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Force spectroscopy of single DNA and RNA molecules
Mark C Williams* and Ioulia Rouzina†
Experiments in which single molecules of RNA and DNA are
stretched, and the resulting force as a function of extension is
measured have yielded new information about the physical,
chemical and biological properties of these important molecules.
The behavior of both single-stranded and double-stranded
nucleic acids under changing solution conditions, such as ionic
strength, pH and temperature, has been studied in detail. There
has also been progress in using these techniques to study both
the kinetics and equilibrium thermodynamics of DNA–protein
interactions. These studies generate unique insights into the
functions of these proteins in the cell.
Addresses
*Department of Physics and Center for Interdisciplinary Research on
Complex Systems, Northeastern University, 111 Dana Research
Center, Boston, MA 02115, USA; e-mail: [email protected]
† Department of Biochemistry, Molecular Biology and Biophysics,
University of Minnesota, St Paul, MN 55108, USA
Current Opinion in Structural Biology 2002, 12:330–336
0959-440X/02/$ — see front matter
© 2002 Elsevier Science Ltd. All rights reserved.
Abbreviations
AFM
atomic force microscopy
bp
base pairs
ds
double-stranded
NC
HIV-1 nucleocapsid protein
ss
single-stranded
Introduction
In the past decade, several techniques have been developed
for measuring small forces acting on single DNA and RNA
molecules. In these experiments, one end of the molecule is
held at a fixed position, while the other end of the molecule
is extended at constant force or to a fixed position. These
techniques include atomic force microscopy (AFM) [1],
optical tweezers [2] and magnetic tweezers [3,4•], as shown
in Figure 1. All of these instruments are able to measure
the force required to stretch DNA under various conditions.
In optical tweezers, one end of a single DNA or RNA
molecule is attached to a polystyrene bead in an optical
trap, while the other end is held a fixed distance from the
trap (Figure 1a). The resulting force on the bead in the
trap is measured over a force range of 0.1–150 pN. In
magnetic tweezers, one end of a single DNA molecule is
attached to a magnetic bead, while the other end is
attached to a glass surface (Figure 1b). The magnetic field
exerts a constant force, so the resulting extension of the
molecule as a function of force can be measured. This
method can be used to measure forces well below 1 pN.
In AFM experiments, DNA molecules are attached to a
fixed surface at one end and a cantilever at the other end
(Figure 1c). As the fixed surface is pulled away from the
cantilever, the deflection of the cantilever can be used to
determine the force required to stretch the DNA molecule.
The resolution of this method is about 5 pN, but it can also
be used to measure forces in the nanonewton range. This
wide range of techniques has been used to study several
regimes of DNA stretching behavior in detail and has also
been extended to study DNA–protein and DNA–drug
interactions. In addition, high-resolution force measurements have been obtained from the stretching of single
RNA molecules, suggesting that these methods can be
extended to the study of sequence-specific RNA–protein
interactions.
Stretching nucleic acids at low forces: DNA
elasticity, and DNA and RNA unzipping
The force/extension curve of double-stranded (ds) DNA
can be fit to the following equation:

FPds
bds
1 
1
= •
− 1 + max
max
kBT
4  (1 − bds /bds + F/K ds )
 bds
(1)
where Pds is the persistence length, Kds is the elastic stretch
modulus, bds is the extension of the molecule per base pair
and is the dsDNA contour length per base pair. F is the
force required to extend the molecule, kB is Boltzmann’s
constant and T is the temperature. This expression is an
interpolation between exact solutions of the worm-like chain
model at high and low forces. It describes the persistence
length and stretch modulus of dsDNA to within 5% at all
extensions. A more accurate interpolation has been proposed
by Bouchiat et al. [5], which can be used when very
accurate force/extension data are available in the entire
range of forces. In 1997, Baumann et al. [6] used the
high-force limit of Equation 1 to describe the persistence
length and stretch modulus of dsDNA as a function of
monovalent salt concentration. The observed increase
in persistence length with decreasing monovalent salt
concentration was in agreement with the predictions of
polyelectrolyte theory. In contrast to expectations from a
theoretical model of DNA as a classical homogeneous rod,
the authors also showed that the stretch modulus of
dsDNA decreased with decreasing salt concentration.
