81 research outputs found
Pulling a polymer out of a potential well and the mechanical unzipping of DNA
Motivated by the experiments on DNA under torsion, we consider the problem of
pulling a polymer out of a potential well by a force applied to one of its
ends. If the force is less than a critical value, then the process is activated
and has an activation energy proportinal to the length of the chain. Above this
critical value, the process is barrierless and will occur spontaneously. We use
the Rouse model for the description of the dynamics of the peeling out and
study the average behaviour of the chain, by replacing the random noise by its
mean. The resultant mean-field equation is a nonlinear diffusion equation and
hence rather difficult to analyze. We use physical arguments to convert this in
to a moving boundary value problem, which can then be solved exactly. The
result is that the time required to pull out a polymer of segments
scales like . For models other than the Rouse, we argue that Comment: 11 pages, 6 figures. To appear in PhysicalReview
Statistical mechanics of triangulated ribbons
We use computer simulations and scaling arguments to investigate statistical
and structural properties of a semiflexible ribbon composed of isosceles
triangles. We study two different models, one where the bending energy is
calculated from the angles between the normal vectors of adjacent triangles,
the second where the edges are viewed as semiflexible polymers so that the
bending energy is related to the angles between the tangent vectors of
next-nearest neighbor triangles. The first model can be solved exactly whereas
the second is more involved. It was recently introduced by Liverpool and
Golestanian Phys.Rev.Lett. 80, 405 (1998), Phys.Rev.E 62, 5488 (2000) as a
model for double-stranded biopolymers such as DNA. Comparing observables such
as the autocorrelation functions of the tangent vectors and the bond-director
field, the probability distribution functions of the end-to-end distance, and
the mean squared twist we confirm the existence of local twist correlation, but
find no indications for other predicted features such as twist-stretch
coupling, kinks, or oscillations in the autocorrelation function of the
bond-director field.Comment: 10 pages, 13 figures. submitted to PRE, revised versio
Unzipping Dynamics of Long DNAs
The two strands of the DNA double helix can be `unzipped' by application of
15 pN force. We analyze the dynamics of unzipping and rezipping, for the case
where the molecule ends are separated and re-approached at constant velocity.
For unzipping of 50 kilobase DNAs at less than about 1000 bases per second,
thermal equilibrium-based theory applies. However, for higher unzipping
velocities, rotational viscous drag creates a buildup of elastic torque to
levels above kBT in the dsDNA region, causing the unzipping force to be well
above or well below the equilibrium unzipping force during respectively
unzipping and rezipping, in accord with recent experimental results of Thomen
et al. [Phys. Rev. Lett. 88, 248102 (2002)]. Our analysis includes the effect
of sequence on unzipping and rezipping, and the transient delay in buildup of
the unzipping force due to the approach to the steady state.Comment: 15 pages Revtex file including 9 figure
Comment on ``Phase ordering in chaotic map lattices with conserved dynamics''
Angelini, Pellicoro, and Stramaglia [Phys. Rev. E {\bf 60}, R5021 (1999),
cond-mat/9907149] (APS) claim that the phase ordering of two-dimensional
systems of sequentially-updated chaotic maps with conserved ``order parameter''
does not belong, for large regions of parameter space, to the expected
universality class. We show here that these results are due to a slow crossover
and that a careful treatment of the data yields normal dynamical scaling.
Moreover, we construct better models, i.e. synchronously-updated coupled map
lattices, which are exempt from these crossover effects, and allow for the
first precise estimates of persistence exponents in this case.Comment: 3 pages, to be published in Phys. Rev.
