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

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.