Nonlocal actin orientation models select for a unique orientation pattern

Abstract: Many models have been developed to study the role of branching actin networks in motility. One important component of those models is the distribution of filament orientations relative to the cell membrane. Two mean-field models previously proposed are generalized and analyzed. In particular, we find that both models uniquely select for a dominant orientation pattern. In the linear case, the pattern is the eigenfunction associated with the principal eigenvalue. In the nonlinear case, we show there exists a unique equilibrium and that the equilibrium is locally stable. Approximate techniques are then used to provide evidence for global stability.