Spectroscopic Evaluation of Excited State Depopulation in
Red Fluorescent Proteins Developed Using Fluorescence
Lifetime Selections
by
Srijit Mukherjee
B.S. and M.S., Indian Institute of Science Education and Research Mohali, 2016

A thesis submitted to the Faculty of the Graduate school of the University ofColorado in partial fulfillment of the requirements for the degree of Doctor ofPhilosophy
Department of Chemistry and JILA
2022

Committee Members
Ralph Jimenez (Professor, Department of Chemistry and JILA)
Amy E. Palmer (Professor, Department of Biochemistry and BioFrontiers Inst.)
J. Mathias Weber (Professor, Department of Chemistry and JILA)
Gordana Dukovic (Professor, Department of Chemistry and RASEI)
Joel Kralj (Asst. Professor, Department of MCDB and BioFrontiers Inst.)iMukherjee, Srijit (Ph.D., Chemistry)
Spectroscopic Evaluation of Excited State Depopulation in Red Fluorescent Proteins Developed
Using Fluorescence Lifetime Selections
Thesis directed by Professor (Adjoint) of Chemistry and JILA Fellow Ralph Jimenez
Abstract:
Fluorescent Proteins are intriguing molecules that are ubiquitous tools for biological research. This
thesis investigates the relationship between engineering improved fluorescent proteins andfundamental physical chemistry principles that drive the molecular design of brighter and more
photostable variants of existing fluorescent proteins. This work primarily focuses on designingbrighter variants of the red-fluorescent proteins, FusionRed and mCherry, and the consequentphysical investigations that lead to increments in brightness. To achieve this, droplet-based andsingle stream microfluidic sorters that discriminate members of a cell-based mutagenesis libraryof variants on their excited state lifetime and fluorescence intensity were developed and utilized.
These lifetime-based selections led to variants with greater than 3-fold higher values offluorescence quantum yield in comparison to their progenitors. Finally, the mechanisms andpathways that lead to excited state depopulation after photoexcitation, which govern observables
like fluorescence quantum yield, fluorescence brightness, reversible and permanent
photobleaching, and blinking at the single molecule level were investigated. This work highlights
the progress and the many knowledge gaps in understanding the interwoven relationships ofobserved photophysics in fluorescent proteins, and suggests ways in which one might further
examine the physical basis of brightness and photostability in these molecules.

ii

Dedication
To my teachers, from my parents to professors – thank you for all I know.

iii

Acknowledgements
This thesis is dedicated to all of my teachers who have influenced my life, which makes my parents
the first and foremost to acknowledge. Their role in supporting me and making me the person I am
is beyond instrumental. I have to acknowledge the key role of my uncle, Professor Partha Sarathi
Sanyal, who is an icon I have always looked up to. Professor K. S. Viswanathan deserves special
thanks for allowing a curious undergrad floating through the hallways of Academic Block-1 in
IISER-Mohali to actively contribute in picturing molecules dancing to the melody of infrared andvisible light.
I would like to express my sincerest gratitude to my advisor, Professor Ralph Jimenez for imparting
his scientific expertise and wisdom. His perfect balance of independence and accessibility has been
critical to my progress. Outside mentoring me in methods to perform cutting-edge experiments,
his role in making me an effective science communicator has been significant. I have to thankProfessor Amy Palmer for being the most attentive co-mentor one can ever have in graduate
school. Her guidance has made me a better scientist. I thank the members of the Jimenez Lab
across the years. Special mention to Professor ShengTing Hung, who as a postdoctoral mentor anda friend was the best colleague an incoming graduate student could ever ask for. I have to thankDr. Premashis Manna, on whose foundational work I could build on and explore interesting
directions. Thanks to Dr. Nancy Douglas for being the mutagenesis magician of our lab andimparting me each and every bit of biological insight that I possess. I need to thank fellow graduate
students at the lab - Dr. Samantha Allen (and Rob Wells) and Kristen Parzuchowski for becoming
the best set of work friends I have ever had. Thank you for being there and listening to cries about
failed experiments, corrupted data and other shenanigans of being a graduate student. I sincerely
thank the other lab members who constantly provided scientific and emotional support across theyears – Ryan Wilson, Dr. Richard Erickson, Pia Friis, Dr. Brett Fiedler, Dr. Joshua Slocum andmy fellow soccer fan, Dr. Alex Mikhaylov. I thank the wonderful and scientifically motivatedundergrads who I have interacted with and mentored. Thank you, Emma Simmerman, Connor
Thomas and Annika Ekrem, you have always kept the lab buzzing and my basic pedagogic skills
sharp. I thank the members of the Palmer Lab for their help during the countless times I havewalked into the cell-culture room with a missing reagent or a pipette (and obviously the best groupmeeting snacks). I thank each and every one at JILA – with special mentions to Hans Green, Felixiv

Vietmeyer, Curtis Biemborn and J.R. Raith, whom I have countlessly bugged for every little
problem I have ever faced with instrumentation, electronics or computers!
I have to thank the best set of friends who packed their bags from IISER Mohali and showed up in
different countries to embrace the love of science. Thank you Saumya Gupta, Vivek Sagar, Nakul
Teke and Atul Arora for keeping me sane in the U.S. I thank Yosman Bapat-Dhar, Shwetha
Srinivasan and Evelyn Abraham who kept the messages rolling and making me smile every now
and then. I need to thank the trio I have grown up with – Tanmoy, Biswadip and Haymanti, it isamazing that we’ve stuck for twenty years. I thank my friends in India, Abhinay and Ashish whohave kept in touch and constantly supported me. My wonderful cohort – thanks Nate, Jenny (andFrank), Nicholas, Jona, Marium, Keaten, Tri, Ashutosh, Wyatt (and Livi), Zach (and Katie) andCallum. I thank people from Kolkata in Boulder, who kept the Bengali in me alive – thanks
Shambojit (and Nikita), Souradeep, Sannidhya, Sobhan, Sandip, Aritra, and Subhayan! I thank myextended family who have constantly provided me encouragement and feedback, with special
mention of my cousin Avishek Chandra who made moving to a new country halfway across theglobe an easy transition.
And finally, this thesis would have been incomplete without the constant motivation, love andencouragement from Swarupa. The trust and confidence she instills in me keeps me chugging
forward!

v

Table of contents
Chapter 1 – Introduction

1– 32

·

1.1

Publication Note

1

·

1.2

Introduction

1– 3

·

1.3

Brightness

3– 22

·

1.4

Photostability

23– 29·1.5

Conclusions

29– 30·

1.6

Thesis Aims and Objectives

30– 32

Chapter 2 – Instrumentation: Development of a high-throughput
microfluidic sorter

33– 49·2.1

Publication Note

33

·

2.2

Introduction

33– 35·

2.3

Experimental

36– 39·

2.4

Results and Discussions

39– 48·2.5

Conclusions

49

Chapter 3 – Engineering a brighter version of FusionRed using
lifetime flow cytometry and structure guided
mutations

50– 79·3.1

Publication Note

50

·

3.2

Introduction

50– 52·

3.3

Experimental

52– 63·

3.4

Results

64– 74·

3.5

Discussion

75– 78vi

·

3.6

Conclusions

79

Chapter 4 – Characterizing dark state kinetics from ensemble andsingle molecule fluorescence measurements in
FusionRed variants

80– 100·

4.1

Publication Note

80

·

4.2

Introduction

80– 84·

4.3

Methods

84– 90·

4.4

Results

90– 95·

4.5

Discussion

96– 99·

4.6

Conclusions

100

Chapter 5 – Characterizing the pathways of non-radiative decay
in the lifetime evolution of a brighter variantof mCherry

101– 119·

5.1

Publication Note

101

·

5.2

Introduction

101– 104·

5.3

Methods and materials

104– 105·

5.4

Results

105– 112·

5.5

Discussion

112– 118·

5.6

Conclusions

118– 119vii

Chapter 6 – Brightening FusionRed-MQV using lifetime selections 120– 133·

6.1

Introduction

120

·

6.2

Results and discussions

121– 131·

6.3

Conclusions

132– 133

Chapter 7 – Future directions

·
·

7.1
7.2

134– 141

Development of a sorting platform on darkstate conversion

134– 138

Improving maturation of FPs

139– 141

Bibliography

142– 182

Appendices183– 312·

Appendix 1

183– 206·

Appendix 2

207– 231·

Appendix 3

232– 249·

Appendix 4

250– 272·

Appendix 5273– 307·

References

307– 312

viii

List of Figures
Figure
1.1
1.2
1.3
1.4

1.5

Title
Structure of a Fluorescent Protein and its chromophore.
A schematic representation of the process for engineering geneticallyencodable fluorescent biomarkers employed in our group.
Photophysical data from 89 published FPs was obtained from FPBase.
Expected trends from the weak-coupling low temperature limit ofEnglman-Jortner theory.
Excited-state spectral and structural dynamics in RFPs studied using
ultrafast spectroscopy.

Page
Number
3
6
10–11
15

20

1.6

A graphical summary of results from a TD-DFT study.

22

2.1

Schematic layout of the electronics used in this sorter.

37

2.2

Droplet generation and size.

37

2.3

Lifetime screens of FPs.

40

2.4
2.5
2.6

Fluorescence lifetime versus brightness scatter plots of mixed cells before
and after sorting.
The efficiency of enrichment with various initial fraction of target analyte.
Fluorescence lifetime versus brightness scatter plots of rare mScarlet
enrichment.

43
44
47

3.1

Lifetime screens for the site directed libraries of FusionRed.

3.2

Site-directed mutagenesis based on structural data.

67

3.3

Photophysical properties of the FR family of FPs.

69– 70

3.4

Cellular brightness assays.

71

3.5

Localization Assays.

74

3.6

4.1
4.2

The overall molecular schematic describing the postulated effects of thesubstitutions in FR-MQV.
A three-state model of the photophysics of a fluorophore central to thisstudy.
Analysis workflow.

64– 65

78

84
89

ix

4.3

Results from single molecule blinking experiments.

92

4.4

Variation of rate constants.

93

4.5

Photobleaching fits from a three-state model.

95

4.6

Relating blinking to a cis-trans isomerization of the FR chromophore.

99

5.1

5.2
5.3
6.1

6.2

Directed evolution of mCherry resulted in variants with blue-shifts andincreased lifetime.
The non-radiative rate obtained from the excited state lifetime andfluorescence quantum yield plotted as a function of fluorescence lifetime.
Insights from the crystal structure of mCherry.
Lifetime-brightness screens of the progenitor FusionRed-MQV (WT) with
before and after FACS enrichment populations.
The crystal structures indicating the potential interactions of positions 224
and 71.

106

111
114
121– 122

125

Photophysical characterization of the brightest clones from site-directed
6.3

6.4

mutagenesis of FR-MQV and FR-HQC.

The brightness of FusionRed variants generated from FR-MQV and FRHQC in mammalian cells using FACS.

129

131

7.1

The simulated phase signatures from RFPs.

135– 136

7.2

Off chip phase measurements

136– 138

7.3
7.4

Tentative design of microfluidic sorting device to be used for a dark state
screening platform.
Elucidating the role of the C-terminus tail in RFPs.

x

138
141

List of Tables
Table

3.1

Title
Summary of in vitro photophysical properties of FR mutants developed inthis study.

Page
Number68

3.2

Summary of cellular and molecular brightness for FR variants.

73

4.1

Values of τON and τOFF.

91

4.2

Estimation of kDSC and kGSR.

92

4.3

Estimated kDSC values from fitting ensemble traces.

95

5.1

Spectral and photophysical properties of the mCherry variants.

107

5.2

Fit parameters for fluorescence lifetime measurements.

108

5.3

Calculated rate constants of excited-state population decay.

112

6.1

Mean brightness and lifetime from the screen plots provided in Figure 6.3

122

6.2

Lifetime measurements for the FusionRed-L175X clones

123

6.3

Spectral details for the FusionRed-L175X clones

123

6.4

Lifetime measurements for the FusionRed-M42Q L175X1 C159X2 clones

124

6.5

6.6

6.7

6.8

6.9

Photophysical characterization for the FusionRed-M42Q L175X1 C159X2
clonesLifetime based screens for the FusionRed-MQV/HQC A224X1 I71X2
clonesSpectral properties for the high lifetime FusionRed-MQV/HQC A224X1
I71X2 clones.
Spectral properties for the high lifetime FusionRed-MQV/HQC A224X1
I71X2 clones.
Photobleaching behavior for the high lifetime FusionRed-MQV/HQC
A224X1 I71X2 clones.

xi

125

126

126– 127

127

130

Table of contents for the Appendix•

Appendix 1: Addendum to Chapter 2

Section

Title

Page Numbers

1

Optical layout and microfluidic device

183-1852

Instrument Operation Parameters

186

3

Cell culture and sample preparation

186– 187

4

Data acquisition and signal processing

187– 196

5

Performance of the sorter

196– 198

6

Enriching rare events

198– 201

7

Directed evolution of an RFP library

202– 206•

Appendix 2: Addendum to Chapter 3

Section

Title

Page Numbers

1

Amino acid sequence information for FusionRed variants

207

2

Amino acid sequence results from the site-directed library

208

3

Extinction coefficient and quantum yield estimation

209– 2124

Additional photophysical and biochemical characterization

213– 225

5

Cellular Assays: brightness, maturation and cytotoxicity

226– 2306

Additional structural information

230– 231

7

FR Evolution Table

231•

Appendix 3: Addendum to Chapter 4

Section

Title

Page Number

1

Experimental workflow

232

2

Excitation rate calculations

233

3

Single molecule data analysis addendum

234

4

Ensemble photobleaching

235– 236

xii

5

Simulation results

237– 2456Additional fitting results

246– 248

7

Theoretical estimation of the lowest and highest number of

248– 249

photons/frames
8

Surface charge on FusionRed•

Appendix 4: Addendum to Chapter 5

Section

249

Title

Page Number

1

Mutagenesis Protocols

250– 252

2

Mutagenesis and Directed Evolution of mCherry

252– 257

3

Sequence Alignment of the RFP variants

4

Additional in cellulo assessments

258– 261

5

Additional details for in vitro photophysical assessments

262– 266

6

Variation of the radiative rate constant

7

Modelling non-radiative rate using the Englman-Jortner Low

257

267
268– 272

Temperature/Weak Coupling Formalism•

Appendix 5: Instrument operation, simulation and data analysis codes

Section

Title

Page Number

1

Code for microfluidic screen dot-plots

273– 275

2

Droplet-sorter operation controls

276– 279

3

Simulation code representing the effects of scattering on phase279– 280

shift
4

Simulation code representing the signal of a droplet in flow

5

Codes to analyze in vitro photophysical data

6

Code to simulate role of electrostatics on oscillator strength7

Codes for analyzing photobleaching data

284– 287

8

Codes to simulate dark state kinetics in time and frequency

287– 288

domains using numerical solutions to the three-state model
xiii

280
280– 284
284

9

Codes to simulate dark state kinetics in time and frequency

289– 291

domains using analytical solutions to the three-state model
10

Simulation of single molecule kinetics using Monte-Carlo291– 294

methods
11

Detection code for single molecule trajectories from video (TIFF

295– 299

series) file12

Code for binarizing single molecule trajectories

xiv

300– 307

List of Appendix Figures
Figure

Title

Page
Number

A1.1

Optical diagram of the microfluidic sorter

183

A1.2

Microfluidic chip design

185

A1.3

Simulated and observed signals of a filled droplet

188

A1.4
A1.5
A1.6

A1.7
A1.8
A1.9

Pair matching events to estimate the transit time and the flow speed of
the system.
Comparing signals from filled and empty droplets.
Screening results of a mix of mCherry, FusionRed-M and Kriek(K2C).
Simulation of phase shifts obtained from a convolution of scatteredand fluorescence signals.
Poisson distribution for λ = 1 to λ = 10.
Enrichment efficiency converges as the number of rare events
increases.

189
191
194

195
199
199

A1.10

mScarlet library sorts with the instrument.

204

A2.1

Gradient (4–20%) SDS-PAGE of FR and FR-MQV.

210

A2.2

Quantum yield measurements.

211

A2.3

pka measurements.

213

A2.4

Photobleaching measurements.

216

A2.5

Bacterial brightness assay.

217

A2.6

Absorption and excitation spectra.

218

A2.7

Trp280 nm peak for FusionRed variants.

220

A2.8

pH titrations.

221

A2.9

Emission spectra for the FusionRed and mKate variants.

223

A2.10

Excitation dependent emission spectra.

A2.11

Cytotoxicity assay

228

A2.12

Chromophore maturation kinetics.

229

A2.13

Structural representation of the FR crystal structure.

230

xv

224-225

A2.14
A3.1

Evolution table.

231

Schematic of the experimental workflow from sample preparation todata analysis.

232

A3.2

Spatial corrections.

234

A3.3

Intensity variation.

234

A3.4

Ensemble photobleaching kinetics.

235

A3.5

A3.6

Bi-exponential nature of fluorescence decay from bacteria expressing
FusionRed and FusionRed-MQ.
Schematic representing the algorithm used to simulate single moleculebehavior.

236

237

A3.7

Simulation heatmaps for on and off time with varying rate constants.

238

A3.8

FusionRed blinking simulation (100 ms, 6000 frames)

239

A3.9

FusionRed blinking simulation (50 ms, 12000 frames)

240

A3.10

FusionRed blinking simulation (50 ms, 6000 frames)

241

A3.11

FusionRed blinking simulation (300 ms, 1000 frames

242

A3.12

Ensemble trends from Monte-Carlo simulations

243

A3.13

Variation in ensemble fluorescence decay traces with respect to kDSC,
kex and kGSR.

244

A3.14

Population based numerical simulation of a 3-state model.

245

A3.15

Quality of fit for varying kDSC and kGSR unbound.

247

A3.16

Keeping kGSR fixed while allowing the fitting algorithm to fit the kDSC.

248

A3.17

Location of positively charged residues on the barrel of FusionRed.

249

A4.1

EP-PCR library of C9 and C12 variants.

253

A4.2

Summary of mutagenesis efforts on the mCherry family to achieve
lifetime evolution.

255

A4.3

Role of spatially distant substitutions on the photophysical properties.

256

A4.4

Lifetime & yeast-cell co-evolution trajectory.

258

A4.5

Cellular brightness in mammalian cells.

259

A4.6

Photobleaching trends in E. coli.

260

xvi

A4.7
A4.8
A4.9

Comparing photostability under excitation rate normalized conditions
in E. coli.
Normalized absorption and emission spectra.
Fluorescence anisotropy decay and rotational time-constants (τr ) of
the variants.

261
262
263

A4.10

Fluorescence decay and the average lifetime (τ) of the variants.

264

A4.11

Fluorescence quantum yield (ф) of the variants.

265

A4.12

Analysis of the radiative rate constants for mCherry variants.

267

A4.13

Fit of the total non-radiative rate constant with the energy gap.

268

A4.14

Schematic representations of relevant observables.

269

A4.15
A4.16
A5.1

A5.2

A5.3

Absorbance and fluorescence spectra represented on the wavenumber
scale.
The numerator and denominator functions for in the Eq S2.
The front panel of the NI LabView interface for the droplet sorter
operation.
Additional panels of the NI LabView interface for the droplet sorter
operation.
The block diagram of the sorter GUI displayed in Tables A5.1 and
A5.2

xvii

270
271
276

277

278-279

List of Appendix Tables
Table

Title

A1.1

Screening results of sorting efficiency.

A1.2
A1.3
A1.4

A1.5

Fluorescence lifetime measured in TCSPC and the microfluidic droplet
sorter.
Screening results of sorting efficiency.
The enrichment of rare mScarlet from a mixture with EGFP screened at
a rate of 2 kHz.
The enrichment of rare mScarlet from a mixture with mCherry screened
at a rate of 2.5 kHz.

Page
Number
196
197
198
201

201

A1.6

The sequence of mScarlet-I mutants in the mutated positions.

205

A1.7

Photophysical properties of mScarlet-I mutants.

206

A2.2

A2.2
A2.3
A2.4
A2.5
A2.6

A2.7

A2.8

A2.9

Sequence information for the FR family with respect to the parentalclones from the eqFP578 family
Sequence and screening results of the FR site-directed (FSD) libraryclones.
Measured mean quantum yield and standard deviation errors
The pKa values measured in this study versus the values reported for
known RFPs in the literature.
TCSPC-based lifetime measurements using pure protein samples.
Spectral characteristics of the FR family of proteins investigated in thisstudy.
Mean brightness from FACS measurements with standard deviation
error from multiple biological replicates.
Mean brightness from confocal microscopy measurements with standard
deviation error from the number of cells indicated in each dish.
Number of cells analyzed on Day 2 and Day 6 in the GFP and the RFP
channel using FACS.

xviii

207

208
212
214
215
219

226

227

228

A2.10A3.1
A3.2

Measured versus the reported maturation times (t50) for the RFPs
investigated in this study.
Power measurements

230
233

Fitting details for the biexponential decay traces of FusionRed andFusionRed-MQ.

236

A4.1

Sequence alignment of the mCherry variants analyzed in this study.

257

A4.2

Spectral properties of the RFP variants.

262

A4.3

Difference in energies of the peaks of the 0-0 and 0-1 vibronic bands
and the relative intensities.

xix

272

List of common Abbreviations and Symbols
FP

Fluorescent Protein

RFP

Red Fluorescent Protein

GFP

Green Fluorescent Protein

PDB

Protein Data Bank

CFP

Cyan Fluorescent Protein

EP-PCR

Error-Prone Polymerase Chain Reaction

OSER

Organized Smooth Endoplasmic Reticular assay

B-PER

Bacterial Protein Extraction Reagent

TCSPCTime Correlated Single Photon Counting

FACS

Fluorescence Activated Cell Sorting

FLIM

Fluorescence Lifetime Imaging Microscopy

FRET

Förster Resonance Energy Transfer

QM/MM

Quantum Mechanics/ Molecular Mechanics

MD

Molecular Dynamics

FAPA

Fluorescence Anomalous Phase Advance

FPGA

Field Programmable Gate Array

PMT

Photomultiplier Tube

ADC

Analog to Digital Convertor

DEP

Dielectrophoretic (in context of electrodes)

TIRF

Total Internal Fluorescence Microscopy

SOFISuper-resolution Optical Fluctuation Imaging

SMLM

Single Molecule Localization Microscopy

CMOS

Complementary Metal Oxide Semiconductor camera detector

EMCCD

Electron Multiplying Charge Coupled Device camera detector

FWHM

Full Width at Half Maximum

SNR

Signal to Noise Ratio

OD

Optical Density

RPM

Rotations Per Minute

FR

FusionRedxxmCh

mCherry

EGFP

Enhanced Green Fluorescent Protein

K2C

Kreik

Ex

Excitation

IC

Internal Conversion

ISC

Intersystem Crossing

DSC

Dark State Conversion

GSR

Ground State Recovery

NR/
Non-RadR/ RadNon-radiative pathways of excited state depopulation
Radiative pathways of excited state depopulation

SS

Stokes shift

SM

Spectral moment

EJ

Englman-Jortner

λWavelength (unless specified otherwise, e.g., in the context of droplet loading)/ / QY
ε/ EC
τ/ LT

k

Fluorescence quantum yield (unless specified otherwise)
Extinction coefficient
Fluorescence lifetime (unless specified otherwise)
Subscripts FD and TD denote time or frequency domain measurements.
Rate constants. Subscripts denote the nature of the process under consideration.
e.g, excitation rate constant is denoted as kex.

η

Refractive index of the mediaσAbsorption cross-sectionFrequency

NA

Avogadro’s Constantc

Speed of lighthPlanck’s constantxxi

Chapter 1
Introduction
1.1. Publication Note
Parts of this chapter have been adapted from the article “Photophysical Engineering of FluorescentProteins: Accomplishments and Challenges of Physical Chemistry Strategies.” Mukherjee, S.;
Jimenez, R. J. Phys. Chem. B 2022. https://doi.org/10.1021/acs.jpcb.1c05629.

1.2. Introduction
Since the first isolation of naturally occurring fluorescent proteins (FPs) from marine organisms
several decades ago, subsequent developments in protein engineering have produced a large familyof fluorophores spanning the entire visible wavelength spectrum. [1, 2] Applications of FPs inbioimaging and sensing include multi-color microscopy, [3] Förster resonance energy transfer(FRET)-based tools, [4] fluorescence lifetime imaging microscopy (FLIM), [5] voltage sensing,[6] biosensing, [7] catalytic activity monitoring, [8] aggregation studies, [9] and non-biophysicalapplications such as bio-phosphors for LED lighting. [10] Additionally, the engineering of FPs
exhibiting reversible and photo-activated fluorescence and photo-switching between fluorescencebands has enabled imaging with spatial resolution beyond Abbe’s diffraction limit. [11] Despite
and because of this widespread use, development of new FPs continues. For example, with theincreasing interest in deep-tissue imaging of live animals, significant efforts have focused on the
discovery and development of brighter red FPs (RFPs), as longer excitation and emission
wavelengths generally provide lower scattering and increased penetration-depth.
FP engineering is inextricably tied to consideration of protein structure. Fortunately, hundreds of
X-ray crystallographic structures of FPs at atomic resolution are available (e.g., Figure 1.1). In the
canonical green fluorescent protein superfamily, the chromophore–which is comparable in size tosynthetic small-molecule fluorophores (~1 nm) – is contained inside a β-barrel with an internal 𝞪helix. [12] Several chromophore variants can be autocatalytically formed from the reaction of O2
with a tripeptide in this helix. One common structure typically comprises p-hydroxyphenyl andimidazolinone moieties connected by a methylidyne bridge (Figure 1.1). The electronic
1conjugation across this hydrolyzed tripeptide results in a chromophore with a 𝜋 → 𝜋 ∗ electronictransition excitable at visible wavelengths. The chromophore participates in numerous interactions
with amino-acids and the solvent. These short-range interactions (e.g., hydrogen bonding) or longrange effects (e.g., electric fields) tune the energetics and control the electronic structure of thechromophore. Accordingly, amino-acid substitutions, sometimes surprisingly distant from thechromophore, perturb its electronic structure, influence the energetics of its electronic transition,and cause changes in its conformation and the nuclear degrees of freedom coupled to it.
Additionally, the overall protein structure governs the movement of diffusing species such as wateror O2, which can also lead to alterations in chromophore properties. In general, it is difficult toseparate the impacts of numerous variables that non-additively contribute to the photophysics. All
these factors should be taken into consideration for explaining and tuning properties such as
brightness and photostability. [13-16]
In addition to being useful for imaging, FPs provide an incredible molecular framework forinvestigating diverse photophysical, spectroscopic and dynamical phenomena such as solvation
dynamics, light harvesting, photo-induced excited state intramolecular proton and electrontransfer, photo-transformations such as photoisomerization, and other radiationless transitions.
[17-21] One can examine them with biochemical or physical methods by combining spectroscopic
measurement tools including steady-state and time-resolved optical and vibrational spectroscopy,
with structural approaches such as nuclear magnetic resonance (NMR) and both static and timeresolved X-ray crystallography. Here, we will discuss the development of FPs, focusing on topics
that are of interest to physical chemistry. Though we will focus on the GFP super-family, the topics
discussed here apply to FPs of other lineages, such as those containing tetrapyrrole chromophores.
[22-24] We further center discussion on brightness and photostability, which are arguably the mostrudimentary fluorophore properties. As described below, it has been a difficult task to optimize
them in tandem. [16] Studies of the principles behind brightness and photostability have been
pursued in our lab for over a decade, and they provide a platform for discussing far more general
concepts. For discussion of more complex functionalities, such as photoactivation andphotoswitching, we refer readers to other reviews. [25, 26] In describing some of the biggest
successes, notable failures, and remaining challenges, we also consider the role of physicalprinciples in guiding design strategies.

2

Figure 1.1. Structure of a Fluorescent Protein and its chromophore. (a.) The crystal structure
for enhanced GFP (EGFP; PDB ID: 2Y0G) showing the β-barrel encompassing the internal helix
and the chromophore, for which oxygen atoms are indicated in red, nitrogen in blue and carbon ingray. (b.) A ground state structure of the anionic GFP-type p-hydroxyphenyl-imidazolinone
chromophore (c.) A ground state structure of the anionic RFP p-hydroxyphenyl-imidazolinone
chromophore showing the extension of the electronic conjugation through an acylimine moiety.
Green and red highlighting indicate the bonds participating in electronic conjugation (resonance)
across the chromophore. Structures were generated using VMD and ChemDraw software suites.
[27, 28]

1.3. Brightness
1.3a. Approaches for improving brightness
Fluorescence brightness is a molecular property defined as the product of the molar extinction
coefficient at maximum absorption (𝜖 max) and the fluorescence quantum yield (). However, whenFPs are imaged in cells, the observed cellular brightness is a consequence of additional factors
such as protein folding, kinetics of chromophore maturation, translational efficiency, expression
level (i.e., concentration), environmental sensitivity to pH, nature of the fusion-protein constructand chemical environment of the cellular compartment. [29] The typical development pipeline for3

improving brightness or other FP properties involves generating “libraries” (which may range insize from dozens to >107 variants) using error-prone PCR or site-directed mutagenesis based on
structural, spectroscopic and bioinformatics guidance (Figure 1.2). These libraries are thentypically expressed in a host, such as bacteria, yeast, or mammalian cells that allows for screening
and selection of clones with desired characteristics – such as higher brightness. For example,
Fluorescence Activated Cell Sorting (FACS) and fluorescence imaging are popular tools forselecting on cellular brightness. The mutation and selection cycles are repeated to achieve“directed evolution” in terms of the selection pressure. [30] After several rounds, a small numberof selected clones are expressed, and the purified FPs are individually characterized to determine
values of molecular properties such as the fluorescence quantum yield and peak molar extinction
coefficient. This approach has yielded substantially improved FPs such as EGFP, [31] (1.7-foldbrighter than progenitor avGFP) and the mRubys, [32] (mRuby3; 1.7-fold brighter than thenaturally occurring progenitor eqFP511), of which the best have peak molar extinction coefficientsand fluorescence quantum yields comparable to those of small-molecule dyes. For example,
mNeonGreen [33] has fluorescence quantum yield ~ 80% and a peak molar extinction coefficientat ~ 116,000 M-1cm-1 (brightness of ~ 93) with a peak absorption wavelength comparable to therecently developed, xanthene-based Janelia Fluor (JF) dye JF-503 which has a fluorescencequantum yield ~ 87% and an 𝜖 max ~ 95,000 M-1cm-1 (brightness ~ 83). [34]Despite the historical success of this approach, alternative strategies for obtaining brighter FPs
have been explored, particularly in recent years as the pace of improvements has slowed. For
example, the choice of template has garnered increased attention. In most cases the template iseither a naturally occurring FP or a commonly used FP that has undergone previous rounds ofdevelopment. The notable exception is the brightest RFP as of early 2021, mScarlet, which wasdeveloped from a synthetic gene template. [35] Given this achievement, one might be tempted tothink natural templates have reached their limits. However, Lambert et al. (2020) reported thediscovery of AausFP1, a naturally occurring GFP from the jellyfish Aequorea victoria, from which
the original GFP was obtained. [36] This FP has the highest ever reported value of fluorescencequantum yield (97%) and a peak molar extinction coefficient of ~ 170,000 M-1 cm-1. Although thedimeric structure and the very small Stokes shift of AausFP1 may limit its use for imaging, these
defects could be addressed, and this discovery suggests that nature will continue to be a source forbrighter fluorophores.
4Many FPs have been optimized for specific biochemical applications (for example, cellular
localization or pH sensitivity) and engineering photophysically-improved variants mandates
keeping close attention to their in vivo attributes. For instance, Campbell and co-workers proposedthat GFP-based fluorophores with the Glycine-Tyrosine-Glycine (G-Y-G) tripeptide chromophore
might have attained a local maximum of molecular brightness. Consequently, they focused on
improving properties that can increase cellular brightness, such as solubility, translation efficiency,
protein folding and chromophore maturation. With this approach, they developed mGreenLantern,which is 6-fold brighter in mammalian cells than EGFP. This improvement in cellular brightness
came without an appreciable change in the molecular brightness from its precursor FP - Clover.
[37] This study demonstrates that increasing cellular brightness by generating a fast-maturing FP
with high copy number can be beneficial in some applications, such as imaging of neurons.
However, we found that imaging of small subcellular structures, such as the Golgi apparatus,
sometimes benefits more from controlled expression of FPs with high molecular brightness. [38]This suggests that improvements of both molecular and cellular brightness should be pursued intandem.
The selection step (Figure 1.2) is of particular interest to physical chemists because spectroscopic
measurements, such as fluorescence lifetime (𝜏), can be incorporated on platforms that allow highthroughput screening of cells, such as microfluidic or microscopy-based systems. [30, 35, 38, 39]
Relationships between sequence, structure and any spectroscopically-accessible property can beinvestigated by this approach on 107 or more variants per day. Fluorescence lifetime-based
screening in particular has proven useful because lifetime is independent of concentration, and it
is correlated with higher molecular brightness (with caveats, see below). Lifetime-based selection
on a microscopy platform led to the development of mScarlet from the dim synthetic templatemRed7. [35] Our lab has pioneered the integration of microfluidic flow cytometry withphotobleaching, photoswitching, and fluorescence lifetime selection. [40-44] For example, we
employed a cell sorter based on fluorescence lifetime to variants of FusionRed with 3-fold higher
molecular brightness (discussed later in the text). [38]5Figure 1.2. A schematic representation of the process for engineering genetically encodable
fluorescent biomarkers employed in our group.

Few efforts have directly aimed to alter the absorption properties by tuning the oscillator strengthof electronic transitions in FPs, but initial results in this direction are promising. [45, 46] In a recent
study, Myšková and co-workers determined transition dipole moments of absorption (xTDM) andemission (mTDM) of several well-studied, bright FPs. [47] Their approach combined cryogenic
x-ray crystallography with room-temperature polarized optical transmission and fluorescencemeasurements to determine the orientation of these dipole moments. By characterizing thepropensity of FPs to crystallize into specific space groups with certain molecular orientations, theauthors were able to interpret the optical measurements with two well-defined assumptions. They
assumed the TDM of the chromophore was in plane of the two aromatic rings and furthermore that
there is a cosine squared relationship of the TDM with the polarized absorption or fluorescenceintensity. Information from such studies can inform development of FPs for applications that are
sensitive to the directions of the transition dipoles, such as FRET. Another study based on

6considering the transition dipole moments was reported by Molina et al. (2020) who developed ahigh-throughput, fluorescence microscope-based screening device (GIZMO) for screening
bacterial cells by two-photon excited fluorescence. [48] The two-photon absorption cross-section
can be used to examine the radiative rate and electric fields around the chromophore (the effects
of internal electric fields on FP photophysics are discussed below). GIZMO is capable of screening
104 bacterial cells in ~7 hours, demonstrating great potential for this type of selection in the
directed evolution of FPs.
Unconventional selection strategies that do not directly measure brightness have also been
explored to develop brighter FPs. For example, many FPs exhibit two-state (on/off) “blinking” oftheir fluorescence intensities at the single molecule level. These transitions occur when thechromophore has access to non-fluorescent excited electronic states with microsecond to
millisecond lifetimes. This “dark state conversion” (also sometimes referred to as “reversible
photobleaching”) leads to rapid blinking, and the depopulation of the ground state can result in an
apparent reduction in brightness. This connection between blinking, dark-state conversion, andbrightness has been exploited. In particular, FLINC (Fluorescence fLuctuation INcrease by
Contact) – an imaging technique with threefold higher resolution than the diffraction limit, is basedon the observation that the blinking frequency of TagRFP-T varies ~25% as a function of thelength of a linker peptide altering its spatial proximity to the non-fluorescent Dronpa FP. [49]Charged residues on the β-barrel participate in electrostatic interactions that control the dark state
conversion rates. Consequently, libraries were developed by targeting positions with externallyfacing side chains (acidic: D159, D196 and basic: R157, R198) and selections on reduced rate ofdark-state conversion through FLINC were successful for developing SuperTag-RFP, which is 2fold brighter than TagRFP-T. [50]The properties of new variants must be characterized carefully to avoid potential misapplications,e.g., in imaging modalities for which the photophysical properties are unsuitable. For example,
population transfer to dark states can be a bottleneck for continuous excitation, especially at highirradiances. Dark states typically are related to chromophore conformational changes or intersystem crossing to the triplet state, and lead to trapping on timescales several orders of magnitude
longer than an excitation-emission cycle. [51,52] For detailed discussions of this topic, we referreaders to reviews on dark state conversion and related photo-transformations such as
7

photoswitching. [16, 53] On a practical note, dark state conversion, which is distinct fromsaturation of the optical transition in a 2-level system, can lead to inaccuracies in measurements offluorescence quantum yield, as shown by Ruhlandt and coworkers for photo-switching FPs. [54]Partially in response to this complication, Prangsma and co-workers developed methods toaccurately determine the fluorescence quantum yield by tuning the local photon density of statesnear a metal surface. [13] Looking beyond the influences on brightness, investigations of darkstate conversion and engineering of fluorescence blinking are valuable for probe development insuper-resolution microscopy. It remains challenging to measure the rates of dark-state conversion,
ground-state recovery, and photobleaching which, depending on the FP, may vary by many ordersof magnitude (and may overlap in timescales) over the wide range of irradiances relevant toimaging, even for variants with closely related sequences. [55, 56]

1.3b. The photophysical basis of increased brightness
i. General principles
The improved molecular brightness of many newer FPs is attributable to increases in fluorescencequantum yield () and fluorescence lifetime (𝜏). (Figure 1.3a) Consider the relationship between
the fluorescence quantum yield and the radiative (krad) and non-radiative (knon-rad) rate constants:

 = 𝑘𝑟𝑎𝑑 ∗ 𝜏 (1) = (𝑘𝑘𝑟𝑎𝑑
𝑟𝑎𝑑 +𝑘𝑛𝑜𝑛−𝑟𝑎𝑑 )(2)

In principle, a particular value of fluorescence lifetime can arise from different combinations ofvalues of krad and knon-rad. We extracted lifetime and quantum yield data from the online repository
FPBase [57] to estimate radiative and non-radiative rates. We assumed the reported lifetime values
from FPBase can be used to estimate the radiative and non-radiative rates, despite the use ofmultiple measurement techniques, with FPs in different environments (in vitro vs. in vivo), and theuse of average values to represent what is typically a multiexponential decay. The analysis reveals
only a 5-fold variation in the values of the radiative rate constant but a 50-fold variation in thevalues of the non-radiative rate constant (Figure 1.3c vs. Figure 1.3e). A similar observation for asmall set of RFPs was made by Drobizhev et al. [58] Furthermore, a correlation of higher
8

fluorescence quantum yields with longer fluorescence lifetime is clear, though the relationship is
not perfectly linear. While a higher fluorescence quantum yield most often seems to be due to alower non-radiative rate constant, increasing the radiative rate constant also increases fluorescencequantum yield, as seen for BrUSLEE (evident as out-lying points in Figure 1.3a and 1.3c). [59]This EGFP variant exhibits a short fluorescence lifetime of 0.8 ns but a relatively high fluorescencequantum yield (30%), with a 1.6-fold increase in the radiative rate constant. Mamontova et al.,achieved this by reducing the fluorescence lifetime of EGFP while maintaining its brightness. They
isolated a triple mutant EGFP T65G-Y145M-F165Y, with spectral properties similar to EGFP, butwith a 20% lower brightness and a 70% shorter fluorescence lifetime (cf. 2.6 ns for EGFP).
Although this result shows that radiative rate engineering is possible, molecular strategies to guidethe design have not been reported. In this context, we briefly consider well-known models forradiative and non-radiative transitions.

910Figure 1.3. Photophysical data from 89 published FPs was obtained from FPBase. [57] (alongwith values for FusionRed-Q, -MQ and -MV variants from [38]) Points in blue indicate FPs withpeak emission wavelength λ < 500 nm, green with peak emission wavelength in the range 500 nm< λ < 530 nm, and red with peak emission wavelength λ > 530 nm. The boxplots indicate the
distributions of values: the mean of the distribution is indicated by black solid squares; the box
indicates the 25th and 75th percentiles and the whiskers the 5th and 95th percentiles of the
distribution. The solid line in the box indicates the median value of the distribution. (a-b.) Trends
for the fluorescence quantum yield (): Increases in fluorescence lifetime (𝝉) generally correlatewith a higher fluorescence quantum yield. (c-d.) Trends for radiative rate constant (krad): Thereis a ~5-fold variation in the radiative rate constant – where higher wavelength emission canpotentially lead to lower radiative rate values. The GFP BruSLEE stands out as an exception(krad>350 us-1). (e-f.) Trends for the non-radiative rate constant (knon-rad): The non-radiative
rates decrease up to ~50-fold with increasing lifetime. The observed values indicate the means andthe standard deviations of knon-rad Blue~ 137 ± 112 µs-1; knon-rad Green ~ 130 ± 158 µs-1; knon-rad Red ~346 ± 345 µs-1. (g.) Trends for the peak extinction coefficient: Red emitting FPs tend to exhibit
larger peak extinction coefficients than green and blue counterparts based on chromophores
extended by an acylimine moiety.

ii. The radiative rate constant (krad)
The experimentally-observable parameters underlying the magnitude of radiative rate can be seenin the Strickler–Berg relationship,
𝑘𝑟𝑎𝑑 = 1

𝑟𝑎𝑑= 8𝑥2.303𝜋𝑐𝜂2 ⟨𝜐𝑓−3 ⟩−1∫ 𝜖 𝑑𝑙𝑛𝜈(3)which shows radiative rate is linearly proportional to the squared value of the refractive index of
the medium containing the chromophore (𝜂), the strength of the optical transition to the excitedelectronic state (∫ 𝜖 𝑑𝑙𝑛𝜈; where 𝜖 is extinction coefficient integrated over the absorption band),−1

the inverse of the mean inverse-cubed emission frequency (⟨𝜐𝑓−3 ⟩ ) and c denotes the speed oflight. [60] For chromophores with relatively narrow fluorescence spectra, the cube of the peak−1

3
fluorescence frequency, (𝜈𝑝𝑒𝑎𝑘) is approximately equal to the value ⟨𝜐𝑓−3 ⟩ . [58] The Strickler-

11

Berg equation shows that strong absorbers have higher radiative rates than weakly absorbing
chromophores. As a secondary effect, there is a linear dependence of radiative rate on the cube of
the fluorescence frequency. [61] A long wavelength emitter will radiate slower than a shorterwavelength emitter with the same integrated absorption cross-section embedded in a medium of
the same refractive index. Although this dependence does not represent a direct relationship to the
Stokes shift, it does indicate that blue shifting the peak emission can increase the radiative rate.
Equation 3 is qualitatively in agreement with Figure 1.3d. The extension of the electronic
conjugation through the acylimine moiety is likely to be the largest factor in making red FPs
stronger absorbers. However, Figure 1.3g shows that many green FPs absorb as strongly as red
FPs. The increased extinction coefficient of the red chromophore can be partially offset by thelower frequency emission to decrease the radiative rates.
Lin et al. found good agreement with the Strickler-Berg equation for a set of GFP variants
involving residues directly interacting with or forming the chromophore. [62] These FPs showeda nearly constant radiative rate and an inverse relationship of the peak molar extinction coefficientwith the width of the absorption band. The first observation is consistent with the trend seen in
Figure 1.3c and Figure 1.3e, where the variation in radiative rates is much smaller compared to thevariation in non-radiative rates. Accordingly, they suggest that large changes in the fluorescencequantum yields of FPs are unlikely to be the result of variations in krad, However, the example of
BrUSLEE shows that tuning the radiative rate by protein engineering is possible. [59] EGFP and
BrUSLEE have nearly identical absorption and emission spectra and peak wavelengths, and theincreased molar extinction coefficient (𝜖 max) and radiative rate constant of BrUSLEE follow whatis expected from the Stricker-Berg relationship: a ~1.5-fold higher value of 𝜖 max results in a ~1.6fold increase of the radiative rate.
A final point that should be made about the Strickler-Berg equation is that it might be inaccurate
to assume the refractive indices of FPs hardly vary. We used equation 3 and the spectral data fromFPbase to calculate values of η for blue (Cerulean), green (EGFP) and red (mScarlet) FPs, all threeof which show nearly mono-exponential fluorescence lifetime decays in aqueous environments.
[57] The refractive indices show the expected trend of increasing value with decreasing
wavelength, but the increase is considerably larger than expected (ηmScarlet~1.21; ηEGFP~1.25;
ηCerulean~1.49). The refractive index of water only varies by 2% over this wavelength range. [63]12The sensitivity of FP fluorescence lifetime to refractive index has been explored as a sensing
technique in cellular environments. [64] These observations may provide a route for design of FPs
with increased radiative rate by exploring a connection with the polarizability of the amino acids
comprising the β-barrel.

iii. The non-radiative rate constant (knon-rad)
In the absence of photochemistry, excited-state non-radiative population loss follows two majorroutes, internal conversion (IC), and inter-system crossing (ISC). The factors influencing theprobability of the transition W12 can be described by Fermi’s Golden Rule (Equation 4).
𝑊12 =2𝜋|𝑀12 |2
ħ

𝜌2

(4)

For IC between the initial (1) and the final (2) vibronic states of the two electronic manifolds, M12
is the matrix-element for the electronic interaction that couples them, and 𝜌2 is the density ofvibrational states of the final configuration. This expression also applies to the rate of ISC to a
triplet state. In highly fluorescent FP chromophores, the ISC rate is much smaller than IC due to achange in the spin multiplicity. [16] Investigations of ISC and triplet states in FPs merit further
attention as such states can play a pivotal role in oxidative photochemistry and photobleaching.
[65]
While equation 4 accounts for the physics of the non-radiative transition rate, it does not provide
useful insight for FP engineering. Reports on new fluorophores mention a dependence of the nonradiative transition rate on the S1 – S0 transition energy (i.e. the “energy-gap law”) which resultsfrom further theoretical development. [66-68] The classic theory of Englman and Jortner provides
a framework for understanding non-radiative transition rates in terms of experimental observables
such as the electronic energy gap (∆E), the Stokes-shift (from vibrational reorganization) andvibrational frequencies. [69] Their theory makes assumptions very similar to those of Marcus
theory of electron transfer, [70] namely that population transfer between weakly coupled initialand final states occurs by means of environmental fluctuations. This approach considers the highand low temperature limits of strong and weak coupling between the chromophore vibrations andelectronic transitions. The low temperature limit, ℏ〈𝜔〉 ≳ 𝑘𝐵 𝑇 is defined in terms of the mean
13

vibrational frequency 〈𝜔〉 = 𝑁 −1 ∑𝑗 𝜔𝑗 , where N is the number of modes and 𝜔𝑗 is the frequency𝐸𝑀
of each mode. In the low temperature - strong coupling regime, the coupling strength 𝐺~ ℏ〈𝜔〉> 1.

Where, EM ~ Stokes shift/2 in the absence of excited state processes such as excited state protontransfer (ESPT). In the low-temperature/strong coupling limit, the expression for the non-radiative
rate resembles that derived by Marcus for the electron transfer rate:
1 𝐶 2 √2𝜋

𝑊=ℏ

√𝐸𝑀 𝑘𝐵 𝑇(∆𝐸−𝐸 )2

exp −(4𝐸 ∗𝑘𝑀𝑇 ∗) (5)∗𝑀

𝐵

Where T* is the effective vibrational temperature 𝑇 ∗ ~ ℏ〈𝜔〉/𝑘𝐵 , C (~102-104 cm-1) represents the
Herzberg-Teller coupling of the vibronic transition, and the other variables were previously
defined. With experimental Stokes shifts from below 300 cm-1 to above 3000 cm-1 and energy gaps
from below 15000 cm-1 to 22500 cm-1, FPs can theoretically fall into either weak or strong couplingcases or in between them. In the weak coupling limit (G<1) suited to most FPs, the observed Stokes
shift is severalfold smaller than electronic transition energy (ΔE). In this case one arrives at thefollowing expression for the non-radiative rate,
1 𝐶 2 √2𝜋

𝑊=ℏ

𝛾Δ𝐸

√ℏ𝜔𝑀 Δ𝐸

exp −(ℏ𝜔 ) (6)𝑀

Here, 𝜔𝑀 is the frequency of the normal mode vibration with the maximum frequency in the
Δ𝐸chromophore, the parameter 𝛾~log(𝑑𝑒 ) – 1; where 𝑑 is the degeneracy and 𝑒𝑚 is a measure of𝑚the reorganization energy of this vibrational mode in the excited state. While more applicable to
FPs the weak-coupling form is less intuitive in its relation to experimental observables. Further
theoretical work is necessary to address the possible intermediate regimes of this formalism in thecontext of FP engineering. Both strong and weak-coupling regimes indicate that the non-radiativetransfer probability (W) is dependent on the Stokes shift (from vibrational reorganization),vibrational frequencies that couple to the electronic transition and the transition energy gap. To
illustrate the effects of these parameters on the non-radiative rate, we plot the trends expected fromthe weak coupling expression in Figure 1.4, which shows that decreasing energy gap and increased
reorganization energy lead to an increased non-radiative decay rate (W).

14

Figure 1.4. Expected trends from the weak-coupling low temperature limit of EnglmanJortner theory (equation 6): The super-exponential increase of the non-radiative rate (W) forsmaller energy gaps (Δ𝐸) and larger reorganization energies (dem). The values 𝜔𝑀 ~3000cm-1 andC2~107 cm-2 were fixed, as discussed in reference [69].

The Englman-Jortner approach can qualitatively explain the difference in average non-radiative
rate for GFPs relative to RFPs. The lower energy emission of the latter is due to their larger
chromophores. RFPs contain an acylimine moiety over which the electronic conjugation isextended compared to GFPs (Figure 1.1b and 1.1c). The larger number of vibrational degrees of
freedom and smaller electronic energy gap of RFPs could possibly lead to a higher density ofstates. One can thus predict RFPs to have lower fluorescence quantum yields than GFPs, in-partdue to the expected higher values of the non-radiative rate constant. However, an outstanding
exception to this trend is mScarlet, which has a smaller non-radiative rate constant than manybright blue-shifted counterparts such as EGFP (knon-rad mScarlet~77 µs-1 v. knon-rad EGFP~113 µs-1), [57]despite a significantly lower ∆E (by ~3000 cm-1) and near identical values of EM (~ 375 cm-1).
This RFP was designed with a focus on conformationally restricting the chromophore, which could15

have resulted in a lower density of accessible vibrational states in the ground electronic state. [35]The causes of this exceptional behavior merit further investigation. Further theoretical andexperimental studies are warranted to examine the extent to which energy-gap effects are the main
contributor to nonradiative relaxation especially in red and far-red emitting chromophores. [58]iv. Spectral features
In the descriptions of Strickler-Berg and Englman-Jortner models for the rates of radiative andnon-radiative transitions, we pointed out where correlations with steady-state spectral properties
are to be expected. For example, small Stokes shifts and blue shifted emission peaks are correlatedwith high radiative rates and low non-radiative rates. The Stokes shift reflects the reorganizationenergy for solvation of the excited electronic state (half of the Stokes shift=EM, as in equation 5
and 6) but this is correct only in the absence of excited state photochemistry such as excited state
proton transfer (ESPT) which occurs in the “large Stokes shift (LSS)” FPs. In addition toabsorption and emission peak values, photophysical properties are correlated with absorption
lineshapes and linewidths. Chromophore spectral lineshapes are sensitive to the underlying
femtosecond to nanosecond timescale protein and solvent dynamics and protein conformational
heterogeneity. Ultrafast spectroscopy experiments such as time-resolved fluorescence Stokes shiftmeasurements and photon echo techniques resolve the timescales of nuclear motions. [71, 72] An
understanding of the interplay between protein structure and dynamics would provide useful
insight for FP engineering efforts. [73] To date, most ultrafast spectroscopy of FPs has focused oninvestigating excited-state photoreactions such as chromophore isomerization, ESPT, andhydrogen-bond dynamics (see below). We now turn to a consideration of structural features andmechanisms for excited state depopulation, such as hydrogen bonding and electrostatic effects.
[15, 58]16

1.3c. Discussion of specific cases:i. Structural arguments
Often, the rationale for mutations to improve brightness is centered on trying to make thechromophore more “planar” and the FP more “rigid.” It is expected from molecular orbitalarguments that a planar or flatter chromophore would result in stronger 𝜋 → 𝜋 ∗ electronictransitions and thus a larger value of extinction coefficient due to improved electronic
delocalization through the methine bridge. [74] The second rationale is difficult to examine
critically due to the complexity of quantifying “rigidity.” Furthermore, the existence of a conicalintersection in the excited-state potential energy surface of FPs, linked to the twisting of themethine bonds between the two rings complicates the straightforward picture of planarity andrigidity. [75] Although they are not certain to capture the average chromophore conformation or
excited state distortions, x-ray crystal structures show a correlation between chromophore
planarity and brightness. [16] The structures of mCherry and mStrawberry revealed that thedecreased fluorescence quantum yield of these FPs are correlated with non-planarity of thesechromophores compared to the parent DsRed and sibling mOrange. [76] The x-ray crystal structureof mScarlet (PDB ID:5LK4) shows a dihedral angle of ~1.9o between the methine bridge andphenol ring (or the P-bond rotation), which is significantly smaller than the ~13.1o for the dimmer
RFP mCherry (PDB ID:2H5Q). [35] The flatter chromophore has a ~1.5-fold higher 𝜖 max, ~3-foldhigher fluorescence quantum yield, ~2.5-fold higher radiative rate constant and ~7-fold lower nonradiative rate constant. Along these lines, mutagenesis to introduce residues that improve thepacking around the chromophore have often been used to generate brighter variants. This strategy
was employed in the development of mTurquoise2, where a fluorescence quantum yield of 93%(the highest of all engineered FPs) was achieved by introducing an I146F substitution in
mTurquoise (fluorescence quantum yield ~84%). [77] This residue was identified as a target formutagenesis by a combination of fluorescence lifetime screening, x-ray crystallography, andclassical MD simulations, which suggested that a bulkier, non-polar residue might restrict theconformational freedom of the chromophore, resulting in a higher fluorescence quantum yield.
Inspiration for molecular design has been provided by spectroscopic and theoretical studies of
specific interactions and excited-state processes in relation to hydrogen bonding and protontransfer - particularly in GFP model chromophores. [78-80] While a majority of these studies have17

been based on a combination of vibronic spectroscopy, computational methods, X-ray crystal
structure analysis and bioinformatics, [81-84] NMR and electron paramagnetic resonancespectroscopy have also proven useful (and perhaps under-utilized) for providing further insight
into FP structure and conformational dynamics. [85-87] For example, high-resolution 2D 1H-15N
solution-based NMR backbone relaxation study revealed a light-induced conformational change
in the photo-switchable protein rsFolder. [88] The use of kinetic crystallography for revealing thestructural transitions associated with long-lived dark states has also been fruitful. [89] This
promising approach combines real-time crystallization of FP molecules with optical measurements
such as Raman spectroscopy. The work of Bourgeois and co-workers has provided insights into
the mechanisms behind photo-transformations in photo-switchable FPs like mEos4B. [90] A
structural perspective can be helpful for identifying specific interactions that might governbrightness. [16-19]

ii. Influence of local hydrogen-bonding networks
Though hydrogen bonding has a variety of impacts on the photophysics of various types of FP
chromophores, we will limit our considerations to RFPs, and in particular the role of hydrogenbonding with regard to the acylimine moiety. In RFPs, the introduction of a single hydrogenbonding interaction with the acylimine moiety was proposed for red-shifting the emission.
However, the major outcome of this new motif is the introduction of picosecond timescaleconformational changes which influence the brightness and the Stokes shift of emission. These
processes have been investigated both with experiments and QM/MM simulations. [15, 79, 91-93]
In mPlum, which has a large 1540 cm-1 (60 nm) Stokes shift, Boxer and coworkers observed apicosecond timescale red shift of the emission spectrum, which they explained as a dynamic Stokes
shift associated with reorganization of the E16 hydrogen bond. [94] We used time-resolved
fluorescence experiments to reveal the two-state interconversion between the direct and watermediated hydrogen-bonding interactions of the acylimine with the E16 residue (Figure 1.5a). [79]QM/MM simulations confirmed the connection between the structural dynamics and the Stokes
shift obtained from the experiments. [93] What remains uncertain is exactly the connection
between the large Stokes shift and the small fluorescence quantum yield of mPlum (10%).

18

The availability of multiple hydrogen bonding possibilities in the acylimine region appears to bea detriment to brightness. For example, TagRFP-675 (Figure 1.5b) was engineered from mKate to
red shift the emission by introducing hydrogen bonding to the acylimine carbonyl, but thesemodifications resulted in a decrease in the fluorescence quantum yield (33% to 8%). [95] Our timeresolved emission measurements revealed the presence of four emitting species of varying red
shifts, which independently decay to the ground-state. Classical MD simulations also revealed
multiple interconverting structures of this hydrogen-bonding network, but it was not possible toassign the spectral forms to individual structures. [15] Interestingly, acylimine hydrogen bonding
does not always lead to FPs with low fluorescence quantum yield. In developing the bright
FusionRed mutant FR-MQV, [38] we hypothesized that the M42Q mutation would be beneficial
by occupying a cavity near the acylimine and thus locking it into a favorable geometry. This
interaction increased the molecular brightness of the FP by 2-fold in comparison to FusionRed. It
may be productive to focus attention on these issues using quantum and classical molecularsimulations to examine models in which specific interactions with the chromophore is predicted
to stabilize a single long-lived structure.

