considerably reducing thedebugging search space, and maintaining DNA controls is critical for reducing time determining
the root cause of experimental failure (i.e. determining the culprit among the sample, surface, andcantilever). A positive control is always a good use of time prior to the day’s ‘proper’ experiments,
whether the control validates a ‘new’ cantilever’s activity on last week’s surface or tests a ‘new’surface using last week’s cantilever. Consistently taking time to verify the controls are working will

42

Figure 2.6: Verifying surface functionalization via fluorescence imaging. Fluorescenceintensity (red circles, mean ± std. dev.) of silane-PEG-Azide surface as a function of concentrationof DBCO-PEG-AlexaFluor647, with representative images above their indicated concentrations.
Fluorophores were incubated for 1 hour in PBS on the surfaces before rinsing with PBS. Imaging
was carried out with a 652 nm emission filter and 631 nm excitation LED. Green line is a fit of thedata yielding a dissociation constant of 620 ± 20 nM (mean ± fitting error), assuming 10 µM wasclose to the surface saturation point.

50 m

25000

Intensity (au)

20000
15000
10000
5000
0

KdApp = 620 ± 20 nM
10 3

10 2

10 1

100

[DBCO-PEG-AF647] ( M)

101

102

43
save time, on average.
Bulk methods should be regularly employed to assay sample activity and general ‘health’.
In particular, since single-molecule experiments are slow, bulk controls should be performed, anda positive result should be obtained before performing single-molecule experiments. For example,
an electrophoretic mobility shift assay (EMSA) can easily yield sizes of the largest populationsof nucleic or amino acids present in a sample. Unfortunately, EMSA results do not generally giveinformation about the structure of a sample. In other words, the sample may be the correct size but
be misfolded or (for enzymes) be inactive. However, including a binding partner in an EMSA may
give useful information on the activity or labeling efficiency of the sample. For example, an EMSA
of a sample with the appropriate control lanes can yield the fraction of biotin- or DBCO-labeled
sample as assayed by a shift when incubated with streptavidin or bovine serum albumin labeledwith azide, respectively. Activity assays are generally enzyme-specific, but verifying bulk activity
should be a pre-requisite for any single-molecule study.

2.2.3

Data acquisition

Functionalized cantilevers should always be gently moved into and out of the appropriate
buffer (i.e. never into or out of air or an non-physiological buffer). Other than ensuring thesurface and tip are never exposed to an inappropriate buffer, the process for loading surfaces
and calibrating cantilevers for force spectroscopy is the same as in Section 2.1.3. For example,
cantilevers functionalized with streptavidin are stored in plastic wafers with a small amount ofPBS, and before securing the cantilever to the cantilever holder, a small amount of PBS shouldbe placed on the region of the holder where the cantilever will be fixed. In general, cantilevers
and surfaces with functionalized biomolecules (as opposed to commercially available, ‘off-the-shelf’imaging cantilevers) should never be exposed to pure water or organic solvents, to avoid damaging
the biomolecule of interest on the surface or cantilever.

44

Figure 2.7: Flowchart for AFM SMFS operation.

Conventions are as in Figure 2.3.

Load surface
into AFM

Rinse, dry holder

Add 0.1 mL buffer to holder
Secure cantilever to holder
Rinse holder with buffer
Raise stage, load cantilever
Cantilever folded or Sum < 1 V
Cantilever visible and Sum > 1 V

Wet/dewet
Cantilever

Cantilever visible and Sum > 1 V Cantilever folded or Sum < 1 V
Position cantilever
50 microns above surface

Unload current cantilever

Slowly approach surface

Setpoint not triggered

Setpoint triggered
Measure InVOLS, k
Set FEC parameters
Create grid of points
No more grid points
Probe new grid point

No attachment
or multiple attachment

Single attachment
Unreliable attachment
Equilibrium

Adjust parameters
depending on data needs

Unreliable attachment

Reliable attachment Force ramp Reliable attachment

Program pauses at stage positions
exhibiting transitions using indenter

Program constant stage velocity
near region of interest

45
Loading and calibrating a cantilever for a force-spectroscopy experiment is as described for
imaging methods in Section 2.1.3, but acquiring SMFS data has different steps (see Figure 2.7).
Once at the surface, molecules are found by searching a two-dimensional grid (e.g. 30 µm by 30µm) with between 100 and 1000 points, and a force extension curve is acquired at each point on
the grid. Brief pauses or an event detection algorithm facilitate re-visiting a grid point whichshows an attachment signature (Figure 2.8 A). For BioLever Long cantilevers, drag forces become
appreciable (one pN or more) for approach velocities greater than several hundred nanometers per
second. Therefore, unless the assay of interest is qualitative (e.g. determining surface activity),
approach velocities using BioLever Longs should be limited to 500 nm/s or less (or a loading rateof about 3 nN/s or less) to avoid introducing errors on the order of 1 pN or higher.
If a surface-bound molecule has appreciable extension at zero force (e.g. a polyprotein), thenudger panel or a sweep of the x and y positions should be employed to find the attachment pointof the molecule and move the cantilever to that position [70]. A centered molecule which easily
refolds can be repeatedly un- and re-folded for minutes or hours. For the Cypher AFM, a simple
way to refold a centered molecule or to take equilibrium data (long dwells at forces near F1/2 , see[36]) is to program the desired stage positions into the function editor provided by the Asylum
software for the Cypher in the indenter panel.

2.2.4

Data analysis and processing

Analysis of force spectroscopy data necessitates several stages of processing, as shown in
Figure 2.8. In brief, each curve is filtered, zeroed, and aligned to one or more regions in the force
extension curve. These processed curves are used as an input to one or more energy landscapeanalysis schemes, as described in Chapter 1.
The first step in processing SMFS data necessitates filtering force-extension curves (FECs)
in order to reduce data size and processing time. Typically, a second-order Savitsky-Golay filter

46[71] is used, since it excels at preserving edges (Figure 2.8 A).
After filtering the data, the separation and force of the FEC must be zeroed. Zeroing thedata obtained from modified cantilevers is often complicated by an optical interference artifact
which corrupts the measured deflection voltage (and hence the measured force) [72]. Fortunately,
for relatively drift-free data, the artifact is a simple function of the stage position (Figure 2.8
B). Therefore, a smooth spline fit to the approach portion of the force-extension curve (hereafter‘approach’) provides an excellent approximation to the optical interference which can then be subtracted from the retract curve (Figure 2.8 C–D). After subtracting out any interference artifact(and assuming minimal drift and drag force), the zero force is estimated as the mean force after the
final molecular detachment in the retract, and the zero separation is approximated by the value ofthe separation at the first time when the force is equal to the zero force in the rupture curve.
Even after zeroing, overlaying multiple FECs necessitates alignment, since the curves exhibit
high apparent variation due to tip attachment location or heterogeneity in linker length. Aligning
to a well-characterized and obligate rupture event typically yields higher-quality results (Figure
2.8 E). If a particular transition is of interest, the closest obligate rupture event to that transition
should be used to improve the local alignment at that event. Rupture events can be detected using
the algorithm discussed in Chapter 4.
Figure 2.8 (following page): Processing AFM force-extension curves (FECs). (A)A plot of the force applied during the approach (red) and retract (blue) portion of the cantilever
movement. Raw data is 50 kHz, smoothed data is 400 kHz. (Inset) A detailed plot of the low-force
interference artifact present in both the approach and retraction. (B) The raw force during theapproach curve (light red) is plotted alongside a fit of a spline to the force as a function of the stage
position. The spline is only fit above the surface as defined by the trigger force and loading rate.
Therefore, for small stage positions the spline is set to its boundary value. (C) The interference
artifact and zero force offset are greatly reduced by subtracting the approach spline of panel B fromthe filtered data from panel A. (Inset) A detailed plot of the low-force behavior demonstrates thesubtraction was successful. (D) As panel C, but the data are now plotted at force-versus extension.
(E) A detailed plot of the region in panel D where a molecule is present. A freely-jointed chain
model (black dotted line) is fit to the region preceding the final rupture.

47

48
Once the curves are aligned, energy landscapes are reconstructed using non-equilibrium methods like the Inverse Weierstrass Transform (Chapter 5), reconstructed using equilibrium methods
such as the Inverse Boltzmann (Section 1.3.1), or energy landscape parameters are calculated via
other methods (e.g. Equation 1.4).

Chapter 3
Imaging DNA Equilibrated onto Mica in Liquid using Biochemically Relevant
Deposition Conditions

Reprinted (adapted) with permission from:

Patrick R. Heenan and Thomas T. Perkins. Imaging DNA Equilibrated onto Mica in Liquid Using
Biochemically Relevant Deposition Conditions. ACS Nano, 13(4):4220–4229, April 2019.

Copyright (2019) American Chemical Society.

3.1

Abstract

For over 25 years, imaging of DNA by atomic force microscopy (AFM) has been intensely
pursued. Ideally, such images are then used to probe the physical properties of DNA and characterize protein-DNA interactions. The atomic flatness of mica makes it the preferred substrate forhigh signal-to-noise ratio (SNR) imaging, but the negative charge of mica and DNA hinders deposition. Traditional methods for imaging DNA and protein-DNA complexes in liquid have drawbacks:
DNA conformations with an anomalous persistence length (p), low SNR, and/or ionic deposition
conditions detrimental to preserving protein-DNA interactions. Here, we developed a process tobind DNA to mica in a buffer containing both MgCl2 and KCl that resulted in high SNR imagesof equilibrated DNA in liquid. Achieving an equilibrated 2D configuration (i.e., p = 50 nm) not50
only implied a minimally perturbative binding process, it also improved data quality and quantity because the DNA’s configuration was more extended. In comparison to a purely NiCl2 -based
protocol, we showed that an eight-fold larger fraction (90%) of 680-nm-long DNA molecules could
be quantified. High-resolution images of select equilibrated molecules revealed the right-handed
structure of DNA with a helical pitch of 3.5 nm. Deposition and imaging of DNA was achieved
over a wide range of monovalent and divalent ionic conditions, including a buffer containing 50
mM KCl and 3 mM MgCl2 . Finally, we imaged two protein-DNA complexes using this protocol:
a restriction enzyme bound to DNA and a small three-nucleosome array. We expect such deposition of protein-DNA complexes at biochemically relevant ionic conditions will facilitate biophysicalinsights derived from imaging diverse protein-DNA complexes.

3.2

Introduction

Atomic force microscopy (AFM) is widely used to image and thereby characterize the properties of DNA and diverse proteins bound to DNA, including RNA polymerase, restriction enzymes,
and nucleosomes [9–24]. Biophysical insights arise by acquiring images with a high signal-to-noise
ratio (SNR) and rely upon preserving the native properties of protein–nucleic-acid complexes thatcan vary strongly with ionic conditions. Tapping-mode imaging in liquid rapidly emerged as theimaging modality of choice as it minimizes the lateral forces that can damage or disrupt fragile
biological samples [42]. Unfortunately, a complementary and consensus method for preparing DNA
and protein-DNA samples has yet to emerge. For instance, current protocols for imaging DNA in
liquid capture DNA in compact, mechanically unequilibrated conformations that hinder analysis
and interpretation. An ideal protocol would be rapid, preserve the native properties of the DNA
and protein-DNA interaction in liquid, and yield high SNR images. Because of the lack of suchan accessible protocol, protein-DNA complexes are still often imaged in air after rinsing them inultrapure water [74–76], a distinctly non-physiological protocol.

51
Mica is the preferred substrate for high SNR images due to the simplicity of generating
clean, atomically flat substrates. For imaging in liquid, two main strategies have emerged to bindnegatively charged DNA to negatively charged mica: mica derivatized with a positively charged
silane [11] and Ni2+ -treated mica [47, 77], where Ni2+ ions have been preferred over Mg2+ due
to stronger binding of the DNA to mica that facilitates imaging [47]. However, each techniquepresents important drawbacks. For instance, condensation and/or clumping of DNA can occur onsilanized mica in the presence of divalent cations [78]. For Ni2+ -treated mica, it has been difficult
to deposit and image DNA when monovalent cations are present [79–81]. Yet, numerous ensemble
protein-DNA assays contain both MgCl2 and a monovalent salt (e.g., KCl or NaCl). Hence, tominimally perturb protein-DNA complexes, one should deposit them in a buffer containing both
MgCl2 and KCl and image in liquid, a difficult regime for AFM studies.
The benefits of silanized mica, including those prepared with silatranes [82], are that they bindDNA under a relatively broad range of buffer conditions [23, 48]. Two drawbacks of silanized micaare (i) the time needed to prepare silanized surfaces, and (ii) the reduced SNR of the images due tohigher surface roughness, a drawback that is partially mitigated when using a more time-intensive
sample preparation process [11, 23, 83]. A notable recent application of silanized mica in liquid [23]was successfully deducing the correct persistence of DNA (p ≈ 50 nm) [84], indicating such images
can yield the native backbone stiffness of DNA. To do so, however, the authors needed to apply a 3D
worm-like chain (WLC) model to analyze select 2D conformations of DNA. This analysis indicatesthe DNA was rapidly absorbed and thereby adopted a “kinetically trapped” polymer configuration[17, 23, 48]. If a 2D WLC model is used to analyze the fraction of interpretable conformations,then the derived p is ≈ 25 nm, well below the consensus value of p. As expected for such a low
apparent p, kinetically trapped DNA molecules have a more compact configuration and thereby anincreased number of multiple strand crossings that hinder analysis (Figure 3.1 A, red). In contrast,
if the deposition process achieves an “equilibrated” 2D WLC configuration, the conformations are
more extended (Figure 3.1 A, green) and thus a higher percentage of conformations that contain

52

Figure 3.1: Configuration of DNA on mica depends on the details of the deposition
process.
(A) A cartoon illustrating AFM imaging of DNA in two different configurations: anextended, equilibrated one (green) and a compact, kinetically trapped one (red). Yield is definedas the ratio of DNA configurations containing one or zero strand crossings divided by the numberof total molecules fully contained in a set of images. The persistence length (p), a measure ofpolymer backbone stiffness, is determined by the angle between tangent vectors (θ) along the path
length s using a 2D WLC model. Credit: S. Burrows/JILA. (B) An AFM image of DNA in liquid
when deposited under biophysically relevant ionic conditions (10 mM MgCl2 + 25 mM KCl) andsubsequently imaged in 10 mM NiCl2 + 25 mM KCl after pre-treating the mica with 100 mM
NiCl2 . The yield was high (90%) and analysis of the resulting DNA configurations yielded thecorrect persistence length (≈ 50 nm). (C) An image of DNA deposited on mica at 10 mM NiCl2 +25 mM KCl and imaged in the same buffer after gentle rinsing. (D) An image of DNA depositedat 25 mM KCl on mica coated with APTES. All solutions were buffered with 10 mM HEPES(pH 7.5). We note that these conditions were not optimized for the NiCl2 deposition buffer and
APTES-derivatized mica protocol used in panels, C–D respectively. All images are 2×2 µm2 andare colored using the same vertical scaling. Acronym: APTES, (3-Aminopropyl)triethoxysilane.

53
zero or one strand crossings. Quantitatively, a DNA molecule is defined as equilibrated if analysis
of its 2D conformation with a 2D WLC model yields the correct of value of p, a definition consistent
with prior DNA imaging studies [23, 40]. Such equilibration is distinct from other studies that haveobserved real-time adsorption and desorption of local segments of DNA from bare mica in liquid[85].
In Ni2+ -treated mica, the interstitial K+ ions at the surface of the mica lattice are ion
exchanged with Ni2+ , yielding a positively charged surface [79, 86]. The DNA is typically depositedin the presence of ~1–20 mM NiCl2 [47, 86, 87]. The benefits of Ni2+ -treated mica are that it yields ahigher SNR and requires less preparation time than silanized mica. There are, however, drawbacks:[23] (i) the resulting DNA configurations are kinetically trapped, when imaging in liquid [40];(ii) non-physiological ionic conditions (NiCl2 with little or no monovalent cations) are required
to achieve sufficiently tightly bound DNA that in turn yields interpretable images [23, 47, 79];
and (iii) extensive tuning of buffer conditions [47, 79, 88]. For completeness, as noted above,
a popular protocol deposits protein-DNA complexes onto Ni2+ -treated mica followed by rinsing
with ultrapure water and then imaging in air [41, 87, 89]. While such a protocol has achieved
equilibrated DNA when imaging in air, [40] we avoided this class of protocols to preserve native
protein-DNA interactions. Moreover, a recent study shows partial conversion of DNA’s structurefrom the traditional B-form to A-form when bound to Ni2+ treated mica in air [78]. Summarizing,
the consensus in the field is that stable DNA imaging on Ni2+ -treated mica requires a narrowwindow of ionic conditions (e.g., Ni2+ cations in the absence of monovalent cations) [23, 79, 83].
Here, our goal was to develop a simple and reproducible protocol for acquiring high SNR
images of equilibrated DNA in liquid when deposited at biochemically relevant ionic conditions (e.g.,
10 mM MgCl2 + 25 mM KCl). Our protocol was not based on a single modification to an establisheddeposition scheme, but instead on a set of changes including pre-incubating the mica with 100 mM
NiCl2 , gentle rinsing, and never dewetting the sample. For increased robustness during imaging, we
subsequently exchanged an equimolar concentration of NiCl2 for MgCl2 . Analysis of the resulting

54
DNA configurations yielded the correct persistence length (≈ 50 nm) when using a 2D WLC modeland did so over a wide variety of monovalent salt concentrations. These equilibrated configurations
were more extended (Figure 3.1 B) than when 10 mM NiCl2 replaced the 10 mM MgCl2 in thedeposition buffer (Figure 3.1 C) or the DNA was deposited onto silanized mica (Figure 3.1 D).
Importantly, our protocol used only standard, commercially available reagents, took ~5 min, andworked over a range of DNA substrate lengths (300–2,000 bp) and in a standard commercial AFM.
Unexpectedly, divalent cations in the imaging buffer were not required; we successfully imaged
DNA on mica pre-incubated with 100 mM NiCl2 when using an imaging buffer containing only
monovalent ions albeit at some loss in data throughput and a reduction in p (35 nm). Biophysicalapplicability was demonstrated by imaging two protein-DNA complexes, a restriction enzyme boundto DNA and a small nucleosome array.

3.3

Results and Discussion

We first present the final protocol, then discuss the process of achieving this protocol andhow it generalizes to an unexpectedly broad range of ionic conditions for deposition and imaging,and finish by imaging a pair of protein-DNA complexes. In developing our protocol, we used two
primary metrics: yield and persistence length. Yield was defined as the ratio of DNA configurations
containing zero or one strand crossing divided by the number of total molecules fully contained
within a set of images; such configurations facilitate analysis and the effect of proteins on the
DNA conformation. Persistence length was determined from the 2D WLC model by analyzing the
average tangent angle as a function of arc length along the DNA for molecules displaying zero or
one crossing (Figure 3.7) [40, 90]. Achieving a persistence length of ≈ 50 nm—in agreement withensemble [84] and single-molecule force-spectroscopy [23, 91, 92] studies—would therefore reflect
DNA bound to the mica in an equilibrated state (see Methods).

55
3.3.1

Rapid and biochemically relevant DNA deposition protocol

Our final protocol consisted of three main steps (Figure 3.2). In the first step, we placed a
20-µl drop of unbuffered 100 mM NiCl2 onto freshly cleaved mica for 1 min followed by rinsing
with ultrapure water and drying by touching the mica surface with filter paper. Importantly, thisstep— before depositing any DNA or protein-DNA complexes—was the only time the surface wasdried and indeed the method of drying affected the final outcome (Figure 3.8). In the second step,
we deposited a 20-µl drop of dilute DNA in Deposition Buffer [10 mM MgCl2 , 25 mM KCl, 10 mM
HEPES (pH7.5)] onto the mica for 2 s before gently rinsing with 9 ml of Deposition Buffer (seeMethods for details). Successful imaging of the DNA after such extensive rinsing demonstrated
that DNA stayed attached to the Ni2+ -treated mica in the presence of 10 mM MgCl2 . Finally, inthe third step, we rinsed the mica with Imaging Buffer [10 mM NiCl2 , 25 mM KCl, 10 mM HEPES(pH7.5)] where the NiCl2 -containing buffer trapped the equilibrated state of the DNA bound to themica by increasing the DNA-mica interaction strength. This entire process starting from cleaving
the mica to loading the sample into the AFM typically took ~5 min.

3.3.2

Improved protocol relies upon a series of refinements

Our final protocol evolved via a series of modifications that collectively were critical to achieving high yield while minimizing the influence of the substrate on the nanomechanics of the DNA,
as evidenced by the deposited DNA adopting extended conformations with the correct persistence
length. For conciseness, a subset of the deposition conditions tested are shown in Figure 3.3 toillustrate sequential improvement. Figure 3.3 A shows representative images of the DNA configurations at select steps along this evolution accompanied by a summary of the deposition conditions
at each step. The change in the conditions between the steps is highlighted in blue. Figure 3.3
B–C reports the yield and average persistence length of analyzed molecules. We note that thesedata (images, yield, and persistence length) were representative of our results at each step, not56

Figure 3.2: Rapid three-step protocol for preparing DNA for imaging on mica in liquid.
This protocol consisted of three main steps. First, freshly cleaved mica was incubated with NiCl2
at a ~10-fold higher concentration than traditionally used, rinsed with ultrapure water, and thengently dried. Second, dilute DNA was deposited onto the Ni2+ -treated mica at biochemically
relevant ionic conditions and then the mica was extensively rinsed with deposition buffer. In the
final step, the equilibrated configuration of the DNA was fixed for more robust imaging by increasing
the interaction between the DNA and the mica by using an imaging buffer that contained 10 mM
NiCl2 . As discussed in the text, imaging in NiCl2 was not required.

57
necessarily the best achieved. We did not optimize intermediate steps along the process but rather
looked for a set of conditions that led to a simple and robust deposition protocol at biochemically
relevant conditions. In total, over 2,500 molecules were analyzed in this work when including the
Supporting Information.
The starting point for our modifications featured ionic conditions typical of Ni2+ -treated mica
protocol (10 mM NiCl2 in the pre-treatment, deposition, and imaging buffers with a 2 mL rinse). As
expected, these conditions resulted in a high proportion of kinetically trapped molecules that led toa low yield and persistence length (Figure 3.3 A, Step 1). By increasing the concentration of NiCl2
used to pre-treat the mica, we marginally increased the yield (Figure 3.3 A, Step 2). Perhaps more
importantly, we observed that the uniformity of the DNA on the surface dramatically increased(Figure 3.9), presumably because the higher NiCl2 concentration overcame the previously described
patchiness of Ni2+ on mica when incubating at 15 mM NiCl2 [86]. [Note, uniformly charged Ni2+ treated mica may be broadly useful in a variety of AFM applications. As a proof of principle, we
imaged the 2D lattice of bacteriorhodopsin (Figure 3.10)].
Next, we replaced the NiCl2 in the deposition and imaging buffers with MgCl2 , which led toa fraction of the DNA molecules exhibiting the correct persistence length (Figure 3.3 A, Step 3).
However, the fraction of molecules exhibiting that equilibrated confirmation was low due, in part,to the weak DNA-mica interaction. In other words, these initial imaging experiments with only
MgCl2 in solution featured well-equilibrated DNA, but the DNA was too weakly bound for reliabletapping-mode imaging. We note that this intermediate finding is consistent with previous studies
in air [40] and liquid [47], though our final protocol does allow us to deposit and image in buffer
containing MgCl2 and KCl but, notably, no NiCl2 . In other words, NiCl2 in the final buffer is
not necessary but improves data quality by binding the DNA more strongly to the surface (Figure3.11); successful imaging in NiCl2 is therefore less stringent in its requirement of gentle imaging
conditions (e.g., low-amplitude tapping, see Methods for details).