As the stiffness of DNA has a contribution from the repulsion
between the negatively charged phosphate groups that
make up its backbone, Podgornik et al. [7•] developed a
theory to describe the expected salt dependence of the
stretch modulus and persistence length. However, their
predictions for the stretch modulus of dsDNA disagreed
with the measurements of Baumann et al. [6]. Recent
measurements of the salt dependence of DNA stretching,
coupled with a new fitting procedure using the theory of
Podgornik et al. [7•] to relate Pds and Kds, however, indicate
that the stretch modulus data are consistent with the
theory of Podgornik et al. [7•] (JR Wenner, MC Williams,
I Rouzina, VA Bloomfield, unpublished data).
Force spectroscopy of single DNA and RNA molecules Williams and Rouzina
331
Figure 1
Single-molecule force spectroscopy. (a) In an optical tweezers
instrument, one or two laser beams are focused to a small spot,
creating an optical trap that attracts polystyrene beads. Single DNA
molecules are attached at one end to a bead in the trap, while the
other end is attached to a moveable surface, which, in this example,
is another bead on a glass micropipette. As the DNA molecule is
stretched by moving the micropipette, the resulting force on the
bead in the trap is measured. (b) In a magnetic tweezers instrument,
single DNA molecules are attached at one end to a glass tube,
while the other end is attached to a magnetic bead. Magnets
located outside the tube generate a magnetic field that exerts a
constant force on the magnetic bead. The extension of the DNA
molecule as a function of the applied force is then measured.
(c) In an AFM experiment, single DNA molecules are attached to a
surface. The other end of one of these molecules is attached to a
cantilever. As the surface is pulled away from the cantilever, the
deflection of the cantilever is monitored by measuring the position of a
reflected laser beam, which determines the force required to stretch
the attached DNA molecule.
In the presence of a critical concentration of multivalent
ions, dsDNA condenses and forms compact rods and
toroidal structures [8]. Single-molecule stretching methods
have been used to measure the forces that cause this DNA
condensation. If the two ends of a DNA molecule are
stretched, they are prevented from condensing. The force
required to prevent condensation, the attractive condensation force, has been shown to be constant, with a
magnitude between 1 and 4 pN [9,10]. These results are
consistent with the low attractive condensation force
measured in bulk experiments. In contrast to these
observations, high concentrations of the nonspecific DNAbinding protein integration host factor (IHF) induce
compaction by locally bending the DNA, but do not
induce collapse [11•]. It is therefore likely that the
nonspecific binding of this protein to DNA strongly affects
the large-scale structure of the bacterial nucleoid.
(a)
Laser beam
Microscope
objectives
Polystyrene
bead
Laser beam
DNA molecule
Glass micropipette
(b)
S
N
→
F
N
S
Glass surface
Bead
DNA
(c)
Detector
Laser
Precise measurements of the elasticity of single-stranded
(ss) DNA have been made at very low forces. The results
show a strong sequence dependence, indicating the
importance of secondary structure formation at low forces
[4•,12]. Bockelmann et al. [13] have demonstrated that
the force required to cooperatively remove hairpin secondary
structure as DNA is unzipped varies between 12 and
15 pN, depending on the sequence of the DNA. This is
consistent with the observed sequence dependence of
ssDNA elasticity at forces less than 15 pN. Several theoretical treatments of DNA unzipping have recently been
published [14–16].
Liphardt et al. [17••] have recently demonstrated the
force-induced unfolding/refolding of small RNA hairpins
(Figure 2). In these experiments, they unzipped various
single-molecule hairpins by pulling on their ends with
DNA–RNA hybrid handles attached to beads. They
measured forces of about 15 pN when pulling apart simple
double-stranded portions of RNA, similar to earlier
measurements of the forces needed for DNA unzipping.
