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

Semiflexible polymers under external fields confined to two dimensions

The non-equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions are investigated by molecular dynamics simulations. Three different scenarios are considered: The force-extension relation of tethered polymers, the relaxation of an initially stretched semiflexible polymer, and semiflexible polymers under shear flow. We find quantitative agreement with theoretical predictions for the force-extension relation and the time dependence of the entropically contracting polymer. The semiflexible polymers under shear flow exhibit significant conformational changes at large shear rates, where less stiff polymers are extended by the flow, whereas rather stiff polymers are contracted. In addition, the polymers are aligned by the flow, thereby the two-dimensional semiflexible polymers behave similarly to flexible polymers in three dimensions. The tumbling times display a power-law dependence at high shear rate rates with an exponent comparable to the one of flexible polymers in three-dimensional systems.Comment: Accepted for publication in J. Chem. Phy

Cooperativity and Frustration in Protein-Mediated Parallel Actin Bundles

We examine the mechanism of bundling of cytoskeletal actin filaments by two representative bundling proteins, fascin and espin. Small-angle X-ray studies show that increased binding from linkers drives a systematic \textit{overtwist} of actin filaments from their native state, which occurs in a linker-dependent fashion. Fascin bundles actin into a continuous spectrum of intermediate twist states, while espin only allows for untwisted actin filaments and fully-overtwisted bundles. Based on a coarse-grained, statistical model of protein binding, we show that the interplay between binding geometry and the intrinsic \textit{flexibility} of linkers mediates cooperative binding in the bundle. We attribute the respective continuous/discontinous bundling mechanisms of fascin/espin to differences in the stiffness of linker bonds themselves.Comment: 5 pages, 3 figures, figure file has been corrected in v

Microrheology probes length scale dependent rheology

We exploit the power of microrheology to measure the viscoelasticity of entangled F-actin solutions at different length scales from 1 to 100 mu m over a wide frequency range. We compare the behavior of single probe-particle motion to that of the correlated motion of two particles. By varying the average length of the filaments, we identify fluctuations that dissipate diffusively over the filament length. These provide an important relaxation mechanism of the elasticity between 0.1 and 30 rad/sec

Microrheology, stress fluctuations and active behavior of living cells

We report the first measurements of the intrinsic strain fluctuations of living cells using a recently-developed tracer correlation technique along with a theoretical framework for interpreting such data in heterogeneous media with non-thermal driving. The fluctuations' spatial and temporal correlations indicate that the cytoskeleton can be treated as a course-grained continuum with power-law rheology, driven by a spatially random stress tensor field. Combined with recent cell rheology results, our data imply that intracellular stress fluctuations have a nearly $1/\omega^2$ power spectrum, as expected for a continuum with a slowly evolving internal prestress.Comment: 4 pages, 2 figures, to appear in Phys. Rev. Let

Force-Extension Relation and Plateau Modulus for Wormlike Chains

We derive the linear force-extension relation for a wormlike chain of arbitrary stiffness including entropy elasticity, bending and thermodynamic buckling. From this we infer the plateau modulus $G^0$ of an isotropic entangled solution of wormlike chains. The entanglement length $L_e$ is expressed in terms of the characteristic network parameters for three different scaling regimes in the entangled phase. The entanglement transition and the concentration dependence of $G^0$ are analyzed. Finally we compare our findings with experimental data.Comment: 5 pages, 1 eps-figure, to appear in PR

Entanglement, elasticity and viscous relaxation of actin solutions

We have investigated the viscosity and the plateau modulus of actin solutions with a magnetically driven rotating disc rheometer. For entangled solutions we observed a scaling of the plateau modulus versus concentration with a power of 7/5. The measured terminal relaxation time increases with a power 3/2 as a function of polymer length. We interpret the entanglement transition and the scaling of the plateau modulus in terms of the tube model for semiflexible polymers.Comment: 5 pages, 4 figures, published versio

Visualizing the strain field in semiflexible polymer networks: strain fluctuations and nonlinear rheology of F-actin gels

We image semi-flexible polymer networks under shear at the micrometer scale. By tracking embedded probe particles, we determine the local strain field, and directly measure its uniformity, or degree of affineness, on scales of 2-100 micron. The degree of nonaffine strain depends on polymer length and crosslink density, consistent with theoretical predictions. We also find a direct correspondence between the uniformity of the microscale strain and the nonlinear elasticity of the networks in the bulk.Comment: 9 pages (double-spaced) of text, 4 figures + 1 supplementary figur

Loops versus lines and the compression stiffening of cells

Both animal and plant tissue exhibit a nonlinear rheological phenomenon known as compression stiffening, or an increase in moduli with increasing uniaxial compressive strain. Does such a phenomenon exist in single cells, which are the building blocks of tissues? One expects an individual cell to compression soften since the semiflexible biopolymer-based cytoskeletal network maintains the mechanical integrity of the cell and in vitro semiflexible biopolymer networks typically compression soften. To the contrary, we find that mouse embryonic fibroblasts (mEFs) compression stiffen under uniaxial compression via atomic force microscopy (AFM) studies. To understand this finding, we uncover several potential mechanisms for compression stiffening. First, we study a single semiflexible polymer loop modeling the actomyosin cortex enclosing a viscous medium modeled as an incompressible fluid. Second, we study a two-dimensional semiflexible polymer/fiber network interspersed with area-conserving loops, which are a proxy for vesicles and fluid-based organelles. Third, we study two-dimensional fiber networks with angular-constraining crosslinks, i.e. semiflexible loops on the mesh scale. In the latter two cases, the loops act as geometric constraints on the fiber network to help stiffen it via increased angular interactions. We find that the single semiflexible polymer loop model agrees well with our AFM experiments until approximately 35% compressive strain. We also find for the fiber network with area-conserving loops model that the stress-strain curves are sensitive to the packing fraction and size distribution of the area-conserving loops, thereby creating a mechanical fingerprint across different cell types. Finally, we make comparisons between this model and experiments on fibrin networks interlaced with beads as well as discuss the tissue-scale implications of cellular compression stiffening.Comment: 19 pages, 17 figure