58

Figure 3.3: Improved DNA deposition required a sequence of refinements.
(A) A
set of tapping-mode images of DNA in liquid deposited under different deposition protocols assummarized in each box. The change between each deposition process is highlighted with blue text,
and protocols associated with images are denoted with magenta boxes. (B–C) The percentage yieldof interpretable DNA molecules and their corresponding persistence length (p) is depicted below
each protocol. These values were computed from ~90 DNA molecules per condition with necessarily
more images acquired at deposition protocols with a poor yield. Error bars represent the standard
deviation for the yield and the fitting error for the persistence length. Persistence length was
deduced using a 2D worm-like chain model. Solid symbols are associated with the images shownin panel A.

59
We next combined the merits of depositing in MgCl2 (to facilitate DNA equilibration) withimaging in NiCl2 (for more robust imaging)(Figure 3.3 A, Step 4). A useful analogy may befound in film photography, where an image is first developed before it is fixed or stabilized. In
this analogy, the surface-bound DNA is the image, MgCl2 -based equilibration is the development
process, and the NiCl2 -based imaging buffer is the fixing procedure. We continued to refine ourdeposition process to enhance the yield of molecules showing only one or zero strand crossings byreducing the deposition time and increasing the DNA deposition concentration (Figure 3.3 A, Step
5). Although the underlying mechanism for this improvement is unclear, it was experimentally
reproducible across multiple samples on multiple days. Finally, we found that extensive (9 mL),but gentle, rinsing improved the equilibration of the DNA onto the mica (Figure 3.3 A, Steps 6–7;
see also Figure 3.2, Step 3). Introducing a small tilt during the extensive rinsing further improved
yield, presumably because it helped avoid accidental dewetting (Figure 3.12) and the resulting highforces generated by a receding meniscus on a surface-bound DNA [i.e., molecular combing (F > 65pN)] [93, 94].

3.3.3

High yield of equilibrated DNA on mica in liquid

By analyzing images acquired with our final protocol, we quantified the yield and the persistence length. The yield was 90% when imaging 680-nm-long DNA molecules [N = 142], an 8-foldimprovement over depositing the DNA under identical DNA concentration and total ionic strength
but substituting 10 mM NiCl2 for the 10 mM MgCl2 and rinsing with 2 mL of buffer (N = 116).
Analysis of the DNA images yielded an average persistence length of 46.8 ± 0.6 nm (mean ± fitting
error; N = 126)]. (Figure 3.3 C; Figure 3.7), demonstrating the analyzed molecules had adopted
a 2D equilibrated configuration on the mica. Indeed, of those molecules that contributed to the
90% yield, about 20% contained a looped configuration, consistent with expectations from a simple
simulation that did not account for excluded volume effects (Figure 3.13). As a cross check, we
deduced p from the distribution of end-to-end distances as a function of arc length, yielding p = 45

60
± 4 nm [mean ± fitting error (Figure 3.14)] in quantitative agreement with p derived from the tangent vectors analysis. Finally, we note that the values for persistence and contour lengths obtained
from human-annotation (see Supporting Information) were consistent with the values obtain using
an automated analysis routine (Figure 3.15) [66].

3.3.4

High-precision measurements of DNA conformation

To quantify the SNR of the resulting images, we first measured the height of the DNA boundto mica using a metric based on the maximum height of each pixel along the spline defined along
the full contour length of each molecule, rather than a single line or set of line scans per molecule( Figure 3.16 A–B). The results yielded 2.0 ± 0.3 nm [mean ± Std. Dev.; N molecules = 100 (Figure
3.16 C)] in quantitative agreement with the DNA’s width (2.0 nm) [95]. Such agreement reflects
the gentle imaging conditions, akin to earlier results that measured a height of 1.9 ± 0.2 nm whenusing peak-force tapping set to 40 pN [81], with the advantage that the tapping-mode imaging
used here leads to higher image acquisition rates. To quantify the noise, we measured the averagesurface roughness of bare mica, Ni2+ -treated mica, and APTES-coated mica (Figure 3.17), yielding
1.14 ± 0.07 Å, 1.95 ± 0.06 Å and 4.3 ± 0.2 Å (mean ± Std. Dev.), respectively. Hence, we havemeasured the correct height for DNA and at a SNR of 10, a high SNR compared to traditional
AFM imaging of DNA [81].
To illustrate the quality of the resulting images, we show a gallery of representative DNA
configurations (Figure 3.4 A). The average persistence length for the six molecules shown is 50.8
± 0.9 nm (mean ± SEM), similar to the persistence length determined for all molecules analyzed
using the deposition protocol depicted in Figure 3.2. High-resolution scans of select segments ofindividual molecules revealed the right-handed helical structure of DNA (Figure 3.4 B). The helicalpitch of DNA has been previously resolved in liquid [81, 96] with clearer images recently achieved
when using frequency-modulated AFM [97, 98]. Here, using tapping-mode imaging, we quantified

61

Figure 3.4: Images of individual DNA molecules highlight the resulting high signalto-noise ratio. (A) A set of representative raw tapping-mode images of DNA in liquid selectedfrom a larger scan area (2×2 µm2 ) with traditional flattening. (B) An exemplary image of the
double helix of DNA acquired using a tip featuring a sharper tip radius (r nom ≈ 2 nm) and smaller
pixel size (0.5 Å) than those used in the remainder of the paper (see Methods). This image was
fit with a third order, two-dimensional spline to subtract the background, then smoothed with aGaussian with a width of two pixels (1 Å).

62
the helical pitch of equilibrated DNA to be 3.51 ± 0.04 nm (mean ± SEM) (Figure 3.18) based on
15 images from 4 different molecules and 3 different cantilevers. Our result agrees with ensemble
enzyme digestion studies that report a helical pitch of 3.6 nm [99]. This high-resolution study was
facilitated by using a cantilever featuring a sharper tip radius [r nom ≈ 2 nm (Bruker SNL-10A)]
than used in the rest of the paper [r nom ≈ 8 nm (Olympus BioLever Mini)] and by having the
fast-scan axis parallel to the DNA axis. Approximately, one out of every three of these sharper
cantilevers resolved the helical pitch of select DNA segments.
Quantification of the DNA’s contour length agreed within 1% of the expected length (Figure3.19), when using the standard rise per base pair for B-form DNA (0.34 nm/bp). [Note, as a counterexample, DNA imaged in air on mica had a 20% reduction in contour length after depositing in
MgCl2 consistent with the DNA adopting a partial A-form structure, as confirmed by spectroscopic
studies.] [78] Successful application of our protocol was not restricted to relatively long DNA, butalso worked well for 300-bp long DNA (Figure 3.20). Summarizing, we measured the correct physicalproperties of DNA (persistence length, rise per base pair, width, and helical pitch) when imaging
in liquid.

3.3.5

Depositing and imaging DNA under biochemically relevant ionic conditions

Our deposition protocol performed well across a wide range of monovalent and divalent
combinations. For example, as the concentration of KCl in the deposition buffer was varied from0 to 75 mM at fixed MgCl2 concentration (10 mM), the yield and the persistence length remained
essentially unchanged (Figure 3.5 A–B), indicating the DNA continued to adopt an equilibrated
conformation. A global fit to the dependence of p as a function of monovalent ionic strength [100]yielded 49.6 ± 0.4 nm (mean ± fitting error) (Figure 3.21), again consistent with an equilibrated
2D conformation. Equally important, the quality of the resulting images remained high (Figure 3.5
C). At the highest KCl concentration tested (225 mM), the yield remained high but the persistence

63

Figure 3.5: Equilibrated DNA deposited across a broad range of monovalent ionicconditions.
(A–B) The percentage yield of interpretable DNA molecules and their corresponding persistence length (p) plotted as a function of monovalent ionic concentration at fixed
MgCl2 (10 mM). Closed symbols are associated with images shown in panel C. For comparison,yield and persistence length acquired under typical published conditions [10 mM NiCl2 or APTESfunctionalized mica] are shown. The NiCl2 + KCl and APTES + KCl data points were determinedfrom DNA deposited as in Figure 3.1 C and Figure 3.1 D, respectively. Error bars represent thestandard deviation. (C) Sets of three representative images plotted vertically acquired at 0, 2.8, 8.3,
25 and 75 mM KCl. Nanoscale precipitates became prevalent ≥75 mM KCl but the configurationof individual DNA molecules could still be traced and hence persistence length determined.

64
length decreased to ~35 nm (Figure 3.5 A–B). At the higher KCl concentrations (≥ 75 mM), there
were also some small surface artifacts (several nm wide by 1 nm tall), presumably salt crystals.
Unexpectedly, we could deposit and image in 3 mM MgCl2 and 50 mM KCl (Figure 3.11),
ionic conditions typical of many protein-DNA assays. As expected the persistence length remained
approximately unchanged (~ 55 nm), but there was a reduction in yield to ~60% and successful
imaging required gentle imaging conditions. We could also reduce or eliminate the divalent salt
in the deposition and imaging buffers (MgCl2 and NiCl2 , respectively) after pre-treating the mica
with 100 mM NiCl2 . In the absence of any divalent cations, the yield was reduced from ~90%
to ~50% and p decreased to ~35 nm, but the configuration of individual molecules remained wellresolved (Figure 3.22). Overall, the robustness of our protocol to variations in KCl and divalention concentrations show that our methodology produced high-quality images of DNA deposited on
Ni2+ -treated mica over a wide range of monovalent and divalent salt concentrations, a regime thatwas previously thought inaccessible. That said, it remains critical to deposit with MgCl2 [or CaCl2(see below)] in lieu of NiCl2 to equilibrate the DNA on the mica. Replacing MgCl2 with NiCl2 inour deposition buffer while keeping the rest of the final protocol the same led to kinetically trappedmolecular configurations (p ≈ 25 nm) (Figure 3.23), recapitulating earlier results [40].

3.3.6

Imaging protein-DNA complexes in liquid

To demonstrate the broader applicability of our protocol, we next imaged two protein-DNA
complexes: a restriction enzyme bound to DNA and a three-nucleosome array (Figure 3.6). Restriction enzymes, which cleave DNA at specific sequences, have been repeatedly studied by AFM[16, 18, 19, 101, 102]. BspMI is a type IIs restriction enzyme that binds to the sequence 5’ACCTGC-3’ and cleaves down stream of this recognition site. Cleavage occurs efficiently when
BspMI binds to and bridges two recognition sites[103]. Like many restriction enzymes, BspMI canbind its recognition site without cleaving if Mg2+ is replaced by Ca2+ . Hence, to image BspMI

65

Figure 3.6: High signal-to-noise ratio images of protein-nucleic acid complexes deposited at biochemically relevant conditions.
(A–B) Images of the type IIs restriction
enzyme BspMI bound to a 650-nm-long DNA via the single recognition site located at the center of the DNA. CaCl2 was substituted for MgCl2 in the deposition buffer to suppress cleavage.
(C) An image showing two separate DNA molecules bridged via a BspMI complex bound to tworecognition sites. Such bridging is a key step to efficient cleavage by BspMI [101]. (D) An imageof three nucleosomes on a 621-bp-long DNA substrate containing three high affinity binding sites
for nucleosomes (i.e., the 601 Widom sequence) deposited using our standard protocol containing
MgCl2 (Figure 3.2).

66
bound to uncleaved DNA, we developed a 650-nm-long DNA with a single recognition site at its
center and replaced MgCl2 with CaCl2 in our deposition buffer (see Methods for details). With
these modifications, we acquired high-SNR images of BspMI bound to DNA in liquid (Figure 3.6
A–B). As expected, BspMI bound to the center of individual DNA molecules. In addition, we
observed DNA dimers formed by BspMI complexes bridging two separate DNA molecules (Figure
3.6 C). This behavior is well established in ensemble studies [103]. More recently, AFM studies
in air showed BspMI complexes bridging two separate binding sites after rinsing with ultrapure
water [74]. Here, we can now visualize DNA bridging by BspMI imaged in liquid and do so withsignificantly higher SNR than the prior results in air. In addition, this result validates Ca2+ as analternative divalent cation, as it also produced equilibrated DNA (p ≈ 52 nm). Finally, building
upon earlier AFM studies characterizing un-crosslinked nucleosomes in liquid [104, 105], we imaged
nucleosomes bound to three high-affinity binding sites embedded in a 621-bp long DNA (Figure
3.6 D) [106]. Hence, the robustness and flexibility of our method permitted high-SNR imaging inliquid of a variety protein-nucleic acid complexes.

3.4

Conclusions

In summary, we deposited and imaged DNA in an equilibrated conformation on mica in liquid,
implying a gentle deposition process. Equilibrated conformations were more extended and therefore
easier to analyze when determining the DNA’s configuration and the effect of proteins on that
configuration. Importantly, we used a deposition buffer that contained both MgCl2 and KCl, ionicconditions conducive to preserving native protein-DNA interactions. This success was not basedon a single modification to an established protocol, but a set of changes including pre-incubating
the mica with 100 mM NiCl2 , drying with a filter paper, gentle rinsing, and never dewetting thesample. Imaging using such Ni2+ -treated mica yielded images with high SNR. To demonstrate theutility of this protocol, we imaged two protein-DNA complexes: a restriction enzyme bound to
DNA and a nucleosome array. Looking forward, we speculate that the unexpectedly wide range of67ionic conditions that yielded such images enables tuning the binding strength of the DNA to thesurface, akin to earlier studies [88], but in buffers containing both MgCl2 and KCl. Such tuning, inturn, should facilitate studying the dynamics of protein-DNA complexes by AFM, in general, andby high-speed AFM, in particular, [88, 107] at higher SNR coupled with conditions that preserve
native protein-DNA interactions. Finally, our success in imaging protein-DNA complexes should
immediately translate to the AFM studies of DNA origami and their applications.

3.5

Methods

3.5.1

DNA samples

We purchased 300 and 2,000 base pairs (bp) DNA constructs that were HPLC purified (Fisher
SM1621, SM1701). These DNAs were diluted to 50 ng/µL in TE Buffer [10 mM Tris-HCl (pH 8.0),
1 mM EDTA] and 20-µL aliquots were flash frozen and stored at -20 °C. Individual aliquots were
thawed to room temperature and then stored at 4 °C for at most one week. For the BspMI assay,
we developed a DNA construct from λ bacteriophage (NEB N3011S) by amplifying from position
9,887 to 11,785. This PCR-amplified 1,899 bp (≈ 650 nm) segment was chosen to position the
BspMI recognition sequence (5’-ACCTGC-3’) at the center of the resulting PCR product. Afterthe DNA was purified via an agarose gel, the agarose was removed (Bio-Rad 7326165), the DNA
was concentrated (Millipore UFC501024), and purified a final time (Qiaquick 28106) before elution
into TE Buffer. The final DNA was diluted down to 180 nM in TE Buffer, aliquoted, and flash
frozen.

3.5.2

DNA deposition protocol

We deposited the DNA as outlined in the text and illustrated in Figure 3.2. More specifically,
we diluted the aliquoted DNA to 20 nM (for 2,000-bp DNA) or 80 nM (for 300-bp DNA) in our Base

68
Buffer [10 mM HEPES (pH 7.5), 25 mM KCl] using KOH to adjust the pH. A higher concentrationof smaller DNA was used to increase the number of molecules per image. We then cleaved 10-mm
diameter mica (Ted Pella, 50) affixed to a metal puck (Ted Pella, 16218). We next placed a 20-µl
drop of unbuffered 100 mM NiCl2 (Sigma 654507) onto the freshly cleaved mica for 1 min followedby rinsing with 50 mL of ultra-pure water (18.2 MΩ, Barnstead GenPure Pro). The mica was thenquickly dried by touching filter paper (Whatman 1002-042) to the center of the water droplet on
the mica, and completely drying the surface. This step was the only time where the surface wasallowed to partially or completely dewet. Immediately after drying, we deposited 20 µL of DNA in
Deposition Buffer [10 mM HEPES (pH 7.5), 10 mM MgCl2 + 25 mM KCl] where the concentrationof the DNA was 1 nM for the 2,000-bp construct or 4 nM for the 300-bp construct. After 2 s, we
gently rinsed the surface with ~1 mL of Deposition Buffer, tilted the surface to about 10°, andthen gently rinsed with an additional 8 mL of Deposition Buffer. Care was taken during rinsing to
avoid exposing any part of the surface to air or forces from a water droplet overcoming meniscus
forces and/or rapidly flowing off of the side of the mica, which could perturb the sample and may
cause salt to precipitate out of solution onto the surface. Finally, the surface was gently rinsed
with 2 mL of Imaging Buffer [10 mM HEPES (pH 7.5), 10 mM NiCl2 + 25 mM KCl]. Note, during
deposition and rinsing, solutions were kept at room temperature (19 °C for the room containing
our AFM). At all other times, the reagents were kept at 4 °C. Buffers were re-made each day fromconcentrated, 0.2-µm filtered stocks. For completeness, we note that we unexpectedly found that
NiCl2 solution made from seven-month-old NiCl2 powder yielded poor results in comparison to a
freshly purchased stock of NiCl2 or a seven-month-old 1 M stock solution NiCl2 (Figure 3.24).
The ‘NiCl2 + KCl’ protocol shown in Figure 3.1 and Figure 3.3 was prepared as above,
except using a 10 mM NiCl2 pre-treatment, and Imaging Buffer during deposition, rinsing, andimaging. Moreover, we only rinsed with 2 mL of Imaging Buffer, and omitted additional tilting andrinsing to better match more traditional NiCl2 deposition conditions. The sample was dried using
a filter paper as described above. To study DNA deposition on APTES-modified mica, we used69
our standard protocol, except substituting 0.1% APTES dissolved in water for 100 mM NiCl2 , andrinsing and imaging in the absence of divalent salt (i.e., Base Buffer), as is typical with APTEScoated mica [83]. Before DNA deposition, the APTES-treated sample was also dried using a filter
paper.

3.5.3

Depositing protein-DNA complexes

Importantly, we did not need to alter our deposition protocol for imaging protein-DNA complexes. The tri-nucleosome array was a gift of Anne Gooding and Tom Cech and based on publishedwork from the Cech lab [106]. For depositing the tri-nucleosomes, we diluted them in Deposition
Buffer to the same concentration used with the 300-bp DNA. The rest of the process, including
deposition time, remained unchanged.
For the restriction-enzyme assay, we incubated 650-nm-long DNA at 20 nM with 40-folddiluted BspMI (New England BioLabs, R0502s, 50 units/mL incubation concentration) and 10
mM HEPES (pH 7.5), 10 mM CaCl2 + 25 mM KCl as the buffer. After letting the enzyme andDNA incubate for 30 min at 30 °C, the deposition proceeded as described above, except with the
MgCl2 replaced by CaCl2 . Replacement of MgCl2 with CaCl2 allowed for site-specific binding but
without cleavage (Figure 3.6 A–C). When the same process was repeated in our standard Deposition
Buffer, the DNA was cleaved due to the expected activity of BSP-MI in the presence of MgCl2(data not shown).

3.5.4

AFM imaging

We imaged all samples on a commercial AFM (Cypher ES, Asylum Research) featuring atemperature-controlled, closed-fluidic sample holder. Sample temperature was held at 19 °C. All
images, except high-resolution images of the double helix, were obtained using an Olympus BioLever

70
Mini (r nom = 8 nm; k typ = 90 pN/nm) with a 25-kHz resonance in liquid. For imaging the double
helix, we used a Bruker SNL-10A (r nom ≈ 2 nm; k typ = 350 pN/nm), which had a 16-kHz resonancein liquid.
Prior to imaging, we let the sample and cantilever settle for at least 30 min. All images wereobtained in tapping mode with a typical set point amplitude of about 2 nm and a free amplitudeof 150% of the set point. We chose the drive frequency as the closest peak of the drive transfer
function to the thermal resonance when measured ~ 1 µm above the surface. All data presented
in this paper used 2×2 µm2 images with 512 pixels acquired at a 2-Hz scanning rate, except thoseof the double helix (Figure 3.4 B and Figure 3.18), images with protein-DNA complexes (Figure3.6), and bacteriorhodopsin (Figure 3.10). The images of the double helix were taken with thesame parameters, except the following changes: set point amplitude (~ 0.5–1 nm), free amplitude(~ 0.7–1.5 nm), and image size (20–100 nm). The images of bacteriorhodopsin or protein bound to
DNA used similar imaging parameters to the double helix, except the image size varied as follows: ~25 nm for bacteriorhodopsin, ~ 200 nm for the trinucleosomes, and ~ 600 nm for BspMI. The double
helix images were taken with the fast-scan axis along the axis of the DNA to improve resolution by
reducing low-frequency noise between line scans and tip-convolution artifacts.

3.5.5

Surface roughness of bare and treated mica

To quantify the difference in surface roughness between Ni2+ -treated mica and our APTEScoated mica, we created mica surfaces without adsorbed DNA and thereby measured the noise
floor of our AFM measurement system in liquid as a function of surface treatment. The NiCl2
and APTES test surfaces were prepared as described above, except omitting DNA in any of thebuffers. As a control, we used unmodified mica that was rinsed and imaged in Base Buffer. All
measurements that quantified the noise were obtained in the appropriate imaging buffers with thesame individual cantilever on the same day. Other imaging parameters were consistent with the

71
DNA experiments as discussed above, and we analyzed 3 images at each condition. As shown in
Figure 3.17, bare mica showed the lowest surface roughness as measured by the standard deviationof the height [0.74 ± 0.03 Å (mean ± Std. Dev.)], with a measurable increase due to Ni2+ -treatment(1.18 ± 0.03 Å). As expected, the noise floor on APTES-coated mica was significantly higher (2.5
± 0.1 Å).

3.5.6

Imaging bacteriorhodopsin

To see if Ni2+ -treated mica might be useful in other AFM applications, we imaged bacteriorhodopsin embedded in its native lipid bilayer, the prototypical protein for AFM studies ofmembrane proteins [108]. In initial experiments using standard bacteriorhodopsin imaging conditions (10 mM TrisHCl (pH 7.8), 150 mM KCl) [109], we resolved voids in the trimer lattice. Note,
this proof-of-principle experiment was not optimized for image quality (Figure 3.10). Rather, we
just wanted to demonstrate that the benefits of Ni2+ -treated mica were not limited to protein-DNA
complexes.

