Mechanics and dynamics of biopolymer networks

MacKintosh, F.C. [Promotor

Nonlinear elasticity of stiff biopolymers connected by flexible linkers

Networks of the biopolymer actin, cross-linked by the compliant protein filamin, form soft gels. They can, however, withstand large shear stresses due to their pronounced nonlinear elastic behavior. The nonlinear elasticity can be controlled by varying the number of cross-links per actin filament. We propose and test a model of rigid filaments decorated by multiple flexible linkers that is in quantitative agreement with experiment. This allows us to estimate loads on individual cross-links, which we find to be less than 10 pN. © 2009 The American Physical Society

Modeling semiflexible polymer networks

This is 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, cross-linked 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, the physics of semiflexible bundles, entangled solutions, and disordered cross-linked networks are reviewed. Finally, recent developments on marginally stable fibrous networks, which exhibit critical behavior similar to other marginal systems such as jammed soft matter, are discussed. © 2014 American Physical Society

Molecular motors stiffen non-affine semiflexible polymer networks

Reconstituted filamentous actin networks with myosin motor proteins form active gels, in which motor proteins generate forces that drive the network far from equilibrium. This motor activity can also strongly affect the network elasticity; experiments have shown a dramatic stiffening in in vitro networks with molecular motors. Here we study the effects of motor generated forces on the mechanics of simulated 2D networks of athermal stiff filaments. We show how heterogeneous internal motor stresses can lead to stiffening in networks that are governed by filament bending modes. The motors are modeled as force dipoles that cause muscle like contractions. These contractions "pull out" the floppy bending modes in the system, which induces a cross-over to a stiffer stretching dominated regime. Through this mechanism, motors can lead to a nonlinear network response, even when the constituent filaments are themselves purely linear. These results have implications for the mechanics of living cells and suggest new design principles for active biomemetic materials with tunable mechanical properties. © The Royal Society of Chemistry 2011

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

Nonlinear effective-medium theory of disordered spring networks

Disordered soft materials, such as fibrous networks in biological contexts, exhibit a nonlinear elastic response. We study such nonlinear behavior with a minimal model for networks on lattice geometries with simple Hookian elements with disordered spring constant. By developing a mean-field approach to calculate the differential elastic bulk modulus for the macroscopic network response of such networks under large isotropic deformations, we provide insight into the origins of the strain stiffening and softening behavior of these systems. We find that the nonlinear mechanics depends only weakly on the lattice geometry and is governed by the average network connectivity. In particular, the nonlinear response is controlled by the isostatic connectivity, which depends strongly on the applied strain. Our predictions for the strain dependence of the isostatic point as well as the strain-dependent differential bulk modulus agree well with numerical results in both two and three dimensions. In addition, by using a mapping between the disordered network and a regular network with random forces, we calculate the nonaffine fluctuations of the deformation field and compare them to the numerical results. Finally, we discuss the limitations and implications of the developed theory. © 2012 American Physical Society

Combinatorial thin film methods for the search of new lightweight metal hydrides

The search for new lightweight metal hydride storage materials is essentially like looking for a needle in a haystack. Over the years, a number of combinatorial methods have been developed to scan the properties of materials in an efficient way. We demonstrate that combinatorial techniques are also applicable for the search of suitable hydrogen storage materials. This applies especially to hydrogenography, a novel optical screening method that measures simultaneously the enthalpy of hydride formation of thousands of materials on a single thin film wafer. © 2007 Acta Materialia Inc

Highly destabilized Mg-Ti-Ni-H system investigated by density functional theory and hydrogenography

Using hydrogenography, we recently mapped the thermodynamic properties of a large range of compositions in the quaternary Mg-Ti-Ni-H system. The enthalpy of hydride formation of Mg-Ni alloys is significantly altered upon Ti doping. For a small range of compositions, we find a hydrogenation enthalpy ΔH=-40 kJ (mol H2) -1, which is the desired enthalpy for hydrogen storage at moderate temperature and pressure. This enthalpy value is surprising since it is significantly less negative than the ΔH of the Mg-Ni and Mg-Ti hydrides. The nanostructure of the Mg-Ti-Ni-H films hinders a direct determination of the hydride phases involved by x-ray diffraction. Using density functional theory calculations for various hydrogenation reaction paths, we establish that the destabilization of the Mg-Ni-H system by Ti doping is due to the formation of Mg2 Ni and Ti-Ni intermetallics in the as-deposited state, which transform into a metastable Ti-doped Mg2 Ni H4 phase upon hydrogenation. The Ti-doped Mg2 Ni H4 phase can be considered as a heavily doped semiconductor. © 2008 The American Physical Society

Origins of Elasticity in Intermediate Filament Networks

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. © 2010 The American Physical Society