Cantilever
DNA
Piezoelectric stage
Current Opinion in Structural Biology
Pulling and relaxing force curves for some types of
hairpin were indistinguishable at low pulling rates, thus
indicating thermodynamic reversibility. The area under
the reversible force/extension curves yields a direct
measurement of the equilibrium free energy of structure
formation. This area for a simple 49 bp hairpin structure
332
Nucleic acids
Figure 2
(a)
∗
20
+Mg
–Mg
20
∗
15
15
15
10
∗
10
200
∗
∗
10
Force (pN)
Force (pN)
(b)
20
250
5
5
100 nm
100
150
(c)
200
Extension (nm)
2 nm
5′
250
13 nm
3′ 5′
P5a
A-rich bulge
P5c
3′
A-rich bulge
P5c
Three-helix
junction
P5b
P5b
26 nm
3′
Force/extension curves for the P5abc domain of the T. thermophila
ribozyme. (a) In the presence of Mg2+, an RNA structural transition
occurs as the RNA molecule is stretched to about 20 pN (blue line)
and the relaxation curve (green line) shows hysteresis. The blue arrow
indicates the typical unfolding force when stretching — the green
arrow shows a refolding transition upon relaxation. Inset: a detailed
stretching curve (light blue line) of the P5abc RNA structure reveals
the presence of intermediate structural elements stabilized by metal
binding (red stars). The lower blue arrow shows the lowest unfolding
force. In other stretches (dark blue line), unfolding occurs suddenly at
a much higher force (top blue arrow). (b) RNA stretching curves
(blue lines) differ significantly in the presence and absence of Mg2+,
whereas the relaxation curves (green lines) exhibit similar intermediate
transitions at lower forces (black stars and green arrows). These
intermediate transitions are also observed when stretching this RNA
in the absence of Mg2+. (c) A model for the unfolding of P5abc in the
presence of Mg2+, in which two possible unfolding paths are shown.
The blue arrow shows an unfolding path in which the molecule
suddenly unfolds and increases its length to 26 nm, consistent with
data indicated by the blue arrow in (a). A two-step model is shown by
the red arrows, in which an intermediate state 13 nm in length is
formed during stretching. Transitions to this intermediate state are
indicated by green arrows in (a) and (b). (Reproduced with
permission from [17••].)
was in good agreement with the theoretical predictions
of the MFOLD method [18]. Another structure, the
P5abc domain of the Tetrahymena ribozyme, forms tertiary
contacts in the presence of Mg2+. As shown in Figure 2,
the resulting force/extension curves map out the secondary
structure of such an RNA molecule and identify metalbinding pockets. This will be an extremely valuable
technique for the study of RNA folding, as well as
RNA–protein interactions, as will be discussed below.
Stretching DNA at high forces: DNA
overstretching and strand separation
Torsionally relaxed DNA
As a single molecule of dsDNA is stretched beyond its
B-form contour length, the force required to further stretch
the molecule increases dramatically. If one end of the
DNA molecule is allowed to rotate freely, a cooperative
overstretching transition occurs at about 65 pN, after
which very little additional force is required to stretch the
Force spectroscopy of single DNA and RNA molecules Williams and Rouzina
To test the force-induced melting model, Williams et al.
[28] measured DNA overstretching as a function of pH. As
extremely high and low pH lower the melting temperature
of dsDNA, the overstretching force should also decrease if
melting occurs during the transition. This decrease in the
overstretching force was demonstrated and the value of the
change in entropy of DNA upon melting, determined from
the ratio of the change in overstretching force to the
change in melting temperature as a function of pH, was in
agreement with calorimetric measurements of this parameter
at room temperature. As a further test, Williams et al. [29•]
also measured the temperature dependence of DNA
overstretching. Although their data were consistent with
earlier temperature-dependent measurements using AFM
[26•], the high-resolution data obtained using optical
tweezers allowed them to directly calculate the helix-coil
transition free energy as a function of temperature from
the force/extension curves. The resulting parameters
describing this temperature dependence — the heat
capacity of DNA upon melting and the entropy of DNA
upon melting at the melting temperature — were in very
good agreement with independent calorimetric measurements of these parameters. Finally, measurements of the
Figure 3
100
80
Force (pN)
molecule to 1.7 times its contour length [2,19]. To describe
this transition, a model of overstretched DNA as a new
double-stranded form of DNA, referred to as S-DNA,
was proposed [19]. Although models describing S-DNA
did predict an overstretching transition, the predicted
transition was less cooperative and occurred at a higher
force than that observed experimentally [20–22]. Rouzina
and Bloomfield [23,24] have proposed an alternative
model for DNA overstretching as a force-induced melting
process. In this model, the base pairs holding the two
DNA strands together break as the DNA unwinds during
the transition. This model was shown to be consistent
with all available data on the dependence of DNA
overstretching on changes in solution conditions such as
ionic strength and temperature. It has also been shown that
poly(dG•dC)poly(dG•dC) has an overstretching transition
about 30 pN higher than that of poly(dA•dT)poly(dA•dT)
[25]. This result is consistent with the difference in
melting temperature between these molecules. However,
the authors also observed an additional strand separation
transition at forces higher than the overstretching force. In
later work [26•], they showed that this strand separation
force depended on the rate at which the dsDNA was
stretched. In the force-induced melting theory, the overstretching transition is an equilibrium melting transition,
whereas the second transition at higher force is a nonequilibrium strand separation transition, during which
the last base pairs holding the two strands together are
irreversibly broken. A rate-dependent force is expected
when single bonds are irreversibly broken [27]. Thus, the
rate dependence observed when stretching DNA at forces
greater than 65 pN indicates that this portion of the
transition is irreversible, consistent with the idea that
these forces are due to irreversible strand separation.
