527 research outputs found
A coil-globule transition of a semiflexible polymer driven by the addition of spherical particles
The phase behaviour of a single large semiflexible polymer immersed in a
suspension of spherical particles is studied. All interactions are simple
excluded volume interactions and the diameter of the spherical particles is an
order of magnitude larger than the diameter of the polymer. The spherical
particles induce a quite long ranged depletion attraction between the segments
of the polymer and this induces a continuous coil-globule transition in the
polymer. This behaviour gives an indication of the condensing effect of
macromolecular crowding on DNA.Comment: 12 pages, 4 figure
Thermodynamics and Topology of Disordered Systems: Statistics of the Random Knot Diagrams on Finite Lattice
The statistical properties of random lattice knots, the topology of which is
determined by the algebraic topological Jones-Kauffman invariants was studied
by analytical and numerical methods. The Kauffman polynomial invariant of a
random knot diagram was represented by a partition function of the Potts model
with a random configuration of ferro- and antiferromagnetic bonds, which
allowed the probability distribution of the random dense knots on a flat square
lattice over topological classes to be studied. A topological class is
characterized by the highest power of the Kauffman polynomial invariant and
interpreted as the free energy of a q-component Potts spin system for
q->infinity. It is shown that the highest power of the Kauffman invariant is
correlated with the minimum energy of the corresponding Potts spin system. The
probability of the lattice knot distribution over topological classes was
studied by the method of transfer matrices, depending on the type of local
junctions and the size of the flat knot diagram. The obtained results are
compared to the probability distribution of the minimum energy of a Potts
system with random ferro- and antiferromagnetic bonds.Comment: 37 pages, latex-revtex (new version: misprints removed, references
added
Localization in simple multiparticle catalytic absorption model
We consider the phase transition in the system of n simultaneously developing
random walks on the halfline x>=0. All walks are independent on each others in
all points except the origin x=0, where the point well is located. The well
depth depends on the number of particles simultaneously staying at x=0. We
consider the limit n>>1 and show that if the depth growth faster than 3/2 n
ln(n) with n, then all random walks become localized simultaneously at the
origin. In conclusion we discuss the connection of that problem with the phase
transition in the copolymer chain with quenched random sequence of monomers
considered in the frameworks of replica approach.Comment: 17 pages in LaTeX, 5 PostScript figures; submitted to J.Phys.(A):
Math. Ge
Mechanical coupling in flashing ratchets
We consider the transport of rigid objects with internal structure in a
flashing ratchet potential by investigating the overdamped behavior of a
rod-like chain of evenly spaced point particles. In 1D, analytical arguments
show that the velocity can reverse direction multiple times in response to
changing the size of the chain or the temperature of the heat bath. The
physical reason is that the effective potential experienced by the mechanically
coupled objects can have a different symmetry than that of individual objects.
All analytical predictions are confirmed by Brownian dynamics simulations.
These results may provide a route to simple, coarse-grained models of molecular
motor transport that incorporate an object's size and rotational degrees of
freedom into the mechanism of transport.Comment: 9 pages, 10 figure
Equation of State for Macromolecules of Variable Flexibility in Good Solvents: A Comparison of Techniques for Monte Carlo Simulations of Lattice Models
The osmotic equation of state for the athermal bond fluctuation model on the
simple cubic lattice is obtained from extensive Monte Carlo simulations. For
short macromolecules (chain length N=20) we study the influence of various
choices for the chain stiffness on the equation of state. Three techniques are
applied and compared in order to critically assess their efficiency and
accuracy: the repulsive wall method, the thermodynamic integration method
(which rests on the feasibility of simulations in the grand canonical
ensemble), and the recently advocated sedimentation equilibrium method, which
records the density profile in an external (e.g. gravitation-like) field and
infers, via a local density approximation, the equation of state from the
hydrostatic equilibrium condition. We confirm the conclusion that the latter
technique is far more efficient than the repulsive wall method, but we find
that the thermodynamic integration method is similarly efficient as the
sedimentation equilibrium method. For very stiff chains the onset of nematic
order enforces the formation of isotropic-nematic interface in the
