1,501 research outputs found
Deformation of crosslinked semiflexible polymer networks
Networks of filamentous proteins play a crucial role in cell mechanics. These
cytoskeletal networks, together with various crosslinking and other associated
proteins largely determine the (visco)elastic response of cells. In this letter
we study a model system of crosslinked, stiff filaments in order to explore the
connection between the microstructure under strain and the macroscopic response
of cytoskeletal networks. We find two distinct regimes as a function primarily
of crosslink density and filament rigidity: one characterized by affine
deformation and one by non-affine deformation. We characterize the crossover
between these two.Comment: Typos fixed and some technical details clarified. To appear in Phys.
Rev. Let
Elastic response of filamentous networks with compliant crosslinks
Experiments have shown that elasticity of disordered filamentous networks
with compliant crosslinks is very different from networks with rigid
crosslinks. Here, we model and analyze filamentous networks as a collection of
randomly oriented rigid filaments connected to each other by flexible
crosslinks that are modeled as worm-like chains. For relatively large
extensions we allow for enthalpic stretching of crosslinks' backbones. We show
that for sufficiently high crosslink density, the network linear elastic
response is affine on the scale of the filaments' length. The nonlinear regime
can become highly nonaffine and is characterized by a divergence of the elastic
modulus at finite strain. In contrast to the prior predictions, we do not find
an asymptotic regime in which the differential elastic modulus scales linearly
with the stress, although an approximate linear dependence can be seen in a
transition from entropic to enthalpic regimes. We discuss our results in light
of the recent experiments.Comment: 10 pages, 11 figure
Non-equilibrium mechanics and dynamics of motor activated gels
The mechanics of cells is strongly affected by molecular motors that generate
forces in the cellular cytoskeleton. We develop a model for cytoskeletal
networks driven out of equilibrium by molecular motors exerting transient
contractile stresses. Using this model we show how motor activity can
dramatically increase the network's bulk elastic moduli. We also show how motor
binding kinetics naturally leads to enhanced low-frequency stress fluctuations
that result in non-equilibrium diffusive motion within an elastic network, as
seen in recent \emph{in vitro} and \emph{in vivo} experiments.Comment: 21 pages, 8 figure
Driven diffusive systems with mutually interactive Langmuir kinetics
We investigate the simple one-dimensional driven model, the totally
asymmetric exclusion process, coupled to mutually interactive Langmuir
kinetics. This model is motivated by recent studies on clustering of motor
proteins on microtubules. In the proposed model, the attachment and detachment
rates of a particle are modified depending upon the occupancy of neighbouring
sites. We first obtain continuum mean-field equations and in certain limiting
cases obtain analytic solutions. We show how mutual interactions increase
(decrease) the effects of boundaries on the phase behavior of the model. We
perform Monte Carlo simulations and demonstrate that our analytical
approximations are in good agreement with the numerics over a wide range of
model parameters. We present phase diagrams over a selective range of
parameters.Comment: 9 pages, 8 Figure
Active biopolymer networks generate scale-free but euclidean clusters
We report analytical and numerical modelling of active elastic networks,
motivated by experiments on crosslinked actin networks contracted by myosin
motors. Within a broad range of parameters, the motor-driven collapse of active
elastic networks leads to a critical state. We show that this state is
qualitatively different from that of the random percolation model.
Intriguingly, it possesses both euclidean and scale-free structure with Fisher
exponent smaller than . Remarkably, an indistinguishable Fisher exponent and
the same euclidean structure is obtained at the critical point of the random
percolation model after absorbing all enclaves into their surrounding clusters.
We propose that in the experiment the enclaves are absorbed due to steric
interactions of network elements. We model the network collapse, taking into
account the steric interactions. The model shows how the system robustly drives
itself towards the critical point of the random percolation model with absorbed
enclaves, in agreement with the experiment.Comment: 6 pages, 7 figure
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
Dynamic characteristics and processing of fillers in polyurethane elastomers for vibration damping applications
Polyurethane elastomers have the potential of being used to reduce vibrational noise in many engineering applications. The performance of the elastomer is directly related to matching the nature of the mechanical loss characteristics to the frequency and temperature dependence of the source of the vibration. Materials with a broad frequency response and good mechanical properties are desirable for situations were load bearing and isolation becomes an issue. Because automobile, and other related vehicles operate over a broad temperature range, it is desirable for the damping characteristics of the elastomer to ideally be independent of temperature and frequency. In practice, this is not possible and the creation of materials with a broad spectrum response is desirable. In this paper, the effects of various fillers on the breadth and temperature dependence of the vibration damping characteristics of a filled and crosslinked polyurethane elastomer are explored. The fillers studied are wollastonite, barium sulphate and talc. These materials have different shapes, sizes and surface chemistry and undergo different types of interaction with the matrix. The vibration damping characteristics were further varied by the use of a crosslinking agent. Data presented on the rheological characteristics indicate the strength of the filler-polyol interactions. Dielectric relaxation and dynamic mechanical thermal analysis demonstrate the way in which changes in the type of filler, concentration and amount of crosslinker lead to changes in the location and breadth of the energy dissipation process in these elastomers. The vibration damping characteristics of a selected material are presented to demonstrate the potential of these materials
Multi-scale strain-stiffening of semiflexible bundle networks
Bundles of polymer filaments are responsible for the rich and unique
mechanical behaviors of many biomaterials, including cells and extracellular
matrices. In fibrin biopolymers, whose nonlinear elastic properties are crucial
for normal blood clotting, protofibrils self-assemble and bundle to form
networks of semiflexible fibers. Here we show that the extraordinary
strain-stiffening response of fibrin networks is a direct reflection of the
hierarchical architecture of the fibrin fibers. We measure the rheology of
networks of unbundled protofibrils and find excellent agreement with an affine
model of extensible wormlike polymers. By direct comparison with these data, we
show that physiological fibrin networks composed of thick fibers can be modeled
as networks of tight protofibril bundles. We demonstrate that the tightness of
coupling between protofibrils in the fibers can be tuned by the degree of
enzymatic intermolecular crosslinking by the coagulation Factor XIII.
Furthermore, at high stress, the protofibrils contribute independently to the
network elasticity, which may reflect a decoupling of the tight bundle
structure. The hierarchical architecture of fibrin fibers can thus account for
the nonlinearity and enormous elastic resilience characteristic of blood clots.Comment: 27 pages including 8 figures and Supplementary Dat
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.
Actively Contracting Bundles of Polar Filaments
We introduce a phenomenological model to study the properties of bundles of
polar filaments which interact via active elements. The stability of the
homogeneous state, the attractors of the dynamics in the unstable regime and
the tensile stress generated in the bundle are discussed. We find that the
interaction of parallel filaments can induce unstable behavior and is
responsible for active contraction and tension in the bundle. Interaction
between antiparallel filaments leads to filament sorting. Our model could apply
to simple contractile structures in cells such as stress fibers.Comment: 4 pages, 4 figures, RevTex, to appear in Phys. Rev. Let
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