title: An affine continuum mechanical model for cross-linked F-actin networks with compliant linker proteins.
abstract: Cross-linked actin networks are important building blocks of the cytoskeleton. In order to gain deeper insight into the interpretation of experimental data on actin networks, adequate models are required. In this paper we introduce an affine constitutive network model for cross-linked F-actin networks based on nonlinear continuum mechanics, and specialize it in order to reproduce the experimental behavior of in vitro reconstituted model networks. The model is based on the elastic properties of single filaments embedded in an isotropic matrix such that the overall properties of the composite are described by a free-energy function. In particular, we are able to obtain the experimentally determined shear and normal stress responses of cross-linked actin networks typically observed in rheometer tests. In the present study an extensive analysis is performed by applying the proposed model network to a simple shear deformation. The single filament model is then extended by incorporating the compliance of cross-linker proteins and further extended by including viscoelasticity. All that is needed for the finite element implementation is the constitutive model for the filaments, the linkers and the matrix, and the associated elasticity tensor in either the Lagrangian or Eulerian formulation. The model facilitates parameter studies of experimental setups such as micropipette aspiration experiments and we present such studies to illustrate the efficacy of this modeling approach.
authors.affiliation: Institute of Biomechanics, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria. Electronic address: holzapfel@tugraz.at.
authors.forename: Gerhard A
authors.initials: GA
authors.lastname: Holzapfel
authors.affiliation: Institute of Biomechanics, Graz University of Technology, Kronesgasse 5-I, 8010 Graz, Austria.
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Unterberger
authors.affiliation: School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow G12 8QW Scotland, UK.
authors.forename: Ray W
authors.initials: RW
authors.lastname: Ogden
mesh_terms: D000199:Actins / Q000737:chemistry* / Q000378:metabolism*; D001696:Biomechanical Phenomena; D004548:Elasticity; D020342:Finite Element Analysis; D055595:Mechanical Phenomena; D008954:Models, Biological; D013314:Stress, Mechanical; D013816:Thermodynamics
chemical_list: D000199:Actins
keywords: Actin filaments; Actin networks; Continuum mechanics; Cross-linker proteins; Finite element analysis