Branching and capping determine the force–velocity relationships of branching actin networks

Abstract

A branching actin network is the major engine that drives cell motility. A measure of the effectiveness of an engine is the velocity the engine is able to produce at a given resistance—the force–velocity relationship. Concave force–velocity relationships consist of a force-insensitive region, indicative of an adaptive response. In contrast, convex force–velocity relationships would reflect a passive response. Even in in vitro experiments, branching actin networks can exhibit both concave and convex force–velocity curves. However, the exact mechanism that can explain both force–velocity curves is not yet known. We carried out an agent-based stochastic simulation to explore such a mechanism. We discovered an emergent behavior of a branching actin network: Upon resistance, it remodels itself by increasing the number of filaments growing in contact with the load. The remodeling is favored by branching events and limited by capping. The force–velocity relationship hinges on the relative time-scale between the intrinsic kinetics of the branching actin network and the loading. Shortly after encountering resistance (∼seconds), the force–velocity relationship of the actin network is always convex, as it does not have enough time to remodel itself. A concave force–velocity relationship requires network remodeling at longer time-scales (∼tens of seconds to minutes) and the faster branching event relative to capping. Furthermore, our model explains the observed hysteresis in the force–velocity relationship of actin networks. Our model thus establishes a unified mechanism that can account for both convex and concave force–velocity relationships observed in branching actin networks.