Here, we provide an overview of theoretical approaches to semiflexible polymers and their networks. Such semiflexible polymers have large bending rigidities that can compete with the entropic tendency of a chain to crumple up into a random coil. Many studies on semiflexible polymers and their assemblies have been motivated by their importance in biology. Indeed, crosslinked networks of semiflexible polymers form a major structural component of tissue and living cells. Reconstituted networks of such biopolymers have emerged as a new class of biological soft matter systems with remarkable material properties, which have spurred many of the theoretical developments discussed here. Starting from the mechanics and dynamics of individual semiflexible polymers, we review the physics of semiflexible bundles, entangled solutions and disordered cross-linked networks. Finally, we discuss recent developments on marginally stable fibrous networks, which exhibit critical behavior similar to other marginal systems such as jammed soft matter.
Disordered fibre networks are the basis of many man-made and natural materials, including structural components of living cells and tissue. The mechanical stability of such networks relies on the bending resistance of the fibres, in contrast to rubbers, which are governed by entropic stretching of polymer segments. Although it is known that fibre networks exhibit collective bending deformations, a fundamental understanding of such deformations and their effects on network mechanics has remained elusive. Here we introduce a lattice-based model of fibrous networks with variable connectivity to elucidate the roles of single-fibre elasticity and network structure. These networks exhibit both a low-connectivity rigidity threshold governed by fibre-bending elasticity and a high-connectivity threshold governed by fibre-stretching elasticity. Whereas the former determines the true onset of network rigidity, we show that the latter exhibits rich zero-temperature critical behaviour, including a crossover between various mechanical regimes along with diverging strain fluctuations and a concomitant diverging correlation length.
Systems in thermodynamic equilibrium are not only characterized by time-independent macroscopic properties, but also satisfy the principle of detailed balance in the transitions between microscopic configurations. Living systems function out of equilibrium and are characterized by directed fluxes through chemical states, which violate detailed balance at the molecular scale. Here we introduce a method to probe for broken detailed balance and demonstrate how such nonequilibrium dynamics are manifest at the mesosopic scale. The periodic beating of an isolated flagellum from Chlamydomonas reinhardtii exhibits probability flux in the phase space of shapes. With a model, we show how the breaking of detailed balance can also be quantified in stationary, nonequilibrium stochastic systems in the absence of periodic motion. We further demonstrate such broken detailed balance in the nonperiodic fluctuations of primary cilia of epithelial cells. Our analysis provides a general tool to identify nonequilibrium dynamics in cells and tissues.
Intermediate filaments are common structural elements found in abundance in all metazoan cells, where they form networks that contribute to the elasticity. Here, we report measurements of the linear and nonlinear viscoelasticity of networks of two distinct intermediate filaments, vimentin and neurofilaments. Both exhibit predominantly elastic behavior with strong nonlinear strain stiffening. We demonstrate that divalent ions behave as effective cross-linkers for both networks, and that the elasticity of these networks is consistent with the theory for that of semiflexible polymers. DOI: 10.1103/PhysRevLett.104.058101 PACS numbers: 87.15.La, 83.60.Df, 83.80.Rs, 87.16.Ka The mechanical response of cells depends largely on the structure and elasticity of their cytoskeleton, consisting of a variety of biopolymer networks, including filamentous actin, microtubules, and intermediate filaments (IFs) [1]. While filamentous actin and microtubules have been extensively studied, much less is known about IFs, although some key parameters such as their persistence length have been measured. Compared to actin and microtubules, IFs are more varied and specialized. Their networks are nevertheless cytoskeletal components contributing to the elasticity of the cell: there are five families of IFs found in a variety of cell types, ranging from muscles to neurons. Intermediate filament networks exhibit pronounced nonlinear elasticity similar to that observed in actin networks that are cross-linked. However, there are myriad associated actin-binding proteins that lead to this cross-linking; by contrast, fewer cross-linking proteins have been identified for IFs. Thus, the origin of the nonlinear elasticity in IF networks has not been identified.Here, we investigate the elasticity of two different IF networks, vimentin and neurofilaments (NFs). The networks exhibit remarkably similar mechanical properties: they are weak elastic solids even at the lowest frequencies probed and they exhibit strong nonlinear strain stiffening over several decades in stress. This behavior requires cross-linking of the network and we show that divalent ions act as effective cross-linkers. By comparing the linear and nonlinear macroscopic behavior, we extract microscopic network parameters. These observations suggest a general design principle for regulating the elasticity of intermediate filament networks even in the absence of specific cross-linking proteins.To explore the generality of this behavior, we use NFs, found only in neurons, and vimentin, found in nearly all mesenchymal cells. The main difference between these IFs lies in the length of their negatively charged carboxy terminal sidearms; NF sidearms are much longer than those of vimentin. Furthermore, optimal assembly is obtained at different ionic conditions, with NFs favoring a pH of 6.2, where vimentin does not assemble properly [2]. Neurofilaments are purified from bovine spinal cords [3][4][5]: fresh tissue is homogenized, then centrifuged, after which the crude NF pellet is purified ove...
Animal cells in tissues are supported by biopolymer matrices, which typically exhibit highly nonlinear mechanical properties. While the linear elasticity of the matrix can significantly impact cell mechanics and functionality, it remains largely unknown how cells, in turn, affect the nonlinear mechanics of their surrounding matrix. Here, we show that living contractile cells are able to generate a massive stiffness gradient in three distinct 3D extracellular matrix model systems: collagen, fibrin, and Matrigel. We decipher this remarkable behavior by introducing nonlinear stress inference microscopy (NSIM), a technique to infer stress fields in a 3D matrix from nonlinear microrheology measurements with optical tweezers. Using NSIM and simulations, we reveal large long-ranged cell-generated stresses capable of buckling filaments in the matrix. These stresses give rise to the large spatial extent of the observed cell-induced matrix stiffness gradient, which can provide a mechanism for mechanical communication between cells.
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