MULTICOLOR FLUORESCENCE OPTICAL TWEEZERS METHODS AND

APPLICATIONS TO NUCLEIC ACID FOLDING

By

Cho-Ying Chuang

A DISSERTATION

Submitted to

Michigan State University

in partial fulfillment of the requirements

for the degree of

Physics - Doctor of Philosophy

Quantitative Biology - Dual Major

2019

ABSTRACT

MULTICOLOR FLUORESCENCE OPTICAL TWEEZERS METHODS AND

APPLICATIONS TO NUCLEIC ACID FOLDING

By

Cho-Ying Chuang

Nucleic acids and proteins are fundamental molecular units of life. To understand

their properties, we need powerful tools that allow investigation at the single-molecule level.

Over the past three decades, the development of single-molecule force and fluorescence tech-

niques has provided us new knowledge that was previously unattainable through ensemble

measurements. However, we lack methods that allow us to precisely measure the mechanical

properties of these molecules while visually detecting multiple molecules at the same time. In

this dissertation, we maximize the information obtained in single-molecule measurements by

pushing the techniques to be more precise and more complex. We then utilize our instrument

to directly observe the folding and unfolding of the nucleic acid G-quadruplex structure.

Among the single-molecule force techniques, angstrom-resolution has been achieved

by optical tweezers using the dual-trap instrument design. Dual-traps can be produced by

acousto-optic (AO) devices, which have many advantages, but trap positioning inaccuracies

have limited their usage at high-resolution. We have designed a method to remove the

inaccuracies by randomizing the phase of the radio frequency that drives the AO device.

We demonstrated that the trap inaccuracies are completely eliminated and high-resolution

trapping quality is achieved. This advance allows us to perform long duration measurements

with reduced drift in trap measurement over time.

Next, we present instrumentation advances that combine high-resolution optical tweez-

ers and multicolor confocal fluorescence spectroscopy along with automated single molecule

assembly. Multicolor not only allows the detection of multiple observables but also increases

the flexibility in the choice of fluorophores. We demonstrated the ability to simultaneously

measure angstrom-scale changes in tether extension and single fluorophore signals. The

biggest challenge in integrating optical tweezers and fluorescence is the potential for greatly

enhanced photobleaching which can make experiments impossible. We showed that the mean

number of photons emitted before bleaching is unaffected by the trap laser when interlacing

the fluorescence and optical trap lasers. We investigated the photostability of quantum dots

and fluorophores. Finally, we devised computer-controlled automation to conserve the fluo-

rophore lifetime. This advance enables us to observe multiple molecules or multiple degrees

of freedom within a molecular complex while mechanically manipulate and detect them.

Taking advantage of these method and instrumentation advances, we investigate

the folding and unfolding of a DNA secondary structure: thrombin-binding aptamer G-

quadruplex (TBA-GQ). Studying the kinetics of G-quadruplex formation is essential for

understanding telomere regulation (the ends of chromosomes) and therapeutic approaches

for disease. TBA-GQ is the smallest G-quadruplex. Although many experiments and simula-

tions have been done on G-quadruplex, the small size and low stability make it very difficult

to observe folding and unfolding of TBA-GQ directly. Our high-resolution optical tweezers

have the sensitivity and stability to directly observe TBA-GQ at very low forces. We found

that with increasing force, the folding rate decreased and the unfolding rate increased. Our

work demonstrates that at a given force, the TBA-GQ formation is facilitated by metal

ions and is stabilized by thrombin.

It also indicates that the equilibrium force increased

as KCl concentration increased. From a detailed analysis of the folding and unfolding rate

constants vs applied force, we were able to detect a single transition state conserved across

all conditions and identify the structure of the transition state as the G-triplex structure.

To my parents Fu-Mei and Ching-Shiang

iv

ACKNOWLEDGMENTS

This dissertation would not have been possible without the guidance and support of many

people.

I would like to start by thanking my advisor, Professor Matt Comstock, for being

supportive and challenging. He gave me the opportunity to enter the field of single-molecule

biophysics. I gained invaluable experience on setting up a new lab from scratch. He pro-

vided training and resources that guided me through the process of being an independent

researcher. I would also like to express my deepest gratitude to Professor Lisa Lapidus for

providing insightful suggestions. As a faculty in biophysics, she has been one of my mentors

in these years. I’m extremely grateful to my guidance committee members: Professor Matt

Comstock, Professor Lisa Lapidus, Professor Heedeok Hong, Professor Carlo Piermarocchi,

and Professor Stuart Tessmer, for offering helpful suggestions. I would like to extend my

thanks to our collaborator, Professor Hamza Balci (Kent State University), for his inputs in

the project.

Many thanks to all the past and present members of Comstock Lab and Lapidus Lab,

especially to Dena Izadi, Jess West, Miles Whitmore, Matt Zammit, and Drew Baker. The

time we spent together was the greatest moment in my graduate school life. I also wish to

thank the members in our dissertation writing group, Aimee Shore and Matt Mondragon,

for their emotional support and pushing this dissertation over the finish line. I would like to

thank the secretaries in the department: Kim Crosslan, Cathy Cords, and Debbie Barratt,

for their assistance in both work and life. I very much appreciate for getting hug from Kim

whenever I needed it. I would also like to extend my sincere thanks to graduate directors,

Professor Scott Pratt and Professor Kirsten Tollefson, and the department chair (now the

v

dean of College of Natural Science) Professor Phil Duxbury. This work would never have

been possible without their advice and support.

Thanks also to National Science Foundation, Department of Physics and Astronomy

at MSU, and College of Natural Science at MSU, for the financial support.

Finally, I’m deeply indebted to my family and friends. Their love helped me build

resilience against the stressful life events through these years. My mom Fu-Mei Chiu, my

dad Ching-Shiang Chuang, and my sister Po-Han Chuang, have always been there for me

through all the ups and downs. My in-laws, Hui-Jen Chien and Ching-Tsai Pan, provided

unparalleled support and encouragement. My child, Chensi Pan, brought me endless joy.

Last but not least, I would like to express my appreciation to my husband, Kuo-Chuan Pan,

for his continued support and the precious memories we share together through the journey.

vi

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

Chapter 1

1.1 Nucleic acid molecules

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Nucleic acid structures . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Polymer model of unfolded DNA . . . . . . . . . . . . . . . . . . . .
1.1.3 Folding and unfolding: Free energy landscape model . . . . . . . . . .
1.1.4 Beyond Watson-Crick pairs: G-quadruplex structure
. . . . . . . . .
1.2 Single-molecule measurements . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Optical tweezers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 Optical tweezers + fluorescence microscopy . . . . . . . . . . . . . . .
1.3 Outline of this dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
2
2
4
7
12
18
21
29
33
36

Chapter 2 Randomizing phase to remove acousto-optic device wiggle errors 37
38
40
43
43
45
48
51
53

2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 AO device positioning inaccuracies
. . . . . . . . . . . . . . . . . . .
2.3.2 Untethered beads . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Tethered beads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 3 Combined high-resolution optical tweezers and multicolor single-

3.1
3.2 Material and methods

molecule fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 DNA tether construct preparation . . . . . . . . . . . . . . . . . . . .
3.2.2 Experiment conditions . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Instrument Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Optical tweezers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Multicolor single-molecule fluorescence . . . . . . . . . . . . . . . . .
3.3.3 Bright-field imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Cryptic quantum dot binding for robust signal confocal alignment . .
3.4.2 Multicolor DNA probe binding demonstration . . . . . . . . . . . . .

3.3

54
55
57
57
58
60
61
63
65
71
71
71
77

vii

3.4.3 Cy5 outperformed other organic fluorophores . . . . . . . . . . . . . .
3.4.4 Automated single molecule assembly line . . . . . . . . . . . . . . . .
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81
83
85

4.1
4.2 Material and methods

Chapter 4 Mechanical folding pathway of the thrombin-binding aptamer
G-quadruplex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
4.2.1 Dual-trap high-resolution optical tweezers
. . . . . . . . . . . . . . .
91
4.2.2 Construct preparation . . . . . . . . . . . . . . . . . . . . . . . . . .
91
4.2.3 Experimental procedure . . . . . . . . . . . . . . . . . . . . . . . . .
92
4.2.4 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
4.3.1 Force dependent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
4.3.2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3.3 Thrombin dependent . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.4.1 Bell model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.4.2 Force-dependent structure diameter model
. . . . . . . . . . . . . . . 105
4.4.3 Finding transition state structure . . . . . . . . . . . . . . . . . . . . 107
4.4.4 G-triplex as the transition state . . . . . . . . . . . . . . . . . . . . . 112
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Salt dependent

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Appendix A Protocols for performing experiments . . . . . . . . . . . . . . . . . . 116
Appendix B List of essential parts for the construction of the multi-color fleezers . 128

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

viii

LIST OF TABLES

Table 4.1:

Bell model fit parameters of rate constants and distances to transition
state.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Table 4.2:

Fit parameters of rate constants and transition state diameters with a
segment of ssDNA (0, 4, and 8 free nucleotides) in 800 mM KCl buffer.

109

Table 4.3:

Fit parameters of rate constants and transition state position with a
range of KCl concentration using the G-triplex plus 4 free nucleotides
model.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Table A.1: Complementary hairpin sequence and probe strand for “cryptic binding”

experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Table A.2:

ssDNA Insert for synthesizing the “hybridization” construct and the com-
plementary fluorophore-labeled probes.

. . . . . . . . . . . . . . . . . . 124

Table A.3:

ssDNA Insert for synthesizing the “fixed probe” construct and the com-
plementary fluorophore-labeled probes.

. . . . . . . . . . . . . . . . . . 125

Table A.4:

ssDNA Insert for synthesizing the “TBA-GQ” construct.

. . . . . . . . 125

ix

LIST OF FIGURES

Figure 1.1: DNA and RNA are polymer chains.

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

Figure 1.2: Freely-jointed chain and worm-like chain polymer models.

. . . . . . .

Figure 1.3: Free energy landscape for a two-state reaction.

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

Figure 1.4:

Schematic view of how optical tweezers apply forces to the ends of the
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
molecule.

Figure 1.5: Effect of the applied force on the free energy landscape for a two-state
system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

6

8

10

10

Figure 1.6: Nucleobases are components of nucleotides that form DNA and RNA.

.

12

Figure 1.7: Alternative base pairing explains how nucleic acids form a variety of
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

structures.

13

Figure 1.8: G-quadruplex structure.

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

15

Figure 1.9:

Schematic structure of thrombin binding aptamer G-quadruplex (TBA-
GQ).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

Figure 1.10: Biomolecules in action.

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

20

Figure 1.11: High-resolution optical tweezers combined with confocal microscopy.

.

21

Figure 1.12: Ray optics diagrams of optical trapping.

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

23

Figure 1.13: Schematic of the dual-trap optical tweezers setup.

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

25

Figure 1.14: Principles for acousto-optic devices and electro-optic devices.

. . . . . .

26

Figure 1.15: Position detection by back-focal-plane interferometry.

. . . . . . . . . .

27

Figure 1.16: Power spectrum of a trapped bead.

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

29

Figure 1.17: Jablonski energy diagram of the fluorescence process.

. . . . . . . . . .

30

Figure 1.18: Cy3-Cy5 FRET pair.

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

32

x

Figure 1.19: Optics layout of confocal microscope.

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

33

Figure 1.20:

Interlacing and time-sharing of the optical traps and fluorescence exci-
tation lasers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

Figure 2.1:

Interference patterns in acousto-optic device.

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

39

Figure 2.2: Optical tweezers layout. . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

Figure 2.3: RF phase control.

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

42

Figure 2.4: Force versus extension measurements pulling on DNA. . . . . . . . . . .

44

Figure 2.5: Wiggles shift over time with acousto-optic device temperature.

. . . . .

44

Figure 2.6: Demonstration of positioning and measurement inaccuracies and the cor-
. . .

responding spatial power spectra for dual-optical tweezers setups.

47

Figure 2.7: Bead measurement noise for coherent versus random phase methods. . .

48

Figure 2.8: Trap laser profile after AOD and the corresponding Fourier power spectra. 50

Figure 3.1:

Schematic of the instrument layout.

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

62

Figure 3.2:

Interlacing and time-sharing of optical traps and fluorescence excitation
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
lasers.

64

Figure 3.3: Excitation and emission spectra of the fluorescent molecules.

. . . . . .

66

Figure 3.4: PSD scan images from all three fluorescence excitation lasers using the
piezo mirror stage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

Figure 3.5: Axial alignment of confocal spot. . . . . . . . . . . . . . . . . . . . . . .

70

Figure 3.6:

“Cryptic binding” experiments with quantum dots.

. . . . . . . . . . .

73

Figure 3.7: Representative time trace of hairpin cryptic binding experiments. . . . .

75

Figure 3.8: Confocal alignment scan images using quantum dots.

. . . . . . . . . .

76

Figure 3.9: Multi-color single fluorophore-labeled oligonucleotide hybridization ex-
periment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

Figure 3.10: Force dependent DNA extension change upon hybridization.

. . . . . .

78

xi

Figure 3.11: Simultaneous measurements of fluorescence and tether extension.

. . .

79

Figure 3.12: Multi-color single fluorophore-labeled oligonucleotide hybridization ex-
. . . . . . . . . . . . . . . . . . . . . . . .

periment under 10 pN force.

80

Figure 3.13: Experimental setup for fluorophore lifetime experiments.

. . . . . . . .

81

Figure 3.14: Fluorophore lifetime experiments with fixed probes.

. . . . . . . . . . .

83

Figure 3.15: Multi-channel flow chamber.

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

84

Figure 3.16: Molecular assembly line with the multi-channel flow chamber. . . . . . .

85

Figure 4.1:

Structure of thrombin-binding aptamer G-quadruplex (TBA-GQ).

. . .

90

Figure 4.2:

Schematic of the TBA-GQ experimental setup using optical tweezers.

.

92

Figure 4.3:

Single-molecule optical tweezers study of thrombin-binding aptamer G-
quadruplex (TBA-GQ). . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4.4: Folding and unfolding dwell times show single exponential distribution.

93

95

Figure 4.5: Equilibrium measurements of TBA-GQ under force.

. . . . . . . . . . .

99

Figure 4.6: Force-dependent rate constants of TBA-GQ over a range of KCl concen-

tration with Bell model fitting. . . . . . . . . . . . . . . . . . . . . . . . 100

Figure 4.7:

Salt effects on TBA-GQ formation.

. . . . . . . . . . . . . . . . . . . . 102

Figure 4.8: Thrombin effects on TBA-GQ resolution.

. . . . . . . . . . . . . . . . . 104

Figure 4.9:

Schematic possible transition state structures during the folding and un-
folding pathway of TBA-GQ. . . . . . . . . . . . . . . . . . . . . . . . . 108

Figure 4.10: Force-dependent rate constants of TBA-GQ over a range of KCl concen-

tration with force-dependent structure diameter model.

. . . . . . . . . 111

Figure 4.11: Proposed reaction diagram explains the folding and unfolding pathway

of TBA-GQ.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Figure A.1: Gel purification.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

xii

Chapter 1

Introduction

Life comes with various forms. Despite the different appearances on the large scale, all

life consists of similar components at the molecular level: nucleic acids (DNA and RNA)

and proteins. Nucleic acids and proteins are fundamental biomolecules of life. Therefore,

studying the properties of nucleic acids and proteins is essential to unveil the secret of life.

All living cells contain nucleic acid molecules that encode the genetic information

and utilize the information to synthesize proteins. On the other hand, proteins are the

molecular machines that cells use to read the genetic information in nucleic acid molecules.

The Central Dogma of Molecular Biology [1] describes how genetic information flows in cells

from DNA sequences to RNA transcripts to proteins. The genetic information in DNA is

transcribed to messenger RNA (mRNA) molecules, and the mRNA molecules are translated

to proteins. All cells in the human body contain the same DNA. Yet the cells are trans-

formed into all kinds of different types (e.g. muscle, nerve, skin, etc.). How do the cells

know what genes to turn on and when to do which reaction? It is regulated by the nu-

cleic acid-protein interactions and the physical conformations of these biomolecules. Beyond

protein-encoding genes, nucleic acids play another essential role: regulation. In fact, only

a small percentage of the genome is for coding proteins. The vast majority of functional

DNA in human genome is for regulation purpose [2]. Some non-coding DNA sequences form

unique structures, e.g. G-quadruplex, under certain conditions (see discussion below). Some

non-coding DNA is transcribed into non-coding RNA molecules including ribosomal RNA

1

(rRNA), transfer RNA (tRNA), micro RNA (miRNA) etc. They involve in many cellular

processes and regulate the gene expression. For example, ribozymes are structures formed

by RNA molecules with catalytic properties. Thus, the structure and stability of the nucleic

acid and proteins are very important to their function. The more we understand how they

work, the more we understand the life. The knowledge is also applicable to curing diseases

and creating new technology.

1.1 Nucleic acid molecules

1.1.1 Nucleic acid structures

DNA, RNA, and proteins are three fundamental biopolymers. Both DNA and RNA consist of

nucleotide chains while proteins consist of amino acid chains. Each nucleotide is composed of

three subunits: a nitrogenous base, a 5-carbon sugar (a deoxyribose sugar molecule for DNA

and a ribose sugar molecule for RNA), and a phosphate group. The sugar and phosphate

group link together by phosphodiester bonds to form DNA or RNA polymer (Fig. 1.1).

In the following discussion, we focus on DNA polymers. DNA is built by four different

nucleotides with same sugar and phosphate group. The phosphate groups carry negative

charges, so DNA is a negatively charged polymer. In addition, DNA strand has polarity.

The sugar molecule has carbon that labeled from 1’ to 5’, and the phosphate is linked to the

sugar through the 3’ carbon and 5’ carbon. The polarity of the sugar-phosphate backbone

defines the 3’ and 5’ directionality in DNA.

There are two types of bases for nucleotides: purines (adenine and guanine) and

pyrimidines (cytosine, DNA only thymine, and RNA only uracil). The polymers can be held

2

together by hydrogen bonds between bases to form secondary structures. In the primary

canonical form, two single-stranded DNA (ssDNA) form DNA double helix. It follows the

base paring rules that proposed by Watson and Crick in 1953 [3]: adenine (A) binds to

thymine (T), and cytosine (C) binds to guanine (G). In RNA, thymine (T) is replaced by

uracil (U) [4].

Figure 1.1: DNA and RNA are polymer chains.
(a) The sugar molecule has 5 carbons
that labeled from 1’ to 5’. The difference between the deoxyribose sugar in DNA and the
ribose sugar is RNA is at the 2’ carbon. Deoxyribose has a hydrogen atom while ribose has
a hydroxyl group at the 2’ carbon. (b) Each nucleotide is composed of a base, a sugar, and a
phosphate group. The figure here shows a ribose sugar with a base Uracil and a phosphate
group. (c) ssDNA polymer chain. The sugar and phosphate group of the nucleotides link
together to form DNA polymers. New nucleotides are added on the 3’-OH of the strand.
Hydrogen atoms that are bonded to carbon atoms are not drawn.

3

1.1.2 Polymer model of unfolded DNA

Nucleic acids and proteins are biological polymers that consist of a sequence of nucleotides

or amino acids. They are stiff at short length scales and flexible at long length scales. The

behavior of the biological polymers such as nucleic acids and proteins can be described using

polymer chain models. Freely-jointed chain model and worm-like chain model are two models

we used here.

In the freely-jointed chain model (Fig. 1.2a), each segment is a fixed length rigid rod

(vector (cid:126)r) and its orientation and position are independent of the other segments. A freely-

jointed chain polymer is only flexible between the freely hinged segments. It also assumes

the polymer is inextensible and neglect the interactions between segments.

Worm-like chain (WLC) model (Fig. 1.2b) describes the behavior of the polymer as

a continuously semi-flexible rod. It assumes the polymer is inextensible which means the

bonds connecting each segment do not stretch. The stiffness of a worm-like chain polymer

corresponds to its persistence length Lp.

It is the length over which correlation of the

orientation of the tangent vector (cid:126)t(s) is lost. The longer the persistence length, the stiffer

the polymer. When the maximum length of the polymer (contour length Lc) is much short

than persistence length, Lc << Lp, the polymer behaves like a rigid rod. It has been shown in

single-molecule force spectroscopy studies that the force-extension behavior can be described

by WLC model [5, 6]. The persistence length is about 50 nm (150 base pairs) for dsDNA,

about 1 nm for ssDNA, and about 0.6-0.7 for polypeptides [7–9].

Both WLC and FJC models consider the polymer is inextensible which means the

extension of the polymer cannot be stretched beyond its contour length. Since real polymer

is extensible, the elastic response from the extension needs to be taken into account [10, 11].

