-
Developing Single-Molecule Fluorescence Techniques and
Their Application in the DNA Nanotechnology Field
Thesis submitted in partial fulfillment
of the requirements for the degree of
“DOCTOR OF PHILOSOPHY”
by
Roman Tsukanov
Submitted to the Senate of Ben-Gurion
University of the Negev
January 2014
Beer-Sheva
-
Developing Single-Molecule Fluorescence Techniques and
Their Application in the DNA Nanotechnology Field
Thesis submitted in partial fulfillment
of the requirements for the degree of
“DOCTOR OF PHILOSOPHY”
by
Roman Tsukanov
Submitted to the Senate of Ben-Gurion
University of the Negev
Approved by the advisor______________
Approved by the Dean of the Kreitman School of Advanced
Graduate
Studies____________
January 2014
Beer-Sheva
-
This work was carried out under the supervision of Dr. Eyal
Nir
In the Chemistry Department
Faculty of Natural Science
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i
Research-Student's Affidavit when Submitting the Doctoral
Thesis
for Judgment
I Roman Tsukanov, whose signature appears below, hereby declare
that:
√ I have written this Thesis by myself, except for the help and
guidance offered by
my Thesis Advisors.
√ The scientific materials included in this Thesis are products
of my own research,
culled from the period during which I was a research
student.
___ This Thesis incorporates research materials produced in
cooperation with others,
excluding the technical help commonly received during
experimental work.
Therefore, I am attaching another affidavit stating the
contributions made by myself
and the other participants in this research, which has been
approved by them and
submitted with their approval.
Date: Student's name: Roman Tsukanov Signature: __________
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ii
Acknowledgments
As a first member in Eyal’s research group, I have gained the
unique experience of
being a part of establishing single molecule fluorescence lab
out of scratch. Eyal’s
never-ending energy, ideas, dedication and aggressive problem
solving made it
possible for me to build and optimize the performances of three
optical setups, which
are currently serving all the lab members. I also thank Eyal for
great project he gave
me and the high level equipment, which ensured the quality of
the data. I am grateful
to Eyal for sending me to relevant scientific conferences, where
I enjoyed very
much.
I indebted to many people who were interacting with me on this
intensive period. I
would like to thank all former and present lab members, who
provided me great
support and shared inter-disciplinary knowledge, which
contributed largely to my
current expertise. So, Tommy Yaron, Miran, Michael, Noa, Rula,
Hagai, Gai, Tapasi
thank you! Special thanks to Tommy Tomov for great ideas,
discussions and fun.
I’m grateful to Yaron Berger and Michael Muzika, who were taking
data for my
project and especially for night and early morning shifts in the
lab. Thanks to Miran,
Rula and Noa for establishing the labeling procedure in our lab
and rapid labeling,
once it was needed.
I thank our collaborators Dr. Doron Gerber and Yair Glick from
Bar Ilan university
for providing us microfluidics equipment, sharing the knowledge
and help in
problem solving. Yaron Berger, for taking an active part in
early stages of
establishing the microfluidics technology in our lab and his
great technical abilities
which were very helpful on the daily basis.
Prof. Victor Kagalovsky, for his precious advices.
Michael Lubker for help with electronics for the whole period of
this work.
Hagai Drori for contribution in the development of Matlab
software.
Dmitry and Yulia Matiuhin for the support.
I thank my lovely wife for huge patience, understanding and
providing me support
during my research. I also thank her for giving a birth to our
child, who became an
origin of inspiration and an energy source for finishing this
work.
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Last but not least, I would like to express my appreciation and
respect to my parents,
who have always encouraged me and were supporting me during all
my academic
studies.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1. Measuring Biomolecular Dynamics. . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 1
1.2. Single Molecule Fluorescence. . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 1
1.3. Probability Distribution Analysis (PDA) . . . . . . . . . .
. . . . . . . . . . . . . . 2
1.4. DNA as a Model Molecule for Single-Molecule
Fluorescence Studies. . . . . . . . . . . . . . . . . . . . . .
. . . . . .. . . . . . . . . . . . . 3
1.5. DNA Hairpin. . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 4
1.6. DNA Origami. . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 6
1.7. DNA Hairpin Design. . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 7
1.8. Dependency of the Dynamics on NaCl Concentration . . . . .
. . . . . . . . . 9
1.9. DNA Nanotechnology. . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 10
1.10. DNA Motors. . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 10
1.11. Non-Autonomous Motors. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 11
2. Objectives. . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 13
3. Methods. . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1. Immobilization-Based sm-FRET-TIRF. . . . . . . . . . . . .
. . . . . . . . . . . . 15
3.1.1. Experimental Setup . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 15
3.1.2. Data Analysis Procedures . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 18
3.1.3. Surface Immobilization of Biomolecules . . . . . . . . .
. . . . . . . . . 20
3.2. Diffusion-Based Technique . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 22
3.2.1. Experimental Setup . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 22
3.2.2. Alternating Laser Excitation (ALEX) . . . . . . . . . . .
. . . . . . . . . . 24
3.2.3. Data Analysis and Presentation . . . . . . . . . . . . .
. . . . . . . . . . . . . 26
3.3. Probability Distribution Analysis (PDA) . . . . . . . . . .
. . . . . . . . . . . . . . 27
3.3.1. PDA Algorithm . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 28
3.3.2. Rational of the PDA . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 28
3.4. Calculating the Opening Rates using MFOLD and Transition
State
Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 30
3.5. Sample Preparation. . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 31
3.5.1. Single-Stranded DNA Labeling . . . . . . . . . . . . . .
. . . . . . . . . . . . 31
3.5.2. Origami Design . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 32
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3.5.3. Annealing Procedures . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 32
3.5.4. Origami purification . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 32
3.5.5. DNA Origami Structure Validation . . . . . . . . . . . .
. . . . . . . . . . . 33
4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1. Comparison of the Fraction of Open State . . . . . . . . .
. . . . . . . . . . . . . . 37
4.2. Comparison of Immobilized Hairpin-Only and
Hairpin-Origami
Opening and Closing Rates . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 37
4.3. Probability Distribution Analysis . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 41
4.3.1. Experimental E-Histograms and the PDA Fitting . . . . . .
. . . . . . . 41
4.3.2. PDA Validation . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 43
4.4. DNA Hairpin Dynamics . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 46
5. Combination of Microfluidics and Single-Molecule
Fluorescence
Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 47
6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 49
7. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 52
8. Appendix . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 53
8.1. Microfluidics Technology . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 53
8.2. Dwell-time analysis, semi-logarithmic plot . . . . . . . .
. . . . . . . . . . . . . . . 54
8.3. PDA Calculation – E-histograms shape . . . . . . . . . . .
. . . . . . . . . . . . . . . 55
8.4. Transition State Free Energies for Opening and Closing
Reactions . . . . 56
9. Publications . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 57
10. References . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 58
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List of Figures
Figure 1. Schematic of the influence of the shot-noise and the
dynamics on the
shape of E-histogram. . . . . . . . . .. . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 3
Figure 2. Quasi-two-state behavior of DNA hairpin. . . . . . . .
. . . . . . . . . . . . . . . 4
Figure 3. Unfolding reaction rates of DNA hairpins with
different number of
base pairs in the stem. . . . . . . . . . . . . .. . . . . . . .
. . . . . . . . . . . . . . . . . 5
Figure 4. DNA Origami. . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . 7
Figure 5. Design of the DNA hairpins constructs studied in this
work. . . . . . . . 9
Figure 6. Influence of ionic strength on DNA hairpin dynamics. .
. . . . . . . . . . . 10
Figure 7. Non-autonomous motor operation and design. . . . . . .
. . . . . . . . . . . . 11
Figure 8. A compression of the operational yield of motors
operating using
fuels and hairpin-fuels measured after each step. . . . . . . .
. . . . . . . . . . 12
Figure 9. Principle of the immobilized-based sm-FRET experiment.
. . . . . . . . . 16
Figure 10. TIRF image of single DNA hairpin-only molecules
A31-bp6-M
Immobilized to surface. . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 17
Figure 11. Pictures of immobilized-based TIRF setup, built as a
part of this work. 17
Figure 12. Sample TIRF time trajectories for immobilized hairpin
A31-bp6-S for
three different salt concentrations. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . 19
Figure 13. Specific binding of Hairpin-Origami to coverslip by
Biotin-
Avidin chemistry. . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 21
Figure 14. Principle of diffusion-based setup. . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 23
Figure 15. Picture of diffusion-based optical setup, built as a
part of this work. . . 24
Figure 16. Sorting capabilities of smALEX-FRET spectroscopy. . .
. . . . . . . . . . . 25
Figure 17. DNA Origami structure and integrity . . . . . . . . .
. . . . . . . . . . . . . . . . . 33
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vii
Figure 18. Typical two-dimensional E/S-histogram and E- and S-
one-dimensional
histograms . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 34
Figure 19. Diffusion-based sm-FRET-ALEX measurements of dynamics
of
hairpin-only A31-bp6-M and hairpin-origami A31-bp6-M. . . . . .
