Protein Friction and Filament Bending Facilitate Contraction of Disordered Actomyosin Networks

Abstract

We use mathematical modelling and computation to investigate how protein friction facilitates contraction of disordered actomyosin networks. We simulate two-dimensional networks using an agent-based model, consisting of a system of force-balance equations for myosin motor proteins and semi-flexible actin filaments. A major advantage of our approach is that it enables direct calculation of the network stress tensor, which provides a quantitative measure of contractility. Exploiting this, we use repeated simulations of disordered networks to confirm that both protein friction and actin filament bending are required for contraction. We then use simulations of elementary two-filament assemblies to show that filament bending flexibility can generate contraction on the microscopic scale. Finally, we show that actin filament turnover is necessary to sustain contraction and prevent pattern formation. Simulations with and without turnover also exhibit contractile pulses. However, these pulses are aperiodic, suggesting that periodic pulsation can only be achieved by additional regulatory mechanisms.