333
60
40
20
0
0.2
0.3
0.4
0.5
0.6
DNA extension (nm/bp)
Current Opinion in Structural Biology
The effect of changing solution conditions and protein binding on DNA
overstretching. As dsDNA is stretched beyond its B-form contour
length in 500 mM NaCl at room temperature, the force required to
extend the molecule to 1.7 times its contour length is almost constant
at 65 pN (black line). A model describing this transition as
force-induced melting of DNA predicts that solution conditions that
destabilize DNA will lower the force at which the transition occurs [24].
This is observed at high temperature (35°C, green line; [29•]), low pH
(pH 3.5, orange line; [28]), high pH (pH 10.6, purple line; [28]) and
low ionic strength (10 mM NaCl, red line; JR Wenner, MC Williams,
I Rouzina, VA Bloomfield, unpublished data). The dashed black line
shows the force/extension curve of ssDNA in 150 mM NaCl, pH 8
and room temperature [2]. The area between the solid and dashed
black lines represents the helix-coil transition free energy [23]. The
solid and dashed blue lines are force/extension curves for dsDNA and
ssDNA, respectively, with NC [47•]. Binding of the protein lowers the
helix-coil transition free energy and the cooperativity of the
overstretching transition.
monovalent salt dependence of DNA overstretching
showed that the DNA strands must remain close together
during the transition (JR Wenner, MC Williams, I Rouzina,
VA Bloomfield, unpublished data). These salt dependence
data are consistent with both the S-DNA and forceinduced melting models. These results are summarized in
Figure 3, which shows the effect of changing solution
conditions on DNA overstretching. This work has
recently been published [30].
Torsionally constrained DNA
In contrast to torsionally relaxed DNA, dsDNA that is not
allowed to rotate freely when stretched does not exhibit an
overstretching transition at 65 pN. Instead, a much less
cooperative transition at a force of 110 pN is observed [31].
It has been shown that, after unwinding the DNA, the
stretching curve exhibits two transitions, one at 50 pN and
another at 110 pN, and, as the amount of DNA unwinding
334
Nucleic acids
is increased, more of the transition occurs at 50 pN [31].
Overwinding the DNA results in an additional transition at
25 pN, which is attributed to the removal of DNA supercoiling [31]. The currently accepted model is one in which
the data are interpreted as transitions between five separate forms of dsDNA [32]. However, as it is known that
underwound DNA is locally denatured even at low forces
[33], it seems likely that there is DNA denaturation during
this transition as well, but this will require further study. In
particular, a detailed study of the dependence of these
transitions on solution conditions would help to explain the
effect of torsional strain on DNA overstretching. Because
torsional strain can build up under many physiological
conditions [34], this is an important problem to solve.
DNA–protein interactions from
single-molecule stretching
Single-molecule DNA stretching studies have been used
to probe a wide range of DNA–protein interactions. These
include dynamic studies, in which the action of a processive
enzyme or molecular motor is directly observed as a
function of time, as well as equilibrium studies, from
which transition free energies have been derived. In the
case of RecA, both dynamic and equilibrium properties
were measured. First, the time dependence of the polymerization of RecA along a single DNA molecule was
directly measured [35]. Leger et al. [36] showed that the
rate of RecA binding to DNA without ATP hydrolysis
increased tremendously at high forces approaching the
overstretching transition. As it is known that, in the
absence of ATP hydrolysis, RecA binds much more strongly
to ssDNA [37], these experiments support the idea that
DNA overstretching induces strand denaturation. After
polymerization, the equilibrium elastic properties of
RecA–DNA filaments were measured and shown to be
dominated by the properties of the RecA protein [35].