. . . . 35
Figure 20. Immobilization-based sm-FRET-TIRF measurements of
hairpin dynamics. Data are of A31-bp6-M. . . . . . . . . . . . .
. . . . . . . . . . 36
Figure 21. Very good agreement between the fraction of open
state of
freely diffusing and immobilized hairpin-only and
hairpin-origami . . 37
Figure 22. Very good agreement between the closing and opening
dwell-
time histograms. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 38
Figure 23. Opening and closing dwell-time histograms. . . . . .
. . . . . . . . . . . . . . . 39
Figure 24. Summary for immobilized-based transition rates. . . .
. . . . . . . . . . . . . 40
Figure 25. PDA fit to hairpin-origami A31-bp6-FF E-histogram. .
. . . . . . . . . . . . 41
Figure 26. E-histograms of the hairpin-only and hairpin-origami
constructs
studied in this work. . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 42
Figure 27. Agreement between rates obtained using the
diffusion-based PDA
method and the immobilization-based TIRF. . . . . . . . . . . .
. . . . . . . . . . 43
Figure 28. Validation of PDA for hairpin A31-bp6-F free and
attached to
origami in diffusion-based method. . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 45
Figure 29. Opening rates and closing rates for series of four
hairpins. . . . . . . . . . . 46
Figure 30. Picture of the microfluidics device positioned on the
single-
molecule TIRF setup. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 47
Figure 31. Efficiency and kinetics of DNA motors immobilized to
surface
inside microfluidic device. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 48
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Figure 32. The range of rates that could be measured with
single
molecule fluorescence techniques. . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 49
Figure 33. Microfluidic chip scheme. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 53
Figure 34. Opening and closing dwell-time histograms of
A31-bp6-M and
A31-bp6-S with fit to exponent function in semi-log plot. . . .
. . . . . . . 54
Figure 35. The shape of E-histograms can be predicted by PDA
calculation . . . . 55
Figure 36. Energy for opening and closing for the four hairpins
. . . . . . . . . . . . . . 56
List of Tables
Table 1: Hairpins names and sequences. . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 8
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Abstract
The structural dynamics of large biomolecules such as DNA, RNA,
and proteins can
be studied in great detail using single-molecule fluorescence
techniques. Because of
the complexity of the experiments and the data analysis,
however, various
experimental aspects are yet to be examined to validate the
technique.
In my research I compared diffusion-based and immobilized-based
single-molecule
fluorescence techniques by measuring a series of DNA hairpin
molecules, different
only by their stem sequences. These DNA structures presumably
have relatively
simple dynamics, making them a favored model system. The opening
and closing
rates of hairpins immobilized to coverslip surfaces and hairpins
attached to DNA
origami were measured using total internal reflection
fluorescence (TIRF) and
compared to rates obtained for freely diffusing hairpins and DNA
origami-bound
hairpins using the probability distribution analysis (PDA)
method. The data from
diffusion- and immobilization-based techniques were consistent
for all constructs
and for all NaCl concentrations examined, cross validating the
TIRF and PDA
techniques. From the excellent agreement between rates of
opening and closing of
free hairpins and of hairpins bound to origami, we concluded
that the origami has no
influence on the hairpin dynamics and that the PDA method
correctly separates the
diffusion from the dynamic component. The experimental opening
rates were in
excellent agreements with rates predicted using MFOLD and
transition state theory
for melting of duplexes with sequence identical to that of the
stems, leading to the
conclusion that the hairpin unfolding mechanism resembles that
of duplex melting.
The closing rates were identical for all hairpins suggesting
that the folding reaction
depends on counterion concentration and not on stem sequence.
Thus, the hairpin
loop influences the folding reaction and the stem influences the
unfolding reaction.
Finally, I present a single-molecule fluorescence application in
DNA
nanotechnology. The immobilization-based technique was combined
with
microfluidics technology to operate a DNA bipedal walker that
strides on a 100-
nanometer-sized DNA origami track with unprecedented efficiency
and speed.
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Keywords
Single-molecule fluorescence, FRET-ALEX Spectroscopy, DNA
Dynamics, DNA
Hairpin, DNA Origami, DNA motors, TIRF, Microfluidics.
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1. Introduction
1.1. Measuring Biomolecular Dynamics
The functions of biomolecules are strongly dependent on their
molecular structure
and the dynamics with which these structures fold and unfold.
Molecular structures
are often studied in high resolution using transmission electron
microscopy (TEM),
X-ray crystallography, NMR, and atomic force microscopy (AFM).
Acquiring
dynamic information, however, is complex. Because a solution
ensemble of
biomolecules are often out of phase in respect to each other, to
move beyond the
ensemble average and to obtain reliable dynamic information it
is often necessary to
use the single-molecule fluorescence approach. As the physics
Nobel laureate
Richard Feynman famously said, “It is very easy to answer many
of these
fundamental biological questions; you just look at the thing!”,
and single molecule
fluorescence techniques enable exactly that.
1.2. Single-Molecule Fluorescence
Single-molecule Förster resonance energy transfer (sm-FRET) is a
powerful
technique for measuring real-time conformational dynamics of
biomolecules. The
immobilization-based total internal reflection (TIRF) technique,
in which each
molecule is continually observed, provides direct structural
dynamics information on
the transitions between molecular states, and as a result, most
sm-FRET
measurements of transition rates to the date have been conducted
using this
technique. Immobilizing biomolecules, however, adds experimental
complexity, and
the immobilization procedure and proximity to surface
potentially influence the
dynamics. Previous pioneering studies of immobilized DNA
hairpins yielded
somewhat ambiguous data due to the fact that only 2-5% of the
hairpins were active
(exhibiting dynamics), suggesting that surface immobilization
influenced the
dynamics.[1] Furthermore, the immobilized-based TIRF technique
resolution is
limited by the EMCCD camera frame rate. Single-photon detectors
can increase the
resolution; however, in this approach data accusation is tedious
and slow as it
requires scanning the surface and acquiring data for one
molecule at a time. As a
result, very few surfaced-immobilized systems with fast dynamics
have been studied
thus far [2, 3].
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1.3. Probability Distribution Analysis (PDA)
In diffusion-based approaches, the limitations due to
immobilization are avoided
and, due to the use of single-photon detectors, the temporal
resolution is potentially
higher. To obtain the dynamics from the shape of the resultant
FRET efficiency
histogram (E-histogram) a semi-empirical probability
distribution analysis (PDA)
method has been developed. The method includes statistical
descriptions of the shot-
noise contribution [4-6], and the dynamics are incorporated by
calculating the
expected distribution of mean E values of any assumed dynamics
scenario [5, 7-9].
The influence of dynamics and shot-noise on the shape of the
E-histogram is
illustrated in Figure 1. For a molecule with a single and fixed
E value (Figure 1A),
the E-histogram has a single peak with a shape that can be
described by a binomial
function that is dependent on the averaged E value and on the
burst size distribution
[4, 5]. Bursts containing larger numbers of photons yield
narrower histograms than
those with fewer photons. A molecule that interconverts between
states during the
burst yields an E value that is the average of the E values of
the states, weighted by
the fraction of time the molecule spends in each of the states
during the burst [5, 7,
8]. The probability of detecting such events depends on the
transition rates and on
the burst duration. A molecule that interconverts between E =
0.2 and E = 0.8 states
at a rate significantly slower than the time the molecule spends
in the confocal spot
(burst duration) has low probability of interconverting during
the burst, and, as a
result, the E-histogram shows two distinct peaks, each dominated
by shot-noise
(Figure 1B).
Only minor intermediate E values, collectively called ‘bridge’
and corresponding to
molecules that undergo transitions, are observed. A molecule
that interconverts
between the states at rates that are comparable to the diffusion
time (Figure 1C)
yields the two peaks and a larger bridge. Even more frequent
transitions result in the
formation of a single peak with an averaged E value (Figure
1D).
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Figure 1. Schematic of the influence of the shot-noise and the
dynamics on the shape of E-histogram.
In addition, PDA method and the relationship between the
dynamics and the E-
histogram was reviewed elsewhere [10]. An alternative approach
based on maximum
likelihood analysis has also been described [11].
The PDA method has been used experimentally to analyze the
dynamics of DNA
hairpins [5, 7, 9], of LacY protein [12], and of DNA
polymerase-I [13]. PDA has
been validated theoretically by demonstrating that the
transition rates of numerically
simulated two-state system can be obtained with high accuracy
[5-7]. Because the
shape of the E-histograms may be influenced by experimental
artifacts, such as
population mixing, photobleaching, and misalignment of the donor
and acceptor
detection volumes, experimental validation of the method is
essential to demonstrate
reliability under experimental conditions. We will show here the
first experimental
validation of the PDA method.