19

Figure 1.5. Excited-state spectral and structural dynamics in RFPs studied using ultrafast
spectroscopy. (a.) mPlum: Two-state interconversion of direct and water-mediated hydrogenbonding states. [79, 91, 93] (b.) TagRFP-675: The sidechains of residues F62-Q42-Q107-S28R41 constitute a hydrogen-bonding network leading to four spectral forms (with populations given
as percentages) and widely varying excited-state 𝜏. [15]iii. Electric fields and electrostatic effects
Theoretical and experimental studies have examined the influence of electric fields andelectrostatics on radiative and non-radiative rates. [46-48, 62, 82, 96-98] For example, TD-DFT
calculations on the isolated GFP chromophore (Figure 1.6) predict that electric fields can change
the oscillator strength of an electronic transition, and therefore the radiative rate constant. [97, 98]

20

Park and Rhee performed non-adiabatic molecular dynamics simulations on the GFP chromophoreand found that electrostatic effects can outweigh steric factors impeding the twisting of the methine
bridge between the phenoxy and imidazolinone rings, suppressing a major pathway for nonradiative relaxation. [74] Drobizhev and coworkers investigated these issues by measuring twophoton absorption cross-sections of RFPs. [58] This cross-section is sensitive to the change inpermanent dipole moment upon electronic excitation, which in part is controlled by the electricfield on the chromophore. [58] They proposed that brighter fluorophores could be produced byfine tuning the strength and directionality of the field, especially along the axis from the center ofthe imidazolinone ring to the phenolate ring. Electric fields along this axis are expected to change
the amount of single bond vs. double-bond character in the methine bridge, and therefore tune therate of non-radiative decay associated with chromophore twisting followed by passage through a
conical intersection to the ground state. Since this motion is accompanied by charge transfer acrossthe methine bridge, the rate can be described by Marcus electron transfer theory. [70]It is clearly a drastic oversimplification to characterize the electrostatic environment around thechromophore by specifying the electric field along different directions. In their tour de force 2019
publication, [62] Lin et al. circumvented this issue by treating the GFP absorption band as anintervalence charge transfer band between two resonance structures corresponding to the negative
charge residing either on the phenolate oxygen or the carbonyl oxygen of the imidazolinone ring.
The energetics of this charge transfer is described by Marcus-Hush theory. [99] The ground andexcited state potential energy surfaces were described by coupling the diabatic electronic states forthe two resonance forms through a bond-length alternation (BLA) coordinate. They demonstrate
the electron-donating or electron withdrawing nature of the sidechains at positions 203 and 96(located at either end of the chromophore) controls the driving force for the charge transfer. Thismodel quantitatively explains trends in absorption maxima, Stokes shifts, molar extinction
coefficients, lineshapes, and other properties. For example, eliminating the Thr203 hydrogen bondwith the phenolate oxygen reduces the driving force, leading to a decreased transition dipole
moment, red-shifted absorption, a decreased Stokes shift, and a smaller vibronic sideband. The
effect on the spectral lineshape is due to the relative intensity of 0-0 and 0-1 vibronic peaks of the1340 cm-1 BLA mode, and occurs in addition to inhomogeneous broadening due to sensitivity ofthe electronic transition energy to an electric field. The theory can be applied to otherchromoproteins such as photoactive yellow protein but it assumes the chromophore undergoes
21

small geometry changes upon excitation and does not consider mutations that modify the electronic
conjugation, so it does not explain the behavior of FPs such as BrUSLEE, where radiative rates
are significantly modified by mutations. The model however, provides a significant physicalinsight for FP design, and it would be very useful to develop a similar approach which reduces thedimensionality of protein electrostatic effects to an energetic coordinate, for modeling other classesof FPs. With this, we move on to a discussion of FP photostability.

Figure 1.6. A graphical summary of results from a TD-DFT study. A study performed by Kang
et al., [98] demonstrates that the oscillator strength and the absorption maxima for the GFP
chromophore can be modulated with changes in the electric field.

221.4. Photostability
1.4a. Photobleaching measurements and mechanisms
Irreversible photodamage or photobleaching is a hurdle to all applications. Despite the protection
offered to the chromophore by encapsulation within the β-barrel, FPs generally photobleach fasterthan many small molecule fluorophores. This photoreactivity is possibly due to the diversity ofchromophore interactions with the surrounding amino acid side chains and with freely diffusing
species such as O2, which provide opportunities for photo-oxidation and electron-transfer
reactions. [100] Identifying the mechanisms and/or structures of the photobleached products has
been a major challenge in FP development, most likely because several mechanisms are
simultaneously at play and multiple products are formed. As a result, simple physical models havebeen of limited utility in guiding molecular design for higher photostability.
Photostability is influenced by the photophysics of the fluorophore and by the properties of theexcitation source. A wide range of continuous wave (cw) or pulsed lasers, LEDs and arc-lamps
have been used for imaging and spectroscopic studies. Furthermore, in an attempt to investigate
photobleaching under conditions corresponding to various imaging techniques, measurements
have been performed with irradiances spanning several orders of magnitude, from µW/cm2–
kW/cm2. [101] Often, the decay of fluorescence intensity vs. time is found to be non-exponential.
As a result, the bleaching half-life is typically reported as a function of excitation irradiance.
However, this half-life, or the corresponding average photobleaching rate, is highly dependent on
the particular irradiation conditions such as the photon flux, excitation wavelength, peak intensityand pulse duty cycle. [55, 56] Furthermore, biochemical factors such as the buffer conditions forin vitro measurements, the host organism and cellular localization (e.g., cytoplasmic, nuclear or
membrane-associated construct) are also important considerations. FPBase provides a note ofcaution for researchers interested in using posted values for comparing the photostability ofdifferent fluorophores. [57] The lack of standards for measuring and reporting photostability
complicates decisions on which FP to select for a particular application and thus choices are often
made on anecdotal evidence.
To address inconsistencies in reporting of photobleaching and other parameters, Cranfill et al.
systematically measured the photobleaching and other properties of more than 40 FPs. [101] A
23

major revelation from their measurements is that the relationship between excitation intensity andphotobleaching rates is typically supra-linear, i.e., the average photobleaching rate 𝑘𝑏𝑙𝑒𝑎𝑐ℎ ∝ 𝐼 𝛼
where 𝛼 > 1 and is nearly quadratic for some FPs. For example, they found that mCherry emission
decays with a half-life of 318 seconds when bleached with a 590 nm scanning-laser illumination
at 80 µW excitation power vs. 88 seconds when bleached with a 594 nm widefield LED source at
200 µW excitation power. Although this study represents a major step forward in characterizing
FPs so that data-driven choices in experimental design can be made, the authors did not aim for amechanistic understanding of photostability.
The lack of consistency in measuring and reporting photobleaching has posed challenges tocreating models that connect photostability with other photophysical properties. To advance thisfield, it is recommended that quantum yield of photobleaching (PB) be adopted as the goldstandard for reporting and comparing FP photostability. Since, as discussed above, the power
dependence of FP photobleaching may be nonlinear, and the value of 𝛼 might vary in different
illumination regimes, PB should be reported as a function of irradiance, like what is done for the
2-photon upconversion yields of lanthanide nanomaterials. [102] This measure relies on
normalizing the bleaching rates with excitation rates, which is determined by multiplying theirradiance on the sample with the absorption cross section at the excitation wavelength (Equation
7).

𝑃𝐵 (𝐼) =𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 𝑝ℎ𝑜𝑡𝑜𝑙𝑦𝑧𝑒𝑑
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝ℎ𝑜𝑡𝑜𝑛𝑠 𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑𝑘(ln 2 ) 𝑁ℎ𝑐

= 𝑘 𝑏𝑙𝑒𝑎𝑐ℎ𝑖𝑛𝑔 = (2303 ) 𝐼 × 𝜆 × 𝜖 ×𝐴 𝑡
𝑒𝑥𝑐𝑖𝑡𝑎𝑡𝑖𝑜𝑛

𝜆1
𝑏𝑙𝑒𝑎𝑐ℎ𝑖𝑛𝑔
2(7)Where, 𝑁𝐴 is the Avogadro’s constant, ℎ is the Planck’s constant, 𝑐 is the speed of light, 𝐼 is theirradiance (power per unit area), 𝜆 is the wavelength of excitation, 𝜖𝜆 is the extinction coefficientat 𝜆, and 𝑡1𝑏𝑙𝑒𝑎𝑐ℎ𝑖𝑛𝑔 is the half-life obtained from the bleaching decay profile. Zak et al. followed2

this approach in considering the potential use of molecular fluorophores for luminescentconvertors in LEDs. [103] According to their calculation, one of the most photostable dyes forlaser spectroscopy, tetramethylrhodamine, has a PB of 3.3 x 10-7. Photostability data from FPBase
suggests that the most stable FPs have PB of ~10-4 when analyzed with this approach. [57] Given
that photon output before photobleaching limits the imaging duration and quality in many
experiments, this 1000-fold difference in photostability between dyes and FPs indicates there is
likely far more to be gained by improvements in photostability than in brightness.
24

The fluorescence profile is often found to decay on multiple timescales. The fastest time constantis typically associated with “reversible photobleaching,” the same process which we alreadyreferred to as “dark state conversion,” whereas the slower decay usually is due to permanent
photobleaching. The relationship between the photobleaching rate constant and the half-life value
is exact in the absence of dark-state conversion, and the photobleaching decay can be fit with asingle-exponential, or in cases where the photobleaching is exponential and much slower than darkstate conversion (e.g. EGFP and mScarlet). However, many FPs do exhibit long lived dark states,and photo-activation or photo-switching processes compete with the first order kinetics ofpermanent photobleaching. Moreover, chromophores can permanently bleach from dark states.
[104] Analogous dynamics are observed in azobenzene dyes, which like many FPs participate ina trans-cis isomerization under irradiation. [105] For azobenzenes, the dark cis conformer also
bleaches without emitting, leading to non-linearity of the photobleaching. We and others havereported methods for decoupling these processes from permanent photobleaching and extracting
the corresponding rate constants using other experiments such as fluorescence recovery
measurements. [55, 56, 106]
The brightest FPs often suffer from the highest photobleaching rates, in part because thephotobleaching quantum yield is inversely proportional to the excited-state lifetime. For example,
in the development of FR-MQV, as we selected for progressively longer fluorescence lifetimeclones, we observed a trend towards shorter photobleaching half-life under excitation normalized
widefield conditions (~5 W/cm2). FR-MQV has ~ 4-fold lower photostability than the parent
FusionRed despite a 1.6-fold longer fluorescence lifetime. [38] Another example is mScarlet,
which is 5-fold brighter than its variant mScarlet-H but has a 3-fold longer lifetime and a ~2-foldlower photostability (under 6.9 W/cm2 widefield excitation and 1.35 W/cm2 spinning-disk
confocal excitation). [35] However it is interesting to note that the drop in photostability does notscale exactly linearly with the increase in fluorescence lifetime for these two cases: it can be larger
or smaller than expected. This observation suggests that different mechanisms of photobleaching
may be at play within the two RFP families. More generally, examining the cases which deviate
from the expected linear scaling within a closely related series of FPs might provide some insight
into the structural features associated with photobleaching.

25

Turning to molecular mechanisms, computational and experimental studies suggest thatphotodamage is associated with the availability of molecular oxygen and diffusion of watermolecules inside the β-barrel. [100, 107, 108] Excited electronic states have higher reduction
potentials than the ground state and are therefore more susceptible to reacting with species such as
1

O2, which has been shown to be a major participant in photobleaching in certain cases. [100, 107]

Mechanistic investigations of phototoxic FPs that have found applications in chromophoreassisted light inactivation (CALI), have provided important insights into photobleaching. [109] Inthese systems, photobleaching seems to be directed into one overall reaction. To understand thisprocess, Grigorenko and coworkers employed QM/MM simulations to investigate the reactivity of
the FP KillerRed. Their analysis revealed that a model excited-state FP chromophore can reactwith O2 through several possible charge transfer intermediates. By sampling many reaction
pathways, their analysis identified a low activation barrier pathway (~13 kcal/mol) in which thehydroxyphenyl moiety is oxidized to a benzoquinone species that can diffuse out of the β-barrel.
This result is consistent with electron density maps from an X-ray crystal structure ofphotobleached KillerRed. [109] Sen et al. recently performed QM/MM simulations to explore therole of T65/S65, the first chromophore-forming residue in EGFP and EYFP, respectively. For
EGFP, a T65G substitution reduced the fluorescence lifetime but increased photostability, with areduction of the characteristic green-to-red oxidative photoconversion, or “redding” behavior
commonly observed for EGFP. [110] This phenomenon is observed when the GFP chromophoreis oxidized to red-shifted absorption and emission species by high irradiance illumination. The
transfer of fluorescing populations to such species has been linked to faster photobleaching. [111,112] We refer the reader to the work of Acharya et. al for a detailed explanation of thisphenomenon. [16]Dark states can also contribute to photobleaching. The lifetimes of triplet states, for example, areorders of magnitudes longer than the S1 state and can, in fact, catalyze the formation of 1O2, which
greatly speeds up photochemistry promoting chromophore destruction. [55, 65] Therefore,
reagents like oxygen scavengers and triplet-state quenchers are promising tools for slowing therate of photobleaching, as they create apoxia in the system or depopulate non-fluorescent triplet
states. [113] Another complication is that cases have been observed where the effect of dark stateson photobleaching depends on the illumination conditions. For example, we found that the RFP
mCherry was more photostable under pulsed illumination than under cw illumination, particularly26

at high irradiances (25 kW/cm2), suggesting that mCherry’s dark state is photoreactive, whereas
for the variant TagRFP R67K S158T, we found that the dark state is more photoprotective thanphotoreactive. [55]

1.4b. Development of photostable FPs
Despite these challenges, several studies have advanced fluorophore photostability. For example,
Single-cell Phenotypic Observation and Tagging with light (SPOTlight), a cell sorting technique,led to the most stable yellow FP (YFP) observed to date, mGold. [114] In this case, eight libraries,
each of 8000 variants were produced by targeted mutagenesis of 21 positions in the YFP mVenus(six near the chromophore) and expressed in yeast. SPOTlight then photobleached cells at an
irradiance of ~2 W/cm2 and selected photostable variants from up to 700,000 cells in multiple
rounds of selection. Similarly, high-throughput screening for photostable FPs using a Lego-based
robot led the development of another YFP, Citrine2, which is ~2-fold more stable (in widefield
and laser bleaching assays) than its precursor, mCitrine. [115] In this case, directed evolution oferror-prone mutagenesis libraries was used with photostability selection with a 300 W white light
Xenon lamp source that had an effective white light irradiance of ~3.5 W/cm2. This study identified
8 mutations that improved the photostability of Citrine2 in comparison to mCitrine but also led tounfavorable consequences such as dimerization and a drop in fluorescence lifetime from 3.6 ns to
3.3 ns. Surprisingly, these changes also led to a 5% increase in the radiative rate and 25% increaseof the non-radiative rate. [115] These examples provide proof-of-principle demonstrations thatscreening large numbers of variants with new technologies can generate more photostable variants,
but much more work remains to be done beyond the demonstration phase.
Our efforts to improve the photostability of mCherry using microfluidic technology led to thedevelopment of Kriek, which is 4-fold more photostable in confocal fluorescence microscopy.
[108] This variant was selected from a 144,000-member library designed with guidance from MD
simulations. The simulations identified a region of the β-7/10 strand interface that showed nstimescale fluctuations inconsistent with a rigid barrel structure, and we identified additional
positions adjacent to this region which appeared tolerant to mutations. Selection was performed tominimize the amplitude of fluorescence signal lost after excitation from four sequential excitation27

beams (to mimic pulsed excitation in flow) under irradiance of ~ 2 kW/cm2. We later found thathigh irradiance-pulsed excitation tends to populate dark states in mCherry and TagRFP variants.
Since the microfluidic-based selection of Kriek was carried out with a similar excitation scheme,
we also found that Kreik had lower rate constants for dark state conversion. [55] Previously, wedemonstrated that the progenitor mCherry has a photoreactive dark state. Therefore, a reduction in
the rate of dark state conversion may have resulted in an additional boost to the photostability ofKreik. Unfortunately, we observe a significant drop in the fluorescence quantum yield of Kriek(8%) with respect to the precursor mCherry (22%) with this strategy. The lesson here is that MD
simulations can provide useful insight for library design, but that screening only on photobleachingis likely to produce variants with compromised brightness.
Other site-directed mutagenesis studies have been fruitful, as evident in the development ofSiriusGFP - which is 2-fold more stable than its precursor EGFP and was found to be well suitedfor imaging at high irradiance (~kW/cm2) and long time-lapse imaging assays. [116] In this case,site-directed mutagenesis was guided by considering photochemical reactions of the model GFP
chromophore. They found that S147R and S205V mutations in EGFP greatly enhanced thephotostability under high irradiance laser-based imaging. [117] As with other efforts to improve
photostability, SiriusGFP suffers from reduced brightness in comparison to EGFP due to a ~3-fold
reduction in its fluorescence quantum yield. When Ren et al. (2016) introduced a cysteine groupnear the chromophore of the RFP mKate2, it resulted in the 12-fold improved variant, “mStable.”
The photostability of mStable was attributed to the sulfoxidation of a cysteine residue facing thep-hydroxyphenyl moiety of the chromophore. Similar substitutions in mPlum resulted in a 23-foldmore stable variant. [118] The development of mGold from mVenus and Citrine2 from mCitrine,
demonstrates that photostability can be improved without significant compromises in molecularbrightness. This outcome suggests that it is possible to evolve existing bright FPs into more
photostable variants, and vice-versa, perhaps by screening libraries simultaneously on
photostability and fluorescence lifetime.
Inspiration for FP design and applications may draw from effective techniques that minimize
photobleaching in molecular fluorophores, such as utilizing triplet state quenchers and using
systems that induce anoxia. [119] In addition, a promising strategy was recently reported where
deuteration of small molecule dyes such as tetramethyl-rhodamine and JaneliaFluor (JF) dyes
28

substantially improved photostability without causing detrimental changes to the electronic orphotophysical properties. [120] For these types of dye molecules, alkylamine oxidation produces
a distinctive secondary isotope effect, where deuteration of hydrogen atoms may reduce a twistedintermolecular charge transfer process, as is commonly observed for many FPs and in xanthene
based JF dyes. Deuteration additionally increases the strength of the C-D bond and also affects the1O2 oxidation rate, which manifests in higher (~1.2 fold) photostability. In addition to thesemolecular strategies, methods that involve the light source, such as control of photon statistics,
pulse shaping, or excitation with squeezed light may also be promising tools for imaging FPs forlonger periods of time by increasing the measurement precision attainable for a particular photon
dose, even if these techniques do not directly reveal the chemistry behind photobleaching. [121]1.5. Conclusions
A few themes emerge when we consider the evolution of this field over the past 30 years. Initially,
FP development relied on relatively straightforward structure-guided design and chemical intuition
with screening on cellular brightness. As the productivity of this approach has started to decline,
new variants have been introduced by relying on more advanced screening methods, withnarrowly-focused photophysical and biochemical goals. Our knowledge of FP structure and thediversity of their photophysics has dramatically expanded, however, at the same time, the pace of
new FP development has slowed, e.g. of the more than 1500 FPs collected in FPbase, 270 werereported in the peak years of 2009-2010, decreasing to about half that number in subsequent twoyear periods since then. Is this slow-down due to the limits of our technology or of our insight?
We think mostly the latter. How will the field continue to advance? Technology for faster, more
precise screening of large libraries can partially make up for our knowledge gaps. Screening of
RNA aptamer or protein libraries several orders of magnitude larger than those in FP development
have frequently been used to successfully evolve high-affinity, specific ligand binding when
physical insight is not applied to the library designs. [122, 123] Nevertheless, screening on
complex functions such as photophysical properties will require more physical insight applied tothe molecular design, and we feel that a renaissance of FP development might follow frominvestments in new experimental and theoretical approaches.

29

Experimental studies combining selections that go beyond “skimming the crème off the top” oflibraries and simply keeping and studying the best clones could lead to unexpected insights. If thescreening is performed such that the evolution of the properties and the structures within thelibraries are monitored on a large scale, then bioinformatics and machine-learning techniques
could be used to obtain more information about why some selections work and why someselections do not produce improvements. [124] Computational methods such as classicalmolecular dynamics and hybrid quantum-molecular mechanics would be valuable for creating
models that advance our understanding of FP conformational dynamics and photoreactions suchas photobleaching. These efforts should be accompanied by refinement of classical physicalchemistry theories of, e.g. internal conversion so that it can be understood when we are facing
issues particular to a small class of chromophores vs. hitting fundamental physical limits. These
investigations could help us develop protein design strategies that bridge structural measures suchas chromophore planarity and rigidity, with photophysical parameters such as fluorescence
lifetime or dark-state conversion rates. Clearly, physical chemists could make fundamental
contributions to the development of new fluorescent proteins or utilize the progress in this field to
explore new avenues in chemistry. [125] Progress on these topics may have impacts on areas
beyond bio-imaging, such as solar-energy conversion materials, bio-hybrid LED lighting, and biophotonics such as display technologies.

1.6. Thesis aims and objectives
The central theme of this thesis is to advance fluorescent protein design driven by the fundamentalsof physical chemistry, particularly with respect to understanding the basis of brightness andphotostable red FPs. This work first involved the development of a multi-parameter, highthroughput, droplet-based microfluidic sorting system, integrating high-throughput fluidics withlaser spectroscopy (Chapter 2). The instrument advanced our existing capability by 3-orders ofmagnitude with respect to multi-parametric cell sorting (~108 RFP expressing cells in 3 hours).
This device and the pre-existing microfluidic sorting technology enabled selection of FPs withincreased fluorescence lifetime (and corresponding increase in fluorescence quantum yield or thebrightness) from libraries of rationally or randomly mutated FPs.

30

Subsequent chapters describe protein design based on crystal structure, bioinformatics, andexperimental guidance from ultrafast spectroscopy to identify target residues and generate mutant
libraries of FusionRed and mCherry. Consequently, lifetime-based selections lead to thedevelopment of bright RFPs - FusionRed-MQV (Chapter 3) and mCherry-XL (Chapter 5). The
FusionRed-MQV variant was then characterized in cells to explore the potential for cell biology
applications.
Chapter 4 describes investigations of FusionRed-MQV focused on quantitative analysis ofphotobleaching and dark state conversion in vitro. The parental proteins of FusionRed-MQV –FusionRed and FusionRed-MQ displayed efficient dark state conversion tendencies compared totheir progeny, and thus were selected for detailed study, with a focus on potential applications insuper-resolution imaging. The dark state kinetics were investigated with a new approachcombining single molecule imaging, ensemble dark state conversion experiments, Monte-Carlosimulations, and data fitting protocols. It was found that measured single molecule blinking
timescales could be accurately predicted from their ensemble dark state conversion timescales.
Chapter 5 describes a study of the evolution pathway from mCherry to mCherry-XL. The increasein quantum yield was largely found to be due to the suppression of non-radiative pathways of
excited state depopulation. Modeling the reduction of non-radiative pathways with the EnglmanJortner formalism for excited state non-radiative decay in this lifetime evolution trajectory reveals
likely involvement of excited-state ultrafast dynamics rather than internal conversion directly to
the ground electronic state.
Chapter 6 describes mutagenesis strategies undertaken to further increase the quantum yield ofFusionRed-MQV using increased lifetime selections. Error-prone PCR and saturation mutagenesisof sites 71, 159, 175 and 224 identified variations such as FR-MQV-VA and FR-HQC-TT. These
FPs have 1.2-1.4-fold longer lifetimes than FusionRed-MQV, with scaling increments in quantum
yield due to a lower non-radiative rate. Furthermore, photobleaching studies on these mutants
indicate that the dark state in FusionRed variants with a cysteine residue at position 159 is probably
photoprotective.
Finally, Chapter 7 provides a perspective for future work based on preliminary experiments.
Exploratory measurements indicate the feasibility of developing a microfluidic sorting system forselecting FPs on dark state conversion using the technique Fluorescence Anomalous Phase31Advance (or FAPA). This is followed by a discussion of chromophore maturation and protein
expression in limiting the in-cellulo fluorescence of bright FP molecules. Initial mutagenesis
efforts and all-atom explicit solvent classical molecular dynamics (MD) simulations elucidate theplausible mechanistic role of the C-terminus of the FP in protein expression and chromophorematuration. Further investigations along these mechanistic lines may present an opportunity forthe application of bright FPs like FR-HQC-TT in biological imaging.

32

Chapter 2
Instrumentation: Development of a high-throughput
microfluidic sorter
2.1. Publication Note
Parts of this chapter have been adapted from the article “Enrichment of Rare Events Using a
Multi-Parameter High Throughput Microfluidic Droplet Sorter.” Hung, S. T.; Mukherjee, S.;
Jimenez, R. Lab Chip 2020, 20 (4), 834–843. https://doi.org/10.1039/c9lc00790c.

2.2. Introduction
Fluorescence lifetime is an intrinsic molecular property that is independent of excitation andemission intensity, local fluorophore concentration, and can be detected even with spectral
overlaps among fluorophores and in the presence of cellular auto-fluorescence. Fluorophore
lifetime is often sensitive to the solvent and biochemical environment, so it has been used as adetection parameter in imaging and sensing techniques. [126-129] Fluorescence lifetime imaging
microscopy (FLIM) is a powerful tool complementing fluorescence brightness-based imaging
methods. It has been applied to subcellular pH measurements, [130, 131] intracellular refractive
index sensing, [132, 133] molecular interactions in cells, [134-136] drug evaluation and discovery[137-139], drug delivery and cancer studies. [140-143] Nonetheless, FLIM applications arehampered by its throughput. Flow cytometry incorporating fluorescence lifetime measurements
could significantly improve the throughput, advancing applications to biological and biomedical
research such as directed evolution of FPs, [30] protein subcellular localization, [144] proteinprotein interaction, [145] drug discovery, [146] and cellular physiology. [147, 148]
Lifetime-based flow cytometry has been demonstrated at a sorting throughput of hundreds of cells
per second. [149] However, there are limitations associated with fluorescence detection in acontinuous flow stream. For cellular applications, it restricts the fluorescent markers and reactions
to be inside or on the cellular surface and is limited to applications that are insensitive to intercellular interactions. One approach for overcoming these limitations is to encapsulate cells or other33

analytes into isolated droplets that retain their integrity throughout the analysis, and sorting. Theease with which stable droplets can be formed with pL-scale, tunable volumes make droplet
microfluidics particularly useful for analyzing individual molecules, cells or other discrete analytes
such as beads. These capabilities have been utilized for studying enzymatic activity in cellulo [150,151] and in vitro, [152] single-cell analysis and sorting, [153] screening for antibiotic resistance,[154, 155] directed evolution of enzymes, [156] genetically-encoded biosensors, [157, 158] andquantifying heterogeneity at the single cell level. [159, 160] Moreover, microfluidic droplet
platforms can be designed for novel flow cytometry applications such as those simultaneously
requiring temporally well-defined mixing of cells with reagents followed by time-resolved
detection. Fiedler and coworkers have demonstrated resolution and sorting of genetically-encodedbiosensors based on various Förster Resonance Energy Transfer (FRET) ratios measured withdelay time in seconds. [158] The same platform can be readily modified for directed evolution offluorescent proteins or enzymes.
The throughput of lifetime-based droplet sorters is impacted by several factors. First, the statistics
of cell loading into droplets typically follows the Poisson distribution. [161] To ensure single cellloading, the proportion of non-empty droplets is often limited to < 10% of the whole droplet
population. Unfortunately, this sparse loading limits the throughput and is therefore often regarded
as a disadvantage of the droplet platform. Deterministic single cell encapsulation methods
overcome the limitation imposed by Poisson statistics, but there are other limitations such asincreased device complexity, substantial proportion of unsorted or wrongly selected droplets, andhigh flow rates limiting the ability of integrating with other systems. [162] Second, the throughput
of a conventional droplet sorter is limited to 2~3 kHz due to the use of a hard divider to separate
the collection and waste channels, but new geometries have been investigated to surpass thislimitation achieving brightness-based sorting at 30 kHz. [163] Finally, fast data processing offluorescence lifetime signatures and real-time sorting decision and actuation components are
crucial for achieving kHz sorting rates. Despite advances in incorporating fluorescence lifetime
measurements into droplet selection methods, the throughput is much lower than purely
brightness-based droplet sorting. For example, the throughput of a recently reported fluorescence
lifetime droplet microfluidic sorter is 50 droplets/s. [164] A FACS enrichment step is often used
to enrich a subset of targets from a large pool prior to selection or investigation on other parametersand platforms. [30, 165-167] Performing fluorescence lifetime selection with this combination of34

methods is disadvantageous. In addition to the restrictions imposed by a continuous flow stream
in the FACS step, the use of two different instruments imposes uncertainties into the overall
selection because the fluorescence intensity values are difficult to calibrate between instruments.
Within the general realm of sorting applications, the analysis, enrichment, and isolation of raremacromolecules, cells and particles from a large population constitutes an important subset that isof great importance across a broad area of biomedical, biotechnological, and environmental
science. Several papers have described approaches to this challenge in which a rare population is
individually analyzed without isolation, or first enriched rather than attempting one-step, singleparticle isolation. For example, fluorescence brightness-based droplet digital detection has been
applied to the detection of single bacteria in unprocessed blood [168] and profiling circulatingtumor DNA, [169] and the implementation of fluorescence lifetime detection was demonstrated toincrease the specificity of particle counting. [170] An ensemble sorting approach which repeatedly
analyzes and sorts batches within a sample was recently proposed for enriching or separating
fluorescent particles. [171] Many microfluidic systems have been developed to enrich and isolate
circulating tumor cells, as reviewed in reference 172. [172] Thus, we quantitatively consider theadvantages of a batch sorting technique for increasing the throughput of rare-clone isolation.
Here, we discuss the development of a multiparameter high throughput water in oil droplet
microfluidic sorter capable of screening and sorting analytes based on emission spectra, emission
brightness, and fluorescence lifetime. We raised the throughput of lifetime sorting to the upper
limit for a droplet sorter incorporating a hard divider between collection and waste channels, [163]which constitutes a 50-fold increase comparing with the recently reported lifetime droplet sorter.
[164] We also describe and demonstrate a novel selection strategy, similar to an ensemble-based
approach, which exploits the Poisson statistics of analytes in droplets overloaded with multiple
analytes. This method provides a several-fold enhancement in sorting throughput. The strategy canbe used to analyze and enrich rare events from a large population in either a qualitative mannerwithout the prior knowledge for the initial frequency of the rare events, or in a quantitative fashion
with controls for the efficiency and precision of enrichment when the initial frequency of the rare
events is estimated. The enriched sub-population can be subjected to further multiparameter
analysis and selection with single-cell resolution on the same microfluidic platform. We
demonstrate the power of this multiparameter droplet sorter and the enrichment strategy in thecontext of directed evolution of red fluorescent proteins (RFPs) expressed in E. coli.
352.3. Experimental
2.3a. Optical Layout
The optical layout of the instrument is depicted in Appendix Figure A1.1. Both 561 nm and 450
nm continuous wave (CW) laser beams excite fluorescence from the cells encapsulated in droplets.
The 561 nm beam is focused into an electro-optic modulator that can amplitude modulate the CW
beam to a sinusoidal profile. The red and green fluorescence signals are separated by a dichroic
mirror and detected by photomultiplier tubes (PMTs).

2.3b. Electronics and microfluidic device
The main improvement of sorting throughput in this work is due to the implementation of fasterelectronics. The layout of the detection electronics is schematically described in Figure 2.1. The
electro-optic modulator (EOM; ThorLabs EO-AM-NR-C4) is used to modulate the 561 nm laser
light and is driven using a function generator (Agilent 33520B) that provides a 1 V peak to peaksinusoidal signal at 29.5 MHz to a resonator circuit. When screening or sorting based on
fluorescence lifetime, the red fluorescence signals from PMT1 are separated into a radio frequency(RF) component (that bears the lifetime information) and the direct current (DC, <83KHz)
component using a bias tee. To improve the signal to noise ratio, the DC signals from the biasedtee and from PMT2 (green fluorescence) are amplified using home-built trans-impedance log orlinear pre-amplifiers, depending upon the experiment and sample in use, [30] then digitized using
Analog to Digital Converter (ADC) boards (Analog Devices, EVAL-AD7986FMCZ, 18 bit). The
RF component of the signal is passed onto a commercial high-speed lock-in amplifier (Zurich
Instruments UHFLI), which calculates the phase shift of the fluorescence signal relative to thesinusoidal modulation signal to extract information of fluorescence lifetime. The phase shift value
from the lock-in amplifier is then digitized using the same type of ADC boards employed forbrightness measurements. The digitized signals from the boards are then fed into a customized
field programmable gate array (FPGA) board that makes decisions based on user definedparameters interfaced through a LabView program. FPGA has been implemented to enhance thedata processing rate for fluorescence lifetime calculation. [173] Brightness and lifetime signals
from encapsulated cells in droplets that fulfil the selection criteria are then sorted using
dielectrophoresis (DEP) technique. [158] The FPGA sends a sort signal to trigger a function36

generator (Keysight 33509B) which provides a square wave pulse which is amplified 1000x in ahigh voltage amplifier (TREK), before being sent to the electrodes of the microfluidic device. The
flow is biased towards the waste channel, so droplets are only directed to the collection channel
when the FPGA sends a signal to trigger a high voltage pulse to DEP electrodes. The fluorescence
detection and cell selection regions of the device are shown in Figure 2.2a. Further details on the
microfluidic device are provided in Appendix 1: Section 1.

Figure 2.1: Schematic layout of the electronics used in this sorter.

Figure 2.2. Droplet generation and size. (a.) Camera image shows the typical droplet flow withboth excitation beams on. The microfluidic chip is designed such that droplets are biased towards
the waste channel. (b.) Image of droplets containing Rhodamine B generated with the microfluidic
chip. The scale bar indicates 50 µm.
372.3c. Instrument operation
The microfluidic sorter is configured with excitation beams at 450 nm and 561 nm, wavelengths
which allow for screening based on green and/or red fluorescence signals respectively. The 561
nm excitation beam is modulated at 29.5 MHz, enabling fluorescence lifetime screening in the redchannel. To count the number of droplets passing each channel and monitor the flow (number ofdroplets per second) throughout an experiment, the laser intensities and PMT voltages were set
such that a small portion of scattered laser light from each droplet bleeds through the dichroic
mirror and the emission filters, and thus can be detected in both PMT channels. We previously
reported fluorescence lifetime sorting in a microfluidic flow cytometer, however, the sorting speed
was limited to ~30 cells/s because communication among instruments, target and host computers,
calculation of fluorescence phase shifts, and sorting decisions relied on software developed on a
LabView platform. [30] In the current sorter, the phase shifts are obtained directly from a highspeed lock-in amplifier, and an FPGA coordinates communication among all electronics andperforms sorting decisions. A LabView user interface is designed only for setting selection
parameters, acquiring data from the FPGA and real time plotting. As a result, the new instrument
operates at ~100-fold higher screening and sorting speeds. For both fluorescence-activated droplet
sorting (“brightness sorting”) and fluorescence lifetime-activated droplet sorting (“lifetime
sorting”), the FPGA and LabView program are designed such that the sorting thresholds can be
set to exclude empty and unwanted droplets for sorting purposes, while counting the total numberof droplets and monitoring the flow (number of droplets per second). Both brightness and lifetime
measurements have been tested at droplet generation rates up to 4 kHz (~0.7 mL/hr volumetricflow rate) for screening and 2.5 kHz (~0.45 mL/hr volumetric flow rate) for sorting. A typicalimage of droplets generated at ~2.5 kHz (Figure 2.2b), demonstrates their size uniformity andagreement with the estimated droplet volume ~50 pL which is determined from the droplet
generation rate and the 0.45 mL/hr volumetric flow rate. More details about instrument operation
are available in Appendix 1: Section 2.

2.3d. Cell culture and sample preparation
The droplet microfluidic sorter can be employed to assay diverse cell types, such as bacteria,
phytoplankton, yeast, and mammalian cell lines. To test the performance of this sorter, various FPs
with distinct fluorescence lifetime, brightness, and spectra were expressed in E. coli. Cells
38expressing FPs were prepared at desired concentrations according to the measurement of their
optical density (OD) and connected to the aqueous inlet of the microfluidic chip. The details ofcell culture and sample preparation are described in Appendix 1: Section 3.

2.4. Results and Discussion
This instrument control software is designed such that one can choose the desired combinations ofscreening and/or sorting based on emission spectrum, brightness, and red fluorescence lifetime.
The scattered excitation light from each droplet can be detected by the PMTs, which allows us tomonitor the flow, count the number of droplets, and pair-match two events in green and redchannels for a particular droplet. Details of data acquisition and signal processing are described inAppendix 1: Section 4. The performance of brightness and lifetime sorting with different
screening/sorting criteria is evaluated here. We also present some examples of the strategy forenriching rare events with multiple cell encapsulation.

2.4a. Performance of two-color brightness-sortingTo evaluate the performance of brightness detection in the green and red channels, E. coli cells
expressing EGFP and mScarlet were screened respectively to find the mean brightness in eachchannel. An approximately 1:1 mixture was prepared and droplets with a brightness threshold
greater than mean brightness in red channel was sorted to select mScarlet from ~105 droplets. The
sorted cells were subsequently grown overnight and screened 16 hours after induction of
expression to evaluate the sorting efficiency. All screening and sorting experiments were
performed at a rate of 2 kHz with an average cell concentration of 0.1 cell/droplet, where 9.5% of
the droplets are filled and 95% of filled droplets contain a single cell. The results shown inAppendix 1: Section 5 reveal a sorting efficiency of 86±1% averaged from 3 experimental trials,
i.e. 86% of re-grown cells have mScarlet and 14% of them have EGFP. The 14% re-grown cells
expressing EGFP reflects several factors including the 5% of filled droplets containing multiple
cells, varying cytotoxicity for cells expressing different FPs, and the excitation conditions. [174]
These issues are discussed in the lifetime sorting section, below.

39

2.4b. Performance of lifetime sorting
The phase shift measured in the frequency domain technique is sensitive to the modulation
frequency, [56] transit time of cells passing through the laser beam, and settings of the PMT andlock-in amplifier. Determination of the lifetime and its dependence on these experimental factors
is described in Appendix 1: Section 4. E. coli cells expressing mCherry, mApple, or mScarlet werescreened with brightness and lifetime at a rate of 2.5 kHz. The major population of each RFP is
distinguishable by its fluorescence lifetime as shown in Figure 2.3a. The results reveal
heterogeneity in both fluorescence brightness and lifetime, as observed in our previous work onother RFPs. [30] The spread of lifetime values is about 0.5-1 ns for these RFPs at full width at half
maximum (FWHM) of the histograms in Figure 2.3b.

Figure 2.3. Lifetime screens of FPs. (a.) Fluorescence lifetime and brightness plots of empty
droplets and individual RFPs expressed in E. coli screened sequentially (104 cells each).
Pseudocolor indicates the normalized cell counts with a particular bin of fluorescence lifetime andbrightness on the plot, ranging from yellow for the highest to indigo indicating the lowest counts.
The mean fluorescence lifetime is 1.7 ns (set as reference), 2.6 ns, and 3.3 ns for mCherry, mApple,
and mScarlet respectively. (b.) Corresponding fluorescence lifetime histograms. (c) Fluorescence
lifetime histograms of Rhodamine B (RhB) and three purified proteins measured in the
microfluidic sorter. The mean fluorescence lifetime is 1.6 ns (set as reference), 1.6 ns, 2.8 ns, and
3.5 ns for RhB, mCherry, mApple, and mScarlet respectively.
40

The asymmetric histograms of fluorescence lifetime in Figure 2.3b can be understood as an effectresulting from the contribution of scattered excitation light detected along with the fluorescencesignal. This effect is modeled with a simulation in Appendix 1: Section 4. Ideally, scattered light
has a constant phase shift (which is converted to the fluorescence lifetime) relative to themodulated laser beam due to optical and electronic delays. This is included in the total phase shiftby setting the reference phase shift of a bacterial colony expressing mCherry on a plate to 45
degrees. In this particular experiment, the total offset phase shift of empty droplets corresponds toa fluorescence lifetime centered on ~2.35 ns with a wide distribution due to low signal-to-noise
ratio (SNR). The scattered light is added to the fluorescence signal and both signals have the same
modulation frequency but different phase shift values, so the lock-in amplifier extracts an averaged
phase value from the combined signals. The influence of scattered light is more significant at low
fluorescence brightness, whereas the average lifetime value approaches the actual fluorescence
lifetime value as the fluorescence brightness increases.
The distribution of lifetime measured from a single-FP population can be attributed to cellular
heterogeneity, excitation condition and electronics. Cellular heterogeneity is an intrinsic
biochemical property that can only be resolved in single cell analysis methods such as thismicrofluidic droplet sorter. On the other hand, the noise originating from the excitation condition
may be further reduced. The diameter of the droplet is estimated to be ~46 µm, but the Rayleighlength of the excitation beam is ~10 µm, hence the location of the cell inside a droplet could leadto variations in fluorescence brightness resulting in uncertainties in lifetime measurement.
Theoretically the lifetime is independent of fluorescence signal level, but in practice the scatteredexcitation light affects weaker fluorescence signals more than stronger ones as discussed above.
We further investigated the spread of lifetime due to electronics by performing in vitro
measurements. In addition to eliminating the cellular heterogeneity, in vitro measurements also
minimize the fluctuations from excitation condition since a droplet has homogeneous fluorophore
concentration and the Rayleigh length is always within the droplet. It is worth noting that various
in vitro assays can be performed with a droplet platform, but it is difficult to perform them with acontinuous stream cytometry. Three purified proteins, mCherry, mApple, and mScarlet, and anorganic dye, Rhodamine B, were screened for fluorescence lifetime using the sorter. The histogramof fluorescence lifetime is shown in Figure 2.3c, with FWHM ~0.1 ns for Rhodamine B and ~0.20.3 ns for FPs. The widespread in lifetime for mCherry is likely due to its low SNR resulting from41

a low quantum yield (hence low molecular brightness). Nonetheless, the FWHM of fluorescence
lifetime measured from an in vitro experiment is much narrower than that from a cellularmeasurement. The result indicates that the uncertainty originating from electronics is significantly
less than other sources. This also suggests that the lifetime resolution for cellular screening could
be improved by reducing the droplet size and/or expanding the beam size to extend the Rayleighlength to ensure that the encapsulated cells are within the Rayleigh length, i.e. an improved uniform
excitation condition. This effect will be reduced with larger cell types such as yeast or mammaliancells. Finally, note that the disagreement in the average lifetime among cellular and in vitro
measurements suggests that the cellular environment differs from the in vitro environment. For
example, fluorescence lifetime of FPs varying with environmental pH [130, 131] and refractive
index [132, 133] has been reported and used for sensing and imaging applications. Details of thein vitro experiment including the comparison of fluorescence lifetime measured using the sorterand Time-Correlated Single Photon Counting (TCSPC) are described in Appendix 1: Section 5.
To demonstrate the performance of lifetime-based sorting, E. coli cells expressing mScarlet or
mCherry were mixed in a ~1:1 proportion and sorted at 2.5 kHz with two parameters, fluorescence
lifetime and brightness, at an average concentration of 0.1 cell/droplet. This sort rate represents
the fastest fluorescence lifetime droplet sorting reported to date. Approximately 3x103 droplets
were sorted from ~2.5x105 droplets with the selection gates set to the mean brightness value andmean fluorescence lifetime of mScarlet. The sorted cells were subsequently grown, expressed for
16 hours and re-screened to evaluate the sorting efficiency. The screening results before and after
sorting are shown in Figure 2.4, demonstrating an 85% sorting efficiency. The experiment was
additionally repeated 3 times with a new mixture, sorting mScarlet or mCherry, and the average
efficiencies were 80±1% and 97±1% respectively, as described in Appendix 1: Section 5. The
discrepancy between sorting mScarlet and mCherry can be attributed to the process of re-growing
and expressing enriched cells in the experiment with the assumption that bacteria expressing
different FPs have the same growth rate, which may not be accurate. Some mCherry mutants,
mApple, and EGFP have been reported to show a range of cytotoxicities when expressed in E.
coli. [174] The difference between two batches of mScarlet enrichment experiments may be dueto the flow condition, the biological variation (two biological duplicates in two batches ofexperiments) and the uncertainty of cell concentration in the sample preparation causing variations
in λ, which affects the sorting efficiency that will be further discussed below.
42Figure 2.4. Fluorescence lifetime versus brightness scatter plots of mixed cells before andafter sorting. Solid boxes indicate the thresholds for counting cells expressing mScarlet. N is thenumber of cells expressing each RFP. (a.) Mixture of E. coli cells expressing mCherry andmScarlet before sorting. The dashed box indicates the two-parameter sorting gates. (b.) Screening
results after sorted cells were grown overnight and expressed for 16 hours. The brightness
threshold was set slightly higher than pre-sort to exclude the stronger scattered excitation signals
from droplets in the post-sort screening, because changing microfluidic chips introduces variationsin the focus of the excitation beam and thus the amount of scattered light.

2.4c. Strategy for enriching rare fluorescent events
For a large library containing rare events, the overall throughput can be greatly increased by sorting
droplets by encapsulating multiple cells in a single droplet as an initial round of enrichment. The
efficiency of this strategy can be estimated by considering the Poisson distribution, thecombination of cells resulting fluorescent droplets, and the percentages of fluorescent cells in alibrary. We present a schematic to consider the combination of cells encapsulated in droplets
illustrated in the inset of Figure 2.5. A droplet will be detected with fluorescence as long as it
contains one or more fluorescent cells. The probability of number of cells (N) encapsulated in a
droplet is Prob(𝑁) = (𝑒 −𝜆 × 𝜆𝑁 )/𝑁!, where 𝜆 is the average number of cells per droplet.

43Figure 2.5. The efficiency of enrichment with various initial fraction of target analyte. (cells,
molecules, or beads). Presented also, the required enrichment time as a function of average numberof cells per droplet. Inset (dashed box): Illustration of cells encapsulated in droplets. The red andblack dots indicate fluorescent and non-fluorescent cells, respectively. The green check and red
cross marks indicate fluorescent and non-fluorescent droplets.

Assuming a library with initial fraction F of fluorescent cells, the probability of finding fluorescentcells after sorting, 𝑝𝐹 , is𝑛∑𝑛𝑖=1 ( ) ∙ 𝑖 ∙ 𝐹 𝑖 ∙ (1 − 𝐹)𝑛−𝑖𝑖𝑝𝐹 = ∑,𝑛𝑛𝑖 ∙ (1 − 𝐹)𝑛−𝑖
∑
𝑛
∙
(
)
∙
𝐹
𝑖=1 𝑖
𝑛=1
∞

where 𝑖 is the number of fluorescent cells and n is the number of cells per droplet. Since theprobability of encapsulated cells per droplet decreases quickly with the increasing number of
encapsulated cells, the 𝑝𝐹 can be numerically calculated using n50 for λ≤10. The Poisson
distribution for λ≤10 is plotted in Appendix 1: Section 6. The efficiency of the multiple-cell
encapsulation enrichment, which is indicated by the improvement in the fraction of fluorescentcells after sorting (i.e. 𝑝𝐹 ), is estimated with F=0.01 and F=10 ppb for various 𝜆 as shown in Figure2.5. The results indicate that with one round of sorting, the fluorescent cells in the library can be44

enriched to about the same fraction regardless of the initial fraction F, thus this selection strategy
is more powerful for enriching rarer events from a large pool (i.e. small F). It is not surprising thatthe enrichment efficiency is significantly affected by the average number of cells per droplet (𝜆),but the influence from the fraction of fluorescent cells in the original library is not significant,because the selected droplets all contain fluorescent cells. Assuming a sorting speed of 2.5 kHz,the time required for screening 108 cells as a function of 𝜆 is plotted in Figure 2.5. The resultclearly shows that the time can be drastically reduced by including multiple cells in a droplet. The
estimation of 𝑝𝐹 only considers the statistical probability, i.e. the number of screened cells is muchlarger than the inverse of the initial fraction F. Such enrichment efficiency, 𝑝𝐹 , is estimated to holdfor enriching ≥0.5 ppm targets from 108 cells, the limit for current throughput to complete
enrichment in a few hours without losing cell viability, in Appendix 1: Section 6. However, thisdoes not limit the application of the enrichment strategy from sorting smaller fraction of rare
events. With a smaller fraction of rare events, the enrichment efficiency may deviate from theexpected value plotted in Figure 2.5, but it still provides approximately the same order ofmagnitude of enrichment efficiency as illustrated in Appendix 1: Section 6.
To further illustrate the power of this enrichment strategy, we consider two examples of rare events
that fluoresce or exhibit a distinct fluorescence lifetime relative to the main fluorescent population.
Assume the enrichment is carried out with brightness or lifetime sorting operating at 2.5 kHz withan average 4 cells/droplet encapsulation. In the first example, we assume that the fraction of therare events is 1 ppm. It would take less than 3 hours to enrich rare events from a 108 population,
resulting in a subset of 100 fluorescent cells mixed with 203 unwanted cells (𝑝𝐹 =0.33), i.e.
3.3x105-fold enrichment (𝑝𝐹 /F) in one round of sorting. The enriched subset can be further
cultured, analyzed, or sorted with single cell resolution to isolate the final, purified population. In
the second example, we consider a cell-based library containing 33x106 distinct mutants. To ensure
the enrichment covers 95% of this library, at least 3 times of the library size must be screened,[175] which is ~108 cells. Assuming the desired clones comprise 1% of the original library, thisenrichment reduces the library size from 33x106 down to 1x106 within 3 hours with 0.33x106
fluorescent cells, thus a 33-fold enrichment. The enriched library can be further analyzed or sorted
at 𝜆=0.1 (single-cell resolution) using brightness or lifetime sorting. Using the conventional
encapsulation strategy (𝜆=0.1) without the enrichment, it would take ~117 hours to complete theselection in both examples with brightness or lifetime sorting at the speed of 2.5 kHz developed in45this work. It would take 50 times longer (~5848 hours) for a recently reported lifetime droplet
sorting to perform the selection. [164] Using a state-of-the-art droplet sorting at 30 kHz, [163] theselection would require ~10 hours, which is more than 3 times longer than the lifetime enrichment
demonstrated here, to complete a brightness-only selection in single cell resolution without
fluorescence lifetime information. The combination of this new sorting technology and enrichment
strategy enables fast multiparameter analysis and selection of rare events from a 10 8 -member
population based on fluorescence lifetime, brightness, and spectrum, as a preparation for further
investigation and sorting with single cell resolution on a single instrument.
To demonstrate the effectiveness of this strategy, we enriched mScarlet from a mixture of EGFPand mScarlet transformed in E. coli using dual color brightness sorting. Since EGFP does not emit
red fluorescence, EGFP can be regarded as the non-fluorescent population and mScarlet as the rare
fluorescent population observed in the red channel. The number of EGFP cells can be counted in
the green channel since only EGFP contributes to the green emission. Thus, the fraction ofmScarlet (i.e. the fluorescent events in the red channel) in the mixture was determined to be
F~0.01. After one round of enrichment with 𝜆=3 encapsulation, the sorted cells were subsequently
grown and screened with 𝜆≤0.1 encapsulation. The mScarlet population was enriched to an
average 35±4%, which agrees with the expected value (𝑝𝐹 x0.86) ~37%, considering the 86%
efficiency of single cell two-color sorting described earlier. Detailed experimental protocols canbe found in Appendix 1: Section 6.
The enrichment strategy can also be applied in lifetime sorting when the rare events have a distinct
fluorescence lifetime from the major population, despite the overlap in emission spectra andbrightness. We demonstrate the enrichment of rare cells expressed with mScarlet from a mixtureof mCherry and mScarlet, which have large overlap in both emission spectra and cellularbrightness. The first test was carried out the same day using the same batch of sample generating
results in Figure 2.4. The fraction of mScarlet in the mixture before enrichment was estimated tobe F~5x10-3. The enrichment was performed with 𝜆=3 at 2.5 kHz, and the sorted cells were
subsequently grown, expressed, and screened with 𝜆≤0.1. We attained an enrichment of themScarlet population to 40% (Figure 2.6), which is consistent with the expected value, including
the 85% efficiency of single cell lifetime sorting demonstrated in Figure 2.4, (𝑝𝐹 x0.85) ~37%.
Another enrichment for rare mScarlet was performed using the second batch of sample with
F~5x10-3, resulting in an average enrichment of the mScarlet population 30±5%, in agreement46

with the expectation (𝑝𝐹 x0.80) ~35%. Details of experimental protocols for this assay aredescribed in Appendix 1: Section 6.

Figure 2.6. Fluorescence lifetime versus brightness scatter plots of rare mScarlet enrichment.
Solid boxes illustrate thresholds for counting cells expressing mScarlet. N is the number of cells
expressing each RFP. (Left) Mixture of E. coli cells expressing mCherry and mScarlet before
enrichment. The dashed box indicates the two-parameter sorting gates. (Right) Screening results
after enriched cells were grown overnight and expressed for 16 hours.

2.4d. Enrichment of an RFP library
The directed evolution of FPs often involves the screening of cell libraries with rare bright clones.
Library size increases exponentially with the number of target residues, and FP libraries are
typically found to have a narrow fitness landscape, [124] i.e. the fraction of fluorescent clones
dramatically decreases as the mutational space increases due to protein mis-folding, incomplete
chromophore maturation, and other photophysical factors. We used this sorter to enrich the
population of fluorescent RFP mutants and select the brightest ones for further development.
Taking mScarlet-I as the template, we constructed a site-directed library with the size ~1.7x107,
which requires screening >5.1x107 cells to cover 95% of the library size. In our previous studies
of site-directed and/or error-prone PCR libraries of red FPs (RFPs), some non-fluorescent colonies
were observed to grow larger than fluorescent ones on plates, likely due to variations incytotoxicity of various mutations in RFPs. [174] Therefore, we expect reduced sorting efficiency
47

due to the re-growth and expression processes after enrichment as described above. With thisconsideration in mind, we decided to load the droplets with 𝜆=3, and a total number of ~8x107 E.
coli cells expressing this RFP library was screened in two batches (ensuring the health of cells) toenrich fluorescent cells at ~2 kHz. The proportion of fluorescent cells was enriched from initially~5% to ~30%. This is lower than the expected, empirically corrected enrichment efficiency(43%x0.86) 37% for 𝜆=3. The enriched population underwent 3 more rounds of enrichments withhigher thresholds in fluorescent brightness with 𝜆=1 or 𝜆=0.1 at 2 kHz, resulting in >95%
fluorescent population. The final round of sorted cells was re-grown overnight then expressed onagar plates. Three distinct mutants were identified from the agar plates for further development.
More information on the library and the detailed enrichment procedure are provided in Appendix
1: Section 7.
This platform is sufficiently flexible to support further enhancements. For example, additional
excitation wavelengths with RF modulation can be implemented to expand the information content
in both spectral and fluorescence lifetime dimensions. Furthermore, it is possible to increase thesorting speed further by modifying the microfluidic chip design. In particular, brightness sortingat 30 kHz has been demonstrated in a design where the hard divider is replaced with a gapped
divider to separate outlets. [163] In addition, increasing the modulation frequency of the excitation
beam shortens the phase acquisition time, and therefore increases the fluorescence lifetime
detection speed. As such, a modulation frequency of 100 MHz could support a ~3.4-fold increasein sorting speed. However, the modulation frequency may set the limit for the throughput offluorescence lifetime measurement. When the modulation frequency increases to higher than 100
MHz, the period of the modulation wave becomes less than 10 ns, the same order of magnitude as
the fluorescence lifetime of commonly used fluorophores. This may disturb the phasemeasurement under a strong excitation rate used in frequency domain measurement. On the other
hand, to further increase the sorting speed to ≥10 kHz, the adjoining scattering or fluorescencesignals are ≤100 µs apart. In current setup, the FWHM of the scattering and fluorescence signals
is approximately 25 µs at 2 kHz, which is sufficiently small for sorting at 10 kHz. If needed,
decreasing the droplet size can not only reduce the noise as previously discussed, but also shorten
the transient time of the droplet and cells since they only pass the Rayleigh length region, resulting
in narrower FWHM of the scattering and fluorescence signals. Thus, it is feasible to improve thethroughput of this multiparameter droplet sorter to ≥10 kHz.
48

2.5. Conclusion
We developed a multiparameter microfluidic droplet sorter combining the detection offluorescence lifetime, brightness, and spectra. The throughput of the fluorescence lifetime
measurement and sorting, up to 4 kHz for screening and 2.5 kHz for sorting with current chip
design, is greatly enhanced by using a FPGA for the communication among all electronics andsorting decisions. This is the fastest fluorescence lifetime droplet screening and sorting speed todate. The high-throughput fluorescence lifetime droplet sorting opens the opportunity ofintegrating fluorescence lifetime detection with other high throughput detection methods in a
microfluidic droplet platform to increase the information content of biological and biomedical
assays with single cell resolution. We have also proposed a novel multiple-cell encapsulation
strategy enriching the rare events to overcome the obstacle of droplet sorting throughput limitedby the nature of Poisson distribution for random cell/molecule encapsulation – by taking theadvantage of Poisson statistics. The effect of enrichment increases tremendously as the fraction ofrare events decreases. The efficiency and precision of enrichment can be quantitatively controlled
if the rare event frequency is estimated before sorting. The enrichment strategy has been
demonstrated to be effective in both brightness and lifetime sorting. Combining the enrichment
strategy and the multiparameter microfluidic platform allows one to analyze and enrich rare eventsfrom a population >108 within a few hours. Though the enrichment does not provide single
cell/analyte resolution, it greatly reduces the time required to search for rare events, thus is anefficient way to analyze or prepare rare events for further investigation or selection with single
cell/analyte resolution. It is also feasible to improve the throughput of the multiparameter sortingto ≥10 kHz. Together with the new sorting strategy, the speed of droplet-encapsulated rare events
analysis and enrichment can potentially exceed FACS, achieving an unprecedented throughput for
microfluidics-based cell sorting.

