14 research outputs found
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
Force-Extension Relations for Polymers with Sliding Links
Topological entanglements in polymers are mimicked by sliding rings
(slip-links) which enforce pair contacts between monomers. We study the
force-extension curve for linear polymers in which slip-links create additional
loops of variable size. For a single loop in a phantom chain, we obtain exact
expressions for the average end-to-end separation: The linear response to a
small force is related to the properties of the unstressed chain, while for a
large force the polymer backbone can be treated as a sequence of Pincus--de
Gennes blobs, the constraint effecting only a single blob. Generalizing this
picture, scaling arguments are used to include self-avoiding effects.Comment: 4 pages, 5 figures; accepted to Phys. Rev. E (Brief Report
Knots in Charged Polymers
The interplay of topological constraints and Coulomb interactions in static
and dynamic properties of charged polymers is investigated by numerical
simulations and scaling arguments. In the absence of screening, the long-range
interaction localizes irreducible topological constraints into tight molecular
knots, while composite constraints are factored and separated. Even when the
forces are screened, tight knots may survive as local (or even global)
equilibria, as long as the overall rigidity of the polymer is dominated by the
Coulomb interactions. As entanglements involving tight knots are not easy to
eliminate, their presence greatly influences the relaxation times of the
system. In particular, we find that tight knots in open polymers are removed by
diffusion along the chain, rather than by opening up. The knot diffusion
coefficient actually decreases with its charge density, and for highly charged
polymers the knot's position appears frozen.Comment: Revtex4, 9 pages, 9 eps 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
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
Statistical-Mechanical Analysis of Enzymatic Topological Transformations in DNA Molecules
Kinetic proofreading can explain the supression of supercoiling of circular DNA molecules by type-II topoisomerases
The elusiveness of polymer knots
36.20.Ey Conformation (statistics and dynamics), 02.10.Kn Knot theory,