1.4. DNA as a Model Molecule for Single-Molecule
Fluorescence Studies
In principle, DNA, RNA, proteins, beads, and any large
fluorescent complex can be
used to calibrate single-molecule fluorescence techniques. We
chose to use DNA
hairpins because (1) these molecules can be synthesized in high
yield and purity, (2)
DNA oligonucleotide synthesis is affordable, (3) DNA
oligonucleotides are
chemically stable, ensuring the robustness and repeatability of
the experiments, (4)
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4
hairpin folding and unfolding is presumably a two-state system,
(5) labeling
oligonucleotides with fluorescent dyes is a straightforward
procedure, and, most
importantly, (6) modifications can be introduced in a design
manner to control the
dynamics and stability (energy landscape) of the hairpin as we
show in this work. A
wide range of interconversion rates were achieved by alterations
of the stem
sequence and the NaCl concentration. The hairpin quasi-two-state
dynamics proved
very valuable for the development and characterization of the
single-molecule
fluorescence techniques.
1.5. The DNA Hairpin
The hairpin is a nucleic acid secondary structure motif, formed
by the hybridization
of complementary segments; these structures are frequently
observed in DNA and
RNA. DNA hairpin structures are involved in many biological
processes, such as the
regulation of gene expression and DNA recombination and may
facilitate mutagenic
events [14-16]. Hairpin structures are not static. In a
simplified description, the
conformational ensemble can be divided into two dominant states,
the open state and
the closed state (quasi-two-state behavior). The closed state is
characterized by a low
enthalpy, due to pairing of complementary bases to form the
stem. The open state is
stabilized by high entropy, due to the large number of
configurations available by the
single-stranded chain [17-20].
Figure 2. Quasi-two-state behavior of DNA hairpin. The hairpin
fluctuates between open and
closed states. The open state is characterized by high entropy
at a local minimum of free energy; the
closed state is characterized by low enthalpy, also yielding a
local minimum of free energy.
Conversion between the states requires passing through an energy
barrier involving high free energy
transition states.
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5
Hairpin dynamics is of relevance to several scientific fields.
In DNA
nanotechnology, hairpins are utilized for powering DNA-based
artificial motors and
for controlling reaction rates and hierarchies [17-23] and were
used as biosensors
[24, 25]. Because of the presumably uncomplicated structure and
dynamics, hairpins
are often used as model systems in the development of
experimental [1, 5, 9, 26-28]
and computational techniques [29-31]. Hairpin dynamics have been
studied by
fluorescence correlation spectroscopy (FCS) [26, 32-36],
temperature-jump (T-jump)
and stopped-flow (ion-jump) [37, 38], single-molecule optical
trapping [28, 39], and
sm-FRET techniques [1, 5, 9, 27, 40, 41].
Despite the extensive study, important aspects of hairpin
dynamics remain
unresolved [33, 38, 42]. Experimental uncertainties could result
from different time
scales available for the experimental techniques applied,
leading to discrepancies in
the assignment and interpretation of the obtained rates [33, 36,
38] (Figure 3).
Figure 3. Unfolding reaction rates of DNA hairpins with
different number of base pairs in the stem.
Various techniques used for the measurements are categorized by
FCS (filled circle), T-jump (open
circle), single molecule force measurement (filled square), and
smFRET (open square). Large
uncertainties arise, especially for stem with six base pairs.
Reproduced from Van Orden et al. [33]
In early FCS studies the results were explained using a
two-state model, and the
obtained rates were assumed to reflect transitions between open
(unfolded) and
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6
closed (the presumably fully zipped, folded) states [26, 32].
Recent dual-beam FCCS
measurements [33, 34], FCS measurements of diffusion-decelerated
hairpins [36],
and stopped-flow (ion-jump) measurements [42] led to questioning
of this
interpretation. These data suggest that the fast relaxation
rates (< 1 ms) observed in
FCS measurements are transitions into and out of one or more
metastable
intermediates rather than between fully open and fully closed
states. In addition, the
different relaxation times observed after T-jump and ion-jump
perturbations may be
the result of populating distinctly different conformational
ensembles, a scenario that
rules out a simple two-state model and indicates that the
folding energy landscape is
rather rugged. The FCS technique is sensitive to many time
scales, but the obtained
rates cannot be straight forwardly associated with a particular
transition. Ion-jump
and T-jump techniques are excellent for measuring kinetics from
a defined state;
however, the change in conditions introduces additional
complications, and the data
may not directly reflect dynamics in equilibrium. Here we will
use direct single-
molecule measurements to unambiguously determine the hairpin
opening and
closing rates.
1.6. DNA Origami
A beautiful new technology called DNA-origami, recently
developed by Rothemund
[43], offers exciting new possibilities for assembling complex
molecular structures.
Here, a long bacterial ss-DNA called a scaffold is annealed with
up to several
hundred short synthetic ss-DNA called staples. The staple
sequences are designed to
bind to nonconsecutive complimentary scaffolds’ sequences,
forcing the scaffold to
fold into 2D or 3D designed structures. Using available computer
software,
researchers can easily program desired shapes by annealing
staples and scaffold to
form structures of up to several hundred nanometers (Figure
4).
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7
Figure 4. DNA Origami. Top row diagrams showing the bend of
helices at crossovers. Color
indicates the base-pair index along the folding path. Lower
rows, AFM images. All images and panels
without scale bars are the same size, 165 nm times 165 nm. Scale
bars for lower AFM images: b, 1
µm; c–f, 100 nm. Reproduced from [43].
The highly specific and designable origami structure can serve
as a template for
assembling molecules besides DNA. Elongated staples that branch
out from the
DNA-origami can bind to a complementary DNA sequences that are
pre-attached to
various molecules. The chemistry of attaching DNA to nanotubes,
gold
nanoparticles, proteins, quantum dots, and many other molecules
is well known,
therefore, it is possible to use DNA origami to organize these
molecules in space in a
very precise manner [44].
In this work we use a rectangular shape DNA origami for the
following purposes: (1)
as a platform for biocompatible investigation, (2) to slow the
diffusing through the
confocal spot and by that making slow rates available for PDA,
(3) to examine the
influence of the coverslip on the hairpin dynamics by comparing
results of hairpin
directly immobilized to the surface to that attached to origami
which is immobilized
on the coverslip and, (5) to operate a DNA walker on a DNA.
1.7. DNA Hairpin Design
The DNA hairpins were designed with poly(A) loops of 31
nucleotides (A31) and
six base-pair stems; the stem sequences differed in the numbers
of G-C and A-T
pairs. The hairpin names and sequences are given in Table 1.
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8
Name Hairpin Sequence # of G·C
pair
A31-bp6-S 5’-TCGCCG-(A)31-CGGCGA-3’ 5
A31-bp6-M 5’-TCGCCT-(A)31-AGGCGA-3’ 4
A31-bp6-F 5’-TGGGTT-(A)31-AACCCA-3’ 3
A31-bp6-FF 5’-TGGATT-(A)31-AATCCA-3’ 2
Table 1. Hairpin names and sequences.
The hairpins were examined when anchored to origami
(hairpin-origami) or not
anchored to origami (hairpin-only). Previous diffusion-based
sm-FRET and FCS
studies found that hairpin dynamics was influenced by the
presence of a
complementary strand located adjacent to the stem [45] and by
the fluorophores due
to, among other reasons, dye-dye interactions.[41] Our hairpins
were designed to
minimize such possible interfering interactions. Two T bases
(Figure 5B; spacer)
separated the stem section from the dsDNA linker [9], and the
donor-acceptor
interactions were minimized by placing the donor and the
acceptor such that when
the hairpin was closed, the donor-acceptor distance remained
significant (larger than
10 base pairs, Figure 5B) [5]. A 35-bp long, double-stranded DNA
(dsDNA-linker,
Figure 5B) was used to distance the hairpin section from the
coverslip or the origami
surfaces. To enable binding of the hairpin-only construct to the
avidin-coated
coverslip, the 5′ end of the bottom strand of the dsDNA linker
was extended with
TTTT-biotin. The hairpin was anchored to the origami by
extending the 5′ end of the
bottom strand of the linker with TT attached to origami staple.
To anchor the origami
to the avidin-coated coverslip, four biotinylated origami
staples were introduced in
the annealing process. The hairpins were labeled with donor and
acceptor
fluorophores (ATTO-550 and ATTO-647N, respectively) positioned
such that the
hairpin open state yielded low FRET values (E) and the closed
state yielded high E
values. To enable differentiation between the hairpin-origami
and residual free
hairpins in the diffusion-based experiments by means of the ALEX
technique, an
additional strand labeled with ATTO-647N was anchored to the
origami sufficiently
far from the hairpin to prevent energy transfer (Figure 5C).
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9
Figure 5. Design of the DNA hairpins constructs studied in this
work. The hairpin sequences and
labeling positions were designed to minimize possible
interfering interactions between the
fluorophores when the hairpins are closed, and the TT spacer was
introduced to minimize interactions
between the stem and the duplex. The origami was labeled with an
additional acceptor to enabled
separation of hairpin-only events from hairpin-origami using the
ALEX technique [46].
