Modeling Inelastic Effects in Reconstituted Crosslinked F-Actin Networks

J. F. Rodriguez
Chemistry, Materials, and Chemical Engineering Department “Giulio Natta”, Politecnico di Milano
Wednesday 30th November 2016
Aula Seminari "Saleri" VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano
The interplay between the conventional cross-linked actin filaments by means of actin-binding proteins, and physical bundling, by means of spatial organization of nucleating factors can be an alternative to understand several inelastic effects that take place in the cytoskeleton. In this regard, in vitro actin networks without active molecular motors have been considered to be in thermodynamic equilibrium[1]. However, recent experiments performed by Schmoller et al. [5] in artificially reconstructed crosslinked actin networks have shown this networks to be non-equilibrium networks. In their experiments they have observed that, the internal stress trapped during network formation gives this material a unique behavior. Differently to most soft materials, such as rubber and living soft tissues, where nonlinear deformations irreversibly alter the mechanical properties of the material by causing a pronounced softening when cyclically deformed, reconstituted crosslinked actin networks show softening and hardening effects when the network is subject to cyclic shear strain. As a continuation of a previous work [2], here we propose a constitutive model within the framework of continuum mechanics for the inelastic stress-strain behavior of reconstituted crosslinked actin networks. The network will be described using an homogenized framework based on the eight chain model [3]. A dynamic model for the crosslinks is introduced in order to account for the inelastic response of the network. In this regard, we assume that crosslinks can be disrupted in either a reversible or irreversible manner. Reversible disruption of a crosslink is modeled as a two state process [4] in which the transition rates are modulated by the out of equilibrium forces. On the contrary, irreversible crosslink disruption will be modeled as a Bell-like bond rupture. These effects are introduced in the model by considering the bundle contour length, Lc as an stochastic variable dependent on the reversible and irreversible dynamics of the crosslink. References: [1] O. Lieleg, J. Kayser, G. Brambilla, L. Cipelletti, A.R. Bausch, Slow dynamics and internal stress relaxation in bundled cytoskeletal networks. Nat Mater, 10(3): 236–242,2011. [2] H. Lopez, J.F. Rodriguez, Microstructural model for cyclic hardening in F-actin networks crosslinked by -actinin. J. Mech. Phys. Solids, 91: 28–39, 2016. [3] J.S. Palmer, M.C. Boyce, Constitutive modeling of the stress-strain behavior of F-actin filament networks. Acta biomaterialia, 4(3): 597–612, 2008. [4] R. Phillips, J. Kondev, J. Theriot, Physical Biology of the cell. Garland Science, 2009. [5] K.M. Schmoller, P. Fernandez, R.C. Arevalo, D.L. Blair, A.R. Bausch, Cyclic hardening in bundled actin networks. Nat Commun 1, 2010. contact: