Nonlocal actin orientation models select for a unique orientation pattern

TL;DR

This paper analyzes two mean-field models of actin filament orientation, demonstrating that both models uniquely select for a dominant orientation pattern, with stability properties established.

Contribution

The study generalizes and analyzes two mean-field models, proving the uniqueness and stability of the selected actin filament orientation pattern.

Findings

Both models uniquely select a dominant orientation pattern.

The linear model's pattern is the eigenfunction of the principal eigenvalue.

The nonlinear model has a unique, locally stable equilibrium.

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.