1.8. Dependency of the Dynamics on NaCl Concentration
The phosphate groups in DNA and RNA are negatively charged
resulting in
intramolecular repulsion that destabilizes compact folded
conformers and stabilizes
the unfolded structurally extended state (Figure 6). In the
presence of positively
charged counterions this repulsion is reduced due to screening
[47-49]. Thus, the
fold state dominates in high NaCl concentrations whereas the
unfolded state is
dominant at low salt concentrations [26, 38, 45, 46].
(C)
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10
Figure 6. Influence of ionic strength on DNA hairpin
dynamics.
1.9. DNA Nanotechnology
The DNA nanotechnology field picked up momentum in the early
1980s with the
recognition that DNA is not just a one-dimensional molecule. By
careful design of
synthetic sequences, branched DNA motifs can be formed. Using
their single
stranded ends, these motifs can be further organized to create
3D structures that are
“limited only by imagination and a few physical properties”, to
quote Seeman [50].
Indeed, in the following years, researchers constructed a
variety of DNA structures
[51-53], and, most relevant to this, DNA-origami [43]. Recent
advances in DNA
nanotechnology has led researchers to suggest that this
technology could be
developed, and harnessed, for the benefits of other fields,
including the study of
biomolecules [54, 55].
1.10. DNA Motors
Motivated by the success in constructing DNA dynamical
structures and inspired by
biological motors in nature, researchers began exploring the
possibility of creating
artificial DNA-based motors. Several autonomous motors, which
achieve
unidirectionality [17, 18] by damaging or changing the track,
were published.
Turberfield and his coworkers [56] published a bipedal walker
that, at least in
principle, is autonomous, processive, and bidirectional
(direction can be switched by
changing the fuel sequence). In our work, we chose to sacrifice
autonomy in favor of
controllability, processivity, and directionality.
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11
1.11. Non-Autonomous Motors
Most relevant to our study, Shin and Pierce [57] (Figure 7, our
design) developed a
processive bipedal DNA walker that traveled hand-over-hand by
moving its rear feet
to the front for each step. Two legs, each with a different
sequence, walk on a track
containing four different footholds. Each step requires the
sequential addition of two
instruction strands: the first lifts the back feet from the
track and the second
reconnects the feet just lifted from the rear to the front of
the walker. Such a design
requires alternating additions of fuel and anti-fuel for each
step, and a total of eight
additions are needed to complete a cycle, altogether, enabled
increase external
controllability. By giving up autonomy and externally dictating
the sequence of fuel
and anti-fuel and their incubation periods at each step, the
authors obtain control
over travel direction and gain increased processivity while
keeping the walker and
the track chemically unchanged. Our group further developed this
motor by
incorporating the track into origami (Figure 7).
Figure 7. Non-autonomous motor operation and design. (A1-6)
Fuels attaches foothold to walker leg,
and anti-fuel detaches leg from foothold. Sequential addition of
fuels and anti-fuels results in walker
striding along the track. (B) Top view of the origami track.
Non-autonomous motor operational yield (defined as the fraction
of devices that
operate as intended) can be further improved by rational design
of asymmetrical
hairpin-fuels that by regulating the reaction hierarchy avoid
consecutive binding.
The best yield which have been achieved in our lab in a
diffusion-based experiment
is 4% per reaction, see Error! Reference source not found.
(reproduced from
Tomov and Tsukanov, 2013 [58]).
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12
Figure 8. A compression of the operational yield of motors
operating using fuels and hairpin-fuels
measured after each step [58].
The basic limitation in a diffusion-based experiment follows
from the fact that fuels
and anti-fuels accumulate in the solution and interact with the
motors to inhibit
further reaction. Immobilizing the motors to the coverslip
surface inside a
microfluidics device should enable removal of the excess fuels
and anti-fuels.
Combining the single-molecule technique with the microfluidics
technology is a
significant challenge but, once enabled, will contribute to the
development of new
generation of highly efficient and fast DNA motors that will be
able to perform many
tasks.
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13
2. Objectives
General Aim
Our first aim was to develop a single-molecule fluorescence
toolkit capable of
accurate acquisition of structural dynamic information of
biomolecules and, more
specifically, to examine and validate the diffusion-based and
the immobilized-based
methods. This was conducted by using a series of four DNA
hairpins as a model
system and a rectangular DNA origami as a platform to which the
hairpin were
attached. After validating the spectroscopic methods, the
dynamic data obtained for
the four hairpins was analyzed in terms of the hairpin states
and transition
mechanisms. Finally, DNA-made molecular motors, developed by me
in
collaboration with other members of our group, were created as
an example of usage
of single-molecule fluorescence methods in the field
nanotechnology.
Aim 1: Development and validation of single-molecule
fluorescence techniques
The dynamics of a series of DNA hairpin-only and
hairpin-origami, differing only in
their stem sequences, were measured using the diffusion-based
and immobilized-
based techniques. The opening and closing rates and the fraction
of open state of
hairpin-only and hairpin-origami were measured using the two
techniques. The
following experimental aspects were examined:
By comparing the dynamics of hairpin immobilized to coverslip to
the dynamics
of hairpin anchored to origami, which is in turn immobilized to
coverslip, we
were able to determine the influence of the coverslip on the
hairpin dynamics.
By comparing the dynamics of free hairpin to that of hairpin
anchored to
origami we examined the influence of origami on the dynamics of
the nearby
hairpins.
The diffusion-based PDA method was verified by comparison of the
opening
and closing rates of freely diffusing hairpins to those of
immobilized hairpins.
To further verify the PDA method and to demonstrate that the
method can
correctly separate the dynamics component from the diffusion
component, we
compared the opening and closing rates of hairpin-only and
hairpin-origami; the
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14
latter diffuses more slowly. Using the origami we extended the
time window
available to PDA to slower dynamics.
The validity of the immobilized-based technique was examined by
analysis of
the single exponential of the dwell-time histograms.
Aim 2: Detailed study of DNA hairpin dynamics
The second aim was to study the dynamics of the two-state
hairpin model system.
The hairpins structures, the presence/absence of intermediate
states, the opening and
closing rates, the opening and closing energies, and the folding
and unfolding
mechanisms were examined. More specifically:
The presence/absence of intermediate states was examined using
the fast
snapshot ability of the diffusion-based method.
The hairpin opening and closing reaction orders were examined by
analysis of
the shape (single-, double-exponential decay) of the dwell-time
histograms
obtained from intensity time trajectories in
immobilization-based method.
The influence of different stem sequences (i.e., different
thermodynamic
stabilities) on the dynamics were examined both in diffusion-
and
immobilization-based techniques.
The influence of the buffer ionic strength on the opening and
closing rates was
determined by measuring the dynamics under different NaCl
concentrations.
The unfolding mechanism was investigated by comparing the
opening rates to
rates predicted from MFOLD and transition state theory.
Compression of the data obtained by the two single-molecule
fluorescence
techniques, with and without the origami, and for four hairpins
different only
in their stem sequence, cross validated the techniques, the use
of origami, and
our conclusions regarding hairpin structural dynamics.
Aim 3: Combination of immobilization-based technique with
microfluidics
technology for the development of DNA-made motors possessing
high
operational yield and speed
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15
We demonstrate the application of single-molecule fluorescence
in DNA
nanotechnology. Immobilized-based experiments were combined with
microfluidics
technology to operate a DNA motor on a DNA origami track. The
motor was
immobilized inside the microfluidic channel. This novel approach
enabled efficient
fuel and anti-fuel exchange, significantly improving motor
operational yield and
speed relative to previously described designs.
3. Methods
3.1. Immobilization-Based sm-FRET-TIRF
3.1.1. Experimental Setup
The sm-FRET-TIRF experiments were carried out on an in-house
built optical setup.
In brief, a green CW laser beam (532 nm, MLL-FN-532, Changchun
New Industries
Optoelectronics Tech. Co., Ltd.) was aligned into a single-mode
fiber. After the
fiber, the beam was collimated, expanded by factor of 4.16X and
then focused
(achromatic lens 180 mm, Thorlabs AC508-180-A) on the back
focal-plane of a high
numerical aperture oil objective (NA 1.45, 60×, Olympus America,
Melville, NY)
mounted on a commercial inverted microscope (IX71, Olympus
America, Melville,
NY). The excitation laser intensity was tuned to meet two
requirements, according to
the experimental conditions. First, it has to be strong enough
to ensure sufficient
signal-to-noise ratio and weak enough to allow molecules of
study to contain several
transitions in time trajectory. We found that power of 30-100 mW
(depends on the
hairpin rates) allows identification of several transitions
before photo-bleaching
(time trajectories of 4-12 seconds, camera frame rate of 5-15
msec, respectively).
The emitted fluorescence was separated from the excitation light
by a dichroic mirror
(ZT532/638RPC, Chroma), split based on their wavelength (donor
and acceptor) by
a second dichroic mirror (FF650-Di01, Semrock), passed through a
filter (band-pass
filter, FF01-580/60, Semrock, for the donor channel and a
long-pass filter BLP01-
635R, Semrock for the acceptor channel), and focused into a fast
CCD camera
(IXON DU-897E, Andor), donor channel on the left and the
acceptor channel on the
right.
