Download Denaturation transition of stretched DNA

Topological Aspects of DNA Function and Protein Folding
Denaturation transition of stretched DNA
Andreas Hanke1
Department of Physics and Astronomy, University of Texas at Brownsville, Brownsville, TX 78520, U.S.A.
Abstract
In the last two decades, single-molecule force measurements using optical and magnetic tweezers and
atomic force spectroscopy have dramatically expanded our knowledge of nucleic acids and proteins. These
techniques characterize the force on a biomolecule required to produce a given molecular extension. When
stretching long DNA molecules, the observed force–extension relationship exhibits a characteristic plateau
at approximately 65 pN where the DNA may be extended to almost twice its B-DNA length with almost no
increase in force. In the present review, I describe this transition in terms of the Poland–Scheraga model
and summarize recent related studies.
Introduction
Under physiological conditions in vitro, the thermodynamically stable configuration of DNA is the Watson–Crick double
helix (however, in vivo DNA is supercoiled and constrained
by proteins such as nuclear-associated proteins in prokaryotes
and histones in eukaryotes). In this configuration, the
nucleotides A, T, G and C of each helix pair with those
of the complementary helix according to the key–lock
principle, such that only the base pairs AT and GC can
form [1]. As hydrogen bonds contribute only little to the
helix stability, the major support comes from stacking of base
pairs [2]. However, important biological processes require
the unzipping (denaturation) of a specific region of base
pairs [3,4]. Examples include the docking of single-strandedDNA-binding proteins to DNA, such as DNA replication
via DNA helicase and polymerase and transcription via RNA
polymerase [1,3]. Local unzipping and subsequent rejoining
of base pairs occurs spontaneously in vivo due to thermal
fluctuations in a process named breathing of double-stranded
DNA, which opens up denaturation zones of a few tens
of base pairs; such breathing fluctuations have been studied
experimentally by following the exchange of protons from
imino groups with water [5] and by fluorescent labelling of
synthetic DNA constructs [6]. In a theoretical study, the
probability density of finding a region of open base pairs
of size n at time t was obtained using the Fokker–Planck
equation [7]. Breathing fluctuations may be supported by
accessory proteins which bind to transient single-stranded
DNA, thereby lowering the DNA base-pair stability [4].
DNA denaturation in vitro is accomplished traditionally
by heating, or by titration with acid or alkali. Since GC base
pairs are bound more strongly than AT base pairs (by three
compared with two hydrogen bonds), they denature at a
higher melting temperature, T m . Accordingly, upon heating,
double-stranded DNA starts to unwind in regions rich in
Key words: DNA stretching, helix–coil transition, mechanical properties of DNA, single-molecule
biophysics.
Abbreviations used: FJC, freely jointed chain; PS, Poland–Scheraga.
1
email [email protected]
Biochem. Soc. Trans. (2013) 41, 639–645; doi:10.1042/BST20120298
AT base pairs and then proceeds to regions of higher GC
content. Depending on the fraction of GC base pairs, T m
ranges between 60 and 110◦ C [2]. An important application
of thermal DNA melting is PCR, in which copies of a DNA
sample are created by repeated cycles of thermal unwinding
and subsequent reannealing in a solution of invariable primers
and single nucleotides [8].
A different way to induce local unwinding in DNA
in vitro is subjecting the molecule to mechanical stress. Singlemolecule force spectroscopy has opened the possibility to
induce denaturation regions in DNA by traction in an atomic
force microscope or optical tweezers instrument. In these
experiments, the end-to-end separation, L, of a single DNA
molecule is varied and the force, F, between the ends is
recorded as a function of L. When stretching long DNA,
e.g. λ-DNA, the observed force–extension relationship, F(L),
exhibits a distinct plateau at approximately 65 pN where the
DNA may be extended to approximately 1.7 times its natural
B-DNA length with almost no increase in force, before the
DNA duplex unbinds at larger forces [9–12]; this process has
been named the overstretching transition.
Since its discovery, the overstretched configuration
of DNA has been a matter of debate. In the early
stretching experiments of DNA, it was proposed that the
overstretching transition at 65 pN is a transition of BDNA to a new stretched form of DNA, named S-DNA, in
which base-pairing remains but canonical intra-strand base
stacking is absent [9–13]. This hypothesis was supported
by molecular modelling studies of DNA duplex stretching
which reproduced a transition to a base-paired ladder-like
structure [14–16]. The occurrence of S-DNA found also
support by thermodynamic examination of experimental
force–extension relationships [13] and by studying the
dynamic behaviour in a model of DNA overstretching [17].