4

We use the modified version: extensible WLC (XWLC) and extensible FJC (XFJC), to

predict and fit our experimental data. The polymer model for entire tether is the sum of

each component (dsDNA handles and ssDNA inserts).

Figure 1.2c shows an example force-extension curve of a single hairpin construct

measured by our high-resolution optical tweezers. The DNA hairpin construct is well-

described by two dsDNA XWLC polymer handles plus one ssDNA hairpin XFJC polymer

insert. The length of the entire tether changes when the hairpin unfolds (increases in exten-

sion) and folds (decreases in extension) with the corresponding force changes. The size of the

transition corresponds to the length change of the insert. We can calculate force-extension

changes based on the number of nucleotides involved in the process.

5

Figure 1.2: Freely-jointed chain and worm-like chain polymer models. (a) Freely-
jointed chain polymer model considers each DNA segment as a rigid rod. (cid:126)r is the vector
of each segment, and (cid:126)R is the total end-to-end vector. (b) Worm-like chain polymer model
considers DNA as a continuously flexible rod. (cid:126)t(s) is the tangent vector along the chain
at point s. (c) Force-extension curve of a DNA hairpin tether. The folding and unfolding
behavior of a single hairpin construct during pulling (blue) and relaxing (green) is well-
described by the folded hairpin (red dashed) and unfolded hairpin (black dashed) polymer
models.

6

1.1.3 Folding and unfolding: Free energy landscape model

Thermodynamics

Nucleic acids participate in almost every function in the living cells. Under certain conditions,

the nucleic acids transformed from the unfolded polymer chain of nucleotides into a folded

structure. It is fundamental to understand how nucleic acids fold because the mechanical

properties are critical to their biological function.

The folding and unfolding dynamics of nucleic acids as well as proteins can be de-

scribed as the Gibbs free energy landscape of the molecule (Fig. 1.3). Gibbs free energy

landscape theory provides a way to understand the structure formation of biopolymers. For

a particular reaction, each structure of the molecule in the progress, which is the macrostates

of the molecule, are represented as sets of microstates sharing the same property (i.e. the

end-to-end extension in this dissertation). The landscape consists of a surface representing

the free energy of the macrostates (e.g., folded state, unfolded state and transition state)

along the reaction coordinate. The molecules diffuse on the landscape and tend to stay at a

state with the minimum free energy, which is typically the folded state. The changes of free

energy from macrostate A to macrostate B at constant temperature is,

∆G = ∆H − T ∆S.

(1.1)

∆H is the change in enthalpy of the molecule, T is the absolute temperature, and ∆S is the

change in entropy of the molecule. The enthalpy of the molecule is from the electrostatic

bonding energy between different parts of the molecule, e.g., the hydrogen bonds. The en-

thalpy includes the intrachain interaction in nucleic acids or proteins and the intermolecular

interaction with surrounding molecules such as water and ions. The entropy is derived from

7

the quantity Ω which represents the number of possible conformational states (microstates)

of the molecule as

where kB is the Boltzmann constant.

S = kB · ln Ω

(1.2)

Figure 1.3: Free energy landscape for a two-state reaction. ‡ indicates the transition
state.

Here, we describe the free energy surface in a two-state system where the molecule is

in either the folded state or the unfolded state with an energy barrier, transition state (indi-
cated by ‡), in between. In general, the folded state is a very specific structural conformation

of the molecule with a maximum number of intramolecular noncovalent bonds. As such, for

the folded state, there are very few conformation states. Thus the folded state has a minimal

entropy. However, for the unfolded state, the unfolded state polymer has the largest number

of possible conformational states because the molecule is a polymer chain with no bonds

between subunits there are many random microstates with the same end-to-end extension.

Therefore, the unfolded state has the highest conformational entropy. If we add one bond,

8

the molecule moves to the left on the diagram because the end-to-end extension is shortened.

The enthalpy is lower by the addition of the bond while the entropy is also lower due to the

reduced number of microstates. The enthalpy term and the entropy term of the free energy

of the molecule compete with each other resulting a free energy landscape along the reaction

coordinate. Generally, when we start adding bonds, the entropy goes down more than the

enthalpy does, so the free energy is a net increase. At some point, the molecule reaches the

top of the barrier (transition state). Adding bonds start to outweigh the loss of entropy, and

the free energy starts goes down. Eventually, the molecule arrives at the folded state.

Force-dependent free energy landscape

In the absence of force, the minimum free energy for biological molecules is generally the

folded state and thus the molecules are most likely found folded. When applying a force to

the ends of a molecule (Fig. 1.4), work is done on the molecule. It changes the enthalpy

of the molecule, thus the free energy changes. The force tilts the energy landscape along

the mechanical reaction coordinate by a factor F∆x where ∆x is the distance between the

point of interest and the reference point. As the force increases, the unfolded state becomes

more and more energetically favorable. At equivalent force F1/2, the change in free energy is

zero, the molecule has equal probability to stay in either the folded state or unfolded state.

When the applied force is larger than equivalent force, the reaction favors unfolded state

(Fig. 1.5).

9

Figure 1.4: Schematic view of how optical tweezers apply forces to the ends of
the molecule. The introduction of optical tweezers will be given in Section 1.2.1.

Figure 1.5: Effect of the applied force on the free energy landscape for a two-
state system. The red curve is the free energy surface at zero force, the green curve is at
equivalent force F1/2, and the blue curve is at the force higher than F1/2. With the applied
force, the relative free energy differences between the transition state and folded (unfolded)
state are changed. Curves are vertically shifted for clarity.

10

Transition state theory provides an approach to describe the rate constants of the

reaction. The rate constant of reaction depends on the free energy and the temperature.

k0 = A exp(−∆G‡

kBT

)

(1.3)

A is the intrinsic rate constant for the system (like an attempt frequency), and ∆G‡ is the

activation energy (barrier height) for unfolding or folding. The simplest Bell model describes

how the applied force affect the barrier height. In the presence of force F, the Gibbs free
energy will be lower by F∆x. The activation energy becomes ∆G‡ - F∆x. Because what

is limiting is overcoming the energy barrier, all that matters for the effect of force is the

distance to the transition state. Therefore, the force dependent rate constant become

k = A exp(−∆G‡

kBT

) exp(

F ∆x
kBT

) = k0 exp(

F ∆x
kBT

)

(1.4)

where k0 is the rate constant at zero force. The force affects the energy landscape by

changing the relative barrier height to the transition state, and thus the rate constants of

reaction are affected. By measuring the force dependent rate constants, we can obtain the

distance to transition state from folded and unfolded states and furthermore reconstruct

energy landscape along the mechanical reaction coordinate. The energy landscape allows us

to characterize the mechanical properties of biopolymers.

11

1.1.4 Beyond Watson-Crick pairs: G-quadruplex structure

The mechanical properties of the biopolymers depend on the binding between subunits.

Although Watson-Crick base pairs are the most abundant base pairs in nucleic acids, a

nucleotide has more than one edge available for hydrogen bonding [12]. Figure 1.6 shows

the Watson-Crick edge and Hoogsteen edge of the nucleobases. Through the Watson-Crick

base pairs and Hoogsteen base pairs (observed in 1963) [13], nucleic acids can form alternative

nucleic acid structures (Fig. 1.7) like stem loop, pseudoknot, triplex and G-quadruplex.

Figure 1.6: Nucleobases are components of nucleotides that form DNA and RNA.
Depending on the edges of the bases involved in the hydrogen-bonded base pairing, DNA and
RNA form canonical base pairs with Watson-Crick edge (blus solid curves) and non-canonical
base pairs with Hoogsteen edge (red dashed curves). R represents the sugar-phosphate
backbone.

12

Figure 1.7: Alternative base pairing explains how nucleic acids form a variety of
structures. (a) DNA duplex. Watson-Crick base pairs (blue dashed lines) are the building
blocks of the most common double-stranded DNA (dsDNA) helix. T is paired with A via two
hydrogen bonds. C is paired with G via three hydrogen bonds. (b) DNA triplex. One DNA
strand binds to the dsDNA helix via Hoogsteen base pairs (red dashed lines) form triple-
stranded DNA. In triple-helix base pairing, Watson-Crick base pair is indicated by -, and
Hoogsteen base pair is indicated by :. (c) G-quadruplex. Four G bases form G-tetrad via 16
Hoogsteen base pairs. Two or more G-tetrads stack on top of each other form G-quadruplex.

13

G-quadruplex

G-quadruplex is formed by guanine-rich single-stranded nucleic acids via Hoogsteen base-

pairing [14]. Four coplanar guanines that held together by 8 Hoogsteen hydrogen bonds and

associate with a monovalent metal ion such as Na+ and K+ to form G-tetrad (Fig. 1.8a),

the building block of G-quadruplex. Two or more G-tetrads stack on top of one another

form G-quadruplex. Recent studies have indicated that G-quadruplex structures play cru-

cial regulatory roles in replication, transcription, and translation [15]. During these bio-

logical processes, the double-stranded DNA (dsDNA) becomes single-stranded that permits

the guanine-rich sequence to form G-quadruplex. The highest abundance of guanine-rich se-

quences is at telomeres, the 3’ single-stranded DNA tail at end of the eukaryote chromosomes.

Telomeres protect the linear ends of eukaryote chromosomes. The telomeric G-quadruplex

inhibits the activity of telomerase, a reverse transcriptase which is active in cancer cells.

Since G-quadruplex is under mechanical force before interaction with proteins, investigation

of the folding mechanism of G-quadruplex under force is important for molecular biology

understanding and structure-based drug designs.

The types of G-quadruplex structure can be categorized based on the number of

the nucleic acid strands involved (intramolecular or intermolecular) (Fig. 1.8b) and the

orientation of strands (parallel, hybrid, or antiparallel) (Fig. 1.8c). The intramolecular G-

quadruplex is formed by a single-strand guanine-rich nucleic acids, while the inter molecular

G-quadruplex consists of two or four separate strands.

In parallel type of G-quadruplex

structure, the direction of all strands is the same. For example, all strands are aligned

from 5’ to 3’ direction. In hybrid type, one of the runs of guanine bases has the opposite

orientation to the other three runs. In antiparallel type, two runs have opposite orienta-

tion to the other two runs. The conformation of the G-quadruplex is influenced by the

14

nucleic acid sequence, length, and the environmental conditions such as cation species and

molecular crowding [16–21]. Even very similar sequences can produce different conformation.

Figure 1.8: G-quadruplex structure.
(b) Examples of intermolecu-
lar G-quadruplex (tetramolecular and bimolecular) and intramolecular G-quadruplex (uni-
molecular). Strand polarities are from 5 to 3. (c) Possible geometries of intramolecular
G-quadruplex.

(a) G-tetrad.

Thrombin binding aptamer G-quadruplex

The G-quadruplex structures has been adopted by several aptamers. Aptamers are short

DNA or RNA strands that bind to target molecule with high affinity and specificity via their

unique folded structures. They are selected from a large pool of sequences through poly-

merase chain reaction (PCR) process, known as systematic evolution of ligands by exponen-

15

tial enrichment (SELEX) [22–24]. G-quadruplex forming aptamer is one of the most popular

categories among the nucleic acid aptamers. Even with similar sequences, G-quadruplex

forming aptamers are able to produce a large variety of conformations, which make them

recognize a wide range of protein targets. The identification of the target is critical in drug

discovery. Compared to the protein-based antibodies, nucleic acid-based aptamers have the

advantages because of their smaller size, lower immunogenicity, low cost, and easiness to

synthesize [25]. It can be widely used for therapeutics, diagnostics, biosensor, and molecular

biology studies.

Thrombin binding aptamer G-quadruplex (TBA-GQ) is a minimal model system of G-

quadruplex [26]. Its a 15-nucleotide long single-stranded DNA that folds into a chair-like two-

layer G-quadruplex with one TGT loop and two TT connecting loops (Fig. 1.9). Because

it is the simplest G-quadruplex, understanding the mechanical properties of TBA-GQ is

desired to further investigate the mechanism of other important G-quadruplex structures

such as telomeric G-quadruplex.

Figure 1.9:
Schematic structure of thrombin binding aptamer G-quadruplex
(TBA-GQ). TBA-GQ is an intramolecular, antiparallel G-quadruplex with a chair-like
conformation.

TBA-GQ is also an important DNA aptamer on its own. The protein thrombin is

16

the central enzyme in the process of blood clotting. The regulation of thrombin activity

is important for anticoagulant and cardiovascular diseases therapy. TBA-GQ specifically

interacts with thrombin to inhibit the blood coagulation. As a result, TBA-GQ has been

tested in phase I clinical trials that known as ARC183 or HD1 (Archemix Corporation) [27].

G-quadruplex is functionally important in genome. To understand how G-quadruplex

works in cells, we need to understand the structure stability (i.e. the folding and unfold-

ing mechanism). TBA-GQ is a small DNA structure. Compared to other G-quadruplex

structures, it only has two layers that means it contains fewer bonds thus less stable. The

small size and low stability make it very technically challenging to directly observe the fold-

ing/unfolding of TBA-GQ. As a consequence, a high-resolution measurement is needed to

study TBA-GQ formation and thrombin-aptamer interaction.

17

1.2 Single-molecule measurements

To comprehensively study the structure and function of the biomolecules as well as the inter-

actions between them, we need powerful tools that allow investigation at the single-molecule

level. It is technically challenging to study these small but fundamental biomolecules indi-

vidually. Over the last three decades, single-molecule force and fluorescence techniques have

been developed. These techniques have been used to characterize the mechanical properties

and the basic mechanisms of the DNA, RNA, and proteins.

Single-molecule methods characterize the properties of individual molecules. In the

past and to this day, the majority of molecular biology experiments are ensemble-based

methods. These experiments measure the average properties of molecules. The information

we can learn from the average properties is limited because the details in the biological sys-

tems are dynamics. For example, the ensemble measurements can give us the ratio of folded

to unfolded state in a group of molecules, but we are not able to observe how a molecule

changes its configuration between unfolded state to folded state. In contrast, single-molecule

methods [28] provide information about the biological systems that was unattainable through

the ensemble experiments. Without the averaging of time and population, single-molecule

methods not only provide the mean values of the system but also the dynamics and nonuni-

form behavior such as the transient states. Force-based and fluorescence-based are two major

branches of the single-molecule methods. Single-molecule force spectroscopy is a powerful

tool to study the mechanical properties and the dynamics of biomolecules such as protein

folding, nucleic acid folding, and the nucleic acid processing molecular motors. Atomic

force microscopy (AFM) [29], optical tweezers [30], and magnetic tweezers [31] are three

commonly-used single-molecule force spectroscopy. Force spectroscopy can manipulate in-

18

dividual molecules as well as quantitatively apply and measure the force on the biological

system. Single-molecule fluorescence microscopy uses fluorophores conjugated to individual

biomolecules as a reporter in a wide variety of measurements including the detection of the

presence, location and/or the conformation of the molecules of interest. The commonly used

single-molecule fluorescence microscopy includes confocal microscopy [32], total internal re-

flection microscopy (TIRF) [33], light sheet microscopy [34], and super resolution microscopy

[35].

Each technique has its own strengths and limitations. It is important to push the

instrument capabilities to more complexity and higher precision to maximize the informa-

tion and details obtained. Typical single-molecule techniques mentioned above measure a

single quantity, e.g. the displacement via optical tweezers or the location via fluorescence.

However, biomolecules are complex. A reaction requires many components and involves

many degrees of freedom (Fig. 1.10). Typical single-molecule techniques are not sufficient

to understand the complexity of biology. The development of single-molecule techniques has

been moving towards the combination of multiple techniques to directly probe the complex

biological systems. By combining force and fluorescence, we can visualize the single molecule

fluorescence while mechanically manipulate and detect the molecules. Here we describe the

principles of optical tweezers and fluorescence, and the hybrid technique (Fig. 1.11) that

combining both, the main technique we use in this dissertation.

19

Figure 1.10: Biomolecules in action. (a) The telomeric DNA replication fork. (b) The
coordination of multiple proteins is required for telomeric DNA replication, and multi-degree
of freedom conformational changes in DNA and proteins are essential to function properly.
See Reference [36] for details. Figure is reused under permission of a Creative Commons
license (CC BY 4.0).

20

Figure 1.11: High-resolution optical tweezers combined with confocal microscopy.
Combining both force and fluorescence approaches provide complementary information.

1.2.1 Optical tweezers

How do we trap?

Optical tweezers are a technique utilizing a laser to trap and manipulate objects [37, 38].

The trapped objects need to be transparent (no absorption) and have the refractive index

higher than the medium. A trapped object senses a net force due to the momentum transfer

from the scattering and refracting photons. The forces exerted by light on an object can be

divided into two categories: the scattering force and the gradient force. Depends on the size

of the trapped objects and the wavelength of the trapping beam, there are two models to

quantify the forces: the dipole model and the ray optics model. For a trapped object with

21

diameter d much smaller than the wavelength λ (d << λ), the object can be considered as

a point dipole in an inhomogeneous electromagnetic field. The restoring force pushes the

dipole to the focus of the trapping beam which is the location of the highest field. For a

trapped object with diameter d much larger than the wavelength λ (d >> λ), the forces can
be explained using ray optics (Fig. 1.12). For the intermediate regime (d ∼ λ)), which is our

case (800 nm bead and 1064 nm trap laser), behavior of a trapped object is the combination

of these two models.

When the incident light hits the object, some photons are absorbed and some pho-

tons are reflected on the surface. The net scattering force pushes the object forward in the

direction of light propagation. The gradient force results from the refraction of light between

the object and the surrounding medium as the light passes through the object. What mat-

ters most is the rays at the edge because they have bigger refraction angles. In the lateral

direction, the object experiences a light gradient because the trapping beam has a Gaussian

beam profile. The resulting gradient force pulls the object toward the center where the

intensity of the light is the highest. In the axial direction, the scattering force pushes the

object out of focus as previously described. The axial gradient force needs to pull the object

back to compensate the scattering force so that the object can be stably trapped. As shown

in Fig. 1.12d, a strong axial intensity gradient can be created by tightly focusing the beam

using a high numerical aperture microscope objective. The net force pulls the object to the

focus of the optical traps.

22

Figure 1.12: Ray optics diagrams of optical trapping. The momentum transfer occurs
when a beam of light (orange arrows) hits a dielectric bead (grey spheres). (a) Scattering
forces. The incident light is reflected on the bead surface and results in the momentum
changes of photons (green arrows). The net force pushes the bead forward in the direction
of light propagation. (b) Lateral gradient force. The bead experiences an intensity gradient
(orange bars) from the incident light. The light is refracted from the bead and results in
the momentum changes. The net force pulls the bead to the center of the beam. (c) Axial
gradient force. The net force pulls the bead toward the highest intensity. (d) Axial gradient
force with a high numerical aperture lens. The incident light comes in at large angles. The
net force pulls the bead to the focal point.

23

How do we manipulate?

One of the advantages of optical tweezers in biology is the ability to manipulate the biological

objects. The position of the optical traps can be controlled by 1) moving the sample chamber

with respect to the traps or 2) steering the trapping beam itself. The first approach provides

large scale (tens of millimeters) distance changes.

It can be achieved by using a 3-axis

motorized stage. The second approach provides sub-nanometer scale distance changes. It

can be done by changing the incoming angle of the trapping beam using piezo scanning

mirrors, acousto-optic devices (AO devices) or electro-optic devices (EO devices).

The biomolecules such as nucleic acids and proteins are too small to be trapped.

Instead, we trap and manipulate the micron-sized dielectric particles (polystyrene or silica

beads) that are attached to the molecules of interest. To apply the force, we need the

other end of the tether to be fixed. For early generation single optical trap instruments,

the other end is either attached to the sample chamber or a bead attached by the suction

of a micropipette. In this configuration, the measurement spatial resolution is limited by

the drift of sample stage and surface. Recently, high-resolution optical tweezers has been

achieved by the dual-trap design [39]. Two traps are generated by rapidly switching the laser

between two trap positions. Therefore, the drift of sample stage and surface is removed by

isolating the tether from the sample chamber. Moreover, because the dual traps are created

from the same laser source and share an almost identical optical path, the fluctuations are

reduced by differential detection of the two trapped beads. For a typical dual-trap optical

tweezers experimental setup (Fig. 1.13), the molecule of interest is tethered between two

trapped beads via long DNA handles. By increasing trap separation, the force is applied to

the molecule. When the structure of molecule changes (e.g. unfolding DNA or protein), the

tether extension changes and thus the positions of the bead move. By measuring the bead

24

position versus time, we are actually recording the biomolecule configuration versus time.

The dual trap are generated by steering the light via AO devices [40] or EO devices

[41]. The time-sharing switch rate needs to be high enough to reduce the effect on bead

positions. Both devices can rapidly switch the beam between trap positions. The schematic

operating principles of AO devices and EO devices are shown in Fig. 1.14. AO devices

contain an acousto-optic crystal with a piezoelectric element at the end. When applying a

RF signal to the piezo, the vibrating piezo generates acoustic waves in the crystal act like the

diffraction grating and deflect the trap laser light. EO devices contain an electro-optic crys-

tal. When an electric field is applied, the refractive index changes and the light is deflected.