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16
Figure 9. Principle of the immobilized-based sm-FRET experiment.
(A) Total Internal Reflection
Fluorescence (TIRF) setup: The excitation lasers are focused on
the side of the back focal-plane of a
high numerical aperture objective, creating an evanescent field
of ~100 nm, thereby reducing the
background florescence. A low concentration of fluorescently
labeled molecules is immobilized on a
coverslip surface via biotin-avidin chemistry, and a flow cell
(or a microfluidic chip) allows
exchanging buffer during the experiment. (B) Total internal
reflection optical path for objective-type
TIRF: the beam enters on the side of the objective. (C) After
having been split to donor and acceptor
channels, the emitted photons are imaged on a fast CCD camera
and recorded as a function of time.
(D) Time-traces of each individual molecule are analyzed by
means of FRET.
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17
Figure 10.TIRF image of single DNA hairpin-only molecules
A31-bp6-M immobilized to surface.
On the left - green channel, on the right - red channel.
Figure 11. Pictures of immobilized-based TIRF setup, built as a
part of this work. (A) Excitation
path, microscope and microfluidic chip. (B1) Emission path,
green filter and slit, (B2) imaging lens
and dichroic mirror, separating based on wavelength to green and
red channels.
(A)
(B1) (B2)
((A) ((B)
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18
3.1.2. Data Analysis Procedures
After acquiring the movies, data processing has been performed
with in-house built
Matlab software (MathWorks, Natick, Massachusetts).
3.1.2.1. Overlapping the Donor and Acceptor Images
For each movie, several donors and the corresponding acceptors
spots were manually
selected. To each spot, a two-dimensional Gaussian was
automatically fitted,
yielding the X and Y positions of the donor and the acceptor
spots. Based on these
sets of positions, a non-linear polynomial transformation was
applied to overlap the
donor and acceptor images, compensating for optical aberrations
and imperfect
alignment of the optical setup.
3.1.2.2. Generating Donor and Acceptor Time Intensity
Trajectories
For each movie, 15-50 of the brightest pixels in the acceptor or
donor channels were
manually selected followed by automatic selection of the
corresponding spots in the
donor or acceptor channel. The intensity of each of the selected
pixels was summed
with the intensity of the 8 surrounding pixels (altogether, a
3×3 box, centered on the
brightest pixel). The per-pixel averaged background was
estimated by averaging the
intensity of the 16 surrounding pixels (around the 3×3 box).The
background was
subtracted from the intensity (after multiplication by 9 to
reflect the 3×3 pixels
contribution to the signal). This operation was performed for
the donor and the
acceptor channels, for all the selected spots and for all the
movie frames, generating
15-50 donor and acceptor background-corrected intensity
trajectories for each movie.
E time trajectories were calculated by dividing the intensity in
the acceptor trajectory
into the sum of intensities in the acceptor and donor time
trajectories (as in a
conventional calculation of E).
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19
Figure 12. Sample TIRF time trajectories for immobilized hairpin
A31-bp6-S for three different salt
concentrations: (A) low salt, 10 mM NaCl; (B) medium salt, 25 mM
NaCl; (C) high salt
concentration, 70 mM NaCl. Upper plots show the intensities in
green and red channels, lower plot
(violet) is FRET trajectory. Time bin is 30 msec.
3.1.2.3. Selecting the Best Trajectories
First, the end-time of each trajectory was determined as the
time at which the sum of
the donor and acceptor intensities (for any given time bin)
falls under a certain
threshold (well above the background noise). If all the time
bins were above the
threshold, the trajectory’s duration was the same as that of the
movie. Second, the
averaged intensity per bin (sum of donor and acceptor channels
divided into the
number of bins) was calculated. Finally, to ensure data quality,
only time trajectories
with average intensity and duration above a certain thresholds
were further
considered. The data were then analyzed in two ways.
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20
3.1.2.4. Generating E Histograms and Calculating the Fraction of
Open State
E time trajectories from more than 100 individual molecules
(several movies) were
projected and accumulated to generate each E histogram (bin =
0.01). Two
prominent histogram peaks are observed; the open state peak with
E < 0.35 and the
closed state peak with E > 0.7. The fraction of open state
was calculated by dividing
the size of the open state peak into the sum of sizes of the
closed and open state
peaks.
Generating Open and Closed States Dwell-Time Histograms and
Calculating
Opening and Closing Times. For each E, time trajectory periods
at which E < 0.5
were considered as open state and periods at which E > 0.5
were considered as
closed state. Open and closed states dwell-time histograms were
generated from
more than 100 E time trajectories (accumulated from several
movies). These
histograms were fitted to single- or double-exponential
functions, from which,
opening and closing time constants (and, respectively) were
calculated. To prevent
bias caused by photo-bleaching, for each time trajectory, the
last time segment in
each trajectory (open or closed states) was ignored.
3.1.3. Surface Immobilization of Biomolecules
To regulate the immobilization process, good control over the
solutions volumes,
incubation periods, and solutions flow rates has to be achieved.
It was done using a
flow channel (Ibidi sticky Slide VI, Martinsried, Germany). The
lower coverslip (the
one which faces the objective) was pre-treated with HF
(sonication 1 min) and then
washed thoroughly with distilled water. The immobilization
process included
following steps: (i) introduction of 60 µL (1 mg/mL) of
biotin-coated BSA (BSA-
biotin A8549 Sigma-Aldrich) into the channel, incubation for 5
min, and thorough
washing with 0.5 mL T50 (Tris 10 mM, 50 mM NaCl); (ii)
introduction of 60 µL
(0.2 mg/mL) of NeutrAvidin (ImmunoPure NeutrAvidin Protein,
Pierce, Rockford,
USA) followed by thorough washing with 0.5 mL T50; (iii) gentle
and slow
injection of 60 µL of biotinylated hairpin-only or
hairpin-origami in concentration ~
5-10 pM in imaging buffer (Tris 10 mM, EDTA 1 mM, 2-3 mM Trolox
and different
concentrations of NaCl) and then incubation for 5-15 minutes;
and finally (vi)
thorough and gentle washing with the measurement solution (0.5
mL) to remove the
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21
unbound molecules from the channel. The immobilization was
performed in room
temperature of 22-230 C.
3.1.3.1. Specificity Validation of Biomolecules
Immobilization
To test the specificity of the biotin-avidin immobilization
procedure, several
validation experiments were conducted. The surface was treated
with biotin avidin in
all the experiments. First, high concentration (~50pM) of
hairpin-only molecules
lacking biotin were injected into the flow channel. After
incubation of 15 minutes the
molecules were washed with the buffer solution, and then no
immobilized molecules
were detected (in both channels). In next experiment (conducted
in the same flow
channel), hairpin-only molecules with biotin modification at 5'
of the bottom
sequence were injected at the concentration of ~10 pM. Tens of
molecules were
attached to the surface within tens of seconds (data not shown).
Extensive wash did
not influence the number of molecules attached to surface.
Similar check was
conducted with biotinylated origami-hairpin. First,
origami-hairpin lacking
biotinylated staples was very slowly injected into flow channel.
No immobilized
origami molecules were detected (Figure 13A1-2). Then, after
slow injection of 10
pM hairpin-origami solution and incubation for 5 min tens of
immobilized molecules
seen in both channels (Figure 13B1-2).
Figure 13. Specific binding of Hairpin-Origami to coverslip by
Biotin-Avidin chemistry. Less than
1% of the hairpin-origami without biotin attached to surface
(non-specifically, A1-2), and even less
than 1% for hairpin-only (data not shown). Hairpin-Origami with
biotin attached to surface
specifically after incubation of 5-10 minutes (B1-2).
(A2) (B1) (B2) (A1) (A1)
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22
Additional validation procedure proved then if the BSA-biotin or
avidin layer
missing in the surface then both biotinylated and
non-biotinylated molecules did not
attach to the surface. Then, only proper biotin-avidin
immobilization procedure can
be used to attach molecules to surface in a specific manner.
It is important to mention, that while immobilizing the
biotinylated origami-hairpin
complex specifically, slow injection (few microliters in 10 min)
is crucial. Once the
non-biotinylated hairpin-origami molecules were injected in fast
fashion, numerous
molecules were attached to surface, due to non-laminar flow in
the flow channel
(Data not shown).