A different scenario for the DNA overstretching transition
assumes force-induced melting of B-DNA into two strands
of single-stranded DNA, similar to that observed for thermal
melting (Figure 1). Williams, Rouzina, Bloomfield and coworkers have shown that force-induced DNA melting
quantitatively explains experimental DNA force–extension
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Figure 1 Force–extension relationship for stretched DNA
The extension data for a typical λ-DNA molecule is shown as the
continuous black line, whereas the relaxation data is shown as
the broken line. Minimal hysteresis is observed under the solution
conditions of the experiment (100 mM Na + , 10 mM Hepes, pH 7.5,
T = 20◦ C). The worm-like chain model describes double-stranded DNA
(green line) and the FJC model describes single-stranded DNA (blue
line). Upon stretching the molecule beyond its double-stranded contour
length, the DNA duplex undergoes a force-induced melting transition
from double-stranded to single-stranded DNA. Reproduced from Physics
of Life Reviews, 7(3), Chaurasiya, K.R., Paramanathan, T., McCauley, M.J.,
Williams, M.C., Biophysical characterization of DNA binding from single
c 2010, with permission from
molecule force measurements, 299–341, Elsevier.
relationships for a broad range of solution conditions set by
ionic strength, pH, temperature [18–21], and the presence
of DNA-binding ligands [22–26]. Force-induced melting
has also been observed in molecular dynamics simulations
of short DNA oligomers when entropic contributions of
denatured DNA regions are taken into account [27,28].
DNA overstretching in the presence of glyoxal demonstrated
that base pairs were indeed exposed to solution during
overstretching [29]. Experiments have demonstrated forceinduced melting of λ-DNA directly using fluorescent labels
specific to double-stranded and single-stranded DNA [30].
Force-induced melting was also observed for stretching
short DNA duplex molecules of given GC and AT content
[31]. In DNA-stretching experiments, strand separation
may occur either from free ends or nicks by one strand
peeling off from the other [30–34], or by DNA melting
in the middle, in close analogy to thermal melting;
interestingly, DNA overstretching was found to occur
at 65 pN for topologically closed but rotationally free
DNA, and at 110 pN for torsionally constrained DNA,
which implies that overstretching DNA does not require
peeling from free ends or nicks [35]. Whereas singlestranded-DNA-binding proteins are expected to favour
DNA melting by peeling from free ends or nicks, intercalators
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Authors Journal compilation and other DNA-binding ligands that stabilize doublestranded DNA preferentially lead to DNA melting in the
middle [36].
Force-induced destabilization of DNA has become a
valuable tool to probe the interaction of proteins that bind
to single-stranded or double-stranded DNA at physiological
melting temperatures T m (F), well below T m (0) of free DNA
[22–26] (for a review on protein and small-molecule binding
on DNA probed by DNA-stretching experiments, see [37]).
The current body of experimental data suggests that forceinduced DNA melting is the prevalent mechanism in the
presence of DNA-binding ligands, whereas S-DNA may
occur as an intermediate in the absence of binding ligands.
DNA denaturation can be described by the classical PS
(Poland–Scheraga) model, which views DNA at the transition
as an alternating sequence of bound double-stranded and
denatured single-stranded domains. Double-stranded regions
are governed by hydrogen-bonding of base pairs as well as
base stacking, whereas denatured regions are governed by
the entropy gain upon disruption of base pairs [38,39]. The
PS model is fundamental in biological physics and has been
progressively refined to obtain a quantitative understanding
of the DNA-melting process [40,41]. In what follows, I
describe the force-induced melting transition of DNA in
the framework of the PS model in its simplest form, in
which bound domains are modelled as rigid segments of
double-stranded DNA and denatured domains as flexible
freely jointed chains of single-stranded DNA [42]. Modelling
force-induced DNA melting in terms of the PS model is
appropriate when DNA melts in the middle, such as in the
presence of DNA-binding ligands which stabilize doublestranded DNA. The PS model reproduces essential features
of force-induced DNA-denaturation experiments, including
a lower melting temperature T m (F) for finite stretching forces
F compared with free DNA, and a plateau in the force–
extension relationship F(L).
PS model for stretched DNA
The denaturation transition is most easily discussed in the
grand-canonical ensemble in which the total number N of
base pairs and the end-to-end vector R of the chain are
allowed to fluctuate. The grand-canonical partition function
of a chain with an applied external force F in the x-direction
is given by [42]
Z (z, F ) =
∞ d3 RZcan (N, R) zN exp(β FRx )
(1)
N=1
where β = (kB T) − 1 (T is the temperature and kB is
Boltzmann’s constant) and z is the fugacity conjugate to N.