The refractive index is linearly proportional to the applied electric field. AO devices have

been used extensively in optical tweezers because of their exibility and speed. However, the

AO devices have trap positioning inaccuracies, likely caused by the standing acoustic waves,

that limit their usefulness especially for high-resolution applications. EO devices have been

used to avoid the errors from AO devices [42], but the deflection range of EO devices are 10

times less than AO devices. In Chapter 2, we discuss a method we devised to remove these

inaccuracies and allows AO devices to be used in high-precision measurements.

Figure 1.13: Schematic of the dual-trap optical tweezers setup. Two beads (grey
spheres) are held in optical traps (orange cones). A molecule of interest (cyan) is tethered
between two beads via two long DNA handles (red). The figure is not drawn to scale.

25

Figure 1.14: Principles for acousto-optic devices and electro-optic devices. (a)
Acousto-optic device. The incoming beam is diffracted by the RF driven acoustic waves.
The angle of the diffracted beam is controlled by the RF frequency. The first-order diffracted
outgoing beams cause by two different frequencies (f1 and f2) are shown. (b) Electro-optic
device. The incoming beam is deflected by different amounts with the control of applied
voltage. The refractive index of electro-optic crystal is changed with the applied electric
field. The deflected outgoing beams cause by two different refractive indexes (n1 and n2)
are shown.

How do we detect?

Optical tweezers are not only a manipulation tool but also used for quantitative measurement.

To quantitatively detect the displacement of a trapped object and the applied force, several

methods have been developed such as video-based [43], direct imaging [38], and laser-based

detection [44]. One method has become the standard for the position detection is the back-

focal-plane interferometry [45]. Back-focal-plane interferometry uses the interference pattern

produced by the forward-scattered light from the trapped object and the unscattered light

from the trapping beam. Any displacement of the trapped object results in a change of the

light pattern. The interference pattern is monitored by a position sensitive photodetector

(Fig. 1.15). The pattern can be calibrated to yield the location of the trapped object.

26

Figure 1.15: Position detection by back-focal-plane interferometry. The interference
pattern of a trapped bead is detected by a position sensitive photodetector. The bead is (a)
at its equilibrium position, (b) displaced by dy, and (c) displaced by dz. Changes in all three
dimensions can be detected.

The output signals from the detector are voltage readings. To convert the voltage

readings to real displacements and forces, we need to know the conversion factor α which

converts the photodetector voltage output to the displacement of the trapped object x = αV ,
and stiffness κ of the trap which determines the force F = −κx.

Calibration can be done with a known displacement or a known force. In our lab,

we use Brownian motion as a test force for bead displacement calibration. The equation of

motion for the bead can be written as

γ

dx
dt

+ κx = F (t),

(1.5)

where x is the position of the bead, γ = 3πηd is the hydrodynamic drag coefficient of the

object (for Stokes drag on a sphere of diameter d in a medium with viscosity η), and κ is

the trap stiffness. The hydrodynamic drag force plus the trap force equals to the fluctuating

Brownian force.

27

Because the average value of the thermal force is zero, a Lorentzian power spectrum

Sxx(f ) = | ˜F (f )|2 =

kBT
c + f 2)

π2γ(f 2

(1.6)

can be obtained by taking the Fourier transform of the force F(t). Sxx(f ) is in unit of

nm2/Hz, kB is Boltzmanns constant, T is the absolute temperature, and fc = κ

2πγ is the

corner frequency with the trap stiffness κ. The signals from detector are calibrated by

measuring the power spectrum of the Brownian motion of a trapped bead [40].

The power spectrum measured by the detector is Svv(f ) in unit of Volt2/Hz. It is

related to the true power spectrum by

Svv(f ) =

Sxx(f )

α2

,

(1.7)

where α represents the linear conversion between the detector output and bead displacement

in unit of nm/Volt. For low frequency f << fc, Svv(f ) approaches the limit

4kBT γ
κ2α2 . For high
kBT
πγf 2α2 . By fitting the power spectrum (Fig. 1.16), we

frequency f >> fc, Svv(f ) becomes

obtain the conversion factor α and stiffness κ.

For a trapped object, the force and displacement follow the Hooke’s law

F = −κx.

(1.8)

Once the trap stiffness is calibrated, the readout of the detector can be converted to the

displacement of the object and the force. The typical trap stiffness is on the order of 0.1

pN/nm. With these techniques, the resolution of optical tweezers has been pushed to mil-

lisecond time scale, sub-nanometer spatial scale, and sub-piconewton force scale.

28

Figure 1.16: Power spectrum of a trapped bead. The raw power spectrum (blue) of
an 800 nm polystyrene bead from our optical tweezers and the fit (black) to a Lorentzian.
The spectrum is asymptotic to the red dashed straight lines at high frequencies and low
frequencies.

1.2.2 Fluorescence

Photobleaching

Fluorescence is a process of emitting a photon via electronic state transitions. Fluores-

cence occurs when the electron of a fluorescent molecule relaxes to its ground state from an

excited state via emitting photon. By specifically labeling the molecule of interests with fluo-

rescence molecules (for example, organic fluorophores, inorganic quantum dots or fluorescent

proteins), we can localize and track the dynamics of the target molecules. The fluorescence

process (Fig. 1.17) starts by exciting the fluorescent molecule through absorbing the light at

a resonance wavelength. The fluorophore is unstable at high energy configuration, so it de-

29

cays to the lowest energy excited state via vibrational relaxation with a loss of energy. From

the semi-stable excited state, the electron then decays to the ground state by emitting the

light with longer wavelength. The wavelength of an emitted light is always longer than the

absorbed light due to the energy loss in the vibrational relaxation. Because the wavelength

is longer, that emitted light can be separated from the much brighter excitation laser light

via filters. The fluorescence process can cycle multiple times, emitting many photons, until

the fluorophore permanently enters the dark state. When a fluorophore is no longer be able

to fluoresce, it is called photobleaching. By counting the photobleaching events, the number

of individual labeled molecules presence in a complex is determined. The applications are

discussed in Chapter 3.

Figure 1.17: Jablonski energy diagram of the fluorescence process. Step 1) Ab-
sorption. An absorbed light (green) excites the electron from ground state to excited state.
Step 2) Relaxation. The electron decays to the lowest energy excited state via vibrational
relaxation. Step 3) Emission. The electron emits a longer wavelength light (yellow-green)
and returns to the ground state.

30

FRET

Two fluorophores with different colors not only provide us the ability to observe two kinds of

molecules, but also provide distance information. Two-color detection measures the dynam-

ics and relative distance between a pair of fluorophores, donor and acceptor, through the

F¨orster resonance energy transfer (FRET). The emission spectrum of the donor (the energy-

giving molecule) overlaps with the excitation spectrum of the acceptor (the energy-receiving

molecule) (Fig. 1.18a). The excitation of the donor results in the emission of the acceptor.

The energy is transferred by nonradiative dipole-dipole interaction. The FRET efficiency,

E =

1

1 + ( R
R0

)6

=

IA

ID + IA

(1.9)

is distance dependent. R is the distance between donor and acceptor, R0 is the F¨orster radius

at which energy transfer FRET efficiency is 50% (a property of a specific pair of fluorophore

molecules), and IA and ID are the fluorescence emission intensity of the acceptor and the

donor, respectively. One of the most commonly used fluorophore pair for FRET is the Cy3-

Cy5 pair. Figure 1.18b shows the distance dependence of FRET efficiency using Cy3-Cy5

pair as an example. R0 for Cy3-Cy5 is about 6 nm. FRET is sensitive at the distance 1-10

nm, giving distance measurements way beyond the diffraction limit of the optical microscope

direct imaging. The range is comparable to the dimensions of biomolecules, so it has been

used as a spectroscopic ruler [46] to investigate the structural changes of proteins and the

relative motion between two biomolecules.

31

Figure 1.18: Cy3-Cy5 FRET pair. (a) The excitation (dashed lines) and emission (solid
lines) spectrum of Cy3 (donor, green) and Cy5 (acceptor, red). The spectral overlap between
the emission of Cy3 and the excitation of Cy5 makes Cy3-Cy5 an ideal pair for FRET study.
(b) Distance dependence of FRET efficiency. When the distance between donor (green disk)
and acceptor (red disk) equal to R0 (about 6 nm for Cy3-Cy5 pair), the donor transfers half
of its energy to the acceptor.

Single-molecule fluorescence confocal microscopy

The single-molecule fluorescence detection can be realized for a variety of microscope de-

signs. Individual photons are collected and counted with rates only on the kHz scale. Thus,

in all cases, great care must be taken in design to minimize background detection and maxi-

mize signal detection. Here we introduce the confocal microscopy. In a confocal microscope

(Fig. 1.19), the excitation beam is reflected by a longpass dichroic mirror and focused in the

focal plane of the objective to a minimal nearly diffraction limited volume in the sample. The

emission signals are collected by the same objective, passed through the longpass dichroic

mirror, passed through the pinhole, and recorded by a single photon counting avalanche pho-

todiode (APD). To obtain a 2D image, a raster scan is made, where fluorescence is collected

in sequence for each point in the image. The pinhole is located in the conjugated focal plane.

It acts like a “spatial filter” so that the out-of-focus fluorescence signals are blocked by the

32

pinhole. Due to the elimination of out-of-focus fluorescence background, confocal microscope

has been widely used in biological imaging.

Figure 1.19: Optics layout of confocal microscope. Single channel excitation (green)
and emission (yellow-green) are shown. A dichroic mirror (D) spectrally separate lights by
reflecting excitation light and transmitting emission light. The filter (F) further blocks the
exceed excitation light.

1.2.3 Optical tweezers + fluorescence microscopy

Force-fluorescence approaches

Both optical tweezers and single-molecule fluorescence microscopy have been widely used

to study biological systems, but each technique has its strengths and drawbacks. Optical

tweezers provide direct detection of the molecular motion, but all motions are projected onto

one single axis. It lacks the ability to observe the internal changes in the system. In con-

trast, fluorescence can probe changes within the complex but no mechanical manipulation.

These limitations motivate the development of the hybrid techniques. The biggest challenge

for implementing optical tweezers with fluorescence microscopy is the photobleaching. The

33

fluorescence signal from a single fluorophore molecule is already very dim. Optical tweez-

ers use a high-intensity trapping laser, > 1 watt, while fluorescent excitation intensity at a
single fluorophore is typically ∼1 micro watt. The presence of the optical trapping beam

not only makes it harder to detect single molecule fluorescence (contributing background

photons) but also greatly speeds up photobleaching [47]. One way to tackle this issue is

separating the trapping laser and the fluorescently labeled molecules in space [48] to min-

imize the impact from trap beam. This approach requires long spacers so it comes at the

cost of the instrument resolution (longer spacers are softer and do not transmit signals as

well). Another strategy is to separate the trapping and fluorescence excitation beams in

time by interlacing [49]. Using the AO devices or EO devices described above, both light

sources can be switched rapidly on and off out of phase from each other. This approach

minimizes the photobleaching by preventing the fluorophores expose to both light sources at

the same time. Moreover, neither optical tweezers spatial resolution nor fluorescence detec-

tion sensitivity is sacrificed. By time-sharing and interlacing between trap and fluorescence

beams (Fig. 1.20), a high-resolution optical tweezers with single-color confocal microscope

has been realized [50]. The simultaneous measurement of sub-nm mechanical changes and

single-molecule fluorescence detection has been demonstrated. Since then, similar instru-

ments combining optical tweezers and single-color fluorescence excitation have been utilized

to address the questions that is difficult to answer by either technique alone [51–54].

Three colors and more

The functions and interactions in the biological systems are often very complex that require

coordination of multiple proteins and multi-degree of freedom conformational changes. The

single excitation laser with two-color FRET limits its ability to observe single species or

34

Figure 1.20:
Interlacing and time-sharing of the optical traps and fluorescence
excitation lasers. Two optical traps (orange) are created in sequence. The trap laser is
switched off while the fluorescence excitation laser (green) is turned on.

one pair of relative motion. It also limits the choices of fluorescence molecules. The ability

to observe multiple fluorescently labeled molecules and get stable signals are necessary to

resolve the detail mechanism. In Chapter 3, we implement the optical tweezers with mul-

ticolor fluorescence. We demonstrate the ability to probe three different colors at the same

time while mechanically manipulate the biological systems. The photostability of organic

fluorophores and inorganic quantum dots are evaluated in this hybrid instrument. We also

devised computer-controlled single-molecule assembly line which enables the precise assem-

bly of multi-molecule complexes while preserving fluorophores.

35

1.3 Outline of this dissertation

Three projects are presented in this dissertation. The main focus of these projects is to

address the fundamental questions in biology, the mechanical properties of DNA, using a

newly developed high-resolution hybrid single-molecule technique. The method and tool we

developed fulfill the need to study individual complex that contains multiple components

and multi-degree of freedom at base-pair resolution. Therefore, it can be broadly applied to

investigate a wide range of molecular systems such as nucleic acid folding, protein folding,

and the interactions between nucleic acids and protein molecular machines.

This dissertation contains two major parts. The first part (Chapter 2 and Chap-

ter 3) describes the single-molecule instrumentation advances we developed. We present a

hybrid single-molecule technique that combines high-resolution optical tweezers with multi-

color confocal fluorescence microscopy. We discuss the advances in optical tweezers and the

fluorescence performance that increase the instrument accuracy and capability. In the sec-

ond part (Chapter 4), we utilize our technique to investigate the conformational stability

of the nucleic acid secondary structure, G-quadruplex.

36

Chapter 2

Randomizing phase to remove acousto-optic
device wiggle errors∗

Acousto-optic (AO) devices have been used extensively in optical tweezers because of their

flexibility and speed; however, these devices have trap positioning inaccuracies that limit

their usefulness, especially for high-resolution applications. We show that these inaccura-

cies are due to interference patterns within the AO device sound fields. We have devised

a method that removes these inaccuracies by reducing the coherence of the sound fields by

directly controlling and randomizing the phase of the radio frequency voltage input signal.

We demonstrate that the trapping inaccuracies are eliminated, for both constant trap po-

sition and force-ramp measurements, and that no additional noise is added. We show that

this random phase method is applicable to both acousto-optic modulator and deflector type

devices and can be easily integrated via software upgrade into existing instruments.

∗The work in this chapter has been published as [55]:

A. G. Baker, Cho-Ying Chuang, M. L. Whitmore, and M. J. Comstock, Applied Optics, 57, 1752-1756
(2018)

37

2.1

Introduction

Optical trapping has been used to study molecular machines, cells, and other physical and

biological phenomenon at the single particle level and recently at sub-nm spatial resolution

[39,40,56,57]. Utilizing a high numerical aperture objective, a powerful laser can be focused

to a spot and used to trap transparent dielectric micrometer-sized objects such as polystyrene

beads, bacteria and viruses [40]. In single molecule studies, a trapped bead is commonly

tethered to a sample chamber surface or a second trapped bead by custom-designed single

strands of DNA. The tether is designed so that changes in the tether length over the course

of an experiment reveal, for example, the step-wise motion of a motor protein or unfolding

of a protein. The positioning of the optical traps via deflection of the incoming trapping

laser applies tension to the tether and is used for common methods such as force ramp

measurements and active force feedback.

High-resolution optical tweezers require precise and stable trap laser deflection con-

trol. High stability piezo mirror stages and AO devices have been used previously for this

purpose. AO devices deflect lasers by diffracting the laser beam from a periodic grating,

created by sound waves traveling in a crystal (Fig. 2.1). This sound wave is generated by

a piezoelectric element glued to the crystal and driven by an radio frequency (RF) volt-

age signal. AO trap positioners have many advantages including high speed (> 100 kHz);

all-electronic control enabling, e.g., trap intensity stabilization using active feedback; active

force feedback; and the ability to generate multiple traps from a single laser via timesharing

[44]. The trend in single-molecule instrumentation development is towards new methods

that combine measurement capabilities, such as the recent combination of high-resolution

optical tweezers with single molecule fluorescence measurements [50, 54]. This combination

38

was made possible by using an AO device to control a pair of traps via timesharing and

interlacing with fluorescence excitation and detection [49].

Indeed, timeshared dual trap

designs have the potential to be the most stable high-resolution optical tweezers (compared

to, for example, polarization splitting methods [39]): the two trap beams share a complete

spatial beam path and only experience an environment that differs in time on the timeshar-

ing switching timescale (typically > 50 kHz), which is far faster than any optical component

drift timescale.

Figure 2.1: Interference patterns in acousto-optic device. Model of an acousto-optic
device indicates the primary and reflected sound waves that produce the interference patterns
responsible for the trap wiggles.

However, AO devices have well known drawbacks: semi-periodic trap positioning and

bead measurement inaccuracies commonly referred to as “wiggles”. Commonly used AO

deflectors (AOD) have trapping inaccuracies on the 10 nm scale [41]. It has been speculated

that these wiggles derive from sound wave interference patterns that vary sensitively with

RF drive details. These inaccuracies are substantially reduced but not entirely removed by

using an AO modulator, a simpler AO device compared to an AOD, but at the substantial

cost of reduction in positioning range (approximately 10x reduced) and flexibility (e.g., 1D

39

instead of 2D positioning).

Here we show that the AO device wiggles are indeed generated by the changing in-

terference patterns of sound waves bouncing around in the AO device crystal as the trap

positions are changed. We use direct digital synthesis (DDS) to produce the RF drive, and in

addition to the typically controlled RF frequency and amplitude, we add to this direct digital

control of the RF phase. We then periodically randomize the RF wave phase. The resulting

decoherence removes the RF frequency dependent interference pattern and thus removes the

trap positioning wiggles. We show that this method is effective for both AOM and AOD

type devices, and indeed it should be applicable to all AO-based positioning methods.

2.2 Methods

Two home-built optical tweezers instruments were used in these investigations: one con-

taining an AOM (IntraAction ATM-803DA6B) and the other an AOD (IntraAction DTD-

274HD6C) to control the traps. The tweezers were both time-shared dual-optical traps

constructed and operated generally as described in references [44] and [52], and shown in

Fig. 2.2. An acousto-optic device rapidly deflects a trap laser between two positions to cre-

ate two independent optical traps (each trap A and B is on for 5 µs duration, in alternating

succession). The trap position and intensity are set by the RF frequency and amplitude

driving the AO device.

40

Figure 2.2: Optical tweezers layout. Simplified layout of dual-trap optical tweezers
setups used in this investigation containing an acousto-optic device. Orange and pink lines
indicate trap laser and visible imaging illumination paths respectively. The trap laser passes
through the AO deflecting device and then is expanded and imaged by a pair of telescopes
(T1 and T2) onto the back aperture of the trap-forming objective lens (O1), which focuses
the laser within a sample chamber (S). A small portion of the beam is picked off and sent
to QPD2 for intensity monitoring and feedback. A second objective lens (O2) collects trap
laser light exiting the sample chamber and passes it to a bead position detector (QPD1).
Electrical control and measurement signals are indicated by black dashed lines. A FPGA
chip is responsible for all measurement and control including the direct digital control of the
DDS RF source.

Using the established “coherent phase” method, the RF is synthesized via a direct

digital synthesis (DDS) chip (Analog Devices AD9852 PCB Z) where RF parameters are

digitally set for each trap on-cycle in real time by a field programmable gate array (FPGA)

chip on a PC data acquisition and control card (National Instruments PCIe-7852). The

synthesized RF is phase continuous (i.e., there are no discontinuities in the RF sine wave

when changing the amplitude or frequency between traps). For the new “random phase”

method, the RF phase is additionally set to a random value for each trap at the start of each

on-cycle, synchronous with the change in RF frequency and amplitude (Fig. 2.3).

41

Figure 2.3: RF phase control. (a) The time-sharing dual traps were created by an acousto-
optic device driven by RF frequency and amplitude. (b) The RF phase is continuous in the
“coherent phase” method. The RF phase is set to a random value at the start of each trap
cycle in the “random phase” method.

The trap position is calibrated in the standard way by scanning a trapped bead,

imaging the bead position and performing a linear fit to the result. Bead positions were

measured once per trap on-cycle using the trapping laser itself via the back-focal-plane

interferometry method [45]. Bead position measurement calibration is performed in the

standard way via fitting to untethered bead Brownian motion power spectra [58].

While the AOD-deflected beam does not have a perfect Gaussian shape (see Fig. 2.8a),

a bead in the AOD-produced trap does behave as if bound in a simple harmonic potential

with a well-defined center, for sufficiently small excursions from the center (which is generally

true for a trap produced by any method).

