Impact of motor molecules on the dynamics of treadmilling filaments

We study a driven lattice gas model for the length dynamics of treadmilling filaments in the presence of molecular motors. A treadmilling filament grows by subunit addition at one end and shrinks by subunit removal at the other. Molecular motors can attach to the filament, move towards the shrinking end, and detach from the filament. We consider motors that are also capable of inducing subunit removal at the shrinking filament end. Stochastic simulations reveal a phase of unimodal length distribution and a phase of unbounded growth. Exploiting a condition on the motor flux, we explore the system's phase diagram. In certain limits we can define random walks that allow us to estimate the full length distribution. The width of steady state distributions decreases with increasing motor activity. Our analysis indicates possible ways that cells can use to regulate the size of cytoskeletal structures such as mitotic spindles by controlling various motor properties.