Rotational model for actin filament alignment by myosin.

Dynamics of the actomyosin cytoskeleton regulate cellular processes such as secretion, cell division, cell motility, and shape change. Actomyosin dynamics are themselves regulated by proteins that control actin filament polymerization and depolymerization, and myosin motor contractility. Previous theoretical work has focused on translational movement of actin filaments but has not considered the role of filament rotation. Since filament rotational movements are likely sources of forces that direct cell shape change and movement we explicitly model the dynamics of actin filament rotation as myosin II motors traverse filament pairs, drawing them into alignment. Using Monte Carlo simulations we find an optimal motor velocity for alignment of actin filaments. In addition, when we introduce polymerization and depolymerization of actin filaments, we find that alignment is reduced and the filament arrays exist in a stable, asynchronous state. Further analysis with continuum models allows us to investigate factors contributing to the stability of filament arrays and their ability to generate force. Interestingly, we find that two different morphologies of F-actin arrays generate the same amount of force. We also identify a phase transition to alignment which occurs when either polymerization rates are reduced or motor velocities are optimized. We have extended our analysis to include a maximum allowed stretch of the myosin motors, and a non-uniform length for filaments leading to little change in the qualitative results. Through the integration of simulations and continuum analysis, we are able to approach the problem of understanding rotational alignment of actin filaments by myosin II motors.