Zcan (N,R) is the canonical partition function of a chain with
fixed N and R, and Rx is the x-component of R (Figure 2).
The grand-canonical partition function Z(z,F) in eqn (1) can
be expressed in terms of a sum over alternating sequences of
bound segments and denatured loops. Assuming that bound
segments and denatured loops are statistically independent,
Topological Aspects of DNA Function and Protein Folding
Figure 2 Stretched DNA in the PS model with bound segments B
Figure 3 Bound segment and denatured loop in the PS model for
and denatured loops The DNA is attached between O and R and subject to an external force
stretched DNA
(a) Bound segment of double-stranded DNA modelled as a rigid rod
F in the x-direction.
with end-to-end vector r and applied force F in the x-direction. The
length of the rod is r = kxds , where k is the number of base pairs of
length xds and x = rcos(θ ) is the x-component of r. (b) Denatured loop
of single-stranded DNA modelled as an FJC of segments of equal length
b. The FJC forms a loop with end-to-end vector r and applied force F
in the x-direction. Segment vectors ti and si with i = 1, . . . , k form two
arcs of equal length corresponding to perfect matching of base pairs.
each sequence factorizes and one obtains (Figure 2)
∞
2e B
n
Z (z, F ) = e + e
[Be ] Be = e +
1 − B
n=0
(2)
B(z,F) and (z,F) are the statistical weights of bound
segments and denatured loops within the chain respectively,
and e (z,F) is the statistical weight of the end unit at both
ends of the chain. Eqn (2) is generally valid as long as bound
segments and denatured loops are statistically independent;
conversely, the statistical weights B, and e as functions of
z, T and F (and possibly other control parameters) depend
on the choice of specific models. In what follows, we discuss
the simplest case in which bound segments are modelled as
rigid rods and denatured loops as flexible FJCs (freely jointed
chains).
Bound segments
Double-stranded DNA is fairly stiff on microscopic length
scales, corresponding to a relatively large persistence
length Pds of 50 nm. It is therefore justified to model a segment
of bound intact DNA with k base pairs as a rigid rod of length
kxds where xds = 0.34 nm is the length of a bound base pair
in B-DNA [18] (Figure 3a). For simplicity, we assume that
the binding energy per base pair has the same value E0 < 0
for all base pairs. The statistical weight of a bound segment
with k base pairs and fixed spatial orientation is then given by
ωk where ω = exp(βε) and ε = − E0 > 0. Assuming that the
segment is free to rotate about one end while the other end
is subject to a force F in the x-direction, the statistical weight
becomes [42]
sinh(φk)
ωk
(3)
d2 r̂ exp (β F x) = ωk
B (k, F ) =
4π
φk
S
where r is the end-to-end vector of the segment and x is the
x-component of r (Figure 3a). In eqn (3), we have introduced
the dimensionless force variable
φ = β F x dS
(4)
The integration in eqn (3) is over the surface of the threedimensional unit sphere S of area 4π , corresponding to an
integration over orientations of the unit vector r̂ = r/r , where
r = |r| = kxds . B(k,F) is normalized such that B = ωk for F = 0,
in accordance with previous calculations for free DNA [43].
If the number of base pairs k of the segment is allowed to
fluctuate at given fugacity z, the statistical weight becomes
∞
1 − ωz exp(−φ)
1
ln
(5)
B (k, F ) zk =
B (z, F ) =
2φ
1 − ωz exp(φ)
k=1
For F = 0, corresponding to the limit φ→0 in eqn (5), one
obtains B(z,0) = ωz/(1 − ωz) as found previously for free
DNA [43].