1 µm diameter polystyrene beads were used. Tethers consisted of 3 kb double stranded

42

DNA and were prepared using standard polymerase chain reaction (PCR) methods.

2.3 Results

2.3.1 AO device positioning inaccuracies

Figure 2.4 demonstrates typical AO device positioning inaccuracies when scanning trap

positions. Figure 2.4 shows simple force vs extension measurements of a pair of beads

tethered together by a single 3 kb DNA molecule acquired by the AOM-based instrument.

Curve (1) is obtained and plotted using standard methods. A very clear and substantial

“wiggling” error is observed on what should be a smooth curve. This error can be mitigated

to some extent by first acquiring an untethered bead position vs trap position measurement

(e.g., the curves in Fig. 2.6) and subtracting that “offset curve” from the raw bead position

measurements prior to position and force calibration. Then, as seen in Fig. 2.4 curve (2),

the error wiggles mostly vanish. The offset curve must be acquired prior to tethering the

beads, and there will be a delay before performing measurements. However, wiggle inaccu-

racies are not stable and shift over time (Fig. 2.5) leading to inconsistent subtraction and

the strong return of wiggles eventually (Fig. 2.4 curve (3)), thus introducing errors and

limiting measurement time.

43

Figure 2.4: Force versus extension measurements pulling on DNA. Traces (1)-(3)
used coherent phase methods: (1) “raw” data, (2) raw data with offset scan subtracted,
(3) offset scan subtracted but after 30-minute delay. Trace (4) used random phase method.
(Inset) difference between force and a simple polynomial model (error) for corresponding
traces (1) (blue) and (4) (purple) showing zoom of wiggles and measurement resolution.

Figure 2.5: Wiggles shift over time with acousto-optic device temperature. Bead
measurement wiggle frequency drift (upper) and AOM device temperature versus time while
trapping. Time t=0 is when trapping experiments started and the acousto-optic device was
first powered on.

44

2.3.2 Untethered beads

The untethered bead offset curves are shown in Fig. 2.6. Here a pair of untethered beads

were trapped then their separation increased by moving trap A at a constant velocity while

trap B remains stationary (as in, e.g., a force ramp measurement). Without a tether con-

necting the beads, each bead should remain at the center of their respective trap and there

should be no measured displacement of the beads during the scan. However, using the usual

“coherent phase” AO device method (colored traces), the measured bead positions oscillate

during the scan, for both the moving and stationary traps, in both the direction of trap

motion (x) and orthogonal to it (y). The amplitudes of these wiggles vary by trap (moving

versus stationary) and dimension (x versus y) and are as large as 1 nm and 25 nm for the

AOM- and AOD-based tweezers respectively. For the AOM, the wiggle pattern is dominated

by a single sine wave component, as apparent in the simple bead position versus trap position

pattern (Fig. 2.6a) and also the Fourier power spectra of the patterns (Fig. 2.6b) which

are dominated by single peaks. For the AOD, the pattern is more complex and composed

of multiple significant sine wave components as seen both directly (Fig. 2.6c) and in the

power spectra (Fig. 2.6d).

It is especially surprising, and also revealing, that the undesired wiggles are present

in bead measurements not only for the moving trap A, whose RF drive signal changes

as the trap is scanned, but also the stationary trap B, whose RF signal remains fixed.

The stationary trap also shows the simplest wiggle pattern (e.g., trap By (purple curve)

measurement in Fig. 2.6a), with a wiggle period corresponding to the trap A RF frequency

being incremented by 190 kHz. A detailed consideration of how the RF is applied to the

AOM to create the traps provides insight. Each trap is created in sequence by instantaneously

45

changing the RF frequency without introducing a discontinuity in the RF sine wave output

(continuous phase accumulation). Hence the starting phase of each trap RF signal is the

final phase of the previous trap. The time interval of each trap is fixed. As the frequency of

trap A is scanned, its final phase oscillates, and hence the starting phase of the stationary

trap also oscillates. For the AOM-based instrument, trap A begins scanning at 80 MHz

which corresponds to 400 RF cycles during the 5 µs trap A on duration. The phase shift is

back to zero when 401 RF cycles fit perfectly into the 5 µs duration, which corresponds to

80.2 MHz, or an increase of 200 kHz, nearly matching the observed stationary trap wiggle

pattern. A similar correspondence is also seen for the AOD-based instrument; however,

the patterns are more complicated. This implies that the wiggles originate from a phase-

dependent combination of the drive RF from successive trap on intervals, i.e., trap A wiggles

derive from the superposition of the present trap A sound wave with the previous trap

A sound waves and similarly for trap B. This is consistent with previous hypotheses that

sound waves reflecting within the AO device crystal can combine and interfere to create

wiggle patterns (Fig. 2.1).

We were able to completely obliterate the trap scanning wiggle interference patterns

by reducing the coherence of the sound waves within the AO crystal. We introduced dis-

continuities in the RF signal phase at the start of both trap A and B intervals by specifying

a random digital phase value synchronous with switching the RF frequency between traps.

The resulting wiggle-free bead offset measurements (black traces) are shown in Fig. 2.6a

and 2.6c for both the AOM- and AOD-based instruments respectively. The corresponding

power spectra of the curves also show a dramatic elimination of the spurious wiggle patterns

(Fig. 2.6b and 2.6d). Not surprisingly, wiggle errors are also completely eliminated in force

versus extension measurements of tethered beads (Fig. 2.4 curve (4)).

46

Figure 2.6: Demonstration of positioning and measurement inaccuracies and the
corresponding spatial power spectra for dual-optical tweezers setups. (a-b) AOM-
based optical tweezers. (c-d) AOD-based optical tweezers. (a) and (c) show the bead position
measurement for each bead (A versus B) and dimension (x versus y) while trap B was held
constant, and trap A was scanned. For bead and dimension, there is a pair of measurements:
upper (colored) used the coherent phase method, and the lower (black) is corresponding mea-
surement after switching to the random phase method. (b) and (d) show the corresponding
spatial power spectra of the Ax (blue) and Ay (red) bead position versus trap position using
the coherent versus random phase.

47

2.3.3 Tethered beads

The random phase method did not result in any noticeable degradation in the performance

of the optical tweezers. In particular, the random phase method did not introduce any extra

measurement noise compared to the coherent phase method as seen in the fixed trap position

measurement of tether extension vs time in Fig. 2.7a, and the corresponding power spectra

comparing the two methods in Fig. 2.7b. The offset in extension upon changing to the

random phase method is due to the coherent phase method sampling a particular wiggle

phase pattern for the particular fixed trap locations.

Figure 2.7: Bead measurement noise for coherent versus random phase methods.
(a) Tether extension versus time for both traps held at fixed positions. Initially the coherent
phase method is used and then abruptly switched to the random phase method (indicated
by dashed line). (b) Corresponding power spectra of the coherent phase (blue) and random
phase (red) portions of the data in (a) are indistinguishable.

Not all AO device interference effects are removed by the random phase method. In

particular, interference for the AOD is more complicated than for the AOM. This is likely

because the AOD uses a phased array set of piezo oscillators compared to a single piezo

oscillator for the AOM. In addition to the bead measurement errors seen when positioning

traps, the AOD also imposes a strong inference pattern visible in the trap laser beam profile.

Figure 2.8 shows the trap laser beam profile following AOD deflection using the coherent

48

or random phase method. Using either the coherent or random phase method, the AOD de-

flected beam profile shows a strong interference pattern compared to the initially Gaussian

beam profile. The usual coherent phase method beam profile shows additional interference

patterns that transiently change as the beam is scanned. However, when using the random

phase method, the beam profile is fixed while it is scanned and there is no longer fine in-

terference structure variation while scanning (as pointed out in Fig. 2.8c and 2.8d). It is

when the interference patterns change with trap position that they cause measurement and

positioning errors.

49

Figure 2.8: Trap laser profile after AOD and the corresponding Fourier power
spectra. (a) Trap laser profile after AOD using coherent phase methods. (b) Trap laser
profile after AOD using random phase methods. Images have same scale, as indicated by
white bar in (b) whose length is the full width at half maximum (FWHM) of the beam
profile. (c) and (d) are corresponding Fourier power spectra of images in (a) and (b) (log
scale, spectra image pixels summed into 8 x 8 pixel bins). Images have the same scale, as
indicated by the white bar in (d) whose length is 1/FWHM of (b). Arrows in (c) highlight
transient structure that appears during AOD beam scans only when using the coherent phase
method.

50

2.4 Discussion

We have shown that AO device bead measurement inaccuracies systematically vary with trap

positioning and can be completely removed by reducing the coherence of the AO device RF

drive signals. This is a hallmark of wave interference where the observation of interference

patterns depends on sufficient coherence between interfering waves. It is unlikely that the

interfering waves are the electronic RF signals themselves. The reflections at RF electronic

signal path interfaces are suppressed by many orders of magnitude and should be negligible

given the quality RF cabling and components that were used, and the particular patterns we

observe depend on the particular AO device under test and its optical alignment. Further,

we have shown that dephasing the currently on trap interval from its previous on interval

(>5 µs previous) is sufficient to remove the wiggles. The sound waves within the AO device

crystal are resident in the crystal on this time scale: the speed of sound within the crystal
(TeO2) is ∼4 mm/µs, while the crystal size is ∼5 mm and absorption of the sound waves

at crystal surfaces is imperfect. We also observe that the wiggle offset curves exhibit a

phase shift that is strongly correlated with the AO device temperature (Fig. 2.5). The shift

with temperature is consistent with the thermal expansion of the AO device crystal and the

subsequently changing phase of reflected waves relative to the incoming waves. This is all

consistent with the physical model that the wiggling trap positioning error is due to fine

structure of sound waves reflecting and summing within the AO device crystal.

The shifts in the wiggles over time with the changing AO device temperature should

be derived from slow drift in the sound field interference patterns. If the size of the crystal

changes on the order of the wavelength of the sound wave, only 50 µm, then changes in

the interference patterns will occur. Changing the temperature of the crystal will lead to

51

thermal expansion or contraction which will change the size of the crystal. AO devices are

generally very susceptible to overheating and temperature drift as the weak acousto-optic
effect requires very large input RF power (∼2 W in our case) while the insulating crystals
are on the ∼1 cm size scale. For the devices we used, we found that heating to a steady

temperature takes tens of minutes and that the temperature is very dependent on the recent

on/off duty history. Ways to reduce wiggle drift are: 1) never turn off power to the AO

device and 2) improve the temperature control of the AO device. However, by simply using

our random phase method, the wiggles are completely obliterated and none of these concerns

matter any longer.

We explored other protocols to introduce random phase jumps in the RF signal to

reduce the wiggles. Generally, these alternate methods introduced more phase jumps at
random times during the trap on-cycles. Using the synthesis method described above, ∼5

additional phase jumps could be added during a 5 µs trap on-cycle. However, these phase

jumps during the trap on-cycle, as opposed to at the start, introduced significant kicks to the

trapped beads and dramatically increased the trap measurement noise. Similarly, random

phase jumps can be introduced by using a fancy RF signal generator (e.g., the Stanford

Research Systems SG380) as an RF reference clock and using built-in phase noise features.

Wiggles are removed, but unacceptable measurement noise is added.

We noticed that for the AOM as opposed to the AOD, the magnitude of the wiggle

error is significantly larger in the y compared to the x dimension. Again, we note that the

details of the AO device interference patterns, e.g., its amplitude, vary from device to device

and very likely depend on the details of the device construction. We note that comparing an

AOM to an AOD, the AOM device is asymmetric in that there is a single crystal operating

in the x-axis direction only, while the AOD has a pair of crystals operating orthogonally in

52

x and y.

2.5 Conclusion

While AO device wiggle inaccuracies do vary qualitatively and in magnitude from device to

device and in different instrument setups, their straightforward elimination using our method

provides broad benefits, particularly for high resolution applications. Force versus extension

scans can be performed for long durations without concern for drifting wiggles that cannot

easily be subtracted later in post-processing. Active force feedback methods which rely on

real-time active and precise trap positioning are improved. Measurement drift generally is

reduced because shifting wiggle patterns convert to shifting measurement offsets even for

fixed trap measurements. Further our method allows AODs to be used in high-resolution

optical trapping experiments, increasing the usable scan range by nearly 10-fold and allowing

two-dimensional positioning. The application of the random phase method should also be

widely used as it can be integrated into existing optical tweezer setups as a straightforward

software change.

53

Chapter 3

Combined high-resolution optical tweezers
and multicolor single-molecule fluorescence†

We present an instrument that combines high-resolution optical tweezers and multicolor

confocal fluorescence spectroscopy along with automated single molecule assembly. This

hybrid instrument provides the detection of sub-nanometer mechanical displacements via

optical tweezers with single-fluorophore sensitivity via confocal microscope. Three fluores-

cence excitation lasers provide a wide spectrum range that covers the most commonly used

single-molecule fluorophores. Multicolor allows the simultaneous observation of multiple

proteins or F¨orster resonance energy transfer (FRET) measurements within a molecular

complex. Simultaneous tweezers and fluorescence measurement is particularly challenging

due to fluorophore photobleaching, even more so if multiple fluorophores are to be measured.

We present the general design principles to overcome the challenges. We demonstrate the

ability to simultaneously measure sub-nanometer extension changes and single fluorophore

signals. We investigate the photostability of quantum dots and fluorophores. Lastly, we

present the computer-controlled single molecule assembly line that enables the precise as-

sembly of multi-molecule complexes while preserving fluorophores.

†The work in this chapter will be published as:

Cho-Ying Chuang, M. Zammit, M. L. Whitmore, J. L. West, and M. J. Comstock.
Combined high-resolution optical tweezers and multicolor single-molecule fluorescence with automated single
molecule assembly line

54

3.1

Introduction

Single-molecule techniques have become powerful tools to investigate fundamental biological

systems over the last two decades. In contrast to ensemble assays which provide measure-

ments of the average behavior of molecules, single-molecule measurements provide another

level of detail which can only be accessed by directly observing the behavior of individual

molecules. Two major single-molecule methods approaches are force- and fluorescence-based

measurements. Force-based measurements, as made by optical tweezers, magnetic tweezers

or atomic force microscopes, can be used to observe the motions and conformations of indi-

vidual proteins for long time durations over large distances with sub-nm resolution [29–31].

In addition, applied force can tune molecular stability and probe free energy landscapes.

Single-molecule fluorescence methods can also be used to detect the motion and conforma-

tion of individual molecules [46, 59]. However, biological molecules generally possess many

important degrees of freedom and assemble into complexes composed of many interacting

molecules. Any individual single-molecule method is generally limited in its view of this

complexity. Recent progress has been made by devising instruments and methods that com-

bine force and fluorescence measurements allowing the simultaneous observation of complex

multi-protein or multi-degree of freedom systems [47,48,50,60–66]. A hybrid instrument that

combined high-resolution optical tweezers with a single-color confocal microscope showed the

promise of the method by resolving controversy and directly revealing the relationship of he-

licase conformation and oligomeric coupled to DNA unwinding [50, 52].

While the helicase experiment above revealed unprecedented detail, its single excita-

tion laser limited it to observing either a single protein conformation or counting a single

protein species. To make progress, we need to increase the number of excitation and detection

55

channels integrated into the instrument. While multi-color confocal fluorescence microscopes

have existed for some time, it is not trivial to integrate this into a high-resolution optical

tweezers instrument. This is in part because 1) high powered optical trapping lasers tend to

quickly photobleach fluorophores before measurement can take place and 2) high-resolution

tweezers are complicated instruments that must be modified carefully in order to preserve

their performance. Further, increasing the number of fluorophores used in a measurement

increases the overall chance that one of them will bleach and end the measurement. Data

throughput is crucial as high-resolution force measurements cannot be made in parallel.

Here we present a multi-color hybrid instrument that combines three fluorescence ex-

citation and detection channels with dual-trap high-resolution optical tweezers and enhanced

computer automation. We precisely aligned the confocal spot by imaging inorganic fluores-

cent quantum dots via a novel “cryptic binding” protocol. We evaluated the performance of

the most commonly used organic fluorophores and surprisingly found that Cy5 and related

fluorophores outperformed Cy3. We demonstrated the instrument performance by measur-

ing the binding/melting of fluorophore-labeled short ssDNA probes to a tethered strand of

DNA. To minimize photobleaching and improve the data acquisition efficiency, we devised

a precise computer-controlled single-molecule assembly line. Trapping takes place within

a sample chamber. Multiple adjacent laminar flow fluid streams contain uniquely labeled

molecules which bind to a DNA tether. The computer automatically turns on the appro-

priate excitation laser then quickly turn it off again upon molecule binding, and thereby

moves the tether through the chamber precisely. The molecules were adding one by one

while minimally wasting fluorescence and enabling maximal fluorophore lifetime. We believe

these methods will be broadly applicable to many research groups investigating a wide range

of protein-nucleic acid processing reactions.

56

3.2 Material and methods

3.2.1 DNA tether construct preparation

Three types of DNA construct were used here: the “cryptic binding” hairpin construct, the

“hybridization” construct, and the “fixed probe” construct. The cryptic binding hairpin con-

struct was used for fluorescence scan imaging, the hybridization construct was used for DNA

probe binding experiments, and the fixed probe construct was used for fluorophore bleaching

lifetime experiments. These constructs were designed to have two similar double-stranded

DNA (dsDNA) handles that have biotin and digoxygenin on opposite ends and a unique in-

sert in the middle for particular experiments. Both dsDNA handles were produced by PCR

reaction. The left handle “LH” was functionalized with biotin on the 5’ end, and the right

handle “RH” was functionalized with digoxigenin on the 5’ end. The PCR products were

then digested by the restriction enzymes to expose single-stranded DNA (ssDNA) overhangs.

The sequence of the “Insert” was extended to hybrid to a complementary sequence on DNA

handle. We annealed and ligated all segments together using T4 ligase, ran the ligation

product on a 1% agarose gel, then purified and extracted the gel slices using a nucleic acid

gel extraction kit (Qiagen). The concentration of the final product was determined using a

Nanodrop UV-Vis spectrophotometer (Thermo Fisher Scientific). The digoxigenin and bi-

otin ends of the DNA construct were linked to the anti-digoxigenin- and streptavidin-coated

beads before the single-molecule measurements.

The cryptic binding hairpin construct contained three DNA segments: two 1.5 kb

dsDNA handles (LH and RH) and one 89-bp dsDNA hairpin insert (Insert). The final 3 kb

57

product has an 89-bp dsDNA hairpin in the middle.

The hybridization construct contained three DNA segments: 1.5 kb dsDNA handle

(LH), 19- to 47-nt ssDNA insert (Insert), and 1.7 kb dsDNA handle (RH). The final 3.2 kb

product has an exposed ssDNA section in the middle.

The fixed probe construct contained four DNA segments: 1.5 kb dsDNA handle (LH),

14- or 32-nt ssDNA insert (Insert), 3’ fluorophore-labeled complementary probe strands

(Probe), and 1.7 kb dsDNA handle (RH). The final 3.2 kb product has a fluorophore-labeled

probe in the middle.

The “Probe” strands for both fixed probe construct and hybridization construct are

the same, but the sequences of the “Insert” are slightly different. The “Insert” has 5-nt

poly(dT) spacer on one side for the fixed probe construct, and 5-nt poly(dT) on each side for

the hybridization construct. The shortened insert for the fixed probe construct allows us to

anneal and ligate the phosphorylated fluorophore-labeled probes directly to the construct.

This is for fluorophore property measurements so that we don’t have to worry about probes

unbinding during measurement and giving a false bleaching signal.

The sequences of the probe strands and inserts are shown in Appendix A.

3.2.2 Experiment conditions

The DNA constructs were incubated with streptavidin-coated polystyrene beads (Spherotech

Inc) for 30 minutes at room temperature for the biotin-streptavidin bonds to form, then di-

luted in the sample buffer before single-molecule experiments. The single construct molecule

was tethered in situ between a trapped streptavidin-coated polystyrene bead and a trapped

anti-digoxigenin-coated polystyrene bead. Both beads were approximately 800 nm in diam-

58

eter.

For the cryptic binding experiments, the sample buffer contained 100 mM Tris-HCl

pH8, 50 mM NaCl, 20 mM MgCl2, 2 mM Trolox, 7.5 nM Qdot705-labeled probes (Qdot 705

streptavidin conjugate, Q10163MP, Invitrogen) and an oxygen scavenging system. For the

fluorophore bleaching lifetime experiments, the sample buffer contained 100 mM Tris-HCl

pH8, 50 mM NaCl, 2 mM Trolox, and an oxygen scavenging system. For the DNA probe

binding experiments, the sample buffer contained 20 mM Tris-HCl pH8, 100 mM NaCl, 20

mM MgCl2, 2 mM Trolox, 5-10 nM fluorophore-labeled probes and an oxygen scavenging

system. The oxygen scavenging system consisted of 1% glucose and 1% pyranose oxidase

(or glucose oxidase) with catalase, and was used to improve fluorophore stability and tether

lifetime [67, 68]. Trolox is a triplet-state quencher that reduces blinking and photobleaching

[69]. Buffer conditions were chosen to optimize the probe strand binding rate.

