Aster formation and rupture transition in semi-flexible fiber networks with mobile cross-linkers

Abstract

Fibrous active network structures whose properties are regulated by motor proteins, or simply motors, are fundamental to life. Here, a full elastic and three dimensional model for such networks and motors is presented. The effects of surface anchoring are accounted for and we demonstrate that for unidirectional motors two basic contractile phases emerge in these systems. The transition is governed by a single parameter (τ_b/τ_c) which is the ratio of the breaking strain (τ_b) and the motility limiting strain (τ_c) of the motors. For τ_b/τ_c ≲ 2 and clamped boundaries, the network ruptures and formation of local asters occurs with a high density of motors at the centre and the fibers radially spanning out. This phase displays contraction strain during the formation of asters but the network stress is relaxed once the asters have emerged, demonstrating that the formation of aster-like structures provides a mechanism for stress relaxation. For 2.7 ≲ τ_b/τ_c the network remains intact, but reaches a force equilibrium with a high contraction strain in the case of clamped boundaries. Between these two limits the network is partly ruptured. Experimental measurements (e.g. J. T. Nishizaka, H. Miyata, H. Yoshikawa, S. Ishiwata and K. Kinosita Jr., Nature, 1995, 377, 251 and J. F. Finer, R. M. Simmons, J. A. Spudich, Nature, 1994, 368, 113) indicate that actin filament and myosin motors interact with τ_b/τ_c ≈ 2.7 which is right at the limit of motor induced fracture for a random network, indicating that e.g. a cytoskeleton with active myosin is susceptible to rupture. This is perhaps not a coincidence and may well be an important factor contributing to cellular dynamics. In the case of free boundaries the network collapses onto one single aster. We also show that the distribution of energy on the motors is a power-law, below the motility limit energy, with the exponent −0.5.