3.5.7

Image analysis

We analyzed all AFM images of DNA using a semi-automated algorithm to determine theyield and persistence length. First, all DNA molecules fully contained within a single 2×2 µm2 image were manually classified as either an interpretable individual DNA configuration that contained
zero or one strand crossings (Figure 3.1, green), uninterpretable configurations that contained 2
or more strand crossings (Figure 3.1, red) or multiple overlapping individual DNA molecules. We
classified molecules with two or more loops as kinetically trapped due to their low apparent persistence length. Surface artifacts (e.g. a salt crystal) that could be reliably identified as not a DNA
molecule were ignored. The yield, Y, was defined as:

72
Y = 100 * N interpretable /(N interpretable + N uninterpretable + N overlapping ) Eqn. 1
where a yield of 0 indicates completely uninterpretable data, and a yield of 100 indicatescompletely interpretable data.
We quantified the angle θ between two tangent vectors separated by arc length s to measure
the persistence length (p) of a molecule via AFM imaging (Figure 3.1 A). The tangent vector wasdetermined by fitting a third-order, least-squared polynomial spline through user-defined points
spaced about every 10 nm along interpretable DNA molecules, excluding the looped sections ofinterpretable molecules that contained a loop (20%). The persistence length at a given condition
was then obtained by a least-squares fit of the following equation for all interpretable molecules atthat condition:ln(<cos(θ(s))>) = -s/2p Eqn. 2.
The helical pitch was quantified by marking the position where the periodic structure of one
DNA strand repeated. The position where a repeat crossed the axis of the DNA was manuallybounded by two points, and the region in between these human-annotated points was fit with aparabola. The maximum of the parabola was considered the location of the repeat, where the fit
was localized to a line of length 10 Å or less along the DNA axis. In other words, the humanannotated helical pitch location was refined by determining the local maximum in the DNA heightfrom a parabolic fit. From two adjacent helical pitch locations on the same DNA strand, major
pitch values were recorded as the total change in contour length. Both strands were measured
separately in our estimation of the helical pitch.

3.5.8

Automated annotation

To verify that the human-annotated DNA contours were unbiased, we adapted a previously
published method [66] for automated contour tracing. Briefly, the start and end of the each DNA

73
were manually annotated. A second point near the start of the DNA molecule was needed todefine an initial tangent. After determining an initial tangent vector, the algorithm then iteratively
update its estimation of the tangent vector until it reaches the opposite end of the DNA. The
algorithm did not converge in roughly 20% of cases (i.e. took over 1000 steps of length 2 nm on
a 680 nm piece of DNA), due to the presence of loops in DNA causing recursion. The analysis
for the automatically generated contours was the same as described for the manually annotateddata, except the computationally generated contour was used directly (i.e., there was no splineinterpolation for the automatically traced data).

3.6

Author contributions

P.R.H. and T.T.P. designed the experiment. P.R.H optimized the assay conditions andacquired all of the data. P.R.H. developed the analysis techniques and algorithms. P.R.H. and
T.T.P. wrote the manuscript.

3.7

Acknowledgments

We thank Anne Gooding and Tom Cech for their gift of the trinucleosome array.

3.8

Supporting Information

3.8.1

Figures

74

Figure 3.7: Determining persistence length from AFM images. (A) AFM images of
DNA deposited under biophysically relevant ionic conditions per our protocol as outlined in Figure
3.2. (B) A human-annotated spline denoting the DNA configurations shown in panel A. The path
length along the configuration is s and θ is the angle between the tangent vectors separated by s.
(C–D) Plots of angular correlation as a function of s. When plotted as –ln <cos(θ)> vs s, the data
yields a linear relationship. A fit to the equation ln(<cos(θ(s))>) = -s/2p yields the persistence
length (p). A single trajectory is shown in panel C while the average value of 130 molecules isshown in panel D. The solid green line represents the mean value and the green shading denotes
the standard error of the mean across all 130 molecules (though the error is so small as to look likea line). Fit shown as a dashed line.

75

Figure 3.8: Drying method after NiCl2 treatment influences data quality.
For thetwo conditions tested, the yield (purple) and the persistence length p (green) are plotted using theleft and right vertical axis, respectively. The surfaces were prepared using (left) our final protocol,
including drying by a filter paper, and (right) the final protocol, except drying by a gentle streamof N2 gas for one minute. Note, that in both conditions tested, the drying occurs before DNA
deposition.

76

Figure 3.9: Higher concentration of NiCl2 during pre-treatment improves subsequentimaging. (A–B) The percentage yield of interpretable DNA molecules and their corresponding
persistence length (p) plotted as a function of the concentration of the NiCl2 used in the preincubation step. The deposition condition, rinsing, and imaging conditions were per the standard
final protocol, which is 10 mM MgCl2 + 25 mM KCl for deposition and rinsing, and 10 mM NiCl2+ 25 mM KCl for imaging as detailed in Figure 3.2. Approximately 140 molecules were analyzed
per condition tested. (C) Sets of three representative images plotted vertically when 1, 10, 33, and100 mM NiCl2 was used for the pretreatment.

77

Figure 3.10: Proof-of-principle image resolves a void in the 2D-trimer lattice of bacteriorhodopsin. This image was taken using Ni2+ -treated mica, illustrating that such Ni2+ -treatedmica can be used for other biophysical systems. We note this image was not optimized by typicaltechniques used high-resolution imaging of bacteriorhodopsin, such as selecting for a particularly
sharp tip (1 in 20).

78

Figure 3.11: Depositing and imaging DNA at biologically relevant ionic conditions.
Comparison of our standard protocol that deposits in 10 MgCl2 + 25 mM KCl and images in
NiCl2 + 25 mM KCl to depositing and imaging in 3 mM MgCl2 + 50 mM KCl, ionic conditions
typically of many protein-nucleic acids. Quantification of 40 molecules showed that persistence
length (p) remained high, indicating an equilibrated conformation on the DNA (as expected for abuffer containing MgCl2 ). The yield was reduced due, in part, to the technical difficulties associatedwith imaging DNA weakly bound to the mica. That said, the yield was still relatively high (58%),
which is excellent given the historical difficulties of imaging DNA on Ni2+ -treated mica in thepresence of MgCl2 , [47] let alone MgCl2 + KCl. Imaging under these conditions required lower
set points during tapping mode imaging. In addition, since the DNA was less well bound, the riskof tip fouling and motion of the DNA is increased relative to our standard protocol (potentiallya feature for high-speed AFM studies). Note, the successful demonstration of imaging in MgCl2+ KCl by tapping mode leveraged the other incremental improvements of the deposition protocol
illustrated in Figure 3.3 (e.g., pre-treating with 100 mM NiCl2 , drying with filter paper, gentle but
extensive rinsing).

79

Figure 3.12: Partial dewetting of the sample decreases data quality. The “Solvated”
surfaces were prepared using the standard protocol whereas partial dewetting of the sample occurredin the “Dewet” sample. More explicitly, results shown in the right column were disrupted by ameniscus force generated by adding too much liquid to the mica surface. In contrast, the data
shown in the left column was rinsed using a gentle fluid flow through the sequential addition andremoval of liquid using a micropipette. For both the left and right datasets, the total volume ofliquid exchanged remained constant at about 10 mL, as detailed in Figure 3.2. The yield (purple)
and the persistence length p (green) are plotted using the left and right vertical axis, respectively.
Representative images for each condition are shown below.

80

Figure 3.13: Concurrence between the number of experimentally observed looped
configurations and a simulation of a 2D WLC equilibrated on a surface. (A) A galleryof simulated configurations where configurations containing no loop are colored green while thosecontaining a loop are colored purple. (B) Histogram of the fraction of looped DNA molecules based
upon 100 simulations of 100 configurations. The simulated fraction of looped structures was 22 ± 4% (mean ± std. dev.) agrees with the measured value 20% derived from 142 individual molecules.
We note that in the presence of excluded volume effects, we would expect the fraction of looped
DNA in the simulation to be lower.

81

Figure 3.14: End-to-end distance of DNA is consistent with 2D WLC equilibrated ona surface. (A) Cartoon of an example DNA image showing the end-to-end distance (Rend-to-end ,purple arrow) as a function of arc length along the molecule (s, green line). (B) Mean Rend-to-end as
a function of s for all 101 unlooped molecules at the standard salt conditions [10 mM divalent salt,
25 mM KCl]. Green dotted line and shaded area give mean and standard error of the mean at eachL, and the purple line is a least-squared fit weighted by the error at each L yielding a persistence
length of 45 ± 4 nm (mean ± standard deviation).

82

Figure 3.15: Contour and persistence lengths obtained from human and computationally annotated data are consistent. (A) An example DNA molecule shows a high signal tonoise. (B) The same image as panel (A), with a manually annotated spline overlayed as a green
line. (C) The same image as panel (A), with an automatically annotated contour overlayed. The
automatic annotation is detailed in the methods section. (D and E) Comparing the automated andmanual determinations of persistence lengths and contour length yields good agreement between
human- and machine- annotated data. The values obtained by the automated contour tracing for
p and L0 were 44.9 ± 0.4 nm and 680 ± 70 nm (mean ± std. dev.), respectively. The values
obtained by the human-annotated data as 44.6. ± 0.6 nm and 683 ± 13 nm (mean ± std. dev.),
respectively.

83

Figure 3.16: Measured height of the DNA. (A) Images of the DNA taken under our typicalconditions (see AFM imaging). Line scans (green) and traces (purple) are overlaid. (B) The heightfrom the line scan (green) and trace along the DNA (purple) from panel A are plotted versus the
distance along the line scan and the path along the DNA backbone, respectively. Notably, the data
concurs with the expected width of the DNA helix (2.0 nm). (C) Histograms of the height along
the contour length skeletonized DNA configurations derived from the raw images. Note, the top
0.5% of heights, representing rare line noise or surface defects, were ignored.

84

Figure 3.17: Characterizing the surface roughness of mica in liquid for different mica
treatment protocols. The top plot lists the standard deviation (σ) of the height for untreatedmica, mica treated with the protocol described in this work, and mica treated with APTES 0.1% as
described in Materials and Methods. Note, no DNA was deposited on these surfaces. Below eachmeasurement of σ are representative images and the distribution from which the σ was deduced.
Error bars in the top panel are standard deviations of σ from 3 separate images, each with about
250 thousand points.

85
Figure 3.18: High-resolution imaging reveals the right-handed helical structure ofDNA. (A). Successive images of the same DNA molecule. These images were fit with a thirdorder, two-dimensional spline to subtract the background, then smoothed with a Gaussian with awidth of two pixels (1 pixel = 0.5 Å). (B) Histogram of the helical pitch measured from 15 imagesof 4 molecules using 3 different tips, where N is 89 and represents the number of individual helicalturns measured. A Gaussian fit to the measured distribution yields 3.51 ± 0.40 nm (mean ± std.
dev.). The uncertainty in the mean helical pitch is 0.04 nm as defined by the standard error in the
mean.

Figure 3.19: Measured contour length agrees within 1% of the expected contour lengthfor B-form DNA. (A) Raw DNA image with a diagram illustrating the contour length L0 used
to measure distance along the configuration. We note the actual contour length is calculated bymanually tracing the entire DNA molecule, as illustrated in Figure 3.7 B is 680 nm based upon thenumber of base pairs times the rise per base pair for B-form DNA (2,000 bp × 0.34 nm/bp). (B)Histogram of from 130 molecules. A fit to the measured distribution (black line) yields 683 ± 13
nm showing that was within 1% of 680 mn.

86Figure 3.20: Images of short (300-bp) DNA deposited using our protocol. A slightly
higher deposition concentration (4 nM) was used given the reduced likelihood of 100-nm DNA
forming internal loops or overlapping with adjacent molecules.

Figure 3.21: Dependence of persistence length on ionic strength is consistent with
2D equilibrated DNA. The total persistence length (p, red markers give mean ± standard
deviation) from Figure 3.5 is plotted versus ionic strength (I ). A blue dotted line represents thefollowing dependence of the total persistence length in nanometers on ionic strength in molar
units: p = pnon-electrostatic + 0.0324/I. The non-electrostatic component of the persistence length(pnon-electrostatic ) is consistent with an 2D equilibrated conformation (~50 nm). The point with thelargest ionic strength (black marker) is omitted, since the high salt inhibits binding of DNA to
the surface and artificially lowers the persistence length. Note the dependence of p on the ionicstrength I is calculated using [100], assuming that 10 mM MgCl2 has an effective ionic strength of
30 mM.

87

Figure 3.22: Efficient deposition and imaging is possible with little or no divalentcations in solution.
(A–B) The percentage yield of interpretable DNA molecules and theircorresponding persistence length (p) plotted as a function of divalent ionic concentration at fixedKCl (25 mM). Error bars represent the standard deviation for the yield and the fitting error for thepersistence length, as in Figure 3.3. On average, 120 molecules were analyzed per condition. (C)Sets of three representative images plotted vertically acquired at 0, 1.25, 2.5, 5 and 10 mM divalentcations. We note both concentrations of MgCl2 and NiCl2 in the deposition and imaging buffers
were varied at the same time to keep a consistent divalent ionic strength at each condition tested.

88

Figure 3.23: Replacing NiCl2 for MgCl2 during deposition leads to kinetically trapped
configurations even when using our final protocol that includes extensive but gentle
rinsing. (A) A set of tapping-mode images of DNA in liquid deposited under different deposition
protocols as summarized in each box. The change between each deposition process is highlighted
with blue text and protocols associated with images are denoted with magenta boxes. (B–C)
The percentage yield of interpretable DNA molecules and their corresponding persistence length(p) is depicted below each protocol. These values were computed from ~95 DNA molecules percondition. Error bars represent the standard deviation for the yield and the fitting error for thepersistence length (p). Persistence length was deduced using a 2D WLC model. Overall, DNA
deposited in NiCl2 showed more compact structures leading to reduced yield and a lower p for
those conformations that were interpretable. These results are consistent with the long-standing
conclusion that these conditions would lead to kinetically trapped configurations. Note that ourseries of improvements in the deposition process significantly improved the yield and interpretabilityof the images when comparing the left most and right most image in panel A.

89

Figure 3.24: Age of NiCl2 powder appeared to influence data quality. Age of NiCl2
powder appeared to influence data quality. The yield (purple) and the persistence length p (green)
are plotted using the left and right vertical axis when using NiCl2 of different ages and stored under
different conditions. (left) Images acquired using stock NiCl2 solution made from freshly purchased
NiCl2 powder immediately after first opening. (middle) Images acquires using stock 1 M NiCl2
solution stored at 4 °C for 7 months, and (right) Images acquires using stock NiCl2 solution madeafter storing NiCl2 powder for 7 months. Hence, if poor results are observed with NiCl2 powder thatis not recently purchased, we suggest purchasing fresh NiCl2 powder and immediately suspending
it in a concentrated stock solution that is stored at 4 °C.

Chapter 4
FEATHER: Automated Analysis of Force Spectroscopy Unbinding/Unfolding
Data via a Bayesian Algorithm

This chapter and its supporting information were adapted from [110]:

Patrick R. Heenan and Thomas T. Perkins. FEATHER: Automated Analysis of Force Spectroscopy
Unbinding and Unfolding Data via a Bayesian Algorithm. Biophysical Journal, 115(5):757–
762, September 2018.

4.1

Abstract

Single-molecule force spectroscopy (SMFS) provides a powerful tool to explore the dynamics
and energetics of individual proteins, protein-ligand interactions, and nucleic-acid structures. In
the canonical assay, a force probe is retracted at constant velocity to induce a mechanical unfolding/unbinding event. Next, two energy landscape parameters, the zero-force dissociation rate
constant (k o ) and the distance to the transition state (∆x‡ ), are deduced by analyzing the mostprobable rupture force as a function of the loading rate, the rate of change in force. Analyzing the shape of the rupture force distribution reveals additional biophysical information, such as
the height of the energy barrier (∆G ‡ ). Accurately quantifying such distributions requires highprecision characterization of the unfolding events and significantly larger datasets. Yet, identifying
events in SMFS data is often done in a manual or semi-automated manner and is obscured by

91
the presence of noise. Here, we introduce a new algorithm, FEATHER (Force Extension Analysis
using a Testable Hypothesis for Event Recognition), to automatically identify the locations of unfolding/unbinding events in SMFS records and thereby deduce the corresponding rupture force andloading rate. FEATHER requires no knowledge of the system under study, does not bias data interpretation towards the dominant behavior of the data, and has two easy-to-interpret, user-definedparameters. Moreover, it is a linear algorithm, so it scales well for large datasets. When analyzing
a dataset from a polyprotein containing both mechanically labile and robust domains, FEATHER
featured a 30-fold improvement in event location precision, an 8-fold improvement in a measureof the accuracy of the loading rate and rupture force distributions, and a 3-fold reduction of false
positives in comparison to two representative reference algorithms. We anticipate FEATHER being leveraged in more complex analysis schemes, such as segmentation of complex force-extension
curves for fitting to worm-like-chain models, and extended in future work to datasets containing
both unfolding and refolding transitions.

4.2

Introduction

Over the last ~25 years, single-molecule force spectroscopy (SFMS) has emerged as a powerfultool to quantify diverse biological systems, including the strength of protein-ligand bonds [29, 30]
and the unfolding and refolding of individual protein domains [25, 26]. In one widely used assay,
an atomic force microscopy (AFM) cantilever or an optically trapped bead is attached to the
biological system under study and retracted at constant velocity (Figure 4.1 A). Force is deduced
as the displacement of the force probe away from its equilibrium position. Abrupt drops in force at
the rupture force (F R ) arise from unfolding/unbinding events ( Figure 4.1 B). Because these events
are thermally activated, there is not a unique rupture force but rather a distribution (Figure 4.1 C).
The Bell-Evans model rapidly emerged as a way to characterize a 1D projection of the underlying
free-energy landscape along the stretching axis [30, 111, 112]. In this analysis, a fit to the mostprobable rupture force (FRMP ) as a function of loading rate yields two parameters, the zero-force

92
dissociation rate constant (k o ) and the distance to the transition state (∆x‡ ) (Figure 4.1 D). Moreadvanced models that analyze the shape of the F R distribution provide additional informationon the free-energy landscape, such as the height of the energy barrier (∆G ‡ ) [52] but require
higher precision event detection and larger numbers of events. Yet, event detection is obscured
due to the presence of Brownian motion and instrumental noise and is often done manually or in asemi-automated manner, including in recent work from our lab [69]. Thus, accurately quantifying
hundreds to thousands of rupture events in an automated, reliable, and reproducible way is criticalfor gaining insight into the diverse biomolecular systems studied by SMFS.
To address this need, multiple groups have developed algorithms to detect rupture eventsin AFM data and other SMFS modalities. For example, such techniques have applied worm-likechain models to compute contour lengths at each extension [113, 114], used thresholding basedon signal or noise characteristics [115, 116], and classified traces based on transformations of thedata into frequency or derivative spaces by spatially localized Fourier series or wavelets [117–119].
These methods provide increased automation, but their use is limited by their lack of generalization.
Ongoing efforts and interest in automated analysis continues [e.g., recent work integrated several
steps in SMFS analysis of unfolding data into a single package [120]]. Contour-length alignment
algorithms bias results towards dominant features and necessarily require a model. Thresholding
or transformation algorithms typically require many parameters. For example, previous techniques
have 6 [118, 119] and even up to 14 or 17 parameters [120, 121]. Large numbers of parameters help
tune an algorithm to a particular dataset, but they also increase the search space for parameter
optimization and may be difficult to apply to datasets containing unfolding events occurring overa broad range of forces.
Here, we present a new algorithm for detecting unfolding/unbinding events and apply it
to SMFS datasets representative of a variety of typical experimental conditions. The algorithm,
named FEATHER (Force Extension Analysis using a Testable Hypothesis for Event Recognition),requires no special knowledge of a specific system’s polymer properties, detects both rare and dom-

93

Figure 4.1: An overview of force spectroscopy analysis. (A) A cartoon illustrating an
AFM cantilever unfolding a polyprotein containing four mechanically robust domains (NuG2, red)and one mechanically labile one (α3 D, blue). (Inset). A sketch of a 1D free-energy landscapeand associated parameters: k o , the zero-force dissociation rate constant; ∆x‡ , the distance to thetransition state; and ∆G ‡ , the height of the energy barrier. (B–D) Typical analysis scheme for apolyprotein unfolding assay illustrated with a computationally generated dataset based on a modelby Dudko and colleagues ([52]). (B) A force-vs.-time curve for the unfolding of the polyproteinwith segments colored coded based on the domain prior to unfolding. (C) A distribution of rupture
forces (F R ) for the α3 D domain fit to the Dudko model. (D) Most probably rupture force (FRM P )versus log of the loading rate (∂F/∂t) fit with a line per the Bell-Evans model ([30, 111, 112]). (E)An experimental force-vs.-time curve of the polyprotein shown in panel A, with unfolding events
marked by green arrows. Colored coded data was smoothed to 500 Hz with higher-bandwidth data
(50 kHz) plotted in grey. (F) A high-time resolution plot of a single rupture event used to define
metrics for comparing automated algorithms: a true event is manually defined by an expert user as
detailed in the Supporting Material; dt→p is the distance from a true event to the closest predicted
event; and dp→t is the distance from an algorithmically predicted event to the closest true event.
Predicted events are illustrative, not actual.

94
inant data behavior, and outperforms recently published algorithms over a wide range of pulling
velocities and two common systems of interest (polyproteins and DNA) and a computationallygenerated dataset. FEATHER is a Bayesian algorithm because it calculates the probability of eachpoint in the retraction curve given a model automatically calculated from the event-free approach
curve. Because FEATHER’s improved performance requires just two easy-to-interpret parameters, a smoothing factor and a significance threshold, we anticipate FEATHER being leveraged to
improve the throughput, quality, and reproducibility in SMFS analysis schemes.

4.3

Materials and Methods

FEATHER is written in Python 2.7, with interfaces written for MATLAB and Igor Pro.
The source code, working examples, and accompanying documentation is freely available (https://doi.org/10.5281/zenodo.1306884). Importantly for analyzing large datasets, FEATHER’s
execution time scaled linearly with the number of data points and offered an order of magnitudeimprovement in runtime relative to the faster of the two algorithms used for comparison (Figure 4.4).
The basis for the statistical analysis used by FEATHER and performance metrics are presented
in the Supporting Material. All timing and tuning results were obtained using a desktop PC
with 32 GB of RAM, an AMD Ryzen 5 1500X Quad-Core CPU, and a 500 GB hard drive. To
test FEATHER, we used two datasets: (i) 152 force-extension curves of a previously describedpolyprotein that contains one mechanically labile target protein (α3 D) with a measured change
in contour length (∆L0 ) of 23 nm upon rupture (8) positioned between four mechanically robust
marker domains of NuG2 [∆L0 = 18 nm per NuG2 monomer [122]] (Figure 4.1 A and Table4.2), and (ii) 600 force-extension curves of DNA deposited at purposely high surface coverage topromote multiple tip-DNA attachments and therefore multiple rupture events per force-extension
curve (Figure 4.5 and Tables 4.3–4.4). As described in detail in the Supporting Material, bothdatasets contained curves acquired over a range of retraction velocities (v). Finally, FEATHER’s
performance was tested using a simulated dataset containing purposely challenging-to-analyze force-

95
extension curves, as described in the Supporting Material.