Micromechanics of Single Supercoiled DNA Molecules
Abstract. The theory of the mechanical response of single DNA molecules un-der stretching and twisting stresses is reviewed. Using established results for the the semiflexible polymer including the effect of torsional stress, and for the free energy of plectonemic supercoils, a theory of coexisting plectonemic and extended DNA is con-structed and shown to produce phenomena observed experimentally. Analytical results for DNA extension and torque are presented, and effects of anharmonicities in the plec-tonemic free energy are described. An application of the theory to the problem of torsional-stress-induced cruciform extrusion is also discussed. Key words. DNA, molecular biology, statistical mechanics, polymer physics. AMS(MOS) subject classifications. 82D60, 92C05, 92C40
Conformations of Linear DNA
We examine the conformations of a model for under- and overwound DNA. The
molecule is represented as a cylindrically symmetric elastic string subjected
to a stretching force and to constraints corresponding to a specification of
the link number. We derive a fundamental relation between the Euler angles that
describe the curve and the topological linking number. Analytical expressions
for the spatial configurations of the molecule in the infinite- length limit
were obtained. A unique configuraion minimizes the energy for a given set of
physical conditions. An elastic model incorporating thermal fluctuations
provides excellent agreement with experimental results on the plectonemic
transition.Comment: 5 pages, RevTeX; 6 postscript figure
Theory of High-Force DNA Stretching and Overstretching
Single molecule experiments on single- and double stranded DNA have sparked a
renewed interest in the force-extension of polymers. The extensible Freely
Jointed Chain (FJC) model is frequently invoked to explain the observed
behavior of single-stranded DNA. We demonstrate that this model does not
satisfactorily describe recent high-force stretching data. We instead propose a
model (the Discrete Persistent Chain, or ``DPC'') that borrows features from
both the FJC and the Wormlike Chain, and show that it resembles the data more
closely. We find that most of the high-force behavior previously attributed to
stretch elasticity is really a feature of the corrected entropic elasticity;
the true stretch compliance of single-stranded DNA is several times smaller
than that found by previous authors. Next we elaborate our model to allow
coexistence of two conformational states of DNA, each with its own stretch and
bend elastic constants. Our model is computationally simple, and gives an
excellent fit through the entire overstretching transition of nicked,
double-stranded DNA. The fit gives the first values for the elastic constants
of the stretched state. In particular we find the effective bend stiffness for
DNA in this state to be about 10 nm*kbt, a value quite different from either
B-form or single-stranded DNAComment: 33 pages, 11 figures. High-quality figures available upon reques
Fluctuating Filaments I: Statistical Mechanics of Helices
We examine the effects of thermal fluctuations on thin elastic filaments with
non-circular cross-section and arbitrary spontaneous curvature and torsion.
Analytical expressions for orientational correlation functions and for the
persistence length of helices are derived, and it is found that this length
varies non-monotonically with the strength of thermal fluctuations. In the weak
fluctuation regime, the local helical structure is preserved and the
statistical properties are dominated by long wavelength bending and torsion
modes. As the amplitude of fluctuations is increased, the helix ``melts'' and
all memory of intrinsic helical structure is lost. Spontaneous twist of the
cross--section leads to resonant dependence of the persistence length on the
twist rate.Comment: 5 figure
Statistical mechanics of semiflexible ribbon polymers
The statistical mechanics of a ribbon polymer made up of two semiflexible
chains is studied using both analytical techniques and simulation. The system
is found to have a crossover transition at some finite temperature, from a type
of short range order to a fundamentally different sort of short range order. In
the high temperature regime, the 2-point correlation functions of the object
are identical to worm-like chains, while in the low temperature regime they are
different due to a twist structure. The crossover happens when the persistence
length of individual strands becomes comparable to the thickness of the ribbon.
In the low temperature regime, the ribbon is observed to have a novel
``kink-rod'' structure with a mutual exclusion of twist and bend in contrast to
smooth worm-like chain behaviour. This is due to its anisotropic rigidity and
corresponds to an {\it infinitely} strong twist-bend coupling. The
double-stranded polymer is also studied in a confined geometry. It is shown
that when the polymer is restricted in a particular direction to a size less
than the bare persistence length of the individual strands, it develops zigzag
conformations which are indicated by an oscillatory tangent-tangent correlation
function in the direction of confinement. Increasing the separation of the
confining plates leads to a crossover to the free behaviour, which takes place
at separations close to the bare persistence length. These results are expected
to be relevant for experiments which involve complexation of two or more stiff
or semiflexible polymers.Comment: 20 pages, 11 figures. PRE (in press
Tops and Writhing DNA
The torsional elasticity of semiflexible polymers like DNA is of biological
significance. A mathematical treatment of this problem was begun by Fuller
using the relation between link, twist and writhe, but progress has been
hindered by the non-local nature of the writhe. This stands in the way of an
analytic statistical mechanical treatment, which takes into account thermal
fluctuations, in computing the partition function. In this paper we use the
well known analogy with the dynamics of tops to show that when subjected to
stretch and twist, the polymer configurations which dominate the partition
function admit a local writhe formulation in the spirit of Fuller and thus
provide an underlying justification for the use of Fuller's "local writhe
expression" which leads to considerable mathematical simplification in solving
theoretical models of DNA and elucidating their predictions. Our result
facilitates comparison of the theoretical models with single molecule
micromanipulation experiments and computer simulations.Comment: 17 pages two figure
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