single molecule fluorescence and force...
TRANSCRIPT
SINGLE MOLECULE FLUORESCENCE AND FORCE SPECTROSCOPY OF HAIRPIN RIBOZYME
BY
MICHELLE K. NAHAS
B.S., McGill University, 2000 M.S., University of Illinois at Urbana-Champaign, 2002
DISSERTATION
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics
in the Graduate College of the University of Illinois at Urbana-Champaign 2006
Urbana, Illinois
ii
iii
For Hanna Bustros
iv
Acknowledgments
Firstly I would like to thank my advisor, Taekjip Ha. His creativity, attention to
detail, and endless enthusiasm for understanding physically biological mechanisms has
changed my way thinking for the better. His clarity of thought and emphasis on careful
meticulous controls has been an example time and again for how to uncover the basic steps
behind a seemingly endlessly complex mechanism. He has set the bar high and I can only
thank him and try to continue to live up to the example he has set. Additionally I would
like to thank our principal collaborators on this project professor David Lilley and his
postdoc Tim Wilson. They have been irreplaceable sources of information on the relevant
biochemistry of our system and bridged the gap between the biochemical and physical
questions. Their enthusiasm for RNA catalysis and biochemistry has largely motivated
much of this work. I also am grateful both personally and professionally for Lilley lab’s
hospitality while visiting their lab in Dundee, Scotland.
The members of the Ha laboratory have also been a large part of any success I
achieved here. In particular Dr. Sungchul Hohng who taught me all the optics I learned in
the lab and was patient enough to allow me to work under him. I also thank Chirlmin Joo
whose physical intuition and creativity made him an invaluable source to get advice from
and bounce ideas off of. I also cannot thank enough Sua Myong, Rahul Roy, Sean and
Cathy McKinney, Burak Okumus, Ben Stevens, and all the other Ha lab members for their
personal and professional support.
I would also like to acknowledge the many discussions with the Bezryadin group
that helped develop our ideas on the nanochannel fabrication and Matt Mittel from the John
Rogers laboratory for teaching me the phase mask technique and giving me the fabrication
stamps. I am also indebted to the Clegg lab for their expertise and passion for
fluorescence, these people put the physics back into biophysics.
Most importantly I would like to thank my parents, Diane and John, and my sisters
Marie and Julie, for their love, support, humor and strength. I will always be sorry this
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took so long. I thank Sua Myong, Swagatam Mukapondahay, Chirlmin Joo, Benjamin
Brown, Hector Garcia, Evan Graves, Emily Klein, Carla Heitzman, John Veysey and
Dyutiman Das whose friendship made my stay in Urbana wonderful in the good times and
bearable when things were at their worst. Finally I thank Zigurts Majumdar for his
encouragement, support and dedication in my last years here and in the future years to
come.
I would like to acknowledge my financial support from the NIH and the Molecular
Biophysics Training Grant.
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Table of Contents
1. Introduction.....................................................................................................1 1.1 Ribozymes...................................................................................................1 1.2 Hairpin ribozyme and the dissertaion outline...............................................2 1.3 Fluorescence...............................................................................................5 1.4 Foerster Resonance Energy Transfer (FRET).............................................7 1.5 Single molecule FRET..............................................................................12 1.6 Data analysis.............................................................................................14 1.7 Hairpin ribozyme preparation ....................................................................16 1.8 Single molecule deposition........................................................................19
2. Cleavage and ligation of the hairpin ribozyme .........................................24 2.1 Hairpin ribozyme enzyme activity .............................................................24 2.2 Hairpin ribozyme Mg2+dependence ..........................................................26 2.3 Overview of cleavage and ligation experiments .......................................27 2.4 Simple cleavage experiment ....................................................................28 2.5 Cycling between cleavage and ligation ....................................................30 2.6 Assigning the ligated and cleaved states ................................................31 2.7 Undocking of the cleaved ribozyme is faster than ligation or cleavage ...34 2.8 Kinetics of the non natural cleavage products ..........................................35 2.9 Dependence of the enzyme reaction on pH ............................................36 2.10 Conclusions.............................................................................................38
3. Hairpin ribozyme intermediate folding state .............................................41 3.1 Background .............................................................................................41 3.2 Junction dynamics...................................................................................42 3.3 Proximal state in the natural ribozyme ....................................................45 3.4 Proximal state in the C25U mutant..........................................................46 3.5 Kinetic heterogeneity...............................................................................48 3.6 Conclusions.............................................................................................52
4. Combining confocal and optical tweezer microscopes ............................55 4.1 Background .............................................................................................55
vii
4.2 Setup ......................................................................................................58 4.3 Optical trapping and back focal plane detection ......................................59 4.4 Confocal and optical tweezer calibrations ................................................61 4.5 Trap stiffness............................................................................................64 4.6 Calibrations for combining confocal and optical tweezers ........................66 4.7 Force extension model:WLC ....................................................................67 4.8 Experimental procedure ............................................................................69 4.9 Conclusions...............................................................................................71
5. Probing the hairpin ribozyme folding path.................................................73 5.1 Background .............................................................................................73 5.2 Biasing equilibruim populations with force...............................................83 5.3 Effect of force on the transition state .......................................................88 5.4 Heterogeneity ..........................................................................................90 5.5 Conclusions.............................................................................................93
References ........................................................................................................96
Appendix I Bead annealing protocol............................................................100
Appendix II Condenser alignment .................................................................102
Author’s Biography ........................................................................................104
1
1. Introduction
1.1 Ribozymes
Ribozymes are RNA molecules that are able to carry out enzymatic activity.
Enzymatic activity can be defined as the ability to act as a catalyst by accelerating the rate
of chemical reactions relevant for biological processes, such as ATP hydrolysis, synthesis,
cleavage and ligation reactions, in which energy can be expended to “make” different types
of molecules. Proteins are the most common category of enzymes and it was long thought,
that only proteins could be enzymes, which was partially rationalized by the broad range of
chemistry possible through combinations of the 20 amino acid side chains that vary in
charge, hydrophobicity and activating groups. On the other hand the nucleobases seemed
to have limited potential to function as enzymes. Even aside from their small number (only
four) which would give a much smaller combinatorial set of they are also non charged and
chemically inert.
This perception of RNA fit well to the central dogma of biology which viewed
DNA as the stable, robust blueprint, RNA as a short-lived transcript of this blueprint, and
proteins as the final product. The proteins were the desired end product necessary for
catalyzing the mirad of reactions that keep the cell alive and thriving. This view changed
when RNA enzyme activity was discovered by Thomas Cech working on tetrahymena
RNA and Sidney Altman working on RNaseP who would later share the Nobel Prize for
this discovery. Soon after their discovery, ribozyme activity was demonstrated to occur in
many RNA sequences and to cover a variety of chemical synthesis reactions. In the
contemporary biosphere, RNA catalysis is used to splice 3 and process functional RNA
species, to facilitate metabolite-responsive control of gene expression and even to form
peptide bonds in the ribosome 4. The repercussions of this discovery are far reaching. In
particular, since RNA can act as both an information storage system and an enzyme, the
“chicken and egg” dilemma of whether life began with protein or DNA molecules could be
solved if the original molecule of life were RNA and hence the postulate of the RNA
world5.
2
The catalytic capacity of ribozymes is intricately connected with their folded
structure. The folded structures can drastically change the environment and precisely
position a select few nucleobases so that they become catalytically active. The complexity
of the cleavage reaction mechanism and the three dimensional structure of the active site
varies considerably among different ribozymes. For these reasons we have chosen to focus
attention on the simplest ribozyme, the hairpin (HP) ribozyme in order to better understand
the fundamental physical mechanisms of this process.
1.2 Hairpin ribozyme and the dissertation outline
The hairpin ribozyme consists of two internal loops that are present on adjacent
arms of a four-way helical junction as shown in Figure 1.1. The site where the catalytic
cleavage and ligation reactions occur lies in loop A on strand d and is indicated by an
arrow. Intimate association of these loops, called docking, is stabilized by divalent metal
ions and generates the local environment in which catalysis occurs. From the several
crystal structures6 1that exist of this docked form, it
Figure 1.1 Hairpin ribozyme secondary structure. The 4 strands a,b,c and d are annealed and the form the arms A, B, C, and D.
GUCCUGA
CAG A UC GC GA UG C
AGAAA
CA
CA
UUA
UA
UGC G
C GA U
C GC G
A U
UGC
25
+1A
B
C
D
a strand
Cy3
G - C
Cy5
d strand
c strand
b strand
5’ 3’
biotinCG
C G
GC
-1
a
GUCCUGA
CAG A UC GC GA UG C
AGAAA
CA
CA
UUA
UA
UGC G
C GA U
C GC G
A U
UGC
25
+1A
B
C
D
a strand
Cy3
G - C
Cy5
d strand
c strand
b strand
5’ 3’
biotinCG
C G
GC
-1
a
GUCCUGA
CAG A UC GC GA UG C
AGAAA
CA
CA
UUA
UA
UGC G
C GA U
C GC G
A U
UGC
25
+1A
B
C
D
a strand
Cy3
G - C
Cy5
d strand
c strand
b strand
5’ 3’
biotinCG
C G
GC
-1
a
3
is known that it is stabilized by a network on non-canonical (non Watson-Crick) base pairs
between nucleotides of loop A and B and by a single Watson Crick base pair between a
cytosine on loop B and a guanine at the cleavage site of loop A. One important aspect of
this entire process is the rate with which the chemical groups can come together to react,
i.e., dock. It has been shown7 that the rate of this docking interaction is intimately tied to
the dynamics of the four-way junction structural motif which is common in Group I introns
as well as DNA structures in genetic recombination and was first postulated by Holliday.
In Chapter 2 the enzymatic reaction of the hairpin ribozyme is studied at the single
molecule level. It is known that cleavage and ligation will occur within the docked state. In
typical biochemical studies of the cleavage reaction, the product RNA piece once cleaved
is bound weakly to the ribozyme by 3 base pairs which leads to its quick dissociation,
effectively rendering the reaction irreversible. In order to observe multiple
cleavage/ligation cycles, we lengthened the RNA piece to 7 base pairs which allows the
cleavage product to remain bound. Since the ribozyme must be in the cleaved form
immediately after the long product strand binds, we were able to assign an observed change
in kinetics to the cleaved form. We were then able to record the exact moment when the
cleavage or ligation reaction occurred via the changes in the docking/undocking kinetics.
We were able to show that the dynamics of the cleaved and ligated forms of the hairpin
ribozyme are very different, and are readily distinguished using single-molecule FRET
methods. This enables us to observe multiple cycles of cleavage and ligation in the same
molecule, and to measure the rates of these conversions free of uncertainties about
conformational processes8. In this way we can perform single-molecule enzymology on a
simple ribozyme, observing the fundamental processes in a direct way.
In Chapter 3 the folding transition from the docked to undocked state were analyzed
at the single-molecule level. Many biological molecules consist of distinct structural
modules that are critical for their functions and the dynamic interplay between such
elements needs to be understood for a complete elucidation of their mechanisms. The
hairpin ribozyme comprises two major structural elements; a four-way RNA junction and
two internal loops carried by two arms of the junction. We have used single-molecule
4
spectroscopy to probe the previously unknown origin for the thousand-fold faster folding of
the ribozyme compared to a minimal form that lacks the junction. Surprisingly, we find that
the ribozyme fluctuates between three distinct states: the folded state and two additional,
rapidly inter-converting states that are devoid of loop-loop interaction. We were able to
identify an intermediate in the folding path called the proximal state that positions the two
loops such that the docked state forms. The proximal state has an energy very close to the
undocked state and we have revealed that the junction-containing form of the ribozyme,
while it is undocked, exhibits conformational fluctuations derived from the junction 7,9. The
ribozyme docking occurs only through the junction conformation that brings the two loops
in close proximity, and repeated juxtapositions of the loops accelerate docking by three
orders of magnitude compared to the minimal form of the ribozyme10 ensuring that docking
is significantly faster than cleavage.
The proximal state is an obligate intermediate that predisposes the RNA to efficient
folding. Thus the hairpin ribozyme exploits the dynamics of the junction module in order to
facilitate the interaction of the loop elements that are required for the active site formation.
Such branched helical structures are found in many RNA molecules and may have been
optimized to utilize not only static structures but also their structural dynamics.
We next will return to a situation where the loops are considered again and see that
this adds a heterogeneity to the kinetics not seen when only the junction element is present
done by base pairing the loops. Our hypothesis was that the kinetic heterogeneity was due
to interactions in the intermediate state that lead to the folded state. Comparison of crystal
structures of the docked ribozyme6 and NMR structures of the separate loops11,12 indicates
that for the folded structure there are several of the interactions within the loops need to be
disrupted and formed differently. Our hypothesis has been that there are several pathways
that are stable enough to form and that the decision is made in the intermediate state. We
had tried several buffer conditions to induce switches in behavior trying incubations in
denaturing agents such as urea, formamide, heating the molecules, and leaving them for
extended periods of time. None of these conditions seemed to induce a substantial amount
5
of switching within a population, at most 1-5% and hence a memory is seen for these
molecules.
In Chapter 4 we discuss a microscope that has combined optical trapping capability
with single molecule FRET detection. This microscope is the first of its kind. It maintains
the very sensitive distance sensitivity of FRET on the application of forces by the optical
trap. In Chapter 5 preliminary data from these force FRET experiments on hairpin ribzyme
will be presented. We first use it to explore the energy landscape of the ribozyme locating
transition state distances from equilibrium states. We then begin experiments that aim to
perturb the memory of the ribozyme kinetics by varying the speed, duration and amount of
force applied.
1.3 Fluorescence
Fluorescence resonance energy transfer (FRET) is the primary technique we have
used to probe distance changes in the hairpin ribozyme. Before discussing FRET a brief
outline of fluorescence will be given. Consider a molecule with an outer electron in its
ground electronic and vibrational state. When this molecule is excited by light of an
energy comparable to transitions from the ground electronic state to a higher excited state,
the transition takes place on the order of 10-15s, roughly a few cycles of the light field for
our wavelengths. In typical organic fluorophores, which we use for our studies, following
this excitation, vibrational relaxation will occur to the lowest vibrational state of the first
excited singlet electronic state with a decay on the order of picoseconds. Fluorescence is
the process of photon emission (spontaneous emission), which can take place from this
lowest lying excited singlet state to the electronic ground state (to a distribution of
vibrational states within the electronic ground state) and takes place on the order of
nanoseconds Fig. 1.2a.
6
This lifetime of the excited state is not only dependent on the rate of spontaneous
emission, but is also dependent on any other interaction which can cause transitions to the
ground state. Environmental conditions that affect the molecular electron cloud
distributions such as heavy ions, solvent polarizability, viscosity and temperature, influence
the lifetime. Thus, changes in the lifetime of the excited state can be used to measure the
rates of other dynamic processes which are on the order of this rate and compete with
photon emission. As these interactions change the relative probability for photon emission
(fluorescence quantum yield), the photon flux, or, measurements of the intensity of
fluorescence which are proportional to the total number of emitted photons, can also be
used to measure the dynamics of these other processes. As shown in Fig 1.2b an electron in
the excited state has several decay paths leading to the ground state such as quenching,
internal conversion, fluorescence, or the case that will be of interest for this thesis,
fluorescent resonant energy transfer FRET.
Figure 1.2 (a) Fluorescence energy diagram. (b) Some decay pathways from the excited state.
a b
7
1.4 Foerster Resonance Energy Transfer (FRET)
Fluorescence resonant energy transfer, FRET, occurs when a fluorescent molecule,
called the donor, in an excited state is nearby another molecule (not necessarily
fluorescent) called the acceptor, which is in the ground state. Energy can be transferred
non-radiatively from donor to acceptor through near-field coupling of the electronic dipole
moments. The rate of this transfer is very sensitive to the probe separation distance and
will be shown to go as 1/R6. The probes must have very specific properties in order for
FRET to occur. These properties briefly summarized are: the donor probe must absorb the
excitation light (short-wavelength experimentally applied photons), the acceptor probe
must have a high absorption in the emission wavelength range of the donor, and third, the
Figure 1.3 (a) Acceptor and donor energy level diagrams. (b) The donor and acceptor relative dipole orientations.
ϑ
pD
a
bφ
pA
pD
pA
8
donor and acceptor dipoles (averaged over the excited state lifetime) must be oriented
optimal for dipole-dipole coupling (averaged over a distribution of orientation which is
typically present).
To understand how these conditions, arise consider the energy diagrams of acceptor
and donor molecules shown in Fig 1.3a. The initial state and final state of the two electrons
are written as:
*
*
DA
AD
f
i
=
=
ψ
ψ
The rate of transition can be described using Fermi’s Golden Rule:
iffiiT Uk ρψψπ 22→=
h
The interaction term has two components the first being the dipole-dipole
interaction between the two probes, the second involves the potential describing the
vibrational bands. This first potential term can be derived from the dot product of one of
the dipole’s electric fields with the second dipole:
−
=⋅
−
= 3232
^^
coscoscos3cos3
Rnppp
Rn
prpU DA
ADA
D
Dipoleϕφϑ
ϑr
where as shown in Fig1.3b R is the distance between the donor dipole, pD and acceptor
dipole, pA.
Equation 1.1
Equation 1.2
Equation 1.3
9
×=
∑ ∑
→
fiAADD
vibvib
ADAD
DAAEUADEUD
DAppRn
ADk
,*,*,,
22
2^^
32
*)()(*)(*)(
**2
ρρ
κπh
The density of states and vibrational term of the transition controls the degree of
energy overlap and thus resonance between the donor and acceptor dipoles. This term is
related to an experimentally measurable quantity known as the overlap integral, J:
∫
∫∞
∞
=
0
0
4
)(
)()(
λλ
λλλλε
dI
dIJ
D
DA
where λ is wavelength, εA is the absorption coefficient of the acceptor and ID is the
emission spectrum of the donor. Thus, only interactions in which there is non-zero overlap
between the emission of donor and absorption of acceptor, will energy transfer take place.
This overlap is made possible by absorption and emission bands which are sufficiently
broad due to the vibrational envelopes and the density of states for the individual
transitions. Combining the electronic part and the overlap integral, the rate of energy
transfer can is proportional to
64
2 1Rn
Jkk AD×
=→
Including all of the physical constants, the rate of energy transfer can be shown to be equal
to:
64
225 11078.81Rn
Jkxt
kD
AD××
=−
→
where τD is the lifetime of the donor in the absence of acceptor.
Experimentally it is useful to define the efficiency of energy transfer, E as:
Equation 1.4
Equation 1.5
Equation 1.6
Equation 1.7
10
∑+=
→
→
kkkEAD
AD
where the denominator expresses the sum of all de-excitation pathways, thus E describes
the relative probability for an energy transfer event and is also known as the quantum yield
of energy transfer. A convenient way to relate this to distance is to define
6
0
1
1
+
=
RR
E
defining R0 as the distance at which E is 0.5, or 50% of excitations of the donor result in
energy transfer to the acceptor. From equation 1.7 and 1.8 R0 can be shown to be equal to
⋅⋅⋅⋅=
−
4
2225
01079.8
nJR D κφ
The FRET efficiency is plotted in Fig 1.4. The steep distance sensitivity is its
greatest near R0 and tapers off quickly +-x of R0 where R0 is given by. R0 also known as
Equation 1.11
Equation 1.8
Equation 1.10
Figure 1.4 FRET distance dependence as a function of donor and acceptor distance, R. When R=R0 the FRET efficiency is 0.5.