49

Chapter 3
Engineering a brighter version of FusionRed using lifetime
flow cytometry and structure guided mutations
3.1. Publication Note
Parts of this chapter have been adapted from the article “Engineering of a Brighter Variant of the
FusionRed Fluorescent Protein Using Lifetime Flow Cytometry and Structure-Guided
Mutations.” Mukherjee, S.; Hung, S. T.; Douglas, N.; Manna, P.; Thomas, C.; Ekrem, A.;
Palmer, A. E.; Jimenez, R. Biochemistry 2020, 59 (39), 3669–3682.
https://doi.org/10.1021/acs.biochem.0c00484.

3.2. Introduction
The availability of genetically-encoded fluorophores such as fluorescent proteins (FPs) initiated a
revolution in biological imaging. [2] Routine use of FPs in assays involving technologies such as
Förster resonance energy transfer (FRET), [176] fluorescence lifetime imaging microscopy(FLIM), [177, 178] molecular sensing, [179] and nanoscopy, [180] make them indispensable tools
for biological research. Current efforts focus on developing FPs with excitation and emission in
the far-red/near-infrared wavelengths and with photophysical properties such as photoswitching
and fluorescence intermittency optimized for super-resolution imaging modalities. [23, 24, 181,
182] Nevertheless, all imaging applications benefit from increased cellular brightness, which isstrongly dependent on molecular brightness (defined as the product of the molar extinction
coefficient and the fluorescence quantum yield). [57, 101] Lifetime-based selection methods have
exploited a correlation between fluorescence lifetime and quantum yield to develop FPs withhigher quantum yield such as NowGFP, [183] mTurquoise2, [77] and mScarlet, [35] which is thebrightest red FP observed to date.
FPs selected for higher fluorescence lifetime generally show a decreased rate constant of nonradiative decay (knon-rad), ultimately resulting in increased quantum yield and higher brightness.
However, quantum yield is also linearly related with krad, therefore there is an interplay between
50

the absorption probability and radiative emission probability. The Strickler–Berg equation
formalizes the relationship between the krad and extinction coefficient, as well as other spectral
properties such as the energies and profiles of the absorption and emission bands. [60] For
example, blue shifts and decreased spectral width can lead to higher probabilities of radiative
decay. [184] The relationship between spectral characteristics and the rate constants of population
decay have recently been discussed for FPs. [59, 66] An engineering strategy that maximizes theradiative rate constant while simultaneously minimizing the non-radiative rate constant should bean effective way to brighten a FP.
These issues are particularly acute for red FPs (RFPs), which generally have lower values offluorescence lifetime and quantum yield compared to shorter wavelength variants, and are
therefore not as bright. [185] The RFP chromophores contain an acylimine moiety, which expands
their electronic conjugation and leads to a ~50 nm red shift in their absorption and emission spectrawith respect to green analogues like EGFP. [53, 186] Many potential non-radiative decay
mechanisms that lead to lower quantum efficiencies in such systems have been investigated,
including transitions to dark states; [13, 187] charge accumulation and twisting of the acylimine
moiety; [92] changes in hydrogen bonding patterns; and electrostatic, steric and conformational
effects associated with their increased number of vibrational degrees of freedom. [14, 74]
Cellular brightness depends on both photophysical and non-photophysical factors such astranslational efficiency, protein folding and chromophore maturation. [29] FPs like FusionRed-M(FR-M) and mScarlet-I were developed to enhance cellular brightness over their brighter parents
FR-1 and mScarlet, respectively. [30] Although there have been many efforts to improve thecellular and molecular brightness of FPs, performance in cell biology applications may still sufferfrom cellular toxicity, poor or over expression in certain cellular contexts and in cellulo
oligomerization. [29, 101] As discussed below, in the course of evaluating the performance ofbright and commonly used RFPs, we found a trade-off between cellular brightness and localization
fidelity of the GalT fusions of mScarlet, which led us to question whether the high cellularbrightness associated with very high expression level leads to appearance of mis-localized FPs.
FusionRed (FR) was developed as a non-cytotoxic RFP that shows efficient and correct
localization in multiple fusion constructs in different organisms. [188] However, this FP has notbeen widely adopted because it is relatively dim, in part due to its low quantum yield (0.19). We
51

recently developed the FR-M variant (FR-L177M, numbered with respect to mCherry and FRL175M numbered with respect to FR; See Appendix Table A2.1), which is 1.9-fold brighter than
FR in HeLa cells. [30] In this study, we used structure-guided engineering strategies to identify
substitutions M42Q and C159V (sequence numbering with respect to FR) in the vicinity of thechromophore that individually increase the fluorescence lifetime of FR. These mutations led to thedevelopment of the bright triple mutant FR-MQV. We performed detailed in vitro photophysicalanalysis which corroborated the increase in the molecular brightness in FR-MQV based onminimizing knon-rad and increasing the krad. Additionally, we investigated the cellular properties of
FR-MQV and found it is 5-fold brighter in HeLa cells (using FACS) compared to the parent FR,
while preserving its cellular properties such as low cytotoxicity and high-fidelity localization.

3.3. Experimental
3.3a. Mutagenesis, cloning and construct development
i. Yeast Constructs
The QuickChange site-directed mutagenesis method was used for making point mutations using
PfuTurboDNA polymerase and a thermocycler. Libraries with multiple site-directed targets werecreated using a splicing overlap extension reaction. Primers were designed to introduce the desired
mutations and the initial PCRs generate overlapping gene segments that are used as template DNA
for another PCR to create a full-length product. Fresh competent yeast cells (Saccharomyces
cerevisiae BY4741) were prepared prior to electroporation. Cells, DNA and cut pYestDest52
vector were combined and left on ice for 5 min. Electroporation conditions (Bio-Rad Gene Pulser
Xcell) were as follows: C = 25 μF, PC = 200 Ohm, V = 1.5 kV (in 0.2 cm cuvettes). Cells werepassed twice prior to expression. Mutants were transferred to the pBad-His vector for
expression/Ni-NTA protein purification.

ii. Bacterial Expression Constructs
For bacterial expression, FR-Q and FR-MQ were made using the Q5 Site-Directed Mutagenesis
Kit (New England Biolabs) with pBad-FR and pBad-FR-M, respectively, as the templates and the52primers tCGCCACACAGGACACAAG and cCACATATGTCTCATCGTCAGC. FR-MV wasdesigned with similar protocols by inserting the C159V substitution into FR-M, with appropriate
primers. FR-MQ C159V was also made via Q5 mutagenesis with the above primers and FR-M
C159V as the template. The M42Q mutation was also made in pBad-mKate via Q5 mutagenesis
and the corresponding A44Q mutation was made in pBad-mScarlet and pBad-mCherry using
overlap extension PCR.

iii. Mammalian Expression Constructs for FACS
FR-MQ and FR-MQV were expressed as histone H2B fusion proteins in HeLa cells. Specifically,
the FR-MQ and FR-MQV mutants were PCR amplified from the pBad constructs with the
upstream primer GGTATGGCTAGCATGACTGGTG and a reverse primer that introduces a NotI
site adjacent to the stop codon (acatGCGGCCGCTCATTTCCCTCCATC). Similarly, mScarlet-I(mScarlet T74I) was PCR amplified from a Q5-generated pBad construct (primers
AGGGCCTTCATCAAGCACCCC and GCAGCCGTAC-ATGAACTGAGG) with the same
upstream primer and a reverse primer that introduces an XcmI site adjacent to the stop codon. The
FR-MQ and FR-MQV products were cut with BamHI and NotI and ligated into BamHI/NotI cut
piggyBac-H2B and the mScarlet-I product was cut with BamHI and XcmI and ligated into
BamHI/XcmI cut piggyBac-H2B.

iv. Mammalian Expression Constructs for OSER
To assess protein aggregation in mammalian cells, the mutants were expressed as fusions with
CytERM in U2OS cells. FPs were amplified from the pBad construct with an upstream primer that
introduces an AgeI site upstream of the start codon (gcatACCGGTCGCCACCATGGTGTCCGAGCTGATTAAGG) and the reverse primer described above that introduces a NotI site. The
AgeI/NotI cut PCR product was ligated into AgeI/NotI cut CytERM vector and transfected into
U2OS cells as described above for HeLa cells.

53

v. Mammalian Expression Constructs for GalT-FP fusions
To localize our mutants to the Golgi, they were expressed as GalT fusions in U2OS cells. The
BamHI/NotI cut FR, FR-M and FR-MQV PCR products described above were ligated into
BamHI/NotI cut GalT vector. mScarlet-I was cut from pBad with BamHI and SalI and ligated into
BamHI/SalI cut GalT-mScarlet.

3.3b. Microfluidic based selection from site directed libraries
i. Library Targets
We targeted the positions 159, 161, 196 and 198 in FR (using FR numbering; Appendix 2: Section2), expressed the libraries in yeast (Sacchromyces cerevisiae) and screened this library on alifetime flow cytometer. [30] Screening revealed the presence of brighter clones with longer andshorter lifetime than parent FR (lifetime ~ 2.05 ns). We performed another two rounds of FACS
enrichment on a BD FACSAria Fusion Cell Sorter to remove the dim/non-fluorescent clones.
Position 159 was mutated to I, L, V, F, M, C, A, G, T, S, W and R; position 161 was mutated to I,
L, M, Q, N, H and K; position 196 was mutated to I, V, A and T; and position 198 was mutated to
all possible amino acids. The library size was ~ 7,000 clones.

ii. Post-Microfluidic Sorting
After selection, the collected yeast cells were grown in liquid culture and then plated, and 25 clones
with unique lifetimes were picked from these sorter-enriched libraries using a lifetime assisted
plate-based screen discussed in a previous work. [30] The FR site-directed (FSD) clones withunique DNA sequences were further characterized (Appendix Table A2.2).

543.3c. Cell growth, transformation/transfection and protein purification
protocolsi. Bacterial Transformation and Growth
Bacteria (competent E. coli, Top10 strain) were transformed with the DNA encoding a FP ofinterest in the pBad-His vector. Roughly 2–5 µL of DNA (~80 ng/mL concentrations) were slowly
pipetted into ~50 µL of competent cells (Invitrogen). The cells were left on ice for 20 minutes,
heat shocked for 45 seconds at 42ºC and then grown in antibiotic -free medium for 45 minutes.
The cells were then plated (~25–50 µL) onto ampicillin-containing LB agar plates and grown at
37ºC overnight. Colored colonies were picked from these plates and grown in 2XYT medium
containing ampicillin overnight at 37ºC and 230 RPM. The next morning, 1 mL of this culture wasadded to 100 mL of fresh 2XYT with ampicillin, grown for 3 hours at 37ºC to achieve an OD of~0.6, and then 1 mL of 20% arabinose was added to the culture to initiate expression. The
temperature of incubation was lowered to 28ºC to slow down bacterial growth and help protein
folding and chromophore maturation. Depending on the maturation rate of the FP, they were grownat this temperature for 20–30 hours.

ii. Bacterial Cell Lysis and Protein Purification
The induced cell cultures were spun down at 8,000 RPM for 20 minutes at 4ºC and the cell pellet
frozen at −30ºC to ease lysis. B-PER Bacterial Protein Extraction Reagent (ThermoFisher) wasused to lyse the cells in the presence of protease inhibitor. The cells were lysed for 1 hour at room
temperature and then spun down at 11,000 RPM and 4ºC for 15 and then 20 minutes to remove
the cellular debris. The supernatant containing the 6x-His-tagged protein was filtered with a 0.45
µm polyethersulfone membrane syringe filter and incubated with Ni-NTA agarose for 1 hour on
ice. The resin was then loaded into a column, washed with 10- and 20-mM imidazole and then theproteins eluted with 250 mM imidazole. The imidazole was removed using PD-10 desalting
columns (GE HealthCare) or 24 hours of dialysis using SnakeSkin dialysis tubing (ThermoFisher)
into Tris-HCL buffer (pH 7.4) or saline PBS buffer. These samples were used for in vitro
photophysical analyses.

55

iii. Mammalian cell Growth and Transfection
HeLa/U2OS cells were cultured in RPMI medium (Gibco Life Technologies) supplemented withpenicillin/streptomycin (Gibco Life Technologies) and 10% heat-inactivated fetal bovine serum(Sigma-Aldrich) at 37°C with 5% CO2 plus humidity. For imaging experiments, U2OS cells weregrown in 35 mm imaging dishes (made in-house from Corning 35 x 10 mm dishes with VWR 18
x 18 mm #1.5 cover slips). All CyTERM constructs were transiently transfected for 18–24 hours
using Lipofectamine 3000 (Invitrogen) or TransIT-LT1 transfection reagent (Mirus) according to
the manufacturer's instructions. For FACS experiments, we used HeLa cells transiently transfectedusing the TransIT-LT1 reagent (Mirus, catalog #MIR2304) and prepared for FACS analysis after
48 hours.

3.3d. in vitro photophysical measurements
i. Instrumentation
Absorption spectra were collected on a Cary5000 UV-Vis Near IR Spectrophotometer using adouble beam mode with matched cuvettes and blank subtraction. Samples were diluted using 1X-Tris-HCl Buffer (pH ~7.4) and absorbance was measured at optical densities (ODs) between 0.05
and 0.25 to maintain measurements in the linear range of the Beer–Lambert’s law. Fluorescencemeasurements were performed with a HORIBA Jobin Yvon Fluorolog-3 FL3-222.

ii. Extinction Coefficient Measurements
Alkali denaturation was used to estimate the ratiometric values of maximum extinction coefficient(ECmax) for the samples. An average of three or more independent measurements was performed
for FPs and is reported with a standard deviation error. FPs with fewer measurements are reported
without an error bar. To measure the ECmax, the following protocol was used: (a) Blank1: 900 µL
Tris-HCl buffer (pH 7.4) spectrum was recorded.; (b) Blank2: 900 µL Tris-HCl buffer (pH 7.4)+100 µL 10 M NaOH (pH~14); (c) 900 µL Tris-HCl buffer (pH 7.4) + a few µL of concentrated
pure protein sample was added to adjust the absorbance to a value of OD ~0.1. A spectrum from
300–700 nm was recorded.; (d) 100 µL of 10 M NaOH was added to this solution and a spectrum
56

in the same range was recorded immediately. Kinetic effects start playing a role on delaying thespectral measurement as degradation product peaks are known to drift in amplitude andwavelength over time.

iii. Calculation of ECmax
We performed titration-based ECmax calculations for FR-M, FR-MQV and mScarlet-I. The
numbers obtained compare well to the values measured by the one-step alkali denaturing method.
[101] The values were based on the mathematical relationship stated below, as FPs of the FR
family are known to exhibit backbone cleavage. [188] To verify if this method was valid for FRMQV we also performed SDS-PAGE (Appendix Figure A2.1), where purified proteins (~10 µg)
were run on TruPAGE precast 4–20% gradient acrylamide gels (Sigma-Aldrich) in TEA–Tricine
running buffer with the Spectra Multicolor Broad Range protein ladder (ThermoFisher). For otherFPs that do not exhibit backbone cleavage, like mScarlet, the absorption at 380 nm wasdisregarded.
ϵ𝑚𝑎𝑥RFP =Absmax RFP
Abs380 nm
Abs450 nm()+()
ϵ380 nmϵ450 nmiv. Quantum Yield Measurements
Freshly prepared or flash frozen purified protein was diluted with Tris-HCl buffer (pH 7.4) in a 1
cm path length Quartz cuvette to an OD of ~0.1. A matched cuvette was used for baseline
correction to measure absorption spectra. The same cuvette with the solution in it was transferredto the fluorimeter for collecting fluorescence spectra. After each absorption and emission scan,
200–250 µL of the sample was removed and replaced with fresh buffer to create a step dilution.
This step dilution was repeated 4–5 times for each sample. RFPs were excited at 520 nm such thatthe entire emission spectrum was recorded for each FP (even for blue-shifted RFPs) with highenough absorption. For each FP, integrated fluorescence was calculated for the area under the RFP
emission feature on the emission spectra and was plotted against the corresponding OD at 520 nm
from the absorption spectrum. The integrated fluorescence versus OD plot can be fitted with a57

straight line (Appendix 2: Figure A2.2) of the form: y = 𝑠𝑙𝑜𝑝𝑒 × 𝑥, where 𝑦 is the integrated
fluorescence and 𝑥 is the OD.
𝑠𝑎𝑚𝑝𝑙𝑒 =2
𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 × 𝑚𝑠𝑎𝑚𝑝𝑙𝑒 × 𝜂𝑆𝑎𝑚𝑝𝑙𝑒
2
𝑚𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 × 𝜂𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒

Where the m is the slope from a linear fit and refractive index of the sample and the reference are𝑛𝑠𝑎𝑚𝑝𝑙𝑒 and 𝑛𝑟𝑒𝑓, respectively. mCherry (= 0.22 in Tris-HCl, pH 7.4), Cresyl Violet (quantum
yield = 0.54 in EtOH) and mScarlet (= 0.72 with respect to mCherry) were used as references.
[35, 101]

v. pKa Measurements
pKa measurements were performed by preparing buffers in the range of pH 2 to 12. The pH was
measured for each buffer to confirm the calculated pH values using a pH meter. Fixed amounts ofconcentrated pure protein samples were added to 1 mL buffer in a quartz cuvette with a 1 cm path
length and a fluorescence spectrum was recorded in each case with excitation at 520 nm. The
maximum value of fluorescence counts was used to normalize the fluorescence spectra for eachprotein. The data were plotted and was fit to the sigmoidal curve shown in Appendix Figure A2.3.
The calculated pKa values and reported values for published RFPs have been provided inAppendix 2: Table A2.4. Buffers in the pH range 2–3 were prepared with a dilution of glycine and1 M HCl; in the range 3–6 were prepared using dilutions of 0.1 M citric acid and 0.1 M Na-citrate;in the range 6–8 were prepared with dilutions of 0.2 M Na2HPO4 and 0.2 M KH2PO4; in the range
of 9–12 were prepared with dilutions of 0.2 M glycine and 1 M NaOH and Tris-HCl buffer wasused for the pH 7.4 measurement.

58

vi. Fluorescence Lifetime Measurements in the Lifetime Flow Cytometer
The lifetime flow cytometer utilizes frequency-domain phase fluorimetry to select analytes basedon excited state lifetime. The details of this set-up are discussed in references 30 and 41. [30, 41]
The excitation beam is sinusoidally modulated at 29.5 MHz. The observed fluorescence signal ismodulated at the same frequency as the excitation beam, but its lower modulation depth and aphase shift (𝜑) that corresponds to the average time spent by the analyte in the excited state(average lifetime). A high-speed lock-in amplifier determines the phase shift, which is thenconverted to a lifetime value in the time domain.
𝜏𝐴𝑛𝑎𝑙𝑦𝑡𝑒 𝑖𝑛 𝑠𝑜𝑟𝑡𝑒𝑟 = 𝜏𝑅𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (𝑛𝑠) +tan(𝜑𝐿𝑜𝑐𝑘−𝐼𝑛 𝐴𝑚𝑝 )29.5 MHzFor the reference, mCherry (~1.6 ns) was used. FR had a mean lifetime 2.05 ± 0.15 ns on thisdevice.

vii. Steady-State Lifetime Measurements for Pure Proteins and Lysate
All lifetime measurements on purified proteins or filtered cell lysates were performed on acommercial TCSPC system (Fluoro-time 100, PicoQuant) using a 560 nm pulsed laser diode headexcitation source with a repetition rate of 5 MHz. Emission was collected either using a red filterset (600 ± 30 nm) or a far-red filter set (670 ± 30 nm), to check for multiple species in the excitedstate or interconverting forms. The instrument response function (IRF) was collected using Ludox(Millipore Sigma) colloidal silica, whereas the samples were diluted to an OD value <0.05 for themeasurement. A minimum of 20,000 photon counts were used to generate the fluorescence decays.
The fluorescence transient decays were fit to an iterative re-convolution with a bi-exponentialfunction (or-tri exponential depending on the protein). The amplitudes and the components of thefits are provided in Appendix Table A2.5.

59

viii. Photobleaching Measurements
Photobleaching measurements were performed using an LED excitation source (Lumencor) on an
Olympus IX-73 fluorescence microscope with E. coli cells expressing the FP of interest. Bacteria
on plates were washed and dispersed in aqueous blank buffer containing 0.17% (w/v) yeast
nitrogen base (Sigma-Aldrich) and 0.5% (w/v) ammonium sulfate (Sigma-Aldrich) thenphotobleached with excitation rate-normalized LED light. To bleach the sample, a 560 nm LED
was used, whereas for repopulation with blue light, a 438 nm LED light source was used. Detailsof the measurements are discussed in Appendix Figure A2.4.

ix. Brightness in E. coli
To assess the cellular performance of the FR clones in this study, we performed a bacterial
brightness assay at the single cell level on a droplet microfluidic sorting platform. [41] Twobiological replicates with three independent technical triplicates were performed for eachmeasurement. The bacteria were grown, and expression was induced as previously described,
cytometry was carried out at ~20–22 hours after starting induction. Each technical replicate
involved 10,000 cells. Details of the screening protocol have been discussed in Appendix Figure
A2.5 and a reference 41. [41]3.3e. Cellular brightness assays
Brightness in HeLa Cells
Flow Cytometry: The proteins of interest in the FR family, along with some standard RFPs
including mScarlet, mScarlet-I and mCherry, were fused to histone H2B and expressed in HeLa
cells. Single-cell brightness was assessed by selecting single healthy cells based on forward andside-scattering photon counts on a BD FACSCelesta single cell analyzer after 48 hours oftransfection. Untransfected cells were used as a control to background subtract and analyze thefluorescence in the red and green channels for the proteins of interest. In most cases (except
mScarlet-I with only one biological replicate) three or more biological replicates with threetechnical replicates of each were analyzed to determine the mean fluorescence with standard
60

deviation based on the number of measurements (Appendix Table A2.7). The samples were excitedby a 561 nm laser line for collecting red fluorescence through the TRITC filter set (585/30 nm)
and a 488 nm laser line for collecting through a GFP filter set (530/30 nm). The residual
fluorescence from the green channel was effectively at the background level of the EGFP-H2B
control (displaying signal values ~20-fold higher than mScarlet with the highest green
fluorescence in the series). Brighter red mutants had higher green fluorescence background,suggesting red fluorescence bleeding through the green channel.

Confocal Microscopy: HeLa cells grown in 35 mm imaging dishes (made in-house from Corning
35 x 10 mm dishes with VWR 18 x 18 mm #1.5 cover slips) were imaged 48 hours post transfection
to maintain consistency with the FACS measurements. Before imaging, cells were washed threetimes with 2 mL phosphate-free HEPES-buffered Hanks’ balanced salt solution (HHBSS)
containing 20 mM HEPES (Sigma), pH 7.4 and resuspended in 1.5 mL of the same buffer. Imaging
was performed on a Nikon Ti-E spinning disc confocal microscope system. The imaging dishes
were mounted on the microscope in an environmentally controlled chamber (Oko Labs; set to
37ºC, 5% CO2, 90% humidity) and viewed with a 40x (NA 0.95) air objective. A 560 nm laser
was used for illumination and a 590–650 nm band pass filter (TRITC) was used for the detectionof fluorescence with 200 ms exposure time and 20% laser power of the instrument. To minimize
photobleaching, the focus of the microscope was adjusted to a lower laser power (5%) at only thecenter spot of the large image. Prolonged exposure of FR and its mutants to laser light can lead tolower brightness, which was a critical factor for this assay. Large images (~1600 x 1000 𝜇𝑚) weretaken for each dish for each replicate. Details for this assay are presented in Figure 2.4b andAppendix Table A2.8. The imaged cells were analyzed using the suite CellProfiler. [189] A
pipeline was created that would identify objects that are above the noise background. A binarized
image was thus created, then a gate to filter objects typical of the size of nuclei was selected (2–25 𝜇𝑚), which selected the fluorescing nuclei in the H2B construct. The filtered objects in theparent cells were then quantified for mean brightness. Untransfected cells with cellular autofluorescence were the first to be analyzed, which gave us the estimation of bleed-throughfluorescence.

61

3.3f. Cellular localization assays
i. Imaging Conditions
U2OS cells were transfected with the constructs of interest as described previously. The cells wereimaged 24 hours post transfection with a Nikon Ti-E spinning disc confocal microscope. Several
large images (~1,680 × 1,000 𝜇𝑚) were captured while scanning the z-focus (z-stacks) for
optimum focusing of all the cells appearing in the field of view. Typical scanned depth was 5.0–
7.8 𝜇𝑚 and was evenly separated into 5–7 layers. Maximum intensity projection of the z-stacks
was used for the quantification of OSER score. For GalT scoring, Z-stacks and independent frames
were used for quantification of localization of FPs to the Golgi.

ii. Data Analysis
The data analysis for the quantification of OSER scores was done in accordance with our previous
report. [30] In brief, the suite CellProfiler was used to develop a pipeline that can identify cells
based on size (20–50 𝜇m), shape and fluorescence intensity. The program identifies
oligomerization sub-structures in these cells, filters them and then quantifies them as whorls. The
pipeline further continues to relate the number of whorl structures with each cell and a MATLAB
code quantifies the number of perfect and imperfect (cells with whorls). A score of 100 indicates
100% of the cells are whorl free and 0% indicates all cells have whorls in them. FR and its mutants
display a high OSER score, whereas TagRFP-T, was used as a negative control. The imaging data
for the GalT-FP construct was analyzed using a blinding approach where multiple individuals were
provided with image sets that were randomized. Individual images were scored as having
fluorescence signal localized to the Golgi (characterized by a fist-like structure near the nucleus)
or not. The approximate size of a healthy nucleus was estimated using ImageJ. [190] If the cells
expressed FP outside this fist like structure in the form of puncta or just smeared across thecytoplasm, they were considered mis-localized.

623.3.g. Chromophore maturation kinetics and cytotoxicity
i. Cytotoxicity Assay
HeLa cells were transfected with the H2B-FP fusion constructs as discussed previously. Twobiological replicates were prepared for each FP. Day 2 was defined as 48 hours post transfection.
RFP and EGFP transfected cells were mixed at a 50:50 ratio by volume. A sample of the cell
mixture was prepared for a flow cytometry measurement (BD FACSCelesta) to determine theactual RFP:EGFP ratio. The rest of the mixture was re-plated for further growth and proliferation.
Independent screens of just EGFP cells and RFP cells were carried out first. Cells with green
fluorescence higher than background were classified as “EGFP” and cells with red fluorescencehigher than background were classified as “RFP”. On Day 6, the re-plated cells were again
subjected to flow cytometry to quantify the change in the RFP and EGFP populations anddetermine a relative level of cytotoxicity. The cytotoxicity score was then calculated as the change
in the RFP:GFP ratio for each sample. EGFP was used for normalization because it has been shown
to be minimally cytotoxic. [191] The data for the assay is presented in Appendix Table A2.9.

ii. Maturation Kinetics
Bacteria (Top 10, E. coli) expressing FPs were grown in expression media for 4 hours (28ºC, 230
RPM) to facilitate FP production in the exponential growth log phase. Chloramphenicol (250µg/mL) was added to the cultures to stall bacterial growth and protein production. [192] The
cultures were maintained at 37ºC and 230 RPM and aliquots were taken every 30-60 minutes tomeasure the Optical Density (OD) and fluorescence. The t1/2 at 37ºC was calculated by calculating
the time required for the FP to reach half the maximum fluorescence value. The data for the assay
is presented in Appendix Table A2.10.

63

3.4. Results
3.4a. Lifetime-based selection of a site-directed library near the parahydroxyphenyl moiety of the chromophore identifies the C159V mutation.
Four positions near the para-hydroxyphenyl moiety of the chromophore—C159, M161, V196 andH198—were simultaneously mutated in FR to generate a ~7,000-member library. We employed
lifetime-based microfluidic flow cytometry to select variants with increased brightness and valuesof fluorescence lifetime different from the parent (Figure 3.1). [30] Sequencing of selected clones
revealed that H198 and V196 were conserved but positions 159 and 161 showed sequence diversity(Appendix Table A2.2). Furthermore, the selected population contained two clones, FR-C159V
and FR-C159L, with higher cellular brightness than the parent FR, but with differing lifetimes.
FR-C159V had an increased lifetime of 2.0 ns, whereas FR-C159L had a decreased lifetime of 1.2
ns (c.f. 1.8 ns lifetime for FR: Details in Appendix Section 2). Of the two clones, FR-C159V wasselected for further development in combination with the mutations identified below because it
had the longer lifetime and because it did not show the complex photoactivation behavior seen in
FR-C159L (Appendix Figure A2.4)

Figure 3.1. Lifetime screens for the site directed libraries of FusionRed. The fluorescence
lifetime (vertical axis) vs. brightness (horizontal axis) screening dot-plots of the FR site-directed
library targeting sites near the para-hydroxyphenyl moiety, after two rounds of fluorescence64

activated cell sorting (FACS) enrichments. Pseudocoloring represents normalized cell counts,
where yellow indicates higher cell count and blue indicates a lower cell count. Red boxes indicate
the selection gates for multi-parameter microfluidic sorts. (a.) The first round of sorting for
selecting bright clones. (b.) The second round of sorting was performed in two batches using
sorting gates for high brightness with different lifetime ranges. The mean fluorescence lifetime of
FR measured on this instrument was 2.05 ns.

3.4b. The M42Q mutation adjacent to the acylimine moiety of FR increases theextinction coefficient, quantum yield and fluorescence lifetime.
Mutations that alter the hydrogen-bonding structure surrounding and interacting with the acylimine
moiety of the chromophore produce RFPs with extended Stokes shifts. [79, 91, 95] In addition to
the site-directed library aimed at mutating the end of the chromophore near the parahydroxyphenyl moiety, we investigated the end of the chromophore near the acylimine moiety inthe crystal structures of mKate (PDB ID: 3BXB), the far-red emitting FP TagRFP-675 (PDB ID:
4KGE) and FR (PDB ID: 6U1A) using PyMol (Figure 3.2 and Appendix Figure A2.13). [193]Based on the structural similarity, conformational freedom and the fact that the sidechain at
position 42 is a known hot-spot for altering the hydrogen-bonded chemistry in mKate and TagRFP675, we incorporated a single point mutation M42Q into FR. [79, 91] The FR-M42Q (or FR-Q)
mutant shows a 41% increase in the maximum extinction coefficient, an 18% increase influorescence lifetime and a 42% increase in quantum yield (Table 3.1 and Figure 3.3). The
mutation also resulted in blue-shifted and narrower absorption and emission spectra and a minorchange in Stokes shift (Figure 3.3a and Appendix 2: Sections 4e, f and g). These properties reflect
the higher radiative rate constant calculated for this mutant in comparison to FR (Figure 3.3d).
Consequently, we performed site-saturation mutagenesis (library size = 20) at this position in thecontext of FR-M and found that the parent, along with FR-M M42Q (FR-MQ) and FR-M M42I
(FR-MI) were the only variants with observable red fluorescence. FR-MQ was the brightest
species with a quantum yield of ~43% and a further increase of fluorescence lifetime by 0.3 ns.
FR-MI showed decreases in maximum extinction coefficient, quantum yield and fluorescence
lifetime, thus we did not pursue engineering of this variant. We investigated the effects ofanalogous mutations on closely related RFPs and noted rather different outcomes. For example,
65

mKate M42Q shows a decrease in the molecular brightness due to ~50% decreases in bothmaximum extinction coefficient and quantum yield, along with a blue-shifted absorption spectrum
and a significantly increased Stokes shift, all of which are consistent with previous findings. [79,91] In addition, analogous mutations at position A44 on mCherry and mScarlet-I RFPs resulted in
non-fluorescent clones. It should be noted that mCherry, mScarlet-I and FR show multiple
structural differences in the chromophore structure and in the vicinity of the chromophore.
Although crystal structures indicate that there seems to be sufficient space to accommodate a 44Q
sidechain in mCherry and mScarlet-I, there are multiple structural differences between the three
FPs. We cannot explain why this mutation did not produce a fluorescent species in mCherry andmScarlet-I.
While measuring the maximum extinction coefficient with the alkali-denaturation method, we
observed that M42Q containing mutants of FR produce a single hydrolysis product with anabsorption band centered at 380 nm (Appendix Figure A2.8). Most RFPs, such as mScarlet,
mCherry and mRuby3, display GFP-like degradation with an absorption band at 450 nm. The
hydrolysis products of FR variants with the native 42M have both 380 nm and 450 nm absorption
peaks. The 380 nm band is assigned to the cleavage of the chromophore from the β-carbon of the
Tyr moiety in the chromophore. [194, 195] The absence of the 450nm band in FR-Q and FR-MQ
reveals alteration of the chromophore hydrolysis chemistry. This suggests that the 42Q residue
interacts strongly with the chromophore in FR.

66

Figure 3.2. Site-directed mutagenesis based on structural data. (a.) Crystal structure of FRwith positions around the chromophore relevant to the study generated using PyMol. (b.)
Comparative locations of the 42 position in TagRFP-675 (PDB ID: 4KGE, blue, 42Q), mKate(PDB ID: 3BXB, purple, 42M) and FR (PDB ID:6U1A, pink, 42M). The crystal structure of mKate(PDB ID: 3BXB) indicates that the end of the chromophore near the para-hydroxyphenyl moiety
may exist in both cis and trans conformations, with the cis conformer overlapping with that of
TagRFP-675. For FR, the fluorescent chromophore exists in the cis conformation as well. (c.) The
occupancy surfaces (based on PyMol) indicate that the chromophore (green surface) and thesidechain of the M42 residue (red surface) come in close contact.

67

Table 3.1. Summary of in vitro photophysical properties of FR mutants developed in thisstudy vs. re-measured values for some well-characterized RFPs. The standard deviation error has
been reported for measurements where independent triplicates were performed. mCherry andmScarlet were used as references for the quantum yield measurements. [35, 101]
abs

em

τ


FP
(ns)

εmax

Molecular

krad

kNR

(M-1cm-1)

brightness(µs-1)(µs-1)

(nm)

(nm)

FR

574

596

1.780.04 0.240.04

9400070001

1352342726

FR-M

571

591

2.130.05 0.340.02 7800010000

1.2

1601031015

FR-Q

568

587

2.100.05 0.330.01 1330002000

2

1576

31913

FR-V

573

594

1.960.02 0.310.04

845008000

1.2

1544

3619

FR-MV

569

592

2.390.02 0.380.09

850006500

1.4

1665

2549

FR-MI

575

595

1.750.02 0.260.04

82000

1

1491242313

FR-MQ

567

586

2.430.08 0.430.08 1300009000

2.7

1761423319FR-MQV566

585

2.770.07 0.530.03 1440003000

3.4

1911217016mScarlet-I

570

591

3.260.07 0.590.03 1025004500

2.7

1841012812

mKate

588

634

2.260.07

0.33

48000

0.7

130

264

577

654

2.160.05

0.17

25000

0.2

79

384

mCherry586

607

1.670.07

0.22 (ref)750005000

0.8

137

488

mScarlet569

592

3.870.07

0.71 (ref)1030004500

3.3

186

72

mKateM42Q

68

Figure 3.3. Photophysical properties of the FR family of FPs. (a.) Absorption (solid lines) andemission (dashed lines) spectra. (b.) TCSPC lifetime traces. Longer decay profiles indicate thegradual increase in fluorescence lifetime. The black lines indicate exponential fitting for the decay
profiles. (See Appendix 2: Section 4b for fitting details) (c.) Plot of quantum yield versus
fluorescence lifetime. The dashed line indicates the linear rise of quantum yield with increments
in fluorescence lifetime for the FR family of FPs. The values for mCherry, mScarlet and mScarletI are taken from references [35, 101]. (d.) A plot showing the increase in radiative rate constant(black) and decrease in non-radiative rate constant (blue) across the FR family relative to mCherry
and mScarlet (red). Vertical error bars (blue and black) in the FR family indicate the uncertainty69

in the calculated rate constants, the horizontal error bars (black) are the standard deviation error in
the measurement of fluorescence lifetime. (e.) Photobleaching traces for the family of FR mutants,
determined by averaging ~10 decay traces in E. coli cells for each FP under normalized excitation
rates. (f.) The dependence of the fluorescence decay half-life on the excited state lifetime. Error
bars indicate standard deviation errors.

3.4c. Combining mutations M42Q, C159V and L175M led to the generation ofbright FR-MQV.
Each individual mutation results in an increment of fluorescence lifetime by ~0.3 ns in FR.
Therefore, we incorporated all three mutations into FR to yield FR-MQV. The FR-MQV mutant
exhibits a fluorescence lifetime of 2.8 ns which results in a high quantum yield of 53% (Figures
3.3b and 3.3c). The absorption and emission spectra are similar, with a slight blue shift andnarrowing of the spectra in all variants possessing the M42Q mutation (Figure 3.3a and Appendix
2: Section 4f and g). The molecular brightness of FR-MQV is ~3.4-fold higher than that of FR.
Overall, we see increases in fluorescence lifetime and quantum yield, as a result of an increase in
the radiative rate constant and a concomitant decrease in the non-radiative rate constant (Figure3.3d). Steady-state absorbance and fluorescence spectra along with wavelength-dependent lifetime
measurements were collected to assess the heterogeneity of chromophore formation. We foundthat FR-MQV matures predominantly into a red-emitting chromophore which emits as a single
red-emissive species (Appendix 2: Section 4b, i and j). FR-MQV has a low in vitro pKa of ~4.6,
like other members of the FR family (Appendix 2: Section 4a) and breaks down into a single
product of alkali hydrolysis, resembling FR-Q and FR-MQ (Appendix 2: Section 4h). We also
found that FR-MQV was ~2-fold brighter than FR in E. coli (Appendix 2: Section 4d).
The photobleaching traces of FR-MQV and related variants are shown in Figure 3.3e. Whenphotobleaching measurements were performed on multiple FPs illuminated at the same excitation
rate, longer fluorescence lifetime is correlated with faster photobleaching (Figure 3.3f). In thiscase, excitation rates are set by ensuring that the value of excitation power (P, in mW) from theobjective divided by the absorption cross section at 560 nm 𝑃/𝜎560 𝑛𝑚 (defined as 𝜎560 𝑛𝑚 = 2303
x EC560 / NA; where EC560 is the extinction coefficient at 560 nm and NA is the Avogadro constant)70

is the same for the FPs being compared. Furthermore, it was observed that under continuous
irradiance of ~5 W/cm2 at 560 nm, the fluorescence kinetics of FR variants with a C159 residue
show two decay timescales. This behavior is typical of most FPs, which show an initial decay due
to dark state conversion (also sometimes called reversible photobleaching), along with a slower
timescale of permanent photobleaching. [55,56] The C159V and C159L mutations, which
incorporate aliphatic groups, significantly reduce the amplitude of the faster decay component(Appendix Figure A2.4). To verify that the faster component corresponds to a reversible process,we used alternating pulses of 560 nm and 438 nm excitation (Appendix 2: Section 4c). The FRC159V variant showed little recovery and FR-C159L showed slight recovery of the fluorescence,but the recovery was much larger for FR (~20% higher). These results show that the reversible
photobleaching dynamics of FR are influenced by the chemical nature of the sidechain at position
159.

Figure 3.4. Cellular brightness assays. (a.) FACS-based brightness assays of FPs expressed ashistone H2B fusions in HeLa cells. Each biological replicate involved three technical replicate
screens of ~10,000 individual cells. (b.) Mean brightness values of individual HeLa cells obtained
from confocal microscopy for histone H2B fusions. Each dish was an independent biologicalreplicate and contained ~100 cells. For both a and b, the cells were sampled ~48 hours posttransfection. Details of the assays are provided in Appendix 2: Section 5a. Error bars indicate
standard deviation errors.

71

3.4d. FR-MQV is 5-fold brighter in HeLa cells, retains the cellular properties
and high-fidelity localization of FR.
Flow cytometry and confocal microscopy were employed to quantify the cellular brightness of FRMQV in HeLa cells (Figure 3.4). FACS screening of HeLa cells expressing FPs fused to histone
H2B protein after 48 hours of transfection revealed that FR-MQV is 5-fold brighter than the parent
FR, and ~1.4-fold less bright than mScarlet (Figure 3.4a and Appendix 2: Section 5a).
Measurements with confocal microscopy on the same construct revealed that FR-MQV is ~2.3fold brighter than FR and ~1.4-fold dimmer than mScarlet (Figure 3.4b and Appendix 2: Section
5a). We next investigated whether the mutations in FR-MQV would influence cytotoxicity,
chromophore maturation and localization of fusion proteins. FR-MQV exhibited low cytotoxicity,
like the parent FR and in contrast to mCherry, which showed ~80% relative decrease in cells
expressing the FP after 6 days of expression (Details of the assay are discussed in Appendix 2:
Section 5b). FR-MQV showed chromophore maturation kinetics identical to the parent FR (t1/2~195 min at 37ºC; Appendix 2: Section 5c) and similar to mScarlet (t1/2 ~ 130 min at 37ºC), but
slower than mScarlet-I (t1/2 ~45 min at 37ºC).
In the OSER assay, FPs are fused to the cytoplasmic end of the endoplasmic reticular signal anchor
protein (cytERM). [199] Membrane localization increases the local concentration leading to theformation of dimers or higher order oligomers that distort the ER structure which are observed ascellular sub-structures or “whorls”. Figure 3.5a shows confocal microscopy images of cytERMFPs expressed in U2OS cells and the corresponding OSER scores. TagRFP-T (positive control)
shows characteristic oligomerization in the form of sub-cellular “whorls”, while the FR mutants,
mScarlet and mScarlet-I generally lack such structures. In this work, we measured a score of 88
for FR and 87 for FR-MQV which are ~5% higher than measured for mScarlet (84) and ~10%higher than mScarlet-I (80). We also developed GalT-FP fusions to localize the FPs of interest to
the Golgi. Proper and mis-localization to the Golgi in U2OS cells imaged using confocal
microscopy are shown in Figure 3.5b. Our analysis indicates that FR-MQV and other FR-derived
mutants outscore mScarlet and mCherry in terms of proper localization to the Golgi. Our results
are qualitatively consistent with previous observations where FR correctly localizes to the Golgi,
but GalT-mCherry frequently displays puncta in the cytoplasm. [196] We observed higher
occurrences of mis-localization in the bright RFPs mScarlet and mScarlet-I compared to FR
72

mutants. Thus, cellular imaging studies indicate that FR-MQV retains the high-fidelity localization
properties of FR without compromising low cytotoxicity and appropriate maturation andexpression.
Table 3.2. Summary of cellular and molecular brightness for FR variants. The molecularbrightness of FR-MQV is ~3-fold that of FR, while FACS measurements indicate it is ~5-foldbrighter in HeLa cells. In comparison, FR-M has only a 20% larger molecular brightness than FR
but is ~2-fold brighter in HeLa cells. These observations suggest that the ~5-fold increase incellular brightness of FR-MQV relative to FR is due to the combination of an increase in molecularbrightness and the increased cellular expression possibly from the L175M substitution.
Bacterial
Molecular
Protein

HeLa Cell

Cell

Brightness

Normalized relative to FR-M

Brightness
Brightness(εmax * )(58515 nm)(58515 nm)

Molecular

HeLa Cell

Brightness

Brightness

FR

1

1

1

0.9

0.5

FR-M

1.2

1.3

2.1

1

1

FR-Q

2

1.4

-

1.7

-

FR-MQ

2.6

1.7

3.6

2.3

1.7

FR-MQV

3.4

1.9

5.3

2.9

2.5

Over-expression and oligomerization in cells can lead to unwanted effects such as self-quenching,mis-folding, mis-localization and disruption of organelle structure and function. [197, 198] Hence,
we performed the organized smooth endoplasmic reticulum (OSER assay) [199] and examined
localization of a GalT-FP fusion to assess the in cellulo monomericity and localization properties
of FR-MQV relative to FR and the other bright RFPs mScarlet and mScarlet-I.

73

Figure 3.5. Localization Assays. (a.) The OSER Assay: Representative maximum intensity
projected confocal images for U2OS cells expressing cytERM-FP constructs for FR, FR-MQV,
mScarlet-I and TagRFP-T (negative control), and the graphical representation of the OSER scoresfor these cells. The y-axis on the plot indicates the percent cells that do not express sub-cellular“whorls”. The OSER scores for this assay were: FR, 88 (2,250 cells), FR-MQV, 87 (1,580 cells),
mScarlet, 84 (306 cells), mScarlet-I, 80 (291 cells) and TagRFP-T, 45 (406 cells). (b.) The GalTFP Fusion Assay: Confocal microscope images for U2OS cells expressing the GalT-FP fusion
constructs for FR-MQV, FR and mScarlet-I, with the localization scores (indicative of the percent
cells with the FP localized correctly to the Golgi) plotted for each RFP. The microscopy images
show cells expressing GalT-mScarlet localized and mis-localized to the Golgi. The scores for FPs
analyzed in the study have been reported with the FR mutants (including previously published FRXG [30]) outscoring mCherry and mScarlet. Error bars indicate standard deviation errors acrossbiological replicates.
74

3.5. Discussion
In this work we engineered FR using a structure guided approach, aimed to develop mutants withincreased fluorescence lifetime manifesting in higher quantum yield, eventually leading to a FP
with higher molecular and cellular brightness. We examined both the para-hydroxyphenyl and theacylimine sites of the chromophore for sites where we could potentially increase steric effects,
increase rigidity, interact chemically or electrostatically with the chromophore. This approach led
us to mutate multiple residues near the para-hydroxyphenyl moiety, thus motivating the need forlifetime screening of a 7,000-member library. In contrast, near the acylimine moiety we identified
the capacity for an interaction to be added at position M42. Crystal structure data suggests
conformational freedom of the sidechain at position 42 in FR. [200] The position 42 lies in close
proximity to the acylimine moiety of the chromophore and based on our previous work, is criticalto the hydrogen-bond network on that end of the chromophore in closely related FPs mKate andTagRFP-675. [79, 91] A smaller site-saturated library of 20 possible mutants at position 42
allowed us to carry out a plate based screen on FR-M, where Gln stood out as the best possible
sidechain residue in terms of increases in fluorescence lifetime and quantum yield.
Individually L175M, C159V and M42Q substitutions, increased the fluorescence lifetime of FR
by ~0.3 ns (~17% increase), and when incorporated together in FR-MQV exhibited ~1 ns (~55%)
increase over FR, suggesting the effect of each mutation in terms of fluorescence lifetime wasadditive in the triple mutant. FR-MQV closely follows the spectral characteristics of FR-Q and
FR-MQ, all of which have reduced spectral widths in absorbance and emission spectra with blue
shifts in the absorption spectra with ~20% or higher peak absorbance with respect to FR.
Consistent with the Strickler–Berg relationship, we calculate higher rate constants for radiative
decay in FR mutants with the M42Q mutation. Based on these values, we successfully engineered
the decrease of knon-rad with a simultaneous increase of krad in FR, which is an efficient way ofengineering the molecular brightness of a FP. FR-MQV has a krad comparable to the brightest RFP
to date - mScarlet and its cellularly brighter mutant mScarlet-I. Finally, these mutations translate
to high cellular brightness without compromising the cellular properties of the parent FR, as seenfrom the cytotoxicity, maturation and imaging assays performed in this study. Given this favorable
combination of incremental photophysical changes and preserved cellular properties of FR-MQV

75

with respect to FR, further rounds of engineering could produce a new standard for red fluorescentprotein labelling.
Crystal structures indicate that the para-hydroxyphenyl moiety of FP chromophores can adopt
either the trans (non-fluorescing) or the cis (fluorescing) conformation [25, 201],and in FR, thelatter can potentially form a hydrogen bond with the hydroxy group of the S144 residue (Figure3.2). [200] The location of C159 suggests that it may play a similar role for the trans conformer ofthe chromophore. The position 159 was recently discussed to be critical in terms of molecularbrightness for FR. [200] The propensity to switch to the trans conformer may be reduced when theresidue at this position is substituted for an aliphatic group. The cis to trans isomerization is areversible process and is manifested as the reversible component of photobleaching undercontinuous and pulsed (ms to s) illumination. [55, 56] The reduction in dark state conversion in
the photobleaching kinetics of FR-C159V and FR-C159L indicate that there is a reduction in thetendency of the chromophore to switch to a dark, trans conformer. Furthermore, FR-C159V did
not show photo-activation of fluorescence, [202] which suggests the chromophore might be locked
into either the cis- or trans- conformation. Leu has a larger aliphatic sidechain than Val; thus, theshorter lifetime and complicated photo-activation behavior of FR-C159L may be a steric effect,with Val providing a better spatial fit that restricts chromophore movement into the dark, transconformer.
Time-resolved ultrafast spectroscopy previously demonstrated that TagRFP-675 and mKate-Q
display large Stokes shifts because there are multiple emissive species in the form of noninterconverting hydrogen bonded conformers. [79, 91] Multiple emissive species tend to broaden
spectra and correlate with lower quantum yield and shorter fluorescence lifetime values. [79, 91]
Steady state excitation-dependent emission spectra and fluorescence lifetime decay spectracollected in multiple emission windows dismiss the existence of multiple emissive species in
M42Q mutants of FR (Details in Appendix 2: Section 4b and j). This is consistent with the minimalchange in Stokes shift in the M42Q mutants of FR in comparison to mKate-Q (Appendix 2: Section
4f). The polar sidechain of Gln can exist as one of many possible rotamers. [203] It is possible that
this residue at position 42 rearranges itself into a conformation that might restrict the number ofemissive species. This is supported by UV-Vis spectral data. which reveal that incorporating
M42Q decreases the spectral width, blue shifts the absorption and emission spectra and increases
76the radiative rate constant. Other than Gln, we observed red fluorescence from the mutant with Ileat this position. Ile is of similar size to Gln and Met but is aliphatic in nature. Characterization of
the FR-MI mutant revealed a relative decrease in maximum extinction coefficient and quantum
yield with a decrease in fluorescence lifetime with respect to the parent FR-M. We also observed
an undesirable green emitting chromophore in the FR-MI and mKate-Q mutants, which was absent
from the M42Q mutants of FR (Appendix 2: Section 4i), suggesting complete maturation to a red
chromophore in FR-42Q mutants. Alkali denaturation of FR-Q, FR-MQ and FR-MQV showscleavage of the chromophore only from the β-carbon of the Tyr sidechain, which is indicative ofbase access to a single site for hydrolysis (Appendix 2: Section 4h). The β-carbon of the Tyr
sidechain in RFPs is spatially distant (>10Å based on crystal structure data) from the acylimine
moiety of the chromophore. These molecular and photophysical properties suggest that factors
other than steric effects (such as electrostatics, hydrogen bonding, etc.) may be responsible for thechanges observed in the M42Q mutants of FR.
The ~5-fold increase in brightness observed in FR-MQV relative to FR (Table 3.2) is likely an
amalgamation of the higher molecular brightness of the M42Q and the C159V mutations alongwith the higher cellular expression seen for FR-M. [30] The trends for brightness measured throughcytometry and microscopy are similar, but FACS measurements employ short laser exposure times
with fast, sensitive detectors like photomultiplier tubes (PMTs). In microscopy, cells are subject
to relatively longer exposure times and higher irradiances (~ms timescales) imposed by acquisition
times of cameras, which can lead to photobleaching. The correlation between excited-state lifetimeand photobleaching (Figure 3.3f) is evidence that photobleaching occurs due to excited-state
absorption, as discussed for other RFPs. [55] A practical consequence is that brightness values
measured by FACS are systematically higher than those measured in microscopy. This discrepancy
between the absolute brightness values between FACS and confocal microscopy measurements
was also observed for mScarlet.
Figure 3.6 is a schematic indicating the postulated effect of each mutation in the development of
FR-MQV. Overall, the high extinction coefficient, decrease in the spectral width and blue shifts
can be attributed to the M42Q mutation, whereas changes in the dark state behavior withincrements in fluorescence lifetime and quantum yield seem to be additive from incorporating the
C159V and the L175M mutations into the FR-Q system. All three mutations in FR-MQV face77

inward, in the vicinity of the chromophore and therefore seem to minimally perturb the cellular
properties of FR. The high scores for the OSER and Golgi-localization assays for all FR mutants
indicate cellular properties in FPs are not appreciably affected by mutations of residues with side
chains facing towards the chromophore. In the development of FR from mKate and mKate2, mostof the mutations that optimized the FP’s biological properties were facing out from the β-barrel.
We targeted positions to increase brightness, and thus we did not alter these external positions thatwere involved in the development of FR from mKate2. [188] Consequently, the mutants retained
FR’s original performance in terms of localization and cytotoxicity. Though chromophorematuration kinetics can be greatly altered with internal mutations, [29] in this case, chromophorematuration was not substantially slowed by these mutations.

Figure 3.6. The overall molecular schematic describing the postulated effects of thesubstitutions in FR-MQV. The L175M mutation increases the quantum yield (QY), fluorescence
lifetime (LT) and expression in mammalian cells compared to FR. The C159V mutation reduces
the propensity of the cis-trans isomerization of the chromophore and results in subsequent
increments in the quantum yield and fluorescence lifetime. The M42Q mutation interacts strongly
with the acylimine moiety of the chromophore resulting in blue shifts, spectral narrowing,
increased quantum yield, fluorescence lifetime and extinction coefficient (EC) while also changing
the hydrolysis products of the chromophore.

78

3.6. Conclusions
In this study we present the development of FR-MQV, a FP with high brightness that maintains
favorable cellular properties of FR. The C159V mutation appears to play a critical role inrestricting the dark state conversion of the protein and increasing fluorescence lifetime, whichleads to an increase in quantum yield. The M42Q mutation plays an important role in enhancing
the molecular brightness by increasing both the quantum yield and maximum extinction
coefficient. Interestingly, this mutation had different effects in closely related FPs including mKate
and TagRFP-675. The previously reported L175M mutation contributes to robust expression levels
which improves cellular brightness for FR mutants compared to FR. With its increased brightness
and favorable cellular properties, FR-MQV shows promise as a template for further rounds ofengineering suited to specific imaging applications like FLIM and FRET. Increasing fluorescence
lifetime through further rounds of engineering may increase quantum efficiencies of emission tovalues near mScarlet with further reduction in the non-radiative rate constant (Chapter 6).

