F-Actin Bending Facilitates Net Actomyosin Contraction By Inhibiting Expansion With Plus-End-Located Myosin Motors

We investigate whether a microscopic system of two semi-flexible actin filaments with an attached myosin motor can facilitate contraction. Based on energy minimisation, we derive and analyse a partial differential equation model for a two-filament-motor structure embedded within a dense, two-dimensional network. Our method enables calculation of the plane stress tensor, providing a measure for contractility. After deriving the model, we use a combination of asymptotic analysis and numerical solutions to show how F-actin bending facilitates net contraction as a myosin motor traverses two symmetric filaments. Myosin motors close to the minus-ends facilitate contraction, whereas motors close to the plus-ends facilitate expansion. The leading-order solution for rigid filaments exhibits polarity-reversal symmetry, such that the contractile and expansive components balance to zero. Surprisingly, after introducing bending the first-order correction to stress indicates expansion. However, numerical solutions show that filament bending induces a geometric asymmetry that brings the filaments closer to parallel as a myosin motor approaches their plus-ends. This decreases the effective spring force opposing motion of the motor, enabling it to move faster close to filament plus-ends. This reduces the contribution of expansive stress, giving rise to net contraction. Further numerical solutions confirm that this applies beyond the small bending regime considered in the asymptotic analysis. Our findings confirm that filament bending gives rise to microscopic-scale actomyosin contraction, and provides a possible explanation for network-scale contraction.