Elasticity of Semiflexible Biopolymer Networks

We develop a model for gels and entangled solutions of semiflexible biopolymers such as F-actin. Such networks play a crucial structural role in the cytoskeleton of cells. We show that the rheologic properties of these networks can result from nonclassical rubber elasticity. This model can explain a number of elastic properties of such networks {\em in vitro}, including the concentration dependence of the storage modulus and yield strain.Comment: Uses RevTeX, full postscript with figures available at http://www.umich.edu/~fcm/preprints/agel/agel.htm

Nonlinear Elasticity in Biological Gels

Unlike most synthetic materials, biological materials often stiffen as they are deformed. This nonlinear elastic response, critical for the physiological function of some tissues, has been documented since at least the 19th century, but the molecular structure and the design principles responsible for it are unknown. Current models for this response require geometrically complex ordered structures unique to each material. In this Article we show that a much simpler molecular theory accounts for strain stiffening in a wide range of molecularly distinct biopolymer gels formed from purified cytoskeletal and extracellular proteins. This theory shows that systems of semi-flexible chains such as filamentous proteins arranged in an open crosslinked meshwork invariably stiffen at low strains without the need for a specific architecture or multiple elements with different intrinsic stiffnesses.Comment: 23 pages, 5 figures, submitted to Natur

Hysteresis in the cell response to time-dependent substrate stiffness

Mechanical cues like the rigidity of the substrate are main determinants for the decision making of adherent cells. Here we use a mechano-chemical model to predict the cellular response to varying substrate stiffness. The model equations combine the mechanics of contractile actin filament bundles with a model for the Rho-signaling pathway triggered by forces at cell-matrix contacts. A bifurcation analysis of cellular contractility as a function of substrate stiffness reveals a bistable response, thus defining a lower threshold of stiffness, below which cells are not able to build up contractile forces, and an upper threshold of stiffness, above which cells are always in a strongly contracted state. Using the full dynamical model, we predict that rate-dependent hysteresis will occur in the cellular traction forces when cells are exposed to substrates of time-dependent stiffness.Comment: Revtex, 4 PDF 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

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

Counterion-Mediated Attraction and Kinks on Loops of Semiflexible Polyelectrolyte Bundles

The formation of kinks in a loop of bundled polyelectrolyte filaments is analyzed in terms of the thermal fluctuations of charge density due to polyvalent counterions adsorbed on the polyelectrolyte filaments. It is found that the counterion-mediated attraction energy of filaments depends on their bending. By consideration of curvature elasticity energy and counterion-mediated attraction between polyelectrolyte filaments, the characteristic width of the kink and the number of kinks per loop is found to be in reasonable agreement with existing experimental data for rings of bundled actin filaments

The COOH terminus of the c-Abl tyrosine kinase contains distinct F- and G-actin binding domains with bundling activity

The myristoylated form of c-Abl protein, as well as the P210bcr/abl protein, have been shown by indirect immunofluorescence to associate with F-actin stress fibers in fibroblasts. Analysis of deletion mutants of c-Abl stably expressed in fibroblasts maps the domain responsible for this interaction to the extreme COOH-terminus of Abl. This domain mediates the association of a heterologous protein with F-actin filaments after microinjection into NIH 3T3 cells, and directly binds to F-actin in a cosedimentation assay. Microinjection and cosedimentation assays localize the actin-binding domain to a 58 amino acid region, including a charged motif at the extreme COOH-terminus that is important for efficient binding. F-actin binding by Abl is calcium independent, and Abl competes with gelsolin for binding to F- actin. In addition to the F-actin binding domain, the COOH-terminus of Abl contains a proline-rich region that mediates binding and sequestration of G-actin, and the Abl F- and G-actin binding domains cooperate to bundle F-actin filaments in vitro. The COOH terminus of Abl thus confers several novel localizing functions upon the protein, including actin binding, nuclear localization, and DNA binding. Abl may modify and receive signals from the F-actin cytoskeleton in vivo, and is an ideal candidate to mediate signal transduction from the cell surface and cytoskeleton to the nucleus

Contact-induced apical asymmetry drives the thigmotropic responses of Candida albicans hyphae

Acknowledgements We thank Marco Thiel for assistance with data interpretation, Peter Sudbery for the provision of strains and Jeremy Craven for useful discussions. This work was supported by a BBSRC-DTG to D. D. T., NIH award DK083592 to F. J. B. and P. A. J., and a Royal Society URF UF080611 and MRC NIRG 90671 to A. C. B.Non peer reviewedPublisher PD