854 research outputs found
Disordered, stretched, and semiflexible biopolymers in two dimensions
We study the effects of intrinsic sequence-dependent curvature for a two
dimensional semiflexible biopolymer with short-range correlation in intrinsic
curvatures. We show exactly that when not subjected to any external force, such
a system is equivalent to a system with a well-defined intrinsic curvature and
a proper renormalized persistence length. We find the exact expression for the
distribution function of the equivalent system. However, we show that such an
equivalent system does not always exist for the polymer subjected to an
external force. We find that under an external force, the effect of
sequence-disorder depends upon the averaging order, the degree of disorder, and
the experimental conditions, such as the boundary conditions. Furthermore, a
short to moderate length biopolymer may be much softer or has a smaller
apparent persistent length than what would be expected from the "equivalent
system". Moreover, under a strong stretching force and for a long biopolymer,
the sequence-disorder is immaterial for elasticity. Finally, the effect of
sequence-disorder may depend upon the quantity considered
Semiflexible polymers: Dependence on ensemble and boundary orientations
We show that the mechanical properties of a worm-like-chain (WLC) polymer, of
contour length and persistence length \l such that t=L/\l\sim{\cal
O}(1), depend both on the ensemble and the constraint on end-orientations. In
the Helmholtz ensemble, multiple minima in free energy near persists for
all kinds of orientational boundary conditions. The qualitative features of
projected probability distribution of end to end vector depend crucially on the
embedding dimensions. A mapping of the WLC model, to a quantum particle moving
on the surface of an unit sphere, is used to obtain the statistical and
mechanical properties of the polymer under various boundary conditions and
ensembles. The results show excellent agreement with Monte-Carlo simulations.Comment: 15 pages, 15 figures; version accepted for publication in Phys. Rev.
E; one new figure and discussions adde
Entropic forces generated by grafted semiflexible polymers
The entropic force exerted by the Brownian fluctuations of a grafted
semiflexible polymer upon a rigid smooth wall are calculated both analytically
and by Monte Carlo simulations. Such forces are thought to play an important
role for several cellular phenomena, in particular, the physics of
actin-polymerization-driven cell motility and movement of bacteria like
Listeria. In the stiff limit, where the persistence length of the polymer is
larger than its contour length, we find that the entropic force shows scaling
behavior. We identify the characteristic length scales and the explicit form of
the scaling functions. In certain asymptotic regimes we give simple analytical
expressions which describe the full results to a very high numerical accuracy.
Depending on the constraints imposed on the transverse fluctuations of the
filament there are characteristic differences in the functional form of the
entropic forces; in a two-dimensional geometry the entropic force exhibits a
marked peak.Comment: 21 pages, 18 figures, minor misprints correcte
Long Range Bond-Bond Correlations in Dense Polymer Solutions
The scaling of the bond-bond correlation function along linear polymer
chains is investigated with respect to the curvilinear distance, , along the
flexible chain and the monomer density, , via Monte Carlo and molecular
dynamics simulations. % Surprisingly, the correlations in dense three
dimensional solutions are found to decay with a power law with and the exponential behavior commonly assumed is
clearly ruled out for long chains. % In semidilute solutions, the density
dependent scaling of with
( being Flory's exponent) is set by the
number of monomers contained in an excluded volume blob of size
. % Our computational findings compare well with simple scaling arguments
and perturbation calculation. The power-law behavior is due to
self-interactions of chains on distances caused by the connectivity
of chains and the incompressibility of the melt. %Comment: 4 pages, 4 figure
Elasticity of semi-flexible polymers
We present a numerical solution of the Worm-Like Chain (WLC) model for
semi-flexible polymers. We display graphs for the end-to-end distance
distribution and the force-extension relation expected from the model. We
predict the expected level of fluctuations around the mean value in
force-extension curves. Our treatment analyses the entire range of polymer
lengths and reproduces interesting qualitative features seen in recent computer
simulations for polymers of intermediate length. These results can be tested
against experiments on single molecules. This study is relevant to mechanical
properties of biological molecules.Comment: five pages revtex five figures, slightly improved version with recent
references adde
Statics and Dynamics of the Wormlike Bundle Model
Bundles of filamentous polymers are primary structural components of a broad
range of cytoskeletal structures, and their mechanical properties play key
roles in cellular functions ranging from locomotion to mechanotransduction and
fertilization. We give a detailed derivation of a wormlike bundle model as a
generic description for the statics and dynamics of polymer bundles consisting
of semiflexible polymers interconnected by crosslinking agents. The elastic
degrees of freedom include bending as well as twist deformations of the
filaments and shear deformation of the crosslinks. We show that a competition
between the elastic properties of the filaments and those of the crosslinks
leads to renormalized effective bend and twist rigidities that become
mode-number dependent. The strength and character of this dependence is found
to vary with bundle architecture, such as the arrangement of filaments in the
cross section and pretwist. We discuss two paradigmatic cases of bundle
architecture, a uniform arrangement of filaments as found in F-actin bundles
and a shell-like architecture as characteristic for microtubules. Each
architecture is found to have its own universal ratio of maximal to minimal
bending rigidity, independent of the specific type of crosslink induced
filament coupling; our predictions are in reasonable agreement with available
experimental data for microtubules. Moreover, we analyze the predictions of the
wormlike bundle model for experimental observables such as the tangent-tangent
correlation function and dynamic response and correlation functions. Finally,
we analyze the effect of pretwist (helicity) on the mechanical properties of
bundles. We predict that microtubules with different number of protofilaments
should have distinct variations in their effective bending rigidity
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
Polymer chain stiffness versus excluded volume: A Monte Carlo study of the crossover towards the wormlike chain model
When the local intrinsic stiffness of a polymer chain varies over a wide
range, one can observe both a crossover from rigid-rod-like behavior to
(almost) Gaussian random coils and a further crossover towards self-avoiding
walks in good solvents. Using the pruned-enriched Rosenbluth method (PERM) to
study self-avoiding walks of up to steps and variable flexibility,
the applicability of the Kratky-Porod model is tested. Evidence for
non-exponential decay of the bond-orientational correlations for large distances along the chain contour is presented, irrespective
of chain stiffness. For bottle-brush polymers on the other hand, where
experimentally stiffness is varied via the length of side-chains, it is shown
that these cylindrical brushes (with flexible backbones) are not described by
the Kratky-Porod wormlike chain model, since their persistence length is
(roughly) proportional to their cross-sectional radius, for all conditions of
practical interest.Comment: 6 pages, 5 figures, to be published in Europhys. Lett. (2010
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