79

Chapter 4
Characterizing dark state kinetics from ensemble and single
molecule fluorescence experiments in FusionRed variants
4.1. Publication Note
Parts of this chapter have been adapted from the article “Characterizing Dark State Kinetics and Single
Molecule Fluorescence of FusionRed and FusionRed-MQ at Low Irradiances.” Mukherjee, S.; Thomas,
C.; Wilson, R.; Simmerman, E.; Hung, S. T.; Jimenez, ChemRxiv 2022. https://doi.org/10.26434/chemrxiv2022-2dr03

4.2. Introduction
Fluorescence-based bioimaging and biosensing, such as multi-color microscopy, Förster
resonance energy transfer (FRET) and fluorescence lifetime imaging microscopy (FLIM), is theprimary non-invasive approach to image biological systems. [3, 4, 204-207] Due to Abbe’s
diffraction limit, imaging sub-wavelength biological substructures requires innovations beyond
the scope of conventional microscopy. [208] Probing this “super-resolution” scale has high value
to modern biology and has garnered the attention of scientists and engineers from a range of
specializations - making it a popular interdisciplinary field of research and development. [209214] Techniques like stimulated emission depletion microscopy (STED), photoactivatedlocalization microscopy (PALM), reversible saturable optical fluorescence transition microscopy(RESOLFT), and other single-molecule localization microscopy (SMLM) overcome Abbe’s limit
through biochemical or optical modulation of single emitters. [215-218] Most SMLM methods,
including single-molecule active control microscopy (SMACM), bleaching/blinking assisted
localization microscopy (BALM) and super-resolution optical fluctuation imaging (SOFI), rely on
photo-activatable or photo-switchable emitters. [219] These emitters can be activated and/or
converted to a new species upon irradiation, exhibiting either molecular binding/modification or
spontaneous stochastic blinking. [219-223] Techniques that exploit stochastic blinking, such as
SOFI, rely on post-processed data analysis algorithms where traditionally acquired fluorescencetime-lapse images are analyzed to obtain spatio-temporal correlations for stochastic fluctuations
80

during emission. [219] Current efforts in this domain focus on application-based analysis of suchmethods and molecular interpretation of the nature of the blinking process for different emitters.
A majority of the literature treats emitters simply as tools, with limited analysis of their dark statekinetics and photophysics. [224-226] Unwanted artfacts in the determination of spatial locations
for these emitters can thus arise, as a major assumption underlying such stochastic methods is thatthe signals from single fluorophores are additive as long as the fluorescence dynamics of themolecules are independent. [226]
Genetically encoded fluorophores, such as fluorescent proteins (FPs), are popular and powerfulchoices to image biological systems and often exhibit dark molecular states which manifest in
stochastic blinking behavior at the single molecule level. [227-231] Extensive mechanistic studies
have elucidated a diverse range of mechanisms and timescales for stochastic and tuned dark-state
conversion, including electron-transfer reactions, excited-state proton transfer, chromophore andsidechain conformational changes. For example, a number of proteins from the avGFP line display
a spontaneous, light-driven, pH-dependent dark-state conversion pathway. [232-234] In such casesa pH-dependent dark state conversion is often attributed to a proton transfer between amino acidresidues and the chromophore. The red FP (RFP) DsRed exhibits a similar light-driven dark-state
conversion through a different, pH-independent process. [233] Photoconvertible FPs (PCFPs) like
IrisFP, mEosFP and Dendra derivatives exhibit dark-state conversion via chromophore distortions
due to side-chain conformational changes, chromophore twisting motions or by proton transferfrom the triplet or a radical ground state. [90, 235-238] Selectively engineered photo-switchable
or reversibly-switchable fluorescent proteins (rsFPs) exhibit highly efficient transfer to dark states,
allowing the molecules to be switched on and off with either light-driven pH-dependent pathways
or reversible chromophore conformational changes such as a cis-trans isomerization along themethylidine bridge connecting the two conjugated rings in the chromophore moiety. [202, 239240] Dark states can be selectively accessed or depopulated using optical or thermal modulation.
[241-247] For example, pulsed excitation with resonant frequencies was used to populate anddepopulate the dark state in FPs like AcGFP and rsFastLime, providing selective modulation offluorescence. [244] Varied mechanisms of accessing dark states such as those listed above havemade FPs natural choices for several SMLM techniques.

81

Despite the extensive advances in the study of dark-state dynamics, many of the above-mentioned
studies far preceded the development of advanced SMLM techniques such as SOFI. Several
previous studies were constrained by experimental challenges to probing dark state dynamics with
irradiances on the order of kW/cm2 to attain adequate signal to noise ratios. [227-233] While thesestudies explore the fundamentals of dark states in FPs, probing dark-state dynamics at highirradiances comes with a three-fold disadvantage. These conditions accelerate permanent
photodegradation of the fluorophore, make extrapolation to much lower irradiance as in widefieldand SMLM regimes difficult, and cause light-induced photo-toxicity and photodamage tobiological systems. [219, 248, 249] It is also worth noting that blue shifting the excitation lightincreases phototoxicity, thus highlighting the need for development of new bright and red-shifted
fluorophores as well as for detailed photophysical characterization of existing red fluorophores –which additionally allow for deeper imaging in comparison to blue shifted analogues. [249, 250]
When extrapolating the rate constant of ground-state recovery (kGSR) at low irradiances from highirradiance measurements, kGSR is commonly assumed to be proportional to the excitation rate (kEx).
[229, 251] Recovery from a dark to a fluorescent state is often a consequence of conformationalswitching such as a dark-trans to fluorescent-cis isomerization of the FP chromophore. [38] Sincesuch conformational switches are often energetically controlled, the excitation dependence of kGSR
may originate from the absorption of the excitation photons by dark state species and/or the riseof local temperature due to high irradiance. [229, 251, 252]
FusionRed and its sibling TagRFP-T exhibit fluorescence intermittency in live-cell imaging using
TIRF microscopy with camera acquisition timescales of 50 ms. [253] The study demonstrated thepotential to achieve a theoretical spatial resolution beyond the diffraction limit (~25–30 nm) with
FusionRed using SMLM methods like BALM and SOFI. [253] In our previous work, wedeveloped FusionRed-MQV, a FusionRed variant with 3-fold higher molecular brightness
developed using a combination of lifetime-based microfluidic selection and site-directedmutagenesis. [38] Additionally, we found that the substitution C159V in FusionRed resulted in abrighter variant which showed a monoexponential photobleaching trace contrary to thebiexponential behavior exhibited by the parental RFP FusionRed. Variants lacking the C159V
substitution, like the 2.5-fold brighter FusionRed-MQ exhibited biexponential photobleaching
traces with a fast fluorescence decay component (~s) followed by a significantly slower decay
component (>100 s). [38] The faster component was attributed to reversible photobleaching,82

where fluorescent molecules are trapped in the dark state. [38] This was verified by employing ahigh-energy 438 nm pulse (~2 s; 50% duty cycle) with a continuous 560 nm excitation scheme
which resulted in distinct reversible photoswitching for FusionRed variants with a Cys residue at
position 159. [38] High energy 438 nm light prompts a return to the fluorescent state from a darkstate, suggesting that the lower energy 560 nm excitation minimally perturbs the ground state
recovery process. [38] Findings from this and other studies, including crystal structure data,
indicate a possible interconversion of the FusionRed chromophore from a fluorescent cis to a darktrans isomer. [182, 200] Moreover, in the low irradiance regime of 1-10 W/cm2, the temperature
increase in the vicinity of an FP molecule can be considered negligible. [254] Based on theseobservations, we hypothesized that the rate of recovery to the ground state (kGSR) is independentof the excitation rate (kEx) under low irradiances for FusionRed and FusionRed-MQ. To verify
these claims, we explore the relatively uncharted territory of dark state kinetics of these two RFPs
under low irradiances, central to widefield and SMLM techniques like SOFI. We do so by
extracting on-off statistics with single molecule imaging and exploiting the kinetics of reversible
photobleaching using widefield excitation on ensemble RFPs. We combined the strength of eachapproach to quantitatively extract rate constants of dark-state conversion (kDSC) and ground-state
recovery (kGSR) using a three-state model (Figure 4.1). We performed simulations utilizing Monte
Carlo methods to bridge the two extremes in imaging modalities and qualitatively validate thethree-state model. Finally, we propose a structural model to rationalize the dark-state dynamics
observed for these FPs.

83

Figure 4.1. A three-state model of the photophysics of a fluorophore central to this study.
The 561 nm excitation source allows access to the excited electronic (S1) state from the groundelectronic (S0) state. Following this, the fluorophore can either return to S0 or access a long lived
dark (D) state. It was demonstrated in Chapter 3 that the D state can be depopulated efficiently
using a 438 nm light. [38] The arrow labels kex, kIC, krad, kDSC and kGSR indicate the rate constantsfor excitation, non-radiative (internal conversion), radiative emission, S1 to dark state conversion
and dark state to S0 recovery, respectively. Permanent photobleaching from the S1 and the D states
are ignored in the regime of low irradiances.

4.3. Methods
4.3a. Experimental methods and data collection
i. Cell growth and protein purification
FusionRed and FusionRed-MQ in the pBad-His plasmid were transformed into the E. coli Top10
strain via heat shock and grown for 45–60 minutes in LB media in a shaker at 37 C and 230 rpm.
The transformants were plated on agar plates with 100 g/mL ampicillin and 0.2% arabinose(Sigma Aldrich) overnight at 37 C. Colored colonies were grown in 200 mL 2XYT (VWR) liquid84cultures with 100 g/mL ampicillin for 1–3 hours at 37 C and 230 rpm to an OD of 0.6. Arabinose
was then added (0.2%) to induce protein expression for 16–24 hours at 28 C and 230 rpm. The
cells were pelleted, chemically lysed (B-PER, Thermo Fisher Scientific) and the 6-His tagged FPs
were isolated on Ni-NTA columns (Thermo Fisher Scientific) by gravity filtration, eluting with
250 mM imidazole (Sigma Aldrich). Excess imidazole was removed with desalting columns (GEHealthcare) with dialysis buffer (150 mM NaCl, 50 mM Tris-HCL, pH 7.4) as an eluent.

ii. Single molecule measurements
Preparation of glass slides and coverslips: Minimizing the presence of fluorescent impurities isof particular concern in single-molecule studies. To reduce artifacts from impurities in our
measurements, we found that plasma-cleaned glass slide chambers were best suited to single
molecule TIRF. [255] Before plasma cleaning, the slides and coverslips (22 x 40 mm, No 1, VWR)
were cleaned with dilute HCl then washed with Alconox detergent and rinsed with deionizedwater, then soaked in methanol overnight to dislodge large contaminants. A custom aluminum
slide holder held the slides and coverslips inside a reactive ion etcher, such that both sides were
exposed to the plasma. The slides were then exposed to 300 s of O2 (Bias: 50 W and SCCM: 50
mTorr) plasma to remove organic contaminants and to charge their surfaces, followed by 60 s of
Ar plasma (Bias: 50 W and SCCM: 50 mTorr) to minimize presence of remaining reactive oxygen
species. The slides were used within 24 hours after plasma cleaning to avoid recontamination andloss of surface charge.
Sample preparation: The pure protein samples were diluted with Tris-HCl buffer (pH ~7.4–8.0)
and loaded by slow ejection from a 200 µL micropipette. It was determined that FP concentrations>300 pM caused crowding of FPs in the field of view and failure of our spot analysis algorithm toreport blinking trajectories, whereas concentrations <100 pM resulted in such sparse distributionthat it became difficult to find the correct focus height and provided few data points. Additionally,a washing procedure was developed to minimize the presence of non-adhered FPs in solution andthus minimize free FP diffusion into the imaging plane. The loaded chamber was left in the darkfor 10–15 minutes to allow FPs to settle onto the imaging surface, then a volume of imaging buffer(150 mM HEPES, 100 mM NaCl, pH 7.4) equal to the volume of the loaded sample was passed85

through the chamber 4–6 times, with 2-minute intervals between washes. The liquid was slowly
ejected by a micropipette on one side of the chamber while filter paper was used to absorb theliquid flowing out from the other side. This washing procedure helped to maximize signal-tobackground ratios and minimize artifacts from non-specific adhesion to the glass surface for FPs
in solution.
TIRF Imaging: The samples were imaged with TIRF microscopy on an Olympus IX-73 inverted
microscope. The microscope is accessorized with an Olympus cellTIRF-1Line system fiber
coupled to a laser (Toptica iChrome MLE). An Olympus 60x-in-oil (NA:1.42) TIRF objective
and an EMCCD camera (Andor iXon 897) were used for the single molecule experiments. A
schematic of this system has been provided in Appendix Figure A3.1. To measure the excitation
rate, the objective focus was first determined by imaging a dye sample under bright-field
illumination, then the sample was removed and the laser was focused at the ceiling (approximately
2 m beyond the sample location) for this z-position of the objective. The irradiance measurements
were carried in this normal (INormal) to the imaging plane position using a power meter (X-cite).
The excitation intensity of the evanescent field (ITIRF) was calculated from the incident intensity(INormal), the indices of refraction (η2, η1), and the incident angle. [256] The calculations of
excitation rates for normal and TIRF illumination are presented in Appendix 3: Section 2. To image
samples, a cropped area of the imaging plane (~128 x 128 pixels on a 256 x 256-pixel binning)corresponding to the region of highest intensity of the laser profile was selected. Then for thelowest value of irradiance (1W/cm2), 100 nm fluorescent beads (TetraSpeck) were used to first
determine the approximate z-focus, and the motorized stage (Prior) was moved in the x–y plane tothe position of single FP molecules, to determine an accurate focus. The experiment was started
after moving to an adjacent spot (~100 µm) outside this imaging area of the previous step, where
drift on the z-axis was minimal. This was done so as to minimize photobleaching of single
molecules.

iii. Ensemble measurements:
Bright bacterial colonies on the agar plates described above were chosen for time-lapse
photobleaching experiments. Two to three colonies were transferred to microcentrifuge tubes andwashed with 500 µL imaging buffer by vortexing for ~20 s. The cells were centrifuged at 300086

5000 RPM for 60 s, and the washing buffer was removed. The pelleted cells were then resuspended
in the same buffer to an OD in the range of 0.1 to 0.5 to get a cell density suitable for imaging. A
glass coverslip and slide were cleaned with Alconox detergent, rinsed with deionized water, andblown dry with filtered compressed air. 10–20 µL of the cell mixture was added between the
coverslip and slide, which was imaged on an Olympus IX-73 inverted microscope system. Samples
were excited by 560 nm continuous wave LED illumination (Lumencor). Fluorescence bleachingmeasurements were taken with the 20x or 40x-in air objective lens (Olympus). The fluorescence
was collected through a 629/56 nm band-pass filter by a SCMOS camera (Andor Zyla). Videos
were collected with 10–50 ms exposure times and frame rates of 20–32 FPS for the fast andreversible component of the decay and 10–20 FPS for the slow and irreversible component, andwith irradiances ranging from 1–20 W/cm2. We performed three independent trials where eachtrial for an FP involved a technical replicate with ~10–20 cells to gain consistent bleaching traces.

4.3b. Data analysis
i. Single molecule data analysis
Single molecule data analyses from imaging videos were carried out using two independent scripts:
One for spatial identification of bright spots followed by one for temporal and intensity analysisof these bright spots. Figure 4.2 shows a schematic representation of this workflow.

Spot identification script: Despite cropping, there is a systematic ~10% intensity variation acrossthe imaging plane with a Gaussian profile. To account for this, the videos were iteratively fitted toa Gaussian intensity correction function to correct for the laser background, primarily fromresidual scattering, and normalizing for the variation in intensity due to the spatial mode of theexcitation laser. (Appendix Figure A3.1) Following Gaussian correction, our analysis also revealeda biexponential decay of mean intensities across the timeframe of the video. Therefore, the mean
intensity of the videos was fitted to a biexponential function, which revealed a fast component of
decay (~1 s) along with a slow component of decay (>3 s). While the timescale of the slow
component of decay varied with the incident intensity, the fast component was seen to be fairly
consistent (Appendix Figure A3.2). Additional checks with blank solutions also revealed a87

consistent timescale for the fast component of decay. Therefore, after the Gaussian correction, asecondary correction was incorporated to account for the quick exponential drop in the overall
light intensity. Given that this decay was also found in blank medium and was missing from thelaser's temporal profile, we attribute it to diffusion or photobleaching of impurities in our blankmedium or the objective oil. Following the Gaussian and exponential corrections, the algorithm
identifies a number of bright locations equal to an input of the predicted number of single FPs in
the video. This number was set between 50 and 500 FPs depending on the field of view, theefficiency of binding the FPs to the glass surface and the concentration of the protein used. The
algorithm extracts the brightest pixels in the maximum intensity projected image of the video fromthe user defined input value for the number of single FPs. It then iteratively appends the locationof maximum value after it passes a check, which involves scanning a pixel grid surrounding the
pixel centered at maximum value based on the statistical distribution of the brightness around thegrid.

Temporal and Intensity analysis: To extract information on real “on” and “off” blinking events wedrew inspiration from the work of Watkins and Yang. [257] In order to find single on and off
events in a trajectory of a single molecule, we used an intensity change point approach. Our spot
analysis script provides us with intensity corrected trajectories with time for the brightest spots
arranged in the ascending order of mean intensity. We therefore assessed the first five and the last
five trajectories, based on the brightest and the dimmest spots identified through the previous
script. In each case, we estimated the average single molecule on intensity to provide as an input
for this code. Although many approaches utilize histograms from the intensities of each frame toeffectively threshold and binarize a trajectory, it is difficult to use this approach for our data sets
at the lower and the upper bounds of irradiances, which are characterized by increasingly longer
τON or τOFF, respectively. [258]88Figure 4.2. Analysis workflow. (a.) The background correction and molecule selection process.
(b.) Our analysis workflow contrasted against standard thresholding methods. Note that the state
shift recognition workflow identifies points where possible changes occur and binarizes on thebasis of those points. This avoids the noise-based artifacts shown in the thresholding approach,where it can be difficult to set an arbitrary threshold that is not crossed by noise. (c.) The
binarization of a raw trace based on the thresholding algorithm.
Following the input of the five potential on events, our algorithm performs two steps. First, it fits
the change of intensity between frames for the entire dataset to a Gaussian distribution. It should
be noted that a protein turning on or off produces a relatively small change in intensity that falls
within the noise distribution. Therefore, it is not possible to separate these events from backgroundnoise with equal or higher intensity without additional information, whereas noise below thisthreshold can be discarded. As a result, all frames with a change value of the threshold or higher
are earmarked as possible changes of state. Thus, the primary question is where to set the thresholdfor optimal recognition. (Appendix Figure A3.3) The theoretical minimum intensity changes for amolecule result from a case where the protein turns on exactly halfway through a frame’s
acquisition time. This results in a change of intensity of ½ the protein signal, followed by a second
89change of the same magnitude. As such, a good baseline estimate for the noise threshold value is
50% of the expected signal. Empirically, we have found that ~1.5 σ (standard deviation) of theoverall noise produced consistent results. This boundary excludes 86% of overall noise, but it isworth noting that the on state contributes to higher (shot) noise. As such, this boundary excludes
approximately 70% of the larger standard deviation on distribution. The second step of thealgorithm considers the intervals between each on and off point individually and binarizes eachsegment on the basis of a user-defined τON. (Appendix Figure A3.2 and Figure 4.2c) This further
minimizes the contributions of noise by averaging each segment. Segments that are more than 2σ
above the model τON are considered multi-molecule events and the corresponding trace isdiscarded. All segments that end at the last frame of the video (on or off) are also discarded to
avoid artifacts, notably from permanent photobleaching or denaturation.

iii. Ensemble data analysis:
Photobleaching data analysis was carried out with a previously reported scheme. [38] In brief, apipeline in the CellProfiler suite was used to identify bacteria in an imaging plane of uniform
irradiance and provide normalized intensity trajectories. [189] The intensity trajectories wereanalyzed and fit to biexponential traces using a custom fitting program in MATLAB (Appendix
Table S4.1).

4.4. Results
4.4a. Simulations and measurements of single molecule photophysics
We performed simulations of blinking trajectories for single molecules in a three-state (S0, S1 andD) model with our hypothesis. (Figure 4.1) As expected, the results show that τON decreases withboth shorter values of τDSC and higher values of kEx, whereas τOFF depends only on the value ofτGSR. The details of the algorithm and simulated results are described in Appendix 3: Section 5. In
brief, the residence of single FPs in each state (S0, S1 or D) at each time step is simulated using a
combination of Monte Carlo methods weighted by probabilities of state change, governed by thekEx, krad, knon-rad (IC), kDSC and kGSR. An “on” or a fluorescent event is detected every time the90molecule successfully completes an S0-S1-S0 cycle, without going through D. (Figure 4.1) The
predictions of the simulations accurately represent experiments, where data from three
independent trials revealed a hyperbolic dependence of the τON of FusionRed and FusionRed-MQ
on the excitation rates. The τOFF for both FPs showed little or no dependence on excitation rates assummarized in Table 4.1 and Figure 4.3.
Our single molecule measurements were carried out with irradiation on the order of ~10 3
photons/s, which is significantly lower than the optical saturation limit for FPs (~108 excitationphotons/s). Therefore, the population in the S1 electronic state can be treated under a steady state
approximation. At low irradiances, we assume minimal absorption from the dark states andtherefore consider the reverse dark-state conversion to be negligible. [38] The timescales ofpermanent photobleaching are significantly longer than that of dark-state lifetime (Appendix 3;
Section 4), hence it was neglected in this scheme. Incorporating these assumptions, we arrive atequations 1 and 2 to calculate kDSC and kGSR for FusionRed and FusionRed-MQ, [259] and thecalculated values are presented in Table 4.2 and Figure 4.4.
𝜏𝑂𝑁 =𝑘𝑒𝑚 +𝑘𝑛𝑜𝑛−𝑟𝑎𝑑 +𝑘𝑑𝑠𝑐
𝑘𝑒𝑥 .𝑘𝑑𝑠𝑐

𝜏𝑂𝐹𝐹 = 𝑘

1
𝐺𝑆𝑅

(1)

(2)

Table 4.1. Values of τON and τOFF
FusionRed

FusionRed-MQ

kEx (s-1)

τOn (s)

τOff (s)kEx (s-1)

τOn (s)

τOff (s)950

10.9 ± 2.3

5.3 ± 0.51600

4.9 ± 0.3

6.4 ± 1.51200

9.5 ± 1.1

4.7 ± 12400

3.5 ± 1.1

6.6 ± 0.51400

6.2 ± 0.9

5.2 ± 0.23300

2.8 ± 0.3

6.1 ± 0.1

1900

4.4 ± 0.4

4.8 ± 0.75200

2.0 ± 0.3

6.5 ± 0.56000

2.6 ± 0.5

5.3 ± 1.210400

1.3 ± 0.4

6.5 ± 1.012000

1.2 ± 0.5

5.8 ± 0.8

The kDSC and kGSR remain consistent under the range of irradiances probed in this study. However,FusionRed clearly shows an ~30% higher kGSR than FusionRed-MQ.

91

Figure 4.3. Results from single molecule blinking experiments. Measured τON with respect toexcitation rate for (a.) FusionRed and (b.) FusionRed-MQ; and measured τON with respect toexcitation rate for (c.) FusionRed and (d.) FusionRed-MQ. The black data points are the mean
τON/OFF extracted from three independent experiments (error bars indicate the confidence intervals
for the values extracted from fits).
Table 4.2. Estimation of kDSC and kGSR
FusionRed-1

3 -1

FusionRed-MQ-1-1

kEx (s )kDSC (x10 s )kGSR (s )kEx (s )kDSC (x103 s-1)

kGSR (s-1)

950

55 ± 110.19 ± 0.02

1600

52 ± 40.16 ± 0.02

1200

50 ± 50.21 ± 0.03

2400

48 ± 15

0.15 ± 0.01

1400

60 ± 70.19 ± 0.013300

46 ± 50.16 ± 0.01

1900

67 ± 100.21 ± 0.035200

40 ± 60.15 ± 0.01

6000

39 ± 100.19 ± 0.0410400

36 ± 100.15 ± 0.0212000

39 ± 160.18 ± 0.03

92

Figure 4.4. Variation of rate constants. (a.) kDSC and (b.) kGSR with respect to excitation rate
kEx measured from single-molecule blinking experiments. The error bars indicate standard
deviation errors calculated from measured τOFF and τON.

4.4b. Simulating ensemble behavior
We first generated normalized sum fluorescence traces for ~103–104 simulated blinking single FP
trajectories using the average kDSC and kGSR from the single molecule experiments. The simulations
indicated a larger dark fraction for FusionRed-MQ in comparison to FusionRed. We thenperformed simulations to obtain normalized sum fluorescence traces for blinking single FP
trajectories (3 sets of 150 emitters each) by varying one rate constant at a time, including kEx, kDSC
and kGSR. The results indicated that the dark fraction increases with increasing kEx and kDSC but
has no or little dependence on kGSR in the vicinity of measured values in the single molecule
blinking experiments. This observation encouraged us to pursue an alternate analysis compared tosingle molecule experiments, to quantify the kDSC. The results of these simulations are presented
in Appendix 3: Sections 5f, g and h. The normalized fluorescence signals are proportional to thenormalized population of FPs on the ground state S0, thus the fractions of FPs in S0 and dark state
D as a function of time can be estimated as shown in Appendix Figure A3.13.

93

4.4c. Ensemble photobleaching
E. coli expressing FusionRed and FusionRed-MQ were exposed to normalized widefield
excitation. The decay profiles of both FPs were recorded and fit with a biexponential function aspresented in Appendix 3; Section 4. Based on our previously reported pulsed photobleachingmeasurements, we assigned the slower decay component to permanent photobleaching and thefaster component to reversible photobleaching due to dark-state conversion. [38] Experimental
results showed a larger dark fraction for FusionRed-MQ compared to FusionRed.
To extract kDSC, we consider a three-state model to represent the kinetic processes of a fluorescentprotein in the first five seconds of a photobleaching trace, where the contribution of the permanent
bleaching component is minimal (<10%) and reverse dark-state conversion (D to S1) can be𝑑𝒏ignored. The rate equations can be written in the matrix form, 𝑑𝑡 = 𝐴𝒏, as explicitly shown inEquation 3, where 𝑛 is the population for each state.

𝑛𝑆0
−𝑘𝐸𝑥
[𝑛𝑆1 ] = [ 𝑘𝐸𝑥
𝑑𝑡
𝑛𝐷
0
𝑑

𝑘𝑟𝑎𝑑 + 𝑘𝑛𝑜𝑛−𝑟𝑎𝑑−(𝑘𝑟𝑎𝑑 + 𝑘𝑛𝑜𝑛−𝑟𝑎𝑑 + 𝑘𝐷𝑆𝐶 )𝑘𝐷𝑆𝐶𝑘𝐺𝑆𝑅 𝑛𝑆00 ] [𝑛𝑆1 ] (3)−𝑘𝐺𝑆𝑅 𝑛𝐷

The analytical solutions can be obtained by solving the eigenvalues and eigenvectors for rateequations (Appendix 3; Section 6). The observed fluorescence is proportional to the population in
S0 for an ensemble measurement. The resolution of the single molecule measurement in the time
domain is limited by the camera acquisition time and is significantly larger than the τ DSC, but
smaller than the τGSR. Therefore, our single molecule measurements provide an accurate estimationof the 𝑘𝐺𝑆𝑅 , but not the 𝑘𝐷𝑆𝐶 . However, we can utilize the 𝑘𝐺𝑆𝑅 values from the single molecule
measurements to fit the reversible bleaching curves of the ensemble measurements to extract anaccurate estimation for the 𝑘𝐷𝑆𝐶 across an irradiance range. The fluorescence decay data were fit
to the analytical expression of 𝑛𝑆0 to get 𝑘𝐷𝑆𝐶 values (bound 𝑘𝐺𝑆𝑅 ). The fitting results and theestimated 𝑘𝐷𝑆𝐶 values are provided in Figure 4.5 and Table 4.3. While there seems to be minimal
light-driven behavior for 𝑘𝐷𝑆𝐶 for FusionRed, fitting revealed an uptick of the 𝑘𝐷𝑆𝐶 with increasing
excitation rates for FusionRed-MQ.

94

Figure 4.5. Photobleaching fits from a three-state model, for (a.) FusionRed and (b.)
FusionRed-MQ, across varying irradiance ranges. (c.) kDSC obtained from fits. Details of the fit areprovided in Appendix 3; Section 6.

Table 4.3. Estimated kDSC values from fitting ensemble traces
Excitation Rate (s-1)

kDSC (x103s-1)
FusionRed

FusionRed-MQ

1400

22.3 ± 6.7

26.6 ± 3.1

2800

27.9 ± 1.8

28.4 ± 0.9380025.6 ± 1.4

32.3 ± 0.6550026.1 ± 1.6

38.9 ± 0.8

954.5. Discussion
Conventional models to characterize stochastic blinking usually rely on a two-state “on” and “off”
system, [229, 251] when the excitation rate is much higher than the sampling rate of the detector
used. [260, 261] When modeling single molecule blinking with such models under these
conditions, one can assume emission takes place when the emitter is in the fluorescent (S 0) state
for two consecutive simulation time steps (<< dark state lifetime). Imaging methods such as
widefield and TIRF (~10 2-6 photons/s) employ low excitation rates for SMLM schemes. In suchcases, excitation and fluorescence photons are infrequent and long photon acquisition times are
required to quantify blinking of FPs. Therefore, the detector is blind to the molecule entering or
exiting the S1 state, and the process needs to be modeled differently. To address this situation, we
devised an algorithm incorporating Monte Carlo methods with acquisition time steps longer than
excited-state lifetime but shorter than τGSR (~100 ms). This algorithm accurately represents oursingle molecule experiments, where excitation rates and acquisition timescales are comparable.
With this simulation algorithm, it is reasonable to assume that one always observes the FP in S0 or
D, and S1 is only rarely populated in our three-state model. The fluorophore starts from S0 or D
and returns to these states in each time cycle, and the probability of a state change in each cycle isdetermined by rate constants of radiative emission, internal conversion, DSC and GSR processes.
Our simulation of single molecule fluorescence correctly predicted the τON dependence on kEx and
kDSC, and the τOFF dependence on kGSR. By repeating multiple cycles of single molecule
simulations, the average on and τOFF can be obtained based on a probability density function of an
1

exponential distribution: 𝑓(𝑡) = 𝜇 𝑒 −𝑡⁄𝜇 (Appendix 3: Sections 5a-e). The model was thenextended to mimic ensemble behavior (Appendix 3: Sections 5f-g). When varying one rate
constant at a time, the ensemble dark fraction increases with increasing kEx and kDSC, but thefluorescence decay profile shows minor variation in the dark fraction even with 30-45% variationin kGSR. In other words, the dark fraction is controlled by factors affecting processes that populate
the dark state, and the rate-determining ground state recovery process dominates the time constantof the faster component of decay in the fluorescence bleaching profile. Thus, simulations in both
single molecule and ensemble average of RFPs qualitatively validated this three-state model.

96

We then developed a new method combining single molecule imaging and ensemble
photobleaching measurements of RFPs with low irradiances to quantitatively extract dark statekinetic parameters based on the three-state model. The lowest irradiance in our single molecule
measurements corresponds to an excitation rate of ~1000 photons/s. At such low irradiances, we
expect an emission of less than 100 photons per frame from the dimmer FusionRed (Appendix 3:
Section 7). The relatively long τON and low intensity-change thresholds for on to off (or vice versa)
state changes pose a challenge for data analysis under these conditions. For these low irradiances,conventional algorithms to binarize intensity traces inaccurately binarize on and off events due tothe low signal to noise ratios. Thresholding a change of state is a challenging step. [257, 262]
Instead, we used algorithms based on statistics of intensity variation across frames to predictpossible state change points and determine if a “real” on to off (or vice versa) event takes place.
[262] The analysis algorithm is also helpful to predict very short τON for the other extreme casewhere we use ~10-fold higher excitation rates. Outside sample preparation methods and efficient
data analysis algorithms, experimental analysis of such discrete states can also be improved withimproved camera technologies like photon-number resolving detections schemes. [263]
Additionally, to accurately determine on and off events, our algorithm screened out instanceswhere two molecules might fluoresce at the same time or the molecule undergoes permanent
photobleaching or denatures (extracts τOFF only when the event is bounded by an on time and viceversa). Moreover, it is worth noting that that the blinking rates are sensitive to the nature of theelectrostatic interaction between the binding surface and the molecule. Glass surfaces under
treatments like exposure to plasma are generally negatively charged prompting interactions withthe positively charged areas of the protein (Appendix 3: Section 8). [264] For example, the superresolution imaging modality FLINC (Fluorescence fLuctuation INcrease by Contact) is based on
variation of blinking frequency in TagRFP-T (by~25%) through the electrostatic interaction withanother non-fluorescent FP (Dronpa). [49] Assuming that FusionRed binds to the glass surface via
positively charged surfaces facing outward from the β-barrel, we may expect these effects to be
identical for FusionRed-MQ, which has only two internal mutations compared to FusionRed.
Therefore, this method of sample preparation might introduce artifacts to blinking dynamics in thecontext of comparing two FPs with dissimilar residues facing out of the β barrel structure.
Our data analysis algorithms revealed computed rate constants kDSC and kGSR obtained from τONand τOFF histograms, had minimal variation in the irradiance regimes examined for both FPs. The
97

value of kGSR can be accurately determined from the single molecule fluorescence dynamics
because the time resolution of the measurement, which is limited by the camera acquisition time,is smaller than the τGSR. Therefore, we conclusively determined that the kGSR for FusionRed is 1.3fold higher than that of FusionRed-MQ. We also verified our hypothesis that kGSR of both FPs is
independent of kEx under low irradiances. The kDSC values are, however, on the order of kHz,
which is ~2 orders of magnitude larger than the acquisition rate (Hz) of our single-molecule
experiment. While the kDSC values are in the range of expected values from previous
measurements, [56] and despite high precision, accurate values of kDSC under low irradiances had
to be determined by a different method. We used an eigenvector-eigenvalue approach to extract
analytical expressions for fluorescence decay from the kinetics of our three-state model and fit
ensemble biexponential bleaching traces to accurately estimate the kDSC. The fitting analysis
revealed a light-driven dependency for the kDSC (~1.5-fold increase in the kDSC with ~4-foldincrease in the kex) of FusionRed-MQ, whereas kDSC of FusionRed remained almost constant withincreasing excitation rate. While a degree of heterogeneity can be expected between singlemolecule measurements obtained from pure proteins and ensemble measurements in bacterial
cytoplasm, it is encouraging to note that FusionRed has low pH sensitivity in the neutral pH range
and the pH values of our imaging buffer and bacterial cytoplasm are close (~7.4 vs ~7.2–7.8 for
E. Coli). [265] Thus, we extracted quantitative estimates for the kDSC and kGSR by combining thestrengths of each approach.
Next, we consider the photophysics in the context of protein structure. The crystal structure showsthat Met residue at position 42 in FusionRed is located at the imidazolinone end of thechromophore. In FusionRed-MQ position 42 is substituted for a Gln residue, possibly altering thehydrogen bonding patterns at the acylimine end of the chromophore. [38] Meanwhile, the residue
at position 175 located above the phenol ring of the chromophore pocket; is a Leu in FusionRed
and is substituted to the larger sidechain Met in FusionRed-MQ. [30, 182, 200] The effects of these
two mutations on FusionRed’s brightness are complementary. Unlike the C159V mutation, Q42M
and L175M do not change the profile of the ensemble bleaching, likely preserving the efficient cis
to trans dark-state isomerization pathway. [38] It is interesting to note that the amino acid residue
analogous to position 175 in FusionRed influences the dark-state behavior of the two
photoconvertible FPs IrisFP and mEos4B (S173 vs F173). [237] De-Zitter and co-workers
demonstrated that F173 in mEos4B reduced the number of hydrogen bonds maintained by the dark98

chromophore in its green form compared to the smaller-sized but hydrogen-bonding capable S173
residue for IrisFP, providing an explanation for the reduced photoswitching contrast. [237] As
such, the kGSR values can help to identify a possible difference in barrier for dark to fluorescentstate interconversion (Figure 4.6) between FusionRed and FusionRed-MQ. The approximate
difference in the ground state barrier of bond rotation expected for a trans to cis isomerization canbe calculated using a transition state theory approach for interconverting ground state isomers.
[125] Under the assumption that the local temperature does not change on irradiation and a similarvalue of the pre-exponential factor, this difference in barrier (ΔΔG#) is ~ 20 kJ/mol for FusionRed
and FusionRed-MQ. A value of 20 kJ/mol is a reasonable free energy difference that predicts achange of a few possible hydrogen bonds, similar to what was observed for IrisFP, mEos4B andothers. [237, 266- 268] An energetic reluctance to switch back to the bright state can therefore be
explained by a conformationally restricted chromophore for FusionRed-MQ, suggesting amechanism for the higher brightness observed for the FusionRed-L175M variant. [30, 38]

Figure 4.6. Relating blinking to a cis-trans isomerization of the FR chromophore. (a.) The
spatial orientation of the L175 and M42 residues in the FusionRed crystal structure (PDB ID:
6U1A), with the cis and the trans forms of the chromophore. (b.) Schematic depiction of a possible
barrier for a ground state cis-trans isomerization depicting a switch from an off to an on state.

99

4.6. Conclusions
Bright RFPs with desirable biological properties have a growing role as strong candidates for dualusage both for SMLM-based imaging and widefield ensemble assays. [250] To address the latter,in this study we quantified the nature and timescales of dark state conversion and ground state
recovery for FusionRed and its 2.5-fold brighter progeny FusionRed-MQ. Our approach combined
single molecule imaging with ensemble bleaching measurements to extract kDSC and kGSR of these
RFPs. The methods applied in this work are an advancement over our and other previous studies
where rate constants were extracted using time and frequency domain measurements at several
orders of magnitude higher irradiances, which are often not suitable for widefield fluorescence and
SMLM-based imaging assays. [56] To the best of our knowledge, this is the first study to quantify
kDSC and kGSR directly under low irradiances relevant to modern SMLM imaging schemes like
SOFI. We verified our hypothesis that kGSR of FusionRed and FusionRed-MQ is independent of
kEx under low irradiances. This is contrary to high irradiance studies where kGSR was observed tovary with kEx. [229, 251] FusionRed is a plausible candidate for SMLM imaging, [253] and ourinvestigation suggests FusionRed-MQ is a better choice for such applications owing to its 1.8-foldhigher quantum yield and higher kDSC. [38] The methods and results of this work can be extended
to the characterization of other fluorophores with appropriate dark state kinetic models, orincorporated into multi-parametric screening technologies to select FPs with high rates of blinking
for methods like SOFI.

100

Chapter 5
Characterizing the pathways of non-radiative decay in the
lifetime evolution of a brighter variant of mCherry
5.1. Publication Note
Parts of this chapter have been adapted from the article titled “Directed evolution of a bright variant ofmCherry: Suppression of non-radiative decay by fluorescence lifetime selections.” by MukherjeeS., Manna P., Hung S.T., Vietmeyer F., Friis P., Palmer A. E., and Jimenez R. ChemRxiv 2022.
https://doi.org/10.26434/chemrxiv-2022-v3t03

5.2. Introduction
Fluorescence lifetime-based selections on fluorescent protein (FP) libraries, performed on cellscreening platforms such as microscopes or flow cytometers, have been key to the development of
the brightest genetically-encoded fluorophores. [39-41] For example, brighter variants of the red
FP (RFP) FusionRed have been generated with microfluidic cell-sorting. [30, 38] The brightest
RFP and cyan-FP (CFP) to-date, mScarlet ( = 0.70; τ = 3.9 ns) and mTurquoise2 ( = 0.93; τ =4.0 ns), respectively were also developed using lifetime selections on imaging platforms. [35, 77]
Although these lifetime selections have been unquestionably successful in generating brighter FPs
for imaging applications, the intermediates along the evolutionary trajectory generated by these
efforts have generally been set aside in favor of focusing on the final product of molecular
evolution. Although it is widely acknowledged that lifetime and other photophysical properties
such as photobleaching or spectral changes frequently co-evolve, a mechanistic investigation of
their interdependence has rarely been pursued. [250]In the GFP superfamily, the chromophore is formed when a tripeptide of the internal α-helix
embedded in an 11-stranded β-barrel undergoes rearrangement, cyclization, dehydration, andoxidation. [186, 269] This process results in a π-conjugated structure of p-hydroxybenzylidine andimidazolinone rings bridged through a methine carbon. In RFPs, the chromophore conjugation isfurther extended by a N-acylimine moiety that leads to a red-shift of the absorption and emission
spectra. [15, 92] A combination of electrostatic and steric interactions from surrounding amino101

acids tune the ground (S0) and the excited (S1) state potential energy surfaces of the chromophore,
thus influencing the pathways of excited state depopulation. [58, 62, 74, 82, 125, 270] As a result,the unique chromophore environment within each FP determines its fluorescence lifetime. Eachfunctional (i.e., properly-folded and chromophore-matured) FP generated by an engineering effort
provides an opportunity to examine a point within the evolutionary trajectory of fluorescence
lifetime and other photophysical properties. These properties may be correlated with a particularpathway across the mutational landscape. [271] The global photophysical assessment of anevolutionary trajectory therefore contains vital information that can inform strategies for FP
evolution. This is particularly relevant for developing a new FP tailored to a specific application
modality- whether it is fluorescence lifetime imaging (FLIM), Forster Resonance Energy Transfer(FRET), or multicolor widefield imaging. [272]Many theoretical and spectroscopic studies provide an emerging framework for understanding thefactors influencing molecular brightness of FPs. [58, 62, 74, 82, 125, 270]

However,understanding the reasons for interdependence of photophysical properties is a major challenge.
Observables such as fluorescence lifetime that directly report on excited state depopulation
timescales are sometimes found to be correlated with other photophysical properties that are lessdirectly related to these dynamics. For instance, in an attempt to find a bright, far-red emitting FP,
Canty et al. generated and sorted mutant libraries in bacteria by gene shuffling mScarlet, which
has a long fluorescence lifetime, with mCardinal, which has far-red emission (659 nm). Though
the investigators did not meet their original goal, their analysis revealed that fluorescence lifetimeand peak emission wavelength are inversely correlated. [66] We employed high-throughput
microfluidic screening on mOrange2, TagRFP-T and mCherry and found a similar inverse
correlation of fluorescence lifetime and emission wavelength. [40] Moreover, an inverse
correlation of fluorescence lifetime and photostability under constant irradiation also suggested
that increase in fluorescence lifetime leads to molecules bleaching faster, likely due to the higher
reductive potential of the S1 state. This study also showed that the correlation changed withincreasing irradiance, suggesting that mechanisms other than photodegradation from the S1 state
may be at play. An inverse correlation of the fluorescence lifetime and photostability was also
reported in our previous study of FusionRed variants (Chapter 3). [38] Further investigations arenecessary for gleaning mechanistic insights from these observations.

102Spectroscopic, computational, and crystallographic evidence suggest that chromophore planarityand protein rigidity are the primary characteristics of bright FPs. [16, 76, 273] Other investigators
have considered more subtle physical factors that influence brightness. [62, 82, 125] Using
physical models such as the Marcus-Hush theory, these studies focused on quantifying andunderstanding the role of the driving force in charge transfer between the two resonance forms of
the GFP chromophore in the ground and excited electronic states. [62] This driving force isvulnerable to electrostatic control from the environment, which regulates access to non-radiative
pathways of excited state depopulation, and therefore directly influences brightness. Analogous
studies of the RFP chromophore have not yet been reported. Park and Rhee utilized hybrid QMMM approaches to demonstrate the influence of electrostatic effects on controlling the nonradiative rate of GFP. [74] Their analysis revealed that electric fields control access tophotoisomerization channels which dictate ultrafast non-radiative decay. [74] For RFPs,
Drobizhev and co-workers demonstrated that the electric field pointing from the oxygen atom on
the imidazolinone ring to the oxygen atom on the phenol ring in the chromophore controls access
to twisted-intermolecular charge-transfer (TICT) states which promote ultrafast non-radiative
relaxation. [58] In summary, the control of non-radiative decay pathways is a major bottleneck in“brightening” FPs.
Despite its poor brightness, mCherry is a popular RFP for cellular sensing and imaging because of
its widespread availability in a plethora of fusion constructs. [274, 275] This monomeric RFP
traces its lineage from the naturally occurring tetramer DsRed. [276] The consequent engineering
strategies on DsRed resulted in a FP with high expression and fast chromophore maturation, lowphototoxicity, and a favorable red-shift of absorption and emission spectra. However, mCherry ismuch dimmer than its progenitor, primarily due to a three-fold drop in fluorescence quantum yield.
Previous attempts to develop brighter and red-shifted versions of mCherry have been unable torestore its fluorescence quantum yield to that of DsRed. [76, 174, 273, 277] In this chapter, we
present a monomeric variant denoted mCherry-XL (eXtended Lifetime: W143S, I161V, Q163Y
and I197R) which is 3-fold brighter than mCherry, and matches the molecular brightness of
DsRed. We provide insight into the evolution from mCherry ( = 0.22; τ =1.6 ns) to mCherry-XL( = 0.70; τ =3.9 ns). We analyzed functional RFPs with the longest lifetimes at two intermediate
steps in the evolution trajectory to assess co-evolution of other photophysical properties such as
absorption and emission wavelengths. As expected, we observe a near-linear response of103

increasing quantum yield with lifetime, along with blue shifts in the absorption and emission
maxima. Although the analysis of radiative rates reveals small but significant changes, it isprimarily the 6.5-fold reduction in the non-radiative rate that leads to the major increase influorescence lifetime. Furthermore, our analysis reveals the reductions in non-radiative rate are
not entirely due to the changes in the excited state reorganization energy or blue shifting of theabsorption and emission profiles. Our lifetime evolution trajectory agrees with the mechanistic
proposals of Drobizhev et al. and Lin et. al, who emphasize electrostatic and steric control of thechromophore, to minimize non-radiative processes beyond the scope of energy-gap-type models.
[58, 62]5.3. Methods and materials
5.3a. Mutagenesis, cell growth and sorting
Appendix 4; Sections 1, 2 and 3 describes our protocols for cell growth, sample preparation andsorting. Yeast cells (Saccharomyces cerevisiae BY4741) transformed with the pYestDest52 vector
containing FPs were used for lifetime-based screening with a microfluidic sorting systemdeveloped in our laboratory. [30, 38, 40, 41]

5.3b. Protein purification, in vitro measurements
Protocols for in vitro measurements have been provided earlier (Chapter 3). [38] In short, DNA of
selected FP variants from yeast were cloned into the bacterial p-Bad-His vector and protein was
extracted using Ni-NTA-based column chromatography. Steady state data for spectra, quantum
yield and extinction coefficient measurements were collected using a Cary 5000 UV−vis near-IR
spectrophotometer in the double beam mode for absorption, and a HORIBA Jobin Yvon
Fluorolog-3 FL3-222 instrument for fluorescence and excitation spectra. Fluorescence lifetime andanisotropy decay measurements were collected using a commercial time-correlated single photon
counting (TCSPC) system (Fluoro-time 100, PicoQuant) with a 560 nm pulsed laser diode headexcitation source and a repetition rate of 5 MHz using a spectral filter centered at 600 nm (60 nm
FWHM). The methods used in this measurement have been discussed in reference 5 and the details
104

of the fit and the instrument response function have been provided in the Appendix 4; Section 5.
[38] Samples were diluted using 1X-Tris-HCl Buffer (pH ∼ 7.4), and measurements were carriedout at optical densities (ODs) between 0.05 and 0.25 to ensure measurements fall within the linear
regime of the instrument response.

5.4. Results
5.4a. A 2.5-fold increase in lifetime is achieved using directed evolution
strategies on mCherry.
We utilized lifetime-based microfluidic cell sorting to direct the evolution of mCherry in S.
cerevisiae (Figure 5.1) to longer lifetime. First, we created mutagenesis libraries targeting residue
numbers 16, 17, 70, 99, and 197 (numbered with respect to mCherry PDB:2H5Q). The variant C12(mCherry I197R) was identified from the first round of selection. Next, a site-directed library on
variant C12 targeting positions 143, 161 and 163 (C12-X library) resulted in clones with lifetime
ranging from 1 ns to 4 ns (Figure 5.1b). A portion of this library was grown on plates and 20 brightvariants were selected on lifetime. One of these variants, C12-3 (mCherry W143I, I161C, Q163L
and I197R) was selected for further investigation. The C12-X library was then subjected to errorprone mutagenesis followed by another round of lifetime sorting with the sorting gate placed at
3.7 ns (Figure 5.1b). Selection of variants after this round of lifetime enrichment identified themutant “SLT-11” (mCherry N98S, R125H, F129L, Q137L, W143S, I161V, Q163Y, and I197R)
with τ=3.9 ns. Unfortunately, the SLT-11 variant had poor protein yield in bacteria compared toyeast cells. Therefore, mutations distant from the chromophore (>15 Å) were reverted to those ofmCherry (S98N, H125R/K, L129F and L137Q) to boost bacterial expression withoutcompromising the long-lifetime of SLT-11 (Appendix Figure A4.3). This process led to thegeneration of the quadruple mutant "mCherry-XL" (mCherry W143S, I161V, Q163Y, I197R),
which was further characterized. Details of library generation and protocols for mutagenesis havebeen provided in Appendix 4; Sections 1 and 2. The four FPs (mCherry, C12, C12-3 and mCherryXL) were characterized in vitro and in cellulo (Appendix 4; Sections 4 and 5). It was found thatmCherry-XL has a 3-fold higher molecular brightness and is 1.5-fold brighter in HeLa cells
compared to its progenitor mCherry (Appendix Figure A4.5).
105Figure 5.1. Directed evolution of mCherry resulted in variants with blue-shifts and increased
lifetime. (a.) The lifetime evolution trajectory from mCherry (τav =1.6 ns) to mCherry-XL (τav =3.9 ns), with intermediate clones (shown in filled circles) selected for photophysical analysis(barring the exception of SLT-11). SD and EP mutagenesis refer to site-directed and error-prone
mutagenesis respectively. (b.) Lifetime histograms of mCherry libraries at the different stages of
evolution. The lifetime histograms characterize libraries expressed in yeast cells screened on a
microfluidic platform developed in our laboratory. [30, 38, 40, 41] The number of cells screenedin each panel were 52382, 24998 and 25617 for C-X, C12-X and EP-C12-X library respectively.
(c & d.) Absorption and fluorescence lifetime decays of the variants. The arrow in c indicates blueshift in the absorption of the variants compared to their precursor mCherry.

1065.4b. Improved brightness is primarily achieved by suppressing the rate of nonradiative relaxation.
We performed in vitro photophysical measurements on mCherry, C12, C12-3, and mCherry-XL(Table 5.1). Fluorescence lifetime decays were fit to the appropriate exponential decay functions(Appendix Figure A4.10). Except for C12, a shift from multi-exponential to a mono-exponential
decay is observed in this series, where the amplitude and the time constant of the major decay
component both increase. The timescale of the shorter component (~1 ns) is approximately thesame for all four variants (Table 5.2). Fluorescence anisotropy measurements on these FPs
revealed rotational diffusion constants similar to those of monomeric proteins like mCherry,indicating that the mutations did not lead to dimerization or higher order oligomerization(Appendix Figure A4.9).
Table 5.1. Spectral and photophysical properties of the mCherry variants. Error bars indicate
standard deviations from triplicate measurements. Details of the experimental methods have beenpresented in Appendix 4; Section 5.
λabs

Eabs

λem

Eem

Stokes shiftLifetime(nm)(cm-1)(nm)(cm-1)(cm-1)(%)(ns)

mCherry

587

17036

609

16420

615

22 (ref)

1.67  0.07

76000  7000

C12

572

17483

608

16446

1035

24  12.05  0.05

69000  3400

C12-3

571

17513

599

16694

819

40  1

3.15  0.05

59000  4000

mCherry-XL

558

17921

589

16978

943

70  2

3.86  0.05

72000  4000

Variant107

εmax (M-1cm-1)

Table 5.2. Fit parameters for fluorescence lifetime measurements (decay traces and fits inAppendix 4; Section 5c) along with amino acids at the four positions comprising the sequencevariation (full sequences in Appendix 4; Section 3).
τ1

a1

τ2

a2

τ3

a3

τav

(ns)

(%)

(ns)

(%)

(ns)

(%)

(ns)

mCherry

1.7

83

0.95

17

-

-

C12

2.6

64

1.1

29

0.3

C12-3

3.4

93

1.1

7

mCherry-XL

3.9

97

1.1

3

Variant

143

161

163

197

1.6

W

I

Q

I

7

2.0

W

I

Q

R

-

-

3.2

I

C

L

R

-

-

3.9

S

V

Y

R

The fluorescence quantum yields of these FPs show a clear correlation with the average
fluorescence lifetime (Appendix Figure A4.12a), though the trend is not perfectly linear. [38, 250]
The two-fold decrease in the half-life of photobleaching with a 2.5-fold increase in fluorescence
lifetime also follow expected trends, agreeing with observations of higher photobleaching for FPs
with longer fluorescence lifetimes (Appendix Figure A4.6 & A4.7). [38, 250] Additionally, a linear
fit (Radj2=0.95) of the lifetime and quantum yield resulted in a slope of 150 ± 14 µs-1. Based on therelation, = 𝑘𝑟 ∗ 𝜏(1)this slope corresponds to the rate constant of radiative decay or kr. One can also calculate theindividual rate constants for kr and non-radiative rate (knr) for these FPs using equation 2. These
values are presented in Table 5.3.
𝑘

 = (𝑘 +𝑘𝑟
𝑟

𝑛𝑟 )

(2)

Although the 1.3-fold variation in the values of kr seems minor, the values lie outside the range
predicted by the linear fit (Appendix Figure A4.12b). The value of kr can be explained by the
Strickler-Berg equation, which relates radiative rate to the peak extinction coefficient and peakfluorescence frequency. [60, 250] The small variation in kr is further corroborated by theobservation that the peak extinction coefficient for this series only varies 15% from an averagevalue of εmax Avg ~70000 M-1cm-1. This variation is modest compared to a 1.5-fold increase of εmax
108

observed for FusionRed variants reported in our previous study. [38] However, the variation in kr
can also be attributed to the use of an average lifetime value to represent the multi-exponential
fluorescence decay kinetics. The multiple timescales may reflect the presence of multiple
chromophore conformations with differing absorption cross-sections. This is bolstered further by
the poor linear fit between the cubed value of the emission frequency and the estimated k r. Thisfrequency dependence of the radiative rate, predicted by the Strickler-Berg equation, is expected
to yield a linear relationship for chromophores with relatively narrow fluorescence spectra(Appendix Figure A4.12c). [60, 61, 250] Most significantly, we found the value of knr undergoes
the largest change (a 6.5-fold decrease) across this series. A consistent blue-shift in the absorption
and emission peak wavelengths with higher brightness, correlated with this decrease in knr led us
to investigate models that could explain this observation.

5.4c. Lifetime evolution suppresses non-radiative mechanisms beyond theconstraints of an energy-gap.
We first considered an Arrhenius-type dependence of the non-radiative rate constant with thetransition energy, as one might expect from an “energy-gap law” (Appendix Figure A4.13). [66,67, 76] Accordingly, we assumed a single absorbing and emitting species, a lack of excited state
photochemistry, and adherence to the mirror image rule of excitation and emission spectra. Under
these assumptions, we estimate the 0-0 transition energy gap (ΔE00) for each FP from theintersection point of the absorbance and the fluorescence spectra (Appendix Figure A4.14).
However, it is found that the change in non-radiative rate with ΔE00 is not a perfect fit for the
expected exponential dependence. Additionally, we noted the Stokes-shift of mCherry (616 cm-1)
is smaller compared to FPs with the I197R substitution (~900 cm-1). This observation encouraged
us to examine models that consider the role of the excited state reorganization energy in addition
to the energy gap. Englman and Jortner’s treatment of non-radiative rate in terms of the electronicenergy gap (ΔE), the excited state reorganization energy and vibrational frequencies provides abroader foundation for understanding nonradiative transition rates than the energy-gap law. [69,278] Their theory assumes that the electronic transition (S1 to S0 relaxation) is coupled to themolecular vibrations and the environmental fluctuations of the bath. The highest-frequency
vibrational mode in the excited electronic state serves as the primary path for non-radiative109

relaxation based on its coupling strength. The various limiting cases of the theory apply to strong
and weak coupling in high and low temperature limits. [69, 278, 279] The strong coupling limit isapplicable to systems with a large reorganization energy. In the weak coupling limit, where therole of the energy gap is dominant, the model considers a parameter γ that quantifies the role ofthe excited state reorganization.
The sum of mode-specific reorganization energies of the chromophore and bath nuclear motions
is the reorganization energy (λ), which is typically assumed to be half of the experimentallymeasured Stokes shift (SS: Stokes shift). [280] However, this approximation is accurate only forsystems with Gaussian absorption and fluorescence spectra. FPs in this study also exhibit a visible
0-1 vibronic sideband along with the primary 0-0 transition, and therefore deviate strongly fromGaussian lineshapes (Figure 5.1c). Thus, we utilized a model provided by Jordanides et. al toestimate an upper limit for the reorganization energy from the spectra (Details in Appendix 4;
Section 7). [72] The only assumption in this model is that the dielectric medium follows linear
response. In this approach, the reorganization energy (SM: Spectral Moment) is calculated fromthe normalized difference of the first moment between the absorption and fluorescence spectra
around the transition energy. The values of SM for mCherry and mCherry-XL are 812 cm-1 and924 cm-1, which are substantially larger than the corresponding values of 308 cm-1 and 472 cm-1
estimated from half the value of Stokes shift.
We employed these values of the reorganization energy in the Englman-Jortner low
temperature/weak coupling case, as appropriate for FPs where the 0-0 peak dominates theabsorption spectrum. [38, 69, 278, 279]
1 𝐶 2 √2𝜋𝑘=ℏ√ℏ𝜔𝑀 Δ𝐸

𝛾Δ𝐸

exp −(ℏ𝜔 )𝑀(3)Where k is the rate constant of non-radiative relaxation, ωM is the frequency of the normal mode
vibration of the highest frequency in the excited state of the chromophore, the parameter
Δ𝐸

𝛾~log(𝑑𝑒 ) – 1; d is the degeneracy and em is the reorganization energy of the high frequency𝑚vibrational mode in the excited state. We then set ΔE = ΔE00, dem= λ, and ωM = ωC-H Stretch = 3000
cm-1. To estimate the value of Herzberg-Teller coupling (C2), we assume the non-radiative
relaxation in mCherry-XL is entirely accounted for by the Englman-Jortner model (Table 5.3;

110

knrTotal = knrE-J). These approximations lead to an estimate for the C2 = 1.45x104 cm-2 using λSM andC2 = 7.19x105 cm-2 using λSS. The minimal (~10%) variation in the peak frequency and intensityof the 0-0 and the 0-1 bands in the absorption spectra for these variants allow us to assume aconstant value of C2 for the other members of the series (Appendix 4; Section 7b). Doing so, wefind small variations (of ~2%) for the pre-exponent and 𝛾 within a range of 2 to 3, which falls
within the range predicted by Englman and Jortner for weakly-coupled S1-S0 transitions. [38, 69,
278, 279] The results of this analysis are presented in Figure 5.2 and Table 5.3.