Denatured loops
Single-stranded DNA in denatured loops is far more flexible
than double-stranded DNA. Values of the persistence length
Pss for single-stranded DNA were found to range between
0.7 nm [10] and 2 nm [44], corresponding to approximately
one to three nucleotides of length xss = 0.6 nm [18]. It is
therefore justified to model the single-stranded DNA in
a denatured loop as an FJC with 2k segments of fixed
length b (Figure 3b). In the absence of an energetic cost for
bending between successive segments, b is equivalent to the
Kuhn length of the chain, corresponding to twice its
persistence length Pss . To mimic the key–lock principle of
natural DNA, we assume perfect matching of base pairs,
which implies that both arcs of a denatured loop have the
same length. The statistical weight of a loop with 2k segments
and displacement vector r thus corresponds to the number of
conformations of an FJC starting at the origin O, visiting the
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point r after k segments, and returning to O after 2k segments
(Figure 3b). This conformation number is given by
(k, r) = [C(k)ρk(r)a 3 ]2
(6)
C(k) is the number of conformations of a linear FJC
with k segments which is fixed at one end, and ρ k (r) is
the probability density for the end-to-end vector r of this
chain; a is a microscopic length, e.g. the lattice constant of a
supporting lattice. Thus C(k)ρ k (r)a3 in eqn (6) is the number
of conformations of a linear FJC with k segments starting at
O and ending in the volume element a3 at r, corresponding
to an arc of the loop. Since the loop has two such arcs, (k,r)
in eqn (6) is the square of this number. The conformation
number C(k) has the general form
parameters. Using b = 2.5 nm, xds = 0.34 nm and xss = 0.6 nm,
one finds α = 1.08. The amplitude A in eqn (11) is given by
A = σ0
a3
b3
3b
4π xs s
3/2
(13)
where we have included the loop initiation factor σ 0 1,
quantifying the initiation of a loop in previously intact
double-stranded DNA. Thus A 1 if σ 0 1 is included.
If the number of broken base pairs in a loop is allowed to
fluctuate at given fugacity z, the statistical weight of the loop
becomes, using eqn (11),
(z, F ) =
∞
(, F )z = A
=1
C(k) = μk
(7)
where μ is the connectivity constant of the supporting lattice.
The number μ is a measure of the degrees of freedom of one
individual segment in the chain, e.g. μ = 6 for a random walk
on a three-dimensional cubic lattice.
If the displacement vector r of a loop can move freely,
subject to an applied external force F in the x-direction, the
statistical weight becomes
(k, r) exp (β F x)
(k, F ) =
r
= μ2ka 3
d3 rρk(r)2 exp(β F x)
(8)
with (k,r) from eqn (6) and x the x-component of r. The sum
in the first line of eqn (8) is over all displacement vectors r on
a supporting lattice with lattice constant a, and in the second
line, we replace this sum by an integral using the volume
element d3 r = a3 . The statistical weight (k,F) in eqn (8) is
determined by the probability density ρ k (r); in the simplest
case, the FJC is treated in the Gaussian limit (corresponding
to the limit k→∞, b→0 in such a way that kb2 stays fixed),
for which
3/2
3
3r 2
(9)
ρk (r) =
exp
−
2π kb2
2kb2
Inserting ρ k (r) from eqn (9) into eqn (8) one obtains
3/2
3
3
(β F b)2 k
2k a
−3/2
k
exp
(k, F ) = μ 3
b 4π
12
(10)
This equation can be expressed as
(, F ) = As −3/2 exp(αφ 2 )
(11)
where is the number of broken base pairs in a loop of 2k
segments, i.e. k segments in each of the two arcs (Figure 3b).
Since single-stranded DNA contains b/xss nucleotides per
segment of length b, one obtains
=
kb
xs s
(12)
The variable φ = βFxds in eqn (11) has been introduced in eqn
(4), and s = μ2xs s /b and α = bxss /(12xds 2 ) are dimensionless
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u −c = ALic (u)
(14)
=1
where c = 3/2 and
u = szexp(αφ 2 )
The function Lic (u) =
(15)
∞
=1
u −c in eqn (14) is the polylog
function; for |u|<1, Lic (u) converges for any value of c. For
u = 1, there are three cases: (i) c1, Lic (1) diverges; (ii) 1<c2,
Lic (1) converges, but Lic (u)|u = 1 diverges; (iii) c > 2, both
Lic (1) and Lic (u)|u = 1 converge. The limit u = 1 corresponds
to the value
zm(T, F ) = s −1 exp(−αφ 2 )
(16)
of the fugacity (recall φ = βFxds ), thus (z,F) is only welldefined for zzm and diverges for z > zm . The statistical
weight e of an end unit modelled as an FJC in the Gaussian
limit may be derived in a similar way and one obtains
e (z,F) = Ae Li0 (u) (Figure 3b).