3.2. Diffusion-Based Technique
3.2.1. Experimental Setup
The sm-FRET-ALEX experiments were carried out on an in-house
built optical
setup. In brief, a green CW laser beam (532 nm, CL532-025-L,
Crystal Laser) was
aligned/misaligned into a single-mode fiber using an
acousto-optic modulator
(AOM; R23080-2-LTD, Neos Technologies, Melbourne, FL),
alternating with a red
diode laser (640 nm, Cube 640-40C, Coherent Europe, Utrecht, NL)
that was
electronically switched on/off. The AOM and the red laser were
computer controlled
with a 12.4-µs on-time, a 12.6-µs off-time, and a phase shift of
12.5 µs. The laser
intensity rise and fall times were less than 50 ns, and there
was no overlap time
between the lasers. The laser beams were combined by a dichroic
mirror (Z532RDC,
Chroma) and coupled into a single-mode fiber (P1-460A-FC-2,
Thorlabs). The laser
intensities were tuned such that the doubly labeled species
would yield S = ~ 0.5 (90
µW for the green laser and 70 µW for the red laser, measured
after the fiber while
alternating). After collimation (objective PLCN10×/0.25,
Olympus), the combined
green and red beams were introduced into a commercial inverted
microscope (IX71,
Olympus America, Melville, NY) and focused about 70 µm inside
the sample
solution with a water-immersion objective (NA 1.2, 60X, Olympus
America,
Melville, NY). The emitted fluorescence was separated from the
excitation light by a
dichroic mirror (ZT532/638RPC, Chroma), focused into a 100-µm
pinhole (P100S,
Thorlabs), re-collimated, split by a second dichroic mirror
(FF650-Di01, Semrock),
passed through filters (band-pass filter, FF01-580/60, Semrock,
for the donor
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23
channel and a long-pass filter BLP01-635R, Semrock for the
acceptor channel), and
focused into two single-photon avalanche photodiodes (SPAD;
SPCM-AQRH-13,
Perkin-Elmer Optoelectronics, Fremont, CA). The TTL signals of
the two SPADs
were recorded as a function of time by a 12.5-ns resolution
counting board (PCI-
6602, National Instruments, Austin, TX) and in-house prepared
LabView acquisition
software.
Figure 14. Principle of diffusion-based setup. (A) Set up: An
alternating donor-excitation laser (Dex)
and an acceptor-excitation laser (Aex) are focused via the
objective to create a diffraction limited spot.
Picomolar concentrations of fluorescently labeled samples are
freely diffusing into and out of the
confocal spot. The donor dye (D) absorbs a photon that
originated from the Dex laser and either emits
a photon or transfers the energy to the acceptor dye (A), which,
in turn, emits a photon. Alternatively,
the acceptor dye directly absorbs a photon that originated from
the Aex laser and then emits a photon.
The emitted photons are collected by the objective, split based
on their wavelengths, and detected by a
single photon detector (APD). (B) Binned photon time
trajectories: Separate bursts of photons, each
corresponding to a single molecule, are detected. (C1-2)
Schematic representation of E and S
histograms of molecules having different fluorescent dyes
stoichiometry and E values.
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24
Figure 15. Picture of diffusion-based optical setup, built as a
part of this work.
3.2.2. Alternating Laser Excitation (ALEX)
The sm-ALEX reports on the stoichiometry of fluorophores
presence in a given
molecular system. By detecting the presence/absence of several
labeled components,
ALEX method enables excellent monitoring of the structural
integrity of a complex.
By labeling parts of a complex with different fluorophores, the
method enables
monitoring complex assembly and disassembly reactions [59]. In
addition, ALEX
enables sorting population of interests from a mixture
containing other populations.
We show ALEX sorting capabilities on experimental data for
hairpin-origami
measurement. Selecting only the correct ALEX stoichiometry ratio
(2 acceptors and
1 donor in the case of hairpin-origami) and rejecting events
with different
stoichiometry ratios help filtering the data from contribution
of various unwanted
species that were formed in the annealing and filtration
procedures, Figure 16.
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25
Figure 16. Sorting capabilities of smALEX-FRET spectroscopy.
Real experimental data for hairpin-
origami A31-bp6-M. (A1-6) Different species present in
origami-hairpin sample. (B1) 2D ALEX-
FRET plot. (B2) E-histogram of the populations with correct
S-ratio (pink rectangle. (B3) S-
histogram, S = ~ 0.33 corresponds to the complete
hairpin-origami complex (2 acceptors and 1
donor).
For A31-bp6-M hairpin-origami the species that were formed are
as follows (Figure
16): (A1) S = ~ 0.99 – donor only – origami without hairpin loop
and additional
acceptor. (A2) S = ~ 0.5 – one donor one acceptor - origami
without hairpin loop but
with additional acceptor (could be also large burst of
hairpin-only in an open state).
(A3) S = ~ 0.33 – one donor two acceptors – the correct complex:
hairpin-origami
with an additional acceptor (hairpin in an open state). (A4) S =
~ 0.5 - one donor one
acceptor - hairpin-origami complex in a closed state, without
additional acceptor
(could be also large burst of hairpin-only in a closed state);
(A5) S = ~ 0.33 – one
donor two acceptors – the correct complex: hairpin-origami with
an additional
acceptor (hairpin in a closed state); (A6) S = ~ 0.1 – acceptor
only – origami missing
hairpin.
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26
3.2.3. Data Analysis and Presentation
3.2.3.1. Burst Search
Data analysis was performed with the in-house written LabView
software as
described before [23, 27]. The beginnings and endings of bursts
were determined by
the all-photons-burst-search (APBS, parameters: L = 200, M = 10,
and T = 500 s for
the hairpin-only and L = 2000, M = 100, and T = 2500 s for the
hairpin-origami).
For each burst, E and S were calculated according to Eq. 1 and
Eq. 2, respectively,
binned (0.01 bin size), and plotted on one- dimensional E and S
histograms and on a
two-dimensional E/S histogram. The E-histograms were smoothed
with a running
average for visualization purposes.
3.2.3.2. Calculation of E and S Values
Because in ALEX experiments two lasers alternatively excite the
donor and the
acceptor dyes, the calculation of E is somewhat different from
that in a conventional
single laser experiment (Eq. 1).
𝐸 =
(1)
where D is the number of photons recorded in the donor channel,
and A is
the number of photons recorded in the acceptor channel during
times in which the
donor laser is on (donor laser “on time”), as commonly defined
in ALEX
experiments [5, 23, 27]. No correction was made for donor
photons leaking into the
acceptor channel (donor leakage). Stoichiometry, S, is
calculated by dividing the sum
of the photons recorded in the donor and the acceptor channels
during donor laser
on-time by the sum of the photons recorded in both channels
during donor laser and
acceptor laser on-times (Eq. 2).
=
(2)
where D and A are the sums of photons recorded in the donor and
the acceptor
channels during donor laser and acceptor laser on-times,
respectively.
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27
3.2.3.3. Correction of γ-Factor Bias Problem
In our setup and using ATTO-550 and ATTO-647N the product of the
detection
efficiency and the quantum yield of the donor are larger than
that of the acceptor (the
ratio is known as the γ-factor).[60] This is evident from the
fact that a low E
population (open hairpins) exhibits higher S values than those
of a high E population
(closed hairpins) when no correction was applied (data not
shown). This
phenomenon leads to a higher probability to detect open hairpin
events than closed
hairpin events and numerical simulations show that this problem
cannot simply be
solved by multiplying by a γ-dependent factor (data not shown).
To correct for this
bias, therefore, 23% of the donor photons were stochastically
deleted from the data
files (before performing burst search), such that the S values
of the low and the high
E populations were identical (see Figure 18 for example).
Numerical simulations
show that such photon deletion corrects for the γ-factor bias
(data not shown).
3.2.3.4 Generation of E-Histograms and Calculation of the
Fraction of Open State
E-histograms were generated from events having the correct S
values (0.37 < S <
0.63 for the hairpin-only and 0.25 < S < 0.40 for the
hairpin-origami). For the
calculation of the fraction of open state events with 0.1 < E
< 0.35 were considered
as open state, and events with 0.7 < E < 0.95 were
considered as closed state. The
fraction of open state was calculated by dividing the number of
open state events into
the sum of open and closed state events (area under the
corresponding E-histograms
peaks). Intermediate E values, corresponding to transitions
between the states, were
ignored.
3.3. Probability Distribution Analysis (PDA)
The opening and closing rates (kop and kcl) and the averaged E
values of the open and
the closed states (Eop and Ecl) were calculated by fitting the
E-histograms using
previously described methods [5] with some minor modifications.
A slightly
different PDA method was developed and explained in detail
elsewhere [7-9], and
alternative approach, based on maximum likelihood analysis, has
also been
developed [3, 11, 61].
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28
3.3.1. PDA Algorithm
The PDA algorithm calculates a semi-empirical E-histogram and
fits it to the
experimental E-histogram by optimizing the dynamic parameters.
The following
procedure is used:
(i) Choose an oversampling factor N, a physical model that
describes the dynamics
of the molecule and realistic initial parameters (in our case:
Eop, Ecl, kop and kcl).
(ii) For each burst, calculate the overall time the molecule
spent in each of the two
states (τop and τcl) using a Monte Carlo simulation (running for
a time duration
equal to the burst duration, BD, of the corresponding
burst).
(iii) Calculate the shot-noise-free E value (Esnf) using Eq.