11
the Foerster (or critical) radius, sets the distance sensitivity of the measurement. It
depends on specific properties of the selected dye pairs, namely the quantum yield of the
donor, the overlap integral, and the orientation of these dye dipole moments as shown in
Fig 1.4. Depending on these values the value of R0 maximal sensitivity can be made tuned
and using currently available dyes is found to be in the range of 1-10nm.
From a biological perspective because the distance sensitivity of FRET compares
well with many biological structures such as proteins, biological motors and nucleic acids it
has the potential to serve as a technique for probing the dynamics of these constructs. It is
important to understand that the FRET technique on its own would not give much useful
information. But by selecting dye positions based on known crystal structures or
biochemical assays the dyes can be positioned to answer key questions on structural
rearrangements.
Figure 1.5 Cy3 and Cy5 structures and absorbance and emission spectra. The gray shaded region represents the overlap integral.
Cy5
Cy3
Cy5
Cy3
12
1.5 Single molecule FRET
Single molecule FRET (smFRET) allows observation of the dynamics of each
molecule in a population. Heterogeneities within a population can be clearly observed
which leads to the possibility of observations of intermediate states, differences in kinetics,
and multiple reaction/folding cycles that would have otherwise been averaged out in bulk
FRET experiments.
Experimentally building microscopes for single molecule detection requires
sensitive cameras, non-fluorescing optics, small excitation volumes, and finally bright
probes that do not have erratic photophysics (for example, changes in intensity of the
donor are not appreciable affected by things other than the proximity of the acceptor and
that singlet to triplet state transitions are minimized). The detection optics are chosen to
minimize background fluorescence that is intrinsic to the solution as well as elements in the
optical path. Natural glass has many impurities that would lead to background
fluorescence when the laser line passed through them and gives a relatively bright signal
when compared to the photon flux generated by a single molecule at the same excitation
power. For this reason we use fused silica slides (often heretofore referred to as quartz,
which is chemically identical, but fused silica is melted and cooled such that it is
amorphous and does not have the natural birefringent properties of quartz). The cameras
are selected for very low dark counts, high frame transfer rates, and often single photon
sensitivity. We use cooled CCD cameras for our wide field detection and APD’s for the
single point detection.
Another necessary strategy for background reduction is using a small observation
volume so that a minimal signal from the solvent is collected, which drastically reduces the
background. This is done by either confining the excitation to a small volume or
observation, or both. The experiments reported here have been done using setups that
minimize the excitation volume in two different ways via total internal reflection and
confocal microscopes, Fig 1.5 and 1.6 respectively. As shown in Fig 1.6 the prism type
13
TIR reduces the excitation volume by creating an interface for total internal reflection to
occur between the quartz slide and water sample solution. The laser is focused by a 2x
laser onto the back of a prism, when it is directed at a steep enough angle it will undergo
total internal reflection. An evanescent field will propagate beyond this boundary to a
depth given by 14 2 −
=NA
d pπ
λ . Where in our case the NA is 1.4 and excitation
wavelength is 532nm leading to a penetration depth of 67nm.
Ideally, the fluorophores excited in the small excitation volume will either fluoresce
or undergo FRET. The emission signal will pass through the objective along with the
excitation laser light that was not scattered or absorbed. This light will pass through a laser
line filter leaving only the fluorescence emission and FRET emission light. This light then
passes through a dichroic mirror which selected between the two emission spectra (620nm),
such that it passes light from one fluorophore and reflects that of the other in order to split
Figure 1.6 Total internal reflection microscope. The prism and sample slide are enlarged in the inset.
14
the emission light into two parallel off center beams which are then focused onto a single
CCD chip.
In Figure 1.7 a confocal microscope is shown. In this case the excitation volume is
reduced by exciting only the focused laser spot with a oil immersion high numerical
aperture objective at the coverslip surface. To collect emission only from the focal volume,
emitted light is focused onto a pinhole (200 microns) so that the out of focus light is
blocked. On the detection side a laser line filter is again used but this time two separate
Avalanche Photo Diodes (APDs) receive the emission, again split by a dichroic mirror.
For both microscopes incoming intensities are controlled with neutral density filters
and the combination of a 1/2 waveplate and a polarized beam splitting cube.
1.6 Data analysis
Sample images from the CCD or APDs is shown in Fig 1.8a. The right half
represents the signal from the Cy5 channel and the left half represents the signal from the
Cy3 signal. Corresponding points, shown as red circles, can be selected and their intensities
Figure 1.7 Confocal microscope. The excitation is now a point and images are only formed by raster scanning the focal spot through a piezo stage. A pinhole, shown as the white box before the APD dichroic, is placed in the detection path in order to block out of focus excitation. This out of focus excitation is shown in the inset arising from the excitation beam as it passes through the sample.
15
recorded as a function of time for both channels. A sample trace is shown in Fig 1.8b with
the red curve representing the intensity measured from Cy5 channel and the green trace
representing the intensity measured from the Cy3 channel. These detector intensities are then
turned into separation distance information through Equation 1.10. The FRET efficiency is
shown as the blue FRET trace in Fig 1.8b.
Kinetic information such as the rates of the transition from the high to low FRET
state or vice versa can be obtained from these traces. To obtain the docking and undocking
rates of the ribozymes in this report hairpin ribozyme traces have been binned according to
FRET level Figure 1.9. The dwell time in each of these levels has been calculated and a
histogram of those bins fit to a single exponential decay. When a large number of different
molecules are used to build the histograms there is an additional weighting. Every dwell
time contributed by a molecule is divided by the total number of transitions that molecule
under went. This was done because the sample populations have heterogeneous kinetics
(Chapter 3). Treating each dwell time of a docked or undocked state equally would lead to
an over-representation of fast fluctuating molecules since they would undergo a larger
Figure 1.8 Raw TIR data and changing it into FRET time traces. (a) Single frame of typical CCD data split into Cy3 and Cy5 channels. The red circles map Cy3 fluorescence spots on to their corresponding Cy5 spot location. (b) Sample intensity data that is substituted into Eqn 1.10 to obtain a FRET time trace.
( )60DA
A
RR11
IIIFRET
+=
+=
0 1 0 2 0 3 0 4 00 . 0
0 . 4
0 . 8
FRET
(s)0 1 0 2 0 3 0 4 0
0 . 0
0 . 4
0 . 8
FRET
(s)
0 1 0 2 0 3 0 4 0 5 00
1 9 0 0
Inte
nsity
(s)0 1 0 2 0 3 0 4 0 5 0
0
1 9 0 0
Inte
nsity
(s)
a b
16
number of transitions before photobleaching. To avoid such artificial skewing we weighted
each dwell time so that its contribution to the histogram is inversely proportional to the
number of transitions observed in a single molecule. For example each dwell time in a trace
that contains 100 transitions counts for 1/100 of a point while for a trace with only 10
transitions each dwell time counts for 1/10 of a point.
1.7 Hairpin ribozyme preparation
1.7.1 Hairpin ribozyme annealing
Hairpin ribozyme samples were synthesized via our collaborator David Lilley as
described previously [Wilson, 2002 #129]. The synthesizer worked with the first base in
place from commercially bought polystyrene bead. Subsequent bases are added via their in
house synthesizer. These beads were then washed with various solvents to remove the
RNA from the bead, the TBDMS or ACE ribose 2’OH protecting groups, base protection
groups and ribose 5’phosphate protecting groups. The dyes were attached with
phosphoramidite chemistry. Samples taken off the column will be a heterogeneous mix of
Figure 1.9 Sample of for obtaining undocking rates. (a) A sample FRET time trace is shown. The bars above it represent the dwell time in the docked state. (b) By histograming such dwell times from hundreds of molecules within the sample population the histogram can be fit to a single exponentialdecay, the rate of which is the undocking rate.
3 0 6 0 9
t12,3
00
00
Cou
nts
Dwell timesTime (s)
FRET
a b
17
different lengths, and labeling efficiencies. These strands were then separated by PAGE
gel purification.
Several constructs were prepared for the different ribozyme experiments. The
nomenclature for their construction is shown in Figure 1.1 where a, b, c, d represent the
individual strands and A, B, C, and D represent the arms they form on annealing. Figure
1.10 contains a table showing the constructs used throughout this report. In Chapter 2 the
constructs of interest will be the natural four way junction cleavable ribozyme, a
nonligatable cleaved 3’ phosphate terminated and 3’ OH terminated ribozymes, and the
uncleavable ribozyme. In Chapter 3 we have used the uncleavable construct, a junction
construct with the loops base paired, and an uncleavable ribozyme with a mutation at the
C25 site to a U25. Finally in Chapter 5 we have used an uncleavable construct that has the
dye pairs switched from arms A and B to arms C and D and has the a strand extended by 12
DNA bases for lambda DNA annealing.
Cleavable with 12bpr extensionChapter 5
Uncleavable deoxy guanineChapter 2,3,5
4H Junction Chapter 3
CleavableChapter 2
Nonligatable cleaved -OH -PO4
Chapter 2
Construct name
Strand a-aggtcgccgcccCGACAGAGAAGUCAACCAGAGAAACACACUUGCGGgStrand b-biotin-cCCGCAAGUGGUAUAUUACCUGGUACGCGUUCACGGgStrand c:Cy5-cCCGUGAACGCGUGGUGCGAAUCGGgStrand d:Cy3-cCCGAUUCGCACCUGACAGUCCUGGg
Strand a:Cy3-cCGACAGAGAAGUCAACCAGAGAAACACACUUGCGgStrand b:Cy5-cCGCAAGUGGUAUAUUACCUGGUACGCGUUCACGgStrand c:biotin-cCGUGAACGCGUGGUGCGAAUCGgStrand d:cCGAUUCGCACCUGACaGUCCUGg
Strand b, c,d same as aboveStrand a:cCGACAGGACUGUCAACCAGGUAAUAUACCACUUGCGg
Strand a:Cy3-cCGACAGAGAAGUCAACCAGAGAAACACACUUGCGgStrand b:Cy5-cCGCAAGUGGUAUAUUACCUGGUACGCGUUCACGgStrand c:biotin-cCGUGAACGCGUGGUGCGAAUCGgStrand d:cCGAUUCGCACCUGACAGUCCUGg
Strand d 3’-OH form : cCGAUUCGCACCUGACA-3’-OH GUCCUGgStrand d 3’-PO4 form : cCGAUUCGCACCUGACA-3’-PO4 GUCCUGg
Sequence
Cleavable with 12bpr extensionChapter 5
Uncleavable deoxy guanineChapter 2,3,5
4H Junction Chapter 3
CleavableChapter 2
Nonligatable cleaved -OH -PO4
Chapter 2
Construct name
Strand a-aggtcgccgcccCGACAGAGAAGUCAACCAGAGAAACACACUUGCGGgStrand b-biotin-cCCGCAAGUGGUAUAUUACCUGGUACGCGUUCACGGgStrand c:Cy5-cCCGUGAACGCGUGGUGCGAAUCGGgStrand d:Cy3-cCCGAUUCGCACCUGACAGUCCUGGg
Strand a:Cy3-cCGACAGAGAAGUCAACCAGAGAAACACACUUGCGgStrand b:Cy5-cCGCAAGUGGUAUAUUACCUGGUACGCGUUCACGgStrand c:biotin-cCGUGAACGCGUGGUGCGAAUCGgStrand d:cCGAUUCGCACCUGACaGUCCUGg
Strand b, c,d same as aboveStrand a:cCGACAGGACUGUCAACCAGGUAAUAUACCACUUGCGg
Strand a:Cy3-cCGACAGAGAAGUCAACCAGAGAAACACACUUGCGgStrand b:Cy5-cCGCAAGUGGUAUAUUACCUGGUACGCGUUCACGgStrand c:biotin-cCGUGAACGCGUGGUGCGAAUCGgStrand d:cCGAUUCGCACCUGACAGUCCUGg
Strand d 3’-OH form : cCGAUUCGCACCUGACA-3’-OH GUCCUGgStrand d 3’-PO4 form : cCGAUUCGCACCUGACA-3’-PO4 GUCCUGg
Sequence
BB
HOPO4
B
A
B
A
B
A
B
AB
A
A
BB
HO
B
HOPO4
B
A
B
A
B
A
B
A
B
A
B
AB
A
B
AB
A
A
Figure 1.10 Table of the constructs used in this experiment.
18
The strands were sent separately dissolved in ethanol at room temperature. The
ethanol solutions were spun at 14,000rpm for 15 minutes pelleting the RNA at the bottom.
The ethanol was then removed and replaced with a T50 (10mM TRIS 10mM NaCl pH8)
buffer. The full four strand construct was assembled by mixing the component strands with
2:1 molar ratios of unbiotinylated to biotinylated strands. The four strands were annealed
by heating to 80°C in T50 pH8 thus breaking up any misfolded structures. The heating
block was removed from its heating source and the heating block with the four strands were
slow cooled in the dark for at least several hours.
1.7.2 Hairpin ribozyme lambda annealing
Preparation of the hairpin-lambda construct requires attention to the fragility of the
16um lambda DNA. To minimize shearing which can easily occur, whenever lambda
DNA is present wide tip pipettes are used, the sample is mixed by tapping about 10x, and
freeze-thaw cycles are minimized. Lambda DNA is bought from New England Biolabs
(#N3011S [λ ]~17nM) and is gently tapped about 10x to ensure it is well mixed and is then
aliquoted into 20uL 1.5mL eppendorfs using wide tip pipettes and stored at -20C. The
following protocol will expose the lambda to an additional freeze thaw cycle. These two
freeze thaw cycles have been found to leave the lambda sufficiently intact for optical
tweezer experiments.
Samples are prepared by first annealing the hairpin ribozyme as described in section
1.8. One of the lambda aliquots is dethawed and its salt concentration raised to 50mM
NaCl and heated for 10 minutes at 70-80C. The sample is then immediately put on ice for
5 minutes. Lambda DNA is a 48.5kbp circular DNA sequence that and has two twelve
base pair complementary overhangs at its ends that anneal to bring it a the circular form.
The point of this step is to separate the lambda sticky ends which are twelve base pairs long
and of the complementary sequence to the a strand extension of the hairpin ribozyme as
shown in Figure 1.10. The snap cooled lambda and RNA are gently mixed by tapping the
eppendorf about 20x covering the mixture in foil and rotating at room temperature for 1.5
hours followed by a 1 hour rotation in a 4C cold room. After this incubation time excess of
19
a 12mer DNA olio of complementary sequence to the exposed lambda overhang is added.
This 12mer also has a digoxigenin added to its 5’ end and is bought from IDT. This
mixture is again tapped and then incubated for an additional 2 hours in the cold room. The
final concentrations of this mixture that I have used and found successful are
[RNA]~700pM, [λ ]~7.7nm, [NaCl]~34mM, [dig12]~294nM. These annealing ratios will
yeild RNA-dig without lambda. Since the RNA has a biotin this protocol could potentially
lead to many beads appearing stuck to the surface. I have not found these concentrations to
cause a non specific binding problem but this point should be kept in mind when adapting
this protocol. After incubation the sample is aliquoted into volumes that will be diluted for
use in a single experiment. The samples are pipetted using wide mouth pipette tips into
1.5mL eppendorfs and stored at -20C.
=+80C
+ =
lambda
lambda lambda
dig
12mer
12mer12mer
12mer 12mer
dig
lambda 12merlambda =+80C
+ =
lambda
lambda lambda
dig
12mer
12mer12mer12mer12mer
12mer12mer 12mer
dig
lambda 12merlambda 12mer12merlambda
The protocol for coating the polystyrene beads with antidigoxigenin protein was
given to us by Wei Chang and is in Appendix I.
1.8 Single molecule deposition
1.8.1 Hairpin ribozyme surface immobilization
Sample chambers are prepared by sonicating 1x3in slides and 24x40mm cover slips
in a KOH dissolved in milliQ water to a concentration of 1M. These slides and cover slips
are burned, cooled/dried with N2. Pieces of double sticky tape are laid down and a
Figure 1.11 Cartoon of the annealing protocol for preparing the ribozyme-lambda-dig construct.
20
coverslip pressed on top to form fluid channels. Holes are predrilled into the glass slide
with 0.75mm diameter diamond plated drill bits (UKAM 4ED075) at two ends of the glass
for fluid injection with pipette tips once the chamber is sealed.
Neutravidin
Quartz
biotinBSA
FRET
Neutravidin
Quartz
biotinBSA
FRET
Single molecule samples are prepared by incubating the channel for 10 minutes
with 1mg/mL BSA biotin solution. Bovine serum albumin (BSA New England Biolabs
#B9001S) is a zwitterionic protein that sticks very well to the quartz surface. Biotin is a
small vitamin that is attached via an amino acid to BSA. The channel is then rinsed with
T50 (10mM TRIS 50mM NaCl pH8) and then incubated with a 0.2mg/mL neutravidin is
added and incubated for another 10 minutes. The neutravidin protein contains four binding
pockets for biotin as shown in Fig 1.12. The biotin-neutravidin linkage has the strength
similar to a covalent bond and is interaction that immobilizes the single molecules to the
surface. After the 10 minute incubation and following the rinse with T50 100-150pM
hairpin ribozyme with a biotinylated arm is added and incubated for a few minutes. The
hairpin ribozyme is diluted below 1nM by a 0.1mg/mL T50BSA this is done to prevent
nonspecific losses of sample to pipette tips, eppendorf walls, etc. Once the sample has
incubated for ~1min it can be rinsed with the final imaging buffer.
1.8.2 Imaging buffer and the oxygen scavenger system
Imaging buffer is critical to minimizing the dye photobleaching and maximizing
their lifetimes. One of our main goals is keeping the fluorescent dyes from reacting in the
excited state to form either permanently non fluorescent compounds (photobleaching) or
Figure 1.12 BSA biotin neutravidin surface. Drawing courtesy of Sungchul Hohng.
21
entering non fluorescing states (blinking). Both photobleaching and blinking are possible
when the dye is in the excited state. Blinking is often due to the dye entering a triplet state.
One of the most common culprits for both photobleaching and blinking are excited state
oxygen. When these molecules collide with the excited state fluorophore they can
permanently react with it or temporarily send it to a triplet state. These oxygens are also
the good guys in the sense that if a dye is in a triplet state they can also knock it out and
return it to its normal singlet state.
We have typically used an oxygen scavenger system13 to alleviate both
photobleaching and blinking. We take advantage of two proteins glucose oxidase and
catalase that have a net reaction (Equation 1.12) that consumes oxygen, hence decreasing
the amount that is present in the solution.
222
22cos
22cos
OacidgluconicOH
acidglucoicOHOeglucatalase
oxidaseeglu
→+
+ →+
Once the oxygen is removed the likelihood of having excited state oxygen in solution is
greatly decreased. But there is still a probability of having a fluorophore in a non
fluorescing triplet state but now there are not many oxygens available to knock it out of this
state. This would lead to a case where though there are few blinking events when they do
occur they last for much longer times. So for this reason we add either 140mM
betamercaptoethanol to our imaging solution or a saturated solution of TROLOX both of
which are efficient at knocking the electrons out of the triplet state.
For these reasons any imaging buffer must contain the oxygen scavenger system
and TROLOX or bme. The imaging buffers used in my studies contain 1% gloxy
(gluocose oxidase + catalase), 70-80% TROLOX, 0.5% glucose. The solution is buffered
using 10mM MEPES for pH between 6-7, or 10mM HEPES for pH 7-8, or TRIS for pH
between 8-9. Finally 50mM NaCl was present in all buffers. The [Mg2+] is the ion most
commonly varied in this report and it will be noted in any experiment.