4.4

Results and Discussion

4.4.1

Description of FEATHERIn SMFS, unfolding events occur when the force applied to a molecule exhibits an abrupt
drop in a force-vs.-time curve as the molecular configuration passes over an energy barrier (Figure
4.1 E, green arrows). To determine the location of such events, FEATHER first fits a smoothing
spline to the raw data (Figure 4.2 A) with nodes in the spline spaced at a user-defined fractional
spacing (τ ) of the full record length, so the temporal averaging time (5–50 ms) depends on v given
a fixed data acquisition rate, as is typical in such assays. While the model defined by the spline has
a continuous first derivative, unfolding events exhibit a discontinuity in the first derivative. Thus,
unfolding events could be located by computing where the data were inconsistent with the model.
To efficiently detect short-lived events, we recommend users choose the largest τ that preserves
such events in the smoothed data (Figure 4.6).
To compute the statistical significance of an unfolding event at time t, we constructed a noevent hypothesis based on the noise characteristics of the data relative to a reference curve lacking
any events. For AFM data, the approach curve taken with the same individual cantilever served
as an excellent reference. Briefly, the process of computing the significance (P) of an event started
by subtracting the smoothing spline from the high-bandwidth data to yield a force residual with azero-centered mean and variance about that mean (which contained mostly the thermal noise of thesystem within a fractional size of the record defined by τ ). The magnitude of this residual varianceas a function of time is compared to the approach curve that contained no unfolding/refolding
events. Alternatively stated, we determined how the variance of the force variance changes in timesince this metric was found to be insensitive to local variation in curvature of the data but highly

96

Figure 4.2: FEATHER’s analysis scheme. (A) A high-bandwidth force-vs.-time record ofpolyprotein unfolding (grey) with FEATHER’s spline fit overlayed in blue, where τ = 15 ms. (B)The probability (P) of a non-event was obtained by applying Chebyshev’s inequality to the recordin panel A. Unfolding events occur when this probability is near 0. (C) The probability from panel
B transformed to de-emphasize regions near the surface and regions with positive force derivatives.
(D) The probability from panel C was further modified to suppress regions where the force change
was negligible, as determined from a reference curve with no-events (e.g., the approach). (E–H) Force-vs.-time curves and magnified regions highlight event determination, indicated by green
arrows using a significance threshold of P thresh = 0.001.

97
sensitive to unfolding events (Figure 4.7 F). Deviation from this mean magnitude of residual noise
was transformed into a probability using Chebyshev’s inequality (Equation 4.1), which importantly
does not assume any form of the noise distribution [123]. We note that FEATHER requires thatthe noise distribution of the force residuals have zero mean and median, but otherwise does not
impose constraints on the distribution.
Empirically, we observed the statistical significance of an event was enhanced by combining
the no-event probability for the force in combination with the integral force, force derivative, andforce differential, all conceptually based on the same implementation of Chebyshev’s inequality
as shown in Equation 4.2. For instance, the probability from Figure 4.2 B was transformed tode-emphasize stretching of the construct where the force derivative is positive or negligible, andsurface adhesion was ignored by including only events that started after the tip was retracted
off of the surface (Figure 4.2 C). We next suppressed events associated with small force changes
consistent with the force noise in the reference (or approach) curve (Figure 4.2 D) as described in
the Supporting Material (Figure 4.7; see pseudocode listed in Table 4.5). Events were identified
from the probability shown in Figure 4.2 D based on a user-defined threshold (e.g., P event =0.001) (Figure 4.2 E). Importantly, FEATHER correctly identified rupture events even though therupture force varied by an order of magnitude within the same record (Figure 4.2 F–H ). Moreover,this high-fidelity event detection was insensitive to a ~10-fold variation in τ and the thresholding
parameter (P event ), in contrast to other event detection algorithms (see Supporting Material andFigures 4.6–4.8).

4.4.2

Evaluating FEATHER’s performance

We evaluated the performance of FEATHER to accurately and precisely analyze the unfolding of our polyprotein, which exhibited both low- and high-force ruptures. Specifically, we
compared how well FEATHER did relatively to manually annotated data from an expert user and98
two automated analysis routines, the recently published OpenFovea [116] and the wavelet-scheme‘find_peaks_cwt’ method from Scientific Python [124]. These algorithms were chosen to provide arepresentative sample of the viable techniques used in AFM data analysis, since they respectively
utilized thresholding and wavelet transformations, two broad classes of event-detection techniques.
In addition, neither of these reference algorithms requires specialized knowledge of the polymer
under study, such as the worm-like chain model commonly used in contour length alignment algorithms. Three primary metrics were used: the relative location error, the loading rate, and therupture force (Figure 4.3). We note that each algorithm outputs a list of predicted event locations;the loading rate and rupture force were then calculated in the same way for each algorithm, given
the predicted events (see Supporting Material).
Overall, FEATHER did an excellent job, essentially matching the performance of humanannotated data. In comparison to the best performance of either reference algorithm, FEATHER’s
prediction yielded rupture force and loading rate distributions which were 8-fold closer to the humanannotated data and 30-fold better in an event location metric (∆Z95 ), as defined below. The top
panel of Figure 4.3 A shows the distribution in the relative location error of the “true events,”
defined by an expert user, relative to predicted events (dt→p ; green shading) closely matched
the distance distribution from predicted events to true events (dp→t ; blue line) (see Figure 4.1 F
for definitions of dt→p and dp→t and the Supporting Material for details of manual annotation).
The peak of this distribution at low relative error shows precision in determining event location.
The overlap between the two distributions shows that number of true events closely matched thenumber of predicted events. However, such overlap was not present when the data were analyzed
with OpenFovea, which showed a high number of false positives as indicated by the gap between
the distributions of dp→t (black line) and dt→p (green shading). We speculate that OpenFovea’s
performance may be limited in this application by a dataset that contains both low- and highforce unfolding events, despite efforts to optimize OpenFovea’s parameters for this dataset (seeSupporting Material & Figure 4.8). The wavelet-based scheme, which was also had its parameters99
optimized for this dataset, showed better performance on this metric than OpenFovea but still had a
30-fold higher relative location error and a 3-fold higher false positive rate than FEATHER (Figure4.9). Relative to the better performing wavelet scheme, FEATHER improved event localization
precision ~30 fold based on ∆Z95 (Table 4.1), where ∆Z95 is defined as the location of the 95th
percentile of the combined distribution for dp→t and dt→p (see Table 4.6 and Figure 4.3 A, dashedline). As defined, ∆Z95 represents a good metric for the upper bound of the error in determining
event location.
As accurate determination of rupture force and loading rate is critical to deriving biologicalinsight from force spectroscopy data [30, 52, 111], we next compared all three algorithms to humanannotated results for these two metrics (Figure 4.3 B,C). As shown in the top panel of each column,
FEATHER (blue line) essentially matched the human-annotated distributions (green shading) while
OpenFovea showed a surplus of low-force unfolding events (black line) arising from its high false
positive rate. Again, the wavelet scheme showed intermediate performance (red line). Despite
these distributions being oddly shaped due to the presence of both low-force (α3 D) and high-force(NuG2) ruptures over a range of v, we quantitatively compared the degree of overlap between thehuman-annotated and algorithmic results using Bhattacharya coefficient’s complement (BCC, see
Table 4.6) [125]. By this metric, FEATHER outperforms the wavelet scheme by a factor of 8 (Table
4.1). We note that in additional tests on a DNA dataset purposely containing multiple tethers that
led to multiple, closely spaced unfolding events at low forces (10–30 pN)(e.g., Figure 4.5 E–F), we
saw even larger performance improvements of FEATHER by these metrics (Figures 4.10–4.11). In
addition, FEATHER successfully analyzed hundreds of simulated ruptures over a wide range ofcontour length changes, loading rates, and rupture forces (Figure 4.12, Table 4.7). Taken together,
FEATHER’s performance on experimental polyprotein data, an experimental DNA dataset, and acomplex simulated dataset underscored the consistent strength of FEATHER’s predictive power.

100

Figure 4.3: Evaluating FEATHER’s performance. (A) Histograms of fractional errors between human-annotated and algorithmically predicted event locations for the polyprotein dataset
when using FEATHER, OpenFovea ([116]), and the wavelet-based scheme from Scientific Python([124]), where ∆Z is the combined fractional distance between the identified and predicted events
divided by the full range of the record, and the dotted line denotes the location of ∆Z 95 , where∆Z 95 is defined as the location of the 95th percentile of the combined distribution for the fractional error dp→t and dt→p . As diagrammed in Figure 4.1 F, dt→p is the distance from a humanannotated “true” event to the closest predicted event; and dp→t is the distance from an algorithmically predicted event to the closest true event. (B) Histograms comparing the loading rates frommanual-event annotation (green) to algorithmically predicted ones for FEATHER (blue), OpenFovea (black), and Scientific Python (red), respectively. Note, the green shaded distribution in all
3 panels represents the same dataset but appears slightly different due to variations in bin size. (C)Histogram of rupture force for human-annotated and algorithmically determined events using thesame color scheme.

101

4.5

Conclusion

The canonical single-molecule force spectroscopy assay retracts a force probe at constantvelocity to yield records containing unfolding and unbinding events. Here, we introduce FEATHER,
which automatically determines event locations for such records and thereby determines the rupture
force and loading rate. FEATHER requires only two simple-to-understand parameters to accurately
and algorithmically recapitulate human-annotated data. Its fast execution and linear runtime with
the number of data points allows for automated analysis of large datasets that, in turn, will allow
for more sophisticated analysis that yield additional biophysical information, such as ∆G ‡ [52].
When analyzing a complex dataset containing both low- and high-force rupture events, FEATHER
provided more than an order of magnitude improvement in event localization error (∆Z95 ) relative
to other representative algorithms (Table 4.1) and did not bias the data towards high-force events.
We note that the datasets used here were acquired with a relatively long, soft cantilever. Recent
efforts in improving the precision and time resolution of AFM cantilevers will immediately aid
FEATHER’s ability to detect smaller and more closely spaced unfolding intermediates [126, 127].
By predicting where events occur without relying upon any a priori domain-specific model ofthe event, FEATHER provides a powerful tool within a longer SMFS analysis pipeline [116, 120].
For instance, it can be used to segment complex force spectra to then determine the change incontour length between ruptures, a value which in turn can be used to screen large datasets forthe unfolding of particular structures. Finally, we anticipate that FEATHER’s underlying event
detection algorithm can be extended to search for both unfolding and refolding events, increasing
its utility to a broader array of force spectroscopy assays.

4.6

Open data statement

All of the analyzed force-extension curves, along with their annotation, are available fromthe Dryad Digital Repository (doi:10.5061/dryad.1615c2p).

102

4.7

Author contributions

P.R.H. conceived of and developed the algorithm; P.R.H. and T.T.P designed the research;
P.R.H. acquired the data. P.R.H. and T.T.P analyzed the data and wrote the manuscript.

4.8

Acknowledgments

We thank J. Boyd-Graber and R. Frongillo for discussions on algorithm development and
M.-A. LeBlanc for sharing the polyprotein dataset.
Table 4.1: Performance metrics for each algorithm The Bhattacharya coefficient’s complement (BCC) compares the degree of overlap between the human-annotated and algorithmically
predicted 2D distribution of rupture force versus loading rate (e.g., Figure 4.10 B, Table 4.6). ∆Z95
is the metric for the upper bound of the fractional error in determining event location. The symbol(↓) indicates a lower value is better.
Name
FEATHER
OpenFovea
Scientific Python

4.9

Supporting Information

4.9.1

Algorithm Description

4.9.1.1

High-level description

BCC (↓)
0.00370.203
0.030∆Z95 (↓)
0.00650.42
0.19

FEATHER detects unbinding and unfolding events in single-molecule force spectroscopy(SMFS) records characterized by a sudden drop in force (F). FEATHER is based on a probabilistic
model of a signal lacking any events, called the no-event model. FEATHER leverages information contained in a reference record containing no ruptures events, typically the approach curve

103
in atomic force microscopy (AFM) studies (Figure 4.7). The algorithm has the following 5 basic
steps:
1.

Estimate the no-event parameters from an approach curve (see Figure 4.7).

2.

Fit the no-event model to a retraction curve.

3.

Calculate the upper bound on the probability of each retract point using the
Chebyshev’s inequality [123] given the model.

4.

Iteratively update the probability using additional characteristics of the data toremove false-positive events.

5.

Report contiguous regions with probabilities lower than a user-specific thresholdas events.

4.9.1.2

The no-event hypothesis

In SMFS, events occur when the force applied to a molecule exhibits a discontinuity as themolecular conformation passes over an energy barrier. FEATHER assumes that events take placeon time scales much faster than the response time of the probe. If this is not true, the data are
assumed smoothed until this condition is reached. The algorithm models the data assuming noevent is occurring at a given time t and calculates the probability based on that assumption at eacht. Contiguous regions of time with probabilities below a user-given threshold are grouped into asingle event. Hereafter, the definition of an event and these assumptions will be referred to as the
no-event hypothesis.
Importantly, FEATHER’s model for experimental noise is independent of noise distribution,
except for assuming a distribution with zero mean and median. By making such few assumptions
about the data, FEATHER avoids the need for polymer-physics based models, such as the worm-likechain model [128], or other specialized knowledge of the system under study.

104
FEATHER applies this probabilistic model to the retraction portion of the force-extension
curve. As the reference curve for no events, the algorithm uses an approach curve taken with thesame individual cantilever to determine characteristics of the noise. FEATHER initially fits andsubtracts a smoothing spline from the approach curve, yielding a reference mean and force varianceof the residual’s standard deviation within a window of 2τ, where τ is a user-specified fraction of thecurve length. Applying this procedure to the retraction record yields a residual mean and standard
deviation at each point in time. This residual is transformed into a probability using Chebyshev’s
inequality [123] and the reference mean and variance from the approach curve. This probability ateach point in the retraction curve is iteratively updated to remove the effect of adhesion and otherfalse positives, detailed below. As shown in Figure 4.2, the result is a probability at each time
point which drops from one towards zero near events. A threshold probability is set by the user or
optimized by a tuning routine (see Figure 4.7).
We define a single event as a contiguous region of time with probabilities below the threshold.
The rupture force and loading rate are determined for each such region, as described in the “Data
Acquisition and Annotation” section, below.

4.9.1.3

Calculating the no-event parameters:

FEATHER identifies events by focusing on short time scale events while not triggering on
simple Brownian motion of the probe or variation in the compliance of the system. To suppress lowfrequency fluctuations, we first fit the high-frequency data to a spline. The spline, denoted as S t ,was calculated by a least-squares fitting of a second-order basis spline [129] to the high-bandwidth
force-vs.-time curve, F t . The spline was second-order to ensure a continuous first derivative, arequirement of our no-event hypothesis. The spline knots were spaced uniformly at intervals of theuser-specified τ . Figure 4.7 is a representative demonstration of the spline fitting. Determining S t
immediately yielded the force residual r t = F t - S t . We note that r t has essentially a zero mean and105
median as required for FEATHER, but r t was not necessarily Gaussian distributed. This flexibility
to handle non-Gaussian distributed fluctuations motivated the use of Chebyshev’s inequality [123].
Unfortunately, analysis based on the force residual rt did not provide a conclusive signal forthe presence of an event (see Figure 4.7). In order to improve event detection, we determined how
variance of rt changes in time since this metric was found to be highly sensitive to unfolding events
but insensitive to local variation in the curvature of the data. To do so, we computed σr , which isdefined as the standard deviation of r t centered at t with a window of [—2τ ,2τ ]. As illustrated in
Figure 4.7, using σr instead of rt provided a much stronger signal of an event.
To be able to calculate the probability of an event in the retraction curve, we next calculated
two additional metrics based on σr of the approach curve. Specifically, we calculated the medianvalue and the standard deviation in σr , denoted as µσ and σσ , respectively. The median was usedinstead of the mean to remove the influence of possible false positive events in the approach thatskew the mean but not the median. The removal of these pseudo-events was necessary to ensure
accurate estimators for µσ and σσ , which were then used to calculate the probability of an eventat time t using Chebyshev’s inequality as follows:

P (σr ) ≤ (σσ)2σr − µσ(4.1)

where this σr is from the retraction curve being analyzed. Although Equation 4.1 provides
only an upper limit on the probability of no event, the integration of multiple aspects of the data—
see Equation 4.2 below—leads to clear detection of events with high specificity (Figure 4.7 G).
In our application of FEATHER to AFM data, we used the approach curve immediately
preceding the analyzed retraction curve. Both curves shared a common set of noise characteristics because they were taken at the same velocity. In principle, one could use a single common“reference” curve for a multitude of retraction records given that the reference curve had the noise

106
characteristics of the retraction curves. For instance, one could acquire a handful of approach curves
at the retraction velocity for an individual cantilever and use those curves as the reference. In test
cases, the velocity of the approach did not have to equal the velocity of the retraction but suchapplications should be tested on an individual basis, particularly if the ratio between the velocities
is >5.
The quality of FEATHER’s results were improved by multiplying the no-event probability,
as defined in Equation 4.1, by the no-event probability of the integral force, force derivative, andforce differential. The calculation of each of these probabilities was exactly the same as describedabove, with the variables changed appropriately. Specifically, the relevant operation (integration,differentiation, or force difference) was applied to the approach, estimates for the operation-specificµσ and σσ , were obtained, yielding the operation-specific probability. The local force derivative of
the basis spline for the force was calculated in the standard, analytical manner, [129] and the local
differential at each point was calculated centered about that point with a window size of τ /2. Moredetails for the calculation of each of these terms are given in the pseudocode listed in Table 4.5. In
particular, the final probability is given in terms of these operation-specific probabilities as:

Pnoevent = PF × Fintegral × PdF × PdF/dt(4.2)

where P F is defined as Equation 4.1. Each term in the probability calculation improved
the performance of P no event . For example, incorporating P dF made it less likely that cantilever
oscillations after a rupture would trigger a spurious event. The force differential was used inaddition to the force first derivative in order to incorporate higher-order derivative information. In
addition, P no event is set to one if any of the individual distributions (P integral , P dF , or P dF /dt ) areequal to one. This codifies the requirement that an unbinding or unfolding event is statisticallydistinguishable from the dynamics observed during an approach curve. In addition, AFM data has
a region at the start of each retraction curve in which the cantilever is in contact with the surface.

107
To prevent this so-called ‘touchoff’ region from triggering spurious events, FEATHER ignores any
event starting at the beginning of the retraction curve. Further, minor details are listed in thepseudocode of Table 4.5.

4.9.1.4

Algorithm runtime

All timing and tuning results were obtained using a desktop with 32 GB of RAM, an AMD
Ryzen 5 1500X Quad-Core CPU, and a 500 GB hard drive. Figure 4.4 compares the runtime
of FEATHER and the reference algorithms. The runtime of FEATHER, denoted T(N ) in thecomputer science literature, is linear with number of points but with an offset. As a result, a 1,000fold increase in the number of data points in a curve leads to a 20-fold increase in runtime over therange tested (Figure 4.4). FEATHER has a roughly tenfold better runtime performance on larger
datasets than the OpenFOVEA or Scientific Python algorithms, in addition to outperforming themin application-specific metrics (see Figure 4.3).

4.9.1.5

Algorithm tuning

All three algorithms were tuned using 5-fold cross validation. Cross validation is a common
technique for quantifying performance of an algorithm [130]. In our case, the data were split with
80% of the data as a training set for parameter optimization and 20% of the data as a validation set
for measuring algorithm performance. Cross validation was performed five times at fifteen different
values over the useful range of each algorithms tuning parameter (Figure 4.8). The parametervalue that minimized the Bhattacharya coefficient’s complement for an algorithm was considered
the algorithm’s best parameter. Data shown in Figures 4.10–4.11 consist of the concatenation of
the five validation folds for each algorithm’s best parameter.
Since tuning the reference algorithms (Open Fovea and Scientific Python) on the full DNA

108
dataset would have required many cpu-months (compared to about one cpu-day for FEATHER,
see Figure 4.4), a smaller subset of the DNA data was used for comparing the algorithms. In
particular, the subset of the DNA data with the smallest number of points per curve—200 curves
with v = 1,000 nm/s, N points ~ 105 (see Table 4.3)—was used for results comparing FEATHER to
the baselines for Figure 4.10. FEATHER was also tuned separately on the larger, more complex
DNA dataset, with similar results to those reported in the rest of the paper (Figure 4.11). This
demonstrates that FEATHER generalizes well to a wide range of data sets sizes and experimental
parameters. We note that on the DNA data set, FEATHER showed even greater performance gains
than for the polyprotein data set.

4.9.2

Sample Preparation

Site-specific coupling improves the rate and quality of the resulting single-molecule force
spectroscopy (SMFS) data. We used a recently developed site-specific coupling chemistry for boththe polyprotein and DNA studies [69]. Here, we briefly review this procedure for surface- andcantilever-functionalization.

4.9.2.1

Azide-Functionalized Surfaces

Glass coverslips [12-mm diameter (Ted Pella, 26023)] were cleaned by sonicating for 5 min inacetone, 5 min in 95% ethanol, and finally immersed for 3 min in a solution of potassium hydroxide[80 g of KOH (Fisher, P250-500) dissolved in 170 mL of 95% ethanol and 80 mL of ultrapure water(18.2 MΩ)]. We next serially washed the coverslips in two 1-L beakers of ultrapure water. The
cleaned coverslips were dried with 99.8% pure dry nitrogen gas and stored at room temperature in109
a dust-proof container.
Prior to azide-functionalization of the coverslips, we first exposed them to 30 min of UV-ozone(Novascan, PSDP Digital UV Ozone System). We next loaded the coverslips into a custom-madeTeflon-holder and immersed them in 0.15 mg/mL of silane-PEG-azide (Silane-PEG-Azide Nanocs
PG2-AZSL-600) dissolved in warm (60 °C) toluene (Sigma 179418-4L) for 3 h. To achieve uniform
surface coverage, this solution was stirred at 600 RPM. After this incubation, we serially rinsed
the coverslips in 250-mL beakers of toluene, isopropanol, and ultrapure water. The resulting azidefunctionalized surfaces were dried with nitrogen gas and stored in a dust-proof container at 4 °C.