3.
(iv) Calculate the shot-noise-dependent E value (Esn) using Eq.
5.
(v) Repeat steps (ii) through (iv) N times for each burst and
add the results to an E-
histogram.
(vi) Divide the resultant E-histogram by N.
(vii) Improve on Eop, Ecl, kop, and kcl to achieve best
agreement between the
calculated and the experimental E-histograms using a chi-squared
minimization.
The histograms may be slightly smoothed to assist in the
optimization.
3.3.2. Rational of the PDA
Oversampling factor: The purpose of the oversampling factor (N =
200, step (i)) is to
reduce statistical noise caused by the binomial random number
generator and the
Monte Carlo simulation and by the finite number of bursts
collected. For a data set
containing 1000 bursts and burst size similar to that in Figure
18, N = 200 reduced
the noise almost entirely.
Calculating shot-noise-free E value (Esnf): The fitting
procedure requires assumption
of a physical model that describes the hairpin dynamics (step
(i)). We found that a
model consisting of two states that interconvert stochastically
at fixed rates (a two-
state model with first-order transitions) described all data
collected for this work.
Therefore, the Monte Carlo simulation (step (ii)) was performed
according to a two-
state model. The simulation stochastically draws open and closed
states dwell-times
from exponentially distributed dwell-times (with typical kcl and
kop rates,
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29
respectively) for overall time duration equal to the burst
duration. The overall times
the molecule spent in each state (τop and τcl) were then
calculated by summing over
all the open and the closed state dwell-times. Notice that τop
and τcl are the sum over
all the durations a simulated molecule spends in the open and
closed states, not the
typical opening and closing times (i.e., not 1/kop or 1/kcl).
For each burst, the shot-
noise-free E value (Esnf, step (iii)) was calculated by summing
the E values of the
states (Eop, Ecl) weighted by the fraction of the time the
molecule spent in each of the
states (τop /BD and τcl /BD) according to Eq. 3:
𝐸 =
(3)
Calculating the final E value (Esn): The final
shot-noise-dependent E value (Esn, step
(iv)) was calculated for each burst by first drawing the number
of acceptor photons
(A) from a binomial random number generator ( , according to Eq.
3, LabView
v. 7.1, National Instruments) and then calculating Esn by
dividing A by BS (BS, the
sum of the donor plus acceptor photons in a burst), according to
Eq. 4:
| = ( )𝐸
( 𝐸 )
(4)
𝐸 =
(5)
Fitting procedure: Fitting of the calculated E-histogram to the
experimental E-
histogram (step (vii)) was achieved by minimizing chi-squared.
This can be carried
out manually or by using any automatic algorithm. We used a
self-programed
algorithm (LabView) that searches for the set of free variables
(Eop, Ecl, kop and kcl)
that result in a minimum chi-squared (calculated from the
differences between the
experimental and the calculated histograms).
Smoothing the histograms: The experimental and the calculated
E-histograms may
not be smooth due to a low number of bursts or due to photon
statistics (deviation of
rational numbers of acceptor photons to rational number BS), [4,
5] and this can
cause difficulties in the minimization of chi-squared. In such
cases, we
recommended that chi-squared be calculated on smoothed
experimental and
calculated E-histograms. Smoothing was carried using a running
averaged algorithm.
Over smoothing is not recommended because it can erase histogram
features.
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30
Additional width of the E-histograms: Although the theory that
describes the shot-
noise contribution is well understood, none of the experimental
results to date,
including data on molecules that presumably have a fixed
donor-acceptor distance,
show a shot-noise width [4, 5, 7]. For reasons which are not
understood [62], the
widths of the experimental histograms are always broader than
expected from the
shot-noise calculation. It is customary, therefore, to broaden
the calculated
histograms by a Gaussian distribution of E values or
donor-acceptor distances. Here
we broadened the E-histograms by the equivalent of 1.4
Angstroms, which best fit
the results. This was achieved by converting the Eop and Ecl to
distances (Rop and Rcl,
and using R0 = 50 Angstroms), recalculating the distance by
drawing new distances
from a random Gaussian number generator (with a mean value Rop
and Rcl, and
standard deviation 1.4-Angstroms width), and then recalculating
Eop and Ecl. This
calculation was conducted between steps (ii) and (iii).
Background photons: We ignored the negligible contribution of
background photons
(typically less than 2% of the signal), as it was previously
shown that background of
that scale has only marginal effects on the E-histogram [5].
3.4. Calculating the Opening Rates using MFOLD and
Transition State Theory
Transition states energies cannot be directly calculated using
the nearest-neighbor
model and the MFOLD program [63]. Instead, we used MFOLD to
calculate the free
energies of formation (melting) of 6-bp duplexes with sequences
identical to that of
the hairpin stems at 22 °C and at the corresponding Na+
concentrations. Assuming
that in melting of two strands the transition state is the
unzipping of the last base-
pair, the difference between the transition state and the melted
state energy is
expected to come primarily from the translational entropy (the
many micro-states the
unbounded strands can occupy in the volume). Because the
translational entropies of
the four pairs of single-stranded DNA (stems) are expected to be
very close, we
assume that the difference in the heights of the barrier for
opening of the four
hairpins is similar to the difference in stabilities calculated
using the nearest neighbor
approach.
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31
To calculate the opening rates from these energies we used
standard transition state
theory:
= (6)
where is the observed opening rate, is the free energy height of
the barrier
with respect to the free energy of the closed state, and the
pre-exponential factor
reflects the transition rate in the absence of an energy
barrier. The exact value of
factor is unknown. Woodside et al. [28] found that data from
pulling experiments of
DNA hairpins using optical trap are best fitted by = . In these
two
papers, Eq. 6 is called ‘transition state theory’; however, the
formulations used are
identical. In second part of this work, which summarizes data
for opening and
closing rates of four hairpins, we adjusted the pre-exponential
factor such that the
MFOLD/TST opening rates fit best the experimental opening rates,
and the best fit
was achieved for = . With this value all energies decreased
by
around 0.5-0.7 kJ/mol with respect to energies calculated using
= .
3.5. Sample Preparation
3.5.1. Single-Stranded DNA Labeling
HPLC-purified bottom and top strands of DNA were purchased from
IDT
(Coralville, LA, USA) with a C6 dT internal amino modifier
(iAmMC6T) in position
10 from the 3' end and in position 1 from the 5' end. These
positions were labeled
with ATTO-550 and ATTO-647N (ATTO-TECH GmbH, Siegen,
Germany),
respectively, and HPLC purified (reverse-phase C18, Amersham
Bioscience,
Uppsala, Sweden). Typical labeling yields were ~ 70% and
purities after HPLC were
> 99% as determined by reintroduction into the HPLC. To
prevent loss of the
adenine bases during storing, the molecules were maintained in
basic conditions (pH
> 8).
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32
3.5.2. Origami Design
A DNA origami rectangle was prepared following Rothemund’s
design.[43]
M13mp18 single-stranded DNA was used as the scaffold (New
England BioLabs,
Ipswich, MA, USA), and the staples were unpurified. The hairpin
bottom strand
contained a sequence identical to that of one of the origami
staples (r-1t16f) such that
it was incorporated into the origami in the annealing process
and branched out of the
origami plane; the original r-1t16f staple was not introduced.
An additional acceptor
labeled strand (elongated with another staple’s sequence) was
added to annealing.
This helped separate residual hairpin-only from hairpin-origami
based on S
values[46] .
3.5.3. Annealing Procedures
Hairpin-only: The top and bottom strands were annealed at 94 °C
(1.5 µM in 10 µL
TE-NaCl buffer [10 mM Tris, pH 8.0, 1 mM EDTA], and 100 mM NaCl)
and then
gradually cooled (30 min) to room temperature (using PCR).
Hairpin-origami: The annealing mixture consist of 2 nM scaffolds
and 10 fold excess
of staples and 20 fold excess of top and bottom strands in 50 µL
of 50X TAE buffer
(2 M Tris, 50 mM EDTA, 2 M acetic acid) and 12 mM MgAc; we found
that with
this high concentration of buffer, the yield was 50% higher than
1X TAE was used.
To anneal, strands were incubated at 95 °C for 5 min, cooled to
60 °C at 1 °C/2 min,
and cooled again to room temperature at 1 °C/5 min (using
PCR).
3.5.4. Origami purification
After the annealing, the origami was filtered through a
size-exclusion column[64]
(Sephacryl S-300 HR, dsDNA cut-off of 118 bp; GE Healthcare,
Little Chalfont,
UK) that was hand-packed with 750 µL of liquid resin and then
spin at 1000 g for 2
minutes, yielding 500 µL of dry volume. The column was
equilibrated by washing 3
times with 500 µL of 1X TAE buffer (40 mM Tris, 1 mM EDTA, 40 mM
acetic
acid) and centrifuging for 1 minute at 1000 g to remove excess
buffer. Origami
sample of 50 µL was added and centrifuged at 1000 g for 4
minutes; this was
repeated twice to achieve complete removal of excess staples.