sedimentation equilibrium method leading to strong rounding effects and
deviations from the true equation of state in the transition regime.Comment: 32 pages, 18 figures, submitted to Phys.Rev.E; one paragraph added to
conclusions sectio
An integral equation approach to effective interactions between polymers in solution
We use the thread model for linear chains of interacting monomers, and the
``polymer reference interaction site model'' (PRISM) formalism to determine the
monomer-monomer pair correlation function for dilute and
semi-dilute polymer solutions, over a range of temperatures from very high
(where the chains behave as self-avoiding walks) to below the
temperature, where phase separation sets in. An inversion procedure, based on
the HNC integral equation, is used to extract the effective pair potential
between ``average'' monomers on different chains. An accurate relation between
, [the pair correlation function between the polymer
centers of mass (c.m.)], and the intramolecular form factors is then used to
determine , and subsequently extract the effective c.m.-c.m. pair
potential by a similar inversion procedure. depends on
temperature and polymer concentration, and the predicted variations are in
reasonable agreement with recent simulation data, except at very high
temperatures, and below the temperature.Comment: 13 pages, 13 figures, revtex ; revised versio
A model of inversion of DNA charge by a positive polymer: fractionization of the polymer charge
Charge inversion of a DNA double helix by an oppositely charged flexible
polyelectrolyte (PE) is considered. We assume that, in the neutral state of the
DNA-PE complex, each of the DNA charges is locally compensated by a PE charge.
When an additional PE molecule is adsorbed by DNA, its charge gets fractionized
into monomer charges of defects (tails and arches) on the background of the
perfectly neutralized DNA. These charges spread all over the DNA eliminating
the self-energy of PE. This fractionization mechanism leads to a substantial
inversion of the DNA charge, a phenomenon which is widely used for gene
delivery.Comment: 4 pages, 2 figures. Improved figures and various corrections to tex
Abundance of unknots in various models of polymer loops
A veritable zoo of different knots is seen in the ensemble of looped polymer
chains, whether created computationally or observed in vitro. At short loop
lengths, the spectrum of knots is dominated by the trivial knot (unknot). The
fractional abundance of this topological state in the ensemble of all
conformations of the loop of segments follows a decaying exponential form,
, where marks the crossover from a mostly unknotted
(ie topologically simple) to a mostly knotted (ie topologically complex)
ensemble. In the present work we use computational simulation to look closer
into the variation of for a variety of polymer models. Among models
examined, is smallest (about 240) for the model with all segments of the
same length, it is somewhat larger (305) for Gaussian distributed segments, and
can be very large (up to many thousands) when the segment length distribution
has a fat power law tail.Comment: 13 pages, 6 color figure
Free Energy Self-Averaging in Protein-Sized Random Heteropolymers
Current theories of heteropolymers are inherently macrpscopic, but are
applied to folding proteins which are only mesoscopic. In these theories, one
computes the averaged free energy over sequences, always assuming that it is
self-averaging -- a property well-established only if a system with quenched
disorder is macroscopic. By enumerating the states and energies of compact 18,
27, and 36mers on a simplified lattice model with an ensemble of random
sequences, we test the validity of the self-averaging approximation. We find
that fluctuations in the free energy between sequences are weak, and that
self-averaging is a valid approximation at the length scale of real proteins.
These results validate certain sequence design methods which can exponentially
speed up computational design and greatly simplify experimental realizations.Comment: 4 pages, 3 figure
Relaxation of a Single Knotted Ring Polymer
The relaxation of a single knotted ring polymer is studied by Brownian
dynamics simulations. The relaxation rate lambda_q for the wave number q is
estimated by the least square fit of the equilibrium time-displaced correlation
function to a double exponential decay at long times. The relaxation rate
distribution of a single ring polymer with the trefoil knot appears to behave
as lambda_q=A(1/N^)x for q=1 and lambda_q=A'(q/N)^x' for q=2 and 3, where
x=2.61, x'=2.02 and A>A'. The wave number q of the slowest relaxation rate for
each N is given by q=2 for small values of N, while it is given by q=1 for
large values of N. This crossover corresponds to the change of the structure of
the ring polymer caused by the localization of the knotted part to a part of
the ring polymer.Comment: 13 pages, 5 figures, uses jpsj2.cl
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