Figure 5.2. The non-radiative rate of the mCherry mutants obtained from the excited state
lifetime and fluorescence quantum yield plotted as a function of fluorescence lifetime. (a.)
The non-radiative rate calculated with the low-temperature/weak-coupling limit of EnglmanJortner formalism (knrE-J , Eqn. 3) [38, 69, 278, 279] compared to the total non-radiative rate
(knrTotal, Eqn. 1&2) (b.) The difference between knrTotal and knrE-J of the variants, denotated as knrnon
E-J

shown in comparison to the knrTotal. The data in blue circles (with standard deviations) indicate

the experimental values of the knrTotal, whereas the data in gold and red indicate predicted values
from the Englman-Jortner relationship using the reorganization energies from the Stokes shift (λSS)
and the spectral moment methods (λSM) respectively. [72]111Table 5.3. Calculated rate constants of excited-state population decay.
ΔE00

λSS

λSM

kr

knrTotal(cm-1)(cm-1)(cm-1)(µs-1)(µs-1)

mCherry

16728

308

812

132 ± 5

C12

16965

518

987

C12-3

17104

409

mCherry-XL

17450

472

Variant

knrE-J (µs-1)

knrnon E-J (µs-1)

SpectralStokesSpectralStokesmomentshift

momentshift

467 ± 6

76

17

391

450

116 ± 6367 ± 6

180

233

187

134

878

127 ± 4190 ± 4

58

51

132

139

924

179 ± 676 ± 6

76

76

0

0

Due to the small variation in the pre-exponential factor, the exponential dependence of the knr on
the values of ΔE00 and γ dominate the value of the non-radiative rate in this model. [38, 69, 278,
279] We observe that knrE-J differs significantly from the total non-radiative rate (knrTotal) for
mCherry, C12, and C12-3. As a counter example, if the knrTotal in mCherry was a consequence ofthe energy gap and the reorganization energy (knrTotal = knrE-J), this model would have significantly
overestimated the knr for the brighter variants of this family. Thus, the net positive difference
between these two values (knrTotal - knrE-J = knrnon E-J), suggests mechanisms outside the scope of
non-radiative relaxation from reorganization and the energy gap might be operational in mCherry
and its variants, and this particular trajectory of lifetime evolution successfully suppresses thismechanism.

5.5. Discussion
We demonstrated that directed evolution of fluorescence lifetime in mCherry results in a brightfluorescent protein with a high quantum yield. The new “mCherry-XL” RFP is ~1.5-fold brighter
than mCherry in mammalian cells, and its lifetime and quantum yield are on par with those of
mScarlet, which is the brightest RFP to date. [35] The four mutations identified in this study arelocated close to the phenol end of the chromophore (Figure 5.3). The rotation of the phenol ring
about the methine carbon (P-Bond rotation) is considered to be important for non-radiative decay.
[58, 74] The spatial proximity of these mutations to the phenol moiety of the chromophore in112

mCherry-XL possibly impacts these motions. For example, substitution I197R was also seen in
mScarlet, and the positively charged side chain is an electron withdrawing moiety capable offorming multiple hydrogen bonded contacts at this end of the chromophore. [35] The crystal
structure of mScarlet (PDB: 5LK4) shows multiple hydrogen-bonded contacts for the residue R197
which results in a small dihedral angle for the P-bond in comparison to mCherry (2° vs 13°,respectively). Interestingly, all variants of mCherry after incorporating the I197R mutation
displayed a higher reorganization energy in comparison to mCherry. The C12 variant (mCherry
I197R) also exhibited a tri-exponential fluorescence lifetime decay. The charged nature of thesidechain at position 197 and the possibility of forming multiple hydrogen bonds may result in
multiple non-interconverting chromophore conformations as reported for FPs such as TagRFP675. [15] Additionally, the substitution Q163Y might have a similar role to play in the context ofthe phenol end of the chromophore. Q163 is a polar residue and the crystal structure of mCherry
indicates a weak hydrogen-bond of the amine group of this sidechain (3.3 Å) with the phenolic
oxygen on the chromophore (Figure 5.3b). Substitutions such as replacement of Q163 with anelectron withdrawing and positively charged K residue have been shown to increase lifetime andquantum yield in DsRed. [76, 277] In a recent report, the substitution W143S was independently
and computationally recognized in an effort to develop bright and red-shifted variants of mCherry,which yielded the bright red-shifted RFP, mSandy2 (λem = 606 nm; ϕ =0.35). [273] The crystal
structure of mCherry reveals an interaction of the indole ring on W143 with the amine group on
the Q163 residue (3.4 Å).
The minor but significant variation of the extinction coefficients in these variants is correlated withthe small variation of the radiative rates relative to the average value of radiative rate obtained
from a linear fit of the quantum yield vs. lifetime (Appendix Figure A4.12). This variation and theobserved multi-exponential fits for fluorescence lifetime decays suggests the possibility ofmultiple emitting chromophore conformations. Structural dynamics slower than the excited state
lifetime may lead to conformational diversity of environments that perturb the electronic structureof the chromophore and its radiative rate.

113

Figure 5.3. Insights from the crystal structure of mCherry (a.) The structure of mCherry (PDB
ID: 2H5Q). A detailed view of the chromophore (CRO) and the four positions identified in thisstudy for (b.) mCherry and (c.) and in-silico generated structure of mCherry-XL. The dashed lines
indicate the distances measured from the mCherry crystal structure. The in-silico structure was
generated using the mutator plugin of the VMD molecular modelling software. [28]The 3.2-fold increase in quantum yield across this evolution route is dominated by the reductionof the non-radiative rate which exhibits a 6.5-fold decrease across the series. The non-radiative
rates of the variants are correlated with the blue-shifts of their absorption peaks. A similarcorrelation of blue shift with increased lifetime was observed by Canty et. al, who were motivatedto develop a bright red-shifted FP by gene-shuffling the sequences of the far-red emitting
mCardinal with the bright red mScarlet. [66] They performed selections on the resulting library
based on the brightness of bacterial cultures in the 620 to 750 nm emission window. The selectedvariants displayed a near-linear correlation of the emission wavelength with the fluorescence
lifetime. They proposed an upper limit of 625 nm for the peak emission maximum of variants114

created by this method. Furthermore, they concluded that far-red emitting variants are susceptible
to a larger variation in spectral profiles than brighter, blue-shifted variants. Although these spectral
correlations are intriguing, they did not quantify or investigate the mechanism of non-radiative
decay.
The Englman-Jortner model has recently been invoked in discussions of fluorophore design. For
example, modifications to this model were used to explain the low brightness of shortwave infrared
fluorophores. [38, 69, 278, 279] Their low quantum yields are partially explained by the high nonradiative rates resulting from high-frequency vibrations coupled to small electronic energy gaps.
In contrast, when Drobizhev and co-workers plotted the values of the non-radiative rate on thelogarithmic scale against the fluorescence emission frequency for a few RFPs (namely mCherry,
XRFP, mPlum, DsRed2, eqFP670, and mScarlet), they found a poor agreement with the linear fit
expected by Englman and Jortner’s model (Appendix Figure A4.13b). [58] This disagreement
prompted them to consider population loss through a conical intersection seam from a twisted
intermolecular charge transfer (TICT) state. Furthermore, they analyzed the strength and directionof the local electric field from the imidazolinone to the p-hydroxyphenyl ring using classical twophoton excitation spectroscopy and recognized that the local electric field around the FP
chromophore controls access to the TICT states and hence can lead to ultrafast relaxation. Their
analysis revealed a smaller electric field from the imidazolinone to the phenol ring potentiallyleads to a higher quantum yield. This can be achieved by reducing electron density at the phenolichydroxy group through hydrogen bonds and electron-withdrawing contacts or by providing alarger electron density at the imidazolinone. These design principles corroborate findings from a
hybrid QM-MM study that revealed similar ultrafast pathways for non-radiative decay in the GFP
chromophore. [74] They also agree with the findings of Lin et. al, where stabilization of thenegative charge on the phenolic oxygen atom is achieved through hydrogen-bonds between T203
and the phenolic oxygen, and/or through R96 on the imidazolinone oxygen for the GFP
chromophore. Substitutions at these positions result in spectral shifts and changes in brightness.
[62] These observations agree with our results where substitution of a positively charged arginine
residue at the phenolic end of the chromophore in C12 variants suppressed non-radiative pathways,
resulted in blue-shifts and an increased Stokes shift. Incorporation of other amino acid residues
with hydrogen-bond forming side chains, e.g., serine and tyrosine in mCherry-XL resulted infurther decrease in the non-radiative rate. Our efforts possibly led to the suppression of relaxation
115

pathways that contribute to the value of knrnon E-J. While studies by Drobizhev et. al. and others
provide foundations of these mechanisms for non-radiative pathways in FPs, [58, 62, 74] they did
not address the impact of lifetime based directed evolution on the pathways of excited state
depopulation.
In this study, we employed the Englman-Jortner theory to model the variation in non-radiative rate
for a closely-related RFP series selected through lifetime based directed evolution. [38, 69, 278,
279] We examined whether the reduction in non-radiative rate can directly be related to the energy
gap and the excited state reorganization energy. We approximated the 0-0 transition energy gap
using the intersection point of the absorption and the emission spectra, and the upper-limit ofexcited state reorganization energy using a model provided by Jordanides et. al. [72] Furthermore,assuming the entire component of the observed non-radiative rate in mCherry-XL was from thisformalism, we estimate a knrE-J value for the other members of this series. The intriguing outcomeof this analysis revealed almost a 6-fold lower knrE-J than calculated knrTotal for mCherry. Thoughless pronounced, this observation held true for C12 and C12-3, where this model could only
estimate half or less for the values of the calculated non-radiative rate. One also arrives at similar
qualitative outcomes using the traditional method to estimate reorganization energy using the
Stokes shift and repeating this analysis. In such a case the knr E-J is >20-fold lower than the knrTotal
for mCherry. This analysis reveals a large component of non-radiative relaxation is outside therealm of the energy-gap and is suppressed using lifetime selections. This result is consistent withthe ultrafast non-radiative decay mechanisms predicted by Drobizhev et. al and Park et. al. [58,74]
The development of highly emissive fluorophores frequently involves engineering theenvironment around the chromophore to make it more rigid or more viscous. [281] An issue thatarises in connection with this topic is how to probe or quantify molecular rigidity with
spectroscopy (i.e. with parameters beyond the ultimately desired high brightness or emission
yield). One approach which has been suggested is to regard the Stokes shift, as a measure offlexibility. In principle, the Stokes shift can be calculated from the first moment of the spectral
density of modes, 𝜌(𝜔) coupled to the optical transition. This 𝜌(𝜔) function, which can bequantified with time-resolved electronic spectroscopies such as photon echo techniques, represents
the vibrational density of states of the system weighted by the coupling to the electronic transition.
116

To the extent that frequency changes in the vibrational density of states reflect changes inflexibility, e.g. a shift towards high frequencies corresponds to higher rigidity, this change will bereflected in the Stokes shift. This approach to quantifying rigidity of a ligand-binding site wasdemonstrated using three-pulse photon echo peak shift measurements on antibody-antigen
complexes, where decreases in flexibility were correlated with higher affinity binding due tospecific protein-ligand interactions. [73]In this view, a decreased Stokes shift can be interpreted to reflect a reduced flexibility of theenvironment, if the mutations do not strongly perturb the chromophore electronic structure. [282]This idea is central to the weak-coupling case of the Englman-Jortner theory which predicts adecreased non-radiative rate with the decrease in reorganization energy. [38, 69, 278, 279]
Unfortunately this straightforward picture of rigidifying the protein environment around thechromophore may be complicated by the strong interactions of the environment that perturb thechromophore electronic structure. For example, the mutation I197R in mCherry increases the
Stokes shift despite a decrease in non-radiative rate. In contrast, an evaluation of the electro-opticalproperties of the GFP chromophore revealed that blue-shifted absorbers have larger Stokes-shift
values. This is in-part due to a larger driving force between the two resonance forms of thechromophore. [62] Another striking counter-example is provided by AsRed2, which has only a~5% fluorescence quantum yield, despite having a very small Stokes shift (~470 cm -1) andabsorption and emission peak wavelengths similar to those of several bright RFPs (λabs= 572 nm
and λem=592 nm). [283] Although the low apparent brightness of this FP might be attributed to aninaccurate measurement of quantum yield owing to the kindling qualities of its parent asFP595,
closer examination of other FPs with small quantum yield and modest Stokes-shifts is warranted.
It is also interesting that other examples of fluorescence lifetime evolution do not show the same
spectral trends observed for mCherry-XL. For example, consider the evolution trajectory in thedevelopment of FusionRed-MQV (FR-MQV). First, a small but significant (70 cm-1) decrease in
Stokes shift resulted from the M42Q mutation in FusionRed. [38] Subsequently, the FR-Q, FRMQ and FR-MQV variants had similar values of the Stokes shift (~570 cm-1) although consistentdecreases in the non-radiative rate (ultimately resulting in a 60% overall decrease) were observedwith increased lifetime. Another example is provided by mScarlet and mScarlet-I, which havenearly identical 0-0 transition energies and nearly the same Stokes shift, yet the latter has a two117

fold higher non-radiative rate. [35, 38] Consequently, strategies beyond rigidifying thechromophore are necessary for the design of brighter FPs. [273]
These considerations suggest that large variations in absorption and emission wavelengths are
possible for anionic RFP chromophores with similar values of lifetime and quantum yield, because
the non-radiative rate does not depend exclusively on the transition energy gap. The RFP mScarlet
is red-shifted by 10 nm (or 315 cm-1) in maximum absorption and by 6 nm (or 272 cm-1) inmaximum emission compared to mCherry-XL, yet it matches its quantum yield and fluorescence
lifetime values. [35] The two FPs also exhibit nearly identical single exponential fluorescence
lifetime decays measured using TCSPC. While the 0-0 transition energy is red-shifted by 200 cm1, the Stokes shift for mScarlet is 280 cm-1 smaller than that of mCherry-XL. This suggests thepossibility of either red shifting mCherry-XL by reducing the Stokes-shift (while maintaining its
quantum yield) or increasing the quantum yield of mScarlet by reducing its red shift. These
properties are observed in AusFP1, which has a 2.7-fold smaller Stokes shift and a 1.6-fold higher
quantum yield in comparison to EGFP, with the same tripeptide responsible for chromophore
formation. [36] Such observations suggest the possibility of designing FPs with higher brightness
without compromising on the red-shifted absorption and emission as theoretically predicted by thework of Moron et al. [92]5.6. Conclusions
The race to develop bright and red-shifted fluorophores continues to drive FP engineering to newer
technologies and selection schemes. Lifetime based evolution is now an established approach fordelivering bright FPs such as mScarlet, mTurquoise2 and FusionRed-MQV. In this study, lifetime
evolution provides a bright FP in the form of mCherry-XL and reveals the consequent co-evolutionof spectral shifts, increased quantum yield, subtle changes in the radiative rate constants and very
different mechanisms of suppressing non-radiative pathways. Our results strongly support recent
advances by the community to understand the pathways of non-radiative depopulation of FP
chromophores that lie outside the description of the energy gap. Moreover mCherry, C12, C12-3
and mCherry-XL have average fluorescence lifetimes of 1.6, 2.0, 3.2 and 3.9 ns respectively withminimal green-absorbing or emitting species, (Appendix Figure A4.8) which makes them suitable
118

for multi-color FLIM based imaging. Additionally, we do see promise in using mCherry-XL as atemplate for future engineering and a probe for imaging. Four amino acid substitutions on themCherry sequence can offer solutions in the form of mCherry-XL for constructs and applications
that are limited by the brightness of mCherry. Moreover, a blue-shifted absorption (~28 nm) for
mCherry-XL might improve performance relative to mCherry for many FRET related applications
where poor spectral overlap is observed between a green donor and a red acceptor pair. This study
also shows the strength of microfluidics-based lifetime selections to enrich populations with longer
lifetimes, as illustrated by the discovery of the SLT-11 variant in the EP-C12-X library. Tosummarize, the end-product of our selections drove us to a blue shifted variant mCherry-XL witha specific evolution trajectory based on lifetime. In a broad fitness landscape of mutations, ouranalysis reveals that there can be other evolution trajectories (such as the discarded clones withpoor brightness or maturation) with similar end products in terms of lifetime but with different
absorption and emission profiles.

119Chapter 6
Brightening FusionRed-MQV using lifetime selections
6.1. Introduction
Evolution of brighter FusionRed mutants through engineering of excited state lifetime wasdiscussed in Chapter 3. Several rounds of random, site directed and structure-based mutagenesis
strategies on FusionRed generated variants that displayed higher in vitro brightness, lowoligomerization tendency and high fusion efficiencies. Interesting outcomes such as the 1.5-foldincrease of extinction coefficient from the M42Q substitution, drastic changes to the propensity ofdark state conversion from the mutation C159V and a 2-fold increase in cellular brightness fromthe L175M mutation were observed for the FR variants generated in this effort. However, thebrightness in mammalian cell lines of many such mutants remained sub-optimal, which we
hypothesize is due to their slower chromophore maturation or lower levels of protein expression.
Libraries aimed at tackling the protein expression, folding and chromophore maturation in
mammalian cells would therefore expand the utility of such FR variants in cellular imaging.
Additionally, mutations at positions close to C159 can serve as templates for future librarygeneration efforts focused on improving the photostability or photoswitching properties of
FusionRed variants like FR-MQV.

Besides these attractive motivations to generate mutant libraries of FR, the presence of FPs suchas mScarlet and mCherry-XL motivate further investigations into the possibility of improving thebrightness of FusionRed. This goal can potentially be achieved by further suppression of nonradiative pathways in FusionRed-MQV through mutagenesis and lifetime selections. Therefore,
two independent approaches were taken to explore the possibility of further increasing the lifetimeand quantum yield in FusionRed-MQV. In this chapter, we discuss results from error-prone PCR
on FusionRed-MQV performed at varying error rates and further site directed saturation
mutagenesis libraries on positions 71, 159, 175 and 224 to generate variants of FusionRed that canmatch the quantum yield and lifetime of mScarlet and mCherry-XL.

120

6.2. Results and discussion
6.2a. Error-Prone PCR on FR-MQV
In our first approach, EP-PCR libraries of FusionRed-MQV were generated using the GeneMorph
II system (as described in Chapter 3 and Appendix 4) and FACS enriched. EP-PCR mutagenesis
was performed at low (~2 mutations/kb; at the nucleotide level), medium (~4.5 mutations/kb; atthe nucleotide level) and high error rates (~16 mutations/kb; at the nucleotide level) to see apossible diversity of brightness and lifetime. (Figure 6.1) The FACS enriched libraries werescreened on the droplet microfluidic device [41] at single-cell resolution.

Figure 6.1. Lifetime-brightness screens of the FusionRed-MQV (WT) before and after FACS
enrichment populations, for (a.) the high-error rate EP-PCR library, (b.) the medium error-rate
EP-PCR library and (c.) the low error-rate EP-PCR library. The FACS enrichment greatly enriched121

fluorescent population in the high-error rate EP-PCR library, which shows a 1.2-fold greater
variation (See Table 6.1) in lifetime compared to the wild-type encouraging future investigations
and lifetime directed sorting. Approximately 100,000 cells were screened for each library.

Table 6.1.

Mean brightness and lifetime for the FusionRed-MQV random mutagenesis

libraries screened in Figure 6.3. The fluorescence lifetime measured on the sorter is in frequency
domain represented by τFD.
Library (FACS Enriched)

Mean Brightness (V)τFD (ns)Lo

0.61±0.11

2.60±0.6Med

0.53±0.18

2.72±0.7Hi

0.51±0.11

2.73±0.9

FR-MQV

0.55±0.11

2.80±0.4

Despite the low variation in the mean brightness and lifetime of these populations, the consistently
higher spread of fluorescence lifetime is an encouraging indication of variants that outperform FRMQV with longer lifetimes and potentially higher quantum yields. In particular, a 1.25-fold larger
variation of lifetime is observed for the high-error rate EP-PCR library (Table 6.1).

6.2b. Site-directed saturation mutagenesis
Positions identified with random mutagenesis in the directed evolution efforts detailed in Chapters
3 and 5, such as L175M, can be further saturated to identify better steric or electronic fits(electrostatics or hydrogen bonding), thus further increase lifetime and brightness. [30] Therefore,
we employed saturation mutagenesis on some of these positions, to generate small libraries thatcan be screened with respect to lifetime on plates. Future evolution strategies can be formulatedon the basis of these preliminary investigations.

FusionRed-L175X Library
FusionRed L175M was previously recognized in [30], where we provided a proof-of concept forthe directed evolution of fluorescence lifetime. FusionRed-L175M was generated from an errorprone mutagenesis library on FusionRed, which yielded the clone FusionRed-1 (FusionRed;
V19I/L52P/L175M numbered based on FusionRed crystal structure; PDB ID: 6U1A). The
122

mutation L175M in particular was beneficial to the in vitro (1.2-fold higher) and in-cellulo (2-foldhigher) brightness for FusionRed. However, the position L175 was not saturated with all 20 aminoacid residues in that work. When this substitution was mapped on FusionRed-M42Q, which was
designed with guidance from crystal structure data and ultrafast spectroscopy experiments – itcarried over its favorable properties of higher brightness to the clone FusionRed-L175M M42Q.
[38] Despite saturating M42, we did not attempt to saturate L175M in that study, in an attempt toretain the favorable biological properties carried over by the L175 substitution. Consequently, thisposition was targeted with all 20 amino acids to generated variants with, for example, the positively
charged histidine, which led to a higher value of lifetime (2.35 ns) and quantum yield (40%). The
variants identified in this library, their fluorescence lifetime and spectral details are provided below(Tables 6.2 and 6.3).

Table 6.2. Lifetime measurements for the FusionRed-L175X clones. The fluorescence lifetime
measured in bacteria on the sorter in frequency domain are represented by τFD and in-vitro lifetime
measurements using TCSPC in the time domain are represented by τTD.
ProteinτFD (ns)τTD (ns)τ1 (%)

τ2 (%)

τ3 (%)

FR

2.03

1.75

2.55, 30

1.47, 70-

FR-L175R

2.06

1.83

-

1.99, 84

0.99, 16

FR-L175S

1.43

1.43

2.79, 15

1.29, 75

0.42, 10

FR-L175H

2.35

2.41

3.15, 50

1.83, 50-

FR-L175M

2.15

2.13

2.54, 47

1.70, 47-

Table 6.3. Spectral details for the FusionRed-L175X clones
Proteinλabs (nm)λem (nm)

Stokes Shift (cm-1)

FR (WT)

575

596

613

FR- L175R

576

601

722

FR-L175S

572

596

704

FR-L175H

568

588

599

FR-L175M

571

591

593

123

FusionRed-Q L175X1 C159X2 Library
Site-directed mutagenesis on C159, M161, V196, and H198 in FusionRed led to the identificationof the bright FusionRed-C159V (τ=1.96 ns and =31%) variant. [38] As discussed in Chapter 3,
this mutation was then mapped onto the bright FusionRed-MQ (τ=2.43 ns and =43%), resulting
in the bright variant FusionRed-MQV (τ=2.77 ns and =53%). [38] Unlike the position M42, theC159 position also had not been saturated in our previous effort. Therefore, to build on that study
and our library on FusionRed-L175X, which yielded the brighter FusionRed-H (L175H), wetargeted FusionRed-Q with a library targeting the positions L175 (with H/M) and position C159
(with all 20 amino acids). The clones were plate screened for lifetime and we identified that thevariant FusionRed L175H, M42Q and C159 (or FusionRed-HQC), which had a higher lifetimeand quantum yield (Table 6.5) in comparison to FusionRed-MQV. The variants identified in thislibrary, their fluorescence lifetime and photophysical details are provided below.

Table 6.4. Lifetime measurements for the FusionRed-M42Q L175X1 C159X2 clones. The
fluorescence lifetime measured in bacteria on the sorter in frequency domain are represented byτFD and in-vitro lifetime measurements using TCSPC in the time domain are represented by τTD.
τ1

τ2

τ3

(%)

(%)

(%)

2.79

3.19 (65)

1.69 (35)

2.3

2.43

3.41 (27)

2.19 (69)

2.4

2.36

3.30 (86)1.72 (14)

2.2

2.23

3.39 (28)

1.1 (64)

2.9

3.09

3.45 (88)1.66 (12)FR-HQG-

1.97

3.08 (35)

1.49 (57)

FR-HQH

2.6

2.71

3.13 (72)

1.66 (28)FR-HQD

1.9

1.64

3.47 (40)

1.77 (44)ProteinτFD (ns)τTD (ns)

FR-MQV

2.7

FR-MQG
FR-MQC(FR-MQ)
FR-HQVFR-HQC(or FR-HQ)

124

0.59 (4)0.72 (8)0.57 (8)0.65 (16)Table 6.5. Photophysical characterization for the FusionRed-M42Q L175X1 C159X2 clones
Stokes Shift

εmax

 (%)

τav (ns)

574

53

2.8

140000

583

546

59

3.1

127000

586

540

52

2.7

114000Proteinλabs (nm)λem (nm)

FR-MQV

566

585

FR-HQC565

FR-HQH

568(cm-1)(M-1cm-1)

FusionRed-MQV/HQ A224X1 and I71X2 Library
During the development of FusionRed-M, an alternate evolution pathway for extended lifetime
was discovered through the variant FR-13 (H25Y, V49I, F83Y and A224T). [30] Analysis of thisvariant revealed that the mutation A224T on FusionRed led to a 1.8-fold increase in fluorescence
lifetime and a 2-fold increase in quantum yield. This route was not pursued as the incorporation of
the A224T mutation resulted in poor maturation for FPs with this substitution. Additionally, therole of this position was also discussed in the effort to develop the bright mScarlet RFP (A218 numbered with respect to the crystal structure of mScarlet, PDB ID:5LK4). [39] In that study,
Bindels and Haarbosch mutated the position T74I on the α-Helix in mScarlet to generate the fast
maturing variant mScarlet-I. Exploring the crystal structure of these proteins indicated a potential
interaction between the two residues A224 and I71 in FusionRed and mScarlet (Figure 6.2).
Therefore, we saturated the positions A224 and I71 on FusionRed-MQV and FusionRed-HQC
with all 20 amino acids to generate a library of ~400 variants to be selected on lifetime. (Table
6.6) Lifetime based screening led to the identification of variants such as FusionRed-HQ A224T
and FusionRed-HQ A224T I71T, which exhibited high values of quantum yield (~75%) and long
fluorescence lifetimes (~4 ns). The variants identified in this library and their fluorescence
lifetimes are provided below (Table 6.6).

Figure 6.2. The crystal structures indicating the potential interactions of positions 224 and71 - (numbered with respect to FusionRed) in FusionRed (left) and mScarlet (right).
125

Table 6.6. Lifetime screens for the FusionRed-MQV/HQC A224X1 I71X2 clones. The lifetime
measured in bacteria on the sorter in frequency domain are represented by τFD.
Clone Name

71

224

τFD (ns)

FR

I

A

1.8

FR-MQV (WT)

I

A

2.8

FR-MQV-IQ

I

Q

3.2

FR-MQV-IG

I

G

2.7

FR-MQV-IV

I

V

3.6

FR-MQV-IL

I

L

2.5

FR-MQV-VA

V

A

3.3

FR-MQV-TA

T

A

3.2

FR-MQV-AA

A

A

3.5

FR-MQV-MA

M

A

2.9

FR-HQC (WT)

I

A

3.2

FR-HQC -IT

I

T

3.5

FR-HQC-TT

T

T

3.8

FR-HQC-VA

V

A

3.4

FR-HQC-LA

L

A

3.5

FR-HQC-CA

C

A

3.5

FR-HQC-AA

A

A

3.5

Table 6.7. Spectral properties for the high lifetime FusionRed-MQV/HQC A224X1 I71X2
clones.
τTD (ns) (%)εmax (M-1cm-1)

Brightness

krad (s-1)

knon-rad (s-1)

FR

1.78

24

94000

100

135

427

FR-MQV

2.78±0.06

53 (ref)

140800±9700

330

191

169

FR-MQV-VA

3.27±0.0464±196100±6500

273

196

110

FR-HQC3.17±0.1060±1118500±10500

316

189

126

Protein126

FR-HQC-T

3.50±0.01

68±2

65000

196

194

91

FR-HQC-VA

3.36±0.05

66±3123200±1500

360

196

101

FR-HQC-TT

3.74±0.0475±465600±14000

218

200

67

mCherry

1.67±0.07

22 (Ref)

75600±5000

75

137

488

mCherryXL

3.86±0.0570±272000±4000

223

179

76

mScarlet

3.87±0.07

71 (Ref)

104000±4000

327

186

72

These clones also revealed an interesting observation about chromophore maturation in bacteria.
Like the FR-13 variant, FPs that incorporated an A224T substitution suffered from poor
maturation. Whenever I71 and A224 were aliphatic residues (G, A, I, V and L) – higher
fluorescence was observed in cells. FPs such as FR-MQV-VA and FR-HQC-VA displayed higher
lifetime than the parental FPs (FR-MQV/HQC) and exhibited fast maturation, unlike clones such
as FR-HQC-TT. A summary of photophysical characterization of relevant FPs with highest
lifetimes selected from this library are summarized in Figure 6.3, Tables 6.7 and 6.8. As expected,
variants with high quantum yield and lifetime display a consistent drop in the non-radiative rate,
as seen for the mCherry variants presented in Chapter 5.

Table 6.8. Spectral properties for the FusionRed-MQV/HQC A224X1 I71X2 clones.

RFP

λabs (nm)

FWHM
(Abs)

λem (nm)

FWHM
(Em)

λStokes (nm)Stokes shift(cm-1)

FR

574

63

596

54

22

645

FR-MQV

566

55

585

41

19

575

FR-MQV-VA

565

57

582

40

17

515

FR-HQC

565

55

583

40

18

550

FR-HQC-T

566

54

583

39

17

515

FR-HQC-VA

566

55

585

39

19

575

FR-HQC-TT

566

57

583

38

17

515

127

We also performed excitation-normalized photobleaching measurements (with protocols describedin Chapter 3) in bacteria and observed that FPs derived from the FR-MQV lineage clearly show amono-exponential bleaching behavior. These variants retain the mono-exponential bleaching trend
by restricting the chromophore to switch from a fluorescent cis to a dark trans isomer. [38]However, FPs from the FR-HQC family show a bi-exponential behavior, characteristic of the wildtype FusionRed. [38] The time constants for the mono and bi-exponential fits are collected in Table
6.9, where one can observe very different values for the longer component of decay, which wehave previously assigned as the time constant of permanent photobleaching (tBL). Within FR-MQVand FR-MQV-VA, the tBL drops by 1.2-fold with a 1.2-fold increase in lifetime, which ischaracteristic of a reduction in photostability with an increase in fluorescence lifetime. These datasuggest that the dark state might be photo-protective for FPs with bi-exponential bleaching kinetics
because clones of the FR-HQC family with similar lifetimes as those of the FR-MQV family show
higher photostability. Additionally, it appears that FR-HQC-TT doesn’t follow the trend ofincreasing lifetime correlating with reduced photostability. This discrepancy is likely caused by aninaccurate photostability measurement possibly due to the high background noise seen due to thepoor expression/maturation in bacteria.

128

Figure 6.3. Photophysical characterization of the brightest clones from site-directedmutagenesis of FR-MQV and FR-HQC. (a.) The absorption and emission profiles of FR-MQV
variants (b.) The absorption and emission profiles of FR-HQC variants. (c.) The linearity of thequantum yield and lifetime of the FusionRed family in comparison to mScarlet. (d.) The
photobleaching traces of the long lifetime variants from FusionRed-MQV and FusionRed-HQC
under excitation normalized conditions (Irradiance ~5 W/cm2) with a 560 nm widefield excitation
source.

129

Table 6.9. Photobleaching behavior for the high lifetime FusionRed-MQV/HQC A224X1
I71X2 clones. tD and tBL denote the time constants of reversible and irreversible photobleachingobtained from fitting a photobleaching curve to exponential decay functions.

Dark StatetD(s)tBL(s)

FR

Yes

5.01±0.05

1445±169

FR-MQV

No

-

142±5

FR-HQCYes

5.12±0.03

347±3

FR-MQV-VA

No

-

121±1

FR-HQC-VA

Yes

3.84±0.04

163±1

FR-HQC-TT

Yes

2.41±0.04

299±8

RFP

We cloned these FPs into the piggyBac-H2B construct for expression in HeLa cells to test
mammalian cell expression using FACS. Despite an “apparent” increase in maturation/expression
for variants like FR-MQV-VA and FR-HQC-VA in bacterial cultures, these variants were ~2-folddimmer than the previously generated FR-MQV in mammalian cells. However, most of thesevariants were brighter than the wild type FusionRed. As expected, the FR-HQC-TT clone
underperformed significantly, quite possibly due to the A224T mutation. The results of this assay
are presented in Figure 6.4.

130

Figure 6.4. The brightness of FusionRed variants generated from FR-MQV and FR-HQC in
mammalian cells using FACS. FR-MQV still outperforms brighter FP molecules like FR-HQC
variants and FR-MQV-VA in mammalian cells despite lower values of quantum yield. The data
was collected on a BD FACSCelesta single cell analyzer with a TRITC filter set (585/30). Singlecell brightness was assessed by selecting single healthy cells based on forward and side-scattering
photon counts after 48 h of transfection. Untransfected cells were used as a control to backgroundsubtract and analyze the fluorescence in the red channel for the proteins of interest. The raw counts
were normalized with respect to the average number of counts for FusionRed. Each technicalreplicate (represented as black dots) consisted of a screen of ~20000 cells. The boxplots indicate
the distributions of values: the mean of the distribution is indicated by red solid squares; the bluebox indicates the 25th and 75th percentiles of the distribution. The solid line in the box indicatesthe median value of the distribution.

1316.3. Conclusions
Here, we attempted to utilize random mutagenesis on FusionRed-MQV at varying error rates inbacteria to explore the mutational landscape of this bright RFP. The larger diversity of lifetime
identified from the EP-PCR library screens and sorts revealed that further rounds of error-prone ortargeted mutagenesis can perhaps lead to brighter versions of FusionRed-MQV. As a consequence,
we attempted a targeted mutagenesis strategy that saturates positions identified in previous random
EP-PCR libraries on FusionRed. For example, we learned, reverting V159C in FR-HQV unlike
FR-MQV, results in a 20% increase in fluorescence lifetime. Moreover, libraries generated withthe saturated mutagenesis strategies here were small (20-400 unique variants), in comparison tobigger libraries generated in Chapters 3 and 5 (>1000). These libraries were screened and selectedfrom bacterial colonies on plates. This approach is tedious in comparison to single cell, highthroughput microfluidic screening. However, the fluorescence signal from individual colonies islarger, which results in better resolution of fluorescence lifetime, thus allowing for theidentification of dim clones with long lifetimes such as FusionRed-HQC-TT. At single cellresolution, the low signal to noise from clones that show poor expression or maturation in cells
can lead to unnecessary rejections even for FPs that display high molecular brightness. [62] Theseclones are important resources to understand the physical processes that dictate fluorescence.
Detailed characterization of the physico-chemical environments of such variants provide excellent
opportunities to foresee principles or design strategies that can lead to the development of brighter
fluorescent tools. Such strategies can be applied outside the realms of fluorescent proteins fromthe GFP superfamily. [23] Biochemical issues pertaining to the expression or maturation can betackled independently, through efforts targeted to improve solubility, expression or maturation.
[36]

These efforts confirm that lifetime selections consistently reduce the non-radiative rate and remain
the primary pathway for brightening an FP by increasing the fluorescence quantum yield.
However, unlike the mCherry family, the role of reorganization energy and energy gap in thesevariants seems minimal. The absorption and emission wavelengths for the FR-MQV and FR-HQC
variants generated in this study vary by <5 nm, and the Stokes shift by <10%. As described in
Chapter 5, the Stokes shift (or the reorganization energy) can be treated as a measure of132chromophore flexibility or the environmental rigidity, provided that the electronic structure of thechromophore is not dramatically perturbed. A ~2-fold drop in the non-radiative rate is seen forbright variants like FR-HQC-VA in comparison to FR-MQV, yet the absence of a consequent
response on the spectral parameter like the Stokes shift inherently becomes a problem of interest.
Additionally, we again see the saturation of the fluorescence quantum yield at the ~75% mark for
the FusionRed family. The brightest RFP in literature mScarlet and the brightest variant from the
mCherry family, mCherry-XL also saturate around the same values of lifetime and quantum yield.
Such observations can suggest the potential saturation of fluorescence lifetime and quantum yieldaround a theoretical limit, which warrants independent and necessary investigations.

133

Chapter 7
Future Directions
7.1. Development of a sorting platform on dark state conversion
As demonstrated in Chapter 2, our multiparametric high-throughput sorter system is capable ofscreening and sorting analytes on emission spectra, brightness and fluorescence lifetime. Chapter
3 and 4 discussed the role of dark state conversion on the ensemble and single molecule
photophysics of FusionRed variants at low irradiances. These dark state conversion and groundstate recovery processes are critical for applications in super-resolution microscopy such as SOFI.
[219] The effect of lifetime selections on the dark state conversion and ground state recovery
kinetics has not been studied.
Manna et. al demonstrated the phenomenon of Fluorescence Anomalous Phase Advance (FAPA)
for RFPs mCherry, Kreik and TagRFP-T. [56] Analogous to phase-fluorimetry, this spectroscopic
technique incorporates the use of intensity modulated excitation light. However, this method uses
lower modulation frequencies (kHz in comparison to MHz for phase-fluorimetry) which iscommensurate with the dark state lifetime instead of the S1 state lifetime. Instead of lagging behindthe modulated light, fluorescence signal appears to precede the excitation source in time, leading
to an “anomalous phase advance.” FAPA is a promising technique for probing dark state lifetime
as a unique frequency spectrum characteristic of the dark time can be generated by changing theintensity or modulation frequency (Figure 7.1). [56] This spectroscopic tool can potentially be
used to screen analytes based on dark state lifetime in flow. Addition of an excitation beam,
intensity modulated in the kHz regime can thus be used to provide a unique phase signature forthe dark time in FPs. Figure 7.1 displays simulation results that predict the signature of FAPA foran analyte flowing through a kHz modulated beam mimicking a possible in-flow experiment.
These simulations were performed using numerical solutions to a three state (see Appendix 5)model used previously in Chapter 4. To mimic the excitation in flow, the sinusoidal excitation
profile in time was enveloped on a Gaussian function. Correspondingly, the in-phase and out ofphase components of the fluorescence signal was used to extract a phase shift – simulating the roleof a lock-in amplifier for a frequency domain phase measurement.

134

Additionally, using square wave modulation instead of sine waves can provide an opportunity toinvestigate several harmonics of a sine function with a single excitation beam in flow, leading to
the formation of a phase spectra (Figure 7.1; Panels b and c). To validate this method, we used an
optical chopper to create 50 percent and 10% duty cycle square wave illumination, and thenextracted multi-harmonic phase information from pure proteins. Figure 7.2 depicts theexperimental setup schematic and Figure 7.3 depicts pure protein experiments, bolstering thevalidity of the approach.

Figure 7.1. The simulated phase signatures from RFPs. (a.) Phase advances observed for
mCherry, Kreik and TagRFP-T with dark times of ~ 0.2 ms, 1 ms and 2.8 ms for continuous
sinusoidal excitation at 5 kHz (labeled as “Cherry Sin”, “Kreik Sin” and “TagT Sin”) against the135same signal enclosed in a Gaussian profile emulating an in-flow screen (labeled as “Cherry ConvSin”, “Kreik Conv Sin” and “TagT Conv Sin”). (b. & c.) Phase shifts for mCherry with varying
dark times (DSC and GSR times) with a (b.) 50% duty cycle square wave and, (c.) with a 10%
duty cycle square wave modulation in a Gaussian envelope.

136

Figure 7.2. Off chip phase measurements. (a.) The experimental setup used for performing
preliminary phase advance experiments with square waves on pure FP samples in 1:10 FP Octanol droplets. (b.) Comparative measurements of RFPs excited with sinusoidal modulation at
multiple frequencies between 2-10 kHz versus one 10% duty square wave at 2kHz. FPs with longdark times and high dark fractions such as C4PB12 (mCherry variant) and TagRFP-T show higher
phase advances with both excitation schemes. Additionally, the amplitudes of excitation change137

for each harmonic in a square wave at a certain duty cycle. This results in subtle differences in thephase spectra acquired using the two excitation schemes presented above. (c.) Comparison ofphase advance observed in the dye Rhodamine-B (blue) versus mCherry (orange) using a 10%
duty cycle square wave. Rhodamine-B shows negligible dark state conversion in comparison tomCherry, which is reflected in the phase advance obtained from the frequency domain multiharmonic approach proposed here.

The experimental validity of this approach based on preliminary measurements provides exciting
opportunities to select FPs on dark times and dark fractions. A tentative design for a future darkstate conversion sorting device is provided in Figure 7.3.

Figure 7.3. Tentative design of microfluidic sorting device to be used for a dark state
screening platform.

1387.2. Optimizing bright variants of FusionRed and mCherry for
imaging applications
Over the course of this work, we developed FusionRed and mCherry variants with lifetimes
ranging from 1 ns to 4 ns and quantum yields from 20% to 75%. While the molecular brightnessof a FP is critical, the brightness in cells determines the utility of such molecules as imaging tools.
Bright FPs generated in this study such as mCherry-XL and FR-HQC-TT exhibit very highfluorescence quantum yields (~70%), but do not match the performance of mScarlet in cells. [35,38] This can be attributed to the expression and maturation kinetics of these FPs. Additionally, thechromophore maturation and expression problem in FPs is routinely addressed by targeting aminoacid residues on the FP molecule based on anecdotal or bioinformatics evidence. [35,37] Rarely
mechanistic investigations decoupling the kinetics of protein expression and chromophorematuration are pursued in such efforts. [35,37] On the other hand, considerable strides have led
protein engineers to concentrate on enhancing biochemical properties that govern cellularbrightness such as solubility, translation efficiency, protein folding, and chromophore maturation.
These efforts led to mGreenLantern, which is 6-fold brighter in mammalian cells than EGFP. This
increase in cellular brightness occurred without a noticeable change in molecular brightness whencompared to its predecessor, FP - Clover. [37] These approaches will be beneficial for convertingbright molecules such as mCherry-XL and FusionRed-HQC-TT to brighter tools applicable in cellbiology.
Balleza and co-workers were successful in quantifying the role of maturation kinetics in thecellular brightness of many FPs, yet a mechanistic investigation of the same was not pursued. [29]Moreover, the work did not address the problem of protein expression, which remains independentof chromophore maturation, and varies within contexts such as cell types (e.g, HeLa vs. yeast cells)
and constructs (e.g, fusions to other proteins). Most proteins exhibit a peak at 280 nm in theirabsorbance spectra - a signature of the tryptophan residues in the molecule. For the same numberof tryptophan residues, most FusionRed A224T variants displayed similar peak intensities at 280
nm. This suggests that expression levels of these FPs in bacteria (grown for the same period oftime) were similar to the wild-type, yet many variants displayed sufficiently lower peak values forabsorbance of the red-absorbing chromophore (considering the peak width and peak wavelength139are similar). This suggests that many FusionRed A224T variants suffered a maturation problem
over the expression problem. On the other hand, FusionRed-MQV-VA and FusionRed-HQC-VA
appeared to be brighter in bacteria yet did not match the cellular brightness of FusionRed-MQV in
HeLa cells. This brightness variability could be the result of an expression problem.
Focusing on the mutational landscape of the FP outside the barrel, for example, the N-terminus
and C-terminus tail, can reveal interesting insights. Shemiakina and co-workers swapped the Cterminus tail (a disordered chain of ~10-15 amino acids) of mKate2, to the tail of mCherry, toreduce the oligomerization tendency of mKate2. [188] This modification manifested in
reduced maturation rates, fluorescence brightness and pH stability for the generated variant
mKate2.5. To rescue the protein’s spectral and biochemical properties, several rounds of combinedsite-directed and random mutagenesis were performed, which led to the identification ofsubstitutions such as T75P and Q76P between the chromophore-carrying α-helix and the fourth βstrand which come near the C-terminal tail of the FP. This process subsequently led to theidentification of FusionRed which shows greatly improved maturation rates compared to
mKate2.5. [188]
Motivated by these observations, we performed preliminary all-atom explicit solvent classicalmolecular dynamics simulations with the NAnoscale Molecular Dynamics (NAMD) package on
mScarlet and mCherry. [284] Interestingly, we found the C-terminus tail was interacting with theouter side of the protein barrel in mScarlet across long timescales (~100 ns) and was fairly
inflexible in comparison to the mCherry’s C-terminus tail. Preliminary experimental data suggeststhat mutating residues on the C-terminus tail of mScarlet, significantly changes the chromophorematuration rate. These observations, if pursued, can form the mechanistic basis of understanding
chromophore maturation in FPs, and aide the development of versions of mCherry-XL and
FusionRed-HQC-TT for imaging applications.

140

Figure 7.4. Elucidating the role of the C-terminus tail in RFPs. (a.) The oligomerization
tendencies of mKate2 is driven by the C-terminus tail. The image has been adapted from the workof Shemiakina et. al [188] (b.) Snapshots from MD [284] simulations on mCherry and mScarlet
indicating a dynamic “flexible” C-terminus for mCherry and a “rigid” C-terminus for mScarlet.
Each simulation is a 1 µs run, with a structure snapshot captured every 50 ns. Red indicatessnapshots from the beginning of the simulation and blue represents snapshots taken in latertimesteps on the simulation trajectory.

141

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182

Appendix 1
This is an addendum to Chapter 2 and parts of this appendix have been adapted from the
Supplementary Information section of the article “Photophysical Engineering of FluorescentProteins: Accomplishments and Challenges of Physical Chemistry Strategies.” Mukherjee, S.;
Jimenez, R. J. Phys. Chem. B 2022. https://doi.org/10.1021/acs.jpcb.1c05629

Section 1. Optical layout and microfluidic device
1a. Optical Layout
The optical layout of the instrument is depicted in Figure A1.1.

Figure A1.1. Optical diagram of the microfluidic sorter. The excitation light sources are two
CW lasers with wavelengths 561 nm (green dashed line, Coherent Genesis MX) and 450 nm (Bluedashed line, ThorLabs L450P1600MM laser diode on a TCLDM9 temperature control mountshaped by a C230TMD-A f=4.51mm NA=0.55 aspheric lens). EOM is an electro-optic modulator(ThorLabs EO-AM-NR-C4) with a modulation frequency set to 29.5 MHz. PHP are a polarizer, a
half-wave plate and another polarizer. I1 is an iris with an adjustable pinhole size. CL is acylindrical lens with a focal length 150 mm. D1 (Semrock FF493/574-Di01-25x36) and D2(Semrock FF573-Di01- 25x36) are dichroic mirrors. The laser beams are directed into an inverted
objective lens (Olympus UPLSAPO 20X NA=0.75) under a 3-dimensional translation stage where
the microfluidic device is located. L1 and L2 are convex lenses, and F1 (Semrock FF01- 629/56)
183

and F2 (Semrock FF01-520/35) are band pass filters. PMT1 and PMT2 are photomultiplier tubes(Hamamatsu R9880-U-20). The far-red LED (dark red dotted line, Thorlabs M730D2) with a longpass filter (Thorlabs FGL715) allows one to visualize the flow on the Camera (Edmund EO23122M). BS is a 10:90 beam splitter (ThorLabs BSN10R). The green and red fluorescence signals
are shown with dotted green and red lines, respectively.
Both 561 nm and 450 nm continuous wave (CW) laser beams are the primary excitation beams to
induce fluorescence in the cells encapsulated in droplets. The 561 nm beam is focused into anelectro-optic modulator that can amplitude modulate the CW beam to a sinusoidal profile. The
half-wave plate and polarizers can be used to control the laser power and the polarization of thesinusoidally modulated beam. The 450 nm beam is spatially filtered using an adjustable iris (I1).
Both beams are directed onto a cylindrical lens CL that reshapes the circular beams to ellipticalones. The beams are directed into a 20X inverted objective lens using a dichroic mirror D1. The
epifluorescence from the sample staged on the objective passes through D1 into dichroic mirror
D2 that reflects the green fluorescence towards a band pass filter F2 and focused onto a
photomultiplier tube (PMT) PMT2, which is referred as the green channel. The red fluorescencethat passes through D2 and band pass filter F1 is focused onto PMT1 referred to as the red channel.
A far-red LED and a long pass filter are mounted above the objective lens, and the LED light ispartially reflected off a beam splitter and collected onto a monochrome USB camera to provide areal-time display of the system in flow.

1b. Microfluidic device
The microfluidic devices were fabricated in a clean room environment using standard soft
lithography techniques. The photoresist (MicroChem SU-8 3050) was spin-coated evenly on aclean silicon wafer according to the protocol provided with the photoresist SU-8 3050 aiming for
depth 50 µm. The coated wafer was illuminated with a uniform UV light source under an acetatemask printed with an inverted image of the device design that was created using CAD software asshown in Figure A1.2. The exposed wafers were baked shortly, rinsed with the developer(MicroChem SU-8 developer), and subsequently hard baked overnight according to the protocol
provided with the photoresist SU-8 3050. These wafers were exposed to (1H,1H,2H,2H-

184

perfluorooctyl) trichlorosilane (TCS) for more than 3 hours under vacuum for surface passivation.
Polydimethyl-siloxane (PDMS) pre-polymer and bonding agent (Dow Corning Sylgard 184) weremixed in a 10:1 ratio and around 20-25 g of the mix was poured to the master wafer that was laidflat on a petri dish to achieve devices that were ~4 mm thick. These were baked in an oven at 70ºC overnight to harden the PDMS. The PDMS slabs with the device design were cut out from themaster and holes for the tubing to be connected to the devices were punched under a clean room
hood. No. 1.5 glass coverslips and these slabs were washed with isopropanol and dried on a hot
plate at 75 ºC, and subsequently plasma cleaned their surfaces in a Reactive Ion Etcher (AXIC
PlasmaSTAR) with O2 plasma (50 W power, 50 SCCM and 5-10 sec exposure). The PDMS slabs
were bonded to the coverslips immediately after plasma cleaning and heated on a hot plate at 75ºC for a couple of hours, then were stored at room temperature for ~24 hours before filling theelectrode channels with In-Sn solder (In 52% and Sn 48%, melting point 118 ºC). Terminal pins
(Male, GT-150) were used to connect the solder filled channels with wire strips that can be clipped
to high voltage power sources that are necessary for DEP sorting. The pins are fixed to the devices
using epoxy glue to ensure a secure connection. Pneumatic pressure controllers (Parker
Electronics) were used to control pressure from cell and oil reservoirs that are connected to the
input channel of the devices.

Figure A1.2. Microfluidic chip design. The droplet formation and selection junctions areindicated within the solid red box and zoomed in. The laser beams are placed in the dashed blue
box to excite the fluorophores in droplets, where the dimension of the channel is 530 × 90 × 50
µm3 (length × width × depth).
185

Section 2. Instrument Operation Parameters
Excitation intensities for optical transitions are usually about 1-10 kW/cm2 for both beams. The
illumination is a Gaussian beam in the z- profile (out of imaging plane) and is elliptical in the x-yplane. The full width at half maximum (FWHM) of the elliptical beams have the dimension of~2.5 µm and ~4.5 µm in the in-flow direction, and ~45 µm and ~35 µm in the perpendicular
direction for 561 nm and 450 nm beams, respectively. The PMT voltages are usually set to be 1025 V. Electronically controlled pneumatic pressure controllers (Parker Inc.) are operated in therange of 0.5-5 psi for cell channel and 5-10 psi for oil channel in current chip configuration, whichallows uniform droplet generation at the frequency tested up to 4 kHz. All sorting modes are tested
for droplet frequencies up to 2.5 kHz in the current microfluidic chip configuration, and the droplet
volume for such operation frequencies is measured to be around 50 pL. To generate effective force
to sort droplets flowing at 1-2.5 kHz, 1.5 kV peak to peak pulses at 5 kHz frequency are appliedon the electrodes of the chip. The high voltage pulses applied on the electrodes are set to 2-5 µs
with variable delay time (>1 µs) allowing the droplet to travel from the last beam to the collectionwaste junction depending on the position of the last beam in the dashed blue box in Figure A1.2.

Section 3. Cell culture and sample preparation
For this study, FPs were expressed in the unicellular bacterial system, Escherichia coli (E. coli).
Bacterial systems offer high expression efficiencies and fast doubling times (~20 minutes) and arerobust systems for screening and selecting fluorescent proteins with improved photo-physicalproperties. Bacterial cells (Top10) are transformed with the plasmid DNA of a fluorescent protein
of interest and grown on agar plates with ampicillin resistance and arabinose for expression in an
incubator at 37 ºC overnight, then a single bacterial colony is selected and passed into a 5 mL LB
media with ampicillin resistance (referred as LB-amp) culture tube and grown overnight in a shaker
at 37 ºC, 230 rpm. 100 ul of this culture is then passed into a 10 mL of LB-amp flask and grownin the shaker at 37 ºC, 230 rpm for 3 hours till optical density (OD) ~0.6 at 600 nm, post whicharabinose is added to the culture for expression for 16 hours in the shaker at 28 ºC, 230 rpm. After
16 hours expression, 1~2 ml of cells is pelleted (8000 rpm for 2 minutes) and washed with aqueous
blank buffer (composed of 0.17% Nitrogen Base and 0.5% Ammonium Sulfate both in wt%), then186

diluted to desired concentrations determined by the absorbance of the re-suspended cell solution
in blank buffer at 600 nm. These cell solutions are filtered with sterile cell strainers (40 µm) before
being used for screening or sorting. Sorted cells are usually collected on a suspension in oil andadded to a flask with 25 mL LB-amp for overnight growth in a shaker at 37 ºC, 230 rpm, and canbe expressed for further analysis and sorting depending on the needs.

Section 4. Data acquisition and signal processing
4a. Characterizing scattering from droplets
The laser beam focused on the microfluidic chip using a cylindrical lens has a Gaussian intensity
profile I (x, y) with FWHM intensity spreads σx and σy as
2𝑥 2

2𝑦 2

𝑥

𝑦

𝐼 = 𝐼0 exp⁡(− 𝜎 2 − 𝜎 2 ), (1)where 𝐼0 is the peak intensity at the center of the Gaussian beam.
Droplets flowing through this beam result in scattering signals. Despite the presence of emission
filters some scattered signals of excitation light leak into the PMT. The scattered light is used toour advantage, for tracking droplet flow speeds and stability, counting number of droplets, andpair-matching two signals in green and red channels from the same droplet. Depending on theconcentration of cells used in an experiment – droplets can be filled or empty. Only scattering
signals are observed when the droplet is empty, but when the droplet contains a fluorophore – both
scattering, and fluorescence signals are recorded on the PMT. These cases may be represented by
Gaussian profiles that follow the intensity profile in time: the scattering signal Sc(t) from an empty
droplet, fluorescence signal Fl(t) and the total signal C0(t) from a filled droplet (assuming a 10:1
fluorescence: scattering) as presented in Eqs. (2 – 4). In an instance when a droplet is filled with asingle fluorophore, the signals are a convolution of the two functions. The ratio of scattering andfluorescence signals can be varied by adjusting the pump laser intensity, flow speeds, and the PMT
gains for an experiment.
𝑆𝑐(𝑡) = 𝑆𝑐0 exp (−187

𝑡2
2𝜎𝑠𝑡 2)⁡, (2)

𝐹𝑙(𝑡) = 𝐹𝑙0 exp (−𝑡2
2𝜎𝑓𝑡 2) , (3)𝐶0 (𝑡) = 0.1𝑆𝑐0 + 𝐹𝑙0 , (4)The distributions in time for the beams⁡𝜎𝑠𝑡 and 𝜎𝑓𝑡 are dependent on the flow speed 𝑣𝑥 , which inturn is related to the droplet generation frequency. An example of simulated and experimentallyobserved signals is shown in Figure A1.3.
𝜎𝑠𝑡 =√𝜎𝑥 2 + 𝑟𝑎𝑑𝑖𝑢𝑠_𝑑𝑟𝑜𝑝𝑙𝑒𝑡 2
, (5)
2⁡𝑣𝑥

𝜎𝑓𝑡 =

√𝜎𝑥 2 + 𝑟𝑎𝑑𝑖𝑢𝑠_𝑐𝑒𝑙𝑙 2
, (6)
2⁡𝑣𝑥

Figure A1.3. Simulated and observed signals of a filled droplet.