4.9.2.2

Streptavidin-Coated Cantilevers

We used a similar protocol to coat the cantilevers with streptavidin. We first removed thegold and underlying chromium layer off of long, soft cantilevers [L = 100 µm; k = 7 pN/nm(nominal) (Olympus)], which achieves sub-pN force stability over 100 s [131]. To remove the gold,
we immersed the cantilever for 30 s in 10 mL of gold etchant (Transene TFA) followed a rinse
in 250 mL of ultrapure water. The chrome was removed by immersing the cantilever in 10 mL ofchromium etchant (Transene 1020) followed by a rinse in 250 mL of ultrapure water. The cantilevers
were then serially rinsed for 30 s in 50 mL of deionized water, isopropanol, toluene, isopropanol,and ultrapure water. After drying with a Kimwipe, we then exposed the cantilevers to UV-ozone
for 30 min. Akin to the coverslips, we then maleimide-functionalized the coverslips by immersing
them for 3 h in a 0.15 mg/mL solution silane-PEG-maleimide (Nanocs PG2-MLSL-600) dissolvedin warm toluene. The resulting functionalized cantilevers were serially rinsed in 250 mL of toluene,
isopropanol, and ultrapure water. The cantilevers were immediately dried by touching the base of
the cantilever to a Kimwipe. To coat the cantilevers with streptavidin, we next immersed them for
3 h at room temperature in a 0.2 mg/mL solution of thiol-derivatized streptavidin (Protein Mods,
SAVT) dissolved in PBS buffer [10 mM phosphate buffer (pH 6.75), 140 mM NaCl, 3 mM KCl]110
with 1 mM TCEP (Tris(2-carboxyethyl)phosphine, Thermo Scientific 77720)] in small wafer holders(Entegris, H22-100/101-0615). Subsequently, we transferred the cantilevers into these holders to 4
°C for an overnight incubation. After this incubation, we removed the free streptavidin by seriallyrinsing the cantilevers in two 10-mL beakers of PBS at pH 7.4 and then immersed them in a 20-mL
petri dish filled with PBS for 10 min. The resulting streptavidin-coated cantilevers were stored in
50 µl of PBS at pH 7.4 and 4 °C in the wafer holders until loading into the atomic force microscope(AFM). Streptavidin-coated cantilevers were typically stable for 1–2 weeks of storage at 4 °C.

4.9.2.3

Polyprotein Labelling

As previously described [69], the polyprotein used was created by inserting the 73 amino acidprotein α3 D [132] into a plasmid with four copies of the 57 amino acid protein NuG2 [133]. The
plasmid is available via the Addgene nonprofit plasmid repository (Plamid ID 80163).
The protocol for labeling the polyprotein was recently published [69]. Briefly, after overexpression in E. Coli strain BL-21 (DE3), the protein was purified on a Ni-NTA (Qiagen) column
equilibrated with TBS buffer [25 mM Tris (pH 8.0), 150 mM NaCl, 5 mM beta mercapoethanol(βME)]. To convert the cysteine in the aldehyde tags (LCTPSR) to formylglycine (an amino acidcontaining an aldehyde), purified formylglycine-generating enzyme (FGE) was added to purified
polyprotein containing the aldehyde tag in 25 mM triethanolamine (pH 9.0), 50 mM NaCl, 1 mM
βME in a 1:10 FGE:polyprotein molar ratio. The mixture was incubated overnight at 18 °C
with shaking, resulting in ~95% conversion from cysteine to formylglycine. After aldehyde conversion, the sample was buffer exchanged into 50 mM sodium phosphate (pH 6.0), 150 mM NaCl,
1 mM TCEP (Tris(2-carboxyethyl)phosphine) and incubated for 3 days at 37 °C with 10x molar concentration of Hydrazino-Pictet Spengler (HIPS) reagents to functionalize the protein withdibenzocyclooctyne (DBCO) and biotin. Details of HIPS reagent synthesis were also previously
published [69]. As both ends of the polyprotein contained the same aldehyde, at best 50% of the

111
protein would contain both biotin and DBCO. Despite this limitation, only proteins which weredifferentially labeled with both DBCO and biotin at each end were efficiently stretched between
azide-functionalized surfaces and streptavidin-coated AFM tips.

4.9.2.4

DNA Sample Preparation

For the DNA pulling assays, we used 650-nm long DNA labeled at one end with four biotins
and the other end with dibenzocyclooctyl (DBCO), a copper-free click chemistry reagent thatreacts with azide moieties. To introduce these labels, we used PCR and a forward and reverse
primers (IDT) labeled at their 5’ ends (Table 4.3). The template DNA was the M13mp18 plasmid(New England BioLabs N4018S). After PCR, we purified the DNA to remove the primers using a
QiaQuick PCR purification kit (Qiagen 28106) followed by gel electrophoresis. The desired band
was excised with a razor blade and the DNA extracted using a Freeze ‘N Squeeze DNA Gel spincolumn (Bio-Rad). We then concentrated the DNA using a 0.5-mL microconcentrator (Amicon
10K centrifugal filter) and removed residual agarose using a second Qiaquick PCR purification.
The DNA was eluted using TE [10 mM Tris-HCl (pH 8.0), 1 mM EDTA] and stored at 4 °C.
We prepared DNA samples for the AFM by depositing 100 µL of the 8 nM labeled DNA onto
azide-functionalized coverslips and let the DNA incubate at 4 °C overnight in a wafer holder. The
coverslips were then rinsed with 7 mL of TE at pH 8.0 and 7 mL of PBS at pH 7.4 and 1 mM
EDTA and stored at 4 °C.

4.9.3

4.9.3.1

Data Acquisition and Annotation

AFM Experiments

The force spectroscopy data was acquired on a Cypher ES AFM (Asylum Research). The samples were in liquid [PBS (pH 7.4)] and held at a constant temperature (25 °C) using a temperature-

112
controlled, closed-fluidic liquid chamber. The stiffness of each cantilever was calibrated using thestandard thermal method [134], as implemented on our commercial AFM. Sensitivity of the detector(V/nm) was determined by pushing the tip into the sample and fitting the resulting force-extension
curve. After calibration, the sample was repeatedly probed at various locations and retraction
velocities (v) using a standard constant-velocity data-acquisition scheme. For example, within one
cycle, we lowered the tip towards the surface at constant velocity until a user-defined force wasachieved, typically 100 pN. The tip was held in contact at constant F for ~1–2 s and then retracted
at constant velocity while the cantilever deflection was digitized at 50 kHz. The experimental data
sets used for this study consisted of 152 force-extension curves of the polyprotein construct acquired
at four retraction velocities (200, 400, 1,800, and 3,800 nm/s) and 600 DNA force-extension curves
in total acquired in equal number at three retraction velocities (100, 500, and 1,000 nm/s).

4.9.3.2

Polyprotein and DNA manual annotation

The start and end of each event in a curve were obtained through manual annotation as
follows. We first smoothed the data with a 2nd -order Savistky-Golay filter, where the filter length
was set to 0.1% of the retraction curve length. The start and end of each event was manually
identified in each smoothed force-extension curve. The loading rate was determined by a linear fit
to the previous N points of force-vs.-time trace, where N was set to 2% of the curve length, The
rupture force was determined as the last time the high-bandwidth data crossed the line definedby the linear fit. We note that this algorithm for determining loading rate and rupture force wasalso applied to the computationally defined events by all three algorithms (FEATHER, OpenFovea,
Scientific Python). On average, each manual annotation of a curve took 1–2 min. More statisticalinformation on the polyprotein data, including curve lengths and number of events per curve, isgiven in Table 4.2. The equivalent table for the DNA dataset is given in Table 4.4.

113
4.9.4

Simulation

Simulations were performed in order to test for a wider range of parameters (e.g. contour
length changes), pathological examples such as high-force ruptures followed by lower-force ‘shielded’
ruptures, and to complement the manually annotated experimental data with an unambiguous‘ground truth’. Simulated data were generated and analyzed using an algorithm inspired by the
recent work of Hummer and Szabo [39]. For a single simulated curve, the simulation consisted of
the following distinct states:
1. State 1: Probe equilibration.
2. States 2-7: Pulling, including 6 different rupture events.
3. State 8: Probe retraction after final event.
In total, 100 simulated curves were used, with 6 events per curve. The probe position z wasincreased at a constant velocity v starting from 150 nm and moving to a curve-dependent final
position, as described below. The molecular extension q n+1 and force F n+1 k (z n+1 −q n+1 ) was
determined from the previous extension, q n , by the following relation:

qn+1 = qn − Dq δt(√∂V)i + gn 2Dq δt
∂qn

(4.3)

where the parameters definitions and values for Equation 4.3 are given in Table 4.9. The
initial extension before equilibration, q 0 , was assumed to be 150 nm.
A wide range of contour length changes, loading rates, and pathologically complex forceextension curves were created by varying the worm-like chain force, F WLC,i (q n ). Our simulations
modelled the worm-like chain force as a modified Marko-Siggia worm-like chain (WLC) [135] determined by the particular state i. The last state after the final rupture (i.e., state 8) has F WLC,i = 0,

114
since no molecule is attached in that state. All other states share the following parameters: apersistence length p of 0.3 nm, a Boltzmann energy k B T of 4.1 pN nm, and a stretching modulusof 100 pN. In order to achieve a wide range of rupture forces, loading rates, and changes in contour
lengths, the contour length, L0,i , and the total distance spent in a state before rupture, ∆z i, werevaried uniformly at random within the ranges in Table 4.8. The simulated data were analyzed
in the same manner as the experimental data, with unambiguously identified events marked attransitions between adjacent, non-equilibration states. The last 10% of each simulated curve wasused as an effective “approach” input to FEATHER, since no events were present after the final
rupture. For the simulated data, FEATHER used a fractional τ of 0.001 (~10 ms) and a thresholdof 10-5 .
FEATHER’s performance on the simulated data exceeds its performance on experimental
data. As shown in Figure 4.12 and Table 4.7, all performance metrics on simulated data are
improved compared to the results presented in the rest of the paper (e.g. Figure 4.3, Table 4.1).

4.9.5

FiguresFigure 4.4: Runtime of each algorithm. (A) The runtime, denoted T(N), per curve versus
number of points N in the analyzed record for each algorithm. (B) For each algorithm, the numberof points analyzed per second was determine by fitting a line to the data in panel A.

115

Figure 4.5: Representative examples of 650-nm DNA force-extension curves with one
event (A–C), two events (D), and three events (E). Plotting conventions are as in Figure
4.1 and the scale from panel A is used in all 5 panels.

Figure 4.6: Effect of smoothing on BCC. (Left) Force-extension curves at three smoothingτ, formatted as in Fig 1. Note the low-force rupture in the middle panel is real. All curves are
simulated data, as described in the Supporting Material. (Right) The BCC for all simulated data
as a function of τ.

116

Figure 4.7: Overview of the FEATHER algorithm.
(A, B) The approach and retract
forces-vs-time at 25 kHz fit with a spline with knots spaced every 500 ms (τ), for a particularly
low v (100 nm/s) and extended retraction distance (1.2 µm). (C,D) The force-residuals-vs-timeof the approach and retract records after subtracting the spline from the high-bandwidth data.
The subtraction yields a force residual r(t) with a zero-centered mean and variance about thatmean (which contained mostly the thermal noise of the system within a window of 2τ). (E,F)
The variance (σr ) of the force residual as a function of time where σr is the standard deviationof the high-bandwidth data within a time window 2τ. The mean value of this variance (µσ ) andthe standard deviation (σσ ) of it are also plotted. The cyan shaded region in each plot is derived
from panel E. (G) The probability of no event at each time has a sharp minima near the expected
event location based on the application of Chebyshev’s inequality [123]. Changes in color of theretraction curved indicates an event, based on human-annotated data.

117

Figure 4.8: The sensitivity of the Bhattacharya coefficient’s complement (BCC) The
sensitivity of the Bhattacharya coefficient’s complement (BCC), a measure of how well the algorithmically predicted events match human-annotated data, as a function of algorithm specific parameters for the three compared algorithms FEATHER (A), OpenFovea (B), and Scientific Python (C).
Lower BCC is better. The BCC was computed from the polyprotein data set and the resulting
distributions shown in Figure 4.3 B–C.

118
Figure 4.9: Additional metrics for comparing algorithm performance between
FEATHER, OpenFovea, and Scientific Python.
The metrics are precision (A), recall(B), and the false positive ratio (C). Precision is defined as the number of correctly predicted
events (TP) in a data set divided by the total number of predicted events, TP/(TP+FP), where
FP is the number of false positives. Recall is defined (TP/(TP+FN)) where FN is the number ofmissed events or false negatives. For both these metrics, better performance is indicated as closer
to 1. The false positive ratio is defined as (FP/P) where FP is the number of false positives ina data set and P is the number of true events as defined by human annotation. Perfect recall
would also yield a value of 1 because there were no missed events. In contrast the metric FP/P
is better when closest to 0. It is important to note that these simple metrics ignore how closea predicted event is to a true event. Hence, while the wavelet transform has a similar Precision
and Recall to FEATHER, FEATHER does much better for more experimentally relevant metrics(see Figure 4.3). The most common cause of false positives for FEATHER is false triggering on
instrumental artifacts after tip detachment at high pulling velocities (Figure 4.13). FEATHER
most often returns a false negative when attempting to detect a short-lived, transiently-occupied
state. Applications of recently developed cantilevers [126] with improved temporal resolution andhigher force precision as well as optimizing τ for different v should mitigate these issues. (D) A
confusion matrix for FEATHER, where the rows are the human-annotated assignment of eventsand non-events, and the columns are predicted by FEATHER. (E–F) Formatted as panel (D), but
applied to OpenFovea and Scientific Python, respectively.

119
Figure 4.10: FEATHER outperforms the reference algorithms in analyzing a 650-nm
DNA dataset acquired at a high-retraction velocity (1,000 nm/s).
(A) Histograms of
relative errors between human-annotated and FEATHER’s algorithmically predicted event where∆Z is the fractional distance between the identified events divided by the full range of the record,
dt→p is the distance from a true event to the closest predicted event, and dp→t is the distance froman algorithmically predicted event to the closest true event. (B) FEATHER’s 2D distribution oftrue and predicted rupture forces and loading rates. (C,D) The histograms of rupture forces andloading rates from the data in panel B. (E) FEATHER’s performance metrics using Bhattacharya
coefficient’s complement (BCC), which measure the overlap between 2 distributions and ∆Z95,
location of the 95th percentile of the combined distribution for dp→t and dt→p . Ideally, both
metrics should 0. (F–J) OpenFovea’s and (K–O) Scientific Pythons’s performance using the same
analysis as in panels A–E. In the scatter plots (B,G, L), the density of green true points obscuresoverlap with the predicted points.

120
Figure 4.11: FEATHER generalizes well to force spectroscopy of 650-nm DNA data
set containing multiple attachments over three different retraction velocities (100,500, and 1,000 nm/s).
The subplots in this Figure are formatted as in Figure 4.10 but with
FEATHER applied to the full data set, spanning an order of magnitude in velocities and two ordersof magnitude in loading rates.

Figure 4.12: FEATHER generalizes well to a wide range of simulated data. (A) An
example force-extension curve, generated as described in the Supporting Material. The color-coded
regions denote a high-force rupture (blue), several ruptures with small changes in contour lengths(red), and a final lower-force rupture (green). (B) A histogram of contour lengths from all regions
in all simulated force-extension curves. (C). As panel B, but for contour length changes between
adjacent regions. (D–F) Formatted as Figure 4.3 in the main text, but showing FEATHER’s
performance on the simulated data.

121

Figure 4.13: Typical failure mode for FEATHER. (A) A force-versus-time trace, formatted
as Figure 4.1, where FEATHER’s predictions are consistent with the human-annotated data. (B)A trace, formatted as in panel A, where two spurious events are detected in the last half of the data.
Note that the data in panel B is at a 5-fold higher velocity (1.8 µm/s) than panel A (0.4 µm/s),
introducing additional noise and less averaging of Brownian motion since the fractional number of
spline points per record is fixed, not the degree of smoothing per unit time.

122
4.9.6

TablesTable 4.2: Statistical information on the polyprotein data set.
For each loading rate
v in the data set, this table lists the number of curves N curves ; mean number of points in a curve,
N points ; the number of curves with ‘x’ events Ne=x for x=[1,2,3]; and the number of curves withgreater than 3 events, N e>3 .
v (nm/s)
3800
1800
400
200

N curves
25
54
71
2

N points (103 )
62
77
113
200

Ne=3
1
2
0
0

Ne=4
5
8
9
1

Ne=5
6
9
28
0

Ne=6
12
31
27
1

Ne>6
1
4
7
0

123

Table 4.3: Primers sequences The forward and reverse primers amplify a 647-nm piece ofDNA, from positions 1607 to 3520 on the M13mp18 plasmid, as discussed in the text. Unmodified
DNA bases are lowercase. The uppercase letters ‘T’,’B’, and ‘D’ respectively represent biotinylated
Thymidine residues, a terminal Biotin separated from the sequence by triethyleneglycol spacer, anda terminal dibenzocyclooctyl (DBCO) separated from the sequence by triethyleneglycol spacer.
Name
Forward primer
Reverse primer

Sequence
Dagttgttcctttctattctcactccgc
BtcaataaTcggctgtctTtccttatcaTtc

Table 4.4: Statistical information on the 650-nm DNA data set.
Table 4.2.
v (nm/s)
1000
500
100

N curves
200
200
200

N points (103 )
117
200
671

Ne=1
173
130
155

Ne=2
26
49
35

Ne=3
1
9
6

Conventions are as in
Ne>3
0
12
4

124
Table 4.5: Pseudocode for FEATHER
def

Psuedocode for FEATHER. Comments given by #.

predict_events (approach, retraction,threshold, τ ):g* = second-order spline fit to retraction using τ for knots
ga = second order spline fit to approach using τ for knots
dt = spacing between adjacent time pointsr = retraction – g*ra = approach – gas[i] = standard deviation of r[i- 2τ :i+ 2τ ]sa [i] = standard deviation of ra[i- 2τ :i+ 2τ ]# Determine the no-event probability
ϵ = median of sa
σ = standard deviation of sak = (s- ϵ)/ σprobability = minimum(1,k -2 )# Determine the integral probability
integrateds[i] = integrate (s-ϵ) from [i- 2τ ] to [i+ 2τ ]set integrateds where positive to σk integ = (integrateds/ σ)probability = probability * minimum of (1, k integ -2 )# Determine the derivative probability
gderiv = derivative of ga
ϵd = median of derivative of ga
σ d = standard deviation of derivative of ga
g*deriv = derivative of g* with respect to time
k deriv = (g*deriv - ϵd )/ σ dprobability = probability * minimum of (1,k deriv -2 )# Determine differential probability
gdf = change of ga with respect to time in steps of τ /2
g* df = change of g* with respect to time in steps of τ /2
σ df = standard deviation of gdf
ϵd = median of gdf
k df = (g* df - ϵdf )/ σ df
probability = probability * minimum of (1, k df -2 )# find the initial guess for events
events = indices where probability <= thresholdcombine event indices within τ /4 of each other# update the events to remove adhesions
z approach,surface = last point where approach force > 0
z retraction, surface = where retract z retraction crosses approach z approach,surface
z retraction, surface = maximum of (z retraction, surface , first time k deriv =1)
remove events containing z retraction, surface
re-zero retract force to median of all points after last event
update all fits to the retraction and probabilities to where z retraction ≥ zretraction, surface# update the events to remove stretching and low-force noise
remove with positive derivatives and re-zero force as above
remove where g* - g* df ≤ (ϵdf +σ df ) or where g* +(g*deriv ·τ /4·dt) < σ df
re-zero force as above
remove where the average F with a window size of 2τ is less than σ + ϵ+ σ df
remove where the average F difference with a step size of 2τ is greater than -(σ +σ df )remove events within τ /4 of the boundaries
return events

125
Table 4.6: Variable and performance metric definitions. BCC stands for Bhattacharya
coefficient’s complement. Throughout, ’k‘ refers to the index of a force-extension curve, and ‘i’ and‘j’ refer to either true or predicted. For example, d t→p,4 represents the distances from the true tothe predicted events in force-extension curve four.
Name
K
Nk
di→p

∆Zx
νi
Fi
d (ν,F),i
relative error

Notation or definition
Number of curves
Number of points in force-extension curve kDistribution of pointwise distances in ’k‘
from ‘i’ ruptures to the closest ’j’ rupture or
Nk if none, where i and j are true (t) or predicted (p)1kthe ’x’-th % of concatenated N1k dt→p,k and dp→t,khistogram of ‘i’ loading rates over all khistogram of ‘i’ rupture forces over all kjoint histogram of ν i and Fi divided by K
∆Z 95
1

rupture BCC

Range
—
—

Optimum
—
—

—
—
—
—
—
[0,1]

—
—
—
—
—
0

[0,1]

0

1

2
2
1 - < d(ν,F),t |d(ν,F ),pTable 4.7: Table Title The Bhattacharya coefficient’s complement (BCC) and ∆Z95 for
FEATHER, as applied to the simulated data. FEATHER’s performance on simulated data ismore than an order of magnitude improved over the experimental results shown in Table 4.1. The
symbol (↓) indicates a lower value is better.
Name
FEATHERBCC (↓)
0.00014∆Z95 (↓)
0.000012

Table 4.8: Parameters for simulated force-extension curves. This table lists the parameters used for simulating F WLC,i (q n ). A sample from the uniform distribution between numbers x 0
and x f is denoted as Unif (x 0 , x f ), L0,i is the contour length in state i, F R is the mean rupture force,and ∆z i is the total pulling distance spent in state i. Note that ∆z i is proportional to time and to
the number of simulated points spent in a state, since the velocity, v, and sampling rate, ∆t, areconstant.
State i
1
2
3-6
7
8

L0,i
220 nm – 20 Unif[1,2]L0,i-1
L0,i-1 + 20 Unif[1,3]L0,i-1 + 20 Unif[10,100]
N/A, FWLC =0∆z i2000 points (60 ms)
50 * Unif (1,3)

250 Unif[1,2]

F R (pN)
NA
138
98
25
NA

126

Table 4.9: Definition and values of physical parameters used in Equation 4.3. Definitionand values of physical parameters used in Equation 4.3.
Parameter
Dq
∆t
gn
i
k
R
v
∂V
∂qn i

Description
Probe diffusion coefficientTime step
Noise source
Simulation state index
Probe stiffness
Loading rate
Probe velocity
State-dependent force

Value used
250 nm2 /ms
30 µs
Random numbers from a unit Gaussian dist.
0 (equilibration) to 8 (after final detachment).
0.5 pN/nm
25 pN/sR/k = 50 nm/s, except state 0 (v=0)
k (q n – z n ) + F WLC,i (q n ), where F WLC,i isdetermined as described in the text

Chapter 5
Improved free-energy landscape reconstruction of bacteriorhodopsin highlights
local variations in unfolding energy

Reprinted from

Patrick R. Heenan, Hao Yu, Matthew G. W. Siewny, and Thomas T. Perkins. Improved free-energy
landscape reconstruction of bacteriorhodopsin highlights local variations in unfolding energy. The
Journal of Chemical Physics, 148(12):123313, December 2017.

with the permission of AIP Publishing.

5.1

Abstract

Precisely quantifying the energetics that drive the folding of membrane proteins into a lipid
bilayer remains challenging. More than 15 years ago, atomic force microscopy (AFM) emerged asa powerful tool to mechanically extract individual membrane proteins from a lipid bilayer. Concurrently, fluctuation theorems, such as the Jarzynski equality, were applied to deduce equilibrium
free energies (∆G 0 ) from non-equilibrium single-molecule force spectroscopy (SMFS) records. The
combination of these two advances in single-molecule studies deduced the free-energy of the model
membrane protein bacteriorhodopsin in its native lipid bilayer. To elucidate this free-energy landscape at a higher resolution, we applied two recent developments. First, as an input to the recon-

128
struction, we used force-extension curves acquired with a 100-fold higher time resolution and 10-foldhigher force precision than traditional AFM studies of membrane proteins. Next, by using an inverse Weierstrass transform and the Jarzynski equality, we removed the free energy associated withthe force probe and determined the molecular free-energy landscape of the molecule under study,
bacteriorhodopsin. The resulting landscape yielded an average unfolding free energy per amino acid(aa) of 1.0 ± 0.1 kcal/mol, in agreement with past single-molecule studies. Moreover, on a smaller
spatial scale, this high-resolution landscape also agreed with an equilibrium measurement of a particular three-aa transition in bacteriorhodopsin that yielded 2.7 kcal/mol/aa, an unexpectedly highvalue. Hence, while average unfolding ∆G 0 per aa is a useful metric, the derived high-resolution
landscape details significant local variation from the mean. More generally, we demonstrated that,as anticipated, the inverse Weierstrass transform is an efficient means to reconstruct free-energy
landscapes from AFM data.

5.2

Introduction

Membrane proteins perform critical biological functions, such as light harvesting, signaling,
and transport. To carry out these and other diverse functions, they fold into equilibrium structures
within a lipid bilayer [137]. Yet, predicting the structure and stability of membrane proteinssignificantly lags behind the success for globular proteins [137]. For instance, models still struggle
to predict the tilt and overall packing of transmembrane (TM) α-helices. Hence, there is an ongoingneed to better quantify the molecular forces that drive and stabilize the folding of membraneproteins. As with globular proteins [53], the energy landscape provides the fundamental framework
for understanding membrane-protein folding and structure stabilization [138].
Single-molecule force spectroscopy (SMFS) has emerged as an important tool in determining
the energetics underlying the folding and unfolding of individual proteins [25–28]. For membraneproteins, atomic force microscopy (AFM) is the modality of choice [140], since individual proteins

129

Figure 5.1: High-resolution studies of bacteriorhodopsin (BR) (A) A cartoon illustrating
BR being unfolded from its C-terminal end using a modified, ultrashort cantilever. Each helix isdenoted by a letter. Color coding highlights the unfolding topology as helix pairs or the terminal
A helix are extracted. (B) A canonical force-extension curve while stretching at v = 300 nm/s
shows the major intermediates corresponding to pulling on the top of the E, C and A helix. The
initial portion of the force-extension curves was not analyzed due to the confounding effects of nonspecific surface adhesion (grey box). The colored bars correspond to the colored helical regions frompanel a. (C) Force-vs-time record of the highlighted black box in panel b shows near-equilibrium
unfolding and refolding at the top of helix A over a 13-amino-acid (aa) segment. (D) Multiple
force-extension curves of BR show numerous detected unfolding intermediates. Curves were wellmodeled by worm-like chain model within a particular state (dashed lines). (E) Force-vs-time
record shows repeated unfolding and refolding of a 3-aa segment during an equilibrium assay (v= 0 nm/s) near the top of helix E. For clarity, 5-MHz data (light purple) was smoothed to 25
kHz (dark purple). (F) A reconstructed 1D free-energy landscape based on ~100-ms records ofequilibrium data with 1-µs resolution tilted to F 1/2 , the force at which the two states are equally
likely to be occupied. Reconstruction was based on pfold [139]. Error bars represent the standard
error of the mean. Dashed line represent the location of transition state determined from a Bellanalysis of state lifetime, with the grey box denoting the standard deviation in that localization.
The data for Figure 5.1 B–F are from [72].

130
can be mechanically extracted from their native bilayer [141]. In the canonical assay, the tip of a
cantilever is pressed into bacteriorhodopsin (BR) embedded in its native lipid bilayer to promote
nonspecific attachment [141]. The tip is then retracted at constant velocity while force is deduced
from the bending of the cantilever, revealing a series of unfolding peaks in the force-extension curve(Figure 5.1 A–B). The dominant peaks correspond to pulling on the top of TM helix pairs or aterminal helix, notably the ED and CB helix pairs as well as the A helix. Importantly, these AFMbased studies provide insight into the energetics of membrane proteins in lipid bilayers, rather thanin detergent. Moreover, AFM studies provide a reproducible reference state, the fully unfolded
protein. In contrast, the “unfolded” protein in ensemble unfolding assays retains α-helical content
and therefore provides a poor reference state [137].
Complementing experimental advances that led to SMFS studies of individual proteins andnucleic-acid structures, theoretical advances enabled the determination of equilibrium free-energy
values (∆G 0 ) from analysis of non-equilibrium force-extension curves [57]. Such analysis provides
important information beyond the distances to transition states (∆x‡ ) and the zero-force dissociation rate constant (k off ) determined using Bell-Evans analysis of dynamic force spectroscopy data
[30, 111]. In particular, as demonstrated in pioneering studies of structured RNA using opticaltweezers [51, 142], a 1D free-energy landscape can be obtained by extending the Jarzynski equality[143] via the weighted histogram method developed by Hummer and Szabo [57]. Salient to thispresent work, Hummer and Szabo’s original paper applied the weighted histogram method to deduce the free-energy landscape for the ED helix pair bacteriorhodopsin, yielding an average of ∆G 0
of 1.1 per amino acid (aa) estimated from eight force-extension curves. Using significantly more
traces (N ≈ 600), Preiner et al. extended this analysis over five helices (E–A) reported an average∆G 0 of 1.3 ± 0.2 kcal/mol/aa (mean ± SD) [144].
A higher-resolution description of the free-energy landscape enables a more quantitative comparison between the location and lifetimes of short-lived unfolding intermediates and the underlying
energy landscape. Recent advances in applying modified ultrashort cantilevers optimized for 1-µs

131resolution SMFS [145, 146] enabled the measurement of bacteriorhodopsin with a 100-fold higher
time resolution and 10-fold higher force precision that, in turn, revealed rapid near-equilibrium folding (Figure 5.1 C) and a multitude of previously unresolved, transiently occupied intermediates(Figure 5.1 D) [72]. These cantilevers also enabled the first equilibrium study of membrane protein folding, where a particular three-amino-acid transition near the top of the E helix repeatedly
unfolded and refolded (Figure 5.1 E). Reconstruction of the free-energy landscape underlying thistransition (Figure 5.1 F) revealed an unexpectedly large ∆G 0 per aa (2.7 kcal/mol) at F = 0 pN.
Here, we merged these experimental advances in acquiring high-resolution force-extension curves
with theoretical advances in reconstructing the landscape from non-equilibrium records. In particular, we used the inverse Weierstrass transform (IWT) applied in conjunction with the Jarzynski
free-energy integral to avoid convolving the compliance of the AFM cantilever into the resulting
free-energy landscape [39]. Importantly, the IWT works best for studies using a stiffer force probe[39] —making it particularly suitable for AFM-based assays (k ≈ 6–100 pN/nm)—due to theirhigher probe stiffness relative to earlier application in an optical-trapping-based assay (k = 0.4
pN/nm) [147]. The resulting landscape yielded an average unfolding free energy per amino acid(aa) of 1.0 ± 0.1 kcal/mol (mean ± SEM), in close agreement with past single-molecule studies[57, 144, 148]. Moreover, on a smaller spatial scale, this landscape also agreed with the recent
equilibrium measurement that showed an unexpectedly high ∆G 0 per aa near the top of the E
helix. Hence, while average unfolding ∆G 0 per aa is a useful metric, the resulting high-resolution
landscape confirmed significant local variations from the mean.

5.3

Free-energy landscape reconstruction

As background, the Jarzynski equality is remarkable because it relates the work done during
many repetitions of a non-equilibrium process to the equilibrium free-energy difference as a functionof an experimental parameter. For our work, the experimental parameter was the position of thecantilever base relative to the surface, or ‘z’ [38]. More precisely, the Jarzynski equality is a

132
thermodynamic relationship between the Helmholtz free energy of a system A(z) and the measured
work W (z):e−βA(z) = ⟨eβW (z) ⟩N(5.1)

where z is the zero-force equilibrium position of the force probe, β is the inverse of the thermalenergy k B T, and the average is taken over N independent stretching trajectories, each starting andending at the same choice of z [39, 143, 149]. The Jarzynski equality is exact only in the limit as
N →∞, but is approximately true for finite N . In practice, SMFS experiments apply the Jarzynski
equality by repeatedly folding or unfolding a single molecule of interest using a force probe. In thiscase, the work is the integral of the force as a function of the cantilever position z. For example,
in the constant velocity experiments used in our AFM assay, z(t)=vt+z i , and the integral for eachstretching experiment starts at the same well-defined z i associated with the aligned curves (seebelow). Tip-sample separation, which is also the molecular extension (x) in an AFM assay, is notuniquely defined at all values of z. The molecule may be in different folding states and therefore
different molecular extensions, referred to henceforth as q as is common in landscape-reconstruction
literature [39]. The Jarzynski equality requires that all molecules included in the calculation start(z i ) and finish (z f ) in an equilibrium state.
Hummer and Szabo’s original extension of the Jarzynski equality for SMFS studies determines
the landscape as a function of molecular extension (q), instead of SMFS probe position (z), andalso removes the energetic contribution of the force probe via a weighted histogram method [57]. In
subsequent work, they applied an IWT to simplify this calculation and make more efficient use of alimited set of force-extension curves by assuming a stiff, harmonic pulling apparatus[39, 147]. Put
differently, the curvature (i.e., the second spatial derivative) of the true underlying energy landscapeshould not exceed the stiffness of the force probe. Indeed, the consequence of not fulfilling thisassumption was theoretically anticipated [39] and experimentally demonstrated for a RNA pseudo-

133knot studied using an optical trap [147]. In that case, the derived landscape was filtered by the softprobe leading to a lower barrier height (akin to applying a spatial filter that smooths out sharp
features). Hence, energy landscape reconstruction by the IWT is well suited to AFM-based assays
due to the higher stiffness of AFM cantilevers in comparison to optical traps [39, 147].
As input for IWT reconstruction of BR, we used a set of 106 force-extension curves of BR
extracted from its native lipid bilayer (purple membrane for BR) acquired using focused-ion-beammodified BioLever Fast cantilevers (AC10DS, Olympus). The details of this data acquisition andthe force-extension curves have been previously published [72]. Briefly, modified cantilevers (k ≈10–40 pN/nm) were pressed into the purple membrane at ~1 nN for 1 s and retracted from thesurface at a constant velocity (v) of 300 nm/s. Data were recorded at 5 MHz on a commercial AFM(Cypher ES, Asylum Research) and then smoothed with a second-order, 500-point Savitsky-Golay
filter for all subsequent analysis. As is standard for SMFS-studies of BR [140], the curves werelaterally aligned to superimpose the major obligate intermediate associated with pulling on the topof the E helix. These aligned traces (Figure 5.2 A) then served as input to calculate the free-energy
landscape via the IWT. The unfolding of the GF helix pair was not analyzed due to the confounding
effects of non-specific tip-sample adhesion.
The IWT reconstructs the free-energy landscape, approximately removing the contributionof the force probe, by calculating statistics on an ensemble of N force-extension curves. For aparticular curve n with measured force F n (z), the work used by the IWT is defined as∫ z′

Fn (z )dz

Wn (z) =

′

(5.2)

zi

where z runs from z i to z f at a given velocity v for all N force-extension curves. The Jarzynski equality determines the Helmholtz free energy A(z), which includes energy from the probe.
The IWT approximately removes the contribution of the probe by calculating the so-called work-

134
weighted ensemble statistics. The work-weighted force and force squared, denoted with double
brackets, are defined at each z as:<< F (z) >>=⟨eβWn (z) Fn (z)⟩N⟨eβWn (z) Fn2 (z)⟩N
2
and
<<
F
(z)
>>=
e−βA(z)e−βA(z)(5.3)

where <X>N denotes an average of X over the ensemble of force-extension curves at a fixed z.
These work-weighted values are related to the first and second spatial derivatives of the Helmholtz
free energy as follows:Ȧ(z) =<< F (z) >> and 1 −Ä(z)β= (<< F 2 (z) >> − << F (z) >>2 )
k
k

(5.4)

The IWT-based reconstruction uses the first and second derivatives to reconstruct the freeenergy landscape as a function of molecular extension [39]:G(q = z −Ȧ(z)Ȧ(z)2
1Ä(z)) ≈ A(z) −+ln(1 −
)
k
2k
2β
k

(5.5)

Importantly, G(q) is approximately the free energy of the molecule, instead of the free energyof the molecule and the probe. To avoid errors associated with numerical derivatives of noisy data,
we calculated the energy derivatives, Ȧ(z) and Ä(z), directly from the primary work-weighted force
and force squared (see Figure 5.4) which, in turn, allowed G(q) to be determined. To avoid errors
in combining data sets acquired using different cantilever stiffnesses (k), we chose z i = 18 nm + (20pN/k), which corresponded to approximately F = 20 pN at an extension of 18 nm when pullingon the top of the ED helix pair. Each set of data, containing a minimum of 20 force-extension
curves, corresponded to one cantilever and was reconstructed separately. After the transform wascompleted, the resulting free-energy landscapes were functions of molecular extension q (instead ofz) and were averaged based on the number of traces associated with each cantilever data set. As

135

Figure 5.2: Process for free-energy landscape reconstruction of BR using an inverse
Weierstrass transform (IWT). (A) A heat map of all force-extension curves used in this work.
Data within ~18 nm of the surface are excluded due to surface adhesion. (B) Different components
for calculating the molecular free energy ∆G0 as a function of the molecular extension when using
the IWT. The three components used in computing ∆G0 as defined in Equation 5.5: A, (aqua,
dot-dash) and terms involving its first and second derivative (pink, solid line and brown, dashedline; respectively). To promote comparison to panels a and c, the plotted lateral axis is q, molecule
extension. (C) The ∆G0 free energy as a function of molecular extension. Shaded region reports
the standard deviation as deduced from a bootstrap analysis.

136
in previous work, [144] we found that we needed a minimum of 20 traces per cantilever to limit
reconstruction error to reasonable levels.
Uncertainties in the landscape and its first derivative were determined by a bootstrap
analysis[150]. In brief, 250 synthetic data sets were generated from the original set of 106 curves
using random resampling with replacement. Only synthetic data sets with 1 − Ä(z)k > 0, as requiredby the IWT, were counted towards the total of 250. From the resulting ensemble of 250 landscapes,
the standard deviation in simulated mean values was calculated after smoothing with a third order,
piecewise polynomial to 0.4 nm. This smoothing choice was chosen to approximately minimize theproduct of error in Ġ(q) and in the least-squared fitting of G(q) across the bootstrapping rounds(see Figure 5.5). Future work with more traces from individual cantilevers and from cantilevers
with a narrower range in k will decrease the uncertainties in landscape reconstruction.
We illustrate the process of calculating the IWT for BR from Equation 5.5 in Figure 5.2. The
starting data consists of 106 aligned force-extension curves. As shown in Figure 5.2 A, the resulting
heat map represents the ensemble of measurements needed to apply Jarzynski’s inequality and theinverse Weierstrass transform. To highlight the contributions of the three components in Equation
5.5 in determining G(q), we color coded a plot of A(z) and the IWT corrections (Figure 5.2 B).
The corrections were obtained as described above, using work-weighted histogram statistics[39, 149].
The resulting G(q) was deduced from the sum of these three components and represents the freeenergy of the ED, CB, and A helical pairs of bacteriorhodopsin (Figure 5.2 C). Shaded regions
represent the standard deviation deduced from the aforementioned bootstrap analysis.

5.4

Results and discussion

The local unfolding free energy of BR depended on the individual structural element being
unfolded. Our resulting high-resolution free-energy landscape of BR’s final five helices showedsignificant variation in slope as a function of extension and therefore unfolding energy per amino

137acid (Figure 5.2 C). To highlight this variation, we computed the free-energy landscape and ∆G 0
per nm as a function extension for the individual major structural components (ED, CB, andA helices) (Figure 5.3 A–C). The mean ∆G 0 per aa is 1.0 ± 0.1 kcal/mol (mean ± SD) whencalculated from the unfolding of the ED, CB, and A helices [156 ±15 kcal/mol (mean ± SD) over
160 amino acids of helices, traditionally taken as the top of the E-helix in AFM-based assays [151]].
This average value is slightly larger than bulk denaturation studies that report ~0.5 kcal/mol/aa[152] and similar to past single-molecule results of 1.1–1.3 kcal/mol per aa [57, 144, 148].
For completeness, we note that most rigorous to-date experimental determination of the total∆G 0 for the E–A helices is 227 ± 38 kcal/mol (mean ± SD) and is therefore significantly higher
than our value of 156 ±15 kcal/mol, a result not precisely reflected in the reported 1.3 kcal/mol
per aa [144]. The origin of this difference is that this prior work used 171 amino acids in theiranalysis, which includes an extra 11 amino acids associated with the loop between the top of E andF helices and the first turn of the F-helix. If we reanalyze this earlier result with the same numberof amino acids as used in this present work, their value now becomes 1.4 ± 0.2 kcal/mol per aa.
Our average unfolding energy per amino acid therefore lies below this prior experimental result.
Possible origins of this difference could be the improved precision of our force-extension curves
and/or some reduction in the total ∆G 0 values due to the IWT poorly resolving stiff portions of
the landscapes compared to the weighted histogram method (see below) [147]. Finally, a recent
coarse-grained molecular dynamics simulation predicts a free energy of transfer from bulk water
to lipid of -130 kcal/mol for the 160-aa sequence in our work, or about 0.8 kcal/mol per aa for
unfolding BR from its lipid bilayer (see Section S1) [153].
Our work also documented that ∆G 0 per nm varied more than 15-fold, from 11 kcal/mol
at the top of the ED helix pair to 0.6 kcal/mol at the bottom of the same helix pair. Whileit has long been known that hydrophobicity of the amino-acid sequence within the lipid bilayer
and inter- and intra-helix interactions contribute to this variation [154], recent work also shows
variations in the strength of hydrogen bonds within TM helices [155]. To convert this local, single-

138
molecule force spectroscopy derived metric to the more commonly reported ∆G 0 per aa, we notethat there are ~3 amino acid residues per nm of contour length for an unstructured peptide based on
crystallography (0.36 nm/aa) [156]. Given the elevated forces experienced during unfolding portionsof the records, we approximated extension with contour length and therefore approximated a local
value for ∆G 0 per aa as 1/3 of ∆G 0 per nm after taking the spatial derivative of the reconstructed
free-energy landscape (e.g., Figure 5.2 C). As described in the methods section, the landscapes andits derivatives were calculated for each set of data derived from a cantilever of fixed stiffness, aftersmoothing with a piecewise polynomial to 0.4 nm. At the top of the ED helix pair, we observed
the highest local ∆G 0 per aa followed by the top of the CB and A helices.
One immediate trend from this data was a higher ∆G 0 per aa when BR was more fully
folded. Thus, looking forward, an assay that probes the initial unfolding of a membrane protein
where most, if not all of intra- and inter-helix bonds are still intact, offers the best opportunity to
precisely quantify ∆G 0 per aa under native-like conditions. Unfortunately, while a few studies havequantified the initial unfolding of the GF helix [151, 157], precise quantification remains hindered
by non-specific adhesion between the tip and the surface [140, 141, 144]. Another trend in our data
was that ∆G 0 per aa for unwinding the first portion of a TM helix pair was higher than whenunfolding the second helix. Put more simply, once the first helix in a TM helix pair was extracted,
the second helix took significantly less energy to extract.
Interestingly, we also achieved agreement between the unfolding free energies obtained byequilibrium and dynamic assays. As discussed in the introduction, we had previously deduced an
unexpectedly high ∆G0 per aa [2.7 ± 0.1 kcal/mol (mean ± SEM)] for a particular transition near
the top of the ED helix pair after reconstruction of the free-energy landscape from equilibrium data
(Figure 5.1 F) [72]. The present IWT analysis of dynamic data yielded an average ∆G0 per aa
near the top of the ED helix, 2.9 ± 0.5 kcal/mol (mean ± SD), in agreement with the previous
equilibrium result for a specific three amino-acid transition [72].

139
We emphasize that the ∆G 0 per aa measured here does not correspond to breaking a particular hydrogen-bond or fully solvating an amino acid out of a lipid bilayer, but results from a
convolution of angstrom-scale motion of each amino acid along the stretching axis. We also notethat the reported values include the contribution of the extended, unfolded protein. In other words,
since the ED helix was folded at the start of the analysis, the entropic contribution to stretching
unfolded polypeptides to high force is part of the resulting ∆G0 . Future experimental advances
and/or applying more sophisticated analysis can minimize or theoretically separate out the energy
associated with stretching these compliant unfolded peptides [7]. However, the situation for BR
is distinctly different from standard optical-trapping assays which use much longer, 300–600-nm
double-stranded nucleic acids handles to accommodate the geometry of optical-trapping studies[36, 158, 159].
Figure 5.3: Local unfolding free energies as a function of extension vary broadly
between and within BR’s major structural elements (the ED, CB and A helices, respectively).
(A) Local unfolding free energy per nm (left axis) and reconstructed energy
landscape (right axis) for the ED helix pair. The local unfolding free-energy is the spatial first
derivative of the reconstructed landscape. The standard deviations in the deduced values are theshaded region around the measured value as deduced by a bootstrap analysis. (B,C) Same analysis
for the BC helix pair and the A helix, respectively.

Somewhat unexpectedly, we observed a local landscape stiffness—the second derivative of thereconstructed landscape—greater than any particular cantilever stiffness used. Yet, Hummer andSzabo’s implementation of the IWT assumed a stiff probe, which should limit the reconstructed
landscape from having a stiffness that exceeds the force probe [39]. More quantitatively, the greatest

140
landscape curvature for BR was 8 kcal/(mol nm2 ) or 55 pN/nm, larger than the stiffest cantileverused (40 pN/nm). We attribute this small discrepancy to errors in polynomial fitting and numericaldifferentiation. On the scientific front, it is therefore likely that our reconstructed landscape represents a lower bound on the local value of ∆G 0 per nm, akin to early studies of RNA pseudoknots
studied with optical traps[147]. Hence, as shown in that optical-trapping work, [147] the weighted
histogram method is better for reconstructing landscapes containing such “stiff” features. For thevast majority of BR’s landscape, the stiff-spring approximation of the IWT was fulfilled and yieldeda more accurate landscape reconstruction (Figure 5.6). In addition, the almost-negligible correction
to the landscape from the Ä term outside of the ED Helix (Figure 5.2 B, brown) confirmed thathigher-order corrections were unlikely to affect the landscape of the CB and A helices. In fact, thecorrections of the IWT to the Jarzynski equality were small except near the top of the E helix, whichinterestingly is also the same location where equilibrium flickering was previously reported (Figure
5.1 E). Looking forward, using a stiffer cantilever is the obvious means to fulfill the stiff probe
assumption. Yet, stiffer ultrashort cantilevers are not overdamped (quality factor Q > 0.5) [145],
violating an assumption underlying traditional force spectroscopy theories [52, 111, 160]. Hence,
there is also ongoing need to optimize modified ultrashort cantilevers for higher k but low Q.

5.5

Conclusion

As anticipated [39, 147], the IWT provides an efficient and accessible means to reconstruct
free-energy landscapes when using AFM, even for complicated landscapes such as BR. The energy
landscape reconstruction presented here highlights significant variation along the unfolding freeenergy landscape. The overall trend is similar to early work [144] but with improvements associatedwith reconstruction of the landscape from much higher resolution force-extension curves [72, 145]
and using the IWT [39] that efficiently removes the energy contribution associated with the bendingof the cantilever. As a result, we achieved a more accurate and higher-resolution reconstruction.
The resulting landscape yielded an average ∆G0 per aa of 1.0 ± 0.1 kcal/mol, in much better

141
agreement with past single-molecule studies than our one prior determination of ∆G0 per aa (2.7
kcal/mol) derived from an equilibrium assay probing a particular three aa transition near the top of
the ED helix pair. Importantly, on a smaller spatial scale, this high-resolution landscape also agreed
with that prior equilibrium measurement of the three-aa transition (∆G0 = 2.9 ± 0.5 kcal/mol/aa).
Indeed, the highest-measured curvature of the free-energy landscape (~55 pN/nm) was limited bycantilever stiffness (~10–40 pN/nm), and hence represents a lower bound of local determinationof ∆G0 per aa due to the underlying assumption of a stiff probe in applying the IWT [39, 147].
Future developments that enable efficient unfolding and refolding over reversible transitions would
enable comparing energy landscapes deduced from state-based models [37] with those used here,
providing another method for investigating and verifying local free-energy landscape reconstructionof membrane proteins.

5.6

Acknowledgements

We thank Michael Woodside for useful discussions.

5.7

Supporting Information

5.7.1

Figures142

Figure 5.4: Work-weighted statistics are necessary for accurate landscape reconstruction. (a) For an example landscape, the Helmholtz free energy, A, is plotted versus molecularextension (q). A representative region is highlighted in red and detailed in an inset. A(q) has
been smoothed with a second-order, 500-point Savitsky-Golay filter. (b) The change in Helmholtz
energy, dA(q), is plotted versus extension. This derivative was obtained by the finite difference
method (black) and via the work-weighted force (pink). The finite difference method yields curves
with significantly higher noise. The high noise can be attributed to the fact that A(q) and q are
noisy outputs of the IWT. (c) The “Helmholtz force”, Ȧ(q), obtained by work-weighted statistics,
yields the expected shape and order of magnitude of a force-extension curve. Note the extension
starts with pulling on at the top of the E helix as opposed to experimental records that start at
the top of the G helix (e.g., Figure 5.1 B).

143

Figure 5.5: Filtering choice balances fitting and derivative error with spatial resolution.
This figure plots error versus filtering size. Error is defined as the product of the fitting error andderivative error. For a fixed filtering size, the fitting error is the mean over bootstrapping iterationsof the summed least-squared residuals of a spline fit to G(q), and the derivative error is the variancein Ġ(q) over bootstrapping iterations. The error changes very little (<5%) between 0.3 nm and1 nm. The choice of 0.4 nm, highlighted in red, was chosen as a compromise between landscaperesolution and error minimization.

144

Figure 5.6: The mean landscape curvature (or stiffness) plotted versus extension relative to the start of the ED helix. Each helical region is color-coded, with a labeled bar
underneath. The landscape stiffness is almost always less than the cantilever stiffness. A typicalcantilever stiffness of 25 pN/nm is plotted as a dotted magenta line. The ED helix is the only helix
with a significant region exceeding the cantilever stiffness.

145
5.7.2

Methodology for comparison with coarse-grained MD simulation

The amino acid sequence of BR which was unfolded for this work is (listed from C to N
terminus): [72]
AKSTFGFFLVYLIYLMAATSIAWWVFRYSYVKTLAGVLGTGIMIGDAGVLALITGQDADVLLALDLLLLPTTFLWDAYRAWYIPNQEGGFPVMTLGYGLLMSLYMTF
AIAPVLTTIAYFKKADPDSVGMGKVLFYLTGLGMLATGLALWIWEPRGTIQAQ
We used the following table 5.1 (adapted from Yamada et al [153]) to determine the freeenergy of transfer from water to lipid. For the purposes of comparison, the unfolding energy of bR
out of lipid into buffer was assumed to be equal and opposite to the energy of transfer of bR fromwater to lipid:

146

Table 5.1: Amino acid transfer energies Free energy of transfer from water to lipid used by
Yamada et al [153] in coarse-grained MD simulations.
Amino Acid
Ala
Arg
Asn
Asp
Cys
Gln
Glu
Gly
His
Ile
Leu
Lys
Met
Phe
Pro
Ser
Thr
Trp
Tyr
Val
N Terminus

Energy of Transfer (kJ/mol)
-3.5
21
9.6
23.9
-2.7
6.2
19.3
-1.3
2.2
-11.7
-11.7
11.8
-6.8
-14.3
-7
5.8
4.5
-13.4
-9.7
-8.8
9.8

Chapter 6
Conclusions and future directions

AFM-based single molecule imaging and force spectroscopy techniques are powerful tools forinvestigating biological systems at physiologically relevant buffer conditions. Although applicationsof the present work improve the biological relevance of data acquired by AFM-based imaging and
SMFS, new possibilities enabled by the present work will lead to further progress, as detailed below.
Chapter 5 details how energy landscape reconstructions obtained from SMFS data measure
the variations in free energy associated with dissociating specific portions of membrane proteins.
The adoption of site-specific chemistry increases the throughput and quality of data and enables
reproducible unfolding and refolding of near-native biomolecular structure. Such unfolding andrefolding data provide more insight into the energy landscape of the system under interest (seeChapter 1. Therefore, experiments which leverage site-specific chemistry will be much better positioned for unfolding and refolding studies. In addition, performing unfolding-refolding experimentswith site-specific chemistry as a function of perturbation (e.g. protein mutation, buffer conditions,cantilever attachment point), will provide more insight into the molecular structures or energy
landscapes.
Chapter 4 demonstrates how to accurately and automatically extract unfolding event locations (and therefore the loading rate and rupture force) from SMFS data. As mentioned above,
experiments which unfold and refold a system improve biophysical insight. Therefore, extending

148
the method detailed in Chapter 4 from only detecting unfolding events to also detecting refolding
events would greatly improve its utility as an SMFS analysis technique.
Chapter 3 describes a technique for imaging surface-bound DNA, resulting in DNA boundstrong enough for imaging and maintaining a structure consistent with equilibrated, B-form DNA.
As of publication of this method, all other AFM techniques performed in liquid featured kineticallytrapped DNA and therefore DNA with an artificially low apparent two-dimensional persistence
length (i.e. artificially high flexibility). By extension, and perhaps more interestingly, any AFM
imaging method of protein-bound DNA strongly perturbed the system of interest. Therefore, future
work should identify previously studied systems of interest (e.g. DNA-protein complexes exclusively
studied in air or kinetically trapped in liquid) and determine if the prior results hold with surfaceequilibrated samples. In addition, DNA-protein systems which have never been studied via AFM
but which are expected to have a mechanical difference along the DNA contour (e.g. bending,morphological change, oligomerization) are also good applications of the experimental method
outlined in Chapter 3.

Bibliography[1] Taekjip Ha and Philip Tinnefeld. Photophysics of Fluorescent Probes for Single-Molecule
Biophysics and Super-Resolution Imaging. Annual Review of Physical Chemistry, 63(1):595–
617, May 2012.
[2] Rahul Roy, Sungchul Hohng, and Taekjip Ha. A practical guide to single-molecule FRET.
Nature Methods, 5(6):507–16, June 2008.
[3] Benjamin Schuler and William A Eaton. Protein folding studied by single-molecule FRET.
Current Opinion in Structural Biology, 18(1):16–26, February 2008.
[4] Chirlmin Joo, Hamza Balci, Yuji Ishitsuka, Chittanon Buranachai, and Taekjip Ha. Advances in Single-Molecule Fluorescence Methods for Molecular Biology. Annual Review ofBiochemistry, 77(1):51–76, June 2008.
[5] William J. Greenleaf, Michael T. Woodside, and Steven M. Block. High-resolution, singlemolecule measurements of biomolecular motion. In Annual Review of Biophysics andBiomolecular Structure, volume 36 of Annual Review of Biophysics, pages 171–190. 2007.
[6] Keir C. Neuman and Attila Nagy. Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy. Nature Methods, 5(6):491–505, June 2008.
[7] Michael T. Woodside and Steven M. Block. Reconstructing Folding Energy Landscapes bySingle-Molecule Force Spectroscopy. Annual Review of Biophysics, 43(1):19–39, 2014.
[8] G. Binnig, C. F. Quate, and Ch. Gerber. Atomic Force Microscope. Physical Review Letters,
56(9):930–933, March 1986.
[9] H. G. Hansma, J. Vesenka, and et al. Reproducible Imaging and Dissection of Plasmid DNA
Under Liquid with the Atomic Force Microscope. Science, 256(5060):1180, May 1992.
[10] H G Hansma, M Bezanilla, F Zenhausern, M Adrian, and R L Sinsheimer. Atomic force
microscopy of DNA in aqueous solutions. Nucleic Acids Research, 21(3):505–512, February
1993.
[11] Y L Lyubchenko, P I Oden, D Lampner, S M Lindsay, and K A Dunker. Atomic force

150
microscopy of DNA and bacteriophage in air, water and propanol: the role of adhesion forces.
Nucleic Acids Research, 21(5):1117–1123, March 1993.
[12] Michael J. Allen, X. Fan Dong, Timothy E. O’Neill, Peter Yau, Stephen C. Kowalczykowski,
Joe Gatewood, Rod Balhorn, and E. Morton Bradbury. Atomic force microscope measurements of nucleosome cores assembled along defined DNA sequences. Biochemistry,
32(33):8390–8396, August 1993.
[13] M. Guthold, M. Bezanilla, D. A. Erie, B. Jenkins, H. G. Hansma, and C. Bustamante. Following the assembly of RNA polymerase-DNA complexes in aqueous solutions with the scanning
force microscope. Proceedings of the National Academy of Sciences, 91(26):12927–12931,
December 1994.
[14] H.G. Hansma, K.J. Kim, D.E. Laney, R.A. Garcia, M. Argaman, M.J. Allen, and S.M. Parsons. Properties of Biomolecules Measured from Atomic Force Microscope Images: A Review.
Journal of Structural Biology, 119(2):99–108, July 1997.
[15] Sandor Kasas, Neil H. Thomson, Bettye L. Smith, Helen G. Hansma, Xingshu Zhu, Martin Guthold, Carlos Bustamante, Eric T. Kool, Mikhail Kashlev, and Paul K. Hansma.
Escherichia coli RNA Polymerase Activity Observed Using Atomic Force Microscopy.
Biochemistry, 36(3):461–468, January 1997.
[16] Darren J. Ellis, David T. F. Dryden, Torunn Berge, J. Michael Edwardson, and Robert M.
Henderson. Direct observation of DNA translocation and cleavage by the EcoKI endonucleaseusing atomic force microscopy. Nature Structural & Molecular Biology, 6(1):15–17, January
1999.
[17] M. Lysetska, A. Knoll, D. Boehringer, T. Hey, G. Krauss, and G. Krausch. UV light-damaged
DNA and its interaction with human replication protein A: an atomic force microscopy study.
Nucleic Acids Research, 30(12):2686–2691, June 2002.
[18] Neal Crampton, William A. Bonass, Jennifer Kirkham, Claudio Rivetti, and Neil H. Thomson.
Collision events between RNA polymerases in convergent transcription studied by atomic
force microscopy. Nucleic Acids Research, 34(19):5416–5425, November 2006.
[19] Isabelle Sorel, Olivier Piétrement, Loïc Hamon, Sonia Baconnais, Eric Le Cam, and David
Pastré. The EcoRI−DNA Complex as a Model for Investigating Protein−DNA Interactions
by Atomic Force Microscopy. Biochemistry, 45(49):14675–14682, December 2006.
[20] Atsushi Miyagi, Toshio Ando, and Yuri L. Lyubchenko. Dynamics of Nucleosomes Assessedwith Time-Lapse High-Speed Atomic Force Microscopy. Biochemistry, 50(37):7901–7908,
September 2011.
[21] Yuri L. Lyubchenko. Preparation of DNA and nucleoprotein samples for AFM imaging.
Micron, 42(2):196–206, February 2011.
[22] Toshio Ando, Takayuki Uchihashi, and Noriyuki Kodera. High-Speed AFM and Applications
to Biomolecular Systems, May 2013.

151[23] Divakaran Murugesapillai, Serge Bouaziz, L. James Maher, Nathan E. Israeloff, Craig E.
Cameron, and Mark C. Williams. Accurate nanoscale flexibility measurement of DNA and
DNA–protein complexes by atomic force microscopy in liquid. Nanoscale, August 2017.
[24] Mikihiro Shibata, Hiroshi Nishimasu, Noriyuki Kodera, Seiichi Hirano, Toshio Ando,
Takayuki Uchihashi, and Osamu Nureki. Real-space and real-time dynamics of CRISPRCas9 visualized by high-speed atomic force microscopy. Nature Communications, 8(1):1430,
December 2017.
[25] Matthias Rief, Mathias Gautel, Filipp Oesterhelt, Julio M. Fernadez, and Hrmann E.
Gaub. Reversible unfolding of individual titin immunoglobulin domains by AFM. Science;
Washington, 276(5315):1109–12, May 1997.
[26] Miklos S. Z. Kellermayer, Steven B. Smith, Henk L. Granzier, and Carlos Bustamante.
Folding-unfolding transitions in single titin molecules characterized with laser tweezers.
Science; Washington, 276(5315):1112–6, May 1997.
[27] Alessandro Borgia, Philip M. Williams, and Jane Clarke. Single-molecule studies of protein
folding. In Annual Review of Biochemistry, volume 77, pages 101–125. Annual Reviews, Palo
Alto, 2008. WOS:000257596800006.
[28] Keir C. Neuman and Attila Nagy. Single-molecule force spectroscopy: optical tweezers, magnetic tweezers and atomic force microscopy. Nature Methods, 5(6):491–505, June 2008.
[29] V. T. Moy, E. L. Florin, and H. E. Gaub. Intermolecular forces and energies between ligands
and receptors. Science (New York, N.Y.), 266(5183):257–259, October 1994.
[30] R. Merkel, P. Nassoy, A. Leung, K. Ritchie, and E. Evans. Energy landscapes of receptorligand bonds explored with dynamic force spectroscopy. Nature, 397(6714):50–3, January1999.
[31] S. Kasas, N. H. Thomson, B. L. Smith, P. K. Hansma, J. Miklossy, and H. G. Hansma.
Biological applications of the AFM: From single molecules to organs. International Journalof Imaging Systems and Technology, 8(2):151–161, January 1997.
[32] D Fotiadis. Imaging and manipulation of biological structures with the AFM. Micron,33(4):385–397, January 2002.
[33] Andrea Alessandrini and Paolo Facci. AFM: a versatile tool in biophysics. Measurement
Science and Technology, 16(6):R65–R92, June 2005.
[34] Elias M Puchner and Hermann E Gaub. Force and function: probing proteins with AFMbased force spectroscopy. Current Opinion in Structural Biology, 19(5):605–614, October
2009.
[35] Daniel J. Müller and Yves F. Dufrêne. Atomic force microscopy: a nanoscopic window on
the cell surface. Trends in Cell Biology, 21(8):461–469, August 2011.

152[36] Michael T. Woodside, Peter C. Anthony, William M. Behnke-Parks, Kevan Larizadeh, Daniel
Herschlag, and Steven M. Block. Direct Measurement of the Full, Sequence-Dependent Folding Landscape of a Nucleic Acid. Science, 314(5801):1001–1004, November 2006.
[37] Yaojun Zhang and Olga K. Dudko. A transformation for the mechanical fingerprints ofcomplex biomolecular interactions. Proceedings of the National Academy of Sciences of theUnited States of America, 110(41):16432–16437, October 2013.
[38] C. Jarzynski. Nonequilibrium Equality for Free Energy Differences. Physical Review Letters,
78(14):2690–2693, April 1997.
[39] Gerhard Hummer and Attila Szabo. Free energy profiles from single-molecule pulling experiments. Proceedings of the National Academy of Sciences of the United States of America,
107(50):21441–21446, 2010.
[40] C. Rivetti, M. Guthold, and C. Bustamante. Scanning force microscopy of DNA deposited
onto mica: Equilibration versus kinetic trapping studied by statistical polymer chain analysis.
Journal of Molecular Biology, 264(5):919–932, December 1996. WOS:A1996VZ95100007.
[41] Hugo K. Christenson and Neil H. Thomson. The nature of the air-cleaved mica surface.
Surface Science Reports, 71(2):367–390, June 2016.
[42] P. K. Hansma, J. P. Cleveland, M. Radmacher, D. A. Walters, P. E. Hillner, M. Bezanilla,
M. Fritz, D. Vie, H. G. Hansma, C. B. Prater, J. Massie, L. Fukunaga, J. Gurley, and V. Elings.
Tapping mode atomic force microscopy in liquids. Applied Physics Letters, 64(13):1738–1740,
March 1994.
[43] A. L. Weisenhorn, P. K. Hansma, T. R. Albrecht, and C. F. Quate. Forces in atomic force
microscopy in air and water. Applied Physics Letters, 54(26):2651–2653, June 1989.
[44] H G Hansma, R L Sinsheimer, M Q Li, and P K Hansma. Atomic force microscopy of singleand double-stranded DNA. Nucleic Acids Research, 20(14):3585–3590, July 1992.
[45] N. H. Thomson, S. Kasas, Smith, H. G. Hansma, and P. K. Hansma. Reversible Binding of
DNA to Mica for AFM Imaging. Langmuir, 12(24):5905–5908, January 1996.
[46] Magdalena Bezanilla, Srinivas Manne, Daniel E. Laney, Yuri L. Lyubchenko, and Helen G.
Hansma. Adsorption of DNA to Mica, Silylated Mica, and Minerals: Characterization by
Atomic Force Microscopy. Langmuir, 11(2):655–659, February 1995.
[47] H G Hansma and D E Laney. DNA binding to mica correlates with cationic radius: assay byatomic force microscopy. Biophysical Journal, 70(4):1933–1939, April 1996.
[48] Yuri L. Lyubchenko and Luda S. Shlyakhtenko. AFM for analysis of structure and dynamics
of DNA and protein–DNA complexes. Methods, 47(3):206–213, March 2009.
[49] Qi Zhang, Jasna Brujic, and Eric Vanden-Eijnden. Reconstructing Free Energy Profiles from
Nonequilibrium Relaxation Trajectories. Journal of Statistical Physics, 144(2):344–366, 2011.

153[50] Gavin E. Crooks. Entropy production fluctuation theorem and the nonequilibrium work
relation for free energy differences. Physical Review E, 60(3):2721–2726, September 1999.
[51] D. Collin, F. Ritort, C. Jarzynski, S. B. Smith, I. Tinoco, and C. Bustamante. Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies. Nature,437(7056):231–234, September 2005.
[52] Olga Dudko. Intrinsic Rates and Activation Free Energies from Single-Molecule Pulling
Experiments. Physical Review Letters, 96(10), 2006.
[53] J. N. Onuchic, Z. LutheySchulten, and P. G. Wolynes. Theory of protein folding: Theenergy landscape perspective. Annual Review of Physical Chemistry, 48:545–600, 1997.
WOS:A1997YB98900019.
[54] J. N. Onuchic and P. G. Wolynes. Theory of protein folding. Current Opinion in Structural
Biology, 14(1):70–75, 2004.
[55] Ken A. Dill, S. Banu Ozkan, M. Scott Shell, and Thomas R. Weikl. The Protein Folding
Problem. Annual Review of Biophysics, 37(1):289–316, May 2008.
[56] E. Evans. Energy landscapes of biomolecular adhesion and receptor anchoring at interfaces
explored with dynamic force spectroscopy. Faraday Discussions, (111):1–16, 1998.
[57] Gerhard Hummer and Attila Szabo. Free energy reconstruction from nonequilibrium singlemolecule pulling experiments. Proceedings of the National Academy of Sciences of the UnitedStates of America, 98(7):3658–3661, March 2001.
[58] J. P. Hobbs, M. Anand, and B. A. Campion. Fluorinated High-Density Polyethylene Barrier
Containers. In Barrier Polymers and Structures, volume 423 of ACS Symposium Series, pages
280–294. American Chemical Society, May 1990.
[59] Wei Wang. Protein aggregation and its inhibition in biopharmaceutics. International Journalof Pharmaceutics, 289(1-2):1–30, January 2005.
[60] S. Nema and Ke Avis. Freeze-Thaw Studies of a Model Protein, Lactate-Dehydrogenase, in
the Presence of Cryoprotectants. Journal of Parenteral Science and Technology, 47(2):76–83,
April 1993. WOS:A1993LX95900006.
[61] W. W. Cleland. Dithiothreitol, a New Protective Reagent for SH Groups*. Biochemistry,
3(4):480–482, April 1964.
[62] Artur Kr�żel, Wojciech Leśniak, Małgorzata Jeżowska-Bojczuk, Piotr Młynarz, Justyna Brasuñ, Henryk Kozłowski, and Wojciech Bal. Coordination of heavy metals by dithiothreitol,
a commonly used thiol group protectant. Journal of Inorganic Biochemistry, 84(1):77–88,
March 2001.
[63] Wolfgang Walther, Ulrike Stein, Carsten Voss, Torsten Schmidt, Martin Schleef, and Peter M

154
Schlag. Stability analysis for long-term storage of naked DNA: impact on nonviral in vivo
gene transfer. Analytical Biochemistry, 318(2):230–235, July 2003.
[64] Darryl L. Davis, Edward P. O’Brie, and Catherine M. Bentzley. Analysis of the Degradation of Oligonucleotide Strands During the Freezing/Thawing Processes Using MALDI-MS.
Analytical Chemistry, 72(20):5092–5096, October 2000.
[65] J. P. Cleveland, S. Manne, D. Bocek, and P. K. Hansma. A nondestructive method for
determining the spring constant of cantilevers for scanning force microscopy. Review of
Scientific Instruments, 64(2):403–405, February 1993.
[66] Paul A. Wiggins, Thijn Van Der Heijden, Fernando Moreno-herrero, Andrew Spakowitz, Rob
Phillips, Jonathan Widom, Cees Dekker, and Philip C. Nelson. High flexibility of DNA on
short length scales probed by atomic force microscopy. Nature Nanotechnology, 1(2):137–41,
November 2006.
[67] Peter Markiewicz and M. Cynthia Goh. Atomic force microscopy probe tip visualizationand improvement of images using a simple deconvolution procedure. Langmuir, 10(1):5–7,
January 1994.
[68] Nagaraju Chada, Krishna P. Sigdel, Raghavendar Reddy Sanganna Gari, Tina Rezaie Matin,
Linda L. Randall, and Gavin M. King. Glass is a Viable Substrate for Precision ForceMicroscopy of Membrane Proteins. Scientific Reports, 5:12550, July 2015.
[69] Robert Walder, Marc-André LeBlanc, William J. Van Patten, Devin T. Edwards, Jacob A.
Greenberg, Ayush Adhikari, Stephen R. Okoniewski, Ruby May A. Sullan, David Rabuka,
Marcelo C. Sousa, and Thomas T. Perkins. Rapid Characterization of a Mechanically Labile
�-Helical Protein Enabled by Efficient Site-Specific Bioconjugation. Journal of the American
Chemical Society, 139(29):9867–9875, July 2017.
[70] Robert Walder, William J. Van Patten, Ayush Adhikari, and Thomas T. Perkins. Going
Vertical To Improve the Accuracy of Atomic Force Microscopy Based Single-Molecule Force
Spectroscopy. ACS Nano, 12(1):198–207, January 2018.
[71] Abraham. Savitzky and M. J. E. Golay. Smoothing and Differentiation of Data by Simplified
Least Squares Procedures. Analytical Chemistry, 36(8):1627–1639, July 1964.
[72] Hao Yu, Matthew G. W. Siewny, Devin T. Edwards, Aric W. Sanders, and Thomas T.
Perkins. Hidden dynamics in the unfolding of individual bacteriorhodopsin proteins. Science,
355(6328):945–950, March 2017.
[73] Patrick R. Heenan and Thomas T. Perkins. Imaging DNA Equilibrated onto Mica in Liquid
Using Biochemically Relevant Deposition Conditions. ACS Nano, 13(4):4220–4229, April
2019.
[74] Yanwei Wang, Shiyong Ran, and Guangcan Yang. Single molecular investigation of DNA
looping and aggregation by restriction endonuclease BspMI. Scientific Reports, 4, July 2014.