The single-molecule measurements were conducted at 23oC in a laminar flow cham-

ber [70]. The custom-made sample chambers consisted of two No.1 microscope cover glasses

(Fisher Scientific) sandwiching a sheet of Parafilm with channels cut out via a CO2 laser

engraver. Experiments were conducted in a central channel flanked by a pair of side channels

containing beads and connected by glass capillary tubes. The multi-color assembly line ex-

periments were done in a five-channel chamber. The top channel contained anti-digoxigenin

beads and the bottom channel contained DNA-construct-coated streptavidin beads. The

central channel contained three adjacent flow streams. The three central channels merged

smoothly to form a laminar flow. Three fluid flows containing different types of probes were

injected by a computer-controlled syringe pump (Harvard Apparatus) pushing simultane-

ously on three gas-tight glass syringes (Hamilton) to ensure smoothly flowing buffer streams

that do not mix.

59

3.2.3 Data analysis

Data analysis was performed using standard methods implemented via custom codes pro-

grammed in MATLAB version 2016b (Mathworks). Data were recorded at 66.7 kHz and

then boxcar-averaged to a final lower rate (20 ms per data point) for analysis and plot-

ting. Standard polymer models of DNA [8, 71] were used to calculate the extension of DNA.

The extension of dsDNA handles was computed by extensible worm-like chain model, and

the extension of ssDNA insert was computed by extensible freely-jointed chain model. For

dsDNA, the persistence length was 53 nm, the contour length per base pair was 0.34 nm,

and the stretch modulus was 1200 pN. For ssDNA, the persistence length was 0.75 nm, the

contour length per nucleotide was 0.59 nm, and the stretch modulus was 800 pN. For the

single-molecule fluorescence measurements, the lateral set position of confocal spot was de-

termined from the extension of the tether at a given force and the radii of the trapped beads

(provided by bead manufacturer).

In the fluorophore bleaching lifetime experiments, the measured fluorescence intensity

and lifetime of each time trace were determined by derivative-based step finding algorithm

and visually verified. The fluorophore lifetime and total photon number were determined

from the mean of individual molecule distribution. Both distributions were well-described

by single exponential models. Based on the maximum likelihood estimator, the likelihood

of the data was the mean. Error bars were standard error of the mean. In the DNA probe

binding experiments, the changes in tether extension were found at corresponding fluores-

cence locations.

60

3.3

Instrument Design

The special about this home-built hybrid instrument is that it prevents the combination-

specific drawbacks that would sacrifice the sensitivity of either one, as well as taking ad-

vantages of both force and fluorescence techniques. We used the dual-trap design optical

tweezers [39], which are formed from the same laser beam, to achieve high-resolution force

and displacement measurements. The instrument was located in a sound-proof, temperature-

controlled, dark room and controlled remotely outside the instrument room to minimize the

environmental noises. Since the dual traps are away from the sample chamber surface, we

chose confocal microscopy rather than total internal reflection microscopy (TIRF) for the

single-molecule fluorescence detection. The biggest challenge for combining optical tweezers

and fluorescence is the fluorophore photobleaching. Our approach is to interlace fluorescence

excitation and detection with time-shared dual optical traps to avoid enhanced photobleach-

ing.

Since interlacing trap and fluorescence excitation light sources is a critical feature,

precise timing alignment and data acquisition is essential. A field programmable gate array

(FPGA)-based PC card (National Instruments PCIe-7852R) was used for instrument control

and data acquisition. The FPGA provides customizable software flexibility with precise

timing control at 25 ns (40 MHz) resolution which is very important for the high-speed

(µs-level) synchronous control. Custom instrument control software was programmed in

LabVIEW version 2012 (National Instruments).

The instrument consists of three modules: optical tweezers, three-color fluorescence

confocal microscope, and bright-field imaging system. The schematic diagram of the in-

strument is illustrated in Fig. 3.1. Each module has its own light sources and detectors.

61

A detailed parts list is provided in Appendix B. Please note that the detailed setup for

optical tweezers is described extensively elsewhere [40,72]. Here, we focus on the design, con-

struction, and demonstration of the multi-color fluorescence excitation/emission with optical

tweezers.

Figure 3.1: Schematic of the instrument layout. Multi-color optical tweezers instru-
ment contains three modules: Optical tweezers (orange solid lines), three-color confocal
fluorescence excitation and emission (green, red, and blue solid lines), and bright-field imag-
ing system (magenta solid lines). The fluorescence excitation laser sources are on the second
optical table. The coupled laser beams (473 nm, 532 nm, and 633 nm) are sent to the
isolation room through a single-mode fiber. The trapping laser and fluorescence excitation
(532 nm and 633 nm) lasers are interlaced by AOM1, AOM2, and AOM3, respectively. The
fluorescence excitation 473 nm laser has built-in modulation mode. The asterisks indicate
the conjugate image planes. The dashed lines indicate the back-focal planes of the objec-
tives. The arrows indicate adjustable translational or rotational stages. A detailed parts list
is available in Appendix B.

62

3.3.1 Optical tweezers

A pair of traps was generated by time-sharing a 5W single-mode, polarization-maintaining

1064 nm fiber laser via an acousto-optic modulator (AOM). We note that the acousto-optic

deflectors (AODs) are more commonly used to deflect the laser beam in optical trapping and

have a larger defection range than AOM, but the trap positioning inaccuracies have limited

the AOD application in high-resolution optical tweezers. By using AOM, these inaccuracies

can be reduced but not completely removed. With the method we devised in Chapter 2

[55], the semi-periodic trap positioning inaccuracies are completely eliminated in both AOM-

based and AOD-based optical tweezers.

AOM1 was used to deflect the laser and thus position the traps by controlling the

first-order diffraction angle via the radio frequency input signal (RF, 70-90 MHz). The

trap laser intensity was monitored by QPD2 and was modulated via a proportional-integral-

derivative (PID) feedback loop using AOM1. AOM1 was also used to interlace the traps with

the fluorescence excitation by turning the trap beam ON and OFF out of phase with the

excitation laser switching. Since the RF signal was digitally generated, when the RF signal

was off, the traps were completely OFF. Only the undiffracted zeroth order beam emerged

from the AOM. Then the zeroth order beam was captured by a beam dump. In order to

maintain sufficient trap stiffness, we modulated the trap and fluorescent lasers at an overall

rate of 66.7 kHz. For each 15 µs (66.7 kHz) duration cycle, two optical traps were created

in sequence via time-sharing for the first and second thirds of the cycle, and then both were

off for the final 1/3 of the cycle (Fig. 3.2).

A high numerical aperture water immersion objective (O1) focused the trap laser light

to create the traps within a fluid flow sample chamber. The trap laser light scattered by the

63

trapped beads was then collected by the back objective (O2) and sent to an IR-enhanced

quadrant photodiode detector (QPD1) for bead position and force measurement. The posi-

tions of the trapped beads were measured via the standard back-focal-plane interferometry

technique. The signals were calibrated via the standard method of bead Brownian motion

power spectra [58].

Figure 3.2:
Interlacing and time-sharing of optical traps and fluorescence exci-
tation lasers. In one interlacing cycle, we interlace at 66 kHz (15 µs). Two optical traps
are on in sequence during first two time intervals and off during the third interval. The
fluorescence excitation lasers are only on during the third time interval while the trap laser
is off. Signals were measured by the photodetectors (feedback QPD and PDs) and recorded
by a digital oscilloscope.

64

3.3.2 Multicolor single-molecule fluorescence

A critical component of integrating the fluorescence microscopy to the optical tweezers is

to co-align the fluorescence excitation beams with the trapping beam. The high-resolution

optical tweezers alignment is sensitive. To simplify the coalignment of trap laser and fluo-

rescence excitation lasers, we coupled three fluorescence excitation lasers into a single-mode

fiber. The fiber has the property that all light coming out will be coaligned automatically. In

this way, there is only one beam alignment with the trap. Fiber coupling not only simplifies

the alignment of the multi-color confocal microscope, but also gives rooms for future exten-

sion such as adding more excitation sources without realigning current setup. It also allows

us to move a lot of fluorescence hardware off the main trap optical table, even to outside

the room. This saves space on the main table and reduces noise/heat in the instrument

isolation room. The downside is that the useable excitation laser intensity is lower because

the input coupling efficiency cannot be 100%. In our case, we got 50% coupling efficiency.

Generally, it is not a problem because usually a few µW excitation power is enough for

single-molecule confocal fluorescence experiments. We always need to use neutral-density

filters (F8, motorized flip filter) to reduce the laser intensity to desired power.

Three fluorescence excitation lasers provide a wide spectrum range and clear spectral

separation from blue to red: blue (473 nm), green (532 nm), and red (633 nm). It is designed

to work with Alexa 488, Cy3, and Cy5 fluorophores or other substitute fluorophores, the

most commonly used set of in vitro single molecule fluorophores (Fig. 3.3). We used visible

achromatic doublet lenses in the multi-color confocal path to ensure consistent focusing and

handling of all lasers and fluorescence across the entire visible spectrum.

The fluorescence excitation lasers were interlaced with the traps. For the green and

65

Figure 3.3: Excitation and emission spectra of the fluorescent molecules. The
excitation (dashed lines) and emission (solid lines) of Alexa 488 (blue), Cy3 (green), Alexa
647 (purple), Cy5 (red), and Qdot705 (orange). The five fluorescent molecules we studied
in this Chapter cover the visible spectrum.

red lasers this was done by modulating AOM2 and AOM3 respectively. The blue laser was

a diode laser capable of fast intensity modulation by design.

It was directly modulated

with a digital input signal from the FPGA. Fluorescence lasers were only ON when both

traps were OFF to minimize photobleaching [49]. Figure 3.2 shows a direct simultaneously

measurement of the excitation and trap laser intensities during interlacing. Unlike to AOM1

for optical traps, the AOMs for fluorescence only controlled the intensity. The RF frequency

did not change.

Three fluorescence excitation lasers were coupled into a single single-mode polariza-

tion maintaining optical fiber. Three excitation beams went through the same optical path,

focused by the front objective (O1), and coaligned with the traps. The fluorescence excita-

tion beams focused in between the traps in the same focal plane to excite molecules tethered

66

between the trapped beads. The emission fluorescence signals within the confocal volume

were collected by the same objective (O1), then separated by dichroic mirrors, filtered by op-

tical filters, and detected by three single-photon counting fluorescence detectors (avalanche

photodiodes, APD). The timing synchronization (time alignment) between light sources and

data acquisition is important. The APD only recorded the signals during the fluorescence

excitation lasers ON period. Instead of using the APD gate digital input, we kept APD ON

and programed the FPGA to record photon counts during the fluorescence period (i.e. the

final 1/3 of the interlacing cycle).

PD1, PD2, and PD3 are silicon photodetectors for monitoring fluorescence excitation

laser intensity of blue, green, and red lasers respectively. The signals were sent to the FPGA

and a proportional-integral-derivative (PID) feedback loop was used to stabilize the laser

intensity.

We used multiple methods to precisely co-align and position the fluorescence excita-

tion beams relative to the optical traps both axially (z, the focal plane) and laterally (x and

y within the focal plane). Coarse co-alignment of the excitation and trap lasers was achieved

by observing focused trap and excitation laser spots on the visible microscope CCD camera.

Axially positioning (focal depth) of the excitation laser was finely adjusted by translating

the lens L3 of the telescope T3 along the beam path using a precision translation stage. Fine

lateral positioning of the excitation lasers was controlled by a closed-loop piezo mirror stage

(PM). Precise alignment was achieved and verified using complimentary methods.

First, the excitation lasers can serve as back-focal-plane bead detection lasers (same

as the trap laser). The piezo mirror raster-scans the excitation lasers across the trapped

bead region while a position sensitive detector (PSD) records the detection image of a pair

of trapped beads. When the lasers are co-aligned with the bead plane, the detection im-

67

ages of the beads are minimum diameter and circular without distortion (Fig. 3.4a). As

expected, since three fluorescence excitation beams came out from fiber were coaligned and

we used visible achromatic doublet lenses, it is the optimal position for all three fluorescence

excitation beams (Fig. 3.4b).

Next, we fixed the confocal lateral location at the center of one trapped bead and

obtained the bead Brownian motion power spectra. The sensitivity of the measurement is

maximized when the excitation laser is co-aligned in the same plane as the trapped bead. The

PSD voltage to position conversion factor α (nm/V) in the lateral x and y directions were

obtained by fitting the power spectrum in the standard way (just as is done for the optical

trap calibration). If we obtain conversion factor α versus focal depth, the optimal position

coincides with the minimum of α (i.e. the highest detection sensitivity). Figure 3.5a shows

the calibration for the same bead using trap beam (left) and fluorescence beam (right) as

the detection laser. The chamber was aligned relative to the trap beam, so there was no low

frequency noise on both x and y direction using trap detection beam. The low frequency

noise for the fluorescence detection beam may be from the slightly tilt angle between trap

beam and fluorescence beams.

Finally, the focal depth alignment was confirmed with the APD using fluorescence

emission signals. The image of a trapped fluorescence bead was scanned using the piezo mir-

ror stage (Fig. 3.5b). The optimal position would have the maximum fluorescence intensity.

The axial alignment by both PSD and APD methods agreed with each other (Fig. 3.5c).

68

Figure 3.4: PSD scan images from all three fluorescence excitation lasers using the
piezo mirror stage. (a) Scan the confocal spot over one trapped bead. The deflection in x
(upper) and in y (lower) of the green laser when it scans. Red represents positive deflection
and blue represents negative deflection. (b) Scan the confocal spot over two trapped beads.
The deflection in y direction when the blue (top), green (middle), and red (bottom) lasers
scan.

69

Figure 3.5: Axial alignment of confocal spot. (a) Bead calibration with trap detection
laser (left) and fluorescence detection laser (right) in x (upper) and y (lower) direction at the
optimal focal depth position. The power spectra are from the same trapped bead. (b) Scan
images of a trapped fluorescent bead using piezo mirror stage at the optimal focal depth
position. The emission spectrum of the fluorescent bead (F8819, Invitrogen) covers both
green and red APDs detection wavelength. (c) Adjustment of confocal spot focal depth.
(Upper) The conversion factors αx (blue circles) and αy(red crosses) were determined from
the power spectrum fitting in (a). (Lower) The fluorescence signals from green APD (green
circles) and red APD (red crosses) were obtained from the APD scan images in (b).

70

3.3.3 Bright-field imaging

The bright-field imaging system consists of an infrared 940 nm LED as the light source and

an IR-enhanced CCD camera to visualize the sample chamber, beads, trap manipulation,

and tether formation. F1 (short pass, 1000 nm) and F2 (long-pass, 850 nm) were used to

remove excess trap and fluorescence laser intensity as needed.

3.4 Results and discussion

3.4.1 Cryptic quantum dot binding for robust signal confocal align-

ment

Precise lateral alignment of the confocal spot with the tether construct is essential for efficient

single-molecule fluorescence detection. To confirm the lateral alignment with a tethered

construct, the final way is imaging a single fluorescence molecule in between the trapped

beads. While it is possible to directly image a single organic fluorophore such as Cy3 in our

setup and thereby precisely position the confocal laterally [50], it is extremely challenging to

obtain images by raster scanning rather than with a camera due to the practical limitations

of photobleaching.

Inorganic fluorescent quantum dots are semiconductor particles that have brighter

emission signals and less likely to photobleaching compared to the organic fluorophores [73].

Also, quantum dots have a wide excitation spectrum and a narrow emission peak while the

organic fluorophores have a narrow excitation spectrum and a narrow emission range. We

took these advantages and developed a new fluorescence detection scheme that is useful for

71

both instrument alignment and measurement. We used Qdot 705 (emission maximum ∼705

nm) in our demonstration experiment. Qdot 705 can be excited by our three fluorescence

excitation lasers and detected by the red emission detector.

Using replenishable fluorescent-labeled probes in solution allows fresh probes to re-

bind to the tether after photobleaching. However, a major challenge for diffusing fluores-

cent probe experiments is the signal-to-background-noise ratio. Some of this background

comes from probe bound to excess untethered DNA attached to the trapped streptavidin

bead. To remove the fluorescence background from beads, we combined a multi-channel flow

chamber and internal hairpin binding construct to perform “cryptic binding” and “dipping”

experiments (Fig. 3.6). The hairpin constructs reduce fluorescence background from DNA-

construct-coated beads because the only complementary binding site for the probes is the

opened hairpin tether. Once the probe binds, the tether extension changes are observed by

the optical tweezers. We simultaneously measured fluorescence and extension for a hairpin

tether (Fig. 3.7). When hairpin tether opened, it exposed a single-stranded portion near

the center to the complementary quantum-dot-labeled probe. The binding of quantum-dot-

labeled probe changed the tether extension and increased the fluorescence signals.

72

“Cryptic binding” experiments with quantum dots. Hairpin con-
Figure 3.6:
struct creates “cryptic binding” site to reduce fluorescence background from beads. Two
polystyrene microspheres (gray spheres) are trapped by dual optical traps (orange cones)
and tether together by the DNA construct. When the complementary quantum dot-labeled
probes bind to the tether, the fluorescence signals (red disk) are detected by the confocal
microscope (blue cone) and the tether extension changes are monitor by optical tweezers.

73

Next, we performed dipping experiments to image inorganic fluorescent quantum dots

(Fig. 3.8). The tether was moved to the “blank” buffer channel. The fluorescence excitation

lasers were then turned on to collect the signals. The confocal scan image shows the accuracy

of the calculated set spot that computed from the bead size and the DNA tether extension.

The differences between the center of quantum dot and the set spot were only within 0.1

µm.

The excellent brightness and photostability of quantum dot make it a good candidate

for fluorescence alignment. Although quantum dots blinked a lot, it did not bleach after

exciting high laser power 750 µW fluorescence laser for minutes (multiple scan images).

Dramatically reduced photobleaching compared to organic fluorophores allows imaging and

precise fluorophore localization. This “cryptic binding” and “dipping” method significantly

reduced the background fluorescence signals from beads and buffer. This method can be

applied to experiment need long fluorescence probe lifetime or high brightness.

74

Figure 3.7: Representative time trace of hairpin cryptic binding experiments.
Fluorescence excitation laser turned on around 5 seconds. Hairpin construct opened around
15 seconds and revealed a ssDNA section in the middle. Quantum dot didnt bind until 66
seconds. (Insets) A zoomed view of the force (upper panel), tether extension (middle panel),
and fluorescence signal (lower panel) changes when quantum dot bound to the exposed
ssDNA portion.

75

Figure 3.8: Confocal alignment scan images using quantum dots.
(Upper) The
confocal scan image from PSD. The fluorescence beam deflected by two trapped beads as
it scanned across the beads. The red circles indicate the size of trapped beads, the red
dashed line represents the DNA tether, the blue cross is the bound probe position calculated
from the polymer model, and the white crosses are the center of quantum dot determined
from multiple APD scan images. (Lower) the confocal scan image from APD. The bound
quantum dot probe stayed bright and survived for minutes after multiple raster scans.

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3.4.2 Multicolor DNA probe binding demonstration

In order to demonstrate the new instrument capabilities, we measured the binding and

unbinding of fluorophore-labeled single-stranded DNA oligonucleotides to a strand of DNA

tethered between a pair of trapped beads (Fig. 3.9). The tethered DNA had a middle

section with an exposed ssDNA probe binding site. Short complimentary ssDNA probe

molecules labeled with a variety of fluorophores were dispersed in the surrounding solution.

Upon binding of a single probe molecule to the tethered DNA, the ssDNA section of the

tether is converted to dsDNA, which has a different extension generally (Fig. 3.10), and

thus is detected by the optical portion of the instrument. At the same time, the confocal

fluorescence portion of the instrument detects the presence of the fluorophore.

Figure 3.9: Multi-color single fluorophore-labeled oligonucleotide hybridization
experiment. When the complementary fluorophore-labeled probes bind to the tether, the
fluorescence signals (red disk for red laser excited signals) are detected by the confocal
microscope (green, red, and blue cones) and the tether extension changes are monitor by
optical tweezers.

77

Figure 3.10: Force dependent DNA extension change upon hybridization. Force
dependent extension change from 9-nt ssDNA to 9-bp dsDNA was calculated using extensible
worm-like chain polymer model. The end-to-end extension is shorter (longer) when the force
is above (below) the critical force 5.5 pN.