4b. Pair-matching
Our instrument has two beams in the current configuration and since we are interested inspectroscopic signatures from the same analyte from both beams, these two events need to be “pairmatched” in time. The pair matching event depends upon the flow speed. Either using a distribution
feature on the custom-built LabView program or through real time tracking on an oscilloscope wecan calculate the flow speed of droplets. A distribution tab on the program allows us to estimate

188the pair matching times, and a narrow distribution of pair matching times indicates a steady andstable flow. The distance between the two beams can be calculated through a camera image by acalibrated pixel to length conversion ratio. These allow us to calculate the flow speed of thedroplets in the system.
𝑣x =𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒⁡𝑏𝑒𝑡𝑤𝑒𝑒𝑛⁡𝑡ℎ𝑒⁡𝑏𝑒𝑎𝑚𝑠, (7)𝑃𝑎𝑖𝑟⁡𝑚𝑎𝑡𝑐ℎ𝑖𝑛𝑔⁡𝑡𝑖𝑚𝑒

Pair-matching events are schematically illustrated in Figure A1.4. For example, when theseparation distance of two beams d~250 µm and the pair matching time ~500 µs, the flow speedof the droplets is vx ~0.5 m/s. The averaged droplet counts per second from a single beam can beused to check whether the pair matching time is reasonable.

Figure A1.4. Pair matching events to estimate the transit time and the flow speed of thesystem.
Repeated measurements indicate that our droplets are around ~50pL, which gives the estimateddroplet sizes to be ~46 µm in diameter. Our analyte is usually an E. coli cell, which is roughly
assumed to be of the size of 5 µm in diameter. The FWHM of our beams on the device are usually189

~3 µm on the x-(in-flow) dimensions. Using eqns. (5) and (6), 𝜎𝑠𝑡 ~34 µs and 𝜎𝑓𝑡 ~ 25 µs. Thus, afluorescent signal usually has an FWHM of ~25 µs whenever it passes a beam when we have asteady flow velocity ~0.5 m/s.

4c. Raw Fluorescence Brightness
To operate the instrument in each mode, one needs to screen the distribution of empty droplets
signals to separate from droplets that contain the fluorophore. Then by subtracting the backgroundof empty droplets, one can estimate the distribution of the fluorophores in the respective
photophysical parameters that can be analyzed. The operation of the instrument to get the raw peakbrightness of an event is carried out in the following fashion.
•

The ADCs digitize the analog signals from the PMT.

•The data is then handled by the FPGA board.

•

FPGA starts a search algorithm if the data point is higher than threshold.

•

FPGA searches for the next 8 data points to see if they are above threshold.

•

YES: Peak detection – 8 continuous points above threshold. Selects the maximum as thebrightness reading from continuous data points above the threshold.

•

NO: Abandons peak search and looks for next point above the threshold.

Figure A1.5 exhibits an example of screening fluorescence brightness of E. coli cells expressedwith mScarlet, simulated signals and experimental signals output on an oscilloscope.

190

Figure A1.5. Comparing signals from filled and empty droplets. (Left) Fluorescence counts
obtained in Red channel shows the signals from empty droplets and mScarlet. (Upper right) Signals
simulated on MATLAB. (Lower right) Similar responses in flow are also noted real time on an
oscilloscope during an experiment with average number of cells encapsulated per droplet 𝜆=0.1(9.5% of droplets filled).

4d. Fluorescence Lifetime
For phase fluorimetry our laser is amplitude modulated in sine by the EOM. The modulation
frequency of the EOM is set to ν=29.5 MHz, (ω = 2πν) which resonates with the fluorescence
lifetime of fluorophores in the order of ns. The fluorescence signal is therefore also amplitude
modulated in time but is recorded with a phase delay and a lower modulation depth in comparison
to the reference signal. The phase delay corresponds to the average time a fluorophore spends inthe excited state before it emits a photon back to the ground state (eqn. (8)).
𝑡2

𝐹𝑙(𝑡) ∝ 𝐴⁡𝑚⁡sin⁡(𝜔𝑡 − 𝜙 − 𝛿)⁡exp (− 2𝜎 2 ), (8)𝑓𝑡

191The phase shift 𝜙 corresponds to the phase delay in the signal caused by the intrinsic fluorescence
lifetime of the analyte whereas the constant phase shift 𝛿 can be attributed to the delay of the signal
due optics, electronics etc.
1

𝜏 = 𝜔 tan⁡(𝜙), (9)1𝑚 = √1+𝜔2 2 , (10)𝜏In the experimental setup of the system, a biased-Tee filters the high frequency component (>83
kHz) of the signal from the larger gaussian envelope. The gaussian envelope is sent to a preamplifier (logarithmic/linear). The signal from the pre-amplifier is then digitized by the ADCs
and a peak of the signal is determined as discussed previously.
The high frequency component is fed into one of the input ports of the lock-in amplifier. A
reference signal is sent to the lock-in amplifier from a function generator that drives the EOM. The
lock-in amplifier calculates the in-phase (cosine component of the signals) and the out-of-phase(sine component of the signal) with respect to the reference signal, and the phase shift is calculated
from the inverse tangent of these two parameters.
It is critical to note that the phase value of empty droplets is usually a distribution that is close to
the mean of the total phase shift observed from delay due to the optical and electronic lines andthe offset value that sets the reference phase shift of a known RFP to be around 45 degrees.
Whenever a fluorescence event takes place, i.e., the analyte is in a droplet that passes the beam, an
intrinsic phase shift is observed that corresponds to the average fluorescence lifetime of theanalyte. Once the FPGA determines the peak fluorescence value, it picks up the corresponding
phase value that is reported by the lock-in amplifier through an auxiliary output on the lock-in
amplifier. However, the accuracy and stability of phase values are critical to many parameters
including
1. The low-bandpass filter for the signal inputs
2. The time constant (TC) of the corresponding filter
3. The spread 2𝜎𝑓𝑡 which is critical in determining the order of the low-pass filter and thetime constant of the UHF-Lock-in amplifier192

4. The PMT gain and the excitation intensity: the scattered signals are not negligible, if
fluorescent events are not very prominent, one can observe a skewing of the phase shift
towards the mean value of the empty droplets (see Example 2 below).
It is critical to note that the Equivalent Noise Bandwidth (ENBW) is dependent on the time
constant and the order of the filter in use. Lower order filters result in greater noise in the lifetime
measurements, but the wait times for the phase to stabilize to the 99% of the accurate values aremuch lower (as an example, see SRS-830 Lock-in-amplifier Manual).

(SRS-830 Lock-in-amplifier Manual)Hence it is critical that we select a filter and a time constant that provides us enough resolution inlifetime but does not require a long wait time. The noise reduces when the time constant increases,
but the wait time also increases. As flow speed is increased the transient time of the fluorescencesignal keeps dropping. Thus, it is critical to note that for a certain PMT setting and flow speed theappropriate time constant and the filters are selected for a reasonable phase resolution. Some
examples are shown below to illustrate the effects of these settings.
Example 1: A mixture of different fluorescent proteins (mCherry, Kriek and FusionRed-M) are
mixed and are screened in a chip that operates at a speed of 2 kHz droplet generation frequency.
The PMT was set at -650 V and the laser irradiance was at 75 kW/cm2 to obtain strong scattering
signals. The FWHM of the signal is around 25 µs, and the selection of a TC of 50 µs with an order
6 filter results in a noisy phase signal that is centered around the mean of the empty droplets. Thismeans that the FPGA does not pick up the right phase and the values are centered around the
distribution of the empty droplet. The results are shown in Figure A1.6 (a).
Example 2: The same flow settings were used with a time constant of 2.5 µs and an order 4 filter.
While the main populations of each RFP are distinguishable in the mixture, the heterogeneity inlifetime and brightness makes it difficult to distinguish each RFP clearly. Therefore, each RFP was
screened individually and plotted on the same scatter plot in Figure A1.6(b). The lifetimes could193be resolved but the scattering signals are also high due to the strong irradiance, resulting influorescence signals that are skewed in the lifetime axis. Here mCherry was selected as a reference
and its mean lifetime was set at 1.6 ns.

Figure A1.6. Screening results of a mix of mCherry, FusionRed-M and Kriek (K2C) from(a.) Example 1 and (b.) Example 2. The fluorescence lifetime is not resolvable in the settings of
Example 1, whereas the main population of each RFP is resolvable in Example 2 but the lifetime
data is skewed.
The major reason for the data skewing on the lifetime axis in Example 2 can be attributed to thefact that the scattered signals are comparable with the fluorescence signals. The scattered light isadded to the fluorescence signal and both signals have the same modulation frequency but different
phase shift values, so the lock-in amplifier extracts an averaged phase value from the combined
signals. Therefore, the averaged lifetime becomes closer to the actual fluorescence lifetime as thefluorescence brightness increases, but the influence from the scattered light becomes noticeable as
the fluorescence brightness decreases. A simulation of the reported phase values was carried out
by assuming the phase values being the convolution of the offset phase shift of scattered light (setto zero in this simulation) and different intrinsic phase shifts from fluorescence lifetime aspresented in Figure A1.7. As the fraction of scattered signal increases, i.e. the fluorescence isweaker, the measured phase shift of the total signals is skewed towards the phase of scattered light(zero phase shift).

194

Figure A1.7. Simulation of phase shifts obtained from a convolution of scattered andfluorescence signals. This qualitatively indicates the brightness dependent lifetime data observedin Figure A1.6. It clearly demonstrates the effect is more dominant for greater phase shifts andoperations at lower fluorescence: scattering.

4e. Calculation of lifetimes from phase shifts
The lifetime mode of the instrument works on the concept of phase fluorimetry based on relative
lifetime shifts. Therefore, lifetime characterization in the system needs a reference value forcalibration. In most cases either RhodamineB containing fluorescent beads or a fluorescent proteinof known lifetime is used as a reference lifetime value. We have used mCherry as the reference inmost of our measurements. mCherry is set to 1.7 ns as a reference.
The phase shifts are reported to the FPGA in terms of voltages that are digitized using an ADC
board. The least significant bit (LSB) value for the boards is 76 µV. The lock-in amplifier reports
every degree of a phase shift as +10 mV increments.
Given our resonant frequency is 29.5 MHz. Each degree of phase shift is expressed as195⁡⁡⁡ = ⁡1⁡ =1× 10−6 s,
360x29.5

and phase shift is expressed in LSB values,⁡⁡⁡(V) = ⁡(LSB) ∗ 76 ∗ 10−6 ⁡𝑉.
Equating the above two equations, = (LSB) × 7.15 × 10−4 𝑛𝑠.
Or the fluorescence lifetime of an analyte can be expressed as = (reference) + (LSB) × 7.15 × 10−4 𝑛𝑠.

Section 5. Performance of the sorter
5a. Two-color brightness sorting
The samples were prepared as described in Section 3 to obtain E. coli expressed with mScarlet and
EGFP. E. coli cells expressing mScarlet or EGFP were mixed in the proportion of ~1:1 before
sorting. The mixture was screened to obtain the mean brightness of mScarlet, then we sorted ~2000
droplets from ~105 droplets with the selection gate greater than the mean brightness of mScarlet.
The sorting process was repeated 2 times to collect totally 3 sorted samples. The sorted cells were
subsequently grown overnight and screened 16 hours after induction of expression. The screening
results are tabulated in Table A1.1.
Table A1.1. Screening results of sorting efficiency. The sorted cells were re-grown, expressed,
and screened for totally ~1000 cells.
# of trials# of EGFP# of mScarlet

Sorting efficiency

1

153

1016

87%

2

192

1057

85%

3

143

965

86%

196

5b. Lifetime screening with purified proteins
Three purified proteins, mCherry, mApple, and mScarlet, and an organic dye, Rhodamine B, wereprepared with concentrations about 10s µM to obtain brightness in the range comparable withcellular screening in the sorter. Pure proteins were prepared in Tris-HCl buffer (pH=7.4), andRhodamine B was dissolved in deionized water (pH~7). Fluorescence lifetime of each sample wasmeasured using Time-correlated Single Photon Counting (TCSPC), then transferred to themicrofluidic droplet sorter to screen for the fluorescence lifetime. The results are tabulated in Table
A1.2. The deviation between TCSPC and sorter measurements is due to the sorter averaging thephase shifts from the scattered excitation light and the fluorescence signals as described in Section
4. As the fluorescence phase shift (lifetime) being further away from the scattering phase offset,
the averaged phase shift deviates from the actual fluorescence lifetime more, in agreement withthe simulation shown in Section 4.
Table A1.2. Fluorescence lifetime measured in TCSPC and the microfluidic droplet sorter.
The lifetime of Rhodamine B was set as the reference for the sorter measurement, and theuncertainties are the standard deviations from ~25,000 screened droplets.
TCSPC Intensity weighted

Lifetime from frequency domain

lifetime in cuvette (ns)measurement in flow (ns)Rhodamine B

1.63

1.63±0.05 (ref)mCherry

1.54

1.58±0.09

mApple3.07

2.78±0.09

mScarlet

3.78

3.45±0.08

Sample5c. Lifetime-based sorting
The samples were prepared as described in Section 3 to obtain E. coli expressed with mScarlet andmCherry. In each batch of experiment, both cell solutions were grown from their single colony,thus there were two biological duplicates for each RFP in two batches of experiments. In the firstbatch of experiment, E. coli cells expressing mScarlet or mCherry were mixed in the proportionof ~1:1 before sorting. With one round of sorting on mScarlet, an 85% sorting efficiency was
obtained as described in the Chapter 2. In the second batch of experiment, E. coli cells expressing

197

mScarlet or mCherry were mixed in the proportion of ~40:60 before sorting. The mixture wasscreened to obtain the mean brightness and fluorescence lifetime of mScarlet and mCherry, thensorted 3,000 droplets from ~250,000 droplets with the selection gate greater than the mean
brightness and fluorescence lifetime of mScarlet. The sorting process was repeated 2 times tocollect totally 3 sorted samples. Another set of sorting was performed similarly by gating at
brightness and fluorescence lifetime lower than the mean of mCherry. The sorted cells were
subsequently grown overnight and screened 16 hours after induction of expression. The screening
results are tabulated in Table A1.3.

Table A1.3. Screening results of sorting efficiency. The sorted cells were re-grown, expressed,
and screened for ~50,000 cells
Sort for mScarlet

Sort for mCherry# of trials# of mCherry# of mScarlet

Sorting efficiency

1

9688

40030

81%

2

10745

39288

79%

3

9780

38522

80%

1

46799

1208

97%

2

50053

1833

96%

3

47740

1341

97%

Section 6. Enriching rare events
6a. Poisson distribution
The Poisson distribution for 𝜆 = 1 to 𝜆 = 10 are plotted in Figure A1.8. The probability of
encapsulated cells per droplet decreases quickly with the increasing number of encapsulated cells,
so the 𝑝𝐹 can be numerically calculated using n50 for λ≤10.

198

Figure A1.8. Poisson distribution for 𝝀 = 1 to 𝝀 = 10.

6b. Enrichment efficiency
The sorter with current microfluidic chip configuration is capable of enriching rare events from108 population within 3 hours without losing cell viability, when choosing 𝜆 ≥ 4. As the targeted
events become rarer, the enrichment efficiency varies depending on how many unwanted cells areencapsulated with the targeted cells in one droplet. We estimate the convergence of the enrichment
efficiency below.

Figure A1.9. Enrichment efficiency converges as the number of rare events increases.
199

Assume that there are totally n targeted cells in 108 population for enrichment. The droplet
encapsulation obeys Poisson distribution, we assume that there is only one targeted cell found ineach sorted droplet since they are rare events. This is only an approximation, but it does not lose
the generality in the convergence of enrichment efficiency. We simulate sorted n (n = 5, 10, 50,
100, and 1000) rare cells (i.e. droplets) by generating random numbers based on Poisson
distribution with 𝜆 = 4, as the numbers of cells encapsulated in droplets. Repeating the process 50
times for each case to attain a distribution of enrichment efficiency and the mean and standard
deviation, as plotted in Figure A1.9. The average enrichment efficiency is lower than the predictedvalues shown at Figure 2.6 in the Chapter 2, because this is only an approximation considering
only 1 targeted cell per droplet. The standard deviation is ~7% of the mean for enriching 50 cells
from 108 population, and ~5% of the mean for enriching 100 cells from 108 population. The results
indicate that the calculated enrichment efficiency can be expected when sorting 0.5~1 ppm of rare
events from 108 population. Please note that it does not limit the enrichment efficiency for sorting
smaller fraction of rare events. With smaller fraction, the enrichment efficiency may deviate fromthe expected value, but it still provides approximately same order of magnitude of enrichment. For
example, sorting 5 rare cells from 108 population, the enrichment efficiency varies between
approximately 15-50% in Figure A1.9, i.e. enriching rare events from fraction 10-8 to ~10-1
resulting in 107 times enrichment.

6c. Rare RFP enrichment
i. Enrichment of rare mScarlet from a mixture with EGFPThe estimated droplet size is approximately 50 pL, so E. coli cells expressing EGFP and mScarlet
were individually prepared at a concentration less than 2 x 106 cells/ml to ensure an average of 𝜆≤ 0.1 cell/droplet to screen and determine their mean brightness. To prepare the sample forenrichment experiment, the concentration of the mixed cells was estimated to be 5.9 x 107 cells/ml
for an average of 𝜆 = 3 cells/droplet encapsulation. A portion of the mixed cells were diluted toless than 2 x 106 cells/ml to ensure an average of 𝜆 ≤ 0.1, and was used to determine the fractionof mScarlet in the mixture being F~0.01 by screening ~10,000 mixed cells. The selection threshold
was set to be greater than the mean brightness of mScarlet. After one round of enrichment by200

sorting ~2,000 droplets with 𝜆 = 3 encapsulation, the sorted cells were subsequently grown,
expressed and screened with 𝜆 ≤ 0.1 encapsulation. The same process was repeated twice inparallel to obtain totally 3 measurements. The results are tabulated in Table A1.4. The mScarlet
population was enriched from F~0.01 to a weighted average 35±4%.
Table A1.4. The enrichment of rare mScarlet from a mixture with EGFP screened at a rateof 2 kHz.
# of trials

EGFP cells

mScarlet cells%RFP in mix

1

1785

1218

41

2

5109

2722

35

3

1070

299

22

ii. Enrichment of rare mScarlet from a mixture with mCherry
The sample preparation is similar to the mScarlet and EGFP mixture described above. The meanof fluorescence brightness and lifetime was determined by screening individual mScarlet andmCherry cells at 𝜆 ≤ 0.1. The fraction of mScarlet in the mixture before enrichment was estimatedto be F~5x10-3 by screening ~10,000 mixed cells at 𝜆 ≤ 0.1 for both batches of experiments. The
sorting gates were set to be greater than the mean of fluorescence brightness and lifetime ofmScarlet. After one round of enrichment by sorting ~2,000 droplets with 𝜆 = 3 encapsulation, thesorted cells were subsequently grown, expressed and screened with 𝜆 ≤ 0.1 encapsulation. We
attained an enrichment of the mScarlet population to 40% in the first batch of experiment. In thesecond batch of experiment, the same process was repeated 3 times in parallel to obtain totally 3
measurements. The results of the second batch of experiment are tabulated in Table A1.5. The
mScarlet population was enriched from F~5x10-3 to a weighted average 30±5%.
Table A1.5. The enrichment of rare mScarlet from a mixture with mCherry screened at a
rate of 2.5 kHz.
# of trials

mCherry cells

mScarlet cells%RFP in mix

1

31846

17623

36

2

29775

15519

34

3

32251

7750

19

201

Section 7. Directed evolution of an RFP library
7a. Site directed libraries and the sorting for bright mutants
We saturated mScarlet-I with the RRN codon that codes for R, D, E, K, G (2 copies), N and S
amino acids (see Table A1.6). The library size with equal probability for each available amino acidin this case is 88 possible mutants (~1.7x107). To ensure the search covering 95% of a library withequal probability for each available amino acid, at least 3 times of the library size must be screened,
which is >5.1x107 cells. [1]The library DNA was transformed to bacterial cells (Top10 strain), with a standard heat-shock
protocol. These transformed cells were added to LB+ampicillin (~7 mL) and grown overnight forthe cells to reach higher optical densities. 1.5 mL of this culture was then added to 100 mL
2XYT+ampicillin media, grown for ~2 hours to achieve an OD ~ 0.6. Arabinose was then added
to this culture to initiate expression of RFPs in the system. The library selection/sorting was carriedout ~16-20 hrs post induction to select mutants with fast RFP maturation.
Before each sorting round, the to-be sorted library was screened with low cellular concentrations
λ=0.1 to ensure single cell encapsulation in droplets in order to estimate the percent fluorescentcells in the given population. The first two rounds of sorting namely ‘S1’ and ‘S2’ were carriedout using multiple cells per droplet (λ=3 for S1 and λ=1 for S2), because each round had significant
non-fluorescent mutants. S1 and S2 led to significant enrichment of the library with fluorescentmutants. Then onwards, the library was sorted on two independent pathways at λ=0.1 with higher
thresholds in fluorescence brightness. The sorts were repeated to ensure library convergence. Afterevery sort, the cells in oil were transferred to a culture with 25 mL LB+ampicillin to growovernight, consequently, expressed in 100 mL of 2XYT+ampicillin for the next round of sorting.
A few ml of the re-grown cells from each sort were made into glycerol stocks stored at -80 °C for
future use.

202

7b. Sorting processes and results203

Figure A1.10. mScarlet library sorts with the instrument. (a) The progressive enrichment of
the library across the rounds of sorting. All samples were re-grown from their pre-sort glycerol
stocks for expression. (b) The lifetime and brightness screening plots of the post-sort S4A/S4B
and S5A/S5B sorting with respect to the wild type m-Scarlet-I population.

204

7c. Clones and photophysical characterization
We plated 5 plates of S5A and S5B respectively. Both S5A and S5B plates displayed mostly pinkcolonies. We picked 20 colonies of varying brightness with a check on lifetime using our lifetime
beam. All picked colonies had phase shifts that were very close to the shifts observed in mScarletI. We had also plated one plate from the S4B and S4A. Interestingly one of the S4 plates showed
a quick maturing bright colony. On sequencing it turned out to be unique and different from thewild type sequence, we named that clone S4-1 and purified it for further characterization. Fromthe 20 clones we picked from the S5A and S5B plates, we had converged to 2 clones. Both plates
had these clones 7:3 in one case and 8:2 in the other. This was sufficient evidence that our library
had converged from both pathways. We named these clones S5-1 and S5-2 and selected them forfurther photophysical characterization. The mutated amino acids of these clones are listed in Table
A1.6.
Table A1.6. The sequence of mScarlet-I mutants in the mutated positions.
Protein

114

119

121

147

164

174

196

198

mSc-I

E

I

K

T

A

L

D

K

S4-1

L

I

K

T

S

S

D

E

S5-1

E

I

K

T

K

K

N

N

S5-2

L

N

K

R

N

S

D

K

The protein purification and photophysical characterization were described in our previous work.
[2] Fluorescence lifetime measurements were made with the PicoQuant TCSPC with a 560nm
pulsed picosecond laser head. The photophysics of each RFP is listed in Table A1.7.

205

Table A1.7. Photophysical properties of mScarlet-I mutants.
QY

Lifetime (ns)

(3x trial / Avg)

(3x trial / Avg)

ProteinmSc-I (ref)

54

54

54

54

3.22

3.29

3.27

3.260.03

S4-1

40

42

-

411.4

2.88

2.93

-

2.900.04

S5-1

49

53

49

50.32.3

3.00

3.04

3.01

3.020.02

S5-2

48

47

-

47.50.7

3.00

3.03

-

3.020.01

206

Appendix 2This is an addendum to Chapter 2 and parts of this appendix have been adapted from the
Supplementary Information section of the article “Engineering of a Brighter Variant of the
FusionRed Fluorescent Protein Using Lifetime Flow Cytometry and Structure-Guided Mutations.”
Mukherjee, S.; Hung, S. T.; Douglas, N.; Manna, P.; Thomas, C.; Ekrem, A.; Palmer, A. E.;
Jimenez,R.

Biochemistry

2020,

59

(39),

3669–3682.

https://doi.org/10.1021/acs.biochem.0c00484.

Section 1. Amino acid sequence information for FusionRed variants

Table A2.1. Sequence information for the FR family with respect to the parental clones fromthe eqFP578 family. [3] The amino acid sequences of avGFP and DsRed are also listed in thetable for comparison. [4, 5] The relevant mutations in this study have been highlighted in gold.
The chromophore residues are highlighted in blue all other colors are based on the custom
classification for the nature of amino acid sidechains using the suite Clustal-W. [6] The numbering
above is with respect to avGFP while below is with respect to FR. All mutation position numbersin the text are with respect to FR numbering in this table.

207

Section 2. Amino acid sequence results from the site-directed library
2a. Selection of the C159V clone
The eight distinct mutants were screened for brightness in yeast cells in the green and red channel
on a BD-FACS Celesta flow cytometer at the BioFrontiers Flow Cytometry core facility at the
University of Colorado, Boulder. The green channel is an indicator for the undesirable immaturegreen fluorescence peak seen in RFPs such as SDC-5 (an unpublished mCherry mutant with
mutations of W143L, I161T, Q163C, I197R using mCherry sequence numbering). Filtered celllysates of these mutants were also used for measuring lifetime on a time-correlated single photon
counting (TCSPC) system that provided us with lifetimes to select the clones of interest. Sequence,
lifetime and brightness data are summarized in Table A2.2.
Table A2.2. Sequence and screening results of the FR site-directed (FSD) library clones. The
lifetime was measured using cell lysates on a TCSPC system. All fluorescence measurements
were normalized to FR.
Clones159

161

Lifetime (ns)Green Fl (a.u.)

Red Fl (a.u.)

FR

C

M

1.78

100

100

mCherry

-

-

1.67

103

191

SDC-5

-

-

-

811

421

FR-1

-

-

-

185

352

FSD-4

T

M

1.70

112

201

FSD-5

?

?

1.94

100

193

FSD-9

V

M

2.03

163

232

FSD-11

L

M

1.21

107

177

FSD-14

A

H

1.01

147

68

FSD-15

T

M

1.73

105

134

FSD-18

T

I

1.70

111

154

FSD-19

G

M

1.94

105

87

208

Section 3. Extinction coefficient and quantum yield estimation
3a. Extinction coefficient calculation based on SDS-PAGE results
Calculation of extinction coefficient based on published observations of FPs exhibiting backbone
cleavage, including FusionRed [9]:ϵRFP =

Absmax RFP
Abs
Abs( ϵ 380nm ) + ( ϵ 450nm )
380nm
450nm

Where Absmax RFP is the maximum absorbance for the RFP in the undenatured absorption spectrum
and Abs380nm and Abs450nm were the values of absorbance at 380 nm and 450 nm in the alkali
denatured spectrum. We used previously reported values of ϵ380nm = 70,500 M-1cm-1 and ϵ450nm =44,000 M-1cm-1. [2, 9]SDS-PAGE was used to assess the purity of proteins extracted from E. coli
and to examine whether FR-MQV exhibited backbone cleavage like the parent FR such that themathematical formula presented above could be used to calculate the extinction coefficient of the
RFP. Proteins were boiled at 95°C for 10 minutes in the presence of SDS and DTT before loading
onto the gel at 1X and 2X (~10 µM) concentrations. Also, to confirm that boiling alone was not
responsible for the cleavage observed, a control gel was performed without boiling the samples(data not shown). Both gels showed the existence of cleaved fractions for FR mutants and none
for EGFP (control). Cytochrome-C (Cyt-C) was included as an additional size marker. The resultsfor FR are consistent with previously reported data, therefore we used the above-mentioned
relationship to estimate the extinction coefficient of FR and its family of mutants.

209

Figure A2.1. Gradient (4–20%) SDS-PAGE of FR and FR-MQV. Gels with appropriate
controls show backbone cleavage for FR-MQV. Full FP fractions are bands located ~25k Da, while
the cleaved fractions are seen as bands at 16 kDa and 9 kDa for FR mutants.

3b. Quantum yield measurements
The quantum yield for purified protein samples was measured as described in the Methods andMaterials. The data follows expected linear trends as shown in Figure A2.2. Table A2.3 presents
the number of independent trials and the standard deviation error observed in measurements foreach FP.

210

7.00E+008

FR-MQV

Integrated Fluorescence

6.00E+008

FR-MQ
5.00E+008

FR-M

4.00E+008
3.00E+008
2.00E+008

mCh_IntFl
FR_IntFl
FR 41Q_IntFl
FRM_IntFl
FRM 41Q_IntFl
FRM 41I_IntFl

FR

1.00E+008

FR-MI mCh

0.00E+000-1.00E+008
0.00

0.02

0.04

0.06

0.08

0.10

Absorbance 520nm
Figure A2.2. Quantum yield measurements. The linear trend of higher integrated fluorescenceagainst absorption measurements under serial dilution for one of the independent measurements.
Higher slope values indicate higher quantum yields.

211

Table A2.3. Measured mean quantum yield and standard deviation errors. Quantum yieldmeasurements are susceptible to random and systematic errors. Cranfill et al. described protocols
to minimize such errors. [7] Steps such as pH control, minimizing temperature fluctuations, gentle
thawing of FPs and usage of fresh protein were taken into consideration. Replicate measurementsfor quantum yield of relevant proteins were taken from batches of FPs prepared throughindependent transformations, growth and purification protocols. Cresyl Violet, mCherry andmScarlet were usually used as multiple references for the measurements.

Protein

Mean QY

Trials

FR-MI

264

3

FR-MQ

433

4

FR-MQV

53±3

4

FR-Q

331

4

FR

24±4

4

FR-M

34±2

4

mCherry

22 (ref)

4

mKate

33

1

mKate-42Q

17

1

mRuby343

1

mScarlet

72±4

3

mScarlet-I

59±2

3

FR-V

31±4

3

FR-MV

38±3

3

212

Section 4. Additional photophysical and biochemical characterization
4a. pKa measurements
Table A2.4 shows the pKa values of relevant mutants in this study. The pKa was obtained bytaking three measurements for each pH data point and fitting the curve to a sigmoidal function(Figure A2.3). The half value of the maximum fluorescence was calculated to be the pKa of theprotein. The traces for mScarlet, mScarlet-I and FR-MQV are shown in Figure A2.3. BothmScarlet and mScarlet-I scale well with the reported values by Bindels et al. [8]Figure A2.3. pka measurements. Plot of fluorescence versus pH for FR-MQV, mScarlet andmScarlet-I. The pKa is obtained from the 0.5 fractional fluorescence point. FR-MQV retains thelow pKa value of the FR family of proteins.

213

Table A2.4. The pKa values measured in this study versus the values reported for known
RFPs in the literature.
ProteinpKa Calculated

pKa Reported

FR

4.5±0.2

4.5 [Ref 9]FR-M

4.7±0.3

4.8 [Ref 2]

FR-Q

4.3±0.2-

FR-MQ

4.4±0.1-

FR-MQV

4.6±0.2-

mScarlet

5.8±0.3

5.3 [Ref 8]

mScarlet-I

5.2±0.1

5.4 [Ref 8]4b. Lifetime measurements using time-correlated single photon counting(TCSPC)
Fluorescence lifetime was measured using TCSPC by exciting with a 560 nm pulsed laser andcollecting emission in two spectral windows using appropriate bandpass filters. Differences in theamplitudes and time constants from multi-exponential fits of the decay of mKate-42Q are
consistent with the presence of multiple emitting species. Data are presented in Table A2.5.

Table A2.5. TCSPC-based lifetime measurements using pure protein samples. Independent
trials are separated by commas, where 𝛕 indicates the component of fluorescence lifetime in ns
and the % intensity for that component is reported in brackets. As the L175M, C159V and M42Q
mutations are added on FR, there is a progressive increment of 𝛕 in the major component offluorescence decay. The decays for mKate-42Q are fit to a tri-exponential function and are
significantly different in the two emission spectral windows. In contrast, fluorescence decays ofthe other FPs are fit with bi-exponential functions and do not show significantly different decays
in the two emission windows.

214

Emission window (600 ± 30 nm)
Protein

FR

FR-M

FR-Q

FR-MQ

FR-MI

FR-MQV

mKate

mKate-Q

mCherrymScarletmScarlet-I

mRuby3𝛕1 (%Int)

𝛕2(%Int)

1.40(64),

2.49(36),

1.44(63),

2.51(37),

1.42(64)

2.51(37)

1.55(38),

2.43(62),

1.56(33),

2.47(67),

1.49(33)

2.43(67)

1.50(55),

2.92(45),

1.52(53),

2.93(47),

1.56(52)

2.97(48)

1.74(35),

2.82(65),

1.87(40),

2.91(60),

2.05(40)3.02(56)

2.22(55),

1.21(45),

2.21(54)1.29(46)

3.23(68),2.03(32),

3.15(69),

1.94(31),

3.14(69)2.01(31)2.40(92),

0.87(8),2.42(90),0.86(10),2.37(93)0.80(8)3.72(52),

1.29(40),0.21(8),3.61(48),1.25(41),0.19(9),3.65(55)

1.32(39)0.46(6)

1.63(88),

0.59(12),1.75(70)

1.06(30)

3.82(98),

1.27(2),3.80(97),

1.18(3),3.93(99)

1.31(1)3.41(92),

0.92(8),3.57(86),

1.63(14),3.51(88)

1.51(12)2.79(95)

1.16(5)Emission window (670 ± 30 nm)

𝛕3(%Int)𝛕av

𝛕1 (%Int)

𝛕2(%Int)𝛕3(%Int)

𝛕av-

1.780.04

1.37(39)

2.36(61)

-

1.76

-

2.130.05

1.70(53)

2.54(47)

-

2.09

-

2.100.05

2.93(44)

1.51(56)

-

2.13

-

2.450.08

2.98(56)

1.85(44)

-

2.47

-

0.260.04

2.16(56)

1.16(44)

-

1.72

-

2.770.07

3.13(73)

1.91(27)

-

2.80

-

2.260.07

2.38(92)

8.21(8)-2.25

2.160.05

3.62(36)

1.27(61)0.24(3)2.05-

1.670.07

-

-

-

-

-

3.870.07

-

-

-

-

-

3.260.07

-

-

-

-

-

2.71

-

-

-

-

215

4c. Photobleaching experiments
The photobleaching traces of FR, FR-C159V and FR-C159L are shown in Figure A2.4a. The fast
fluorescence decay process may result from transition to a dark state, as has been observed
previously for FPs. [10] The incorporation of a small aliphatic group at position 159 in FR-C159V
eliminates the tendency of the FP to undergo the dark state conversion process. Thus, thephotobleaching profile changed from a bi-exponential-like decay in FR to a mono-exponentiallike decay in FR-C159V and FR-C159L. It is worth noting that FR-C159L shows a slow
photoactivation process in ~50 s under the irradiance regime used in this study. The tendency forphoto-switching, or reversible photobleaching, is the lowest for FR-C159V, followed by FRC159L, and the highest in FR, suggesting that an aliphatic group at the 159 position may help toreduce the cis–trans isomerization of the chromophore.

Figure A2.4. Photobleaching measurements. (a.) FR, FR-C159V and FR-C159L expressed inbacteria were photobleached with 560 nm LED at a constant irradiance of ~4.9 W/cm 2. The inset
exhibits the traces of the first 20 seconds. (b.) Fluorescence signals under alternating
illumination—each cell was illuminated with 560 nm LED for 2 s, then only 438 nm LED for
another 2 s and then the illumination cycle was repeated. The camera only recorded signals when
560 nm LED was turned on. The inset shows the traces of the first 50 minutes. (c.) The alternating216

LED light sources are illustrated for the first 8 s. The irradiance was ~4.9 W/cm2 for 560 nm and~4.5 W/cm2 for 438 nm throughout the experiment. The camera recorded nine frames in 2 s when
the 560 nm LED was turned ON.

4d. Bacterial brightness
The family of FR mutants relevant to this study was expressed in bacteria to test bacterial
brightness in a droplet microfluidic screening platform (summarized in Figure A2.5). [11]Brightness seems to scale well with increasing molecular brightness with FR-MQV being ~2-foldbrighter than FR. Details of the experiment are described in the methods and materials section of
the Chapter 3 of the article. Note that quantitative comparison of brightness across cellular systems
is impacted by many factors. Whereas in vitro brightness is dependent solely on molecularparameters whereas in cells the brightness is additionally the result of multiple processes thatinvolve DNA to mRNA transcription, mRNA stability, translational efficiencies, protein folding
kinetics, chromophore maturation, cellular pH, and protein stability. This makes a quantitative
comparison across systems not possible. Discrepancies in the levels of brightness across systems(molecular, bacterial, yeast and mammalian) have been discussed in our previous publication andby others. [2, 13]

Figure A2.5. Bacterial brightness assay. The brightness (normalized with respect to FR-MQV)
recorded for the family of FR mutants relevant to this study. We see a progressive increase inbacterial brightness for the family, with FR-MQV being ~2-fold brighter than FR.
217

4e. Excitation versus absorption spectra
Excitation and absorption spectra overlaid with each other for FR and the FR mutants generated
in this study. In Chapter 3, our analysis for absorption wavelengths, calculations of Stokes shift,etc., was done with respect to the absorption spectra for the relevant FPs.

Normalized Value (a.u.)

1.0
FusionRed
FusionRed-M
0.8 FR-Q
FR-MQ
0.6 FR-MQV

0.4
0.2
0.0
475

Dotted - AbsorbanceSolid - Excitation
500

525

550

575

600

625

Wavelength (nm)Figure A2.6. Absorption and excitation spectra. Overlaying the absorption and the excitation
spectra for the FPs relevant to this study. The excitation spectra (solid) and absorption spectra(dotted). The y-axis indicates the normalized value of absorption/excitation in normalized arbitrary
units (a.u.).

4f. Spectral characteristics
We observed that both the absorption and emission spectral width decreased as mutations were
progressively incorporated into FR in the development of FR-MQV. The spectra progressively
narrow with decreases in the absorption and emission FWHM (full width at half maximum). Table
A2.6 below summarizes the spectral changes that we observed in this series of mutants.
218

Table A2.6. Spectral characteristics of the FR family of proteins investigated in this study.
There is a progressive blue shift and narrowing of the spectra as one moves from the single, to the
double and then to the final triple mutant FR-MQV. The change in Stokes shift (both in nm andenergy units), unlike mKate-Q, is minimal for the M42Q mutants of FR.
FWHM
Protein

λabs_max (nm)absorption

FWHM
λem_max (nm)(nm)

emission(nm)

Stokes shift

Stokes shift(nm)(cm-1)

FR-MQV

566

53

585

39

19

574

FR-MQ

567

54

586

40

19

572

FR-MV

569

60

591

47

22

654

`FR-V

573

63

594

53

21

617

FR-Q

568

55

587

40

19

570

FR-M

571

61

590

52

19

595

FR

574

63

596

54

22

643

4g. Normalization with respect to the 278nm Trp peak
FR and FR mutants with 42Q have the same number of Trp residues. Normalizing with respect tothe absorption peak of tryptophan at ~280 nm should reflect the true nature of spectral width for
the RFP peak. On doing so we observe the red emission peak is indeed narrower and shifted blue
relative to the parent protein.

219

Figure A2.7. Trp280 nm peak for FusionRed variants. Normalizing the absorption spectra withrespect to the Trp 280 nm feature reveals that M42Q changes the peak absorption. FR-MQ has a~20% higher peak absorbance compared to FR.

4h. pH titrations and alkali denaturation
We collected absorption spectra for FPs in vitro at pH values 2–14. At acidic pH values, FR-MQV
resembles FR and FR-M, but at basic pH values, FR-MQV lacks the 450 nm degradation productthat is present in FR-M and many other red FPs, such as mScarlet-I. Instead, there is a single
product of alkali denaturation at 380 nm whenever the 42Q mutation is incorporated into the FR
protein. However, this effect is not seen in mKate-Q, where we see both the 380 and the 450 nm
peaks. mKate and other RFPs, such as mScarlet-I (also mCherry, mScarlet, mRuby3; data notshown), degrade to only the 450 nm hydrolysis product.

220

Figure A2.8. pH titrations. from pH 2 to 10 of (a) FR-M and (b) FR-MQV show similar behavior
for the functional form and the acid-degraded form of the FPs. Titration in the basic range (pH>12) shows that (c) FR-M breaks down into two products of alkali hydrolysis, with the 380 nm
peak formed at a lower pH than the 450 nm peak; (d) FR-MQV displays only one product of alkali
degradation at 380 nm and; (e) mScarlet-I (along with other RFPs) shows only the 450 nm peak
for alkali degradation. (f) All constructs with the M42Q mutation behave similarly, but such aneffect is not seen in (g) mKate-Q where both the 450 and the 380 nm peaks are observed on
denaturation. The y-axis indicates the normalized value of absorption in normalized arbitrary units(a.u.).

221

4i. Green emission peak
The formation of some RFP chromophores is accompanied by the formation of a green
chromophore that lacks the extension of the acylimine moiety. [12] This is undesirable as it
decreases the amount of mature red species present in a protein sample. Protein engineering efforts,
particularly those that involve mutations internal to the beta barrel often disrupt the chromophorematuration pathway and hence inadvertently result in an increase in the immature or green species.
FR mutants developed in this work employed multiple internal mutations; emission spectra werecollected in the 465–750 nm windows, with excitation at 450 nm for Figure A2.9. It is evident that
the M42Q mutation does not increase the green emission peak relative to FR (both show a shoulder~20% of the major red peak) suggesting a properly mature red chromophore. However, the same
mutation in mKate changes the spectrum considerably. Even the incorporation of a similar-sized,
but aliphatic residue, isoleucine, produces a large green emission peak.

222

1.0

FR

b
.

0.8
0.6
0.4
0.2

Normalized Fluorescence

Normalized Fluorescence

a
.

1.0

0.6
0.4
0.2
0.0

0.0

450 500 550 600 650 700 750

450 500 550 600 650 700 750

1.0

FR-MQ

d
.

0.8
0.6
0.4
0.2

Wavelength (nm)Normalized Fluorescence

Wavelength (nm)Normalized Fluorescencec.

FR-MQV

0.8
0.6
0.4
0.2

450 500 550 600 650 700 750

450 500 550 600 650 700 750

g
.

1.0

0.0

0.0

e
.

FR-M

0.8

Wavelength (nm)Wavelength (nm)

f
.

h
.

Figure A2.9. Emission spectra for the FusionRed and mKate variants. Emission spectra of(a.) FR, (b.) FR-M, (c.) FR-MQ, (d.) FR-MQV, (e.) FR-Q, (f.) FR-MI, (g.) mKate, and (h.) mKateQ excited with 450 nm light. FR mutants except FR-MI exhibit minimal green fluorescence,suggesting proper red chromophore maturation. mKate-Q also displays a significant green peak.

223

4j. Excitation-dependent emission
Konold and co-workers previously demonstrated the existence of multiple non-interconvertinghydrogen-bonded conformations of TagRFP-675 and mKate-Q. [14] We excited the proteins inthis study at 500 nm, 525 nm and 550 nm to find evidence for different emission species in the red
window as shown in Figure A2.10. Although mKate-Q shows excitation-dependence of theemission spectral shape (Figure A2.10h), mKate and the FR variants do not show significant
excitation-wavelength dependence of their emission spectra.
a.

b.
16000000

10000000

Fluorescence (a.u.)

Fluorescence (a.u.)

12000000

FR

8000000
6000000
4000000
2000000

14000000

FR-M

12000000
10000000
8000000
6000000
4000000
200000000-2000000

500

550

600

650

700

750

500

650

700

750

35000000

Fluorescence (a.u.)

Fluorescence (a.u)

d.

21000000
18000000

600

Wavelength (nm)Wavelength (nm)

c.

550

FR-Q

15000000
12000000
9000000
6000000
3000000

30000000
25000000
20000000

FR-MQ

15000000
10000000
5000000

0
0

500

550

600

650

700

750

500

Wavelength (nm)

550

600

650

700

Wavelength (nm)

224

750

f.

e.

35000000

Fluorescence (a.u)

Fluorescence (a.u.)

7000000
6000000
5000000

FR-MI

4000000
3000000
2000000
1000000

30000000
25000000

FR-MQV

20000000
15000000
10000000
500000000-5000000

500

550

600

650

700

500

750

550

600

650

700

750

Wavelength (nm)Wavelength (nm)g.

h.

8000000
7000000

Fluorescence (a.u)

Fluorescence (a.u.)

12000000
10000000
8000000

mKate
6000000
4000000
200000006000000
5000000

mKate-Q

4000000
3000000
2000000
1000000
0

500

550

600

650

700

750

500

Wavelength (nm)

550

600

650

700

750

Wavelength (nm)Figure A2.10. Excitation dependent emission spectra. Emission spectra of (a.) FR, (b.) FR-M,(c.) FR-Q, (d.) FR-MQ, (e.) FR-MI, (f.) FR-MQV, (g.) mKate, and (h.) mKate-Q, with excitation
at 500 (blue), 525 (red) and 550 (black) nm. Consistent with previous results, mKate-Q has
multiple emissive species.

225Section 5. Cellular Assays: brightness, maturation and cytotoxicity
5a. Brightness assays
Brightness was measured using FACS and confocal microscopy. The Methods and Materials
section of Chapter 3 describes the measurement protocols. Table A2.7 reports the values andnumber of biological replicates used for measuring the brightness through FACS. Each biologicalreplicate had ~3 technical replicates of ~10000 HeLa cells each. Table A2.8 reports the number of
HeLa cells analyzed in each sample dish and the mean intensity of each dish.
Table A2.7. Mean brightness from FACS measurements with standard deviation error frommultiple biological replicates. Mean brightness measurements were normalized to FR.
Protein

Biological Replicates

Mean Brightness

FR

5

100±0

FR-M

4

191±31

FR C159V2

164±17

FR-M C159V

2

266±31

FR- Q

2

214±18FR-MQ

3

315±43

FR-MQV4509±20mCherry5176±39mScarlet4715±51mScarlet-I

1

355

226

Table A2.8. Mean brightness from confocal microscopy measurements with standard
deviation error from the number of cells indicated in each dish. Mean intensity measurements
were normalized to FR.
Protein# Cells

Mean Intensity (x100)

mCherry-1

51

77±55

mCherry-2

38171±137FR-1

12100±68FR-2

61

100±78mScarlet-1

131250±194mScarlet-2

71379±273

FR-MQV-1

62

231±154

FR-MQV-2

48

215±187

Untransfected-1

513

4±2

Untransfected-2

469

5±3

5b. Cytotoxicity assay
The detailed protocol for this assay is reported in the Materials and Methods section of Chapter 3.
Briefly, mammalian cells expressing either EGFP or one of the RFP clones were mixed in a 50:50
ratio by volume. Initially, cells expressing EGFP and each RFP were FACS screened individually(~5000 cells) as controls. Part of mixture was analyzed by FACS to quantify the number of cells
carrying EGFP and the RFP at the start (Day 2). The remaining mixture was re-plated. The screens
for the re-plated mixtures were repeated after another 4 days of growth (Day 6). Ratios of RFP:
EGFP mixtures were calculated for technical replicates for Day 2 and Day 6. The change in theratio of RFP to EGFP for each replicate is a measure of the relative cytotoxicity of the RFP to
EGFP. Figure A2.11 is a graphical representation of the assay. We found that FR and FR-MQV
are reproducibly less cytotoxic than EGFP. In contrast, mCherry was consistently more cytotoxic
than EGFP, whereas for mScarlet, in one case the RFP was more cytotoxic than EGFP and inanother case it was less cytotoxic.

227

Figure A2.11. Cytotoxicity assay (a.) The black bars represent the RFP:EGFP ratio in a mix on
Day 2. The blue bars represent the RFP:EGFP ratios measured on Day 6. On each day cells were
measured using FACS. (b.) The change in the ratio is represented as red bars. FR and FR-MQV
are consistently less cytotoxic than EGFP.
Table A2.9. Number of cells analyzed on Day 2 and Day 6 in the GFP and the RFP channel
using FACS.
FP

Day 2 RFPDay 2 GFPDay 6 RFPDay 6 GFP

mCherry_01

8880

8806

1652

12043

mCherry_02

2584

4277

3848

8852

mScarlet_01

5834

4034

10057

5079

mScarlet_02

2013

1119

10081

7621

FR_01

4703

3096

7353

4493

FR_02

1903

1504

9154

6491

FR-MQV_01

4302

2785

14252

7576

FR-MQV_02

2047

1932

10475

4380

228

5c. Chromophore maturation kinetics
Details of maturation kinetics are provided in the Methods and Materials section of Chapter 3.
Briefly, FPs were expressed in E. coli. After induction of protein expression, cultures were treatedwith chloramphenicol to halt new protein production and both the fluorescence and optical density
were measured over time. An increase in fluorescence (after normalization to optical density)
indicates an increase in chromophore formation. FR and FR-MQV show similar maturation
kinetics. The mScarlet and mScarlet-I values are comparable to those reported in the literature.
Hence, the mutations in FR-MQV do not appear to perturb maturation and folding of the FP at
37ºC (temperatures used for mammalian cell growth/imaging experiments).
a.

b.

Figure A2.12. Chromophore maturation kinetics. (a.) The optical density (OD) of bacterial
cultures over time after addition of chloramphenicol at t = 0. The ODs remained fairly constant,suggesting the action of chloramphenicol stalling the growth of bacterial cells in the log phase.
(b.) The measured fluorescence normalized and scaled with respect to the observed ODs at eachtime point.

229

Table A2.10. Measured versus the reported maturation times (t50) for the RFPs investigatedin this study.
Fluorescent Protein~ t50 37ºC

Reported t50 (min)mScarlet-I

45 min36, 25 [Refs 8,13]

mScarlet

165 min174, 132 [Refs 8, 13]FR

195 min

130 [Ref 9]

FR-MQV

195 min-

Section 6. Additional structural information

Figure A2.13. Structural representation of the FR crystal structure. The hydrogen bonding
network in (a.) TagRFP-675 and (b.) mKate. Images modified from Konold et al. [14] Distanceswere calculated using the crystal structures of TagRFP-675 (PDB ID: 4KGE) and mKate (PDB
ID:3BXA). Konold and co-workers describe an extensive network involving the Q106, S28 andM/Q41 residues with a crystallized water molecule at the acylimine end of these RFPs (c.) The

230

crystal structure of FR (PDB ID: 6U1A) also reveals a similar arrangement. Relevant positions
and the distances from the chromophore in the FR structure are shown.

Section 7. FR Evolution Table

Figure A2.14. Evolution table. The evolution of the FR family of proteins. The pathways indicate
the various engineering strategies that led to the development of FR-MQV. All amino acidpositions have been numbered with respect to the parent FR numbering as per Table A2.1.

231

Appendix 3This is an addendum to Chapter 4 and parts of this appendix have been adapted from the article“Characterizing Dark State Kinetics and Single Molecule Fluorescence of FusionRed and FusionRed-MQ
at Low Irradiances.” Mukherjee, S.; Thomas, C.; Wilson, R.; Simmerman, E.; Hung, S. T.; Jimenez,
ChemRxiv 2022. https://doi.org/10.26434/chemrxiv-2022-2dr03

Section 1. Experimental workflow

Figure A3.1. Schematic of the experimental workflow from sample preparation to data
analysis.

232Section 2. Excitation rate calculations
Our TIRF measurements are for proteins (~1–2 nm) bound to the surface of the coverslip, therefore
we estimate the irradiance (I) of the evanescent wave at the interface surface using Fresnel’sequations, given below. [15]

(1)

(2)
Table A3.1. Power measurements
Power (mW)

I (W/cm2)

Ie (W/cm2)

Excitation Rate FR (Hz)

Excitation Rate FR-MQ (Hz)

0.28

0.49

1.23

940

1622

0.42

0.74

1.85

1420

2450

0.49

0.63

1.57

1206

2080

0.56

0.99

2.48

1902

3282

1.24

1.57

3.93

3014

5200

2.48

3.15

7.87

6035

10412

4.96

6.29

15.73

12062

20811

FR = Fusion Red, FR-MQ = FusionRed-MQ

233

Section 3. Single molecule data analysis addendum
3a. Spot identification script corrections

Figure A3.2. Spatial corrections. (a.) Gaussian profile, (b.) after removal of the Gaussian
profile, (c.) after removal of the fast component on a blank sample.

3b. Detection of state changes

Figure A3.3. Intensity variation. (a.) On/ Off and Overall fluctuation histograms, (b.) Levels offluctuations from the on and off state (read and shot noise), (c.) Change point definition.

234

Section 4. Ensemble photobleaching
Figure A3.4 shows the ensemble bleaching of these two proteins in bacteria.

Figure A3.4. Ensemble photobleaching kinetics. Photobleaching traces of E.Coli expressing(a.) FusionRed and (b.) FusionRed-MQ, across varying irradiance ranges.

235

Figure A3.5. Bi-exponential nature of fluorescence decay from bacteria expressing
FusionRed and FusionRed-MQ.

Table A3.2. Fitting details for the biexponential decay traces of FusionRed and FusionRedMQ
kEx
(s-1)

FusionRedτ1(s)

A1 (%)

FusionRed-MQ
τ2
3(x10 s)A2 (%)τ1(s)

A1 (%)

τ2(x103 s)A2 (%)

1400

14.1 ± 2.425.4 ± 0.3

97

27.9 ± 0.5

167.1 ± 0.3

84

2800

12.6 ± 2.2

122.4 ± 0.6

88

15.6 ± 0.1

215.6 ± 0.1

79

3800

9.4 ± 1.816

1.8 ± 0.184

8.2 ± 0.124

4.1 ± 0.1

76

5500

9.9 ± 2.624

1.6 ± 0.676

7.7 ± 0.134

3.4 ± 0.1

66

In both cases, the larger time constant τ2 (most likely for permanent) is ~500-fold larger than the
shorter τ2 (likely reversible component) of photobleaching. Also, with increasing irradiance weobserve accelerated photobleaching for both systems.

236

Section 5. Simulation results
5a. Three state single molecule blinking simulator algorithm
The schematic below indicates the behavior of a single FP molecule at each time step (defined by
the user). The code uses random sampling using Monte-Carlo methods to decide the residence ofthe molecule in each state (S1, S0 or D) based on the probabilities of making a transition from one
state to the other. The probabilities of these transitions are in-turn dependent on the user definedrate constants for kEx, kEm, kIC, kDSC and kGSR.

Figure A3.6. Schematic representing the algorithm used to simulate single moleculebehavior. The schematic for a three (S0 = Ground electronic, S1 = First excited and D = Dark) statemodel represented above. The value of F=1 indicates a fluorescence photon has been generated in
the process.

237

5b. On/Off time dependence on DSC and GSR times and excitation rates
We observe a shorter on-time for both shorter dark-state conversion times and higher excitation
rates (Figure A3.7, Panels A, C and E). We also observed that off-times depend only on the groundstate recovery times (Figure A3.7.2, Panels B, D and F).

Figure A3.7. Simulation heatmaps for on and off time with varying rates constants.
Variations of on and off times with respect to τDSC (=1/kDSC) and τGSR (=1/kGSR) expected fromMonte-Carlo simulations for FusionRed. (a & b.) Variation of on and off times with DSC andGSR times at a fixed excitation rate (1923 Hz). (c & d.) Variation of on and off times withexcitation rate and GSR times at a fixed DSC time (0.5 ms). (e & f.) Variation of on and offtimes with excitation rate and DSC times at fixed GSR time (3 s).
238

5c. Effects of changing time steps on this algorithm
This model considers the time step to be longer than the excited state lifetime and the dark state
conversion time but slower than the ground state recovery time. This is done to mimic millisecond
acquisition times for commercial EMCCD and CMOS cameras employed for single molecule
imaging. We ignore photobleaching in these simulations. We used τDSC  40 µs, τGSR  2 s, Φ 
0.24, τFL  1.78 ns and kex  3500 Hz for these simulations.
Case 1: One FusionRed protein, image acquisition time 100 ms, 6000 frames.

Figure A3.8. FusionRed blinking simulation (100 ms, 6000 frames) (Above) Single molecule
trajectories. The red circles indicate frames where photon counts are lower than most on events,
indicating the switching off of the molecule mid-frame of the acquisition step. Our single moleculebinarization change-point algorithm can recognize these real fluctuations and jumps anddistinguish these from experimental background noise. (Below) The histograms of binarized on
and off traces.

239

Case 2: One FusionRed protein, image acquisition time 50 ms, 12000 frames.

Figure A3.9. FusionRed blinking simulation (50 ms, 12000 frames) (Above) The photon counton the camera reduces by ~50% when the acquisition time is halved. (Below) The statistics of onand off times do not change on changing the frame rate.
Similarly, when the image acquisition time is reduced to 20 ms, the photon counts also reduce
accordingly, but the on/off times are similar to the above two cases.

240

5d. Statistics of on/off time for a single FP blinking versus multiple FPs under
the same time step
Case 3: Repeat 50 simulations of single FusionRed protein, image acquisition time 50 ms andtaking 6000 frames for each FusionRed protein simulation. In comparison to case 2 presented in
the previous simulation.