Equation 1.12
22
1.8.3 Hairpin ribozyme lambda construct deposition
When working with samples that have lambda DNA annealed the problem of non
specific sticking of the lambda or the antidigoxigenin bead becomes troublesome. Sample
chambers are prepared as in section 1.8.1 except that the glass slide is not drilled and the
openings are unsealed. Buffer solutions are not pipetted in through the drilled holes but a
droplet is placed at the opening and gently pulled through by gravity as the slide is tilted in
the direction of desired fluid flow. For my studies with RNA PEG polymer coatings were
not necessary neither was close mechanical control over buffer flow velocity, though when
dealing with high ion concentrations ([Mg2+]>1mM) or protein these become necessary.
The BSA biotin neutravidin surface is prepared the same as in section 1.8.1. Care must be
taken when depositing the RNA lambda construct as its large size makes it very susceptible
to shearing. Aliquoted samples are diluted to a concentration of 300pM and mixed via
tapping. They are pipetted into the opening of the sample chamber using wide pipette tips
and dragged through by gravity. The lambda DNA tethers are large having a length of
16um and need a much longer deposition time of about 45 min to obtain 100pM sample
densitiy. After deposition the sample is rinsed with 10mM TRIS at pH8. It is necessary to
rinse well so a volume at least 10x the sample chamber volume is used for this rinse.
Antidig coated 1um polystyrene spheres are then added to the sample. The incubation is
done for 20 minutes and rinsed gently with 2-4x the sample chamber volume of 10mM
TRIS pH8 buffer. The sample is then filled with a T50-1mg/mLBSA solution and allowed
to incubate for 10 minutes. I have found this step to be critical to maintaining the sample
passivation once the Mg imaging buffer is added. This may be due to a BSA network of
proteins on the surface that form and maintain high enough density only so long as the
BSA concentration is maintained [Forciniti, 2005 #100].
The most sensitive rinse occurs when the imaging buffer (Section 1.8.2) with Mg is
added. For this rinse it is very important that the rinse be done slowly and with minimal
volume. I have rinsed with 2x the sample chamber volume of imaging buffer and have
found successful perfusions take about 2 minutes (~15uL/min). The imaging buffer has
several components 80% trolox, 0.5% glucose, 1mg/mL BSA, 10mM Hepes pH 7.5, and
23
50ug/mL antidigoxigenin. The BSA is critical to prevent beads sticking to the surface
while the antidigoxigenin is critical to the antidigoxigenin remaining bound to the beads.
This second condition though is found to vary, sometimes being necessary and sometimes
not. This may be due to variation in the efficiency of the coupling reaction from the
antidigoxigenin bead binding protocol (Appendix II). This may lead to a variation in the
antidigoxigenin that is covalently bound rather than just absorbed on the bead. The
abosorption would be more sensitive to the amount of antidigoxigenin in the imaging
buffer.
24
2. Cleavage and ligation of the hairpin ribozyme
2.1 Hairpin ribozyme enzyme activity
The hairpin ribozyme serves as an ideal system for understanding RNA catalysis
because of its small size, relatively simple tertiary structure and enzymatic chemistry.
Additionally there are several known crystal structures of the hairpin ribozyme that identify
key nucleotides that are involved in the chemistry and stabilizing the folded structure. The
hairpin ribozyme, Figure 2.1a, is the small RNA enzyme part of a larger viroid that is
carried along with the tobacco ringspot virus. Biologically this enzymatic activity of the
ribozyme is responsible for the viroid replication Figure 2.1b. The negative strand is
produced by an RNA-dependent RNA polymerase using the (+) strand as a template in a
rolling circle process, thus multiple copies of the RNA are produced from one transcript.
These multiple copies are processed into monomeric units by the inherent cleavage activity
Figure 2.1 Hairpin ribozyme as found in nature. (a) The viroid of the tobacco ringspot virus plant. The colored sequence is the hairpin ribozyme. The arrow indicates the nucleotides where the catalytic reaction occurs. (b) The replication cycle of the viroid relies on the cleavage and ligation properties of .
a
RNAP replication
hairpinribozyme cleavage
ligationhairpinribozyme
(+)
(-)
(-)
(-)
Replication
Hairpinribozyme Cleavage
Hairpinribozyme
Ligation
(–)
(–)
(–)
RNAP replication
hairpinribozyme cleavage
ligationhairpinribozyme
(+)
(-)
(-)
(-)
Replication
Hairpinribozyme Cleavage
Hairpinribozyme
Ligation
(–)
(–)
(–)
b
25
of the ribozyme region. Each cleavage reaction creates the 3' end of one monomer and the
5' end of the subsequent monomer. Following dissociation, the increase in translational
entropy will favor the monomer forming a hairpin ribozyme in a unimolecular process. The
internal equilibrium for cleavage/ligation then ensures the efficient production of a circular
template for the synthesis of the (+) strand.
The core catalytic center of this enzyme is found in the 60 nucleic acids that are
indicated by the coloring in Fig 2.1a. The enzymatic reaction catalyzed by the ribozyme
occurs on the green strand between the guanine and adenosine nucleotides indicated by an
arrow. This excised region maintains the same cleavage activity of the entire viroid and it is
this smaller part of the viroid that we have studied. Previous studies have looked at an
even smaller region involving only the two loops without the additional C and D arms.
From previous studies it is know that an overall conformational change must occur
in order for the cleavage reaction to take place. In the absence of counter ions the highly
negative charge of the RNA backbone will keep the hairpin ribozyme in an undocked state.
In the presence of ions the two unpaired loops A and B will interact and stably dock. With
the two loops docked the ribose of the A-1 base is oriented in such a way that a
transesterfication reaction is positioned to occur. The 2’ oxygen of the ribose attacks the
phosphate backbone leading to a cylic phosphate forming on the 3’ end of the cleavage site
and an OH group on the 5’ end as shown in Fig 2.2. This reaction is reversible and hence
the ribozyme is able to cleave and ligate.
Figure 2.2 The transesterfication reaction. Figure taken from Ferre-D’Amare et al1.
A A A
G G G
A A A
G G G
A A A
G G G
AA AA AA
GG GG GG
26
2.2 Hairpin ribozyme Mg2+ dependence
The first experiments were to ensure that single molecule measurements were
possible using our single molecule setup and that the single molecule data supported well
established biochemical studies. Uncleavable hairpin ribozyme molecules were
synthesized and labelled as described in section 1.7.1 of this report and they were deposited
on surfaces as explained in sec 1.8.1. Shown in Figure 2.3 are sample FRET traces taken
on the TIR with 100ms integration time. As the Mg2+ is decreased from 1mM down to 0.2
mM it is clear that the equilibrium population distribution shifts from the docked to the
undocked state. To the right of these traces are FRET histograms made up of hundreds of
molecules at these buffer conditions which also clearly reflect the trend to the low FRET
undocked state with decreasing Mg2+.
0 20
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
E
app
Time (s)
0 20
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
E
app
Time (s)
Figure 2.3 Uncleavable hairpin ribozyme FRET traces for decreasing [Mg2+]. At the lowest concentration the cartoon states are drawn as a reminder of the conformations the FRET values correspond to.
27
2.3 Overview of cleavage and ligation experiments
The rest of this chapter will present experiments that aim to understand the
enzymatic cleavage and ligation reaction of the hairpin ribozyme. For these studies we will
be working with the natural cleavable ribozyme shown in the table in Figure 1.9. We have
used the short substrate construct which has a 3 base pair stem A such that the cleavage
product will dissociate once the cleavage reaction occurs. And we have used the cleavable
construct with the long substrate which has a 7 base pair stem A which so that on cleavage
the cleavage product remains bound. As mentioned in the previous section metal ion-
induced docking of the loops leads to a large increase in FRET between the fluorophores.
Docking is necessary for the cleavage and ligation reactions to occur. We have carried out
three different types of experiments that are summarized schematically in Figure 2.4.
Mg2+ 3?strand
ligation
cleavage
C
D
[1] [2] [3] [4]
3
5
The simple cleavage experiment. We begin with species [1] in which the truncated
3’-end of the d strand limits the extent of the terminal helix of arm A to three basepairs.
Upon ribozyme cleavage, the resulting 3’ product is rapidly lost by diffusion 14. The
remaining species [2] behaves like a simple junction; we have shown previously that this
exhibits rapid two-state dynamics that are easily distinguishable from those of the complete
ribozyme 15.
The simple ligation experiment. Because species [2] is created by ribozyme action,
a cyclic 2’3’ phosphate remains at the end of the retained 5’ product of cleavage, and this
species is competent for ligation. The a strand of the original species [1] had a dangling
5’ end, giving it unused basepairing capacity. Having created species [2] by ribozyme
action, we introduce a new 3’ strand that can hybridise to form 7 bp with the ribozyme
Figure 2.4 Summary of the constructs used in the cleavage and ligation experiments.
28
product, forming species [3]. This can undergo a ligation reaction, to generate the
covalently closed species [4]. As we shall show below, the dynamics of docking of
species [3] and [4] are easily distinguishable.
Cycling between cleavage and ligation reactions. In a third experiment we begin
with species [4] attached to the surface, and initiate folding and cleavage by addition of
Mg2+ ions. The product of cleavage (species [3]) can undergo ligation back to species [4],
and this interconversion between species [3] and [4] enables multiple cycles of cleavage
and ligation to be observed.
From these experiments we can measure the central conversion rates for cleavage and
ligation reactions directly, free from uncertainties of docking-undocking dynamics and
product dissociation rates.
2.4 Simple cleavage experiment
To measure the overall cleavage reaction we immobilized ribozymes with the short
substrate (species [1]) in a buffer containing 0.5 mM EDTA and lacking Mg2+ ions. We
Figure 2.5 Simple cleavage experiment. The short substrate strand is used and it will dissociate on cleavage. (b) A sample FRET trace is shown and the rate of cleavage measured by the dwell time before product dissociation is shown.
a
b
+ 2 mM Mg2+
Cleavage and product releasec
Lu Ld
Junction dynamics
Cd
Mg2+ Cleavage
Cu
0 100 2000
500
1,000
Fluo
resc
ence
inte
nsity
Time (s)
b
0 2 4 6 8 100.2
0.4
0.6
0.8
1.0
k c,a
pp(m
in−1 )
Mg2+ concentration (mM)
a
b
+ 2 mM Mg2++ 2 mM Mg2+
Cleavage and product releasec
Lu Ld
Junction dynamics
Cd
Mg2+
Mg2+ Cleavage
Cu
0 100 2000
500
1,000
Fluo
resc
ence
inte
nsity
Time (s)0 100 2000
500
1,000
Fluo
resc
ence
inte
nsity
Time (s)
b
0 2 4 6 8 100.2
0.4
0.6
0.8
1.0
k c,a
pp(m
in−1 )
Mg2+ concentration (mM)0 2 4 6 8 10
0.2
0.4
0.6
0.8
1.0
k c,a
pp(m
in−1 )
Mg2+ concentration (mM)
29
then obtained FRET time trajectories of single ribozyme molecules while flowing in
buffers containing various Mg2+ ion concentrations, Figure 2.5a. As was reported
previously for 10 mM Mg2+ 15, addition of the divalent metal ion first induces a docking
transition, observed as an increase in FRET efficiency. Subsequently, cleavage occurs and
the 3’ product dissociates. This dissociation event is marked by the onset of rapid two state
fluctuations arising from the dynamics of the RNA four-way junction. Such RNA junction
dynamics will be studied in detail in section 3.2. But for now to understand Figure 2.5b
consider that without the loop A and B interactions the ribozyme would be expected to
folding very poorly. This poor folding will lead to a destabilized docked state which
account for the very fast fluctuations seen after the cleavage product dissociates. These
junction dynamics become faster at lower Mg2+ ion concentrations, and the two states
cannot be clearly distinguished with the 100 ms integration time used here if the Mg2+ ion
concentration is 2 mM or below Figure 2.5b.
The inverse of the time between Mg2+ ion addition and the emergence of junction
behavior is a measure of the apparent cleavage rate, with the caveat that the observed
behavior is actually the product of several steps. At each Mg2+ ion concentration the
apparent cleavage rate was heterogeneous among molecules with at least two populations,
with the dominant population (> 80%) being faster. The apparent cleavage rate for the
major population (kc,app) increases slightly with Mg2+ concentration Figure 2.5c, after
correcting for molecules photobleached before reaction (~20%) as described 15. The
cleavage rate for the minor population could not be determined due to photobleaching.
Since the 3' product strand should be intimately associated with the ribozyme 16, including
the insertion of G+1 into a pocket in loop B, we expect that the dissociation of the 3’-
product will require prior undocking 17,18. If undocking were slower than ligation, multiple
cleavage and ligation events could occur before undocking (and product release) and the
apparent cleavage rate would be significantly lower than the internal cleavage rate.
Conversely, if undocking were much faster than ligation, a single cleavage event would be
enough for product release and the apparent cleavage rate would closely approximate the
internal cleavage rate. In order to determine the rates of undocking and ligation, we studied
30
a ribozyme with a longer substrate strand so that dissociation of the 3’ cleavage product is
largely prevented by basepairing.
2.5 Cycling between cleavage and ligation
The catalytically competent ribozyme with a longer substrate strand (species [4])
switches between distinctly different docking/undocking kinetics in 1 mM Mg2+ Figure
2.6a. Although the molecules remain stably docked for a majority of the time, at other
times they display rapid docking and undocking transitions, and single molecules are seen
to alternate between these two modes multiple times Figure 2.6b. No such behavior was
observed from non-cleavable ribozymes 15.
The docking and undocking rates within the rapidly fluctuating mode are kCdock
=2.5 (±0.1) s-1 and kCundock,obs=2.3 (±0.1) s-1 Figure 2.6c&d. While it seemed likely that
Figure 2.6 Nondissociatable construct. (a) Cartoon and sample FRET traces from TIR experiments using the long (non dissociable) substrate strand. (b) TIR traces identifying the cleaved state dynamics with a purple bar. The rates from exponential fits (c) are kC
dock =2.5 (±0.1) s-1 and (d) kCundock,obs=2.3 (±0.1) s-1.
0 1 2 3 4 50
100
200
300
Num
ber o
f eve
nts
tCundocked (s)0 1 2 3 4 5
0
100
200
300
Num
ber o
f eve
nts
tCdocked (s)
ed
0 1 2 3 4 50
100
200
300
Num
ber o
f eve
nts
tCundocked (s)0 1 2 3 4 5
0
100
200
300
Num
ber o
f eve
nts
tCdocked (s)
ed
b
0 20 40 60 80 1000.0
0.5
1.0
Time (s)
Eap
p
0 20 40 60 80 1000.0
0.5
1.0
Time (s)
Eap
p
0 20 40 60 80 1000.0
0.5
1.0
Eap
pa
Cleavage
Ligation
Ld Cd Cu
31
cycles of cleavage and ligation produced this complex behavior, we performed experiments
to verify this and assign the states unambiguously.
2.6 Assigning the ligated and cleaved states
First we verified that the stably docked state corresponded to the ligated ribozyme.
To do this ribozymes with the long substrate (species [4]) which had not been previously
exposed to Mg2+ were immobilized on a quartz slide in a buffer containing 0.5 mM EDTA.
When a 1mM Mg2+ solution was flowed into the sample chamber, the ribozymes were
observed to dock, and remain in the docked conformation typically for tens of seconds
Figure 2.7a and b. Since the ribozymes must have been in the ligated form initially, we
assign the stably docked mode to the ligated form. A fraction of molecules exhibited a
period of rapid docking/undocking behavior prior to photobleaching, as observed in the
multiple cleavage-ligation cycling experiment.
Figure 2.7 A simple cleavage experiment. (a) Cartoon of the cleavage reaction steps. (b) The corresponding FRET time trace. The ribozyme initially has no exposure to Mg2+. At the time indicated by the blue arrow a buffer containing 1mM Mg2+ is flown in. The molecule then docks and some time later cleaves as indicated by the region under the purple bar.
a
Cd
Figure 4C
Cu Ld
ligation
Pu
b
0 10 20 30 40 50 600.0
0.5
1.0
Time (s)+3’ strandLigation
Eap
p
Ligationa
Cd
Figure 4C
Cu Ld
ligation
Pu Cd
Figure 4C
Cu Ld
ligation
Pu
b
0 10 20 30 40 50 600.0
0.5
1.0
Time (s)+3’ strandLigation
Eap
p
Ligation
32
We next showed that the bursts of rapid docking and undocking are due to the
dynamics of the cleaved form of the ribozyme. Surface-immobilized ribozymes with the
short substrate (species [1]) were induced to undergo cleavage in the presence of 1mM
Mg2+, and the 3’- cleavage product allowed to diffuse away to generate species [2] (Fig.
2.8a). Lacking a 3’ product, this molecule cannot dock and is in a low FRET state in 1mM
Mg2+ (Figure 2.8 a&b, first few seconds). The junction-like structural transitions of this
species are too fast to be resolved with the100 ms integration time used in this experiment 15. At this point we flowed in a solution containing 1 mM Mg2+ and 500 nM of the long 3’
product. Shortly thereafter we observed fast docking and undocking events followed by
stable docking Figure 2.8. We attribute the time lag between buffer exchange and initial
docking mostly to the time taken for binding the long 3’ product to the ribozyme. Since the
ribozymes are in the cleaved form immediately after product annealing, we conclude that
the rapid docking and undocking is characteristic of the cleaved ribozyme. The rates
determined from the initial rapidly fluctuations, kCdock =2.6 (±0.2) s-1 and kC
undock,obs =2.4 (±
Figure 2.8 Simple ligation experiment. The steps shown in the cartoon of (a) correspond to the FRET time trace below in (b) The ribozyme starts with no substrate strand. When the substrate is added the ribozyme is in the cleaved form (purple bar and box) sometime later it ligates.
0 10 20 30 40 50 600.0
0.5
1.0
Time (s)
Docking
a
b
+ 1 mM Mg2+
Eap
p
Lu Ld
Mg2+
Cd Cu
cleavage
ligation
0 10 20 30 40 50 600.0
0.5
1.0
Time (s)
DockingDocking
a
b
+ 1 mM Mg2+
Eap
p
Lu Ld
Mg2+
Cd Cu
cleavage
ligation
33
0.2) s-1 are comparable to the rates measured in the multiple cycling experiment, further
supporting our interpretation.
After the initial period of fast docking and undocking 49 out of 59 molecules
switched to the stably docked mode before photobleaching, indicating that ligation had
occurred. Of the 59 molecules observed, 13 made a direct transition to the stably docked
state, which we interpret as ligation reactions that occur during the first docking event. This
further confirms our assignment: since the ribozyme spends out 10% of its time in the rapid
docking/undocking mode in steady state, the probability that such a large majority, 46 our
59, would show rapid docking/undocking behavior by random coincidence is extremely
small (10-34 according to binomial distribution). Figure 2.9 shows a cumulative histogram
of the number of docking transitions observed before the stably docked state was achieved
(excluding those photobleached before ligation). A better agreement with the data can be
obtained with a double exponential fit with decay constants of 2.2 and 11 transitions than
with a single exponential, suggesting that the ligation reaction rate is not homogeneous.
The average number of docking events before ligation weighted by relative populations is
6.7.
Figure 2.9 Cummulative histogram of the number of docked transitions observed before ligation.
0 10 20 30 400.0
0.2
0.4
0.6
0.8
1.0
Frac
tion
ligat
ed
Number of docking events
34
2.7 Undocking of the cleaved ribozyme is faster than ligation or
cleavage
The preceding experiments allow us to explain the complex behavior observed from
the ribozyme with the long substrate as shown in Figure 2.6b. The ribozyme in the ligated
state is stably docked but it undocks rapidly once a cleavage reaction occurs. Since the 3’-
cleavage product remains bound in this construct, the ribozyme docks and undocks rapidly
in the cleaved form until ligation occurs. From this experiment we obtain an average time
in the cleaved state of 6.7 s and. From the simple ligation experiment we obtain a value of
5.6 s by multiplying the average number of docking events until ligation (6.7) and the
average time for one docking/undocking cycle (1/2.5 + 1/2.3 s). We can therefore estimate
the apparent ligation rate to be between 1/6.7 = 0.15 s-1 and 1/5.6 = 0.18 s-1 (9 - 11 min-1).
