Three-dimensional dynamic Monte Carlo simulations of elastic actin-like ratchets

We present three-dimensional dynamic Monte Carlo simulations of the growth of a semiflexible fiber against a fluctuating obstacle. The natural reference for our numerical study are the elastic and Brownian ratchet models previously analyzed semianalytically. We find that the decay of the velocity versus applied load is exponential to a good degree of accuracy, provided we include in the load the drag force felt by the moving obstacle. If the fiber and obstacle only interact via excluded volume, there are small corrections to the Brownian ratchet predictions which suggest that tip fluctuations play a minor role. If on the other hand fiber and obstacle interact via a soft potential, the corrections are much larger when the obstacle diffuses slowly. This means that microscopic assumptions can profoundly affect the dynamics. We also identify and characterize a novel "pushing catastrophe"--which is distinct from the usual fiber buckling--in which the growth of the fiber decouples from the obstacle movement. The time distribution of catastrophes can be explained via an approximate analytical treatment, and our numerics suggest that the time taken to lose propulsive force is largely dependent on the fiber incidence angle. Our results are a first step in realizing numerical polymer models for the motion of sets or networks of semiflexible fibers close to a fluctuating membrane or obstacle.