Figure 3.11a shows an example simultaneous tether extension and fluorescence

measurement for a Cy3 labeled probe excited by the corresponding green laser. A de-

crease/increase in tether extension is observed simultaneously with an increase/decrease in

the fluorescence signal upon probe molecule binding/unbinding from the DNA tether. In

Fig. 3.11b, we plot the change in tether extension upon fluorophore binding and unbinding

showing clear sub-nanometer trap measurement resolution similar to the previous instru-

ment [50]. Example time traces (Fig. 3.12) show detection of red laser excited Cy5-labeled

probes, green laser excited FRET labeled probes. The blue laser excited Alexa Fluor 488

probes are also shown. Note that consistent with other fluorescence-based instruments, blue

laser excited fluorophores while measurable and usable provide substantially worse perfor-

mance than red and green.

78

Figure 3.11: Simultaneous measurements of fluorescence and tether extension.
(a) (Upper) The tether extension difference between single-stranded and double-stranded
DNA. (Lower) Cy3 fluorophore labeled probes were excited by green laser. The binding and
unbinding events were simultaneously observed by the stepwise increase and decrease of the
fluorescence signals and the changes in tether extension. (b) Histogram for many binding
and unbinding events of the recorded extension differences from the molecule in (a).

79

Figure 3.12: Multi-color single fluorophore-labeled oligonucleotide hybridization
experiment under 10 pN force.
(a) Cy3-Cy5 FRET labeled probes were excited by
green laser. (b) Alexa Fluor 488 fluorophore labeled probes were excited by blue laser. (c)
Cy3-Cy5 FRET labeled probes were excited by red and green lasers separately. At 0-80
seconds, Cy5 from the FRET probes were excited by the red laser. Red laser was off and
green laser was turned on between 370-435 seconds. At 375-395 seconds, Cy5 signals were
obtained through FRET. At 400 seconds, Cy5 bleached and only Cy3 signals were detected.

80

3.4.3 Cy5 outperformed other organic fluorophores

We next quantitatively evaluated the performances of the most commonly used organic

fluorophores for blue, green and red excitation in our instrument. We prepared tethers in

the wet lab with the fluorophore-labeled probe DNA already bound and permanently ligated

to the tether (Fig. 3.13a). This way the loss of fluorescence signal unambiguously indicates

photobleaching rather than the unbinding of the probe (Fig. 3.13b).

Experimental setup for fluorophore lifetime experiments.

Figure 3.13:
(a)
Schematic of experimental setup. Utilizing fixed fluorophore construct to characterize fluo-
rescence performance in high-resolution multicolor fluorescence optical tweezers. A variety
of fluorophores were ligated to DNA construct. (b) Typical time trace of single fluorophore
lifetime measurements. Laser was on at 5 sec, excited the fluorophore and given a 10 kHz
signal. The fluorophore bleached at 23 sec. Total photons collected is the multiplication of
intensity and photobleaching lifetime.

We first investigated the effect of the trap on fluorescence performance using the most

commonly used fluorophore, Cy3. The trap laser power was varied more than 10-fold over

the typically used range. The corresponding trap stiffness was from 0.05 to 0.6 pN/nm while

the power of 532 nm excitation laser was kept constant at 16 µW. As seen in Fig. 3.14a, the

fluorophore emission intensity and lifetime was essentially unchanged by trap laser power,

confirming that the interlacing method successfully protected the fluorophores from the trap
laser. Cy3 can provide ∼45,000 photons before photobleaching.

Next, we measured the effect of the fluorescence excitation laser intensity on Alexa

Fluor 488, Cy3, Cy5, and Alexa Fluor 647 fluorophores (Fig. 3.14b). The fluorescence

81

intensity is proportional to the excitation laser intensity (Fig. 3.14b upper panel), but the

fluorescence intensity at 32 µW were 10% lower than expected linear fit. Although we use

the low power range in most experiments, this would be a concern at higher excitation power

which might be used for high time resolution experiments. Bleaching rate which is the inver-

sion of lifetime (Fig. 3.14b middle panel) is proportional to the excitation intensity. Both

intensity and bleaching rate indicate that bleaching is mostly a single photon effect. There-

fore, the higher the excitation laser intensity, the lower total photon numbers (Fig. 3.14b

lower panel). Surprisingly, we found that the Cy5 performed much better than other fluo-

rophores, particularly Cy3. Cy5 has the most photon numbers. It is tenfold (400k at 4 µW

red laser) higher than Cy3 (80k at 4 µW green laser) and is comparable to the photo num-

ber collected from other fluorescence-based single-molecule instrument such as total internal

reflection fluorescence microscope (TIRF). Alexa Fluor 647 has similar intensity as Cy5, but

slightly shorter lifetime. Alexa Fluor 488 has significantly shorter lifetime and fewer photon

number (3k at 2 µW blue laser). Therefore, in order to optimize the performance, red exci-

tation of Cy5 should be prioritized over green excitation of Cy3.

82

Figure 3.14: Fluorophore lifetime experiments with fixed probes. (a) Effect of the
trap laser intensity on Cy3 photobleaching at 16 µW 532 nm excitation. n = 29, 25, 28,
and 27 for trap stiffness 0.05, 0.2, 0.3, 0.6 pN/nm. The trap stiffness is proportional to trap
power. (b) Effect of the power of fluorescence excitation lasers at 0.3 pN/nm trap stiffness.
The blue-absorbing Alexa Fluor 488 (blue plus) was excited by 473 nm laser. n = 30 for 2
µW. The green-absorbing Cy3 (green diamond) was excited by 532 nm laser. n = 26, 14,
28, and 12 for 4, 8, 16, and 32 µW. The red-absorbing Cy5 (red circle) and Alexa Fluor
647 (pink cross) fluorophores were excited by 633 nm laser. n = 22, 28, 28, and 25 for 4, 8,
16, and 32 µW. n = 17, 23, 21, and 20 for 2, 4, 8, and 16 µW. Error bars are smaller than
symbol sizes.

3.4.4 Automated single molecule assembly line

Due to the finite photon number, it is critical to efficiently excite the molecule. We have

combined multi-channel sample chambers with precise computer control of fluorescence mea-

surement and triggered chamber motion to implement an automated molecular assembly line.

This allows us to precisely add individual molecule of different types to a single DNA tether

while conserving fluorescence photons and reducing photobleaching. We used Laminar flow

chambers and put different fluorescently labeled molecules for assembly in different channels

83

(Fig. 3.15a and 3.15b). Each fluorophore-labeled molecular component is in a separate

buffer and does not mix. The assembly is divided into two routines: detection and motion.

Computer controlled excitation lasers on and off to detect the molecule binding events. The

trapped complex can be moved between channels to add components or change buffer con-

ditions. The software was programed to use the chamber motions as the trigger to turn the

fluorescence excitation lasers on and use the fluorescence emission signals as the trigger to

turn the fluorescence excitation lasers off.

Figure 3.15: Multi-channel flow chamber. (a) Photograph of a 5-hole flow chamber. The
top channel contains anti-digoxigenin beads. The bottom channel contains DNA-construct-
coated streptavidin beads. The central channel consists of three laminar flow streams. (b)
Laminar flow layout. The central channel contains three different buffers: buffer without
probes (“Blank”), buffer with Cy3-labeled molecules (“Molecule 1”), buffer with Cy5-labeled
molecules “Molecule 2”).

Fig. 3.16 shows an example of our molecular assembly line. A single tether is formed

in the “Blank” buffer without any fluorophores, then moves the tether to the next channel.

The green laser is turned on automatically once the tether arrives the set spot. The tether

is sitting in the buffer containing Cy3 labeled molecules and waits for the probes to bind.

When the signal exceeds the pre-set background threshold level, it automatically turns the

green laser off, moves to next channel, turns red excitation on, and repeats the process until

we get all the components. We use computer program carefully turn laser on and off to

84

maximize the photon number and minimize the time of unnecessary exposure to excitation

laser. In multi-fluorophore trapping experiments, multiple fluorophores need to be alive dur-

ing measurement. Therefore, an automated computer-controlled assembly line provides fast,

accurate, and efficient measurement than manual controlled measurement.

Figure 3.16: Molecular assembly line with the multi-channel flow chamber. Ex-
ample time trace for in situ molecular assembly. The DNA tether was formed in “Blank”
buffer, then (1) moved to “Molecule 1” buffer, turned green laser on and waited for the probe
binding, (2) turned green laser off once the probe bound, moved to “Molecule 2” buffer, (3)
turned red laser on and waited for the probe binding, (4) turned green laser on and ob-
serve FRET, (5) Cy5-labeled probe bleached or unbound, only Cy3-labeled probe showed
emission, (6) Cy3-labeled probe bleached or unbound. No fluorophore emission.

3.5 Conclusion

We have demonstrated a multi-color hybrid instrument combined high-resolution optical

tweezers and multi-color confocal fluorescence microscope has a potential to be used to study

the structure, interactions, and dynamics in real biological systems. We showed the robust

and bright quantum dots are a great alternative fluorescent probe in the high-resolution

multicolor fluorescence optical tweezers experiments and alignment. We have measured fluo-

85

rophore photobleaching lifetimes with a set of fluorophores for a variety of excitation powers

in a range of buffer conditions. We also showed that Cy5 has a much better performance

over other fluorophores. In addition, the throughput of the single-molecule measurements

can be improved by our instrumentation development. The multicolor hybrid instrument and

methods we developed open an opportunity to uncover the details of the complex biological

systems. For instance, in addition to measuring the DNA tether extension changes (e.g.,

from helicase or polymerase motion), we can detect multiple fluorophore-labeled proteins in

DNA replication which involves helicase, polymerase, and single strand binding protein. We

can also study conformational changes in RNA polymerase during transcription via interfluo-

rophore distance (FRET efficiency). These instrumentation advancements should enable the

precise single-molecule assembly and measurement of complex, multi-component molecular

machine systems.

86

Chapter 4

Mechanical folding pathway of the
thrombin-binding aptamer G-quadruplex‡ §

We performed high-resolution optical tweezers to directly observe folding and unfolding re-

actions of thrombin-binding aptamer G-quadruplex (TBA-GQ) at very low forces (as low

as 2 pN). Studying the kinetics of G-quadruplex formation is essential for gene regulation

and therapeutic approaches for disease. TBA-GQ is the smallest G-quadruplex. It contains

only two G-tetrads that make it less stable than other G-quadruplexes under force. Utilizing

the sensitivity and stability of our optical tweezers, we were able to directly measure the

folding and unfolding rate constants of TBA-GQ under force. We studied the folding and

unfolding of TBA-GQ over a range of conditions including the impacts of force, monovalent

salt ions, and thrombin. We also identified the transition state structure under a variable

salt concentration.

‡The work in this chapter will be published as:

Cho-Ying Chuang, H. Balci, and M. J. Comstock.
Mechanical folding pathway of the thrombin-binding aptamer G-quadruplex by single-molecule force spec-
troscopy

§Some work in this chapter has been published as [74]:

G. Mustafa, Cho-Ying Chuang, W. A. Roy, M. M. Farhath, N. Pokhrel, E. Anthony, M. J. Comstock, S.
Basu, H. Balci. Biosensors and Bioelectronics, 121, 34-40 (2018)

87

4.1

Introduction

G-quadruplex is a non-Watson-Crick secondary structure formed by single-stranded guanine-

rich DNA or RNA sequences. Four guanines are held in a plane by Hoogsteen hydrogen bonds

[75] and coordination with a monovalent metal ion such as N a+ or K+ to form a G-tetrad

(Fig. 4.1a). Two or more G-tetrads can form in sequence and stack on top of one an-

other, with the ion sandwiched in between, to form G-quadruplex structures. G-quadruplex

structures are believed to be involved in several key biological processes such as replication,

transcription, translation, and telomere maintenance [15, 76–79]. Of particular importance,

telomeres, the end regions of eukaryote chromosomes, are rich in the G-repeat sequences

known to form G-quadruplex structures in vitro.

It was demonstrated that telomeric G-

quadruplex protects the end of eukaryotic chromosomes and inhibits telomerase activity

[80]. These structures are dynamic. In order to understand how they interact with proteins

like telomerase, we should first characterize their folding and unfolding dynamics in isola-

tion. Understanding the dynamics of G-quadruplex formation is crucial for both molecular

biology understanding and structure-based drug design [81–84].

Thrombin-binding aptamer G-quadruplex (TBA-GQ) is a minimal model system of

G-quadruplex. It is a 15-mer single-stranded DNA that folds into a chair-like two-layer G-

quadruplex (Fig. 4.1b) [85, 86]. It is an important DNA structure in its own right as it

specifically interacts with thrombin to inhibit blood coagulation [26] and has been investi-

gated as a potential anticoagulant aptamer-based drug [25, 87]. TBA-GQ is one of the most

studied G-quadruplex forming aptamers [88–99], however its folding/unfolding mechanism

remains unresolved. Previous single molecule investigations have included probing the sta-

bility of TBA-thrombin interactions and the role of salt in stabilizing structure [100, 101].

88

Force spectroscopy can provide powerful methods for identifying folding and unfolding free

energy landscapes and transition states, however TBA-GQs small size and relative instability

under force (unfolding at < 5 pN) have thus far been limiting. Most recently the folding free

energy landscape and transition states of TBA-GQ have been predicted via computational

simulations [102–104]. These molecular dynamics (MD) simulations predict that G-hairpin

and G-triplex are the possible intermediate states in TBA-GQ formation.

Here we present a high-resolution optical tweezers investigation of TBA-GQ where

we directly observed both folding and unfolding reactions at very low forces. Equilibrium

condition measurements allowed us to directly and unambiguously determine folding and

unfolding rate constants under varying conditions. Exploration of salt dependence showed

a very strong increase in the folding rate constant with increasing salt while unfolding de-

pendence was weak. Thrombin showed the opposite effect where increasing the thrombin

concentration was seen to increase the fraction of TBA-GQ folded by decreasing the unfold-

ing rate constant. The present of thrombin is stabilizing TBA-GQ while not changing the

folding rate constant. Measurements of rate constants vs applied force probed the folding

and unfolding free energy landscape. We were able to model both the folding and unfolding

equilibrium data self-consistently using a single transition state clearly identified as the G-

triplex structure. Altogether, these investigations present a clear picture of the folding and

unfolding dynamics of TBA-GQ.

89

Figure 4.1: Structure of thrombin-binding aptamer G-quadruplex (TBA-GQ). (a)
G-tetrad, the building block of G-quadruplex, contains four coplanar guanines that coordi-
nate with a monovalent metal ion. (b) Schematic structure and dimensions of the chair-like
two-layer thrombin-binding aptamer G-quadruplex.

90

4.2 Material and methods

4.2.1 Dual-trap high-resolution optical tweezers

All measurements were performed using a home-built timeshared dual-trap high-resolution

optical tweezers described in references [50, 105]. Two independent optical traps (66.7 kHz

modulation rate) were created by rapidly deflecting a 1064 nm laser (IPG) via an acousto-

optic modulator (AOM, IntraAction). A constant trap stiffness (0.2-0.3 pN/nm) was main-

tained through a PID (proportional-integral-derivative) feedback loop using the same AOM

to stabilize the trap laser intensity during trap positioning. Bead position and trap stiffness

calibrations were performed via the standard analysis of bead Brownian motion power spec-

tra [58]. Instrument control and data acquisition were performed using a field programmable

gate array (FPGA)-based PC card system (National Instruments PCIe-7852R). Instrument

control software was programmed in LabVIEW version 2012 (National Instruments).

4.2.2 Construct preparation

The TBA-GQ insert contained 15 nucleotides (5’-GGTTGGTGTGGTTGG-3’) with 2-nt

poly(dT) linkers on each side. Linkers are added to reduce the interaction of G-quadruplex

with double-stranded DNA (dsDNA) handles. The insert was annealed and ligated to a

biotin labeled 1.5 kb dsDNA handle on one side and a digoxigenin labeled 1.7 kb dsDNA

handle on the other side. Both handles were synthesized by PCR reaction followed by re-

striction digestion. The final product is a 3.2 kb dsDNA plus 19-nt single-stranded DNA

(ssDNA) central region (Fig. 4.2).

91

Figure 4.2: Schematic of the TBA-GQ experimental setup using optical tweez-
ers. The TBA-GQ construct (cyan) is tethered between two optically trapped beads (gray
spheres) via two long dsDNA handles (red).

4.2.3 Experimental procedure

A pair of trapped polystyrene beads were tethered in situ via the single construct molecule

(Fig. 4.3 inset). For each tethered construct, we first performed non-equilibrium force ramp

measurements at a scan speed of 100 nm/s and fit to the worm-like chain model for con-

firming the proper behavior of the TBA-GQ. Three representative force-extension curves

are shown in Fig. 4.3. The dashed lines represent polymer models of TBA-GQ folded (red

dashed) and unfolded (black dashed). For good molecules, next, low force equilibrium mea-

surements were obtained by holding the construct at fixed trap separations corresponding to

desired mean forces. Data were collected at a set of trap positions to probe the folding and

unfolding at set of mean forces. All data were collected at 23oC in a buffer containing 50 mM

Tris-HCl pH 8, 150-1500 mM KCl, and 0-1200 mM NaCl. An enzymatic oxygen scavenging

system (1% glucose and 1% glucose oxidase with catalase) was also included in the buffer to

prevent tether damage. For thrombin experiments, the buffer contained 300 mM KCl, 150

mM NaCl, 50 mM Tris-HCl pH8, 0-150 nM human alpha-thrombin (Invitrogen RP-43100,

92

Thermo Fisher Scientific Inc.), and the enzymatic oxygen scavenging system. The sample

channel consisted of two adjacent laminar flow streams at a constant flow rate 100 µL/hr.

The tethers can be transferred between the adjacent streams (with and without thrombin)

in less than 3 seconds.

Figure 4.3: Single-molecule optical tweezers study of thrombin-binding aptamer
G-quadruplex (TBA-GQ). Non-equilibrium force ramp measurements of TBA-GQ in the
presence of 600 mM KCl. The inset cartoon shows a single TBA-GQ folded and unfolded
under mechanical force via optical tweezers. Three representative force-extension curves for
pulling (blue) and relaxing (red) are shown with horizontal shifts for clarity. The extension
of DNA tether follows the polymer model of TBA-GQ folded (red dashed) and unfolded
(black dashed).

93

4.2.4 Data analysis

Tether polymer model

Standard polymer models of DNA were used for force-extension curve fitting. dsDNA handles

and ssDNA were modeled using the extensible WLC model [7, 8, 11, 106, 107]. For dsDNA,

the persistence length was 53 nm, the contour length per base pair was 0.34 nm, and the

stretch modulus was 1200 pN. For ssDNA, the persistence length was 1.1 nm, the contour

length per nucleotide was 0.59 nm, and the stretch modulus was 800 pN. The ssDNA per-

sistence length 1.1 nm was determined by empirical fit to non-equilibrium force ramp data

and equilibrium time traces. These parameters fit our data well over a range of force and

salt concentration.

Rate constants and transition state fitting

Data were analyzed using standard methods implemented via custom codes programmed

in MATLAB version 2016b (Mathworks). Data were collected at 66.7 kHz then boxcar-

averaged to a final lower rate (between 9 to 90 ms per data point) for analysis. Automatic

step finding was performed by a statistics-based changepoint method and visually verified to

prevent artificial events. The dwell time distributions were plotted as binned histograms and

unbinned cumulative probability. Both were well-fit by single exponential models (Fig. 4.4).

Therefore, rate constants were estimated by taking the inverse of the mean dwell time of the

distribution, which is the maximum likelihood estimate. Error bars were standard error of

the mean.

94

Figure 4.4: Folding and unfolding dwell times show single exponential distribu-
tion. (a-b) Dwell time histogram of the (a) folded states (i.e. unfolding rate constants) and
(b) unfolded states (i.e. folding rate constants) from one example time trace at 300 mM KCl.
Since the data is single exponential distribution, the maximum likelihood estimate (MLE)
of time constant τ is the mean of the dwell times. (c-d) Logarithm plots of the histogram
with least squares linear fits. (c) is corresponding to (a), and (d) is corresponding to (b).
The linear fit at log scale indicates that the data is single exponential distribution. (e-f)
Cumulative probability distributions. The data (blue lines) show very good agreement with
MLE (red lines) and 95% MLE confidence intervals (green dashed).

95

However, we do not directly fit to these rate constants when performing Bell fitting

or modeling the transition state. Instead we implemented a generalized maximum likelihood

global fitting method to analyze the equilibrium data and the corresponding force-dependent

rate constant models. The maximum likelihood method is a powerful parameter estimation

method for a given model and a set of data. It maximizes the value of the data by using

each individual dwell time at its corresponding force rather than the simple mean. Different

molecules were measured for different amount of time and have different number of events.

For each dwell time, we summed the log of the probability of the measured dwell times.

