260 research outputs found
Comment on "Elasticity Model of a Supercoiled DNA Molecule"
We perform simulations to numerically study the writhe distribution of a
stiff polymer. We compare with analytic results of Bouchiat and Mezard (PRL 80
1556- (1998); cond-mat/9706050).Comment: 1 page, 1 figure revtex
Non-equilibrium hydrodynamics of a rotating filament
The nonlinear dynamics of an elastic filament that is forced to rotate at its
base is studied by hydrodynamic simulation techniques; coupling between
stretch, bend, twist elasticity and thermal fluctuations is included. The
twirling-overwhirling transition is located and found to be strongly
discontinuous. For finite bend and twist persistence length, thermal
fluctuations lower the threshold rotational frequency, for infinite persistence
length the threshold agrees with previous analytical predictions
Diffusion of a ring polymer in good solution via the Brownian dynamics
Diffusion constants D_{R} and D_{L} of ring and linear polymers of the same
molecular weight in a good solvent, respectively, have been evaluated through
the Brownian dynamics with hydrodynamic interaction. The ratio ,
which should be universal in the context of the renormalization group, has been
estimated as for the large-N limit. It should be consistent
with that of synthetic polymers, while it is smaller than that of DNAs such as
. Furthermore, the probability of the ring polymer being a
nontrivial knot is found to be very small, while bond crossings may occur at
almost all time steps in the present simulation that realizes the good solvent
conditions.Comment: 11 pages, 4 figure
Modeling Bacterial DNA: Simulation of Self-avoiding Supercoiled Worm-Like Chains Including Structural Transitions of the Helix
Under supercoiling constraints, naked DNA, such as a large part of bacterial
DNA, folds into braided structures called plectonemes. The double-helix can
also undergo local structural transitions, leading to the formation of
denaturation bubbles and other alternative structures. Various polymer models
have been developed to capture these properties, with Monte-Carlo (MC)
approaches dedicated to the inference of thermodynamic properties. In this
chapter, we explain how to perform such Monte-Carlo simulations, following two
objectives. On one hand, we present the self-avoiding supercoiled Worm-Like
Chain (ssWLC) model, which is known to capture the folding properties of
supercoiled DNA, and provide a detailed explanation of a standard MC simulation
method. On the other hand, we explain how to extend this ssWLC model to include
structural transitions of the helix.Comment: Book chapter to appear in The Bacterial Nucleoid, Methods and
Protocols, Springer serie
Universality in the diffusion of knots
We have evaluated a universal ratio between diffusion constants of the ring
polymer with a given knot and a linear polymer with the same molecular
weight in solution through the Brownian dynamics under hydrodynamic
interaction. The ratio is found to be constant with respect to the number of
monomers, , and hence the estimate at some should be valid practically
over a wide range of for various polymer models. Interestingly, the ratio
is determined by the average crossing number () of an ideal
conformation of knotted curve , i.e. that of the ideal knot. The of
ideal knots should therefore be fundamental in the dynamics of knots.Comment: 8 pages, 14 figure
On the Limits of Analogy Between Self-Avoidance and Topology-Driven Swelling of Polymer Loops
The work addresses the analogy between trivial knotting and excluded volume
in looped polymer chains of moderate length, , where the effects of
knotting are small. A simple expression for the swelling seen in trivially
knotted loops is described and shown to agree with simulation data. Contrast
between this expression and the well known expression for excluded volume
polymers leads to a graphical mapping of excluded volume to trivial knots,
which may be useful for understanding where the analogy between the two
physical forms is valid. The work also includes description of a new method for
the computational generation of polymer loops via conditional probability.
Although computationally intensive, this method generates loops without
statistical bias, and thus is preferable to other loop generation routines in
the region .Comment: 10 pages, 5 figures, supplementary tex file and datafil
Getting DNA twist rigidity from single molecule experiments
We use an elastic rod model with contact to study the extension versus
rotation diagrams of single supercoiled DNA molecules. We reproduce
quantitatively the supercoiling response of overtwisted DNA and, using
experimental data, we get an estimation of the effective supercoiling radius
and of the twist rigidity of B-DNA. We find that unlike the bending rigidity,
the twist rigidity of DNA seems to vary widely with the nature and
concentration of the salt buffer in which it is immerged
Mechanical response of plectonemic DNA: an analytical solution
We consider an elastic rod model for twisted DNA in the plectonemic regime.
The molecule is treated as an impenetrable tube with an effective, adjustable
radius. The model is solved analytically and we derive formulas for the contact
pressure, twisting moment and geometrical parameters of the supercoiled region.
We apply our model to magnetic tweezer experiments of a DNA molecule subjected
to a tensile force and a torque, and extract mechanical and geometrical
quantities from the linear part of the experimental response curve. These
reconstructed values are derived in a self-contained manner, and are found to
be consistent with those available in the literature.Comment: 14 pages, 4 figure
Gyration radius of a circular polymer under a topological constraint with excluded volume
It is nontrivial whether the average size of a ring polymer should become
smaller or larger under a topological constraint.
Making use of some knot invariants, we evaluate numerically the mean square
radius of gyration for ring polymers having a fixed knot type, where the ring
polymers are given by self-avoiding polygons consisting of freely-jointed hard
cylinders. We obtain plots of the gyration radius versus the number of
polygonal nodes for the trivial, trefoil and figure-eight knots. We discuss
possible asymptotic behaviors of the gyration radius under the topological
constraint. In the asymptotic limit, the size of a ring polymer with a given
knot is larger than that of no topological constraint when the polymer is thin,
and the effective expansion becomes weak when the polymer is thick enough.Comment: 12pages,3figure
On the size of knots in ring polymers
We give two different, statistically consistent definitions of the length l
of a prime knot tied into a polymer ring. In the good solvent regime the
polymer is modelled by a self avoiding polygon of N steps on cubic lattice and
l is the number of steps over which the knot ``spreads'' in a given
configuration. An analysis of extensive Monte Carlo data in equilibrium shows
that the probability distribution of l as a function of N obeys a scaling of
the form p(l,N) ~ l^(-c) f(l/N^D), with c ~ 1.25 and D ~ 1. Both D and c could
be independent of knot type. As a consequence, the knot is weakly localized,
i.e. ~ N^t, with t=2-c ~ 0.75. For a ring with fixed knot type, weak
localization implies the existence of a peculiar characteristic length l^(nu) ~
N^(t nu). In the scaling ~ N^(nu) (nu ~0.58) of the radius of gyration of the
whole ring, this length determines a leading power law correction which is much
stronger than that found in the case of unrestricted topology. The existence of
such correction is confirmed by an analysis of extensive Monte Carlo data for
the radius of gyration. The collapsed regime is studied by introducing in the
model sufficiently strong attractive interactions for nearest neighbor sites
visited by the self-avoiding polygon. In this regime knot length determinations
can be based on the entropic competition between two knotted loops separated by
a slip link. These measurements enable us to conclude that each knot is
delocalized (t ~ 1).Comment: 29 pages, 14 figure
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