Dynamic single-molecule studies of transcription and
replication have directly measured polymerization velocities
as a function of force, as well as the forces required to stall
polymerization. [4•,38–41] In the case of RNA polymerase,
although specific stall sites were identified at low forces,
the average polymerization velocity was independent of
tension up to forces of 25 pN, at which point transcription
was reversibly stalled. In contrast, Wuite et al. [38] showed
that the polymerization velocity of T7 DNA polymerase
was very sensitive to tension. In addition, replication
stalled at 34 pN, whereas higher forces induced fast
3′–5′ exonucleolysis. Maier et al. [4•] studied replication by
the DNA polymerases Sequenase and Klenow, obtaining
results similar to those of Wuite et al. [38]. Although both
of these studies concluded that the polymerase must
process at least two bases during each enzymatic step, a
later analysis indicates that the data are also consistent
with a step size of one base [42]. The kinetics and
sequence dependence of DNA helicase activity by
RecBCD have also been directly measured [43,44]. In
these studies, the authors were able to directly observe
the processive translocation of single RecBCD enzymes
along single DNA molecules. The observed translocation
rates were consistent with bulk measurements of DNA
unwinding rates.
The interaction of topoisomerase with supercoiled DNA
has been directly observed using single-molecule stretching
[45]. In this study, the authors were able to watch the
removal of two supercoils during a single enzyme turnover.
A recent study showed a direct demonstration of the forces
exerted by a bacteriophage portal motor when packaging
DNA [46••]. The data indicate that an internal force of
about 50 pN is built up within the virus capsid when
packaging the DNA. These results may shed light on the
mechanism by which the virus injects DNA into cells
during infection.
The force-induced melting model of DNA overstretching
[23] has been used to determine the free energy of the
helix-coil transition from DNA overstretching. This is
useful for studying DNA–protein interactions, as many
proteins operate by binding to DNA and changing its
stability. One such protein is HIV-1 nucleocapsid protein
(NC), as was recently demonstrated by Williams et al.
[47•]. NC is a nucleic acid chaperone that facilitates the
rearrangement of the structure of nucleic acids in order
to form the lowest energy state [48]. Until now, the
mechanism of this activity was not understood. However,
Williams et al. showed that NC facilitates this rearrangement
by significantly lowering the cooperativity and stability of
the DNA helix-coil transition (Figure 3). These results
show that DNA overstretching is a powerful technique for
studying proteins that may lower the helix-coil transition
free energy of DNA, including other nucleic acid chaperone proteins, as well as ssDNA-binding proteins such as
Escherichia coli SSB [49] and T4 gene 32 [50]. In addition,
DNA-binding drugs that may stabilize or destabilize DNA
could be investigated using this method. A study of
anticancer drugs using AFM showed that these drugs have
a significant effect on DNA overstretching [51•]. Further
analysis of these results and studies of other DNA-binding
drugs are needed.
Conclusions
Given the ability to stretch single RNA hairpin structures,
as demonstrated by Liphardt et al. [17••], single-molecule
force measurement techniques can be extended to
studying the effect of proteins on the helix-coil transition
of specific sequences and specific hairpin structures.
Although both DNA overstretching and nucleic acid
unzipping experiments provide a measurement of the free
energy of the helix-coil transition [17••,29•], unzipping
experiments allow the determination of sequence-specific
information as the molecule is unzipped. Thus, the biophysics of sequence-dependent DNA- and RNA-binding
proteins, such as transcription factors, could be studied in
detail using this technique. In addition, single-molecule
measurements of the kinetics of enzymes that operate on
Force spectroscopy of single DNA and RNA molecules Williams and Rouzina
335
nucleic acids will continue to provide insights into how
these molecules function.
13. Bockelmann U, Essevaz-Roulet B, Heslot F: Molecular stick-slip
motion revealed by opening DNA with piconewton forces. Phys
Rev Lett 1997, 79:4489-4492.
Update
14. Marenduzzo D, Trovato A, Maritan A: Phase diagram of
force-induced DNA unzipping in exactly solvable models. Phys
Rev E 2001, 64:031901.
In a recent article, single DNA molecule stretching
experiments were used to study the reversible disassembly
of nucleosome core particles [52•]. To do this, DNA
molecules with a repeating array of histone-binding
sequences were prepared. As a single DNA molecule was
stretched in the presence of the histones, a repeating
stretch/release pattern revealed the regular disassembly of
single nucleosome core particles that were 70–80 bp in
length. In addition, detailed measurements of the
unzipping of λ-DNA using optical tweezers were recently
published [53], as well as new measurements of the effects
of DNA-binding drugs on DNA stretching curves [54].
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Now in press
The work referred to in the text as (JR Wenner, MC Williams, I Rouzina,
VA Bloomfield, unpublished data) is now in press:
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