Figure A3.10. FusionRed blinking simulation (50 ms, 6000 frames) (Above) The photon counthistograms are centered at ~45 photons for either case. (Below) The fluctuations for on and offtimes become relatively consistent after ~5 FPs.
The on/off statistics do not change as the photon counts drop. We still remain below the opticalsaturation limit and observe near linear photon counts.

241

5e. Statistics of on/off time relevant to an actual single molecule experiment
Our experiments were carried out using camera acquisition times of ~100–300 ms for 50–500 FPs.
This case describes the simulated data for these settings.
Case 4: In total, 50 simulations of single FR proteins, image acquisition time 300 ms and taking
1000 frames for each FR protein simulation (~5-minute trajectories).
Photon count distribution is shifted ~6 times higher than Case 3, since the acquisition time is 6
times longer. The average ON/OFF time and number of ON/OFF events are also shown below.
The average ON/OFF time is slightly longer than Case 3 because the ON/OFF time is added in theunit of the image acquisition time. The average number of ON/OFF events observed in this caseare slightly less than Case 3, also because of the longer acquisition time, i.e., the shorter theacquisition time, the more the ON/OFF switching events can be observed. However, the numberof events does not change significantly since the average ON/OFF times are much longer than theacquisition time.

Figure A3.11. FusionRed blinking simulation (300 ms, 1000 frames) (Above) At 300 ms, ourphoton counts are significantly higher than at shorter acquisition time. (Below) The fluctuations
for on and off times are almost consistent after ~5 FPs.
242

5f. Ensemble behavior averaged from simulated single molecule blinking withrespect experimental rate constants obtained from experiments.

Figure A3.12. Ensemble trends from Monte-Carlo simulations. Simulation results are obtained
from rate constants reported in Chapter 3; Table 3.2, without permanent photobleaching.
FusionRed-MQ shows a larger dark fraction and faster dark state conversion in comparison to
FusionRed. Each trace represents the normalized sum fluorescence from three simulated single
molecule blinking video with ~150 emitters.

243

5g. Simulation of ensemble behavior averaged from simulated single molecule
blinking with respect to varying kEx, kDSC and kGSR while holding other rate
constants fixed.

Figure A3.13. Variation in ensemble fluorescence decay traces with respect to kDSC, kex
and kGSR. Each trace represents the normalized sum fluorescence from three simulated single
molecule blinking videos, each with ~150 emitters. The panel on the left represents the244simulated traces with respect to photophysical properties of FusionRed and on the right,
photophysical properties of FusionRed-MQ. For each panel, the one rate constant was varied
at a time while keeping the other two rate constants fixed, for example – for FusionRed panel
A, kDSC was varied keeping kex=3000 s-1 and kGSR=0.18 s-1 fixed. These results provide insight
into how each rate constant involved in dark state population and depopulation manifest at an
ensemble level.

5h. Ensemble behavior of the system based on numerical simulations for athree-state system

Figure A3.14. Population based numerical simulation of a 3-state model. A population based
numerical simulation (non-Monte Carlo methods) indicates that the kDSC controls the dark fraction
at the ensemble level. (Left) Photobleaching curve of FusionRed fit with two exponentialfunctions. (Right) Normalized populations in S0 (red) and D (blue) over time (x axis, in seconds)
without considering permanent photobleaching obtained from by utilizing rate constants fromthese fit on the left and numerical simulations for a three-state model.

245

Section 6. Additional fitting results
6a. Analytical expression for fitting the ensemble fluorescent population:
Three-state model equation
S0(t) = A * kDSC * ( 4 * kGSR * ( kDSC + kEm + kIC ) * sqrt ( ( kDSC + kEm + kEx + kGSR + kIC ) 2 –
4 * ( kDSC * ( kEx + kGSR ) + kGSR * ( kEm + kEx + kIC ) ) ) + exp ( - 0.5 * t * ( kDSC + kEm + kEx +kGSR + kIC + sqrt ( ( kDSC + kEm + kEx + kGSR + kIC ) 2 -4 * ( kDSC * ( kEx + kGSR ) + kGSR * ( kEm +kEx + kIC ) ) ) ) ) * kEx * ( kDSC + kEm + kEx + kGSR + kIC – sqrt ( ( kDSC + kEm + kEx + kGSR + kIC ) 2– 4 * ( kDSC * ( kEx + kGSR ) + kGSR * ( kEm + kEx + kIC ) ) ) ) * ( - kDSC + kEm + kEx - kGSR + kIC +sqrt ( ( kDSC + kEm + kEx + kGSR + kIC ) 2- 4 * ( kDSC * ( kEx + kGSR ) + kGSR * ( kEm + kEx + kIC ) ) )) - exp ( 0.5 * t * ( - kDSC - kEm - kEx - kGSR - kIC + sqrt ( ( kDSC + kEm + kEx + kGSR + kIC ) 2- 4 *( kDSC * ( kEx + kGSR ) + kGSR * ( kEm + kEx + kIC ) ) ) ) ) * kEx * ( - kDSC + kEm + kEx – kGSR + kIC– sqrt ( ( kDSC + kEm + kEx + kGSR + kIC ) 2- 4 * ( kDSC * ( kEx + kGSR) + kGSR * ( kEm + kEx + kIC )) ) ) * ( kDSC + kEm + kEx + kGSR + kIC + sqrt ( ( kDSC + kEm + kEx + kGSR + kIC ) 2 - 4 * ( kDSC * (kEx + kGSR ) + kGSR * ( kEm + kEx + kIC ) ) ) ) ) / ( 4 * ( kDSC * ( kEx + kGSR ) + kGSR * (kEm + kEx+ kIC ) ) * sqrt ( ( kDSC + kEm + kEx + kGSR + kIC)2 – 4 * ( kDSC * ( kEx + kGSR ) + kGSR * ( kEm +
kEx

+

kIC

)

)

)

)

+

246

APB*kPB+

COffset6b. Inaccuracies in fitting the ensemble bleaching with a fixed dark-state
conversion rate constantFigure A3.15. Quality of fit for varying kDSC and kGSR unbound. Residuals indicate a poor
quality of fitting. Since single-molecule experiments provide precise measurements for the
GSR in comparison to DSC, fixing the kGSR within the experimental bounds of the singlemolecule measurement and then fitting for kDSC provided better insight and accurate estimationof the kinetics for the dark-state conversion process.

247

6c. Residuals for fitting kDSC with respect to a bound value of kGSR

Figure A3.16. Keeping kGSR fixed while allowing the fitting algorithm to fit the kDSC. This
provides a better quality of fit. Residuals indicate better fitting, with adj-R2 > 0.95.

Section 7. Theoretical estimation of the lowest and highest numberof photons/frames
Lower bound: Lowest excitation rate for FusionRed
kex = 940 photons/s
Fluorescence QY of FusionRed = 0.24
Total fluorescence photons = 226 photons/s
Acquisition time = 300 ms, Quantum Efficiency [16] of Andor iXon at 561 nm ~0.8
Maximum number of fluorescence photons per frame ~60 photons/ frame
Numerical aperture of objective ~ 1.42
% light collected by the objective ~ 0.4
Realistic lower bound ~ 25 photons/ frame
Upper bound: Highest excitation rate for FusionRed-MQ
248

kex = 20800 photons/s
Fluorescence QY of FusionRed = 0.43
Total fluorescence photons = 8950 photons/s
Acquisition time = 300 ms, Quantum Efficiency [16] of Andor iXon at 561 nm ~0.8
Maximum number of fluorescence photons per frame ~2300 photons/ frame
Numerical aperture of objective ~ 1.42
% light collected by the objective ~ 0.4
Realistic upper bound ~ 900 photons/ frame

Section 8. Surface charge on FusionRed

Figure A3.17. Location of positively charged residues on the barrel of FusionRed. The crystal
structure of FusionRed (PDB ID: 6U1A) indicating the location of positively charged amino acidsidechains pointing out of the β-barrel (blue lines). These provide the opportunity to effectively
bind the molecule with a negatively charged glass surface. The mutations acquired in FusionRedMQ point into the barrel facing the chromophore (green). Therefore, we expect similar
perturbations in FusionRed and FusionRed-MQ with respect to electrostatic interactions of theglass surface for both FPs.

249

Appendix 4This is an addendum to Chapter 5. Parts of this addendum will be adapted into the Supplementary
Information section of the manuscript titled “Directed evolution of a bright variant of mCherry:
Suppression of non-radiative decay by fluorescence lifetime selections.” by Srijit Mukherjee,
Premashis Manna, Sheng-Ting Hung, Felix Vietmeyer, Pia Friis, Amy E. Palmer, and Ralph
Jimenez

Section 1. Mutagenesis Protocols
In order to develop RFP variants with higher brightness, we started with mCherry as a template.
mCherry displays high photostability, excellent pH-resistance, fast maturation and a low
cytotoxicity. However, mCherry is significantly dimmer than other recently developed RFPs, e.g.
mRuby3, [17] mScarlet, [8] and FusionRed-MQV [18] in-part due to its lower quantum yield. To
tackle this, we created several site-directed and random mutagenesis libraries and screened forhigher excited state lifetime. Lifetime evolution was carried out using our microfluidic sorting
platforms as previously reported. [19] We present a short discussion of the mutagenesis and librarygeneration protocol below. Detailed protocols have been reported in our previous works. [2, 11,
18, 19]1a. Yeast and bacterial constructs for libraries and pure proteinsTemplate construction: The original DNA templates for mCherry and other FPs were amplified
with gene-specific primers and cloned into pDonr221 using Gateway recombination system (LifeTechnologies) and sequenced. The forward primer for each FP included a recombination
recognition sequence (attB1), a Shine-Dalgarno sequence for prokaryotic expression, a BamH1
restriction endonuclease site, a Kozak sequence for mammalian expression and ∼ 30 nucleotide
sequence complementary to the FP. The reverse primer for each FP included ∼ 30 nucleotides
complementary to the FP, a stop codon, an EcoR1 restriction endonuclease site and an attB2
recombination recognition sequence. Using the Gateway recombination system, the LR reaction250was performed to clone the FP into pYestDest52 vector (Life technologies). After sequences wereconfirmed the FP/pYestDest52 plasmids were used as template for library construction.
Error-prone libraries: GeneMorph II Random Mutagenesis kit (Agilent Cat No. 200550) wasused to create the error-prone libraries. The kit protocol was followed with varying amounts oftemplate DNA and cycles depending on the error rate. Like our work with FusionRed a typicalerror-rate is used that incorporates ~5 mutations (at the nucleotide level) per template. [2, 18] T7
and V5 universal primers (both located on pYesDest52 vector) were used for the amplification.
After first round of PCR, the gel-extracted PCR product was used for a second round of PCR tocreate enough DNA for homologous recombination. After PCR purification the library DNA wasisopropanol precipitated and eluted in a few µl of water.
Site directed libraries: QuikChange site-directed mutagenesis method was used to make point
mutations or switch single amino acids using PfuTurboDNA polymerase and a Thermo cycler.
PfuTurboDNA polymerase replicates both plasmid strands with high fidelity and without
displacing the mutant oligonucleotide primers. The basic procedure utilizes a supercoiled doublestranded DNA (dsDNA) vector with the FP of interest and two synthetic oligonucleotide primers
containing the desired mutation. The oligonucleotide primers, each complementary to opposite
strands of the vector, are extended during temperature cycling by PfuTurboDNA polymerase.
Incorporation of the oligonucleotide primers generates a mutated plasmid containing staggered
nicks. Following temperature cycling, the product is treated with DpnI. The DpnI endonuclease
digests the parental DNA template and makes it possible to select for mutation-containing
synthesized DNA. The nicked vector DNA containing the desired mutations is then transformed
into E. coli (Top10). Libraries with multiple site-directed targets were created using SOE reaction(Splicing overlap extension). Primers were designed to introduce the desired mutations. The initial
PCRs generate overlapping gene segments that are used as template DNA for another PCR tocreate a full-length product. The internal primers generate overlapping, complementary 30 ends
on the intermediate segments and introduce the desired nucleotide changes for site-directedmutagenesis. Overlapping strands of these intermediate products hybridize at these 30 regions in
a subsequent PCR and are extended to generate the full-length product amplified by flanking
primers. The full-length product is gel-extracted and isopropanol-precipitated and eluted in a fewµl water.

251

Electroporation: Fresh Competent yeast cells (Saccaromyces cerevisiae BY4741) were preparedprior to electroporation. Cells, DNA and cut pYestDest52 vector were combined and left on ice
for 5 min. Electroporation conditions (Bio-Rad Gene Pulser Xcell): C = 25 µF, PC = 200-ohm, V= 1.5 kV (in 0.2 cm cuvettes). Cells were passed twice prior to expression. Mutants of weretransferred to pBad-His vector for expression in E. coli and consequent Ni-NTA protein
purification.

1b. Mammalian Expression Constructs for FACS
FPs were expressed as histone H2B fusion proteins in HeLa cells. Specifically, the mutants were
PCR amplified from the pBad constructs with the upstream primer. Consequently, these were cut
and ligated on piggyBac-H2B for expression in HeLa/U2OS cells. Cells were cultured in RPMI
medium (Gibco Life Technologies) supplemented with penicillin/streptomycin (Gibco Life
Technologies) and 10% heat-inactivated fetal bovine serum (Sigma-Aldrich) at 37°C with 5% CO2
plus humidity. HeLa cells transiently transfected using the TransIT-LT1 reagent (Mirus, catalog#MIR2304) were prepared for FACS analysis after 48 hours.

Section 2. Mutagenesis and Directed Evolution of mCherry tomCherry-XL
We summarize our evolution efforts below and in Figures A4.1, A4.2, and A4.3.
•

Site-directed mutagenesis on 16 (E/D/A/K/N/T/V), 17 (H/K/R) , 70 (K/R) , 99 (All 20),143 (All 20), 161 (L/M/V/I/F), 163 (All 20 AA), 173 (All 20), 175 (All 20 AA) and 197(All 20 AA) were triply- FACS enriched and revealed variations at positions 16, 17, 70,
99, 175 and 197.

•

The positions 16, 17, 70, 99, and 197 were thus targeted and the triply FACS enrichedlibrary was addressed as the C-X (Cherry-X) library. Among these variants C9 and C12
were found to have longer lifetimes, but lower brightness in yeast than that of mCherry. In
252order to restore the brightness while maintaining their increased lifetimes, at first, we
performed random mutagenesis. However, the random mutagenesis on C9 and C12 did not
produce bright variants. (Figure A4.1)

Figure A4.1. EP-PCR library of C9 and C12 variants. Microfluidic screening dot plots
displaying lifetime and brightness (fluorescence signal in volts) of mCherry, C9, C12 and errorprone PCR libraries of C9 and C12. The pseudocolor indicates normalized cell counts with respect
to the total number of screened/sorted cells at a certain value of brightness and lifetime on the plot
– black indicating the highest and blue indicating the lowest. Each dot represents an individual
yeast cell. It is evident from these plots that error-prone mutagenesis of C9 and C12 did not
improve the lifetime and brightness of these variants. To collect these data, mCherry, the variants(C9, C12) and their EP-PCR libraries were expressed in yeast cells and screened on our
microfluidic system with ~5000 cell counts. [2, 18]•

We, then performed targeted saturated mutagenesis on C9 and C12 at positions W143, I161
and Q163 based on bioinformatics guidance and sequence diversity of these amino-acidresidues in mFruit series of FPs. [20] We mixed the site-directed C9 and C12 libraries,(Figure 1; Chapter 5) which contained variants with high lifetime and brightness. Thislibrary was called C12-X. The C12-3 mutant was selected from this library, based on platebased lifetime screening.

•

An alternate evolution trajectory from the C12-X library led us to Site-Directed Clones(SDC), where we sorted the variants to enhance the populations with lifetime longer than253

3.5 ns. We selected a few variants from this lifetime-enriched library and called them SDC
variants. (e.g., variant SDC-5; QY~0.55, W143L, I161A, Q163L and I197R). The variantsof the SDC-clones exhibit a green absorption peak – this evolution trajectory wasconsequently not pursued in the context of this study. Further analysis of this lineage canbe found in Reference 21. [21]•The C12-X library was subjected to two rounds of error-prone mutagenesis and selections
for higher lifetime variants (with selection gate, lifetime> 3.7 ns) to generate the SLT(Selected-LifeTime) library. The SLT-11 mutant (mCherry N98S, R125H, F129L, Q137L,
W143S, I161V, Q163Y, and I197R) was selected using plate-based lifetime screening inyeast from the lifetime enriched SLT library.

•A repeated error-prone effort on the SLT library yielded the EP-C12-X library without any
improvement in lifetime or brightness. Consequently, we concluded that we arrived at thesaturation of lifetime with the trajectory for directing the evolution of lifetime in mCherry.

•

The octuple mutant SLT-11 had low protein yield in bacteria, consequently it could not be
purified and fully characterized. Mutations at 98, 125, 129 and 137 were found to be
external and far from the chromophore. Consequently, these positions were sequentiallyreverted to that of mCherry. Detailed investigations (single point reversions) revealed
neither of these mutations had significant impacts on the excited state lifetime of the SLT11 variant. We refer the reader to Section 3 of the SI and Reference 8 for further detailed
investigations.21 This led to the quadruple mutant that we address as mCherry-XL(mCherry W143S, I161V, Q163Y and I197R).

•

Throughout the lifetime evolution a 561 nm excitation source (Coherent Genesis MX) anda 629/56 emission window (Semrock FF573-Di01- 25x36 / Semrock FF01- 629/56)
provided additional selection pressures for selecting on a higher fluorescence brightness inyeast cells along with increased lifetime. [2, 11, 18, 21]254

Figure A4.2. Summary of mutagenesis efforts on the mCherry family to achieve lifetime
evolution. (a.) Evolution tree representative of phenotypic (photophysical) outcomes of theselections. The variants in gold were selected for characterization and study of co-evolution ofother photophysical properties. (b.) A genetic representation of the evolution tree for the mutants
relevant to this study.

255

Figure A4.3. Role of spatially distant substitutions on the photophysical properties. (a.)
mCherry’s crystal structure (PDB ID: 2H5Q) suggests positions that do not impact thephotophysics i.e., 98, 125, 129 and 137 are spatially distant (>15 Å) from the chromophore(denoted in purple). The chromophore and sidechains that perturb the photophysics of mCherry
are denoted in cyan. Sidechains of 98, 125 and 137 also face out from the β-barrel, barring theexception of F129 which is located in the loop region with the sidechain facing inwards. The
sidechain at 125 plays a role in the dimerization tendencies of DsRed derivatives like mCherry. 20
256

A positively charged sidechain e.g. R or K at 125 maintains the monomericity and does not change
the photophysics of the FP. To elucidate this, we present; (b.) The similarity in fluorescence
lifetime decay traces for the 125X variants of mCherry-XL measured using TCSPC. To test themonomericity, we present time-resolved fluorescence anisotropy measurements in Figure A4.9.
Details for the other reversions are available in Reference 21. [21] &, (c.) A minimal effect of
substitutions at 125 on variants of mCherry-XL for the red emission with excitation at 520 nm.
The inset indicates similarity in minimal green emission for these variants along with mCherry for
excitation at 480 nm.

Section 3. Sequence Alignment of the RFP Variants

Table A4.1. Sequence alignment of the mCherry variants analyzed in this study. Variation insequences have been highlighted with yellow/red. The positions highlighted in red show aminoacid substitutions that impact the photophysics of mCherry and its progeny, while the ones inyellow do not.

257Section 4. Additional in cellulo assessments
Note: The version of mCherry-XL with the R125K substitution was used for cellular assessments.

4a. Lifetime selection trajectory: Screening yeast cells for lifetime and cellularbrightness•

Screening on the microfluidic sorting device: The proteins of interest, once selected outof the respective libraries were subjected to a round of microfluidic screening on the
lifetime-sorter. Screenings were carried out at ~18-20 h post induction of FP in yeast cellswith protocols used in the sorting experiments. Lifetime and brightness of biologicaltriplicates of ~10,000 cells were recorded to report the screening data in yeast.

Figure A4.4. Lifetime & yeast-cell co-evolution trajectory. A screen of lifetime and brightnessof single yeast cells on our microfluidic sorting devices [2, 11, 18, 21] indicate the lifetime
evolution trajectory from mCherry to mCherry-XL. Means and standard deviations of biologicaltriplicates are reported. Despite a 2.5-fold higher lifetime, mCherry-XL is roughly 90% of thebrightness of mCherry presumably due to slower chromophore maturation, low expression
efficiency, etc in yeast. [18]2584b. Brightness in mammalian cells•

Flow cytometry: The proteins of interest were fused to histone H2B and expressed in
HeLa cells. Single-cell brightness was assessed by selecting single healthy cells based on
forward and side-scattering photon counts on a BD FACSCelesta single cell analyzer after
48 h of transfection. Untransfected cells were used as a control to background subtract andanalyze the fluorescence in the red and green channels. The samples were excited by a 561
nm laser line for collecting red fluorescence through the TRITC filter set (585/30 nm) anda 488 nm laser line for collecting through a GFP filter set (530/30 nm), to test for green
fluorescence.

Figure A4.5. Cellular brightness in mammalian cells. A fluorescence activated cell sorting(FACS) based brightness assay in the H2B-FP construct in HeLa cells indicates mCherry-XL is
1.5-fold brighter than mCherry. FPs were cloned into a pcDNA3 plasmid C-terminal to H2B.
Screenings were carried out at ~48 h post transfection. The error bars indicate the standard
deviations from mean values of three biologically triplicate measurements. Each biologicalreplicate measurement was comprised of a technical triplicate of 10000-20000 cells. The detailed
methods for this assay have been discussed in a previous work. [2, 18]

4c. Photostability in bacteria
Photobleaching experiments and analysis were carried out in a similar fashion as our previous
studies. [2, 18, 23] We provide short descriptions to the sample preparation and data analysis
below.
259

•

Sample Preparation and Experiment: 2-3 fluorescent bacterial colonies from plates were
washed with 500 µL imaging buffer (150 mM HEPES, 100 mM NaCl, pH 7.4) andcentrifuged at 3000-5000 RPM for 60 s, and the washing buffer was removed. These cells
were then resuspended in the same buffer to an OD in the range of 0.1 to 0.5 to get a celldensity suitable for imaging. 10–20 µL of the cell mixture was added between a clean glass
coverslip and slide. Imaging was carried on a widefield Olympus IX-73 inverted
microscope system. Samples were excited by 560 nm continuous wave LED illumination(Lumencor). Time-lapse fluorescence bleaching measurements were collected through a629/56 nm band-pass filter by a SCMOS camera (Andor Zyla) using an Olympus 20X
objective. Irradiances ranging from 1–20 W/cm2 were employed.

•

Data Analysis: In brief, two pipelines in the CellProfiler suite (V2.2.0) was used to (a)identify bacteria on an imaging plane of uniform irradiance and (b) provide normalized
intensity trajectories for the identified objects. The intensity trajectories were analyzed andfit to mono/bi/tri-exponential traces using a custom fitting program in MATLAB.

Figure A4.6. Photobleaching trends in E. coli. Bleaching profiles of mCherry, C12 andmCherry-XL are largely monoexponential and lack dark state conversion unlike FusionRed
mutants investigated in our previous studies. [2, 18, 23] Data was collected at a continuous
irradiation of ~10W/cm2 (not excitation rate normalized). Kreik is a previously published mCherryvariant selected out of photostability selections on a microfluidic platform. [22]260Figure A4.7. Comparing photostability under excitation rate normalized conditions in E.
coli. Bacteria expressing RFPs of interest were photobleached under excitation normalized
conditions using a 560 nm LED source at irradiances in the range of ~10 W/cm2. These FPs showeda near mono-exponential photobleaching trace (Figure A4.6). [23] Therefore, the t1/2 (s) is an
accurate representation of photostability or the quantum yield of photobleaching under excitation
rate normalized irradiation. [24] The expected trend of lower t1/2 with increased excited state
lifetime is also seen in this evolution study – in accordance with previous observations from thelifetime evolution efforts directed at FusionRed and mScarlet. [2, 8, 18]261

Section 5. Additional details for in vitro photophysical assessments
5a. Spectral data of the variants

Figure A4.8. Normalized absorption and emission spectra. Normalized emission spectra(right) of the variants show blue-shifts from mCherry → mCherry-XL as it is observed in theabsorption spectra (left).
Table A4.2. Spectral properties of the RFP variants. Systematic blue shifts in absorption andemission peaks are observed with increments in fluorescence lifetimes. Integrated fluorescence,calculated from the normalized emission spectra of the variants correlates with the broadness ofthe emission. It is interesting to note that these variants have increased emission broadness andStokes shift compared the parent mCherry.
RFP

𝝀𝒂𝒃𝒔 (nm)𝝀𝒆𝒎 (nm)

Stokes Shift (nm)Int. FluorescencemCherry

587

609

22

66

C12

572

608

35

88

C12-3

571

599

28

77

mCherry-XL

558

589

31

79

262

5b. Time-resolved fluorescence anisotropy

Figure A4.9. Fluorescence anisotropy decay and rotational time-constants (𝝉𝒓 ) of thevariants. Anisotropy decay of the purified FPs were measured with our TCSPC instrument (Fluro
Time 100, PicoQuant) as mentioned in the Chapter 5. 560 nm excitation and 5 MHz repetition rate
were used. The rotational time-constant (𝜏𝑟 ) of each variant was obtained by fitting thefluorescence anisotropy decay with a single exponential function. All the variants were found tohave 𝜏𝑟 similar to the parent mCherry, suggesting they likely retained in vitro monomericcharacter. TagRFP-T was characterized with slower 𝜏𝑟 , relative to the other variants. This isconsistent with its reported in cellulo oligomerization tendencies. [2, 18] The alternate evolution
trajectory into SDC clones was not pursued due to a substantial green absorption peak. Details of
the SDC variants are described elsewhere. [21]263

5c. Excited State Lifetime of the Variants

Figure A4.10. Fluorescence decay and the average lifetime (𝝉) of the variants. Excited state
lifetimes are measured with our TCSPC system (Fluro Time 100, PicoQuant) using 560-nm laser
excitation with a repetition rate of 5 MHz. Lifetime measurements were performed with purified
proteins. The fluorescence transients of the FPs were fitted with iterative reconvolution with a bi
or tri-exponential function (solid black line) and using the measured instrument response function(IRF) of the system (shown in grey). The values of lifetime were obtained by intensity weighted
average of the fitted lifetime constants. [25] The alternate evolution trajectory into SDC clones
was not pursued due to a substantial green absorption peak. Details of the SDC variants aredescribed elsewhere. [21]264

5d. Measurement of fluorescence quantum yield

Figure A4.11. Fluorescence quantum yield () of the variants. The quantum yieldmeasurements were carried out by measuring the absorbance at 520 nm, and then collecting the
integrated fluorescence over the entire red emission band (range 535-800 nm) across a stepdilution series. [2, 18] A higher slope indicates a higher quantum yield, with mCherry ( = 0.22)
and Cresyl Violet in EtOH ( = 0.54; data not shown) were used as references. [2, 18]265

5e. Estimation of the extinction coefficient•

The values of peak extinction coefficient (εmax) were determined using a ratiometricmethod as in our previous reports. [2, 18]

To measure the εmax, the following protocol

was used:•

Sample 1: Blank A - 900 μL of Tris-HCl buffer (pH 7.4). An absorption spectrum wasrecorded in the 250-750 nm range.

•

Sample 2: Blank B - 900 μL of Tris-HCl buffer (pH 7.4) + 100 μL of 10 M NaOH (pH ∼14). An absorption spectrum was recorded in the 250-750 nm range•

Sample 3: 900 μL of Tris-HCl buffer (pH 7.4) + a few μL of concentrated purified protein
sample was added to adjust the absorbance to a value of OD ∼ 0.1. An absorption spectrum
was recorded in the 250-750 nm range.

•

Sample 4: 100 μL of 10 M NaOH was added to this solution. An absorption spectrum wasrecorded in the 250-750 nm range.

•

In each case a 1 cm path length quartz cuvette was used.

•

The ratiometric relationship provided below was used to calculate the value of the peakextinction coefficient. Three independent measurements were performed. Table 1 in the
Chapter 5 represents the value of the mean and the standard deviation errors.

•
•

Abs

RFP
ϵ𝑚𝑎𝑥RFP = Abs380⁡nmmaxAbs
450⁡nm(ϵ380⁡nm)+(ϵ450⁡nm)

Unlike members of the FusionRed family,18 mCherry variants hydrolyze with a single
product of denaturation, with an absorbance peak centered at 450 nm.

266Section 6. Variation of the radiative rate constantFigure A4.12. Analysis of the radiative rate constants for mCherry variants. (a.) A linear fitof the fluorescence quantum yield with the fluorescence lifetime indicates a good fit (R2adj~0.95).
The slope of the linear fit (150 ± 14 µs-1) is indicative of the average radiative rate constant. (b.)
Values of calculated radiative rate constant with the fluorescence lifetime. The calculated valuesof the radiative rate constant lie outside the estimates provided by the average radiative rate
(provided by the range of uncertainty calculated from the linear fit in panel a. on the figure). (c.)
Values of calculated radiative rate constant with the cubed value of the peak fluorescencefrequency. The calculated values of the radiative rate constants do not have a linear response withthe cubed-value of the fluorescence frequency, thereby suggesting the change in the radiative rate
constant is possibly due to multiple inter- or non-interconverting chromophores. This observation
is further bolstered by multiexponential fluorescence lifetime decays. [24]267Section 7. Modelling non-radiative rate in the Englman-Jortner Low
Temperature/Weak Coupling limit
A fit of the total non-radiative rate with the energy gap (or the 0-0 energy) shows a poor agreementwith an Arrhenius type exponential decay. (Figure A4.13) This observation prompts investigatingother models that incorporate the role of excited state reorganization along with the energy gap,
such as the Englman-Jortner model for radiationless decay in large organic molecules. Details of
this model and its treatment in FP systems can be found in ref # 24. [24]Figure A4.13. Fit of the total non-radiative rate constant with the energy gap. (a.) A linear
fit (red line) of the logarithmic values of non-radiative rate (black squares) with the energy gap
indicates a low-quality fit (R2adj~0.79). (b.) A comparison of non-radiative rate versus thefluorescence frequency for the variants investigated in this study with the analysis performed by
the recent work of Drobizhev et. al. (2021) [26] The variants generated in this study display trends
similar to what was investigated by Drobizhev et. al for a subset of unrelated RFPs.
The shapes of absorption and fluorescence spectra for FPs of this family (Figure A4.8), indicatethat the Huang-Rhys factor is < 1 because the 0-0 transition is more pronounced than the 0-1
vibronic shoulder. Additionally, the 0-0 transition energy >> Stokes-shift, and assuming these FPs
lack any excited state photochemistry or excited state proton-transfer encourages the treatment of
the non-radiative rate with a model where two electronic potential energy manifolds couple
weakly. Therefore, we utilize the treatment of excited state vibrational relaxation from the low

268temperature weak/coupling case of the Englman-Jortner formalism. We now proceed to theestimation of the excited state reorganization energy.

7a. Estimation of reorganization energy
The reorganization energy was estimated using the model provided by Jordanides et. al. [27] Thismethod can provide an accurate representation for the reorganization energy for species that do
not exhibit Gaussian absorption and fluorescence spectra (Figure A4.14). For species that do
exhibit near Gaussian absorption and emission spectra a traditional method of estimating thereorganization energy from the Stokes-shift (λSS) can be used, [28]λSS= 0.5 (max[σabs(ω)]- max[σfl(ω)]),Eq. S1

Where σabs(ω) and σfl(ω) are the absorbance and fluorescence spectral lineshape functions in thefrequency domain.

Figure A4.14. Schematic representations of relevant observables (a.) A two state potential
energy surface indicating the visual depiction of the excited state reorganization energy. (b.)
Representative Gaussian absorbance and fluorescence spectra with a 0-0 transition where thereorganization energy is exactly equal to half the Stokes Shift.

269

Figure A4.15. Absorbance and fluorescence spectra represented on the wavenumber scale.
The spectra were scaled, also considering the nonlinear transformation of the wavelength scale to
the wavenumber scale. [29] The pink boxes highlight the 00-transition energy and the arrow
indicates the decrease in the energy gap of the transition.

However as shown in Figure A4.15, the presence of strong vibronic sidebands in the spectra forthese FPs indicates deviation from Gaussian behavior. The model by Jordanides et. al provides ameans of estimating the reorganization energy when this deviation from Gaussian behavior isobserved. The only assumption of this model is that the polarization fluctuations of the dielectric
medium follow Gaussian statistics (or the medium follows linear response). [27] The
reorganization energy is calculated from the normalized difference of the first moment between
the absorption and fluorescence spectra around the transition energy (ω00 ). With this approach wearrive at the following expression for the reorganization energy:

λ𝑆𝑀 = ⁡∫ 𝑑ω⁡σabs (ω−ω00 )−⁡σfl (ω−ω00 )⁡(ω−ω00 ), Eq. S2∫ 𝑑ω⁡σabs (ω−ω00 )+⁡σfl (ω−ω00 )270

Using this method to calculate the reorganization energy, we arrive at significantly higher
reorganization energy estimates. In reference 27, the reorganization energy of Eosin in water was
estimated as 359 cm-1 using half the value of Stokes shift and 877 cm-1 and utilizing the spectral
moments. [27] We estimated values for EosinY in ethanol and observe similar trends with thereorganization energy from the Stokes-shift being 317 cm-1 and 706 cm-1 using the spectral
moments. It should be noted that the tail ends of the absorption and emission spectrum must be
carefully baseline-corrected to ensure accurate integration over the areas of the sum and thedifference spectrum. Poor baseline correction can result in erroneous values of the reorganizationenergy.
We performed this analysis for the RFP variants and observe that the spectral moments
consistently provide larger estimates of reorganization energy than the Stokes-shift but the trends
are consistent with both approaches (Table 3 and Figure 2, Chapter 5). In both models, mCherry
displays the lowest reorganization energy in this series of variants.

Figure A4.16. The numerator and denominator functions for in the Eq S2. The plots indicate
the expected odd and even function behavior for mCherry and mCherry-XL respectively about ωω00.

271

7b. Validity of similar coupling constants for Herzberg-Teller coupling
In our analysis of non-radiative rates, we assume that the entire non-radiative rate in mCherry-XL
derives from the values estimated from the Englman-Jortner approach. We then utilize this value,
the energy gap, and the reorganization energy to estimate the coupling constant in the preexponent. Though the pre-exponent exhibits a very minor dependence on the overall non-radiative
rate (as described in the original work of Englman and Jortner), it is important to provide aquantitative assessment for this assumption. These FPs exhibit a strong vibronic progression for
the 0-1 vibronic transition in their absorption spectra (Figure A4.8). Therefore, to identify thestrength of intensity borrowing of the 0-1 band from the 0-0 band, we fit the bands to two Gaussianfunctions and analyze their energy difference and the relative intensities. The energy difference
can also be calculated using the second derivatives of the absorption spectra that reveal peak
positions of these vibronic progressions. Using the spectral derivative method Lin et. al arrived at
a value of 1340 ± 40 cm-1 for the bond-length alteration (BLA) mode of the GFP chromophore. In
our analysis (results are presented in Table A4.3), we found this difference to be a value of 966 ±45 cm-1, which can indicate a weaker BLA mode for the extended RFP chromophore system. [30]
Table A4.3. Difference in energies of the peaks of the 0-0 and 0-1 vibronic bands and therelative intensities.
FP

ΔE01- ΔE00 (cm-1)

I00/ I01

mCherry

1008

2.05

C-12

924

2.31

C-12-3930

2.17

mCherry-XL

1003

2.42

The minor (~10%) variation in the energy and the relative intensities provide quantitative validity
to the assumption of a fixed Herzberg-Teller coupling constant for the RFP family.

272

Appendix 5
Section 1. Code for microfluidic screen dot-plots
function hAxes = dscatter(X,Y, varargin)%
DSCATTER(X,Y) creates a scatterplot of X and Y at the locations%
specified by the vectors X and Y (which must be the same size), colored%by the density of the points.
%%%[data, params] = fcsread('SampleFACS');%
dscatter(data(:,1),10.^(data(:,2)/256),'log',1)%% Add contours%
hold on%dscatter(data(:,1),10.^(data(:,2)/256),'log',1,'plottype','contour')%hold off%
xlabel(params(1).LongName); ylabel(params(2).LongName);%% Reference:% Paul H. C. Eilers and Jelle J. Goeman% Enhancing scatterplots with smoothed densities% Bioinformatics, Mar 2004; 20: 623 - 628.
lambda = [];nbins = [];plottype = 'scatter';
contourFlag = false;
msize = 10;
marker = 's';logy = false;filled = true;
if nargin > 2
if rem(nargin,2) == 1
error('Bioinfo:IncorrectNumberOfArguments',...
'Incorrect number of arguments to %s.',mfilename);endokargs = {'smoothing','bins','plottype','logy','marker','msize','filled'};for j=1:2:nargin-2
pname = varargin{j};pval = varargin{j+1};
k = strmatch(lower(pname), okargs); %#ok
if isempty(k)error('Bioinfo:UnknownParameterName',...
'Unknown parameter name: %s.',pname);
elseif length(k)>1
error('Bioinfo:AmbiguousParameterName',...
'Ambiguous parameter name: %s.',pname);
else
switch(k)case 1 % smoothing factor
if isnumeric(pval)
lambda = pval;else
error('Bioinfo:InvalidScoringMatrix','Invalid smoothing parameter.');endcase 2
if isscalar(pval)
nbins = [ pval pval];else
nbins = pval;
endcase 3plottype = pval;
case 4logy = pval;
Y = log10(Y);case 5
contourFlag = pval;273

case 6
marker = pval;
case 7
msize = pval;
case 8filled = pval;
end
end
end
end
minx = min(X,[],1);
maxx = max(X,[],1);
miny = min(Y,[],1);
maxy = max(Y,[],1);
if isempty(nbins)
nbins = [min(numel(unique(X)),200) ,min(numel(unique(Y)),200) ];end
if isempty(lambda)
lambda = 10;
endedges1 = linspace(minx, maxx, nbins(1)+1);
ctrs1 = edges1(1:end-1) + .5*diff(edges1);
edges1 = [-Inf edges1(2:end-1) Inf];
edges2 = linspace(miny, maxy, nbins(2)+1);
ctrs2 = edges2(1:end-1) + .5*diff(edges2);
edges2 = [-Inf edges2(2:end-1) Inf];[n,p] = size(X);bin = zeros(n,2);% Reverse the columns to put the first column of X along the horizontal% axis, the second along the vertical.
[dum,bin(:,2)] = histc(X,edges1);[dum,bin(:,1)] = histc(Y,edges2);
H = accumarray(bin,1,nbins([2 1])) ./ n;
G = smooth1D(H,nbins(2)/lambda);
F = smooth1D(G',nbins(1)/lambda)';% = filter2D(H,lambda);
if logy
ctrs2 = 10.^ctrs2;
Y = 10.^Y;
end
okTypes = {'surf','mesh','contour','image','scatter'};k = strmatch(lower(plottype), okTypes); %#ok
if isempty(k)error('dscatter:UnknownPlotType',...
'Unknown plot type: %s.',plottype);elseif length(k)>1
error('dscatter:AmbiguousPlotType',...
'Ambiguous plot type: %s.',plottype);else
switch(k)case 1 %'surf'
h = surf(ctrs1,ctrs2,F,'edgealpha',0);case 2 % 'mesh'h = mesh(ctrs1,ctrs2,F);
case 3 %'contour'[dummy, h] =contour(ctrs1,ctrs2,F);
case 4 %'image'nc = 256;
F = F./max(F(:));
colormap(repmat(linspace(1,0,nc)',1,3));h =image(ctrs1,ctrs2,floor(nc.*F) + 1);
case 5 %'scatter'
F = F./max(F(:));
ind = sub2ind(size(F),bin(:,1),bin(:,2));274

col = F(ind);
if filled
h = scatter(X,Y,msize,col,marker,'filled');else
h = scatter(X,Y,msize,col,marker);end%colormap(repmat(linspace(1,0,256)',1,3));
end
end
if logyset(gca,'yscale','log');end
if nargout > 0
hAxes = get(h,'parent');
end%%%% This method is quicker for symmetric data.
% function Z = filter2D(Y,bw)% z = -1:(1/bw):1;% k = .75 * (1 - z.^2);% k = k ./ sum(k);% Z = filter2(k'*k,Y);function Z = smooth1D(Y,lambda)[m,n] = size(Y);E = eye(m);D1 = diff(E,1);
D2 = diff(D1,1);
P = lambda.^2 .* D2'*D2 + 2.*lambda .* D1'*D1;
Z = (E + P) \ Y;275

Section 2. Droplet-sorter operation controls
2a. Graphical user interface

Figure A5.1. The front panel of the NI LabView interface for the droplet sorter operation. i)
Setting baseline values in least-significant bit (LSB) units for background corrections in each ADC(analog to digital convertor card) channel. Standard mode of operation involves ADC1 for red
channel brightness, ADC2 for green channel brightness and ADC3 for lifetime readout from thelock in amplifier. Other ADCs 4,5, and 6 allow for the data acquisition of the FPGA board forother modes of future operation such as dark state screening. ii) Threshold value for peakdetermination for ADC channels 1,2 and 3. iii and iv) Sorter operation mode selector: redbrightness, green brightness, red+green brightness, red brightness+lifetime etc. Various
combinations of these multiparameter modalities allow for screening/sorting analytes. v) Sortthreshold gates for ADC channels. vi and vii) Real time read outs for sort/screen events and filewriting modalities. viii) Graphical displays of real time screening/sorting events on each ADC
channel. Green dots indicate the events above threshold in the green channel (ADC1) and the pink
dots indicate the events above the threshold ix) Program on/off and data saving controls x) Tabs
that allow to real time data visualization tools for each mode of operation like lifetime, event
pairing etc. The panels are presented in Figure A5.2.

276

Figure A5.2. The additional panels of the NI LabView interface for the droplet sorter
operation. i) Graphical representation of peak data for green brightness, red brightness andlifetime data. This window is an active real time data display mode irrespective of the mode ofoperation ii) Graphical representation of dual color pair matching events. This window is activeon dual color operation. iii) Graphical representation of pair matched events. This window follows
data from window ii only if the events are pair matched iv) Lifetime and brightness data in a single
mode of operation (red brightness and lifetime). This mode is active whenever red channelbrightness and lifetime data are being collected by the sorter.

277

2b. Block diagram for the sorter

278

Figure A5.3. The block diagram of the sorter GUI displayed in Figures A5.1 and A5.2

Section 3. Simulation code representing the effects of scattering onphase shift% This program simulates the effect of scattering on phase shift observed by a lock in amplifier
t=0.001:0.001:2; %0-200us Time step 1ns
phi=pi/16; % 1.8 degree phase shift
fl=0.5*sin(2*pi*29.65*t+phi);
sc=0.5*sin(2*pi*29.65*t);%plot(t(1,1:500),fl(1,1:500));%plot(t(1,1:500),sc(1,1:500));
phase=zeros(1,100)for st=1:1:100;
sig=((st-1)*sc)/100+fl;
I=zeros(1,2000);
Q=zeros(1,2000);279

I=(sin(2*pi*29.65*t));
Q=(cos(2*pi*29.65*t));
Xem=sig*I.';
Yem=sig*Q.';
phase(1,st)=atand(Yem/Xem)
end

Section 4. Simulation code representing the signal of a droplet in flow
% This program simulates a scattering and a fluorescent signal seen on flow
droplet=0.1*scat(1,499001:501000);
cell=co_sig(1,499001:501000);
r=randi([0,5],1,3); %generating random integers
sig=zeros(1,5*2000);for j=0:1:6
if j == r(1,1)
disp('filled')
sig(1,(2000*j)+1:2000*(j+1))=cell(1,1:2000);end
if j == r(1,2)
disp('filled')
sig(1,(2000*j)+1:2000*(j+1))=cell(1,1:2000);end
if j == r(1,3)
disp('filled')
sig(1,(2000*j)+1:2000*(j+1))=cell(1,1:2000);elsejsig(1,(2000*j)+1:2000*(j+1))=droplet(1,1:2000);
end
end
noise=rand(1,14000)
s=sig+0.1*noise;time=0.5:0.5:7000;
plot (time(1,:),s(1,:));

Section 5. Codes to analyze in vitro photophysical data
5a. Quantum yield%Notes for Use:
ASCII data is imported in the form of a wavelength column, the first sample
absorbance for four consecutive dilutions. The first block just extracts data from the spreadsheet
and plots it. Data is characteristic of the csv format of absorption data from the Agilent scan
program of the Cary 5000 UV-Vis spectrophotometer.
SamplAbs=mCherry;
SamplAbs=table2array(SamplAbs);
x=SamplAbs(:,1);y1=SamplAbs(:,2);y2=SamplAbs(:,4);y3=SamplAbs(:,6);y4=SamplAbs(:,8);plot(x,y1,x,y2,x,y3,x,y4)%This is a way of averaging a specified set of points and subtracting the mean from their original
dataset, i.e. setting the tail of the absorption spectrum where no absorbance is expected to zero.
Baseline=y1(1:50,1);

280

Mean=mean(Baseline);y1=y1-Mean;
Baseline=y2(1:50,1);
Mean=mean(Baseline);y2=y2-Mean;
Baseline=y3(1:50,1);
Mean=mean(Baseline);y3=y3-Mean;
Baseline=y4(1:50,1);
Mean=mean(Baseline);y4=y4-Mean;plot(x,y1,x,y2,x,y3,x,y4)%This is for making and visualizing normalized spectra.
Smax=max(y1);Y1Norm=y1/Smax;
Smax=max(y2);Y2Norm=y2/Smax;
Smax=max(y3);Y3Norm=y3/Smax;
Smax=max(y4);Y4Norm=y4/Smax;
RCB2NormAbs=table(x,Y1Norm,Y2Norm,Y3Norm,Y4Norm);% This section is relevant to absorbance values used for exciting fluorescence, for example row
181 in this data set corresponds to the wavelength 520 nm at which fluorescence was excited at.
WL=x(181,1)
A1=y1(181,1);
A2=y2(181,1);
A3=y3(181,1);
A4=y4(181,1);%This extracts and blanks fluorescence data from the Horiba-Yvon Jobin fluorimeter exported to a
csv file an ASCII format. This presumes that there are 5 spreadsheets per sample which need to beimported: the blank and measurements 1-4. Each of these spreadsheets should have 4 columns. The
first specifies the wavelength and the fourth states S1c/R1c; signal CPS corrected for the current.
x=Blank(:,1);
Baseline=Blank(:,4);y1=mCherryFlu1(:,4);y1=table2array(y1);y1=y1-Baseline;
Flumin=nanmin(y1);y1=y1-Flumin;
y2=mCherryFlu2(:,4);y2=table2array(y2);y2=y2-Baseline;
Flumin=nanmin(y2);y2=y2-Flumin;
y3=mCherryFlu3(:,4);y3=table2array(y3);y3=y3-Baseline;
Flumin=nanmin(y3);y3=y3-Flumin;
y4=mCherryFlu4(:,4);y4=table2array(y4);y4=y4-Baseline;
Flumin=nanmin(y4);y4=y4-Flumin;plot(x,y1,x,y2,x,y3,x,y4);%This is largely identical to the block above that makes normalized spectra only this time forfluorescence.
Smax=max(y1);Y1Norm=y1/Smax;
Smax=max(y2);Y2Norm=y2/Smax;
Smax=max(y3);281

Y3Norm=y3/Smax;
Smax=max(y4);Y4Norm=y4/Smax;
RCB2NormFlu=table(x, Y1Norm,Y2Norm,Y3Norm,Y4Norm);% Trapezoidal integration of the area under the fluorescence curve.
F1=trapz(y1);F2=trapz(y2);F3=trapz(y3);F4=trapz(y4);% The variable QY is the linear fit of the integrated fluorescence and the recorded absorbancethat provides the slope value. Comparative values of the slope against a reference value provide
the estimated quantum yield.
Absorbance=table(A1, A2,A3,A4,0);Absorbance=table2array(Absorbance);
IntegratedFluorescence=table(F1,F2,F3,F4,0);IntegratedFluorescence=table2array(IntegratedFluorescence);
Absorbance=Absorbance';
IntegratedFluorescence=IntegratedFluorescence';
RCB2Table=table(Absorbance,IntegratedFluorescence)scatter(Absorbance,IntegratedFluorescence)
QY=fitlm(Absorbance,IntegratedFluorescence)

5b. Extinction coefficient%Notes for Use:
ASCII data is imported in the form of a wavelength column, the first sample
absorbance and consequently the denatured sample. Data is characteristic of the csv format fromthe Agilent scan program of the Cary 5000 UV-Vis spectrophotometer. The data is collected andgraphed out for viewing.
SamplAbs=mCherry;
SamplAbs=table2array(SamplAbs);
x=SamplAbs(:,1);y1=SamplAbs(:,2);y2=DenatAbs(:,4);plot(x,y1,x,y2,x,y3,x,y4)%This is a way of averaging a specified set of points and subtracting the mean from their original
dataset, i.e. setting the tail of the absorption spectrum where no absorbance is expected to zero.
Baseline=y1(1:50,1);
Mean=mean(Baseline);y1=y1-Mean;
Baseline=y2(1:50,1);
Mean=mean(Baseline);y2=y2-Mean;
Baseline=y3(1:50,1);
Mean=mean(Baseline);%This is for making and visualizing normalized spectra.
Smax=max(y1);Y1Norm=y1/Smax;
Smax=max(y2);Y2Norm=y2/Smax;%This is for finding the peak absorbance wavelength of the native FP
result = find(Y1Norm(:,1)==1);%This extracts absorbance (y-axis) values for the peak of the native FP, the value of denatured
species at 380 nm and the value of the denatured species at 450 nm.
A1=y1(result,1); %Peak Absorption
A2=y2(41,1); %Absorption at the 41st data point or 380 nm
A3=y3(111,1); %Absorption at the 111st data point or 450 nm%The variable EC is your extinction coefficient
EC= A1/ ((A2/70000) + (A3/44000));282

5c. Stokes shift and reorganization energy% Code for calculating the reorganization energy using Stokes shift and the spectral moment model
proposed by Jordanides et. al, JPC-B (1999)% Section 1: Loading absorption and emission data from csv files% Make sure the absorption and emission are on the same x-axisload abs_cherry.csv
SamplAbs=abs_cherry;load em_cherry.csv
SamplEm=em_cherry;% Section 2: Normalize absorption and emission data
norm_abs=SamplAbs(:,2)/max(SamplAbs(:,2));
norm_em=SamplEm(:,2)/max(SamplEm(:,2))plot(SamplAbs(:,1),norm_abs);
hold on;plot(SamplEm(:,1),norm_em);
figure;% Section 3: Find peak absorption and emission to calculate Stokes shiftpeak_abs = find(norm_abs==1);
peak_em = find(norm_em==1);
peak_abs_lambda = SamplAbs(peak_abs,1);
peak_em_lambda = SamplEm(peak_em,1);
Stokes_nm= peak_em_lambda-peak_abs_lambda;
Stokes_energy=1E7*((1/peak_abs_lambda)-(1/peak_em_lambda));reorg_trad=Stokes_energy/2;%Section 4: Jacobian Transformation for wavelength to wavenumber scale
len_x_abs= length(SamplAbs);
len_x_em= length(SamplEm);
X1=zeros(len_x_abs,1);
X2=zeros(len_x_em,1);
X1(:,1)= 1E7;
X2(:,1)= 1E7;
X1= X1./SamplAbs(:,1);
X2= X2./SamplEm(:,1);
abs_sq_lam=(SamplAbs(:,1)*SamplAbs(:,1).');
em_sq_lam=(SamplEm(:,1)*SamplEm(:,1).');
abs_cm_scale= norm_abs./abs_sq_lam (:,1);
em_cm_scale= norm_em./em_sq_lam (:,1);
abs_cm_norm = abs_cm_scale (:,1) / max (abs_cm_scale (:,1));
em_cm_norm = em_cm_scale (:,1) / max (em_cm_scale (:,1));plot (X1,abs_cm_norm);hold onplot (X2,em_cm_norm);
figure;%Section 5: Calculate the 0-0 transition energy
cross= (1E7*(1/peak_abs_lambda))-reorg_trad;
X1_shift=X1-cross;
X2_shift= X2-cross;plot (X1_shift,abs_cm_norm);hold onplot (X2_shift,em_cm_norm);
figure%Section 6: Calculate the 0-0 transition energy%Flipping the emission matrix to match data structure
em2=flipud(em_cm_norm);
x_em2=flipud(X2_shift);plot(x_em2,em2);
diff=abs_cm_norm-em2;
sum=abs_cm_norm+em2;
plot (X1_shift,diff);hold onplot (X1_shift,sum);figure283

%Numerical integration
num= trapz(diff*cross);denom= trapz (sum);
reorg_jordanides= num/denom;

Section 6. Code to simulate role of electrostatics on oscillator strength% Energy and wavefunction of a particle in a box under a constant electric field boundary on bothsides to estimate the contribution of a change in electric field on the extinction coefficient.
clc; clear;
m=9.10938356e-31; % mass of electron in kg
q=1.60217662e-19; % charge of electron in Coulomb
l=12e-10; % length of the box --> length of the chromophore, ~ 12 Angstrom
F=-1e10; % electric field in V/m
h= 6.62607004e-34; % Planck's constant in m^2kg/s
hbar=(h/(2*pi));
E1_inf=(hbar^2/(2*m))*(pi/l)^2;
v_L=(q*F*l/E1_inf);
syms D(epsilon)D(epsilon)=(airy(-((pi/v_L)^(2/3))*epsilon)*airy(2,((pi/v_L)^(2/3))*(v_L-epsilon)))-(airy(2,((pi/v_L)^(2/3))*epsilon)*airy(((pi/v_L)^(2/3))*(v_L-epsilon)));epsilon=double(vpasolve(D,epsilon,-21))%A=[13.984445 24.450580528 33.03615085559 40.9371256]; % solutions for epsilon%epsilon=A(4);zeta_0=-((pi/v_L)^(2/3))*epsilon;%zeta_l= ((pi/v_L)^(2/3))*(v_L-epsilon);ratio = -airy(zeta_0)/airy(2,zeta_0); % ratio = b/a; psi= a*Ai(zeta)+b*Bi(zeta)% Normalization
x=0:1e-11:l;%f(x)=(airy(((pi/v_L)^(2/3))*((v_L*x/l)-epsilon))+(ratio*airy(2,((pi/v_L)^(2/3))*((v_L*x/l)epsilon)))).^2;
fun = @(x) (airy(((pi/v_L)^(2/3))*((v_L*x/l)-epsilon))+(ratio*airy(2,((pi/v_L)^(2/3))*((v_L*x/l)epsilon)))).^2;
a=sqrt(1/integral(fun,0,l));b=ratio*a;
psi=a*airy(((pi/v_L)^(2/3))*((v_L*x/l)-epsilon))+(b*airy(2,((pi/v_L)^(2/3))*((v_L*x/l)epsilon)));A= psi*psi';plot(x,abs(psi.^2))hold on;Section 7. Codes for analyzing photobleaching data
7a. Using Cellprofiler V2.2.0•

Pipeline 1: Select objects to bleach284

Input modules
Images: Use only the first image of the experiment for analysis

Analysis modules
Crop: Set the coordinates and radius in pixels
IdentifyPrimaryObjects: Set the "Typical diameter of objects"

OutputView output settings: Select output folder•

Pipeline 2: Export intensity timelapse for each selected object

Input modules
Images: Use all images including the one obtained from SelectBleachObjects
NamesAndTypes: Select "Single image location" that contains the image
obtained from SelectBleachObjects

Analysis modules
ExportToSpreadsheet:
1. Select Sub-folder
2. Set "Filename prefix"

After obtaining the results, open the "Filenam_FirstFrame.csv", copy the data from column"Intensity_MeanIntensity_BleachingFrames" (Column K on the csv output file) without the title
cell and paste in a newly created .mat file in MATLAB. Then analyze with"TimeLapseExp_PB.m" in MATLAB.

7b. Using Matlab code “TimeLapseExp_PB.m”%%

This program splits a column into multiple columns and transpose theresults.

