4,034 research outputs found
Effective medium approach for stiff polymer networks with flexible cross-links
Recent experiments have demonstrated that the nonlinear elasticity of in
vitro networks of the biopolymer actin is dramatically altered in the presence
of a flexible cross-linker such as the abundant cytoskeletal protein filamin.
The basic principles of such networks remain poorly understood. Here we
describe an effective medium theory of flexibly cross-linked stiff polymer
networks. We argue that the response of the cross-links can be fully attributed
to entropic stiffening, while softening due to domain unfolding can be ignored.
The network is modeled as a collection of randomly oriented rods connected by
flexible cross-links to an elastic continuum. This effective medium is treated
in a linear elastic limit as well as in a more general framework, in which the
medium self-consistently represents the nonlinear network behavior. This model
predicts that the nonlinear elastic response sets in at strains proportional to
cross-linker length and inversely proportional to filament length. Furthermore,
we find that the differential modulus scales linearly with the stress in the
stiffening regime. These results are in excellent agreement with bulk rheology
data.Comment: 12 pages, 8 figure
The bend stiffness of S-DNA
We formulate and solve a two-state model for the elasticity of nicked,
double-stranded DNA that borrows features from both the Worm Like Chain and the
Bragg--Zimm model. Our model is computationally simple, and gives an excellent
fit to recent experimental data through the entire overstretching transition.
The fit gives the first value for the bending stiffness of the overstretched
state as about 10 nm*kbt, a value quite different from either B-form or
single-stranded DNA.Comment: 7 pages, 1 figur
Nonlinear elasticity of composite networks of stiff biopolymers with flexible linkers
Motivated by recent experiments showing nonlinear elasticity of in vitro
networks of the biopolymer actin cross-linked with filamin, we present an
effective medium theory of flexibly cross-linked stiff polymer networks. We
model such networks by randomly oriented elastic rods connected by flexible
connectors to a surrounding elastic continuum, which self-consistently
represents the behavior of the rest of the network. This model yields a
crossover from a linear elastic regime to a highly nonlinear elastic regime
that stiffens in a way quantitatively consistent with experiment.Comment: 4 pages, 3 figure
Fluctuation-stabilized marginal networks and anomalous entropic elasticity
We study the elastic properties of thermal networks of Hookean springs. In
the purely mechanical limit, such systems are known to have vanishing rigidity
when their connectivity falls below a critical, isostatic value. In this work
we show that thermal networks exhibit a non-zero shear modulus well below
the isostatic point, and that this modulus exhibits an anomalous, sublinear
dependence on temperature . At the isostatic point, increases as the
square-root of , while we find below the isostatic
point, where . We show that this anomalous dependence
is entropic in origin.Comment: 9 pages, 7 figure
Off-lattice Monte Carlo Simulation of Supramolecular Polymer Architectures
We introduce an efficient, scalable Monte Carlo algorithm to simulate
cross-linked architectures of freely-jointed and discrete worm-like chains.
Bond movement is based on the discrete tractrix construction, which effects
conformational changes that exactly preserve fixed-length constraints of all
bonds. The algorithm reproduces known end-to-end distance distributions for
simple, analytically tractable systems of cross-linked stiff and freely jointed
polymers flawlessly, and is used to determine the effective persistence length
of short bundles of semi-flexible worm-like chains, cross-linked to each other.
It reveals a possible regulatory mechanism in bundled networks: the effective
persistence of bundles is controlled by the linker density.Comment: 4 pages, 4 figure
Reply to "Comment on 'Theory of high-force DNA stretching and overstretching'"
In his Comment to an earlier paper [Phys. Rev. E 67, 051906 (2003)] Lam points out an error in Eq. (20) of the original paper. Here we show that use of the corrected expression produces results very similar to those presented in our original paper, so our qualitative conclusions are unchanged
Critical behaviour in the nonlinear elastic response of hydrogels
In this paper we study the elastic response of synthetic hydrogels to an
applied shear stress. The hydrogels studied here have previously been shown to
mimic the behaviour of biopolymer networks when they are sufficiently far above
the gel point. We show that near the gel point they exhibit an elastic response
that is consistent with the predicted critical behaviour of networks near or
below the isostatic point of marginal stability. This point separates rigid and
floppy states, distinguished by the presence or absence of finite linear
elastic moduli. Recent theoretical work has also focused on the response of
such networks to finite or large deformations, both near and below the
isostatic point. Despite this interest, experimental evidence for the existence
of criticality in such networks has been lacking. Using computer simulations,
we identify critical signatures in the mechanical response of sub-isostatic
networks as a function of applied shear stress. We also present experimental
evidence consistent with these predictions. Furthermore, our results show the
existence of two distinct critical regimes, one of which arises from the
nonlinear stretch response of semi-flexible polymers.
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