The internal ligation rate (kL), defined as the rate of ligation in a docked ribozyme, is about
twice as large (0.29 - 0.34 s-1), because the cleaved ribozyme spends approximately half of
its time in the docked state Figure 2.11. A more direct estimate of the internal ligation rate
can be obtained by recognizing that the observed rate of undocking of the cleaved form is
actually the sum of the rates of undocking and ligation, i.e. kCundock+kL= kC
undock,obs= 2.3 s-1.
The average number of undocking events before ligation (number of docking events - 1)
gives the ratio of the two rates: kCundock/kL= 5.7. Thus, we obtain kL= 0.34 s-1 (20 min-1) and
a corrected undocking rate kCundock= 2.0 s-1. Since kL < kC
undock, upon docking the molecule
is more likely to undock than to ligate, and typically multiple docking events are needed
before ligation occurs. By the same reasoning once cleavage occurs the molecule is more
likely to undock than to re-ligate back and a majority of cleavage events can be detected as
rapid docking/undocking.
The internal cleavage rate (kC) is 1.0 min-1 (0.017 s-1) in the presence of 1 mM
Mg2+, determined from the multiple cycling experiments. This compares with the apparent
cleavage rate determined from the simple cleavage experiment of 0.60 min-1 (0.010 s-1)
Figure 2.5c. Photobleaching in the multiple cycling experiment will lead to an
underestimate of the time spent in the ligated state, and consequently an overestimate in the
rate of cleavage. The apparent cleavage rate obtained in the simple cleavage experiment
will be close to the internal rate of cleavage since kCundock > kL and kC
undock >> kc,app.
35
Therefore, we favor the rates directly obtained in this experiment, and thus we calculate the
internal equilibrium at 1 mM Mg2+ between cleavage and ligation at 1 mM Mg2+ as Kint =
kC / kL = 0.029.
2.8 Kinetics of the non natural cleavage products
In single molecule studies of the minimal form of the hairpin ribozyme, a 5’ product
that was terminated by a 3’-phosphate was used to simulate the cleaved form of the
ribozyme 18, rather than the natural product that has a terminal 2’,3’-cyclic phosphate,
Figure 2.2. The undocking rates measured for the 3’-phosphate form were on the order of
10-2 s-1, similar to those measured from the non-cleavable ribozyme. In contrast, our studies
of the four-way junction form show that the undocking rate of the natural product of
cleavage is markedly accelerated compared to the ligated state.
In principle, this discrepancy could arise from two sources. The relative docking
stabilities of the ligated and cleaved states may be different between the four-way junction
and hinge forms of the ribozyme. Alternatively, the difference in rates may result from
differences in the chemical nature of the 3’ terminus in different experiments. In order to
distinguish between these two possibilities, we studied two different non-natural products
in the context of the four-way junction form of the ribozyme, where the 5’ product had
either terminal 3’ phosphate or hydroxyl groups. In both cases, we observed that the
undocking was almost an order of magnitude slower for these non-natural products
(kCundock=0.28~0.34 s-1, Figure 2.9) compared to the natural product (kC
undock=2.3 s-1). In
addition, the rates of docking for these non-natural products were elevated more than two-
fold. This suggests that the backbone continuity alone can not account for the striking
acceleration of undocking in the cleaved ribozyme and that even the seemingly minor
alterations of the non-natural products can affect the structural dynamics substantially.
36
0 2 40
20
40
60
80
100
120
N
umbe
r of e
vent
s
tOHundocked
(s)
0 2 40
10
20
30
40
Num
ber o
f eve
nts
tPO4
undocked (s)
0 20 40 600
20
40
60
Num
ber o
f eve
nts
tOHdocked(s)
ba
c d
0 20 40 600
10
20
30
N
umbe
r of e
vent
s
tPO4
docked (s)
B
PO4
B
OH
OH
PO4
kOHundcock=2.8 +-0.03s-1kOH
Dcock=6.8 +-0.5s-1
kPODcock=5.0 +-0.6s-1
kPOundock=0.34 +-0.04s-1
0 2 40
20
40
60
80
100
120
N
umbe
r of e
vent
s
tOHundocked
(s)
0 2 40
10
20
30
40
Num
ber o
f eve
nts
tPO4
undocked (s)
0 20 40 600
20
40
60
Num
ber o
f eve
nts
tOHdocked(s)
ba
c d
0 20 40 600
10
20
30
N
umbe
r of e
vent
s
tPO4
docked (s)
B
PO4
B
PO4
B
OH
B
OH
OHOH
PO4PO4
kOHundcock=2.8 +-0.03s-1kOH
Dcock=6.8 +-0.5s-1
kPODcock=5.0 +-0.6s-1
kPOundock=0.34 +-0.04s-1
2.9 Dependence of the enzyme reaction on pH
For a group to function as a catalyst by acid base catalysis it must have the ability to
act as and acid and a base. Such a characteristic can be looked for in a group’s pKa value
which is defined in Equation 2.1. Consider a group that can loose a proton according to
−+ +→ AHHA
Equation 2.1
Figure 2.10 Non ligatable mutants docking and undocking rates were calculated to compare to the natural cleaved ribozyme rates.
37
The pKa value is defined as
[ ][ ][ ]
[ ][ ]
+=
=
−−+
HAApH
HAAHpKa 1010 loglog
As can be seen in Equation 2.2 when the pH equals the pKa, that group can function
as an acid or a base. Nucleic acids have pKa values that are generally too high or low to
allow them to function in acid base catalysis at regular pH. (pKa: G-9.2, C-4.2, U-9.2, A-
3.5) But in the complicated folded structure of the ribozyme enzyme pocket it is possible
for the pKas of some nucleic acids to be perturbed.
To check for this we examined the dependence of the ligation rates upon pH by
performing the multiple cycles experiment. Docking and undocking within the cleaved
form are significantly faster than ligation at all pH values. While the apparent ligation rate
peaks at pH 7, the internal ligation rate, obtained by dividing the apparent ligation rate by
the fraction of time spent in the docked state, is independent of pH above pH 7.5, but
reduces at lower pH values, being approximately three-fold slower at pH 6. The data
(Figure 2.11a) are consistent with a sensitivity of the ligation reaction to a group titrating
with an apparent pKa of 6.2±0.1.
a b
5 6 7 8 9 100
0.2
0.4
0.6
C leavage rate
pH
k obs (m
in−1
)
p
6 7 8 9 100.0
0.1
0.2
0.3
Internal ligation rateApparent ligation rate
k lig(s
− 1)
pH
a b
5 6 7 8 9 100
0.2
0.4
0.6
C leavage rate
pH
k obs (m
in−1
)
p
6 7 8 9 100.0
0.1
0.2
0.3
Internal ligation rateApparent ligation rate
k lig(s
− 1)
pH6 7 8 9 10
0.0
0.1
0.2
0.3
Internal ligation rateApparent ligation rate
k lig(s
− 1)
pH
Equation 2.2
Figure 2.11(a) Single molecule internal ligation rates versus pH. (b) Bulk measurement of the cleavage rate versus pH.
38
We have also measured the pH dependence of the cleavage reaction in bulk
solution Figure 2.11b, under conditions that are closely similar to those used in the single-
molecule experiments, where we know that docking and undocking are not rate limiting.
These reactions required two rates to describe the data. A clear pH dependence was
observed for the fast cleavage rate, consistent with the titration of a group with an apparent
pKa of 6.3 ± 0.1. The slower rate of cleavage (~ 0.02 min–1) does not exhibit the same pH
dependence, suggesting that the reaction of some molecules may be limited by a
conformational change.
2.10 Conclusions
The internal cleavage and ligation reactions have been observed directly for a
ribozyme for the first time. This opens up exciting new opportunities to carry out single
molecule enzymology in the most direct way where the effects of mutations or solution
conditions on the internal chemistry can be looked at without complications arising from
conformational degrees of freedom.
For the hairpin ribozyme this direct observation was possible because the cleaved
and ligated forms can be clearly distinguished by single-molecule spectroscopy, based on
their distinct structural dynamics. This enables us to describe the kinetic pathway for the
reaction of the natural form of the hairpin ribozyme.
The ligation rate has been estimated from two separate experiments. In the simple
ligation experiment, we found that the average duration of the cleaved state was 5.6 s,
giving an apparent ligation rate of 10 min-1 in 1 mM Mg2+ at 20 °C. This is similar to that
estimated by Fedor and colleagues in 2 mM Mg2+ at 30 °C (9.2 min-1) 19 as well as in the
intracellular conditions of yeast (4 min-1) 20. The internal ligation rate of kL = 20 min-1 (0.34
s-1) is obtained after taking into account the proportion of time the cleaved molecule spends
in the docked state.
39
The simple cleavage experiment gave an apparent cleavage rate of 0.60 min-1
(0.010 s-1) in 1 mM Mg2+ at 20 °C. In this experiment the apparent observed lifetime of the
ligated state includes undocking and product dissociation after cleavage. However, product
dissociation is known to be rapid, and we have shown that the undocking rate is two orders
of magnitude faster than cleavage, so these later steps do not significantly contribute to the
observed rate. Consequently, this cleavage experiment gives the best estimate of the
internal cleavage rate. This cleavage rate is very similar to the apparent cleavage rates that
were estimated by Fedor and coworkers in 2 mM Mg2+ at 30 °C (k = 1.3 min-1) 19 as well
as in the intracellular conditions of yeast (k = 0.7 min-1) 14. It is considerably lower than
the internal cleavage rate deduced for the minimal form (12 min-1) 18; however in this
experiment and in a subsequent experiment with mutants 21 the cleavage and ligation
reactions could not be observed directly and their rates were estimated using a model with
several assumptions that were not independently verified. For instance it was assumed that
molecules with highly heterogeneous docking/undocking kinetics share a single cleavage
rate and a single ligation rate. However, our data show that both cleavage and ligation rates
are heterogeneous. It was further assumed that docking/undocking kinetics measured from
non-cleavable mutants and non-ligatable mutants are identical to those of catalytically
competent ribozymes. Again our data show that this assumption is questionable because we
observed much reduced undocking rates, by at least a factor of 10, from non-ligatable
ribozymes. This may explain the much lower undocking rate observed for the cleaved
minimal ribozyme in which the ligation is inhibited via chemical substitutions18,21. From
the measured rates for cleavage and ligation we obtain an internal equilibrium constant Kint
= 0.010/0.34 = 0.029, showing that the equilibrium is significantly biased towards ligation.
Our results show that the dynamic processes of docking/undocking are different for
the natural product of cleavage compared to alternatively-terminated analogs. Only the
product with a cyclic 2’3’-phosphate exhibits the docking/undocking characteristics we
have described above. This raises the question of why the natural product should differ so
markedly in its dynamic properties. The hairpin ribozyme has been crystallized in the
precursor form (non-cleavable ligated), in a non-natural product form (5’ product
terminated by a 3’-OH), in the natural product form, and as a transition state analogue 16,22.
40
These forms are almost identical, with one major difference in the stereochemistry of the
ribose ring at the A-1 position. Sugar pucker in the cyclic phosphate-containing product
was found to be uniquely altered in this form 16. It is possible that this leads to the observed
altered dynamics, but this possibility will need to be explored by further experiments.
Earlier single molecule studies by Zhuang et al 18 led to the proposal that the
structural dynamics, not chemistry, are rate-limiting for the minimal hinged form of the
hairpin ribozyme. We have shown previously that the presence of the four-way junction in
the natural form of the hairpin ribozyme leads to a rate of docking that is two to three
orders of magnitude higher than that for the minimal form 15. Combining this with our
present work that shows that the undocking of the cleaved molecules is also significantly
faster than ligation or cleavage, we can conclude that the reaction of the natural ribozyme is
limited by chemistry, not by structural dynamics.
41
3. Hairpin ribozyme intermediate folding state
3.1 Background
The hairpin ribozyme must undergo significant conformational changes to attain the
right enzymatic binding pocket. The folding path that leads to this specific structure is as
important and complex as the enzyme reaction itself. The known starting points, the
docked and undocked conformation, have been solved by NMR and x ray crystal6
structures. Comparison of the docked and undocked structures (Figure 3.1a and b)
indicates that there must be numerous base pairings within the loops being broken and
different ones formed between the loops. The interactions that promote and stabilize the
docked state from the crystal structure are a G+1-C25 Watson Crick base pair, a ribose
zipper, and a U42 binding pocket, Figure 3.1b. The loop-loop interaction is essential for
the ribozyme activity leading to a 105 fold acceleration of site-specific cleavage and
a b
Figure 3.1 (a) NMR structures of the undocked loops. (b) Crystal structure of the docked ribozyme. The docked structure shows the C25-G+1 base pair and to the sides are the U42 binding pocket and the ribozse zipper
42
ligation reactions. Ensemble FRET studies have shown that the two loops are brought into
close proximity at sub-millimolar Mg2+ concentrations17,23. The folded ribozyme has the
neighboring helical arms coaxially stacked in pairs, A on D and B on C.
Single molecule studies had previously been done using a minimal form of the
ribozyme that is missing the CD arms, hence no junction, and has only the two loops.
While the minimal form without arms C and D can still catalyze the cleavage reaction9, its
folding requires three orders of magnitude higher Mg2+ concentration8,23,24, and the internal
equilibrium between cleavage and ligation is perturbed25. The poor folding of this
junctionless structure when compared to the full ribozyme inspires the question of how the
junction structure affects the ribozyme folding mechanism.
To study the effect of the junction we will be using several constructs. Firstly the
enzymatic activity of the ribozyme will be deactivated by mutating the 2’OH group to a
2’H thereby shutting down the cleavage mechanism shown in Figure 2.2. This construct
has the junction and loops but no cleavage activity and will be called the uncleavable
ribozyme. We have also worked with several mutants but here we will only discuss the
C25U mutant, which has the cytosine at position 25 mutated to a uracil. From the previous
discussion this construct will not be able to form the Watson Crick base pair shown in
Figure 3.1b and hence we will expect an ribozyme with a less stable docked state. Finally
we will work with a riobzyme that has the two docking loops base paired called the 4H
junction. This construct will allow us to study the pure junction, separate from both the
loop-loop interactions and the enzyme activity. Both construct sequences are shown in
Figure 1.9. 26
3.2 Junction dynamics
Single-molecule time records of the 4H junction at various Mg2+ concentrations
exhibit fundamentally different structural dynamics. The 4H junction has been proposed to
convert from a perpendicular to an antiparallel structure with increasing Mg2+
43
concentration 17. Therefore, we expected that the 4H junction would exhibit anti-correlated
changes in the dwell times of the two states with increasing Mg2+ concentrations.
Strikingly, single-molecule studies revealed a qualitatively different behavior. The 4H
junction underwent rapid fluctuations between two states with Eapp~ 0.5 and ~0.15 that we
refer to as UP (proximal) and UU (undocked) respectively, and the rates of fluctuations
increased for decreasing Mg2+ concentration Figure 3.2. Clearly the FRET efficiency of the
higher FRET state is significantly lower than that of the ribozyme. The relative populations
of the two states remained approximately constant as Mg2+ concentration was varied (≤
10mM) (figure S2), in stark contrast to the behavior of the ribozyme. Therefore the
dynamics cannot be synchronized by changing the Mg2+ concentration, and stopped-flow
studies in this Mg2+ concentration range do not reveal changes in FRET. It is very likely
that the proposed perpendicular structure of the 4H junction is in fact due to time-averaging
of the two conformations. At Mg2+ concentrations ≥ 20mM, a bias toward UP is observed
(figure S2), consistent with the previous ensemble studies that indicated the formation of an
antiparallel structure17.
Figure 3.2 A side by side comparison of the (a) ribozyme folding kinetics and the (b) 4H junction folding kinetics as [Mg2+] is varied.
0 10 20 30
Time (s)
5mM Mg2+
20mM Mg2+
50mM Mg2+
UD
UP
b 4H junction 20 °C 50 ms bin
0 20
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
E
app
Time (s)
1mM Mg2+
0.5mM Mg2+
0.2mM Mg2+
0.1mM Mg2+
F
U
4H junctionribozyme
a ribozyme 25 °C 50 ms bin
0 10 20 30
Time (s)
5mM Mg2+
20mM Mg2+
50mM Mg2+
UD
UP
b 4H junction 20 °C 50 ms bin
0 20
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
E
app
Time (s)
1mM Mg2+
0.5mM Mg2+
0.2mM Mg2+
0.1mM Mg2+
F
U
4H junctionribozyme
a ribozyme 25 °C 50 ms bin
5mM Mg2+
20mM Mg2+
50mM Mg2+
UD
UP
b 4H junction 20 °C 50 ms bin
0 20
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
0.0
0.5
1.0
E
app
Time (s)
1mM Mg2+
0.5mM Mg2+
0.2mM Mg2+
0.1mM Mg2+
F
U
4H junctionribozyme
a ribozyme 25 °C 50 ms bin
44
Below 1mM Mg2+, the fluctuations of the 4H junction become too fast to be clearly
resolved and a correlation analysis was used to determine their rates27 Figure 3.3. A
negative cross-correlation between ID and IA was observed and was fit well by a single
exponential decay in all cases, consistent with anti-correlated fluctuations of ID and IA due
to FRET changes.
The cross-correlation time became longer as Mg2+ was elevated, finally merging
with the fluctuation time scales measured via dwell time analysis at higher Mg2+
concentrations Figure 3.4. The fluctuation rate has a power law dependence on Mg2+
concentrations. We conclude that the 4H junction fluctuates between the UU and UP states
over a wide range of Mg2+ concentrations.
Figure 3.3 (a) Fits to the cross correlation of the 4H junction traces IA and ID. (b) Plot of these rates.
0 25 50 75 100
-15
0
∆t (ms)
0.1mM Mg2+ τ =0.6ms0.3mM Mg2+ τ =4.6ms0.5mM Mg2+ τ =8.1ms1.0mM Mg2+ τ =24msC
ross
Cor
rela
tion,
CC
(∆t)
0.1mM 1mM 10mM1
10
100
1000
kD
->P +
kP
->D (s
-1)
Mg2+ concentration
0 25 50 75 100
-15
0
∆t (ms)
0.1mM Mg2+ τ =0.6ms0.3mM Mg2+ τ =4.6ms0.5mM Mg2+ τ =8.1ms1.0mM Mg2+ τ =24msC
ross
Cor
rela
tion,
CC
(∆t)
0.1mM 1mM 10mM1
10
100
1000
kD
->P +
kP
->D (s
-1)
Mg2+ concentration
45
0 20 40 60 80 100
-2
0
∆t (ms)C
ross
Cor
rela
tion,
CC
(∆t)
0.1mM Mg2+ τ=1.0ms0.3mM Mg2+ τ=9.3ms0.5mM Mg2+ τ=15ms
3.3 Proximal state in the natural ribozyme
Since the UP state brings the A and B arms (loop-carrying arms in the ribozyme)
into close proximity we hypothesized that the UP state is an intermediate that precedes the
folding of the ribozyme. We now show that the unfolded state of the ribozyme exhibits
fluctuations quantitatively similar to the 4H junction and that the folded state of the
ribozyme occurs by way of the UP state.