Then iteratively find the parameter values that best describe the data. The uncertainty of

the fit parameters was estimated from the standard bootstrap resampling method.

4.3 Results

4.3.1 Force dependent

In order to perform initial characterization of TBA-GQ unfolding and verify that we have

good individual TBA-GQ tethers we performed standard force-ramp experiments where we

repeatedly oscillated the trap separation to pull and relax the tethers. A set of typical force

vs. extension curves are shown in Fig. 4.3. TBA-GQ tethers began in the folded state at

low force and then unfolded with increasing force in single steps (a simultaneous increase

in extension and decrease in force). For these particular conditions, 100 nm/s scan speed,

refolding occurred at low force and was only sometimes observed. Intermediate states were

not observed. The observed change in contour length before and after the observed ruptures

closely matches the expected change in contour length for a single TBA-GQ molecule. Thus,

96

we verified that our tether constructs each contained a single TBA-GQ molecule.

We then probed the TBA-GQ unfolding and refolding landscape by directly measuring

these reactions under equilibrium conditions with fixed trap separation. While we could

perform similar measurements via out-of-equilibrium force ramp measurements, as others

have commonly done in the past, the data from such measurements have to be analyzed

with careful consideration of the detailed force ramp conditions. High ramp rates and forces

can distort free energy landscapes so much that completely different paths and states are

observed as compared to zero force and equilibrium [108–110]. However, the high-resolution

tweezers allow us to perform equilibrium, low force measurements of TBA-GQ. Figure 4.5a

shows a typical equilibrium measurement of TBA-GQ. The trap separation remains fixed

except for sudden increases that increase the average force (e.g., at t = 200 s, there is

a stepwise increase in the trap separation and the mean force changes from 2 to 3 pN).

At a given mean force, stepwise increases and decreases in the force signal correspond to

TBA-GQ unfolding and refolding respectively. The reaction was dominated by two states,

with no reproducible intermediates. The extensions of the two states agreed with the two

states observed in the force ramp measurements and the polymer modeling of the expected

fully folded and unfolded TBA-GQ contour lengths. Figure 4.5b shows the raw data

distributions in Fig. 4.5a versus mean force. Two peaks are observed corresponding to the

folded and unfolded TBA-GQ states. With increasing mean force, weight shifts from the

folded to the unfolded peak. The equivalence force where TBA-GQ was equally likely to

be found folded versus unfolded was approximately 3 pN (for high salt, 1000 mM KCl; we

discuss deviations with varying salt below). The unfolding rate constants increased with

increasing force and the folding rate constants decreased with increasing force as shown in

Fig. 4.5c. A simple Bell model (black dashed) [111] of exponential dependence of rate

97

constants on force can provide a useful phenomenological description of the data.

k = k0 exp(

∆x · F
kBT

)

(4.1)

where k is the rate constant, k0 is the rate constant at zero force, ∆x is the distance to

transition state, F is the applied force, kB is the Boltzmann constant, and T is the absolute

temperature.

The slope on the log plot corresponds to an approximate distance to transition state

∆x, and the intrinsic rate constant k0 can be obtained from the intercept. For example, in

1000 mM KCl (Fig. 4.5c), we obtained ∆xu=1.6 nm and ∆xf =-1.1 nm from the slope of

the fit (Table 4.1). ∆xu and ∆xf are the changes in extension to transition state from

folded state and unfolded state respectively.

Figure 4.6 shows the force dependent rate constants over a range of KCl concentra-

tion with Bell model fitting. Using single-molecule optical tweezers, we measured a range of

force down to 2 pN. From the salt-dependent data, we observed that the equivalent force is

around 2-3 pN in the high salt concentration we measured. The equivalent force F1/2 was

defined as the point of intersection of rate constants. At force F1/2, the molecule has equal

probability to stay at folded or unfolded states. The equivalent force F1/2 goes up as the

increasing salt concentration. It indicates that folded TBA-GQ structure is more mechani-

cally stable with more salt.

98

Figure 4.5: Equilibrium measurements of TBA-GQ under force. (a) A representative
time trajectory of a single TBA-GQ molecule in constant-position mode at corresponding
mean forces (2, 3, 4, and 5 pN) in the presence of 1000 mM KCl. The upper red line
and lower yellow line are polymer models for folded and unfolded TBA-GQ respectively.
Folded and unfolded dwell times change with forces.
(b) Histograms derived from this
time trace at different forces are fit with two-state Gaussian distribution. The higher force
represents folded state and the lower force represents the unfolded state. The population
shifts from folded state to unfolded state as the applied force increases. (c) Force-dependent
rate constants of TBA-GQ at 1000 mM KCl. The folding rate constants (cross) and unfolding
rate constants (triangle) were fit with Bell model (black dashed lines).

99

Figure 4.6: Force-dependent rate constants of TBA-GQ over a range of KCl
concentration with Bell model fitting. Equivalent force F1/2 decreased as KCl concen-
tration decreased. The folding rate constants (cross) and unfolding rate constants (triangle).
Each KCl concentration was fit with Bell model (black dashed lines).

100

Bell model (force-indep transition extension)

kf 0 (1/s)

[KCl]
600 mM 0.403 ± 0.075
800 mM 0.549 ± 0.075
1000 mM 0.419 ± 0.078
1500 mM 0.580 ± 0.128

∆xf (nm)
-1.7 ± 0.2
-1.6 ± 0.2
-1.1 ± 0.2
-1.3 ± 0.2

ku0 (1/s)

0.056 ± 0.013
0.098 ± 0.019
0.062 ± 0.014
0.034 ± 0.009

∆xu (nm)
2.1 ± 0.3
1.5 ± 0.2
1.6 ± 0.3
2.2 ± 0.3

Table 4.1: Bell model fit parameters of rate constants and distances to transition
state. ki0 are the rate constants at zero force. ∆xf and ∆xu are the distance to transition
state from the unfolded and folded state, respectively.

4.3.2 Salt dependent

It well known that monovalent salt ions such as K+ and N a+ are required for stable TBA-

GQ structure formation with K+ having the strongest effect [112]. Indeed, we observed that

the K+ ion concentration had a strong effect on TBA-GQ mechanical stability. Figure 4.7a

shows both the unfolding and refolding rate constants vs K concentration at a mean force of

3 pN (near the force equivalence point for high salt). The unfolding rate constant decreased

very slightly with increasing [K+]. However, the folding rate constant showed very strong

[K+] dependence and increased strongly with increasing [KCl]. This is consistent with pre-

vious investigations and structural models predicting the need for a K+ ion bound between

G-quadruplex layers. It indicates that the main effect of K+ ions is helping TBA-GQ for-

mation, rather than stabilizing the TBA-GQ structure against mechanical unfolding. The

magnitude of the change in both folding and unfolding rate constants at higher salt was

similar (approximate 2-fold increase versus decrease for folding vs unfolding rate constant

respectively for [K+] increasing from 600 to 1500 mM, at 3 pN force). It was very difficult

to observe TBA-GQ folding with only NaCl present even up to 1000 mM NaCl. We thus

next added an increasing amount of NaCl to a fixed minimal amount of KCl (300 mM).

101

With increasing [NaCl], we still observed the same two folded and unfolded states. The

folding rate constant increased with increasing NaCl, but more modestly compared with

KCl (Fig. 4.7b). This suggests that electrostatic screening by monovalent salt only weakly

contributes to the increasing folding rate constant with increasing salt, and that the primary

K+ concentration dependence indicates the necessity of a bound K+ ion within the TBA-

GQ structure.

Figure 4.7: Salt effects on TBA-GQ formation. (a) Folding (blue circles) and unfolding
(red triangles) rate constants versus KCl concentration at 3 pN. (b) Folding rate constant
versus total salt concentration at 3 pN from a range of KCl concentration (blue diamonds)
and 300 mM KCl plus a range of NaCl (green crosses).

102

4.3.3 Thrombin dependent

We next considered the impact of thrombin on TBA-GQ mechanical stability (Fig. 4.8).

These experiments were conducted in a sample chamber containing two side-by-side fluid

channels with and without thrombin.

Individual tethers were first formed and tested for

quality within the blank fluid. The tethers were next transferred to the adjacent thrombin-

containing fluid and fixed trap measurements were performed as above. Figure 4.8a shows

an example measurement where the tether was in the thrombin solution for 350 seconds

and then returned to the adjacent blank channel as a control. While the same two folded

and unfolded states were observed, it is clear that the folded state dwell times were much

longer with thrombin. Figure 4.8b shows the folding and unfolding rate constants versus

thrombin concentration. While thrombin had almost no effect on the folding rate constant,

it substantially decreased the unfolding rate constant. Thus, thrombin binding to TBA-GQ

does neither induces nor inhibits folding but it does stabilize the already folded TBA-GQ

structure. This is opposite the effect of K+.

103

Figure 4.8: Thrombin effects on TBA-GQ resolution. (a) Representative time trajec-
tory of thrombin-TBA-GQ complex. Tether was in a buffer containing 150 nM thrombin and
then moved to the same buffer without thrombin. (b) Folding (blue circles) and unfolding
(red triangles) rate constant versus thrombin concentration at 3 pN.

4.4 Discussion

4.4.1 Bell model

Both dwell time analysis and histogram analysis revealed that TBA-GQ is a two-state system.

TBA-GQ stays in either folded state or unfolded state with an energy barrier, the transition

state, in between. With the applied forces, the free energy surface is tilted by force along

the reaction coordinate. For a simple two-state system like TBA-GQ, the basic approach

to understand the effect of force on the free energy landscape is Bell model [111] with the

104

assumption that the distance to transition state does not change with forces.

Force dependent folding and unfolding rate constants were determined from dwell

time as described in Section 4.2. All the dwell times (over hundreds of events for each con-

ditions) were used to fit the model by the maximum likelihood global fitting. This method

enables us to have enough statistics to determine the fit parameters. The folding and un-
folding rate constants at force F depend on the barrier height ∆xf · F and ∆xu · F , where

∆xf and ∆xu are the distances to the transition state along the reaction coordinate from

the folded state and unfolded state, respectively. From Fig. 4.6 and Table 4.1, we found

a little surprising that the slopes ∆xf and ∆xu are about the same for both folding and

unfolding processes. Usually the folding has a larger slope because ∆xf is the distance from

an unfolded polymer to a much more compact transition state structure. On the other hand,

unfolding is going from a compact folded structure to another compact folded transition

state structure, so ∆xu could be much smaller. The similar slope values suggest that the

transition state structure is stretchy.

4.4.2 Force-dependent structure diameter model

Note that the assumption for Bell model is that the distance is independent of force. It is only

true when we consider a small range of forces. In most cases, the force dependent extension

must be taken into account especially at low force region due to the large conformation

fluctuations. Here, we consider the force-dependent structure diameter model [113]. The
distance to transition state is changing with force, therefore the energy barrier ∆x· F in Bell

model becomes integral from 0 to F.

105

And the modified force dependent rate constant equations become

(cid:90) F

0

∆x(F )
kBT

dF

(cid:90) F
kf = kf 0 · exp(
(cid:90) F
ku = ku0 · exp(

0

xt(F ) − xu(F )

kBT

dF )

xt(F ) − xN (F )

kBT

dF )

(4.2)

(4.3)

0

where xt, xu, and xN are the end-to-end extension for the transition state structure, un-

folded state structure, and native folded state structure, respectively. The footnote f and u

represent folding and unfolding.

It is straightforward to estimate the force-dependent extension change of the diameter

of the unfolded state structure. The unconstructed 15mer can be described using extensible

worm-like chain polymer model.

xu(F ) = nssDN A · hssDN A · xXW LC (F )

(4.4)

where nssDN A = 15 is the number of free nucleotides, hssDN A = 0.59 nm/nt is the ssDNA

unit length, and xXW LC is the extensible worm-like chain extension over contour.

For the native folded state structure, we consider it as a rigid body and describe the

end-to-end extension using a freely-jointed chain polymer model.

xN (F ) = dN · coth(

dN · F
kBT

) − kBT
F

(4.5)

106

where dN is the end-to-end extension of the native folded state structure along the direction

of force. The dN = 1.5 nm is obtained from the NMR structure (PDB ID: 1C32) [86].

Next, we consider the transition state structure is a structure with the folded portion

and unfolded portion. The end-to-end extension is comprised of a rigid body plus a portion

of unfolded ssDNA [109]. We again describe the rigid body part using the freely-jointed

chain polymer model, and the ssDNA part using the standard extensible worm-like chain

polymer model.

xt(F ) = dt · coth(

dt · F
kBT

) − kBT
F

+ nssDN A · hssDN A · xXW LC (F )

(4.6)

where the end-to-end extension of the rigid body dt and the number of free nucleotides

nssDN A are two fit parameters.

We used the same transition state to fit both folding and unfolding force-dependent

rate constants because we expect TBA-GQ has a single one-dimensional free energy land-

scape.

4.4.3 Finding transition state structure

The transition state structure is the key to understand the folding/unfolding free energy

landscape. Recent MD simulations from Yang et al.

[102] predicted three large barrier-

crossing events (i.e. possible transition state structures) during the TBA-GQ formation: the

mixed triplex-quadruplex structure (“G-TQ”, Fig. 4.9a), the two-layer G-triplex structure

(“G-triplex”, Fig. 4.9b), and the G-hairpin structure (“G-hairpin”, Fig. 4.9c). These

three structures contain different number of free nucleotides where nssDN A = 0 for G-TQ,

107

nssDN A = 4 for G-triplex, and nssDN A = 8 for G-hairpin. From our rate constants versus

force analysis, we are able to verify these transition state structures by comparing the fit

parameter dt to the end-to-end extensions obtained from TBA-GQ crystal structure.

Figure 4.9: Schematic possible transition state structures during the folding and
unfolding pathway of TBA-GQ. Structures and the corresponding end-to-end diameters
of TBA-GQ. (a) G-TQ structure. nssDN A = 0. (b) G-triplex structure. nssDN A = 4. (c)
G-hairpin structure. nssDN A = 8. The orange dots represent guanine bases, and the dots
with gray rectangles represent the guanines pair by Hoogsteen hydrogen bonds.

Considering the polymer model of the transition state structure above, we have one

fit parameter, the end-to-end extension dt of the rigid body portion. We used the force-

dependent rate constants data in 800 mM KCl buffer as the example, and summarized the

fit parameters with different number of free nucleotides (nssDN A = 0, 4, and 8) in transition

state in Table 4.2.

In the force-dependent structure diameter model, the intrinsic rate

constants are similar among all three cases, but the transition state extensions decrease

when more free nucleotides are included.

When the number of free nucleotides is zero, the whole structure is considered as

a rigid body, the transition state extension is 3.3 ± 0.6 nm.

It is much larger than the

end-to-end extension 1.8 nm in G-TQ structure (Fig. 4.9a). The mixed triplex-quadruplex

108

Force-dep transition extension model

# of free nt
nssDN A = 0

(G-TQ)

nssDN A = 4
(G-triplex)
nssDN A = 8
(G-hairpin)

kf 0 (1/s)

0.324 ± 0.030
0.341 ± 0.036
0.340 ± 0.019

ku0 (1/s)

xt0 (nm)
0.156 ± 0.018 3.3 ± 0.6
0.164 ± 0.015 2.2 ± 0.2
0.163 ± 0.010 0.4 ± 0.1

Table 4.2: Fit parameters of rate constants and transition state diameters with a
segment of ssDNA (0, 4, and 8 free nucleotides) in 800 mM KCl buffer. ki0 are
the rate constants at zero force. dt are the end-to-end extension of the rigid body portion
of the transition state along the applied force.

structure does not fit our force-dependent rate constant data. Besides, the transition from the

mixed triplex-quadruplex structure to the native folded TBA-GQ is more unlikely because

it requires the breaking of the misfolded quadruplex layer and the formation of the correct

G-tetrads. The fit extension is also much larger than the size of folded TBA-GQ. We cannot

think of any configuration with the diameter 3.3 nm. It indicates that the transition state

structure cannot be considered as a rigid body only. When the number of free nucleotides is

4, which corresponds to the G-triplex structure with one 4-nt free polymer at one end, the
transition state diameter from the fit is 2.2 ± 0.2 nm. It is close to the diagonal distance 2.1

nm from the G-triplex structure (Fig. 4.9b). Our data is well-represented by the G-triplex

model and the transition from the two-layer G-triplex to the native folded state only requires

the closing of the free end. When the number of free nucleotides is 8, which corresponds

to the G-hairpin structure with two 4-nt free polymers on both ends, the transition state
diameter from the fit is 0.4 ± 0.1 nm. It is much smaller than the end-to-end extension 1.5

nm in G-hairpin structure (Fig. 4.9c). These fit results suggest that the G-triplex is the

transition state structure for both TBA-GQ folding and unfolding pathways.

We used this G-triplex model to fit other salt dependent data. The fit parameters

109

are summarized in Table 4.3. The intrinsic folding rate constant increases and the intrinsic

unfolding rate constant decreases with increasing salt concentration. The trend is consistent

with Fig. 4.7a, the rate constants versus salt concentration analysis. There is no obvious

trend on the transition state distance versus salt concentration. They stay roughly the same

diameter which is well-represented by G-triplex model within errors.

The red solid lines in Fig. 4.10 show the results of the force-dependent structure

diameter model. The rate constant rolls over at low force when force close to 0. Unfolding

rate constant at zero force slightly higher than Bell model, and folding rate constant at zero

force slightly lower than Bell model.

Force-dep transition extension model

kf 0 (1/s)

[KCl]
600 mM 0.203 ± 0.021
800 mM 0.341 ± 0.036
1000 mM 0.330 ± 0.037
1500 mM 0.354 ± 0.044

ku0 (1/s)

0.130 ± 0.016
0.164 ± 0.015
0.097 ± 0.011
0.077 ± 0.011

xt0 (nm)
2.5 ± 0.2
2.2 ± 0.2
2.5 ± 0.2
2.7 ± 0.2

Table 4.3: Fit parameters of rate constants and transition state position with a
range of KCl concentration using the G-triplex plus 4 free nucleotides model.

110

Figure 4.10: Force-dependent rate constants of TBA-GQ over a range of KCl
concentration with force-dependent structure diameter model. Equivalent force
F1/2 decreased as KCl concentration decreased. The folding rate constants (cross) and
unfolding rate constants (triangle) were obtained from 9 (with 303 folding events and 308
unfolding events), 6 (with 645 folding events and 648 unfolding events), 6 (with 377 folding
events and 381 unfolding events), and 4 (with 250 folding events and 253 unfolding events)
molecules at 600 mM, 800 mM, 1000 mM, and 1500 mM KCl concentration, respectively.
Each KCl concentration was fit with Bell model (black dashed lines) and force-dependent
structure diameter model (red solid lines).

111

4.4.4 G-triplex as the transition state

A proposed TBA-GQ energy landscape model of the one-dimensional reaction coordinate

is illustrated in Fig. 4.11. The equilibrium measurement analysis reveals that G-triplex is

the major energy barrier for TBA-GQ formation, not G-TQ or G-hairpin. TBA-GQ goes

through the same transition state, G-triplex, when it is folded and unfolded. The existence

of this two-layer G-triplex structure is supported by other experimental and computational

studies [102–104, 114, 115]. Although the G-triplex structure was not stable enough in our

study to be characterized as an intermediate state, the truncated form of TBA-GQ, TBA-11

(5’-GGTTGGTGTGG-3’) which the last four nucleotides from TBA-GQ were removed, has

been proved to be a stable G-triplex structure by the NMR experiments (PDB ID: 2MKM

and 2MKO) [114, 115].

In addition, our thrombin-aptamer experiments also support the G-triplex model.

Since two TT loops in the TBA-GQ interact with thrombin exosite I pocket [116], the impact

of thrombin on TBA-GQ implies that the TT loops are critical for TBA-GQ unfolding. If

two TT loops bind to the hydrophobic pocket in thrombin, it would prevent either terminals

peel off from the native folded state. Therefore, the unfolding rate constants decrease. Our

results support that the G-quadruplex structure of TBA-GQ is necessary for its interaction

with thrombin [89, 116–119], but we did not find that the thrombin promotes TBA-GQ

formation as some other groups reported with circular dichroism spectroscopy, fluorescence

measurements, and mass spectrometry [120–122]. In those bulk experiments, they measured

the fraction of folded TBA-GQ at the present of thrombin. They are not able to distinguish

the contribution from increasing folding rate and decreasing unfolding rate. Our results

suggest that the fraction folded increased in bulk experiments at the present of thrombin

112

was from the unfolding rate decreased, not the folding rate increased.