%%285

% This section creates "Time" column.
% 1. Create the variable column "Time".
% 2. Choose the proper codes for various number of time intervals in the experiment.
% 3. The formula of Time for 2 time intervals = 0.25s*12(frames) + 1s*897(frames).
% 4. The formula of Time for 3 time intervals = 0.25s*12(frames) + 1s*897(frames) +15s*60(frames).
dt1 = 0.25; % 1st time interval, sec.
dt2 = 1; % 2nd time interval, sec.
nFdt1 = 12; % Number of frames with dt1 (including the first frame, t=0).
nFdt2 = 897; % Number of frames with dt2.
%-------- For 2 time intervals -------nFrames = nFdt1+nFdt2;
Time = zeros(nFrames,1);
for iit1 = 1:nFdt1
Time(iit1) = Time(iit1)+dt1*(iit1-1);
end
for iit2 = nFdt1+1:nFramesTime(iit2) = Time(nFdt1)+dt2*(iit2-nFdt1);
end%-------- For 3 time intervals -------% dt3 = 15; % 3rd time interval, sec.
% nFdt3 = 60; % Number of frames with dt3.
% nFrames2 = nFdt1+nFdt2;% nFrames = nFdt1+nFdt2+nFdt3;% Time = zeros(nFrames,1);% for iit1 = 1:nFdt1%
Time(iit1) = Time(iit1)+dt1*(iit1-1);% end% for iit2 = nFdt1+1:nFrames2%
Time(iit2) = Time(nFdt1)+dt2*(iit2-nFdt1);% end% for iit3 = nFrames2+1:nFrames%Time(iit3) = Time(nFrames2)+dt3*(iit3-nFrames2);% end%%% This section converts MeanIntensity back to 16 bit.
% 1. Set the variable name of measured mean intensity to "MeanIntensity" and save as"FileName.mat".
% 2. Run the above section to create nFrames or manually input nFrames.
%load('mCh03.mat')%nFrames = 720;
Background = 240;
% Convert back to 16 bit image intensity.
TimeLapse = transpose(reshape(MeanIntensity,[],nFrames))*2^16-Background;%%% This section normalizes the 16 bit MeanIntensity.
% !!! NOTE: need to subtract the background before normalize the signal (NormTlapse)!!!
nObjects = size(TimeLapse,2); % size(object, dimension); (dim1,dim2)=(row,col).
NormTlapse = zeros(nFrames,nObjects);
for ii = 1:nObjects
NormTlapse(:,ii) = TimeLapse(:,ii)/norm(TimeLapse(:,ii),Inf);
end%%% This section finds t_1/2 for single measurement on one FP with continuous excitation.
% !!! NOTE: need to create "Time" column!!!
% 1. [C,I] = min(___) finds the indices of the smallest elements (C), and returns them (indices)in output vector I.
%
If there are several identical smallest values, this syntax returns the index of the firstsmallest element that it finds.
% 2. Execute this section with the line containing "NormTlapseSelected" after%
removing bad data points.

286

%-------- Choose the proper [dNormT, idxPBhalf] and nObjectsFinal. -------[dNormT, idxPBhalf] = min(abs(NormTlapse-0.5));
nObjectsFinal = size(NormTlapse,2);% === NormTlapseSelected: NormTlapse with bad data removed ===% [dNormT, idxPBhalf] = min(abs(NormTlapseSelected-0.5));% nObjectsFinal = size(NormTlapseSelected,2);% TimeHalf = Time(idxPBhalf); % Just to check...
t_half = mean(Time(idxPBhalf));
t_SD = std(Time(idxPBhalf));%%% Plot NormTlapse vs Time.
plot(Time, NormTlapse(:,1:nObjectsFinal))% plot(Time, NormTlapseSelected(:,1:nObjectsFinal))%%% This section finds t_1/2 for All measurements (combined final results) on one FP with
continuous excitation.
% [dNormTime, idxPBhalfT] = min(abs(NormTlapseAll-0.5));% nObjectsAll = size(NormTlapseAll,2);% Time_half = mean(Time(idxPBhalfT));% Time_SD = std(Time(idxPBhalfT));% plot(Time, NormTlapseAll(:,1:nObjectsAll))

Section 8. Codes to simulate dark state kinetics in time and frequency
domains using numerical solutions to the three-state model•Part 1: Define function body for the rate equations%Three state: Ground, dark and excited state only%This function allows the user to run the dark state code
% This version allows user inputs for DSC/GSR times in the main code
function xprime = dsc_gsr_10(t,x,ts1d,tgsr)
I=10E3;%laser intensity in W/cm*cm%Define the constants
h=6.626E-34;
c=2.998E8;
na=6.022E23;
lambda=561E-9;
epsilon=100*100;
sigma=2.303*epsilon*1000/(na);%Planck's constant J/s%Speed of light m/s%Avogadro’s number%wavelength of light m%Molar extinction coeff in 1/(Mcm)%Absorption cross section cm*cm%Define the modulation frequency of light if using modulation%Comment out if using CW
nu=5E3;% Defining time constants% Uncomment the DSC/GSR time if using other modalities
ts1g=2.00E-9;% Excited State Lifetime%tgsr=500E-6;% GSR Time = User defined%ts1d=50E-6;% DSC Time = User defined
tds1=500E-6;% Reverse DSC = 500 microseconds% Conversion to rate constants
ks1g=1/ts1g;

287

kgsr=1/tgsr;
ks1d=1/ts1d;
kds1=1/tds1;
kb=1000;% Bleaching times in order of a few seconds

kge0=I*sigma*lambda/(h*c);% Using a sin-modulated excitation source% This can be changed to any waveform of interest% Modulation not needed if a CW source is used
kgs1=0.5*kge0*(sin(2*pi*nu*t)+1);% The rate equations involved in the three state model
xprime=[-kgs1*x(1)+ks1g*x(2)+kgsr*x(3); kgs1*x(1) - (ks1g+ks1d)*x(2)+kds1*x(3); ks1d*x(2)(kds1+kgsr)*x(3)];•Part 2: Main code for extracting state populations in the time-domain and frequency
shifts% Main body of the DSC/GSR codetic; cla; clc; clear;% Please define the range of the DSC/GSR interested to simulate
phi=zeros(100,100); % Phase difference matrix
dsc=zeros(100,1);% Frequency matrix
ts1d=0;% Initial frequency
gsr=zeros(100,1);% Lifetime matrix
nu=5E3;for i=1:1:100;
dsc(i,1)=ts1d+2E-6;
ts1d=dsc(i,1)
tgsr=0;for j=1:1:100;
a=1/(nu*1E4);
b=2*pi/(nu);tot_steps= b/a;t=0:a:b;gsr(j,1)=tgsr+20E-6;
tgsr=gsr(j,1)
tspan=t;%time step size
%total time
%total number of steps%time span for 10 full cycles

x0=[1 0 0];[t,x]=ode45(@dsc_gsr_10,tspan,x0,[],ts1d,tgsr);
xdash=(sin(2*pi*nu*t));ydash=(cos(2*pi*nu*t));
Xem=xdash.'*x(:,2);
Yem=ydash.'*x(:,2);
Xex=xdash.'*(sin(2*pi*nu*t)+1);
Yex=ydash.'*(sin(2*pi*nu*t)+1);phi(i,j)=atand(Yem/Xem)-atand(Yex/Xex);endendsave('phi')save('nu1')
save('tau')
toc

288

Section 9. Codes to simulate dark state kinetics in time and frequency
domains using analytical solutions to the three-state model%(*This program is to simulate the population based on 3-state model, including ground state (S0),excited state (S1) and dark state (D), but not considering reverse DSC*). Note this code is a
Mathematica notebook (*.nb)
ClearAll;
Eigensystem[({{-kEx, kEm+kIC, kGSR},{kEx, -(kEm+kIC+kDSC), 0},{0, kDSC, -kGSR}})];
lambda1=0;
lambda2=0.5 (-kDSC-kEm-kEx-kGSR-kIC-\[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm
kGSR+kEx kGSR+kGSR kIC)));
lambda3=0.5 (-kDSC-kEm-kEx-kGSR-kIC+\[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm
kGSR+kEx kGSR+kGSR kIC)));
v1={(kGSR (kDSC+kEm+kIC))/(kDSC kEx),kGSR/kDSC,1};v2={-(1/(2 kDSC))(kDSC-kEm-kEx+kGSR-kIC-\[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC
kGSR+kEm kGSR+kEx kGSR+kGSR kIC))),-(1/(2 kDSC))(kDSC+kEm+kExkGSR+kIC+\[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm kGSR+kEx kGSR+kGSR kIC))),1};v3={-(1/(2 kDSC))(kDSC-kEm-kEx+kGSR-kIC+\[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC
kGSR+kEm kGSR+kEx kGSR+kGSR kIC))),-(1/(2 kDSC))(kDSC+kEm+kEx-kGSR+kIC\[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm kGSR+kEx kGSR+kGSR kIC))),1};%(* n[t_]={nS0[t],nS1[t],nD[t]}; *)nC[c1_,c2_,c3_]:=c1*v1+c2*v2+c3*v3; (* t=0 *)nBC={1,0,0}; (* Initial condition *)Solve[nC[c1,c2,c3]==nBC,{c1,c2,c3}];
c1=-(\[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm kGSR+kEx kGSR+kGSR kIC)))/(kDSC(-1/kDSC(\[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm kGSR+kEx kGSR+kGSR kIC)))1/kDSC2kGSR \[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm kGSR+kEx kGSR+kGSR kIC))1/(kDSC kEx)kGSR \[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm kGSR+kEx kGSR+kGSRkIC))-1/(kDSC2 kEx)kEm kGSR \[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm kGSR+kEx
kGSR+kGSR kIC))-1/(kDSC2 kEx)kGSR kIC \[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm
kGSR+kEx kGSR+kGSR kIC))));
c2=-(kDSC kEx (-kDSC-kEm-kEx-kGSR-kIC+\[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm
kGSR+kEx kGSR+kGSR kIC))))/(2 (kDSC kEx+kDSC kGSR+kEm kGSR+kEx kGSR+kGSR kIC)\[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm kGSR+kEx kGSR+kGSR kIC)));c3=-(kDSC kEx (kDSC+kEm+kEx+kGSR+kIC+\[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm
kGSR+kEx kGSR+kGSR kIC))))/(2 (kDSC kEx+kDSC kGSR+kEm kGSR+kEx kGSR+kGSR kIC)\[Sqrt]((kDSC+kEm+kEx+kGSR+kIC)2-4 (kDSC kEx+kDSC kGSR+kEm kGSR+kEx kGSR+kGSR kIC)));nS0[t_]:=c1 Exp[lambda1 t] v1[[1]]+c2 Exp[lambda2 t] v2[[1]]+c3 Exp[lambda3 t] v3[[1]];nD[t_]:=c1 Exp[lambda1 t] v1[[3]]+c2 Exp[lambda2 t] v2[[3]]+c3 Exp[lambda3 t] v3[[3]];nS1[t_]:= c1 Exp[lambda1 t] v1[[2]]+c2 Exp[lambda2 t] v2[[2]]+c3 Exp[lambda3 t] v3[[2]];%(*Constants*)
h = 6.626*10^-34;
cLight=2.998*10^8;
NA=6.022*10^23;%(*Set parameters*)
lambda=561*10^-9;%(* Excitation wavelength in m *)I0=24*10^4;%(* Laser Intensity in W/m^2 (W/cm^2=1e4 W/m^2) *)QY=0.41;%(* Quantum yield *)
tau=2.45*10^-9;%(* Excited state lifetime in sec *)epsilon=72.9*10^3;%(* Molar exctinction coefficient in M^-1cm^-1 at lambda *)sigma=2.303*epsilon*1*10^3*1*10^-4/NA;%(* Absorption cross-section in m^2 *)kEx=(I0*sigma*lambda)/(h*cLight);%(* Excitation rate,in Hz *)kEm=QY/tau;%(* Radiative emission rate constant,in Hz *)kDSC=1/(24*10^-6);%(* DSC rate constant,in Hz *)kGSR=1/(20*10^-3);%(* GSR rate constant,in Hz *)289

kIC=(1/tau)-kEm;%(* Non radiative decay rate constant in Hz *)p1=Plot[nS0[t],{t,0,5}, PlotStyle->Directive[RGBColor[0,1.,0.],AbsoluteThickness[2.]], PlotRange> {0.7,1.0}]
pD1=Plot[nD[t],{t,0,5}, PlotStyle->Directive[RGBColor[0,1.,0.],AbsoluteThickness[2.]], PlotRange> {0,0.3}]
p1S1 = Plot[nS1[t],{t,0,5}, PlotStyle>Directive[RGBColor[0,0,1.],AbsoluteThickness[2.]],PlotRange-> {0,0.0001}]%(*Constants*)
h = 6.626*10^-34;
cLight=2.998*10^8;
NA=6.022*10^23;%(*Set parameters*)
lambda=561*10^-9;%(* Excitation wavelength in m *)I0=24*10^4;%(* Laser Intensity in W/m^2 (W/cm^2=1e4 W/m^2) *)QY=0.41;%(* Quantum yield *)
tau=2.40*10^-9;%(* Excited state lifetime in sec *)epsilon=72.9*10^3;%(* Molar exctinction coefficient in M^-1cm^-1 at lambda *)sigma=2.303*epsilon*1*10^3*1*10^-4/NA;%(* Absorption cross-section in m^2 *)kEx=(I0*sigma*lambda)/(h*cLight);%(* Excitation rate,in Hz *)kEm=QY/tau;%(* Radiative emission rate constant,in Hz *)kDSC=1/(18*10^-6);%(* DSC rate constant,in Hz *)kGSR=1/(20*10^-3);%(* GSR rate constant,in Hz *)kIC=(1/tau)-kEm;%(* Non radiative decay rate constant in Hz *)p2=Plot[nS0[t],{t,0,5}, PlotStyle->Directive[RGBColor[0,0,1.],AbsoluteThickness[2.]], PlotRange->{0.7,1.0}]
pD2=Plot[nD[t],{t,0,5}, PlotStyle->Directive[RGBColor[0,0,1.],AbsoluteThickness[2.]], PlotRange->{0,0.3}]
p2S1 = Plot[nS1[t],{t,0,5}, PlotStyle>Directive[RGBColor[0,0,1.],AbsoluteThickness[2.]],PlotRange-> {0,0.0001}]%(*Constants*)
h = 6.626*10^-34;
cLight=2.998*10^8;
NA=6.022*10^23;%(*Set parameters*)
lambda=561*10^-9;%(* Excitation wavelength in m *)I0=4.4*10^4;%(* Laser Intensity in W/m^2 (W/cm^2=1e4 W/m^2) *)QY=0.20;%(* Quantum yield *)
tau=2.01*10^-9;%(* Excited state lifetime in sec *)epsilon=70.7*10^3;%(* Molar exctinction coefficient in M^-1cm^-1 at lambda *)sigma=2.303*epsilon*1*10^3*1*10^-4/NA;%(* Absorption cross-section in m^2 *)kEx=(I0*sigma*lambda)/(h*cLight);%(* Excitation rate,in Hz *)kEm=QY/tau;%(* Radiative emission rate constant,in Hz *)kDSC=1/(38.12*10^-6);%(* DSC rate constant,in Hz *)kGSR=1/(1.9678);%(* GSR rate constant,in Hz *)kIC=(1/tau)-kEm;%(* Non radiative decay rate constant in Hz *)p3=Plot[nS0[t],{t,0,10}, PlotStyle->Directive[RGBColor[1.,0.,0.],AbsoluteThickness[2.]],
BaseStyle->{FontSize->18},PlotRange-> {0.70,1.0},Frame->True,FrameLabel->{"Time (s)","Normalized
population"}]290

pD3=Plot[nD[t],{t,0,10}, PlotStyle->Directive[RGBColor[0.,0.,1.],AbsoluteThickness[2.]],
BaseStyle->{FontSize->16},PlotRange-> {0,0.3},Frame->True,FrameLabel->{"Time (s)","Normalized
population"}]
p3S1= Plot[nS1[t],{t,0,10}, PlotStyle->Directive[RGBColor[0.,1.,0.],AbsoluteThickness[2.]],
BaseStyle->{FontSize->16},PlotRange-> {0.000004,0.000008},Frame->True,FrameLabel->{"Time(s)","Normalized population"}]Show[p1,p2,p3, PlotRange-> {0.70,1.0}]
Show[pD1,pD2,pD3, PlotRange-> {0,0.3}]
Show[p3,pD3, p3S1, PlotRange->{0,1}]

Section 10. Simulation of single molecule kinetics using Monte-Carlo
methods%Single Molecule Behavior Simulator based on Monte-Carlo Simulations on low irradiance trends
collected on a CCD/CMOS camera with acquisition times much slower than radiative and non-radiative
decay. The unit time (or time step) in this simulation is longer than fluorescence lifetime, but
shorter than dark-state lifetime. Therefore, it can be assumed that the molecule must stay orreturn to S0 or D in each unit time cycle.
clc; clear; cla;
% % Number of trajectories
nSim = 500;
sumton=zeros(nSim);sumtoff=zeros(nSim);savetraj=zeros(500,nSim);for nnn=1:nSim% Ensemble parameters for the FP of interest: Tip Use SI
h = 6.626*10^-34; c_light = 2.998*10^8; NA = 6.022E23; % constants
lambda = 561*10^-9; % Excitation wavelength in m
I0 = 1.24e4; % Laser Intensity in W/m^2 (W/cm^2 = 1e4 W/m^2)
epsilon = 71E3; % Molar extinction coefficient in M^-1cm^-1 at lambda;
sigma = 2.303*epsilon*1E3*1E-4/NA; % Absorption cross-section in m^2
kEx = (I0*sigma*lambda)/(h*c_light); % Excitation rate, in Hz
QY = 0.22; % Quantum yield
tau = 1.78e-9; % Excited state lifetime in sec
tGSR=3.76; % D to S0 time in seconds
tDSC=1/(171509); % S1 to D time in Seconds
kEm = QY/tau; % Radiative emission rate constant, in Hz
kDSC = 1/tDSC; % DSC rate constant, in Hz
kGSR = 1/tGSR; % GSR rate constant, in Hz
kIC = (1/tau)-kEm; % Non-radiative decay rate constant, in Hz%Time step data
unitT = 1e-6; % Unit time of the simulation in sec now I am considering each time unit is 10us
NunitT = 1.5e8; % Total number of timesteps you are running the simulation for% At each time step
Sig = zeros(NunitT,1); % Possible fluorescence at each time point [Sig(x,1)=0 (off) or 1 (on)]S = zeros(NunitT,1); % Possible electronic state, 0=S0, 1=S1, 2=D, where D is dark state
TimeAxis = zeros(NunitT,1);
Sig(1) = 0; % Initial fluorescence signal
S(1) = 0; % Initial electronic state
OnCount = 0; % ON state counts% Quick check
kON_En = kEx*kDSC/(kEm+kIC+kDSC);
tauON_En = 1/kON_En;
kON_SM = kEx*kIC*kDSC/(kEm+kIC+kDSC);
tauON_SM = 1/kON_SM;% Parameters below are for ON/OFF time caculation%Defining your experimental detection settings on the camera
time = unitT*NunitT; % Total time of the experiment291

nFrame = 500; % Number of frames your camera will detecttExpo = time/nFrame; % Total time/total frames will be the exposure time per frame
Ndt = round(tExpo/unitT); % Number of unitT in one tExpo [This is the number of events hidden ineach frame]%Defining variables that will be needed for the MC simulations
tExpoAxis = zeros(nFrame,1); % Time axis with respect to the frame rate
PhotonAcc = zeros(nFrame,1); % Accumulated ON/OFF counts in each frame
Status = zeros(nFrame,1); % ON/OFF status, 0=OFF, 1=ON
Switching = 1; % Just give a number
OnTime = zeros(length(Switching),1); % Continuous ON time
OffTime = zeros(length(Switching),1); % Continuous OFF time
OnAcc = zeros(length(Switching),1); % Accumulated ON counts
OffAcc = zeros(length(Switching),1); % Accumulated OFF counts
SigExpo = 0; % Total Sig in one tExpo
mm = 1; % Initial index of OnTime
nn = 1; % Initial index of OffTime

mCount = 0; % mCount default value = 1, so mCount+1 is to prepare for next consecutive ON eventnCount = 0; % nCount default value = 1, so nCount+1 is to prepare for next consecutive OFF event
Sw = 0; % Number of ON/OFF switching events
NoSw = 0; % Number of No switching events% Define probability ProbS is the probability of the molecule leaving state S. Prob_StoF is theprobability of the molecule leaving from S to state F, emProb is the probability of radiative
decay from S1 to S0. First order rate kinetics defining the probability to exist in a state ata time t
ProbS0 = 1-exp(-kEx*unitT);
ProbS1 = 1-exp(-(kEm+kIC+kDSC)*unitT);
ProbD = 1- exp(-kGSR*unitT);
S1_Exit_Rate=kEm+kIC+kDSC; %Exit pathway from the S1 state% Exit rates from each state define the movement of the system from a% particular state
Prob_S0toS1 = 1; % Assume every time a photon comes in you'll excite to S1
Prob_S1toS0 = (kEm+kIC)/S1_Exit_Rate; % QY of recovery to GS [Should be ~ 1 - major pathway]
Prob_S1toD = kDSC/S1_Exit_Rate; % QY of DSC - [This number is tiny- minor pathway]
emProb = kEm/S1_Exit_Rate; % QY of Fluorescence [Part of the major pathway that is fluorescence]% Monte Carlo simulation on single molecule electronic state. You run the iii loop for the numberof steps you initially defined, so your catch details for each timestep (ms,us or ns)%Remember Sig is the fluorescence signal at time point%Remember S is the electronic state at the time point
for iii=1:NunitT-1; %Time Axis is a point in time based on your stepsize
TimeAxis(iii)=(iii-1)*unitT;%S is your initial electronic stateif S(iii)==0; %If in the ground state
if rand>ProbS0;
Sig(iii+1)=0;
S(iii+1)=0;
else
if rand>Prob_S1toS0;
Sig(iii+1)=0;
S(iii+1)=2;
else
S(iii+1)=0;
if rand>emProb;
Sig(iii+1)=0;
else
Sig(iii+1)=1;
OnCount=OnCount+1;

292

end
end
end
end
if S(iii)==2;
if rand>ProbD;
Sig(iii+1)=0;
S(iii+1)=2;
else
Sig(iii+1)=0;
S(iii+1)=0;
end
end
end
TimeAxis(NunitT) = (NunitT-1)*unitT;% save('FR_SigTest', 'Sig');% Calculate ON/OFF time
for ii=1:nFrame;tExpoAxis(ii) = ii*tExpo;
SigExpo = 0;
for jj=1:Ndt; % Signal counts in frame ii
kk = (ii-1)*Ndt+jj;
SigExpo = SigExpo+Sig(kk);endPhotonAcc(ii) = SigExpo; % Accumulated ON/OFF counts in each frame
if SigExpo>0;
Status(ii) = 1;
elseif SigExpo==0;
Status(ii) = 0;
end
if ii==1;
if Status(ii)==1;
mCount = mCount+1;
OnTime(mm) = mCount*tExpo;
OnAcc(mm) = mCount;elseif Status(ii)==0;nCount = nCount+1;
OffTime(nn) = nCount*tExpo;
OffAcc(nn) = 0;
end
else % ii>1;
if Status(ii)==Status(ii-1); % No ON/OFF switchingif Status(ii)==1; % Continue ON
mCount = mCount+1;
OnTime(mm) = mCount*tExpo;
OnAcc(mm) = mCount;elseif Status(ii)==0; % Continue OFF
nCount = nCount+1;
OffTime(nn) = nCount*tExpo;
OffAcc(nn) = 0;
end
NoSw = NoSw+1;
else % Switching ON/OFF
if Status(ii)==1; % OFF to ON
nn = nn+1;
nCount = 0;mCount = mCount+1;
OnTime(mm) = mCount*tExpo;
OnAcc(mm) = mCount;elseif Status(ii)==0; % ON to OFF
mm = mm+1;
mCount = 0;
nCount = nCount+1;
OffTime(nn) = nCount*tExpo;
OffAcc(nn) = 0;

293

end
Sw = Sw+1;
end
end
end
TotOnTime = sum(OnTime);
TotOffTime = sum(OffTime);
nOnTime = length(OnTime);
nOffTime = length(OffTime);% This section is to plot & fit ON/OFF time histogram, obtain the statistical (average) ON/OFF
time, & histogram of photon counts
nBinsOn = 50;
nBinsOff = 50;
nBinsPhoton = 50;% For ON time
figure(1);HistgOn = histogram(OnTime,nBinsOn); hold on % Plot histogram% HistgOn = histogram(OnTime,'BinWidth',0.09) % Alternative option[HcountOn,edgesOn] = histcounts(OnTime,nBinsOn); % Get counts in each bin
FitOn = fitdist(OnTime','Exponential');tOn = FitOn.mu;
AreaOn = sum(HcountOn*HistgOn.BinWidth);% Plot fit curve
XvalsOn = 0:max(OnTime)/nBinsOn:max(OnTime);
FitCurveOn = AreaOn*exp(-XvalsOn/tOn)/tOn; % Compute fit curve. FitOn.mu is to get fit parametermu.
plot(XvalsOn,FitCurveOn); hold off% Just to check...
% hold on% histfit(OnTime,nBinsOn,'Exponential'); hold off% For OFF time
figure(2);HistgOff = histogram(OffTime,nBinsOff); hold on % Plot histogram[HcountOff,edgesOff] = histcounts(OffTime,nBinsOff); % Get counts in each bin% HistgOff = histogram(OffTime,'BinWidth',0.09) % Alternative option
FitOff = fitdist(OffTime','Exponential');tOff = FitOff.mu;
AreaOff = sum(HcountOff*HistgOff.BinWidth);% Plot fit curve
XvalsOff = 0:max(OffTime)/nBinsOff:max(OffTime);
FitCurveOff = AreaOff*exp(-XvalsOff/tOff)/tOff; % Compute fit curve. FitOn.mu is to get fit
parameter mu.
plot(XvalsOff,FitCurveOff); hold off% Just to check...
% hold on% histfit(OffTime,nBinsOff,'Exponential'); hold off% For Photon counts
figure(3);HistgPhoton = histogram(PhotonAcc,nBinsPhoton); hold on[HcountPhoton,edgesPhoton] = histcounts(PhotonAcc,nBinsPhoton);hold off%save('FR_50ms3','OnTime','OffTime','nOnTime','nOffTime','tOn','tOff','HcountPhoton')% This section is to plot single molecule ON/OFF trace
figure(4);stairs(tExpoAxis,PhotonAcc)% Actual ON/OFF trace observed in the experiment
savetraj(:,nnn)=PhotonAcc;
sumton(:,nnn)=tOn;
sumtoff(:,nnn)=tOff;
endsave('trajectories.txt', 'savetraj', '-ASCII','-append')294

Section 11. Detection code for single molecule trajectories from video(TIFF series) file%(* This code uses a TIF/TIFF image series, corrects background, selects
single emitters and saves trajectories as csv files. This is a Mathematica
notebook. *)Data analysis
In[173]:=%(* Data import *)pics=Import["C:\\Users\\Single_Mol_061420\\8.0_02\\*.tif"];
Length[pics]
pic0=Reverse[ImageData[pics[[1]]]];
Dimensions[pic0]
ListDensityPlot[pic0,ColorFunction->GrayLevel,ImageSize>600,InterpolationOrder->0]%(* Raw data conversion using import above *)pixelBorderCutoff=1;%(* If your heat map image has a "dark line" on one of the borders, use thisto cut off pixels around the border*)rawData=Table[Reverse[ImageData[pics[[i]]]],{i,1,Length[pics]}];rawData=rawData[[All,1+pixelBorderCutoff;;-1pixelBorderCutoff,1+pixelBorderCutoff;;-1-pixelBorderCutoff]];
rawData=rawData-Min[rawData];
rawData=rawData+1/10 Mean[Flatten[rawData]];
rawData=rawData/Max[rawData];
additive=Total[rawData];
additiveGaussian=Total[rawData[[Round[Length[rawData]/2];;-1]]];
Dimensions[additive]
ListDensityPlot[additive,ColorFunction->GrayLevel,InterpolationOrder>0,PlotLegends->All]
ListPlot3D[additive,PlotRange->All]%(* Plotting raw data for background Gaussian fit *)ydata=Table[{n,Mean[additiveGaussian[[n,All]]]},{n,1,Dimensions[additiveGaussian][[1]]}];
FindFit[ydata,a E^(-((y-\[Mu])^2/(2\[Sigma]^2)))+b y,{a,\[Mu],\[Sigma],b},y];yparam={a,\[Mu],\[Sigma],b}/.%;
ygauss=Table[{y,yparam[[1]] E^(-(yyparam[[2]])^2/(2yparam[[3]]^2))+yparam[[4]]y},{y,1,Dimensions[additiveGaussian][[1]]}];
xdata=Table[{n,Mean[additiveGaussian[[All,n]]]},{n,1,Dimensions[additiveGaussian][[2]]}];
FindFit[xdata,a E^(-((x-\[Mu])^2/(2\[Sigma]^2)))+b x,{a,\[Mu],\[Sigma],b},x];xparam={a,\[Mu],\[Sigma],b}/.%;
xgauss=Table[{x,xparam[[1]]E^(-(xxparam[[2]])^2/(2xparam[[3]]^2))+xparam[[4]]x},{x,1,Dimensions[additiveGaussian][[2]]}];
Print["x-fit: a E^(-((x-\[Mu])^2/(2\[Sigma]^2)))+b x","\na =",xparam[[1]],"\t b = ", xparam[[4]],"\n\[Mu] = ",xparam[[2]],"\t \[Sigma] =",xparam[[3]]];
ListPlot[{xdata,xgauss}]
Print["y-fit: a E^(-((y-\[Mu])^2/(2\[Sigma]^2)))+b y","\na =",yparam[[1]],"\t b = ", yparam[[4]],"\n\[Mu] = ",yparam[[2]],"\t \[Sigma] =",yparam[[3]]];
ListPlot[{ydata,ygauss}]295

background=Transpose[Table[1/Sqrt[xparam[[1]]yparam[[1]]] (xparam[[1]]E^(-(xxparam[[2]])^2/(2xparam[[3]]^2))+xparam[[4]]x)(yparam[[1]] E^(-(yyparam[[2]])^2/(2yparam[[3]]^2))+yparam[[4]]y),{x,1,Dimensions[additiveGaussian][[2]]},{y,1,Dimensions[additiveGaussian][[1]]}]];
background=Table[background,{i,1,Length[rawData]}];ListDensityPlot[background[[1]],ColorFunction->GrayLevel,InterpolationOrder>0,PlotLegends->Automatic]%(* Defining functions and variables *)calculateDenoisedData[backgroundImage_]:=(
tempDenoised=rawData-backgroundImage;
tempDenoised=tempDenoised-Min[tempDenoised];
tempDenoised=tempDenoised+1/10 Mean[Flatten[tempDenoised]];
tempDenoised=tempDenoised/Max[tempDenoised];
Return[tempDenoised];);
picGeometricAvg[pic_]:=Times@@((Times@@pic)^(1/Length[Flatten[pic]]));
picArithmeticAvg[pic_]:=Total[Total[pic]]/Length[Flatten[pic]];
spectralFlatness[pic_]:=picGeometricAvg[pic]/picArithmeticAvg[pic];backgroundSubtractionResolution=0.05;
backgroundSubtractionStartingFactor=1;%(* Maximizes flatness by optimizing n *)\[Epsilon]=backgroundSubtractionStartingFactor;
previousSpectralFlatness=spectralFlatness[additive];
flatnessVariation={};flatnessVariationPics={};deNoised=calculateDenoisedData[\[Epsilon]/Length[rawData]*background];deNoisedAdd=Total[deNoised];deNoisedSpectralFlatness=spectralFlatness[deNoisedAdd];
AppendTo[flatnessVariation,{\[Epsilon],deNoisedSpectralFlatness}];
While[deNoisedSpectralFlatness>previousSpectralFlatness,previousSpectralFlatness=deNoisedSpectralFlatness;
AppendTo[flatnessVariationPics,deNoisedAdd];\[Epsilon]=\[Epsilon]+backgroundSubtractionResolution;
deNoised=calculateDenoisedData[\[Epsilon]/Length[rawData]*background];deNoisedAdd=Total[deNoised];deNoisedSpectralFlatness=spectralFlatness[deNoisedAdd];
AppendTo[flatnessVariation,{\[Epsilon],deNoisedSpectralFlatness}];];
BSMF=\[Epsilon]=\[Epsilon]-backgroundSubtractionResolution;
deNoisedAdd=flatnessVariationPics[[-1]];
ListPlot[flatnessVariation]
ListDensityPlot[deNoisedAdd,PlotRange->All,PlotLegends>Automatic,ColorFunction->GrayLevel,InterpolationOrder->0]%(* Time-dependence *)tempAnalysisArray=deNoised;
timeAvgBrightness=Table[Mean[Flatten[tempAnalysisArray[[ii]]]],{ii,Length[deNoised]}];
timeStDevBrightness=Table[StandardDeviation[Flatten[tempAnalysisArray[[ii]]]],{ii,Length[deNoised]}];ListLinePlot[{timeAvgBrightness,timeStDevBrightness,Table[Max[tempAnalysisArray[[u]]],{u,Length[tempAnalysisArray]}],Table[Min[tempAnalysisArray[[u]]],{u,Length[tempAnalysisArray]}]},PlotRange->All,PlotLegends>{"Mean","StDev","Max","Min"}]%(* Bi exponential *)tempAnalysisArray=deNoised;
timeAvgBrightness=Table[Mean[Flatten[tempAnalysisArray[[ii]]]],{ii,Length[deNoised]}];

296

exponentialFit=FindFit[timeAvgBrightness,{a1 E^(- t/\[Tau]1)+a2 E^(t/\[Tau]2)+b,{a1>0, b>0, \[Tau]2>\[Tau]1>1,a2>0}},{a1, \[Tau]1,a2,\[Tau]2,b},t]timeParam={a1, \[Tau]1,a2, \[Tau]2,b}/.exponentialFit;
timeFit1=Table[timeParam[[1]] E^(t/timeParam[[2]])+timeParam[[5]],{t,1,Length[timeAvgBrightness]}];timeFit2=Table[timeParam[[3]] E^(t/timeParam[[4]])+timeParam[[5]],{t,1,Length[timeAvgBrightness]}];timeDecayFit=Table[timeParam[[1]] E^(- t/timeParam[[2]])+timeParam[[3]] E^(t/timeParam[[4]])+timeParam[[5]],{t,1,Length[timeAvgBrightness]}];ListLinePlot[{timeAvgBrightness,timeDecayFit,timeFit1,timeFit2},PlotRange>All]
avgBackground=Mean[Mean[background[[1]]]];
backgroundTD=Table[(timeFit1[[i]]/avgBackground)background[[i]],{i,Length[background]}]; (* Change how many exponentials you want here by changing"timeFit1" array to "timeFit2" or "timeDecayFit" *)ListLinePlot[{Table[Mean[Mean[backgroundTD[[j]]]],{j,Length[backgroundTD]}],t
imeAvgBrightness}]
deNoisedTD=calculateDenoisedData[backgroundTD];
tempAnalysisArray=deNoisedTD;
timeAvgBrightness=Table[Mean[Flatten[tempAnalysisArray[[ii]]]],{ii,Length[tempAnalysisArray]}];timeStDevBrightness=Table[StandardDeviation[Flatten[tempAnalysisArray[[ii]]]],{ii,Length[tempAnalysisArray]}];ListLinePlot[{timeAvgBrightness,timeStDevBrightness,Table[Max[tempAnalysisArray[[u]]],{u,Length[tempAnalysisArray]}],Table[Min[tempAnalysisArray[[u]]],{u,Length[tempAnalysisArray]}]},PlotRange->All,PlotLegends>{"Mean","StDev","Max","Min"}]%(* Variables to make protein detection easier to work with *)desiredNumberOfProteins=500;
analysisArray=deNoisedTD;
blinkTraceSmoothing=1;
maxProteinRadius= 2;
brightnessThreshold=Mean[Flatten[Total[analysisArray]]]+StandardDeviation[Flatten[Total[analysisArray]]];%(* Molecule detection code *)tempAnalysisArray=Total[analysisArray];width=maxProteinRadius-1;
proteins={};(* Keep going until it finds the proper number of traces *)For[iterator=0,iterator<desiredNumberOfProteins,iterator++,
i=j=1;%(* Iterate over x to find location of maximum *)While[i<=Length[tempAnalysisArray]&&iterator<desiredNumberOfProteins,
j=1;%(* Iterate over y to find location of maximum *)While[j<=Length[tempAnalysisArray[[i]]]&&iterator<desiredNumberOfProteins,%(* Once you find maximum value, do this *)If[tempAnalysisArray[[i,j]]==Max[tempAnalysisArray],%(* Append location of maximum value and begin scan of (2*width + 1)^2 pixel
grid centered at maximum value *)AppendTo[proteins,{}];
For[ip=Max[i-width,1],ip<=Min[i+width,Length[tempAnalysisArray]],ip++,
For[jp=Max[j-width,1],jp<=Min[j+width,Length[tempAnalysisArray[[ip]]]],jp++,If[tempAnalysisArray[[ip,jp]]>brightnessThreshold,AppendTo[proteins[[Length[proteins]]],{ip,jp}];];297

tempAnalysisArray[[ip,jp]]=0;];];i=Length[tempAnalysisArray];j=Length[tempAnalysisArray[[i]]];
];
j++;
];
i++;
];
];
ClearAll[i,j,ip,jp,iterator];
blink={};
For[prot=1,prot<=desiredNumberOfProteins,prot++,
AppendTo[blink,Table[{t,Mean[Table[
analysisArray[[t]][[
proteins[[prot,i,1]]]][[
proteins[[prot,i,2]]]],{i,Length[proteins[[prot]]]}]]},{t,1,Length[analysisArray]}]];];
ClearAll[prot];
graphicsGridSize=Ceiling[Sqrt[desiredNumberOfProteins]];plots=Table[{},{ii,graphicsGridSize}];
trace=1;
While[trace<=desiredNumberOfProteins,index=Mod[trace,graphicsGridSize];If[index==0,index=graphicsGridSize];
AppendTo[plots[[index]],ListLinePlot[Mean[Transpose[Partition[blink[[trace]],blinkTraceSmoothing]]],PlotRange->All,PlotLabel->ToString[trace]]];trace++;];
GraphicsGrid[plots,ImageSize->1200]
Out[174]= 600
Out[176]= {270,270}
Out[177]=
Out[185]= {268,268}
Out[186]=
Out[187]=
During evaluation of In[173]:= x-fit: a E^(-((x-\[Mu])^2/(2\[Sigma]^2)))+b x
a = 23.2441 b = -0.0149449\[Mu] = 223.885\[Sigma] = 187.199
Out[197]=
During evaluation of In[173]:= y-fit: a E^(-((y-\[Mu])^2/(2\[Sigma]^2)))+b y
a = 21.6005 b = -0.0111732\[Mu] = 139.553\[Sigma] = 146.977
Out[199]=
Out[202]=Out[220]=
Out[221]=
Out[225]=
Mean
StDev
Max
Min

298

Out[228]= {a1->0.00300059,\[Tau]1->14.0738,a2->0.00697043,\[Tau]2->19.3128,b>0.0398134}
Out[233]=
Out[235]=
Out[240]=
Mean
StDev
Max
Min
%(* Exports blink traces*)
fileName="TrFRMQNoOx_25_7_7"
exportData=Table[i,{i,1,Length[blink[[1]]]},{j,1,Length[blink]-1}];
For[ii=1,ii<=Length[blink]-2,ii++,
For[jj=1,jj<=Length[blink[[ii]]],jj++,
exportData[[jj,ii+1]]=blink[[ii,jj,2]];];];Export[fileName<>".csv",exportData];
Out[270]= NewEGFPNoOx_10_02_7_23%(* Brightness histogram video *)brightnessHistVid=Table[
Image[
Histogram[Round[Flatten[tempAnalysisArray[[u]]],0.01],
100,
PlotRange->{{0,1},{0,2750}},
Epilog->Inset[Framed[Grid[{{"Mean =",Mean[Mean[tempAnalysisArray[[u]]]]},{"Max =",Max[tempAnalysisArray[[u]]]},{"Min =",Min[tempAnalysisArray[[u]]]}},
Alignment->{{Left}}],Background->White],{Right,Top},{Right,Top}]],
ImageSize->600],{u,Length[tempAnalysisArray]}];
ListAnimate[brightnessHistVid]%(* Plots all pixel brightnesses in all frames *)allPixelTrace=Flatten[Table[{ii,tempAnalysisArray[[ii,jj,kk]]},{ii,Length[tempAnalysisArray]},{jj,Length[tempAnalysisArray[[ii]]]},{kk,Length[tempAnalysis
Array[[ii,jj]]]}],2];
DensityHistogram[allPixelTrace,allPixelTrace[[-1,1]],PlotRange>{{0,allPixelTrace[[-1,1]]},{0,1}},ColorFunction->"Rainbow"]299

Section 12. Code for binarizing single molecule trajectories% Single Molecule Trajectory Binarizer Readme File
% Matlab Live Script Version Info: Matlab R2021 with fit toolbox% %----------------------------------------------%%% File Name: LoopedBin_5.mlx% Input Data format: time trace tarjectories *.csv format. (col (1): frame/time col (2,:):fluorescence intensity info)% %----------------------------------------------%% Description: This code accepts noisy single-molecule fluorescence time traces and tries tobinarize them based on an input guess "on" value. The code binarizes the on and off time traces,
provides information on the statistics of on and off events, fits the binned on and off data to abiexponential decay to give a time constant based on a Possionian distribution.

% %----------------------------------------------%% # Section 1: Choose upto 8 fluorescence traces to track the frame/time information withfluorescence intensity% * Select upto 5 traces with a "guess value" for a single molecule on event.
% * Note this is a guess "on" only - program will go through re-iterative protocols to polishthis value% * Run this section only.

% # Section 2: Defines selected "On" time and displays it and associated stats% Set the trace number (upto 5) for the 1D array "ChosenOne" and "BlinksStart" and "BlinksEnd" todefine the guess "on" time values% * Check on the plot in section 2 to see if the mean and standard deviations reported for theguess "on" make sense for the trace.
%Example: is the off-event included in standard deviation window of the mean guessed on% * If not: re-define the guess "on"% * If yes: Run the rest of the code.
%% # Section 3: Extracts noise of dataset and fits it to a random distribution.
%%% # Section 4: Identifies state changes and binarizes based on them.
%%% # Section 5: Binarized trace storage%%% Section 6:% * Fits on and off times to mono or biexponential fits and reports relevant stats% * If fits are not converging, starting values can be changed%Section 1:
RawTraces=E3Negative(:,:); % Picks a preimported dataset. Dataset should have Frame # as thefirst column
H=height(RawTraces);
W=width(RawTraces);
RawTraces=table2array(RawTraces);
x=RawTraces(:,1);
Displaytraces = [10,9,8,7,6,5,4,3] %Fill in the #s of 8 traces you would like to look at

for a = 1:8 % Plots 8 traces for viewing. At least 5 on times must be manually identified
subplot(4,2,a)300

plot(x,RawTraces(:,Displaytraces(a)))
title(Displaytraces(a))
ylabel('Fl(a.u)');xlabel('Frame')
end

RawTraces=array2table(RawTraces);
traces = figure();clf%Section 2: Defines selected "On" time and displays it and associated stats
ChosenOnes = [ 5, 5, 5, 5, 5] % Chosen Blinks - Maintain same order throughout
BlinksStart = [ 261, 261, 262, 264, 265] %Start of on time -Frame Number (Can't be 0)
BlinksEnd =[ 299, 299, 298, 297, 295] % Ending Number%Try to pick traces with clear on times that aren't significantly higher%than other blinks (i.e. potential multi fluorophore events)
Mean= zeros(1,5);
SD= zeros(1,5);
LowB= zeros(1,5);
UpB= zeros(1,5);

for a=1:5 %Run stats on selected on times.
chosen = table2array(RawTraces(:,ChosenOnes(a)));blinkduration = linspace(BlinksStart(a),BlinksEnd(a),BlinksEnd(a)-BlinksStart(a)+1);
Samblink = (0);SamBlink=table2array(RawTraces(BlinksStart(a):BlinksEnd(a),ChosenOnes(a)));Mean(a)=mean(SamBlink);
SD(a)=std(SamBlink);
LowB(a)=Mean(a)-2*SD(a);%Segments above this value are considered "on" during that time
UpB(a)=Mean(a)+2*SD(a);%Segments above this value are considered multiprotein and the offending trace removed fromanalysis
Meana= linspace(Mean(a),Mean(a),numel(x));%Makes lines for plotting bounds
LowBa= linspace(LowB(a),LowB(a),numel(x));
UpBa= linspace(UpB(a),UpB(a),numel(x));

subplot(3,2,a)%The selected on time is shown in red. The lower bound should be high enough to distinguishbetween an on and an off event (i.e above background)plot(x,chosen,x,LowBa,x,UpBa,x,Meana,blinkduration,SamBlink,'red')ylabel('Fl(a.u)');xlabel('Frames')
title(ChosenOnes(a))
endsubplot(3,2,6) %Plots a key with a legend to make sure all other plots are legible
plot(x,chosen,x,LowBa,x,UpBa,x,Meana,blinkduration,SamBlink,'red')legend('Trajectory','LowerBound','UpperBound','Mean')title("Key")

MeanAr =Mean %Shows the means of each selected on time. Should all probably be comparable
SDAr = SD
LowBAr = LowB %Boundary values, by their associated reference trace
UpBAr = UpB
UpB = 0;LowB = 0;
RawTrM=RawTraces{:,:}; % Converts the table to a Matrix
TrajAve=sum(sum(RawTrM(:,2:end)))/((W-1)*H) %Average of entire dataset for comparison

301

clf
Section 3
Extracts noise of dataset and fits it
DeltaI=RawTrM(1:end-1,2:end)-RawTrM(2:end,2:end); %Finds difference in intensity between every
consecutive frame in the dataset

B=DeltaI(DeltaI~=0); %Histograms noise, removes any zero values to avoid a large peak @ zero
h=histogram(B,1500,'BinLimits',[min(B),max(B)]); %Always makes 1500 bins, size varies based onnoise spreadxlabel('Delta Intensity')
counts=h.Values.';x3=[min(B):((max(B)-min(B))/1499):max(B)].';
x3=x3(counts~=0);
counts=counts(counts~=0);[NoiseFit,gofnoise] = fit(x3,counts,'gauss1') %Displays fit for noise and goodness of fit statsplot(NoiseFit,x3,counts) %Plots noise fit
xlabel('Delta in A.U.')
coeffNoise=coeffvalues(NoiseFit);%Section 4:

Identifies state changes and binarizes based on them

Fmean=coeffNoise(1,2); %Finds values of noise fit
FSD=coeffNoise(1,3)/(2^(1/2));
FLB=Fmean-1.5*(FSD) %Frames that change by more than one of the bounds are considered points ofinterest
FUB=Fmean+1.5*(FSD) %Points of interest are possible state changes
Points=zeros(1,W);%Where points will be stored
for k=1:1:W-1 %Checks for frames where change is larger than the bounds
FrameNum=1;
for l=1:1:H-1
if DeltaI(l,k)>=FUB
Points(FrameNum,k)=l;
FrameNum=FrameNum+1;
elseif DeltaI(l,k)<=FLB
Points(FrameNum,k)=l;
FrameNum=FrameNum+1;
else
end
end
end
ExperimentBins=zeros(H,W-1);
A=mat2dataset(Points);
A=dataset2table(A);H2=height(A);%Section 5: Binarized trace storage
savedtraces = cell(1,5); %Where extracted on times, off times and binarized traces will be stored
savedontimes = cell(1,5);
savedofftimes = cell(1,5);
for a=1:5
UpB = UpBAr(a);LowB = LowBAr(a);for k=1:1:W-1 %Actually binarizes
for l=1:1:H2 %Checks between every point of interest and finds the average between them
POI=Points(l,k); % Compares averages to the bounds set by selected trace
POI2=0; %If it is below the low bound = 0
if l~=1 % Above the upper bound =2
POI2=Points(l-1,k); % Otherwise = 1
end
if l==1

302

Section=RawTrM(1:POI,k+1);
SectionMean=mean(Section);
if SectionMean>UpB
ExperimentBins(1:POI,k)=2;
elseif SectionMean<LowB
ExperimentBins(1:POI,k)=0;
else
ExperimentBins(1:POI,k)=1;
end
elseif POI==0 && POI2~=0
Section=RawTrM(POI2:H,k+1);
SectionMean=mean(Section);
if SectionMean>UpB
ExperimentBins(POI2:H,k)=2;
elseif SectionMean<LowB
ExperimentBins(POI2:H,k)=0;
else
ExperimentBins(POI2:H,k)=1;
end
elseif POI==0
else
Section=RawTrM(POI2:POI,k+1);
SectionMean=mean(Section);
if SectionMean>UpB
ExperimentBins(POI2:POI,k)=2;
elseif SectionMean<LowB
ExperimentBins(POI2:POI,k)=0;
else
ExperimentBins(POI2:POI,k)=1;
end
end
end
end
for k=1:1:W-1 %Checks for and sets any 1 frame events to neighboring values
for l=1:1:H % i.e. 1110111 = 1111111
if l==1
elseif l==H
elseif ExperimentBins(l,k)~=ExperimentBins(l-1,k) && ExperimentBins(l1,k)==ExperimentBins(l+1,k)ExperimentBins(l,k)=ExperimentBins(l-1,k);
end
end
end
TS=ExperimentBins(:,ChosenOnes(a)-1); %Shows each chosen trace binarized based on that traces
metrics
subplot(3,2,a)plot(x,TS);
title(['Trace ', num2str(ChosenOnes(a))])ylabel('Fl(a.u)');xlabel('Frame')% Section 6% Throws out multi protein events and extracts on and off times
TraceNum=1;
TraceNums = zeros(1,5);
SelectBlinks =[];
for k=1:1:W-1
if max(ExperimentBins(:,k))==1
SelectBlinks(:,TraceNum)=ExperimentBins(:,k);TraceNum=TraceNum+1;
else
end
end
TraceNum=TraceNum-1;
OffNum=1;
OnNum=1;
Ontime=0;Offtime=0;
for k=1:1:TraceNum

303

for l=1:1:H
if l==1 && SelectBlinks(l,k)==1
Ont=1;
elseif l==1 && SelectBlinks(l,k)==0
Offt=1;
elseif SelectBlinks(l,k)==1 && SelectBlinks(l-1,k)==0
Offtime(OffNum,1)=Offt;
OffNum=OffNum+1;
Ont=1;
elseif SelectBlinks(l,k)==0 && SelectBlinks(l-1,k)==1
Ontime(OnNum,1)=Ont;
OnNum=OnNum+1;
Offt=1;
elseif SelectBlinks(l,k)==1
Ont=Ont+1;
elseif SelectBlinks(l,k)==0
Offt=Offt+1;
end
end
end
SelectBlinks = logical(SelectBlinks);
TraceNums(a)=TraceNum;savedtraces{a} = SelectBlinks;
savedontimes{a} = Ontime;
savedofftimes{a} = Offtime;end
TraceNums
Binned =figure();clf%Section 7% Fits on and off times to mono and biexponential fits and reports relevant stats% If fits are not converging, starting values can be changed
Fitinfo = cell(6,8);
Fitinfo{6,1} = "Onfit";
Fitinfo{6,2} = "OnStats";
Fitinfo{6,3} = "Bionfit";
Fitinfo{6,4} = "BiOnStats";
Fitinfo{6,5} = "Offfit";
Fitinfo{6,6} = "OffStats";
Fitinfo{6,7} = "BioffFit";
Fitinfo{6,8} = "Bioffstats";
OnOffRatio=zeros(5,3);

for a=1:5
Ontime = cell2mat(savedontimes(a));
Offtime = cell2mat(savedofftimes(a));[~,edges] = histcounts(Ontime,50);

subplot(5,1,1)
h=histogram(Ontime,50,'FaceColor','yellow');
title(['Trace ', num2str(ChosenOnes(a))])legend('On times')
xlabel('Frames')

xfit = fittype('a*exp(-u/t)','independent','u');
fo = fitoptions(xfit);
fo.Lower = [0 0];
xfit = fittype('a*exp(-u/t)','independent','u','options',fo);%Start Points for On mono fit
startPoints = [20, 20];counts=h.Values.';304

x3=[edges(1,1):((edges(1,51)-edges(1,1))/49):edges(1,51)].';[Onfit,OnStats]=fit(x3,counts,xfit,'Start',startPoints);

subplot(5,1,2)
plot(Onfit,x3,counts)
title('On MonoExponential')
xlabel('Frames')
ylabel('On Events')
onfunc= Onfit.a*exp(-x3/Onfit.t);
onresid=counts-onfunc;
subplot(5,1,3)
plot(x3,onresid,'*')
title('On Residuals')
xlabel('Frames')
ylabel('Delta')

bifit = fittype('a*exp(-u/t)+b*exp(-u/t2)','independent','u');bifo = fitoptions(bifit);bifo.Lower = [0 0 0 0];
bifo.Upper = [1000,1000,1000,1000];
bifit = fittype('a*exp(-u/t)+b*exp(-u/t2)','independent','u','options',bifo);%Start Points for “on” biexp fit
bistartPoints = [30, 12, 1, 50];
[biOnfit,biOnStats]=fit(x3,counts,bifit,'Start',bistartPoints);

subplot(5,1,4)
plot(biOnfit,x3,counts)
title('On BiExponential')
xlabel('Frames')
ylabel('On Events')
bionfunc= biOnfit.a*exp(-x3/biOnfit.t)+biOnfit.b*exp(-x3/biOnfit.t2);
bionresid=counts-bionfunc;
subplot(5,1,5)
plot(x3,bionresid,'*')
title('On Bi Residuals')
xlabel('Frames')
ylabel('Delta')
On =figure();clf
OnLT=(biOnfit.a*biOnfit.t+biOnfit.b*biOnfit.t2)/(biOnfit.a+biOnfit.b);
PercentFast=(biOnfit.a/(biOnfit.a+biOnfit.b))*100;
PercentSlow=(biOnfit.b/(biOnfit.a+biOnfit.b))*100;[N,edges] = histcounts(Offtime,50);
subplot(5,1,1)
h=histogram(Offtime,50,'FaceColor','#7E2F8E');
title(['Trace ', num2str(ChosenOnes(a))])legend('Off times')
xlabel('Frames')
counts=h.Values.';x3=[edges(1,1):((edges(1,51)-edges(1,1))/49):edges(1,51)].';%Start Points for “off” mono fit
startPoints = [40, 20];
[Offfit,OffStats]=fit(x3,counts,xfit,'Start',startPoints);

subplot(5,1,2)
plot(Offfit,x3,counts)
title('Off MonoExponential')
xlabel('Frames')
ylabel('Off Events')
offfunc= Offfit.a*exp(-x3/Offfit.t);305

offresid=counts-offfunc;

subplot(5,1,3)
plot(x3,offresid,'*')
title('Off Residuals')
xlabel('Frames')
ylabel('Delta')%Start Points for “off” biexp fit
bistartPoints = [75, 3, 20, 60];
[biOfffit,biOffStats]=fit(x3,counts,bifit,'Start',bistartPoints);
subplot(5,1,4)
plot(biOfffit,x3,counts)
title('Off BiExponential')
xlabel('Frames')
ylabel('Off Events')
biofffunc= biOfffit.a*exp(-x3/biOfffit.t)+biOfffit.b*exp(-x3/biOfffit.t2);
bioffresid=counts-biofffunc;

subplot(5,1,5)
plot(x3,bioffresid,'*')
title('Off Bi Residuals')
xlabel('Frames')
ylabel('Delta')

Off =figure();clf

OffLT=(biOfffit.a*biOfffit.t+biOfffit.b*biOfffit.t2)/(biOfffit.a+biOfffit.b);
PercentFastoff=(biOfffit.a/(biOfffit.a+biOfffit.b))*100;
PercentSlowoff=(biOfffit.b/(biOfffit.a+biOfffit.b))*100;

Ondata(a,:)=[biOnfit.t,PercentFast,biOnfit.t2,PercentSlow,biOnStats.adjrsquare,OnLT];
Offdata(a,:)=[biOfffit.t,PercentFastoff,biOfffit.t2,PercentSlowoff,biOffStats.adjrsquare,OffLT];

Fitinfo{a,1} = (Onfit);
Fitinfo{a,2} = (OnStats);
Fitinfo{a,3} = (biOnfit);
Fitinfo{a,4} = (biOnStats);
Fitinfo{a,5} = (Offfit);
Fitinfo{a,6} = (OffStats);
Fitinfo{a,7} = (biOnStats);
Fitinfo{a,8} = (biOnfit);

Offtraces = 0;
Ontraces = 0;
for e = 1:TraceNums(a)if min(SelectBlinks(1:2,e)) == 0
Offtraces= Offtraces +1;
else
Ontraces = Ontraces +1;
end
end
OnOffRatio(a,:)= [Ontraces,Offtraces, Ontraces/(Offtraces+Ontraces)];
end
SelectionInfo = [ChosenOnes',BlinksStart',BlinksEnd']%Shows chosen traces and frames, in case the settings need to be reproduced
Ondata%Shown as Component 1, % Component 1, Component 2, % Component 2, Adjusted R^2, Lifetime

306

OfficialOn = [mean(Ondata(:,6)),std(Ondata(:,6))]%Average of the lifetimes of the five traces and standard deviation
Offdata
OfficialOff = [mean(Offdata(:,6)),std(Offdata(:,6))]
OnOffRatio

307

References

1.

Nov, Y. When Second Best Is Good Enough: Another Probabilistic Look at Saturation
Mutagenesis. Appl. Environ. Microbiol. 2012, 78 (1), 258–262.
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