Fraction of bound base pairs and DNA extension
From the grand-canonical partition function in eqn (1), one
obtains the average number of base pairs
N =
∂ln(Z)
∂ln(z)
(17)
If the number of base pairs N is set, one has to choose the
fugacity z such that N = <N > , which implies that z becomes
a function of N. The average number <Nb > of bound base
pairs is given by (see eqns 2 and 3)
Nb =
∂ln(Z)
∂ln(ω)
(18)
Similarly, the average of the x-component of DNA extension
is given by
Rx =
1 ∂ ln(Z)
β ∂F
(19)
Thus z acts as a fugacity for base pairs (bound or unbound), ω
acts as a fugacity for bound base pairs, and βF acts as a fugacity
Topological Aspects of DNA Function and Protein Folding
Figure 4 Behaviour of (z,T,F) and 1/B(z,T,F) as T is varied through the melting temperature T m
z∗ is the smallest value of z for which the thermodynamic limit (TL) <N > →∞ occurs. For T<T m , z∗ is determined by the
intersection of (z) and B(z) − 1 (bound state). For T > T m , z∗ = zm , where zm is defined by the fact that (z) diverges for
z > zm (denatured state). The melting transition occurs if (z) and B(z) − 1 intersect at zm .
for the x-component of DNA extension. The average fraction
of bound base pairs is given by
(z, F ) =
Nb N (20)
Similarly, the average of the x-component of DNA extension
per base pair in units of xds is given by
Rx (z, F ) =
1 Rx xds N (21)
The fraction is the order parameter of the denaturation
transition for free unstretched DNA and can be measured
by light absorption at wavelengths of approximately 260 nm.
For free DNA, the temperature-dependence (T) is referred
to as the melting curve. Conversely, the force–extension
relationship Rx (T,F) is measured directly in DNA-stretching
experiments.
In order to obtain the phase diagram of the model in
the (T,F)-plane, the average fraction of bound base pairs should be evaluated in the thermodynamic limit <N > →∞
(in practice, results derived for the thermodynamic limit
are accurate for N of the order of a few tens of base
pairs and larger). Formally, the extensive parameters <N > ,
<Nb > and <Rx > /xds may be obtained as derivatives of the
thermodynamic potential
(ln z, ln ω, ln φ, V) = ln Z(z, ω, φ, V)
(22)
with respect to the intensive parameters ln z, ln ω and
ln φ (where φ = βFxds ). (In eqn 22, we assume that the
system is enclosed in a finite volume V, with corresponding
pressure p = − ∂/∂V; without the inclusion of V, the Euler
equation implies = 0.) The Gibbs–Duhem relationship for
the thermodynamic potential in eqn (22) is given by (for
constant pressure p)
N d ln z + Nb d ln ω +
Rx dlnφ = 0
xds
(23)
Dividing by <N > , one obtains
d ln z + d ln ω + Rx d ln φ = 0
(24)
with and Rx from eqns (20) and (21). Eqn (24) may be used
to carry out the thermodynamic limit <N > →∞; noting that
z = z(ω,φ,<N > ), one obtains for <N > →∞.
d ln (z∗ ) + ∗ d ln ω + Rx∗ d ln φ = 0
(25)
where z∗ (ω,φ) is the value of the fugacity in the
limit <N > →∞. Similarly, ∗ (ω,F) = (z∗ ,ω,φ) and
Rx ∗ (ω,F) = Rx (z∗ ,ω,φ) are the values of and Rx for
<N > →∞. For constant φ, one obtains from eqn (25)
∗ (ω, F ) = −
∂ ln z∗ (ω, φ)
∂ ln φ
(26)
Similarly, for constant ω, one obtains
Rx∗ (ω, F ) = −
∂ ln z∗ (ω, φ)
∂ ln φ
(27)
Eqns (26) and (27) yield the fraction of bound base pairs and the DNA extension Rx per base pair in units of xds in the
thermodynamic limit N→∞.
Phase diagrams
The quantity z∗ (ω,φ) in eqns (26) and (27) is the lowest value
of z for which <N > in eqn (17) diverges. For T<T m , this
limit occurs for the case that the denominator on the righthand side of eqn (2) vanishes. This implies that z∗ (ω,φ) is
implicitly determined by the condition
(z∗ , φ)B(z∗ , ω, φ) = 1, T < Tm
(28)
Graphically, z∗ is obtained by intersection of (z) and B(z) − 1
as functions of z. Both (z) and B(z) are increasing in z,
thus B(z) − 1 is decreasing. Figure 4 shows schematically the
behaviour of (z) and B(z) − 1 as T is varied through the
transition temperature T m . Here we consider a value c > 1 of
the exponent c > 1 in eqn (14), so that (zm ) is finite {for
1<c2, the slope of (z) at zm diverges, whereas for c > 2,
the slope of (z) at zm is finite; as a result, one finds that in
the former case the denaturation transition is of second order,
whereas in the latter case it is of first order [43]}.