155[75] Divakaran Murugesapillai, Micah J. McCauley, Ran Huo, Nelson Holte, Molly H, Armen
Stepanyants, L. James Maher, Nathan E. Israeloff, and Mark C. Williams. DNA bridging andlooping by HMO1 provides a mechanism for stabilizing nucleosome-free chromatin. Nucleic
Acids Research, 42(14):8996–9004, August 2014.
[76] Maria V. Sukhanova, Sanae Abrakhi, Vandana Joshi, David Pastre, Mikhail M. Kutuzov,
Rashid O. Anarbaev, Patrick A. Curmi, Loic Hamon, and Olga I. Lavrik. Single molecule
detection of PARP1 and PARP2 interaction with DNA strand breaks and their poly(ADPribosyl)ation using high-resolution AFM imaging. Nucleic Acids Research, 44(6):e60–e60,
April 2016.
[77] M. Bezanilla, B. Drake, E. Nudler, M. Kashlev, P. K. Hansma, and H. G. Hansma. Motionand enzymatic degradation of DNA in the atomic force microscope. Biophysical Journal,
67(6):2454–2459, December 1994.
[78] Aleksandre Japaridze, Dusan Vobornik, Ewelina Lipiec, Andrea Cerreta, Jacek Szczerbinski,
Renato Zenobi, and Giovanni Dietler. Toward an Effective Control of DNA’s Submolecular
Conformation on a Surface. Macromolecules, 49(2):643–652, January 2016.
[79] David Pastré, Olivier Piétrement, Stéphane Fusil, Fabrice Landousy, Josette Jeusset, MarieOdile David, Loïc Hamon, Eric Le Cam, and Alain Zozime. Adsorption of DNA to MicaMediated by Divalent Counterions: A Theoretical and Experimental Study. BiophysicalJournal, 85(4):2507–2518, October 2003.
[80] Olivier Piétrement, David Pastré, Stéphane Fusil, Josette Jeusset, Marie-Odile David, Fabrice
Landousy, Loïc Hamon, Alain Zozime, and Eric Le Cam. Reversible Binding of DNA on
NiCl2-Treated Mica by Varying the Ionic Strength. Langmuir, 19(7):2536–2539, April 2003.
[81] Alice Pyne, Ruth Thompson, Carl Leung, Debdulal Roy, and Bart W. Hoogenboom. SingleMolecule Reconstruction of Oligonucleotide Secondary Structure by Atomic Force Microscopy.
Small, 10(16):3257–3261, August 2014.
[82] L. S. Shlyakhtenko. Structure and dynamics of three-way DNA junctions: atomic force
microscopy studies. Nucleic Acids Research, 28(18):3472–3477, September 2000.
[83] Yuri L. Lyubchenko, Luda S. Shlyakhtenko, and Alexander A. Gall. Atomic Force Microscopy
Imaging and Probing of DNA, Proteins, and Protein-DNA Complexes: Silatrane Surface
Chemistry. In DNA-Protein Interactions, Methods in Molecular Biology™, pages 337–351.
Humana Press, 2009.
[84] Pj Hagerman. Flexibility of Dna. Annual Review of Biophysics and Biophysical Chemistry,
17:265–286, 1988. WOS:A1988P532200012.
[85] Willem Vanderlinden and Steven De Feyter. Chain relaxation dynamics of DNA adsorbing
at a solid–liquid interface. Nanoscale, 5(6):2264, 2013.
[86] D. J. Billingsley, A. J. Lee, N. A. B. Johansson, A. Walton, L. Stanger, N. Crampton, W. A.

156
Bonass, and N. H. Thomson. Patchiness of ion-exchanged mica revealed by DNA binding
dynamics at short length scales. Nanotechnology, 25(2):025704, 2014.
[87] M. L. Sushko, A. L. Shluger, and C. Rivetti. Simple model for DNA adsorption onto a mica
surface in 1 : 1 and 2 : 1 electrolyte solutions. Langmuir, 22(18):7678–7688, August 2006.
WOS:000239921800033.
[88] Andrew J. Lee, Michal Szymonik, Jamie K. Hobbs, and Christoph Wälti. Tuning the translational freedom of DNA for high speed AFM. Nano Research, 8(6):1811–1821, June 2015.
[89] Valeria Cassina, Davide Seruggia, Giovanni Luca Beretta, Domenico Salerno, Doriano Brogioli, Stefano Manzini, Franco Zunino, and Francesco Mantegazza. Atomic force microscopy
study of DNA conformation in the presence of drugs. European Biophysics Journal, 40(1):59–
68, January 2011.
[90] L. D. Landau and E. M. Lifshit�s�. Statistical physics. Number v. 5 in Their Course oftheoretical physics, v. 5. Pergamon Press ; Addison-Wesley Pub. Co, London : Reading,Mass, 1958.
[91] S. B. Smith, L. Finzi, and C. Bustamante. Direct mechanical measurements of the elasticity
of single DNA molecules by using magnetic beads. Science, 258(5085):1122–1126, November
1992.
[92] C. Bustamante, J. F. Marko, E. D. Siggia, and S. Smith. Entropic elasticity of lambda-phageDNA. Science, 265(5178):1599–1600, September 1994.
[93] A. Bensimon, A. Simon, A. Chiffaudel, V. Croquette, F. Heslot, and D. Bensimon. Alignment and sensitive detection of DNA by a moving interface. Science, 265(5181):2096–2098,
September 1994.
[94] D. Bensimon, A. J. Simon, V. Croquette, and A. Bensimon. Stretching DNA with a Receding
Meniscus: Experiments and Models. Physical Review Letters, 74(23):4754–4757, June 1995.
[95] Richard R. Sinden. DNA structure and function. Academic Press, San Diego, 1994.
[96] Jianxun Mou, Daniel M. Czajkowsky, Yiyi Zhang, and Zhifeng Shao. High-resolution atomicforce microscopy of DNA: the pitch of the double helix. FEBS Letters, 371(3):279–282,
September 1995.
[97] Shinichiro Ido, Kenjiro Kimura, Noriaki Oyabu, Kei Kobayashi, Masaru Tsukada, Kazumi
Matsushige, and Hirofumi Yamada. Beyond the Helix Pitch: Direct Visualization of Native
DNA in Aqueous Solution. ACS Nano, 7(2):1817–1822, February 2013.
[98] Kfir Kuchuk and Uri Sivan. Hydration Structure of a Single DNA Molecule Revealed byFrequency-Modulation Atomic Force Microscopy. Nano Letters, 18(4):2733–2737, April 2018.
[99] D. Rhodes and A. Klug. Helical periodicity of DNA determined by enzyme digestion. Nature,286(5773):573–578, August 1980.

157[100] Christoph G. Baumann, Steven B. Smith, Victor A. Bloomfield, and Carlos Bustamante.
Ionic effects on the elasticity of single DNA molecules. Proceedings of the National Academyof Sciences, 94(12):6185–6190, June 1997.
[101] Torunn Berge, Darren J. Ellis, David T.F. Dryden, J.Michael Edwardson, and Robert M.
Henderson. Translocation-Independent Dimerization of the EcoKI Endonuclease Visualized
by Atomic Force Microscopy. Biophysical Journal, 79(1):479–484, July 2000.
[102] Kelly J. Neaves, Laurie P. Cooper, John H. White, Stewart M. Carnally, David T. F. Dryden,
J. Michael Edwardson, and Robert M. Henderson. Atomic force microscopy of the EcoKI
Type I DNA restriction enzyme bound to DNA shows enzyme dimerization and DNA looping.
Nucleic Acids Research, 37(6):2053–2063, April 2009.
[103] Abigail J. Bath, Susan E. Milsom, Niall A. Gormley, and Stephen E. Halford. Many Type IIs
Restriction Endonucleases Interact with Two Recognition Sites before Cleaving DNA. Journalof Biological Chemistry, 277(6):4024–4033, February 2002.
[104] Jochen Felix Kepert, Katalin Fejes Tóth, Maïwen Caudron, Norbert Mücke, Jörg Langowski,
and Karsten Rippe. Conformation of Reconstituted Mononucleosomes and Effect of Linker
Histone H1 Binding Studied by Scanning Force Microscopy. Biophysical Journal, 85(6):4012–
4022, December 2003.
[105] Luda S. Shlyakhtenko, Alexander Y. Lushnikov, and Yuri L. Lyubchenko. Dynamics of
Nucleosomes Revealed by Time-Lapse Atomic Force Microscopy. Biochemistry, 48(33):7842–
7848, August 2009.
[106] Xueyin Wang, Richard D. Paucek, Anne R. Gooding, Zachary Z. Brown, Eva J. Ge, Tom W.
Muir, and Thomas R. Cech. Molecular analysis of PRC2 recruitment to DNA in chromatin
and its inhibition by RNA. Nature Structural and Molecular Biology, page nsmb.3487, October 2017.
[107] Yuri L. Lyubchenko, Luda S. Shlyakhtenko, and Toshio Ando. Imaging of nucleic acids withatomic force microscopy. Methods, 54(2):274–283, June 2011.
[108] Daniel J Müller and Andreas Engel. Atomic force microscopy and spectroscopy of native
membrane proteins. Nature Protocols, 2(9):2191–2197, September 2007.
[109] Daniel J. Müller, Dimitrios Fotiadis, Simon Scheuring, Shirley A. Müller, and Andreas Engel.
Electrostatically Balanced Subnanometer Imaging of Biological Specimens by Atomic ForceMicroscope. Biophysical Journal, 76(2):1101–1111, February 1999.
[110] Patrick R. Heenan and Thomas T. Perkins. FEATHER: Automated Analysis of Force Spectroscopy Unbinding and Unfolding Data via a Bayesian Algorithm. Biophysical Journal,
115(5):757–762, September 2018.
[111] E Evans and K Ritchie. Dynamic strength of molecular adhesion bonds. Biophysical Journal,
72(4):1541–1555, April 1997.

158[112] E Evans and K Ritchie. Strength of a weak bond connecting flexible polymer chains.
Biophysical Journal, 76(5):2439–2447, May 1999.
[113] Patrick D. Bosshart, Patrick L.T.M. Frederix, and Andreas Engel. Reference-Free Alignment
and Sorting of Single-Molecule Force Spectroscopy Data. Biophysical Journal, 102(9):2202–
2211, May 2012.
[114] M. Kuhn, H. Janovjak, M. Hubain, and D. J. Müller. Automated alignment and patternrecognition of single-molecule force spectroscopy data. Journal of Microscopy, 218(2):125–
132, May 2005.
[115] C Gergely, B Senger, J. C Voegel, J. K. H Hörber, P Schaaf, and J Hemmerlé. Semiautomatized processing of AFM force-spectroscopy data. Ultramicroscopy, 87(1–2):67–78,
March 2001.
[116] Charles Roduit, Bhaskar Saha, Livan Alonso-sarduy, Andrea Volterra, Giovanni Dietler, andSandor Kasas. OpenFovea: open-source AFM data processing software. Nature Methods;
New York, 9(8):774–5, August 2012.
[117] Sandor Kasas, Beat M. Riederer, Stefan Catsicas, Brunero Cappella, and Giovanni Dietler.
Fuzzy logic algorithm to extract specific interaction forces from atomic force microscopy data.
Review of Scientific Instruments, 71(5):2082–2086, May 2000.
[118] Xavier García-Massó, Matthias C. Huber, Jacqueline. Friedmann, Luis M. Gonzalez, Stefan M. Schiller, and José L. Toca-Herrera. Automated detection of protein unfolding eventsin atomic force microscopy force curves. Microscopy Research and Technique, 79(11):1105–
1111, November 2016.
[119] R. Benítez and V. J. Bolós. Searching events in AFM force-extension curves: A wavelet
approach. Microscopy Research and Technique, 80(1):153–159, January 2017.
[120] Nicola Galvanetto, Andrea Perissinotto, Andrea Pedroni, and Vincent Torre. Fodis: Software
for Protein Unfolding Analysis. Biophysical Journal, 114(6):1264–1266, March 2018.
[121] Kostyantyn R. Partola and George Lykotrafitis. FRAME (Force Review Automation Environment): MATLAB-based AFM data processor. Journal of Biomechanics; Kidlington,
49(7):1221–1224, 2016.
[122] Yi Cao, Rachel Kuske, and Hongbin Li. Direct Observation of Markovian Behavior of the
Mechanical Unfolding of Individual Proteins. Biophysical Journal, 95(2):782–788, July 2008.
[123] Jim Pitman. Probability. Springer texts in statistics. Springer-Verlag, New York, 1993.
[124] Eric Jones, Travis Oliphant, Pearu Peterson, and others. SciPy: Open source scientific tools
for Python. 2001.
[125] A. Bhattacharyya. On a Measure of Divergence between Two Multinomial Populations.
Sankhyā: The Indian Journal of Statistics (1933-1960), 7(4):401–406, 1946.

159[126] Devin T. Edwards, Jaevyn K. Faulk, Marc-André LeBlanc, and Thomas T. Perkins. Force
Spectroscopy with 9-�s Resolution and Sub-pN Stability by Tailoring AFM Cantilever Geometry. Biophysical Journal, 113(12):2595–2600, December 2017.
[127] Matthew S. Bull, Ruby May A. Sullan, Hongbin Li, and Thomas T. Perkins. Improved Single
Molecule Force Spectroscopy Using Micromachined Cantilevers. ACS Nano, 8(5):4984–4995,
May 2014.
[128] John F. Marko and Eric D. Siggia. Stretching DNA. Macromolecules, 28(26):8759–8770,
December 1995.
[129] P. Dierckx. An algorithm for smoothing, differentiation and integration of experimental datausing spline functions. Journal of Computational and Applied Mathematics, 1(3):165–184,
September 1975.
[130] Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar. Foundations of machinelearning. Adaptive computation and machine learning. The MIT Press, Cambridge, Massachusetts, second edition edition, 2018. OCLC: 1041560990.
[131] Allison B. Churnside, Ruby May A. Sullan, Duc M. Nguyen, Sara O. Case, Matthew S.
Bull, Gavin M. King, and Thomas T. Perkins. Routine and Timely Sub-picoNewton Force
Stability and Precision for Biological Applications of Atomic Force Microscopy. Nano Letters,
12(7):3557–3561, July 2012.
[132] J. W. Bryson, J. R. Desjarlais, T. M. Handel, and W. F. DeGrado. From coiled coils to small
globular proteins: design of a native-like three-helix bundle. Protein Science : A Publicationof the Protein Society, 7(6):1404–1414, June 1998.
[133] Sehat Nauli, Brian Kuhlman, and David Baker. Computer-based redesign of a protein folding
pathway. Nature Structural & Molecular Biology, 8(7):602–605, July 2001.
[134] R. Proksch, T. E. Schäffer, J. P. Cleveland, R. C. Callahan, and M. B. Viani. Finite opticalspot size and position corrections in thermal spring constant calibration. Nanotechnology,
15(9):1344, 2004.
[135] M D Wang, H Yin, R Landick, J Gelles, and S M Block. Stretching DNA with opticaltweezers. Biophysical Journal, 72(3):1335–1346, March 1997.
[136] Patrick R. Heenan, Hao Yu, Matthew G. W. Siewny, and Thomas T. Perkins. Improved freeenergy landscape reconstruction of bacteriorhodopsin highlights local variations in unfolding
energy. The Journal of Chemical Physics, 148(12):123313, December 2017.
[137] Ann Marie Stanley and Karen G. Fleming. Process of folding proteins into membranes:
Challenges and progress. Archives of Biochemistry and Biophysics, 469(1):46–66, January
2008. WOS:000251824800006.
[138] Harald Janovjak, K. Tanuj Sapra, Alexej Kedrov, and Daniel J. Mueller. From valleys to160ridges: Exploring the dynamic energy landscape of single membrane proteins. Chemphyschem,
9(7):954–966, May 2008. WOS:000255845500001.
[139] Young Min Rhee and Vijay S. Pande. One-Dimensional Reaction Coordinate and the Corresponding Potential of Mean Force from Commitment Probability Distribution. The Journalof Physical Chemistry B, 109(14):6780–6786, April 2005.
[140] Christian A. Bippes and Daniel J. Muller. High-resolution atomic force microscopy andspectroscopy of native membrane proteins. Reports on Progress in Physics, 74(8):086601,
2011.
[141] F. Oesterhelt, D. Oesterhelt, M. Pfeiffer, A. Engel, H. E. Gaub, and D. J. Müller. Unfolding
pathways of individual bacteriorhodopsins. Science (New York, N.Y.), 288(5463):143–146,
April 2000.
[142] Jan Liphardt, Sophie Dumont, Steven B. Smith, Ignacio Tinoco, and Carlos Bustamante.
Equilibrium information from nonequilibrium measurements in an experimental test of
Jarzynski’s equality. Science, 296(5574):1832–5, June 2002.
[143] Sanghyun Park, Fatemeh Khalili-Araghi, Emad Tajkhorshid, and Klaus Schulten. Free energy
calculation from steered molecular dynamics simulations using Jarzynski’s equality. The
Journal of Chemical Physics, 119(6):3559–3566, July 2003.
[144] Johannes Preiner, Harald Janovjak, Christian Rankl, Helene Knaus, and et al. Free Energy of
Membrane Protein Unfolding Derived from Single-Molecule Force Measurements. BiophysicalJournal; New York, 93(3):930–7, August 2007.
[145] Devin T. Edwards, Jaevyn K. Faulk, Aric W. Sanders, Matthew S. Bull, Robert Walder,Marc-Andre LeBlanc, Marcelo C. Sousa, and Thomas T. Perkins. Optimizing 1-�s-Resolution
Single-Molecule Force Spectroscopy on a Commercial Atomic Force Microscope. Nano Letters,
15(10):7091–7098, October 2015.
[146] Devin T. Edwards and Thomas T. Perkins. Optimizing force spectroscopy by modifyingcommercial cantilevers: Improved stability, precision, and temporal resolution. Journal of
Structural Biology, 197(1):13–25, January 2017.
[147] Megan C. Engel, Dustin B. Ritchie, Daniel A. N. Foster, Kevin S. D. Beach, and Michael T.
Woodside. Reconstructing Folding Energy Landscape Profiles from Nonequilibrium Pulling
Curves with an Inverse Weierstrass Integral Transform. Physical Review Letters, 113(23),2014.
[148] Max Kessler, Kay E. Gottschalk, Harald Janovjak, Daniel J. Muller, and Hermann E. Gaub.
Bacteriorhodopsin Folds into the Membrane against an External Force. Journal of Molecular
Biology, 357(2):644–654, March 2006.
[149] David D. L. Minh and Artur B. Adib. Optimized Free Energies from Bidirectional SingleMolecule Force Spectroscopy. Physical Review Letters, 100(18):180602, May 2008.

161[150] William H. Press, Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling. Numerical
Recipes in C: The Art of Scientific Computing. Cambridge University Press, New York, NY,
USA, 1988.
[151] Daniel J. Muller, Max Kessler, Filipp Oesterhelt, Clemens Moller, and et al. Stability ofbacteriorhodopsin (alpha)-helices and loops analyzed by single-molecule force spectroscopy.
Biophysical Journal; New York, 83(6):3578–88, December 2002.
[152] Florian Cymer, Gunnar von Heijne, and Stephen H. White. Mechanisms of Integral Membrane
Protein Insertion and Folding. Journal of Molecular Biology, 427(5):999–1022, March 2015.
[153] Tatsuya Yamada, Takahisa Yamato, and Shigeki Mitaku. Forced Unfolding Mechanism of
Bacteriorhodopsin as Revealed by Coarse-Grained Molecular Dynamics. Biophysical Journal,111(10):2086–2098, November 2016.
[154] Stephen H. White and William C. Wimley. Membrane protein folding and stability: Physicalprinciples. Annual Review of Biophysics and Biomolecular Structure; Palo Alto, 28:319, 1999.
[155] Zheng Cao, James M. Hutchison, Charles R. Sanders, and James U. Bowie. Backbone Hydrogen Bond Strengths Can Vary Widely in Transmembrane Helices. Journal of the American
Chemical Society, 139(31):10742–10749, August 2017.
[156] L. Pauling and R. B. Corey. The Pleated Sheet, A New Layer Configuration of Polypeptide
Chains. Proceedings of the National Academy of Sciences, 37(5):251–256, May 1951.
[157] Max Kessler and Hermann E. Gaub. Unfolding Barriers in Bacteriorhodopsin Probed fromthe Cytoplasmic and the Extracellular Side by AFM. Structure, 14(3):521–527, March 2006.
[158] J. Liphardt, B. Onoa, S. B. Smith, I. Tinoco, and C. Bustamante. Reversible unfolding of
single RNA molecules by mechanical force. Science (New York, N.Y.), 292(5517):733–737,
April 2001.
[159] C. Cecconi. Direct Observation of the Three-State Folding of a Single Protein Molecule.
Science, 309(5743):2057–2060, September 2005.
[160] G. I. Bell. Models for the specific adhesion of cells to cells. Science, 200(4342):618–627, May
1978.