The origami structural
integrity was validated using AFM (data not shown).
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33
3.5.5. DNA Origami Structure Validation
To ensure that rectangular DNA origami structures formed as
designed, AFM images
were taken. The images shown in Figure 17 reveal the rectangular
DNA origami
structures.
Figure 17. DNA origami structure and integrity. (A-C) Atomic
force microscope images at three
magnifications.
(B)
(C)
(A)
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34
4. Results
We first examined the hairpin dynamics using the diffusion-based
sm-FRET-ALEX
technique [5, 27]. The hairpin-only constructs have a single
donor and a single
acceptor chemically linked to each oligonucleotide. The
hairpin-origami constructs
consisted of a single donor on the hairpin and two acceptors,
one placed on the
hairpin and the other on the origami. To reduce possible
influence of fluorophore
bleaching, incomplete labeling, or missing components on the
E-histograms, only
bursts with the expected fluorophore stoichiometry were
selected. Therefore, the E-
histograms were constructed from events with S values around 0.5
for the hairpin-
only and S values around 0.33 for the hairpin-origami.
Figure 18. Typical two-dimensional E/S-histogram and E- and S-
one-dimensional histograms. (A)
Hairpin-only A31-bp6-S (B) Hairpin-origami A31-bp6-S measured at
25 mM NaCl concentration.
At 25 mM NaCl concentration A31-bp6-S opened and closed very
slowly (5 s-1
).
Thus, only a very minor bridge between the doubly labeled open
and closed states
was observed. The very minor bridges observed between doubly
labeled open and
closed states and the donor-only and the acceptor-only
population indicate very
minor fluorophore bleaching and blinking. A31-bp6-M and
A31-bp6-S, hairpin-only
and hairpin-origami (3 pM concentration) were measured at
buffers with a range of
NaCl concentrations.
-
35
The E-histograms of A31-bp6-M hairpin only and hairpin-origami
are presented in
Figure 19.
Figure 19. Diffusion-based sm-FRET-ALEX measurements of dynamics
of (left) hairpin-only A31-
bp6-M and (right) hairpin-origami A31-bp6-M. E-histograms
obtained over a range of NaCl
concentrations (1-100 mM).
Two prominent peaks were observed in all E-histograms,
corresponding to open and
closed states, respectively, demonstrating that the hairpin is
predominantly a (quasi)
two-state molecule. In all cases, the fraction of hairpins in
the closed state increased
with increasing NaCl concentration.
Unlike the diffusion-based method, which provides only a
millisecond snapshot of
the state of the hairpin, the immobilization-based sm-FRET-TIRF
provides both a
snapshot (with duration depending on the camera’s frame rate,
5-15 ms, in this work)
and a time evolution of the state of individual hairpins (time
trajectories, Figure 12).
This enables determination of the fraction of open state, as in
the diffusion-based
experiments, and of the time periods the hairpin spent in each
state (dwell-times).
From the dwell-times, the transition rates can be directly
obtained. The opening rates
are calculated from the close state dwell-time histograms and
the closing rates from
the open state dwell-time histograms.
A31-bp6-M and A31-bp6-S, hairpin-only and hairpin-origami were
immobilized on
coverslips, and experiments were performed at different NaCl
concentrations. For
the hairpin-only experiments, a 35-bp dsDNA linker modified with
biotin connected
the hairpin to the coverslip coated with avidin (Figure 20B1).
The hairpin was
connected to the origami through a 35-bp dsDNA linker, and the
origami was
immobilized on the coverslip through a biotin-avidin interaction
(Figure 20B2). The
data were analyzed in two ways. First, E values calculated for
each individual
-
36
molecule and for each camera frame were incorporated into an
E-histogram (Figure
20C1-2). Second, open and closed state dwell-times were
determined from the time
trajectories and were incorporated into open and closed
dwell-time histograms
(Figure 20D1-2). These histograms were fitted using a single- or
a double-
exponential function from which the closing and opening rates
were determined.
No inactive hairpins were detected in any of the trajectories
that passed a certain
intensity threshold.
Figure 20. Immobilization-based sm-FRET-TIRF measurements of
hairpin dynamics. Data are of
A31-bp6-M. (A) Typical donor and acceptor emissions recorded by
the EMCCD camera and typical
donor and acceptor intensity time trajectories originating from
an individual molecule and the
corresponding E time trajectory. (B1-2) Schematic of
immobilization of hairpin-only and hairpin-
origami on a coverslip. (C1) E-histograms of hairpin-only and
(C2) E-histograms of hairpin-origami
measured in NaCl concentrations ranging from 1 to 100 mM. (D1)
Open state and (D2) closed state
dwell-time histograms of hairpin-only and fit to
single-exponential functions from which closing and
opening rates were calculated [46].
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37
4.1. Comparison of the Fraction of Open State
To examine the influence of the origami and the coverslip on the
hairpin dynamics,
we calculated the fraction of hairpin in the open state by
dividing the size of the low
E peak by that of the sizes of the low plus high E peaks in each
of the E-histograms.
The results for the freely diffusing and immobilized
hairpin-only and hairpin-origami
are presented in Figure 21.
Figure 21. Very good agreement between the fraction of open
state of freely diffusing and
immobilized hairpin-only and hairpin-origami measured at a range
of NaCl concentrations. (A) A31-
bp6-M, (B) A31-bp6-S.
For both hairpins, the fractions of open state in each of the
NaCl concentrations
were, within the experimental noise (~4%), essentially
identical. The fractions were
different for the two hairpins, however.
4.2. Comparison of Immobilized Hairpin-Only and
Hairpin-Origami Opening and Closing Rates
To further investigate possible influence of the coverslip and
the origami on the
hairpin dynamics, we compared the shape of the open and closed
state dwell-time
histograms of hairpin-only to that of hairpin-origami for
A31-bp6-M and A31-bp6-S.
The shapes of the dwell-time histograms are essentially the same
for hairpin-only
and for hairpin-origami (Figure 22A-B, blue and red symbols,
respectively). Except
for the closed state dwell-time histograms of A31-bp6-S (Figure
22B2), all histograms
were fit reasonably well by a single-exponential function
(Figure 22A1, 5A2, and
5B1). Within the experimental noise, the calculated opening and
closing rates are
similar for hairpin-only and hairpin-origami at all NaCl
concentrations (Figure
22C1-2, blue and red symbols, respectively). The closed state
dwell-time histograms
of A31-bp6-S were not described well by single-exponential
functions and were,
-
38
therefore, fit to a double-exponential function. The results
indicate that kinetic of
opening is dominant (>80%) by a slow component and an
additional but minor fast
component also exists. We suggest that the dominant slow
component is the correct
closing of stem because it is the most stable state and we the
slow rate in this work
for the comparison between hairpin-only and hairpin-origami, and
for activation
energy calculation.
Figure 22. Very good agreement between the closing and opening
dwell-time histograms measured
for immobilized hairpin-only and hairpin-origami and rates
measured at different NaCl concentrations
for (left) A31-bp6-M and (right) A31-bp6-S; hairpin-only is
indicated by blue symbols and hairpin-
origami by red symbols. (A1-2) Closing dwell-time histograms.
(B1-2) Opening dwell-time
histograms. The solid lines in A1, A2, and B1 are fits to
single-exponential functions, and solid lines
in B2 are fits to double-exponential functions. (C1-2)
Calculated closing (closed symbols) and
opening (open symbols) rates. For the opening of A31-bp6-S, only
the dominant slow (exponential)
component is presented. Solid lines are to guide the eye.
-
39
Based on the agreement between the fractions of open state and
between the dwell-
time histograms of hairpin-only and hairpin-origami, we conclude
that (i) the
origami does not influence the hairpin dynamics, (ii)
immobilization on the coverslip
glass does not influence the hairpin dynamics, and (iii) the
diffusion-based and the
immobilization-based techniques are in very good agreement.
Summaries of dwell time analyses for A31-bp6-M and A31-bp6-S are
presented in
Figure 23. Only the A31-bp6-S closed-state dwell time showed
double-exponential
behavior (Figure 23B1); the rest of the curves for open- and
closed-state dwell times
showed clear single-exponential behaviors (Figure 23 A1-2, B2).
For semi-
logarithmic plots of the dwell-time histograms see Figure 34 in
the Appendix 9.2.
Figure 23. Opening (left) and closing (right) dwell-time
histograms of A31-bp6-M (top) and A31-bp6-S
(bottom) all fitted with single-exponential functions, besides
B1, which is fitted with double-
exponential function.
-
40
Summary of the opening and closing rates of hairpin-only
A31-bp6-M and A31-bp6-S
measured using the immobilized-based method is presented in
Figure 24.
Figure 24. Summary for immobilized-based transition rates.
Opening rates (open symbol) and closing
rates (closed symbol) of A31-bp6-M (red) and A31-bp6-S (black)
hairpin-only.
The obtained closing and opening rates showed that the ionic
strength influenced the
opening and closing rea