To explore the ribozyme dynamics within its unfolded state, we performed a cross-
correlation analysis of the unfolded data segments at Mg2+ concentration below 1mM (the
ribozyme is mostly folded at Mg2+ concentrations ≥ 1 mM). The negative cross-correlation
between ID and IA indicates FRET fluctuations between two states, and the decay times
obtained by single exponential fit are within a factor of two of the decay times of the 4H
junction under the same conditions Figure 3.4. Furthermore, the Eapp, histogram of a single
molecule in the unfolded segments binned at 3ms can be fitted by two Gaussian
distributions, centered near 0.15 and 0.43, Figure 3.5, closely corresponding to those of UU
and UP for the 4H junction. We conclude that the unfolded ribozyme fluctuates between
two well-defined states very similar to UU and UP of the 4H junction (henceforth called UU
Figure 3.4 Cross correlation plots and the corresponding fit to the low FRET state of the uncleavable ribozyme.
46
and UP for the ribozyme as well). The existence of three distinct states in the hairpin
ribozyme (UU, UP and D) is a new finding afforded by the sensitivity of single-molecule
measurements. Previous time-resolved ensemble FRET measurements have been
interpreted using a two-state folding model24.
These results provide unique insight into the mechanism of ribozyme folding. The
rapid conformational exchange within the unfolded state (UU ↔ UP) repeatedly brings the
two loop elements into proximity, increasing the probability of interaction between them
and thus folding. As mentioned in Section 3.1 loop-loop interaction involves numerous
specific contacts22, and the local conformation of the loops in the folded ribozyme is
significantly altered from that in the isolated loops11,12. It will therefore require multiple
conformational adjustments to achieve the active state. In fact, the UU ↔ UP transition
occurs at a rate of ~100 s-1 in 0.5 mM Mg2+, whereas the folding is significantly slower, ~ 3
s-1. The folding under these conditions must be limited by the conformational changes
involved in loop-loop interaction rather than the junction dynamics.
3.4 Proximal state in the C25U mutant
This model predicts that the UP state is an obligatory intermediate in a sequential
folding pathway (UU ↔ UP ↔ D). Since the large rate differences between UU ↔ UP and
UP ↔ D make it difficult to test the existence of the UP state in the uncleavable ribozyme,
Figure 3.5 Histogram of the low FRET state of the uncleavable ribozyme.
0.0 0.2 0.4 0.6 0.8 1.00
50
100
150
# of
dat
a po
ints
Eapp
47
we studied a sequence variant (C25U) that is impaired in the folding8. The crystal structure
reveals that G+1 is extruded from loop A and base pairs with C25 of loop B (Figure 3.1b).
This pairing is perturbed in C25U, destabilizing the D state. Indeed, as shown in Figure
3.6a and b, C25U clearly exists in three states corresponding to UU, UP and D.
To our knowledge this is the first observation of structural transitions in individual
molecules between three states in equilibrium, allowing several unique analyses. For
instance, we compared the dwell times of UP based on the previous and next states visited
and found no significant difference within each molecule. Therefore, we can rule out the
existence of an alternative intermediate that cannot be distinguished by the fluorescence
signals, but that possesses very different transition rates. A similar analysis permits us to
investigate if UP is a necessary intermediate. We have observed three-state fluctuations
under many different conditions (2~20mM Mg2+, 7~22 °C) and single-molecule time
records clearly demonstrate that direct transitions between UU and D are very rare. Even
when a transition from D to UU appears abrupt (Figure 3.6b, dashed rectangle) a close
inspection with smaller bin time (3 ms vs. 9 ms, inset) can show that the molecule visits UP
in between (Figure 3.6b inset). Out of 36 transitions from UU to D and D to UU for the
molecules shown in Figure 3.6a, four appeared to be skipping UP within 10 ms time
resolution, whereas the 96 ms average lifetime of UP (Figure 3.6c) predicts 10% of them
will be shorter-lived than 10 ms. Likewise, among 140 transitions observed from 12
molecules at another condition, 25 (18%) showed less than 6 ms duration while the 28 ms
lifetime of UP predicts 19% Figure 3.6 It is therefore highly probable that UP is a necessary
intermediate in the ribozyme folding.
48
0.0 0.1 0.2 0.30
50
# of
eve
nts
Time (s)
τ=28 ms
12 moleculesC25U
2mM Mg2+
15 °C
0.0 0.1 0.2 0.30
50
# of
eve
nts
Time (s)
τ=28 ms
12 moleculesC25U
2mM Mg2+
15 °C
1 moleculeC25U
0.0 0.1 0.2 0.30
5
10
Time (s)
# o
f eve
nts
τ=96 ms5mM Mg2+
22 °C
b
0 100 200
# data points8 9 100.0
0.5
1.0
Eap
p
T im e (s)
14 15 16 170.0
0.5
1.0
Eap
p
Time (s)0 50 100 150
# data points
C25U5mM Mg2+
22 °C
C25U2mM Mg2+
15 °C
a c
d
UD
UD
UP
UP
F
F
3.5 Kinetic heterogeneity
Another aspect of RNA folding that has emerged from single molecule studies is
the variation of folding and unfolding rates throughout an identical sample population.
Even though there is an average trend towards the docked state with increasing magnesium.
For any given magnesium concentration there is a variation in the kinetcs amongst the
population. In Figure 3.7 this is shown for the uncleavable hairpin ribozyme at 0.5mM
Mg2+. In general each ribozyme within a population in the identical surface environment
demonstrates a relatively different docking and undocking rate. These differences among
the population are what we refer to as the ribozyme’s kinetic heterogeneity. In addition to
the different kinetic regimes amongst ribozymes another puzzling aspect is the lack of
switching between these different kinetic regimes within a given time trace which is known
as the single molecule memory.
Figure 3.6. Two sample FRET histograms obtained from ribozymes that have their folding impaired by use of a C25 mutation to a U25 clearly show a the existence of the intermediate proximal state. a. Is at 5mM Mg, b. at 2mM Mg. The inset in (b) shows transition that looks direct from D to UU actually passes through the intermediate when viewed with better time resolution.
49
0 2 0 4 0 6 0 8 00 . 0
0 . 4
0 . 8
1 . 2
0 2 0 4 0 6 0 8 00 . 00 . 40 . 81 . 2
0 2 0 4 0 6 0 8 00 . 0
0 . 4
0 . 8
1 . 2
X A x i s T i t l e
0 2 0 4 0 6 0 8 00 . 0
0 . 4
0 . 8
1 . 2
0 2 0 4 0 6 0 8 00 . 0
0 . 4
0 . 8
1 . 2
Time (s)
FRE
TFR
ET
FRE
TFR
ET
FRE
T
This existence of kinetic heterogeneity and the memory effect suggests that the
hairpin ribozyme has a very rugged energy landscape with many local minima separated by
large activation energies. Such a rugged energy landscape would lead to the observation of
kinetic regimes that represent local minima rather than global minima. But from the
ergodic hypothesis one would expect that given enough time a molecule would sample all
minima and eventually reach the global minimum.
Figure 3.7 Single molecule traces all taken from the same data set at 0.5mM Mg.
50
3 0 6 0 9
Time (s)FR
ET
t1 t6t2 t4t3 t5 t7 t9t8
1τ 8τ7τ6τ5τ4τ3τ2τ 9τ 10τ
∑=N
iidock t
Nt 1
∑=M
kkundock M
t τ1
0.1 1 100.1
1
10
< t un
dock
> (s
)
< tdock> (s)
Uncleavable ribozyme0.5mM Mg2+
a
b
0.1 1 100.1
1
10
< t un
dock
> (s
)
< tproximal> (s)
c4H junction 100mM Mg2+
To characterize statistically significant heterogeneities in the docking and
undocking rates among individual ribozymes we used heterogeneity plots, Figure 3.8.
Average dwell times of D and U states were obtained from each molecule and a scatter plot
Figure 3.8 Characterizing the heterogeneity from a single molecule data set. (a) The dwell times of each state from a given time trace of a single molecule are found. (b) From these times an average dwell time in the docked and undocked state is calculated. Each circle in (b) represents the average dwell time for a single trace. The heterogeneity plot shown is for 125 uncleavable hairpin ribozyme molecules at 0.5mM Mg2+. (c) The heterogeneity plot for 62 molecules of 4H junction at 100mM Mg2+.
51
shows up to a 50-fold variation for both. For comparison in Figure 3.8 we show
heterogeneity plots for both the uncleavable ribozyme at 0.5mM Mg and 50ms time
integration and the 4H junction at 10mM Mg and 50ms time integration. The 4H junction
exhibits a much narrower distribution in the rates. This suggests that the heterogeneity of
the ribozyme arises mostly from the loops, possibly due to their sub-structures18. There are
many other mutant forms of the ribozyme that we have studied. Previous groups had
studied the two way minimal form of the ribozyme. Interestingly this molecule had
heterogeneity only in its undocking rate while its docking rate showed four different values.
Interestingly, unlike the minimal hinged form (only loops A and B) that showed
heterogeneity only in the D state dwell times18, we observe heterogeneity in the dwell times
of both D and U states. It is likely that this difference lies in the rate limiting step for
folding. The junction efficiently juxtaposes the loops such that they are primed for
interaction; the formation of the correct loop-loop contacts is rate-limiting. In the absence
of the junction the encounter between the loops becomes limiting for the folding, and the
effects of the heterogeneity are only observable in the reverse reaction. Indeed, the
dominant component in the folding rate of the natural ribozyme is ~ 3 s-1 at 0.5mM Mg2+,
three orders of magnitude faster than the folding rate measured for the minimal form in the
presence of a much higher Mg2+ concentration (12mM) 18.
0.1 1 100.1
1
10
<tun
dock
> (s
)
<tdock> (s)0.1 1 100.1
1
10
<tun
dock
> (s
)
<tdock> (s) 0.1 1 100.1
1
10
<tdock> (s)
<tun
dock
> (
s)
Cleaved ribozyme1mM Mg2+
Cleaved ribozyme5’ OH 1mM Mg2+
Cleaved ribozyme5’ PO4 1mM Mg2+a b c
Figure 3.9 Heterogeneity is not due solely to the backbone cleavage state. (a) The heterogeneity plot from finding the dwell times in the cleaved state regions of the FRET time traces. (b) The heterogeneity plot from the non ligatable construct with an ‘OH group off the 5’ end of the cleavage site. (c) The heterogeneity plot from the non ligatable construct with an ‘PO4 group off the 5’ end of the cleavage site.
52
We had originally aimed to find a variable that could control the amount of
heterogeneity. Both of the mutants C25U and G+1A did not show an obvious reduction in
heterogeneity. Taking data for long time spans, adding denaturants such as urea or
formamide did not significantly affect the memory of the molecules. The cleaved construct
though did show a marked decrease in the kinetic heterogeneity as shown in Figure 3.9A.
The heterogeneity disappears as shown in the distribution of average docked and undocked
times for 62 molecules. More surprisingly the nick alone is not responsible for the
decrease in heterogeneity. With both the 5’ OH and 5’PO4 permanently cleaved samples
the heterogeneity remained Figure 3.9b and 3.9c.
The relative populations of the three states vary significantly among C25U
molecules indicating the molecular heterogeneity in the stability of the D state as
previously reported for the minimal form of the ribozyme18.
The importance of the junction for the hairpin ribozyme has already been well-
established23-25,28. Our work provides the actual mechanism: the structural dynamics of the
junction, rather than its static structure, promotes rapid active site formation due to the
spontaneous fluctuations between the two states of the junction, UD and UP. The ribozyme
exploits the frequent encounters between the two loops in UP to achieve the D state. Single-
molecule spectroscopy uniquely provides information on the previous and subsequent
history of a given state, allowing us to conclude that the UP state is an obligatory
intermediate in the formation of the ultimate D state. The example of the hairpin ribozyme
shows the important role of a helical junction in the efficient, correct folding of a functional
RNA molecule. It is very likely that the branched helical structures found in many RNA
molecules, such as ribosomal and splicesomal RNA, have been optimized to utilize not
only static structures but also their structural dynamics.
3.6 Conclusions
Using smFRET assays we were able to resolve that the 4H junction previously
proposed as having a perpendicular conformation from bulk studies was actually rapidly
53
switching two conformers UP (proximal state) and UU (undocked state). These two
conformers were then shown to have relevance for the natural ribozyme and explain the
vast folding enhancement seen when the junction structure is included in the ribozyme.
After finding the UP state in the 4H construct we were motivated to look for it
within the natural ribozyme. Using high time resolution we were able to see this third state
in FRET histograms of the UD state of the ribozyme and through cross correlations of the
UU FRET time signal. From these studies we were able to conclude that UU is actually
made up of an additional state Up and hence the hairpin ribozyme folds through an
intermediate state. This intermediate state leads to rapid conformational fluctuations
between this junction and the undocked state, thus bringing the interacting loops A and B
into close contact very often. This mechanism is absent in the two way hinged construct
and hence that minimal ribozyme docks with a much. The ribozyme docking occurs only
thus explaining why the junction conformer is such a poor docking construct. The repeated
juxtapositions of the loops accelerate docking by three orders of magnitude compared to
the minimal form of the ribozyme 18.
Because the natural ribozyme moves very rapidly from the proximal to the docked
state we were not able to see the proximal state directly at higher time integration. But
through a mutation that destabilized the docked state (cytosine mutated to uracil) we were
able to see the proximal state directly.
The existence of heterogeneity within the kinetics of the ribozyme was seen
previously in the minimal form of the ribozyme. Without the junction the ribozyme
exhibits heterogeneity only in the undocking rate and the docked rate was seen to originate
from four states. But with the inclusion of the junction structure this heterogeneity is
greatly amplified. We attribute this enhancement in the heterogeneity to be due to the
enhanced speed that the loops come into contact with each other in the presence of the
junction. With this greater speed there is significantly less time for the loop interactions to
equilibrate and hence many new docked subpopulations can arise. The puzzling point also
seen also in the hinged form remains, that of the single molecule memory. Though most
54
molecules sample the unfolded/proximal state 0.5mM Mg2+ where they potentially could
rearrange into a new slightly different conformations and hence exhibit different kinetics
they do not seem to do that. Instead they retain a memory of the docked state they
originated from. This point has led us (Chapter 5) to develop experiments that combine
force with FRET in an effort to perturb the kinetics.
Additionally whether or not this rugged energy landscape is true in vivo too is an
interesting question. In vivo there could be chaperone proteins that lead to only one type of
folded molecule. This is a topic that will be pursued in the future in our lab.
55
4. Combining confocal and optical tweezer microscopes
4.1 Background
For over ten years researchers have been innovating standalone optical tweezer and
single molecule FRET techniques to tackle new biological systems. But in recent years
there has been much interest in combining the two techniques. There are many biological
systems where combining the two techniques would be of considerable interest. As will be
discussed in more detail in Chapter 5 questions about the responses of biopolymers and
biomotors to force are all driving efforts to merge the two technologies into one
microscope.
The separate technologies are well established. The optical trapping technique
relies on using laser light to trap micron sized particles that are attached directly or through
tethers to the biological molecules of interest. Assuming a taut tether the offset of the bead
from the optical trap focal spot indicates the force the molecule feels. Optical trapping then
0.0 0.5 1.0 1.5 2.0 2.50.0
0.2
0.4
0.6
0.8
1.0
FRE
T
R/R0
0.0 0.5 1.0 1.5 2.0 2.50.0
0.2
0.4
0.6
0.8
1.0
FRE
T
R/R0
0.0 0.5 1.0 1.5 2.0 2.50.0
0.2
0.4
0.6
0.8
1.0
FRE
T
R/R0
R
ba
F=0
F=-kx
Figure 4.1 Optical tweezer and FRET distance measurements. a. The trapping potential is harmonic so the force on the bead, and hence the molecule, scales linearly with the offset distance, x. b. The FRET measurement is highly sensitive to distances near where R=R0. The red circle indicates roughly this region, with the pink lines showing the FRET range and the R/R0 range the circle corresponds too. Thus a small measurable change in FRET (~0.2) can be used to indicate a small distance change (~0.5-2nm).
56
relies on identifying nanometer positioning of the bead relative to the trap center. FRET, as
discussed in Chapter 1, is used to measure the distance change of two labeled points of a
molecule. The fluorescence emission of one of the dyes, the acceptor, is very sensitive to
its distance, R, from the other dye, the donor, as described by Equation 1.10,
FRET=1/(1+R/R0)6 , where R0 is the Forester radius of the dye pair. This expression
indicates how extremely sensitive to distance the FRET value is when R~R0. This sensitive
region is indicated with the red circle in Figure 4.1b. With a good FRET detection setup
distinguishing FRET levels of ~0.2 is tenable and corresponds to distinguishing distances
changes of around 0.5-1nm. A microscope that successfully combines the two techniques
would be able to apply a force and still achieve nanometer distance resolution through the
FRET signal allowing a relatively simpler (in calibration, equipment and monetary costs)
optical tweezer setup. While at the same time gaining access to probing distance changes
distinct from the tether attachment point and as will be discussed later achieving sensitive
distance resolution at low extension forces.
The first experiments that successfully combined fluorescence detection with
trapping capabilities were done by the Yanigida lab29,30. Their setup involved a double
optical trap that was used to support a track molecule (DNA or filament) and they used TIR
illumination to observe a biomolecule move along the track. Using a track of lambda DNA
they observed fluorescent labeled RNA polymerase move along it30. Using the same setup
they also watched unlabelled myosin move along a suspended track of actin through the
turn over of fluorescently labeled ATP29. Neither system was sensitive enough to observe
FRET, the main difficulty being the separatation of the high intensity trapping laser which
was about ten orders magnitude larger than the fluorescence signal. But these experiments
paved the way for future studies combining the two techniques. Attempts were made to
improve the background by passing the wide field emission light through a pinhole such
that the only light collected was from a very small area in the sample plane31. In this setup
again they wanted to maintain a coincident detection and trap laser so they could avoid
using a long tether. This though left a significant in place a significant photobleaching
path of the dyes as discussed below.
57
The most difficult challenges for combining the optical trap technique with the
FRET technique is maintaining the long lifetimes of the probes and minimizing the
background. An effect called enhanced photobleaching 32 becomes a very significant non
fluorescent deexcitation path that leads to destruction of the dye. The phenomenon occurs
when the fluorophore is in the presence of the excitation laser and the trapping laser. As
described in section 1.3 an electron in the ground state absorbs a high energy excitation
photon and then moves to the excited singlet state S1. For the brief time the electron
remains in this state the high intensity trap light will increase its probability of absorbing a
1064 photon and jumping to a higher excited singlet state Sn. In this state there is a much
greater probability for the loosely bound electron to ionize and the dye then to be in a
nonfluorescent state.
One solution to the enhanced photobleaching problem was to temporally separate
the coincident trap and excitation laser2. This was accomplished through AOD modulation
of the excitation and trapping beams. In our system we will avoid the large infrared to
532nm laser signal and the enhanced photobleaching problem by spatially separating the
beams. This will be a key design feature of our setup. The separation will be
accomplished by applying the force through a lambda DNA tether that is about 16.5um
long. This tether will be floppy rather than the stiff short DNA tethers the previously
discussed groups opted for. This choice of this tether will give us a trap capable of high
spatial resolution for a low applied force. This chapter will discuss in detail the design,
calibration, and operation for this microscope that was designed principally by Sungchul
Hohng.
Figure 4.2 Enhanced photobleaching. Absorption of a photon in the near infrared when the dye is in the excited singlet leads to a transition to an unstable state Sn that is easily ionizable. This figure was taken from Brau et al2.