Since our data show that TBA-GQ is a simple two-state system and the fitting results

support the G-triplex structure, we propose the model that the G-triplex is the transition

state with one arm peeled from the core and produced a 4-nucleotide ssDNA. TBA-GQ

is the simplest G-quadruplex structure. Our study has deepened our understanding on G-

quadruplex and paved the way to further investigate the more complex G-quadruplex folding

mechanism. Several telomeric G-quadruplex studies also proposed G-triplex as an interme-

diate state [123–128]. The complex kinetics indicate the presence of intermediates and the

possibility of multi-pathway folding mechanism in telomeric G-quadruplex.

Figure 4.11: Proposed reaction diagram explains the folding and unfolding path-
way of TBA-GQ. TBA-GQ goes through the same transition state, G-triplex, when it is
folded and unfolded.

113

4.5 Conclusion

G-quadruplex has attracted attention in recent years because the G-quadruplex structures

exist throughout the human genome. The high-throughput sequencing-based method has

identified over 700,000 G-quadruplex structures in the human genome [129]. The force-

dependent folding and unfolding kinetics studies are essential for understanding the energy

landscape. Moreover, the nucleic acid structures like G-quadruplex in cells are under me-

chanical force before interacting with proteins (polymerases, helicases, ribosomes, telomerase,

etc.) [130]. Single molecule manipulation is a powerful tool to study the folding kinetics of

nucleic acids and proteins, and the interaction between nucleic acids and proteins. We can

apply the same technique to the G-quadruplex structures in human genome to study their

regulatory roles in biological processes.

In summary, we have investigated the unfolding and refolding of TBA-GQ at low

forces using high-resolution optical tweezers. We have demonstrated that TBA-GQ is a

two-state, force-assisted unfolding system. We have identified that the formation of TBA is

facilitated by metal ions and the resolution of TBA-GQ is reduced by thrombin. We have

also clearly shown that the G-triplex is the transition state between folded and unfolded

TBA-GQ structure. These results provide us a better understanding of the energy land-

scape of the G-quadruplex and the interaction of the thrombin-aptamer.

114

APPENDICES

115

Appendix A

Protocols for performing experiments

A.1 DNA construct

3.2 kb dsDNA construct

This protocol makes a 3.2 kb dsDNA product for trap performance demonstration in Chap-

ter 2. Full construct has a biotin label and a dig label on each end.

Materials

• Forward primer: /5Biosg/ GAC AGC ATC GCC AGT CAC TA

• Reverse primer: /5DigN/ AGC CCT CCC GTA TCG TAG TT

• Phusion high-fidelity PCR master mix with HF buffer (NEB M0531S, 2x concentration)

• pBR322 DNA template (NEB N3033S)

• DMSO (NEB B0515A)

• Nuclease-free water (IDT)

• IDTE (10 mM Tris and 0.1 mM EDTA) pH 8.0 buffer (IDT)

• QIAquick PCR purification kit (Qiagen)

116

Procedure

1. PCR synthesis

(a) Prepare one tube for a final volume of 50 µL.

(b) Mix 17.5 µL of nuclease-free water, 2.5 µL of 10 µM forward primer, 2.5 µL of

10 µM reverse primer, 1 µL of pBR322 DNA template (10 ng/µL concentration),

1.5 µL of DMSO, and 25 µL of Phusion.

(c) Run PCR program for 3.2 kb dsDNA (elongation rate

15 s/kb at 72oC): (1)

98oC for 30 seconds, (2) 98oC for 10 seconds, (3) 59oC for 10 seconds, (4) 72oC

for 48 seconds, (5) repeat steps 2-4 for 30 times, (6) 72oC for 5 minutes, (7) hold

at 4oC.

2. PCR purification To purify PCR product, follow the QIAquick PCR purification kit.

Add 30 uL elution buffer instead of 50 uL to get a higher DNA concentration.

3.2 kb dsDNA construct with short ssDNA insert

This protocol makes a ∼3.2 kb dsDNA product with a short single-stranded insert in the

middle. The sequence of insert is designed for particular experiments. Three segments: left

handle (LH), insert (Insert), and right handle (RH), are synthesized separately and then
joined together by ligation. The biotin-labeled LH is a ∼1.5 kb dsDNA with ssDNA over-
hang. The digoxigenin-labeled RH is a ∼1.7kb dsDNA with ssDNA overhang. The sequence

of insert is extended to anneal to the complementary sequences on both DNA handles. All

constructs we used in Chapter 3 and Chapter 4 follow this protocol. For the cryptic

binding hairpin construct, slightly different steps are being taken. Please see footnotes.

117

Materials

• The sequences of primers, inserts, and probes are listed in Table A.1, A.2, A.3, and

A.4.

• Phusion high-fidelity PCR master mix with HF buffer (NEB M0531S, 2x concentration)

• DNA template pBR322 (NEB N3033S) and lambda (NEB N3011S)

• DMSO (NEB B0515A)

• Nuclease-free water (IDT)

• IDTE (10 mM Tris and 0.1 mM EDTA) pH 8.0 buffer (IDT)

• QIAquick PCR purification kit and gel extraction kit (Qiagen)

• Restriction enzyme PspGI (NEB R0611S) and TspRI (NEB R0582S)

• CutSmart (NEB B7204S)

• GelGreen (Biotium 41005)

• 1 kb DNA ladder (NEB N3232S)

• Gel loading dye (NEB B7025S)

• T4 DNA ligase (NEB M0202S) and T4 DNA ligase reaction buffer (B0202S)

Procedure

1. PCR synthesis

(a) Prepare one tube of a final volume of 50 µL for each handle.

118

(b) For LH: Mix 35 µL of nuclease-free water, 5 µL of 10 µM forward primer, 5 µL of

10 µM reverse primer, 2 µL of pBR322 DNA template (10 ng/µL concentration),

3 µL of DMSO, and 50 µL of Phusion.

(c) For RH: Mix 33 µL of nuclease-free water, 5 µL of 10 µM forward primer, 5 µL of
10 µM reverse primer, 4 µL of lambda DNA template (5 ng/µL concentration)¶,

3 µL of DMSO, and 50 µL of Phusion.

(d) Run PCR program for 2.2 kb dsDNA (elongation rate 15 s/kb at 72oC) on both

reaction mixes: (1) 98oC for 30 seconds, (2) 98oC for 10 seconds, (3) 59oC for 10

seconds, (4) 72oC for 33 seconds, (5) repeat steps 2-4 for 30 times, (6) 72oC for 5

minutes, (7) hold at 4oC.

2. PCR purification

(a) To purify PCR products, follow the QIAquick PCR purification kit. Add 30 µL

elution buffer instead of 50 µL to get a higher DNA concentration.

(b) Measure the PCR products using NanoDrop 2000 spectrophotometer (Thermo

Fisher). The typical concentration is 150-200 ng/µL.

3. DNA handle digestion

Cut the PCR products to produce the single strand overhangs on handles for ligation.

The LH is digested with the restriction enzyme PspGI to produce a 1.5 kb dsDNA with

5-nt overhang on the 5’ end. The RH is digested with the restriction enzyme TspRI
to produce a 1.7 kb dsDNA with 9-nt overhang on the 3’ end.(cid:107)

¶use pBR322 DNA template for cryptic binding hairpin construct
(cid:107)Do not need RH digestion for cryptic binding hairpin construct

119

(a) Add 3.5 µL of CutSmart buffer and 2 µL of PspGI to the 30 µL LH PCR product.

Incubate for 1 hour at 75oC.

(b) Add 3.5 µL of CutSmart buffer and 2 µL of TspRI to the 30 µL RH PCR product.

Incubate for 1 hour at 65oC.

4. DNA handle purification

(a) Make gel. Add 50 mL 0.5x TBE buffer, 0.5 g agarose (low melting point agarose)

to a 125 mL Erlenmeyer flask. Microwave until solution just starts to boil and

then swirl to mix. Microwave a second time to make sure all gel is dissolved. Cool

for 10 minutes, and then add 2 µL GelGreen. Pour gel into a leveled gel box.

Remove any bubbles. Place comb into the upper spot. Cover the gel box with

foil and wait 2 hours at room temperature to solidify. Put in fridge and use the

gel on the same day.

(b) Add 3 uL of 100% glycerol and 2 µL loading dye to the digestion products. Preheat

RH to 65oC for 1 minute before loading to gel because the 9-nt overhang on RH

is too stable at room temperature.

(c) Run one lane for each handle.

(d) Add a ladder lane (1 µL of 1 kb DNA ladder and 2 µL of gel loading dye to 7 µL

nuclease-free water).

(e) Run gel for 90 minutes at 75V.

(f) Visualize bands with blue light gel imaging system. Cut 1.5 kb LH product and
1.7 kb RH product with a razor blade (Fig. A.1a). Discard the ∼500 bp bands.

Typically the digestion yield is 100%.

120

(g) For each handle, put the desired gel slice in a 1.5 mL pre-weighed tube. Get the

gel weigh by subtracting tube weight. Usually it is ∼200 mg per gel slice.

(h) Follow the QIAquick gel extraction kit for gel extraction. Skip the isopropanol

step. To remove the salt from QG buffer, make sure to let the column stand 5

minutes after adding PE buffer. Add 30 µL elution buffer instead of 50 µL to get

a higher DNA concentration. Measure the PCR products using NanoDrop. The

typical concentration is 50-100 ng/µL.

5. Ligation

(a) Calculate the volumes for each components. To achieve a good yield, combine

the three components with an equimolar ratio (LH:Insert:RH = 1:1:1). Mass
of dsDNA per base pair is 660 g/mol. The mass of a 1.5 kb dsDNA is ∼0.99

g/umol. For a 1.5 kb dsDNA, the concentration 50 ng/µL is close to 50 nM.

Typical volumes needed are 25 µL of LH, 25 µL of RH, and 2 µL of Insert.

(b) To prepare a final volume of 80 uL reaction mix, add 8 µL of T4 DNA ligase

buffer and 4 µL of T4 DNA ligase to the calculated volume of handles and insert,

then bring the final volume to 80 µL with nuclease-free water.

(c) Run the ligation program: 23oC for 30 minutes then 65oC for 15 minutes.

6. Ligation product purification

(a) Make gel (as above).

(b) Run gel in two lanes. Put ∼40 µL in each lane. Add a ladder lane. It is also

helpful to add a lane of excess unused handle as a reference.

121

(c) The desired final construct band is ∼3 kb (Fig. A.1b). The ∼1.5 kb bands are

the leftover handles. Combine gel slices from two lanes in one tube. Follow above

steps for gel extraction. Measure the final product with NanoDrop. The typical

concentration is 30 ng/µL.

(d) Store construct in the fridge. Should be good for 1 month.

(a) After digestion. The left lane is the ladder, the middle
Figure A.1: Gel purification.
lane is the left handle, and the right lane is the right handle. (b) After ligation. The left lane
is the ladder, the middle and the right lane is the ligation products. The desired products
are the bands in the red boxes.

122

Primer name

Sequence (5’ to 3’)
/5Biosg/ TGA AGT GGT GGC CTA ACT ACG

LH forward primer
LH reverse primer TTG CAT GAT AAA GAA GAC AGT CAT
RH forward primer

RH reverse primer

Insert name

hp seq

Probe name
29mer oligo -bio

/5Phos/ TTG AAA TAC CGA CCG CTC AGC TAT CAG
CC/idSp/ CTC TGA CAC ATG CAG CTC CC
/5DigN/ CAA CAA CGT TGC GCA AAC T
Sequence (5’ to 3’)
/5Phos/ CCT GG GGC TGA TAG CTG AGC GGT CGG TAT
TTC AA A AGT CAA CGT ACT GAT CAC GCT GGA TCC
TAG AGT CAA CGT ACT GAT CAC GCT GGA TCC TAT
TTT TAG GAT CCA GCG TGA TCA GTA CGT TGA CTC
TAG GAT CCA GCG TGA TCA GTA CGT TGA CTT
Sequence (5’ to 3’)
GG CTG ATA GCT GAG CGG TCG GTA TTT CAA/3Bio/

Table A.1: Complementary hairpin sequence and probe strand for “cryptic bind-
ing” experiments. Quantum dots are labeled to the probe strands via biotin-streptavidin
bonds. Binding sites are shown in bold.

123

Primer name

LH forward primer
LH reverse primer
RH forward primer
RH reverse primer

Insert name

Sequence (5’ to 3’)
/5Biosg/ TGA AGT GGT GGC CTA ACT ACG
TTG CAT GAT AAA GAA GAC AGT CAT
/5DigN/ GGG CAA ACC AAG ACA GCT AA
CCC GTC ATA CAC TTG CTC CT
Sequence (5’ to 3’)

probe site 1 - 5dT - 5dT /5Phos/CCTGG TTTTT AGG ACT TGT TTTTT CCC

probe sites 1 and 2

probe sites 1, 2 and 3

Probe name
probe 1 - Cy3

probe 1 - Cy3-Cy5
probe 1 - AF488

probe 2 - Cy5

probe 3 - AF488

ACTGGC
/5Phos/CCTGG TTTTT AGG ACT TGT TTTTT CAG
TAT CGA TTTTT CCCACTGGC
/5Phos/CCTGG TTTTT AGG ACT TGT TTTTT CAG
TAT CGA TTTTT ATC GCA AGT TTTTT CCCACT
GGC
Sequence (5’ to 3’)
ACA AGT CCT /3Cy3Sp/
/5Cy5/ ACA AGT CCT /3Cy3Sp/
ACA AGT CCT /3AlexF488N/
TCG ATA CTG /3Cy5Sp/
ACT TGC GAT /3AlexF488N/

Table A.2: ssDNA Insert for synthesizing the “hybridization” construct and the
complementary fluorophore-labeled probes. Binding sites are shown in bold.

124

Primer name

Sequence (5’ to 3’)
/5Biosg/ TGA AGT GGT GGC CTA ACT ACG

LH forward primer
LH reverse primer TTG CAT GAT AAA GAA GAC AGT CAT
RH forward primer
RH reverse primer CCC GTC ATA CAC TTG CTC CT

/5DigN/ GGG CAA ACC AAG ACA GCT AA

Insert name

Sequence (5’ to 3’)

probe site 1 - 5dT /5Phos/CCTGG TTTTT AGG ACT TGT CCCACTGGC
probe site 2 - 5dT /5Phos/CCTGG TTTTT CAG TAT CGA CCCACTGGC

29mer - insert

Probe name
probe 1 - Cy3

probe 1 - AF488

probe 2 - Cy5
29mer - AF647

/5Phos/CCTGG TTT TT GAA ATA CCG ACC GCT CAG
CTA TCA GCC CCCACTGGC
Sequence (5’ to 3’)
/5Phos/ACA AGT CCT /3Cy3Sp/
/5Phos/ACA AGT CCT /3AlexF488N/
/5Phos/TCG ATA CTG /3Cy5Sp/
/5Phos/GGC TGA TAG CTG AGC GGT CGG TAT TTC AA
/3AlexF647N/

Table A.3: ssDNA Insert for synthesizing the “fixed probe” construct and the
complementary fluorophore-labeled probes. Binding sites are shown in bold.

Primer name

Sequence (5’ to 3’)
/5Biosg/ TGA AGT GGT GGC CTA ACT ACG

LH forward primer
LH reverse primer TTG CAT GAT AAA GAA GAC AGT CAT
RH forward primer
RH reverse primer CCC GTC ATA CAC TTG CTC CT

/5DigN/ GGG CAA ACC AAG ACA GCT AA

Primer name

Sequence (5’ to 3’)
/5Biosg/ TGA AGT GGT GGC CTA ACT ACG

LH forward primer
LH reverse primer TTG CAT GAT AAA GAA GAC AGT CAT
RH forward primer
RH reverse primer CCC GTC ATA CAC TTG CTC CT

/5DigN/ GGG CAA ACC AAG ACA GCT AA

Insert name

TBA

Sequence (5’ to 3’)
/5Phos/CCTGG TT GGTTGGTGTGGTTGG TT CCC ACT
GGC

Table A.4: ssDNA Insert for synthesizing the “TBA-GQ” construct. TBA-GQ
sequence is shown in bold

125

A.2 Oxygen scavenger system

Materials

• Glucose oxidase (Sigma G2133-50KU)

• Pyranose oxidase from Coriolus sp. (Sigma P4232-250UN)

• Catalase from bovine liver (Sigma C30-100MG)

• T50 buffer: 50 mM NaCl and 20 mM Tris-HCl pH8

Procedure

1. In a 0.6 mL centrifuge tube, add 20 µL catalase solution to 80 µL T50 buffer.

2. Add 10 mg glucose oxidase or 5.8 mg pyranose oxidase to the tube.

3. Carefully dissolve by flicking the tube by hand. Do not create foamy bubbles (a possible

sign of damage to protein).

4. Centrifuge once at 11 krpm for 5 minutes to remove any possible junk particles (possibly

from catalase). Keep the supernatant.

5. Centrifuge filter once at 11 krpm for 1 minute. Keep the flow through.

6. Store the final solution in the fridge. Should last 1-2 weeks.

126

A.3 Anti-blinking system

Materials

• Trolox (Sigma 238813-1G)

• 1M NaOH

Procedure

1. Add 5 mL of MilliQ water and 25 µL 1 M NaOH (raises pH to dissolve Trolox) to 15

mL conical tube.

2. Add 5 mg white Trolox powder to the tube to make a 4 mM Trolox solution (near

saturated).

3. Wrap tube in foil and rotate (LabQuake) in room temperature for ∼1 hour to dissolve.

4. Vortex and filter everything through a 0.22 um syringe filter.

5. Wrap in foil (light sensitive) and store in the fridge. Should last ∼1 month.

127

Appendix B

List of essential parts for the construction of

the multi-color fleezers

Optical tweezers module

• 1064 nm fiber laser, IPG Photonics, YLR-5-1064-LP

• AOM1 (acousto-optic modulator), IntraAction, ATM-803D16B

• QPD1 & QPD2, First Sensor, QP154-Q-HVSD (1064 nm enhanced quad photodiode)

• D1 dichroic mirror, Chroma, T970DCSPXR (short-pass with 1064 nm cutoff)

• O1 & O2 (microscope objectives), Nikon, CFI Plan APO VC 60XWI (60x water-

immersion, 1.2NA)

• Sample chamber stage, Newport, CMA-12CCCL (motor), ESP300 (controller)

• D2 dichroic mirror, CVI, SWP-45-RP1064-TU780-PW-1012-C (short-pass with 1064

nm cutoff)

• F3 filter, Newport, 10LF25-1064 (1064 nm laser line filter)

128

Three-color confocal fluorescence module

• 532 nm laser (green excitation), LASOS, GLK 3250 T01 (LASOS DPSS laser, LasNova

series, 50 mW)

• 633 nm laser (red excitation), Research Electro-Optics (REO), Red Helium-Neon laser

(633 nm, 17 mW)

• 473 nm laser (blue excitation), Cobolt, 0473-06-01-0080-100 (MLD series diode laser,

473 nm, 80 mW)

• AOM2 & AOM3 (acousto-optic modulator), IntraAction, AOM-802AF1

• D10 dichroic mirror, Semrock, LM01-659-25 (659 nm cutoff, short-pass)

• D11 dichroic mirror, Semrock, LM01-552-25 (552 nm cutoff, short-pass)

• D12 dichroic mirror, Chroma, ZT473BCM (473 nm cutoff, long-pass)

• Single-mode optical fiber, Thorlabs, TS0986175-PM460-HP (PM fiber)

• D8 dichroic mirror, Chroma, ZT473BCM (for blue laser)

• D9 dichroic mirror, Semrock, LM01-552-25 (for green laser)

• PD1, PD2, and PD3 (Si photodetector), Throlabs, PDA36A (PD1 for blue, PD2 for

green, and PD3 for red)

• D7 multi dichroic mirror, Chroma, ZT473/532/633RPC-XT

• Piezo mirror stage, Mad City Labs, Nano-MTA2 Invar

• D3 dichroic mirror, Semrock, FF875-Di01-25-D

129

• D4 dichroic mirror, Thorlabs, DMLP900 (long-pass, 900 nm cutoff)

• PSD (position-sensitive detector), First Sensor, DL100-7-PCBA3

• F4 filter, Chroma, ZET473/532/635M

• PH (pinhole), Thorlabs or Edmund, Precision pinholes 20-100 um

• D5 dichroic mirror, Chroma, 540DCXR

• F5 filter, Chroma, ET510/20M

• D6 dichroic mirror, Chroma, 640DCXR

• F6 filter, Chroma, HQ580/60M/2P

• F7 filter, Chroma, ET685/50M

• APDs (avalanche photodiodes), Excelitas Tech, SPCM-AQRH-14

Bright-field imaging system

• LED, Thorlabs, LED940E

• F1 filter, Thorlabs, FES1000 (short-pass filter, 1000 nm cutoff)

• F2 filter, Thorlabs, FEL850 (long-pass filter, 850 nm cutoff)

• CCD camera, Watec, WAT-902H2

130

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131

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