Mechanics of Biophysical Networks with Flexible Cross-links

Abstract

Various mechanical properties and functions of euchariotic cells largely originate from the cytoskeleton. The predominant cytoskeletal constituent is the biopolymer filamentous actin (F-actin). In the presence of various cross-linking proteins, F-actins can comprise two rather different structures: isotropic orthogonal networks or bundled fibers. Actin bundles are formed mostly by short and stiff cross-linking proteins (like α-actinin and scruin), while large and flexible cross-linkers, such as filamin, lead to an orthogonal network. Orthogonal networks can also be formed at lower concentrations of short cross-linking proteins, but rheological experiments of in vitro F-actin networks showed that the mechanical response of such networks is different from that of networks cross-linked with filamin. Moreover, atomic force microscope stretching experiments on filamin demonstrated the possibility of force-induced domain unfolding, characterized by a sawtooth-like pattern in the force-displacement curve.Here we present a 3D discrete model of F-actin networks that extends our previous, rigidly cross-linked network model by incorporating a flexible cross-linking model for human filamin A (hsFLNa). The implemented hsFLNa element has a highly nonlinear response to stretching, incorporating the transition to a softer response that characterizes filamin domain unfolding. Simple shear simulations of F-actin/hsFLNa networks show that the response of such networks is dominated by the behavior of the hsFLNa cross-linkers, while F-actin behaves almost rigid. We observe that force-induced unfolding of the hsFLNa relaxes the stresses in actin filaments, thus allowing for large network strains. By contrast, the shearing of F-actin networks with rigid cross-links leads to a large number of actin filaments stressed well beyond their breaking force. An increase in actin concentration increases the initial shear modulus, while the maximum network stiffening depends on the hsFLNa axial stiffness. The calculated initial modulus of F-actin/hsFLNa networks is found to be comparable with experimental measurements.