58
4.2 Setup
The overall setup design is shown in Figure 4.3. The design keeps the IR trap
stationary while the confocal focal spot can be moved within the sample plane by a
deflecting the piezo mirror. A piezo sample stage is also necessary for calibrations and its
movement from the molecule tether point will determine the amount of force applied. Both
the piezo stage and mirror were purchased from PI instruments. A 1W 1064nm diode laser
(Crystal Laser) is used at full power for trapping. A 30mW 532nm diode laser (TECGL) is
used at about 8uW power for confocal excitation. The objective is a 100x super apo 1.4
NA objective mounted on an Olympus 1X71 microscope.
The confocal detection system is identical to that described in section 1.5. The
excitation though will be different. The excitation light will need to be separated from the
Figure 4.3 Schematic of the combined confocal and optical tweezer microscope. The abbreviations D: dichroic, L: lens, P:pinhole, M: mirror. Figure courtesy of Sungchul Hohng.
59
detection light because of enhanced photobleaching as discussed in the previous section.
This is accomplished by steering the confocal beam by a piezo mirror deflection angle and
then passing it through a 1:1 telescope. As shown in Figure 4.4 the telescope works by
translating the angular rotation of the piezo, θ∆ , into a displacement of in the focal plane
by the objective.
f
θ∆
θ∆−=∆ obfx 2
ff
θ∆
θ∆−=∆ obfx 2
f
4.3 Optical trapping and back focal plane detection
The 1064nm laser will be acting was both the trapping laser and as the detection
laser. The optical trapping will occur slightly beyond the focal spot of the IR laser. A
particle at the laser focus experiences a scattering force due to the laser light and in the
direction of the beam propagation. Additionally there is going to be a gradient force in the
opposite direction originating from the induced dipoles in the trapped dielectric particle.
When this gradient force and scattering force balance the particle is trapped. The steeper
the angle the trapping laser light is focused the higher the intensity gradient and the tighter
the trap will be, hence high NA objectives are desirable for producing strong traps.
The 1064nm laser also acts as a detection laser is accomplished through back focal
plane detection33. The method relies on the far field interference between the unscattered
light at the beam waist and the scattered light due to the dielectric particle, the trapped
Figure 4.4 Principle for steering the confocal spot within the sample plane by deflections from a piezo mirror. .
60
bead, located some distance off the beam access. The one dimensional case is sketched in
Figure 4.5. Depending how far off the bead is from the beam center axis it will be in the
presence of a different electric field. The far field emission from this dielectric particle is
proportional to this electric field. So from this term the far field emission picks up a
dependence on the particle offset position from the IR beam center. The interference
between the unscattered light and the scattered light from the dielectric will result in an
angular intensity pattern. By integrating the intensity over the two halves of the photodiode
separately it was shown that the total intensity measured on the two halves had a sensitive
linear dependence on the bead displacement33. We have extended this one dimensional
detection to four dimensions by using a four quadrant photodiode.
Figure 4.5 Sketch of the back focal plane detection principle in 1-dimension. The bead is located off the trap axis by a distance x. The scattered field from this field will pick up an x dependence by virtue of the off axis electric field it is scattering from. This angular distribution is imaged on the photodiode by placing it at the condenser (dashed line) back focal plane. (Not shown to scale).
θx
222 ωθkdUnscattere eE −∝
θsinfR =
22 /ωxparticle eE ∝
Back focal plane
Con
dens
er
fcondenser
θ
61
Finally the name back focal plane detection refers to the placement of the sample at
the focus of the condenser lens, the back focal plane. With this positioning the far field
detected at a radius R on the QPD will have come from an angle theta of the emitted
radiation as shown in Figure 4.5. In this way you are effectively imaging the angular
interference pattern on the QPD.
The QPD photodiodes are reverse biased silicon p-n semiconductors. Our QPD was
purchased from UDT sensors and is reverse biased to 5V. Fig 4.6 shows the schematic
QPD quadrants and the summations that lead to V1 and V2 signal:
The signal from the QPD is sent to an ONTRAK preamplifier and then through a
low pass filter. To eliminate aliasing the sampling rate chosen such that it is at least two
times faster than filtering frequency. For our setup we use a 10 kHz filtering frequency and
a sampling rate of 40 kHz.
4.4 Confocal and optical tweezer calibrations
A series of calibrations must be preformed before the setup is ready to be used in an
actual experiment. They can be divided into two groups. The first group is the calibrations
necessary for the confocal and optical tweezer microscopes to work independently. The
second are the calibrations necessary for combining the two microscopes.
4.4.1 Confocal calibrations
Figure 4.6 QPD quadrants and the V1 V2 voltage combination we measure.
62
For the confocal microscope the separate APDs for the Cy3 and Cy5 detection need
to be synchronized. This is done by scanning a sample with stuck fluorescent beads while
watching the APD counts. When a bead is in the confocal spot the counts will jump. The
APDs are mounted on micrometers so once a bead is found the signal from both APDs can
be maximized by moving the chips with the micrometers.
4.4.2 Optical tweezer calibrations
For the optical tweezer calibration a mapping between bead displacement and the
resulting QPD voltage must be obtained. From previous work33 the calibration could be
completed by displacing the bead from the center in the x and y direction and determining
the linear proportionality. We have opted to perform the calibration in a more sensitive
way that would account for nonlinearites in the detection34. We scan a stuck bead at the
same height of a trapped bead over a circular area with a radius of 300nm. For this
calibration it will be necessary to determine the height of a trapped bead. This position will
be different from that of the beam focus Figure 4.7a. To determine this height a bead is
trapped and the stage is raised while monitoring the sum signal, as shown in Figure 4.7c.
The bead height is determined by watching the QPD sum signal while the piezo stage
performs a z scan. The signal will abruptly change as the bead comes in contact with the
coverslip which will indicate the height as shown in the graph in Figure 4.7c.
63
QPD Calibration
ObjectiveObjective
b
0 10.2
0.3
0.4
Sum
sig
nal
(V)
Height (um)
Trapped bead height from coverslip
0 10.2
0.3
0.4
Sum
sig
nal
(V)
Height (um)
Trapped bead height from coverslipTrapped bead height from coverslip
c
Raise stage
Objective
Raise stage
Bead height calibration
Objective
Figure 4.7 Diagram of the bead height calibration for performing the QPD calibration. (a) An actual experiment the bead height is below above the trap focus. (b) A sample with immobilized beads as indicated by the red bars, is raster scanned at the trapped bead height to obtain the QPD calibration. (c) Bead height calibration. A free bead is raised while its sum signal is monitored. In the graph below the sum signal jumps around 600nm. This number is used for the trapped beead height in the QPD calibration of (b).
Actual experiment
Objective
a
Objective
64
With the bead trapping height known the bead the QPD calibration can be
preformed. An immobilized bead is positioned roughly in the trap center and the stage is
raised to the height previously determined Figure 4.7c. As shown in Figure 4.7b this
immobilized bead is then raster scanned by the piezo stage stepped in increments of
100nm. For each (x,y) position of the stage the QPD voltage (V1,V2) is recorded see
Figure 4.8. This data is then fit to a 5th order polynomial shown as the gray circles in and
those coefficients are stored for the actual experiment.
4.5 Trap stiffness
The calibration of the stiffness is essential for obtaining accurate forces. The
stiffness calibration is obtained using two different methods the equipartition and power
spectrum method. For the equipartition method we equate the thermal energy to the
trapping potential energy. This method is susceptible to over estimating the trap stiffness
due to low pass filtering effects and under estimating the stiffness due to picking up noise
from electronics.35 From our calibrations finding the trap stiffness by considering only the
bead Brownian motion was not that bad of an estimator. We obtained 215 data points at a
Figure 4.8 The V1, V2 and sum signal measured from the piezo scan of Figure 4.6b. The two screens at the bottom show the fits of the error to a fifth order polynomial.
65
sampling frequency of 200kHz (50kHz per photodiode). From this signal we take the
standard deviation.
2
2
22
i
Bi
iiB
Tkk
kTk
σ
σ
=
=
where i=x,y. We find in our case the trap has and <kx>=0.1 +_0.03 pN/nm and <ky>=0.12
+-0.02pN/nm.
We also look at the power spectrum of the Brownian motion and from the power
spectrum of the Brownian motion. The bead in the trap potential will behave like a
Langevin particle.
)()()( tFtxtxkx =− γ
where γ is the Stokes drag coefficient and F(t) is the random force with γTktF B4)( 2 =
the bead experiences due to Brownian motion of the surrounding fluid. Solving Equation
4.2 by taking the Fourier transform of both sides and solving for the power spectrum:
)()2()*()(
)()(
)(*)(
)()(
220
200
222
2
fffS
fkF
fXfX
iwkF
wX
FiwkwX
dweFewiwXdwewXk
x
x
x
iwtiwtiwtx
+=
+=⋅
−=
=−
=−∫ ∫ ∫
γπ
γ
γ
γ
where, πγ20
xkf = and 2
0 /4 xB kTkS γ= is the cut off frequency and can be read off a fit to
the power spectra. Assuming a spherical bead the Stokes drag coefficient can be written
Equation 4.1
Equation 4.2
Equation 4.3
66
dπηγ 3= where η is the viscosity of the surrounding fluid which in our case is water 23 /10 mNswater
−=η . Solving for the trap stiffness
For our experiments the Brownian motion data are fast Fourier transformed in origin and
averaged over a 20 point window to smooth the curve. This curve is then fit to a Lorentz
function and the cut off frequency is read off. Figure 4.9 shows a sample power spectra
and its fit. The trap stiffness in the x and y direction can then be calculated and we have
obtained a value for the x stiffness 0.18pN/nm.
This method has the advantage that electrical and mechanical noise will not affect the cut
off frequency and hence trap stiffness calibration unlike in the equipartition method.
4.6 Calibrations for combining confocal and optical tweezers
To combine the two microscopes two additional calibrations are needed. First a
mapping between piezo mirror angular steps and the resulting distance in the focal plane is
needed. This mapping will then allow precise control over the confocal spot displacement
from the 1064 trap. To determine the angular displacement in relation to nm position a
Equation 4.4
Figure 4.9 Sample power spectra data for the trap stiffness calibration .
052 109.56 f
nmpNsxdx ×== −ηπκ
10 100 1000
1E-8
1E-7
1E-6
f0=1230kx=0.07pN/nm
1/s
67
stationary fluorescent bead sample is scanned by the piezo mirror and piezo stage. The
bead sample is scanned first with the piezo stage over an area of ~ 30umx30um with a step
size of 100nm. Another image of this same spot is taken by scanning the confocal image
with steps of 32urad. From these two scans three spots are selected manually in the two
images and from these spots a rough mapping is created. With this rough mapping data the
piezo mirror scan is repeated and this time 10 spots are chosen and the true mapping is
created.
The final calibration is that the confocal laser spot center must be aligned with the
IR laser spot. To map the two beams on top of each other the IR beam is focused onto the
coverslip surface and then a scan is performed with the piezo mirror. The APD image is
then recentered by manually selecting the image center which is shown as a gray circle in
Figure 4.10.
4.7 Force extension model: WLC
As mentioned previously the IR and confocal beam are separated to avoid the
problem of enhanced photobleaching of the Cy3 and Cy5. To accomplish this, a long
lambda DNA tether (16.5um) is used to transmit the force from the bead to the molecule
being studied. In order to determine the applied force it is necessary to use a formula that
relates the polymer extension length to the force. There exist several models for relating
the two but consideration to the force regime of interest must be given because the model
Figure 4.10 Alignment of the piezo mirror to the IR trap center. The bright spot is the image of the IR beam on the APDs which is obtained by fixing the stage position and raster scanning the IR scattered emission through the piezo mirror. If the IR spot is not centered, the user manually corrects the centering by positioning the gray circle at the selected beam center.
68
used depends on it. The polymer is described as having a contour length, L, a persistence
length, p, and an elastic modulus, K. The contour length is the total length of the polymer
under zero force. The persistence length represents the smallest independent subunit of the
polymer. So that when L>>p the polymer conformations are dominated by the large choice
of polymer configurations, hence entropy. For our experiments we will be using lambda
DNA which for salt concentrations greater than 10mM has, p~40nm and L=16.5um. At
moderate force ranges (~0-10pN) the formula we that will apply to our data is an
interpolation formula of the worm like chain model (WLC) derived by Marko and
Siggia26,36
This formula is an interpolation formula and is exact only as 0→x or Lx → .
Experimentally Equation 4.3 has been tested and seen to work well for forces below 5pN.
In our experiments this formula is applied after the confocal data is taken at a given lambda
extension. After the measurement the initial stretching curve is fit to Equation 4.3 to
determine the persistence length and polymer length for the particular molecule. These
values are then used throughout the analysis of the experimental to determine the force a
given FRET measurement was taken at.
Equation 4.3
−−
+=41
)1(4
12
LxL
xp
kTF
13500 15000 16500
0
4
8
12
16
Persistence length=52nmContour length=16.3um
Forc
e (p
N)
Extension (nm)
Figure 4.11 Worm like chain fit to sample force extension data. The fit is preformed from 14um to 15.5um. The WLC with the fit parameters is plotted in red. The fit and WLC model are seen to deviate at high forces.
69
The raw data has to be corrected for the bead radius and offsets from the extension
and the force axes. The bead height is very small relative to the DNA total length
(0.5um/16.5um). For this reason we directly subtract out the bead radius, and then recenter
the x direction by symmetrizing the trace along the force dimension. The offset in the force
is found from subtracting the <F> from 0 to 8um from the entire curve. Equation 4.3 is
then fit to the symmetrized curve from ~1pN to 5pN, the extension region that is near the
steep force change. The WLC model fit to lambda DNA is shown in Figure 4.11. Here
Equation 4.3 is plotted with the fit parameters of p=52nm and L=16.3um in red on top of
the raw data. The fit deviates from the data at high force which is expected from the
discussion above.
4.8 Experimental procedure
The previous discussions have gone through the critical design features and
calibrations for our confocal optical tweezer microscope. The actual operation of the
microscope will now be discussed.
The piezo stage calibration, the QPD calibration and the trap stiffness in general do
not have to be preformed before each experiment if the bead size remains the same and the
optics alignment have not been perturbed. Before each experiment three calibrations must
be preformed as shown in Figure 4.12. First the condenser must be aligned so that the QPD
gets the largest amount of the trapping laser signal, this is described in Appendix II.
Second the IR beam is focused on the coverslip the QPD (mounted on micrometers) signal
is zeroed. And third the IR and confocal beam centers must be aligned.
70
Once these calibrations are done the force FRET program is opened. The sample is
illuminated from above by bright field, Kohler, illumination and the user scans the surface
for a tethered bead. When a bead is found it is brought roughly to the center of the IR
beam via stage micrometers. After being centered the IR beam is shut off to reduce the
likelihood of the enhanced photobleaching of the dyes. The IR is then turned on and as
long as the bead is tethered and roughly in the center of the objective the bead will trap.
The program is started that begins a stretching sequence that moves the piezo stage the
lesser of user selected extension force (~15pN in the case of lambda) and user selected
stage displacement (~16um for lambda DNA tether). These values are kept as low as
possible to prevent the tether from ripping of the bead from popping the trap during the
force extension curve acquisition. From these curves it is immediately seen if the bead was
trapped or if the DNA has stuck to the surface at an intermediate point. If the curve looks
reasonable then the bead is centered by moving the stage the distance dx=(xmax-xmin)/2 and
Figure 4.12 Summary of the calibration steps and the general experimental procedure for operating the confocal optical tweezer microscope.
Condenser alignment
QPD zero
Calibration that are done occasionally
IR and piezo mirror center
position alignment
Bead height
Trap stiffness
APD detector alignment
Piezo stage and mirror alignment
Calibrations done before each
experiment
1. Locate a potential tethered bead with bright field illumination.
2. Center the bead with the micrometers. Shut off bright field turn on IR trap and get
a stretching curve.
3. With bead trapped move stage 13-16um off center.
4. Move the confocal spot to the bead tether point and obtain a confocal image of
a 3.2x3.2um area and select potential molecules to probe.
Obtain fluorescence data for given extension translate into precise force later
Experimental procedure
•Check the stretch curve is reasonable•Center the bead•Make sure the 532nm laser remains in focus it serves as the height guide.
5. Obtain confocal data at desired force
If there are no molecules that have Cy3 and Cy5restart from step 1.
Viscosity has a sensitivity height dependence.
Repeat until the molecule photobleaches or the tether snaps.
Repeat for each
bead.
71
dy=(ymax-ymin)/2. This is repeated until the bead is tether point is centered above the
objective.
Now the confocal measurement can begin. The stage with the bead trapped is
moved a user defined distance from the objective center. This distance though should not
be less than 12um in order to avoid a large IR background interfering with the confocal
signal. In the case of lambda DNA about 13um is a typical starting position from the center
(which still corresponds to zero force). This movement is done incrementally by moving
the molecule (stage) in 1um steps at a time to avoid snapping the tether. The piezo mirror
is then raster scanned through an angular range equivalent to a 9um2 area where the bead
tether position is located. This image then shows the location of all dye labeled molecules
that are near the tether point. Several molecules may be identified and apriori it is not
known which if any of the molecules is tethered. To determine which is the tethered
molecule a series of further stage movements are selected say 14um, 15um and 16um. At
these different stage displacements confocal data is taken and using a graphing program the
data is quickly scanned for a force dependence in the FRET signal. If such a trend is seen
in one of the data sets then that molecule is isolated and selected for more force FRET
measurements. These steps are outlined in Figure 4.12.
4.9 Conclusions
The successful design and calibration steps for a confocal optical tweezer
microscope have been described. The key design feature was separating the stationary
optical trap from the confocal excitation which was moved through a scanning mirror. Our
setup did not require ultra sensitive position detection because the burden of accurate
distance changes was left to the FRET level changes detected by the confocal. Our setup
did not require an external detection laser, the trap laser acted as both a trap and a detector.
The force range this tweezer is capable of is from ~0-30pN and the resolution of our
microscope is around 1pN, obtained from the trap stiffness of 0.1pN/nm and the smallest
piezo step size of 10nm.
72
One of the main advances of this microscope is the ability to apply a force and
monitor its effect at completely different locations on the molecule. Equally important we
are now able to measure the nanometer distance changes induced through the application of
very small forces. This is due to eliminating the need for low noise, ie large tethering
force.
Though this is a next generation microscope there are several improvements that
could be made. There is drift and mechanical coupling between certain parts of the
microscope that ideally should be reduced. Light touches to the condenser and body of the
microscope and can add noise to the measurement. Adding force feedback to the current
setup would also increase the experiments possible to perform and implementing a new
calibration for the trap stiffness that could be implemented for each bead during the force
FRET experiments would improve the accuracy persistence length fits.
73
5. Probing the hairpin ribozyme folding path
5.1 Background
5.1.1 Force as an experimental variable
The use of force as an experimental variable opens new doors for understanding
cellular processes and structural properties of biomolecules. In terms of cellular processes
most of the key functions of cells rely on forceful interactions between biological
molecules. For instance the ribosome interacting with mRNA during translation, the DNA
double helix being separated during DNA replication, RNA transcription, DNA
recombination, DNA repair, microtubules pulling sister chromatids apart during mitosis,
kinesin and myosin transporting vesicle cargo as they walk along microtubules or actin are
a just a few examples37. Biopolymers are constantly experiencing forces large fast ones
due to biomotors such as polymerases and helicases but also small forces such as torsional
stresses due to distant binding of proteins or conformation changes. This latter category of
interactions is particularly interesting as researchers begin tackling how information from
distant sites on DNA and RNA is transmitted such as in riboswich gene control.
The structural response of biopolymers to stretching forces is important for not only
understanding cellular processes but also for obtaining more details on the folding pathway
and hence the free energy landscape. Obtaining the folding path of a biopolymer is
theoretically interesting but also biologically relevant since proteins and nucleic acids need
to fold into specific three dimensional structures in order to perform their intended function.
The folding path is characterized through obtaining the free energy diagram versus a
mechanical extension coordinate. Equilibrium properties of the diagram such as the total
free energy change between the equilibrium start and end conformations are available
through bulk biochemical assays and single molecule equilibrium measurements. In single
molecule FRET assays some additional aspects of the folding path can be found using
solution variables such as ion and denaturant concentrations or temperature in particular the
activation energies between transition states. But the location of transition states are not
74
obtainable from bulk or single molecule fluorescence studies alone. Force FRET
experiments can locate transition states, their distance from equilibrium conformations and
the total distance change that characterizes a transition. Such experiments can uncover new
transition states.
Early experiments with optical tweezers have yielded much insight into the folding
of large complex RNAs such as tetrahymena thermophila38,39 and contrasted them with
protein folding studies from both AFM and optical tweezer studies on proteins such as titin.
Current research has used control over a structural parameter such as the end to end
polymer distance to examine the sequence of interactions that stabilize a folded form38,39.
The folding interactions of biopolymers can be grouped into secondary structure formation,
local interactions, and tertiary structure formation which are higher order interactions
between distant secondary structures. From these experiments results have already shown
the difference in folding pathways between proteins and RNA. Optical tweezer and AFM
experiments have shown that proteins fold by collapsing into globular structures with the
secondary and tertiary structures forming together while for RNA folds first through
secondary structure formation and then through tertiary structure formation.38
Locating the distances of the transition states from the endpoints of a folding
transition, also provides insight into the mechanical stability of the folding path. The
location of the transition state relate to mechanical stabilities, which are the most probable
forces for causing unfolding to occur. The closer the transition state is to the initial state
the larger the energy needed to induce a transition when compared to a transition state
located farther out. In general secondary structures are located farther out while tertiary
structures are located nearby the initial state.
As mentioned in the previous chapter most studies with optical tweezers have not
coupled the measurement with FRET and so are limited to investigating parameters
restricted to a structural parameter or to changes occurring at large forces. For the
ribozyme the docked and undocked state have a very small distance change ~5nm that
characterizes the state change. Additionally the change is induced by a relatively small
75
force ~5pN. Optical tweezer measurements alone would not be able to resolve this small
distance change at such a small extension force. Our coupling of the FRET signal change
on two of the arms to a force applied to the A arm of the uncleavable ribozyme will allow
us to locate the transition states.
5.1.2 Theoretical treatment of force on free energies
As shown in Figure 5.1a labeling of the ribozyme arms has been altered to
accommodate the stretching of the immobilized ribozyme. For this chapter the ribozymes
will have their c and d strands labeled with the Cy5 and Cy3 respectively, strand b with a
biotin and strand a was extended for lambda annealing. This switch in labeling was not
seen to affect the docking and undocking kinetics but only to decrease the overall FRET
change between docked and undocked conformations. In Figure 5.1b a sample FRET trace
is shown and a FRET histogram made, Figure 5.1c, from 90 hairpin ribozyme molecules in
a 0.5mM pH 7.5 buffer is shown. The change in labeling is seen to lead to an increase in
FRET for the undocked state Eundock~0.45 while the docked state FRET is roughly the same
FRET EDock~0.9 rougly the same as the previous construct. The kinetics though of the two
constructs are similar so results derived from this construct will be directly applied to that
of previous chapters..
76
As mentioned in the introduction mechanical induced unfolding of a polymer
allows information on transition states and distance changes between the equilibrium
configurations to be found. First consider the free energy diagram for the hairpin
ribozyme. This is roughly sketched in Figure 5.2 for the high Mg2+ case where the docked
state is more stable than the undocked state. The x axis coordinate is the distance between
the CD arms (dye pairs) which is the single state variable xcd we will use to characterize the
system holding the others (T, P, etc) constant. As x is changed so is the state. The minima
Figure 5.1 Data obtained using the new hairpin ribozyme construct. (a) The new labeling scheme with the dyes located on the CD arms rather than the AB arms. (b) A sample FRET time trace taken using the new construct at 0.5mM Mg2+. (c) A FRET histograms is shown for the entire data set indicating the new low state FRET value of ~0.5. This is consistent with the crystal structure measurement which shows that in the undocked state the CD arms have a smaller angle then the AB arms.
0 0 50 1000.0
0.5
1.0
1.5
Time (s)
FRET
a
0.0 0.2 0.4 0.6 0.8 1.0 1.20
500
1000
1500
2000
2500
Uncleavable ribozyme 0.5mM Mg2+
FRET
coun
ts
B
AB
A
old construct Optical tweezerFRET construct
b
c
0 0 50 1000.0
0.5
1.0
1.5
Time (s)
FRET
a
0.0 0.2 0.4 0.6 0.8 1.0 1.20
500
1000
1500
2000
2500
Uncleavable ribozyme 0.5mM Mg2+
FRET
coun
ts
0.0 0.2 0.4 0.6 0.8 1.0 1.20
500
1000
1500
2000
2500
Uncleavable ribozyme 0.5mM Mg2+
FRET
coun
ts
B
A
B
AB
A
old construct Optical tweezerFRET construct
b
c
77
on the energy diagram represent the equilibriua of the molecule which from previous
chapters are the docked, proximal and undocked state. The dashed blue lines of Figure 5.2
indicate the location of these states. While the two maxima, shown as the green dashed
lines, represent the transition states. The relative energies of the free energies will control
the equilibrium population distribution while the height of the transition state energies will
control the rates of transitions between equilibrium states. At the left of the diagram the
ribozyme with CD distance xDocked is in the docked state we expect it to have to overcome a
large activation energy to reach the proximal state characterized by a CD distance xproximal.
Helix CD Distance
P U
+↔∆ PUfx
)(Fx UfD→∆
xD xP xU
Free
ene
rgy
)(Fx DP+→∆)(Fx PD
+→∆
)(Fx PUf+→∆)(Fx UfP
+→∆
+↔∆ PDx
Figure 5.2 The free energy diagram showing the energy landscape versus separation distance of the CD helices. The gray dashed curve shows the energy diagram in zero force regime. While the solid line represents the energy landscape with a stretching force applied. The equilibrium states D, P and U are shown with blue lines intersecting their location on the x axis. Transition states are located between them and indicated with blue dashed lines. The proximal and the undocked state have very similar free energies and a very small activation energy barrier. While the proximal and docked are close there is a large activation barrier separating them. With the application of force, purple dashed line, the energy diagram tilts by an amount Fx to first order. With a large enough force the undocked state becomes the most stable state.
78
The activation energy between the proximal and undocked state will be low as was
seen in Chapter 3 from the very fast kinetics between the two states. We know little about
the second transition state and have located it arbitrarily in Figure 5.2 between xP and xU.
Once force is applied, as shown by the dashed purple line, the entire energy diagram tilts as
and is represented by the solid curve.
For the initial analysis we will temporarily treat the hairpin ribozyme as a two state
system. This will not only simplify the system but additionally because of the 40ms time
resolution experimentally we expect to see transitions between only two states. This
approximation will cause errors in some estimates which will be discussed later.
Figure 5.3. Approximating the three state hairpin ribozyme as a two state system The top figure represents the full three state system while the bottom graph represents its reduction to a two statesystem. The proximal and undocked state are combined into one new state the unfolded state.
Unfolded state=< undocked +proximal >Docked
Docked UndockedProximal
Free
Ene
rgy
Free
Ene
rgy
79
Because the transition from the undocked to proximal state has a very small
equilibrium free energy difference and activation energy. For this reason we will start by
considering the hairpin ribozyme to be a two state system with the states docked and
unfolded.
Consider a force F applied to the two-state hairpin ribozyme system with states
docked (D) and unfolded (Uf) Figure 5.4. The effect of applying a stretching force F will
be to induce a change in the endpoint distance x∆ which will add another term to the
Gibbs free energy
∫−+−=2
1
)(x
x
FdxPVTSEFG
)()()()( 00DDUfUfDUfUfD FxGFxGFGFGFG −−−=−=∆ →
)()( 0DUfUfDUfD xxFGFG −−∆=∆ →→
UfDUfDUfD xFGFG →→→ ∆−∆=∆ 0)(
Where 0G∆ is the standard state free energy change due to the conformation
change. Where we have assumed the force integral in Equation 5.1 can be approximated as
a linear distance dependence. The effect of force is then to proportionately lower all
energy levels relative to the distance of that state from the initial state. As seen in Figure
5.4 the purple arrows show the change in energy for the states. Using the Boltzmann factor
the probability that the ribozyme populates the unfolded or docked state is dependent on
the free energy in that state. The equilibrium constant for the conformation change is then:
kTxFG
TkFxG
TkFxG
UfDUfDUfD
BDD
BUfUf
ee
eFK /)(
/)(
/)(0
0
0
)( →→ ∆−∆−
−−
−−
→ ==
kTG
kTxF
FK UfDUfDUfD
0
))(ln( →→→
∆−
∆=
Equation 5.4
Equation 5.5
Equation 5.1
Equation 5.2
80
After taking the derivative and rearranging Equation 5.5 we arrive at an expression for
UfDx →∆ , which will be used in subsequent sections, in terms of the experimentally
measurable quantities of force and the equilibrium constant.
dFFKd
kTx UfDUfD
)(ln →→ =∆
F
(CD distance)
Free
Ene
rgy
F xUnfolded
x xUnfoldedxDocked
F xDockedF xDockedF xDocked
F xUnfoldedG Uf D0 F xUnfoldedF xUnfoldedG Uf D0
G Uf DG Uf D0
Instead of looking at the equilibrium states we will look at the transition states in
order to see how the forward and backward transition rates will be affected by the applied
Figure 5.4 The effect of a force on the equilibrium free energies. The applied force which biases the ribozyme to the unfolded state is shown in green. Shown in dark blue and light blue are the changes in free energy between the equilibrium unfolded and docked states.
Equation 5.6
81
force. In Figure 5.5 the change in transition state energies are emphasized. The light
green arrows represent the activation energies when no force is applied and the dark green
the activation energies once a stretching force is applied. The activation energies are
essential for determining the rate of a reaction, specifically ±→∆ 0
UfDG is the activation energy
to mover from the docked to the unfolded state and conversely for ±→∆ 0
DUfG . The transition
state energies are related to the rate of a reaction through the Kramers Kroining or
equivalently the Arhenius relations. kTGetConsk /tan
±∆×=
So from Figure 5.5 before force is applied the activation energies are close and
hence from Equation 5.7 the transition rates are close. After the application of force ±→
±→ ∆>∆ 00
UfDDUf GG and hence the rate of docking becomes less than the rate of undocking.
To quantify the effect of force on the rates
)()()(0 FGFGFG UfUfD −=∆ ±±→
)()()( 000DUfDDDUfD xxFGFxGFxGFG −−∆=−−−==∆ ±±
→±±
→
±→
±→→ ∆−∆=∆ 00)( UfDUfDUfD xFGFG
For the docked to unfolded transition
)()()(0 FGFGFG DDUf −=∆ ±±→
)()()( 000UfDUfUfUfDUf xxFGFxGFxGFG −+∆=−−−==∆ ±±
→±±
→
±±
→→ ∆−∆=∆ 00)( UfDUfDUf xFGFG
Equation 5.7
Equation 5.8
Equation 5.9
82
Substituting Equation 5.8 and 5.9 into Equation 5.7 and taking the log and
derivative
( )( )dF
FkdkTx UfD
UfD
)(ln →+→ −=∆
Similarly the distance from the transition state to the unfolded state, +→∆ DUfx , is
( )( )dF
FkdkTx DUf
DUf
)(ln →+→ =∆
energy drops are presented as the changes in activation energy for the transitions.
The force application of force biases the transition to the unfolded state by increasing the
activation energy for the unfolded to docked transition and decreasing the activation energy
for the docked to unfolded transition.
Figure 5.5 The effect of a force on the activation energies. The force in the figure biases the unfolded conformational state and is seen to increase the activation energy for the reverse reaction and decrease it for the forward reaction.
Equation 6.0
Equation 6.1
F
(CD distance)
Free
Ene
rgy
x xUnfoldedxDocked
G D Uf0G D Uf0 G
Uf D0G Uf D
G Uf D0
+ F xUnfoldedG Uf D0 + F xUnfolded+ F xUnfoldedG Uf D0G Uf D
G Uf D0
F xDockedG D UfF xDockedG D Uf
0
83
The path for the unfolding conformation change will require that the docked state first
reach a transition state a distance +→∆ UfDx at the peak of the activation barrier shown. Once
there it will proceed on to the unfolded state a distance +→∆ DUfx from the transition state.
5.2 Biasing equilibrium populations with force
Figure 5.6a shows the experimental setup as described in Chapter 4 with the
polystyrene bead attached to a lambda DNA tether that is linked to an immobilized
ribozyme, In Figure 5.6b three progressive FRET traces from the same molecule as the
pulling force is increased under 0.5mM Mg2+ imaging buffer. From the FRET traces as
expected it is clear that as the force increases the dwell time in the undocked state and
decreases the dwell time in the docked state.
84
0 5 1 0 1 50 . 0
0 . 4
0 . 8
1 . 2
5 10 150
0.40.8
1.2
FRET
0 5 1 0 1 50 . 0
0 . 4
0 . 8
1 . 2
5 10 150
0.40.8
1.2
FRET
0 5 1 0 1 50 . 0
0 . 4
0 . 8
1 . 2
5 10 150
0.4
0.8
1.2
FRET
0 5 1 0 1 50 . 0
0 . 4
0 . 8
1 . 2
5 10 150
0.4
0.8
1.2
FRET
0 5 1 0 1 50 . 0
0 . 4
0 . 8
1 . 2
0.4
0.8
1.2
FRET
5 10 1500 5 1 0 1 50 . 0
0 . 4
0 . 8
1 . 2
0.4
0.8
1.2
FRET
5 10 150Time (s)
c
bF=31pN
F=5.6pN
F=2.3pN
0.0 0.4 0.8 1.20
50
100
F=5.6pN
0.0 0.4 0.8 1.20
50
100
0.0 0.4 0.8 1.20
50
100
FRET
F=2.3pN
F=31pN
0.0 0.4 0.8 1.20
50
100
F=5.6pN
0.0 0.4 0.8 1.20
50
100
0.0 0.4 0.8 1.20
50
100
FRET
F=2.3pN
F=31pN
coun
tsco
unts
coun
ts
aFo
rce
Figure 5.6 The effect of force on the FRET traces. (a) Cartoon of the experimental progression as the stretching force is increased. (b) FRET time traces taken at 40ms integration time. As the force is increased the equilibrium shifts to favor the low FRET state. At the right the FRET values are histogrammed and here it is seen that the magnitude of the low FRET value decreases as the force is increased. (b) The FRET histograms in a. are rotated 90 degrees and an orange arrow points out the location of the low FRET state. As the force increases the low FRET value is seen to decrease.
85
5.2.1 Effect of force on the low FRET state
In Figure 5.6c the small inset histograms of Figure 5.6b are enlarged and shown.
As indicated in the figure by the small orange arrows the FRET histograms in Figure 5.3c
there is a slight decrease in the value of the low FRET peak position as the force is
increased. To account for this we return to the three state model of the hairpin ribozyme
and treat the unfolded state as an average between the undocked and proximal states.
Though the transitions between the proximal and junction state occur far too quickly to be
seen directly or even through cross correlation at our 40ms integration time, they are still
seen through the average FRET value of the low FRET state. Consider the average FRET
between the undocked state and proximal state as an observable called the unfolded state
which would have a FRET value given by ( ) oximalUndockedunfolded EEE Pr1 γγ −+= . As the
force is increased there is a bias for the ribozyme to spend more time in the undocked state.
This alters the populations in the undocked and proximal state. As the force increases the
factor,γ , becomes larger and the unfolded FRET state is weighted more by the distal state
so that 00 =≠ < Funfolded
Funfolded EE .
Though the last chapters reported data acquired from hundreds of molecules there is
only preliminary data in this chapter. This section will discuss the results from three
molecules (taken over 7 months) that had dyes lasting for sets of 5, 6 and 13 force FRET
sequences. For clarity the traces of Figure 5.6a would qualify as what will be referred to as
one force FRET sequence data set. Hence 5 force FRET sequences would qualify as 15
FRET time traces.
86
0 2 4 6 8 10 12 140.0
0.2
0.4
0.6
0.8
1.0
1.2
Extension 14.5um Extension 15.5um Extension 16.5um
Extension 0um
Extension 14um Extension 15um Extension 16um
<FR
ET>
(pea
ks fr
om h
isto
gram
fits
)
Different experiments
Fits to FRET histograms for 14 different force FRET sequences
This data supports the trend that the high FRET state remains relatively stable while
the low FRET states become more biased to the undocked state as the force is increased.
The different shadings identify the molecule pulls were preformed on. The data is also
presented in the form of extension rather and force since for on lambda tether a 14um
extension is equivalent to 1.7pN in the yellow region and 1.32pN in the gray region. This
is due to slight variations in tether persistence length.
5.2.2 Distance between the docked and undocked state
From FRET traces such as those in Figure 5.6a the distance between the folded and
unfolded states can be calculated from Equation 5.5. The equilibrium constant K is
calculated by directly measuring the amount of time spent in the docked state and the
undocked state from a FRET time traces.
><><
=→ )()()(
FFFK
Unfolded
DockDUf τ
τ
Substituting into Equation 5.6
Equation 5.10
Figure 5.7 General shift of the low FRET value as the force is increased. Plotted are the values from Gaussian fits of the FRET histogram for a particular force durning a given experiment. This data is all obtained from three molecules that are grouped according to the shading. For any point on the x axis the 3 points on the y axis indicate the FRET peak locations for the three extensions the FRET was measured at.
87
−=∆ → )(
)(F
FdFdkTx
Unfolded
DockUfD τ
τ
The force for each FRET trace was calculated by a fit to the stretching curve of the
tethered bead as described in section 4.8. From Equation 5.3 the measured distance
between the docked and unfolded state can be obtained for each pull.
The results from three different pulling experiments are shown in Figure 5.8.
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
-4
0
4
8
12
Force(pN)
kTln
(low
/hig
h)(p
N-n
m) ktlnKpull1
ktlnKpull2 ktlnKpull3 ktlnKpull4 ktlnKpull5 ktlnKpull6 ktlnKpull7 ktlnKpull8 ktlnKpull9 ktlnKpull10 ktlnKpull11 ktlnKpull12
Molecule 1
0 2 4 6 8 10 12
-10
-5
0
5
10
15
20
25
Force(pN)
kTln
(low
/hig
h)(p
N-n
m)
ktlnKpull1 ktlnKpull2 ktlnKpull3 ktlnKpull4 ktlnKpull5
Molecule 3
0 2 4 6 8 10 12
-10
-5
0
5
10
15
20
25
Force(pN)
kTln
(low
/hig
h)(p
N-n
m)
ktlnKpull1 ktlnKpull2 ktlnKpull3 ktlnKpull4 ktlnKpull5
Molecule 3
1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8
0
5
10
15
kTln
(low
/hig
h)(p
N-n
m)
ktlnKp1 ktlnKp2 ktlnKp3 ktlnKp4 ktlnKp5 ktlnKp6
Molecule 2
These slopes are histogrammed in Figure 5.6, to find the distance between the
docked and the unfolded state which gave an average distance of 3.2nm.