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Consider a bound state of the DNA chain at T<T m where
the fraction of bound base pairs is finite, i.e. > 0. As T
increases, the curve B(z) − 1 increases, whereas (z) remains
constant. Thus the value z∗ of z at the intersection of the two
curves increases (Figure 4). However, z∗ can only increase
until it reaches the value zm given by eqn (16) because diverges for z > zm . This can only occur for c > 1, since (zm )
itself diverges for c1, which implies that no thermodynamic
phase transition is possible for c1. Conversely, for c > 1,
the denaturation transition takes place for z∗ = zm , where z∗
is determined by eqn (28) and zm is the smallest value of z
for which (z) diverges, given by eqn (16). Combining the
condition z∗ = zm with eqn (28) yields an implicit relationship
for the transition line Fm (T) :
B[zm (T, F ), T, F ] = (zm )−1 .
Figure 5 Transition lines f m = F m xds /ε as a function of t = k B T/ε
for α = 1 and s = 5 as predicted by eqn (29)
Qualitatively, the transition line to the right of the maximum (i.e.
for t > 1.6) shows that, for finite stretching force F, i.e. finite f, the
transition from bound to denatured DNA occurs at a lower melting
temperature T m (f) than for free DNA, i.e. F = f = 0. Thus a finite
stretching force destabilizes the DNA duplex, in accordance with
DNA-stretching experiments.
(29)
Here we have used (zm ) = ALic (1) = Aζ (1), independent
of T and F; see eqn (16). For free DNA, i.e. F = 0, zm is
independent of T and eqn (29) reduces to the condition for
the T m for free DNA.
Figure 5 shows transition lines f m (t) in terms of the
dimensionless variables f = Fxds /ε and t = kB T/ε, using eqn
(29) in conjunction with eqns (10) and (5). The lines f m (t)
separate a finite region of bound states from an infinite region
of denatured states. The point (t0 ,f = 0) with t0 = tm (f = 0)
corresponds to the melting transition for free DNA, i.e. F = 0.
For F > 0, the shape of the transition lines f m (t) depends on
the parameters A, α and s entering the statistical weight of denatured loops in eqn (11); Figure 5 shows f m (t) for
A = 1 and A = 0.01, with α = 1, s = 5. The value A = 0.01
corresponds to the more realistic case of a small loop initiation
factor σ 0 1 (see eqn 13). The lines f m (t) contain a region in
which f m (t) decreases with t, such that increased stretching
forces f lower the melting temperature tm (f ), corresponding
to force-induced destabilization of DNA as observed in
experiments [22–26,37]. Interestingly, f m (t) vanishes for both
t→t0 and t→0. This re-entrant behaviour implies that, for
given 0<f 0 <f max , where f max is the maximum of f m (t), the
chain does not only denature at a large value tm + (f 0 ), but
also at a smaller value tm − (f 0 ).
associated with DNA helix destabilization and DNA–ligand
binding.
In spite of the progress made in single-molecule force
experiments, a poor understanding of the structural and
thermodynamic response of biomolecules to mechanical
stress has limited the insight that such experiments have
provided into helix destabilization and DNA–ligand binding.
A notorious difficulty for modelling force-induced melting
is the vast range of length and time scales spanned by
the process. An important objective of future studies is
therefore to develop biophysical models that capture the
crossing length and times scales from the atomistic to the
macromolecular level. In the present paper, I have shown
that the PS model provides a potential starting point to better
understand force–extension relationships of stretched DNA.
Acknowledgement
I thank Mark C. Williams for helpful discussions.
Summary
Single-molecule force measurements using optical and
magnetic tweezers and atomic force microscopy have
dramatically expanded our knowledge of nucleic acids and
proteins. Specifically, stretching single DNA molecules by
an optical tweezers instrument can induce the unwinding of
the two strands of the DNA duplex. The induced structural
and thermodynamic changes in the DNA double helix upon
stretching alter interactions with DNA-binding ligands in a
controllable and measurable way. Therefore single-molecule
force measurements of DNA and DNA–ligand interactions
provide an unprecedented opportunity for quantitative study
of a wide range of physiologically important phenomena
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Authors Journal compilation Funding
This work was supported by the National Institutes of Health [grant
number 5SC3GM083779-03].
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Received 6 December 2012
doi:10.1042/BST20120298
C The
C 2013 Biochemical Society
Authors Journal compilation 645