Equation 5.11
Figure 5.8 ln(equilibrium constant) versus applied force is plotted for three different molecules. Each line in the graphs represents a sequence of pulls. Molecule 1 was pulled 8 times and data was taken for three traces at 0pN. Molecule 2 was pulled 6 times and molecule 3 was pulled 5 times. The slopes of these lines are estimates on the end to end distance between the docked and unfolded conformation as seen in equation 5.3.
88
5.3 Effect of force on the transition state
The distances from the docked and unfolded states could be calculated from the
traces of data from the force FRET experiment. To use equations the transition state rates
we had to calculate the rates of the transitions from docked to undocked. For these
molecules the time traces are very short (~10sec) so they have at most ~10 transitions in a
snapshot. For this reason we have combined the data from the same molecule that was
taken at the same force. We have used the previous analysis method of histograming
(section 1.7) the transitions and fitting with exponentials. Even on combining the data
taken at the same force one of the three molecules showed too few transitions and could not
be included in this analysis. For data that fits poorly to the exponential the average value
of the state is calculate and the error given by eventsstate Nt /1 >< .
For the two that were used the average slope values were 2.9nm and 4.7nm. The
high and low rates of these molecules were plotted against their force and the slope was fit
Equation 5.5 and 5.6 to obtain +→∆ UfDx , +
→∆ DUfx and DUfx →∆ . The results of these fits are
shown in the table in Figure 5.6.
Figure 5.9 Histogram of the distances obtained from the slopes of Figure 5.7. The fit of this histogram yields an average distance between the docked and unfolded state of 3.2nm
0 4 80
2
4
6
8
Cou
nts
Distance(nm)
Distance between docked and undocked states
0 4 80
2
4
6
8
Cou
nts
Distance(nm)
Distance between docked and undocked states
89
The transition state distances indicate that the transition state is closer to the docked
conformation than the unfolded. This agrees with our model in Chapter 3 on the ribozyme
folding where we proposed that the transition state looked very much like the docked state.
Namely that the unfolded to proximal transition occurs very quickly and will not be rate
limiting. The transition from the proximal to docked state should be the rate limiting step
and hence its activation energy dominate the rate. Since the proximal and folded state have
very similar CD helix distances we would expect +→∆ UfDx << +
→∆ UfDx .
-F Xd-F Xdkd uf (F)=kd uf e /kT0
F XufF Xufkuf d (F)=kuf d e /kT01 2 3 4 5 6 7
- 3
- 2
- 1
1 2 3 4 5 6 7- 3
- 2
- 1
ln(<
t>)
F o r c e( p N )
U n f o l d e d D o c k e d
Molecule 1
1 2 3 4 5 6 7-3
-2
-1
1 2 3 4 5 6 7-3
-2
-1
Force(pN)
ln(<
t>)
Unfolded Docked
Molecule 2
1 2 3 4 5 6 7- 3
- 2
- 1
1 2 3 4 5 6 7- 3
- 2
- 1
ln(<
t>)
F o r c e( p N )
U n f o l d e d D o c k e d
Molecule 1
1 2 3 4 5 6 7- 3
- 2
- 1
1 2 3 4 5 6 7- 3
- 2
- 1
ln(<
t>)
F o r c e( p N )
U n f o l d e d D o c k e d
Molecule 1
1 2 3 4 5 6 7-3
-2
-1
1 2 3 4 5 6 7-3
-2
-1
Force(pN)
ln(<
t>)
Unfolded Docked
Molecule 2
1 2 3 4 5 6 7-3
-2
-1
1 2 3 4 5 6 7-3
-2
-1
Force(pN)
ln(<
t>)
Unfolded Docked
Molecule 2
1.22.91.60.12
2.64.71.80.31
(nm)(nm)(nm)(nm)Molecule
1.22.91.60.12
2.64.71.80.31
(nm)(nm)(nm)(nm)Molecule
a
b
Figure 5.10 Distances from the transition state. (a) Plots of the logarithm of the folding and unfolding rates versus force for two molecules. (b) Table comparing the distances from the transition state to the total conformational change difference.
90
From Figure 5.2 it can be seen that the sum of the distances to the transition state
should equal the total distance change, UfDDUfUfD xxx →+→
+→ ∆=∆+∆ , ie. From the numbers
in the table of Figure 5.10b the transition state distances are off by 2.6 and 1.2nm
respectively for molecule 1 and 2. Some of this error is due to the two state assumption
made in approximating the system as having only the states docked and unfolded. So the
averaging of proximal and undocked state could account for some of this difference.
Additionally the inaccuracy due to the fits of such few transitions is also a source of some
of the error.
5.4 Heterogeneity
As discussed in section 3.5 the hairpin ribozyme undergoes major secondary and
tertiary rearrangements between the undocked and docked states. The slight difference in
contacts and a structural memory that is maintained in the proximal state is a potential
source of the single molecule heterogeneity. Shown in Figure 5.11a are some sample TIR
traces of the uncleavable CD labeled ribozyme at 0.5mM Mg2+ imaging buffer. In Figure
5.11b a heterogeneity scatter plot is shown calculated the same way as Figure 3.7 was for
the AB labeled construct.
91
0 50 100 150 2000.0
0.5
1.0
1.5
0 0 50 100 150 2000.0
0.5
1.0
1.5
0 0 50 1000.0
0.5
1.0
1.5
0 0 50 100 150 2000.0
0.5
1.0
1.5
0.1 1 100.1
1
10
< t un
fold
ed>
(s)
< tdock> (s)
Uncleavable 0.5mM Mg2+
114 molecules
a b
As mentioned in Chapter 3 we have tried to induce changes in kinetic memory by
bulk means such as increased temperature, presence of denaturants such a urea and long
observation times, but none of these conditions yielded significant increases in the kinetic
switching. In general we have qualitatively seen 1-5% of a population exhibit kinetic
switching. Studies by others in our lab have specifically probed if the interactions with the
surface could be the source of the heterogeneity. This was tested by varying the attachment
technique by using BSAbiotin, biotinylated PEG, and most recently vesicle
encapsulation40. The vesicle encapsulation study is the most convincing evidence that the
heterogeneity is not a surface effect since in that experiment the ribozyme is free floating
within a vesicle (ie no surface attachment). None of these methods eliminated the kinetic
heterogeneity.
With the optical trap we have tried to perturb this memory by the application of
force to the loop A region. The motivation was that the memory most likely exists within
Figure 5.11 The kinetic heterogeneity within the new ribozyme labeling scheme. (a) Sample traces all taken from the same sample at 0.5mM Mg imaging buffer. (b) The corresponding heterogeneity plot shows the CD labeling maintains similar heterogeneity as seen in chapter 3.
92
the unfolded state. This seemed to be suggested from Chapter 3 comparison between the
minimal and four way junction form of the ribozyme. With the four way junction the
heterogeneity increases markedly, most likely because the junction structure brings the
loops rapidly into close enough contact so that many subpopulations can dock. Whereas in
the minimal ribozyme the docking rate does not show any heterogeneity which would
imply that the very slow docking rate allowed the loop structures to equilibrate before
being brought into close enough contact for docking. It was then of interest to try applying
a force abruptly and for a relatively long time so that the interactions in the proximal state
would be disrupted and they would have a chance to reform into another state. Namely
pulling on the molecule while it is unfolded with the intent to force a transition out of one
Pull sequence
1st 2nd 3rd 4th 5th
Forc
e
(pN
)
1.72.2
3.1
4.6
7.7
15.7
0 4 8 1 1 1 50 .0
0 .4
0 .8
1 .2
0 4 8 1 1 1 50 .0
0 .4
0 .8
1 .2
0 4 8 1 1 1 50 .0
0 .4
0 .8
1 .2
0 4 8 1 1 1 50 .0
0 .4
0 .8
1 .2
0 4 8 1 1 1 50 .0
0 .4
0 .8
1 .2
0 4 8 1 1 1 50 .0
0 .4
0 .8
1 .2
0 4 8 1 1 1 50 .0
0 .4
0 .8
1 .2
0 4 8 1 1 1 50 .0
0 .4
0 .8
1 .2
0 5 1 0 1 5 2 00 .0
0 .4
0 .8
1 .2
0 5 1 0 1 5 2 00 .0
0 .4
0 .8
1 .2
0 5 1 0 1 5 2 00 .0
0 .4
0 .8
1 .2
0 5 1 0 1 5 2 00 .0
0 .4
0 .8
1 .2
0 5 1 0 1 5 2 00 .0
0 .4
0 .8
1 .2
0 5 1 0 1 5 2 00 .0
0 .4
0 .8
1 .2
0 4 8 1 1 1 50 .0
0 .4
0 .8
1 .2
time (s)
time (s)
time (s)
time (s)
time (s)
time (s)
time (s)
time (s)
time (s)
time (s)
time (s)
time (s)
time (s)
time (s)
time (s)
FRE
TFR
ETFR
ET
Figure 5.12 Data from a molecule that showed a change in memory after 4 pull sequences. All the data is from one molecule. The molecule is pulled five times as indicated in the x axis. The y axis indicates the force and the dashed purple lines emphasize the force increase. The 1st, 2nd and 5th pulls occurred for an identical force sequence 2.2pN, 4.6pN and 15.7pN. While the 2nd and 3rd pulls are at 1.7pN, 3.1pN and 7.7pN. The fifth extension sequence is seen to show a switch in the kinetics.
93
state to a different state that shows up when the force is released. So far this idea has only
been tested on one molecule, the most recent one of the three. For that molecule for 7 force
extension sequences the kinetics remain similar. Then a high force sequence was applied.
When the next low force was applied the FRET trace showed a change in kinetics. Though
this is an interesting result it is only data from this one molecule so no conclusions are
being drawn but it gives a further encouragement for to continuing to pursue this type of
experiment for probing the heterogeneity.
5.5 Conclusions
This preliminary data has shown that the force FRET assay does work and on the
ribozyme system and we have seen through the FRET time traces how the stretching force
perturbation changes the ribozyme kinetics. Additionally we were able to indirectly see
again how the low FRET state is actually composed of at least two states that are normally
indistinguishable at our buffer condition at 40ms (confocal) integration time. By increasing
the force the ribozyme was biased to the undocked state rather than the proximal in the low
FRET state and hence the low FRET state value decreased. From dwell time analysis we
were able to get a first estimate of the distance to the transition state. Through this assay
we have begun to probe the energy landscape of the folding path of the ribozyme. From
the equilibrium dwell times it was possible to attain a distance between the unfolded and
docked conformations. Obtaining the transition state distances is less reliable because of
the very short time traces which make determining a accurate rate constant difficult.
We also returned to investigating the kinetic heterogeneity discussed in Chapter 3.
The heterogeneity in the kinetics of the ribozyme could be due to misfolded states from
either an annealing process that was performed too quickly or an artifact from the fact that
our annealing process is invitro. Perhaps within a cell proteins exist that would encourage
the correct folding conformation amongst a myriad of stable local minima. Or finally the
heterogeneity could be due to a truly rugged energy landscape and a property even in the
true biological setting.
94
Or experiments from this Chapter indicate that the kinetic heterogeneity is truly due
to a truly rugged energy landscape. The strongest arguments against the misfold
hypothesis of not allowing the sample to equilibrate long enough is the observation that in
general after a highly nonequilibrium pulling event the ribozyme maintains the same
kinetics. If some subset of the highly heterogeneous kinetics was due to non equilibriated
states then it would seem likely that yanking a molecule and not allowing it to gradually
equilibriate would send it into a misfolded state with alternate kinetics. But only rarely
after several rounds of pulling we do occasionally see the kinetics switch behavior.
The preliminary experiments on the hairpin ribozyme are very promising. The
main factor that has slowed this experiment is the low labeling efficiency of the strands
which leads to the majority of molecules not being useful for data acquisition. For my
experiments I found an average of 1 good molecule (one with both dyes, tether, and a bead)
for 70 promising molecules (molecules that had a tethered bead). This led to a remarkably
slow data acquision rate of about 1 molecule a month. One of the key points I would want
to pass on is to pursue the most thorough sample purification scheme possible when
designing force FRET constructs. As mentioned in section 1.8.1 our samples were purified
by standard PAGE gel purification. Though such purification works well for single
molecule FRET studies for the combined force-smFRET experiment there can be many
unlabelled strands that pass through. In smFRET studies such unlabelled species do not
interfere because they would not be selected by the user/computer since they are not seen.
But for the force FRET experiment any unlabelled construct that could still anneal a bead
would not be discernable until the stretching curves were obtained and all possible FRET
spots within the 9um2 area were checked. Currently through other lab members there is
evidence that HPLC purification can increase the yield to at least around 50%.
For the future studies we are in a very good position to probe the kinetic memory
switches of the ribozyme. With a scheme for attaining samples of a higher purification it is
feasible to ask and perhaps answer several questions related to the heterogeneity. For
instance we have strong evidence that the increased heterogeneity of the full four way
95
junction versus the minimal two way junction is due to the speed in which the two loops
are frequently brought together by the junction. Then how would the kinetic memory be
affected by a forced excursion to the undocked state through maintaining the trap trapping
force for an extended time? Is there any preference in switching from one type of kinetics
to another? (For instance if the high undock rates tended to switch to low dock rates)
Which type of kinetics is most likely to switch to another? Are there favorable conditions
for inducing the switching such as dependent on the length of time the ribozyme is exposed
to the force? Or the magnitude it is exposed to? How does the heterogeneity distribution
change as the force is increased? These are only a small sampling of the questions we can
begin to answer once a higher sample yield is attained.
Finally the opportunity to probe the enzyme chemistry with force should yield
much insight into the mechanism. Using the cleavable form of the ribozyme the ligation
and cleavage rate as a function of force can be looked at. Additionally with known
mutations of key nucleotides known to be involved in the reaction the force dependence
could also lead to further insight into the mechanism.
96
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14. Yadava, R. S., Choi, A. J., Lebruska, L. L. & Fedor, M. J. Hairpin ribozymes with four-way helical junctions mediate intracellular RNA ligation. J Mol Biol 309, 893-902 (2001).
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100
Appendix I: Bead binding protocol
This protocol was obtained from Michelle Wang’s laboratory at Cornell University.
Materials:
Protein G coated polystyrene beads: Spherotech (#PGP-20-5)
DMP(dimethyl pimelimidate):Pierece(#21667) 1g
Antidigoxigenin:Roche(#133089), 200ug
Buffers:
All buffers should be filtered immediately before use to ensure they are bacteria free.
(1)Xlinking buffer 0.1M Na2HPO4, 0.1M NaCl, or other non-amine containing buffer pH7-
9
(2) Antibody recon buffer:0.019M NaH2PO4, 0.081M Na2HPO4, 0.14 M NaCl, 2.7mM KCl
(3) Bead storage buffer:0.039M NaH2PO4, 0.061 M Na2HPO4, 0.14M NaCl, 2.7mM KCl
Protocol:
(1) Resuspend protein G beads by gently swirling the bottle take 1mL of slurry into a
1.7mL centrifuge tube, centrifuge for 3min at 7000rpm, carefully remove the supernatant,
then pipette 1mL xlinking buffer into the tube and vortex slightly to resuspend the beads.
Repeat this procedure twice to ensure the buffer exchange is complete.
(2) Dissolve 200ug antiDig antibody in 200uL antibody reconstitution buffer. Dissolve
50mg DMP in 1mL xlinking buffer (caution fro handling DMP: the bottle containing
DSMP should be warmed up in the dark before opening the bottle. Also keep in mind
DMP goes bad quick and is cheap so you may be better off ordering fresh.)
(3) add 60uL dissolved antibody and 30ul dissolved DMP into 1mL beads in xlinking
buffer, tumble for 2 hrs at room temp. The left antibody solution can be aliquoted and flash
freezed for future use.
(4) Stop xlinking reaction by adding 1M TRIS pH 6.8 to a final concentration of 50mM.
Continue tumbling for 2hrs at RT.
101
(5) Exchange beads into storage buffer by centrifuge and resuspension as done in step (1).
In the end add concentrated sodium azide solution directly to the bead slurry to reach a
final concentration of 0.02% azide, mix well and store at 4C.
Notes:
(1) Resuspension of beads in centrifuge tube can be achieved by slight vortexing, or invert
the tube several times, or use finger to tap the tube wall.
(2) Before experiment, exchange the beads into desired buffer by centrifuging at 7000 rpm
for 3min as in protocol step 1.
(3) The concentration of beads can be determined by light scattering in a spectrophotometer
at 600nm, using known bead concentration as standard.
(4) Also note that some protocols have the antidigoxigenin incubated with the polystyrene
beads for 15 minutes to improve annealing.
102
Appendix II Condenser alignment
An accurate position measurement requires careful alignment of the condenser
before an experiment. This is done to ensure the condenser is centered on the sample and
that the confocal focal plane is at the back focal plane of the condenser lens. This appendix
will clarify how this calibration is preformed in detail.
The bright field illumination of the sample will be via Kohler illumination. Kohler
illumination provides a uniformly bright sample illumination in spite of an inhomogeneous
illumination source. The condenser region from figure 4.1 is shown in Figure II.1(a) and
the condenser optics are shown in Figure II.1.(b). Centering the condenser will amount to
imaging the octagon aperture in (b) clearly in the confocal focal plane.
CondenserCondenser
As shown in Figure II.1 the lamp filament is located at the slightly before the
precondenser focal length. This leads to an intermediate image of the lamp filament
forming between the condenser and precondenser lens. The condenser lens is located a
focal distance away from this image. The filament is then imaged beyond the condenser at
Figure II.1 Condenser alignment. The lens arrangement inside the condenser is diagramed at the left.
103
infinity leading to the uniform illumination. This lens configuration is commonly used and
referred to as Kohler illumination.
The octagon aperture, seen in Figure II.1, is critical for centering the condenser
optics and locating the condenser a focal distance from the sample. The octagon is located
at the focal point of the precondenser lens. The image of the octagon is then located at
infinity beyond this lens. The condenser lens will then image the octagon at the condenser
focal point. The condenser is aligned by verifying that the octagon shape is in focus and
centered while the confocal beam in focus. This ensures that at the data collection height
the trapped bead is at the back focal plane of the condenser Figure II.2.
Figure II.2 Beam path for IR scattering once the condenser is aligned.
104
Author’s Biography
Michelle K. Nahas was born in Vancouver, WA in 1978. She received a BSc in
physics from McGill University in Montreal, Quebec in 2000. She came to the University
of Illinois at Urbana-Champaign in 2000 and began research with Professor Taekjip Ha in
2002 on the hairpin ribozyme.
Her publications include:
• Wilson TJ, Nahas M, Araki L, Harusawa S, Ha T, Lilley DM. “RNA folding and the
origins of catalytic activity in the hairpin ribozyme.” 1: Blood Cells Mol Dis. 2006.
• Wilson TJ, Nahas M, Ha T, Lilley DM. “Folding and catalysis of the hairpin
ribozyme.” Biochem Soc Trans. 2005 Jun;33(Pt 3):461-5.
• Michelle K. Nahas, Timothy J. Wilson, Sungchul Hohng, Kaera Jarvie, David M. J.
Lilley and Taekjip Ha. “Observation of internal cleavage and ligation reactions of a
ribozyme”. Nature Structural and Molecular Biology 11:1107-1113, 2004.
• McKinney SA, Tan E, Wilson TJ, Nahas MK, Declais AC, Clegg RM, Lilley DM, Ha
T. “Single-molecule studies of DNA and RNA four-way junctions”. Biochem Soc Trans
32(Pt1):41-5, 2004.
• Tan E, Nahas M, Wilson TJ, Clegg RM, Lilley DMJ, Ha, T. “A four-way junction
accelerates hairpin ribozyme folding via a discrete intermediate”. Proceedings of the
National Academy of Science 100 (16): 9308-9313, 2003.