An integrodifferential model for orientational distributions of F-actin in cells

Angular self-organization of the actin cytoskeleton is modeled as a process of instant changing of filament orientation in the course of specific actin-actin interactions. These interactions are modified by cross-linking actin-binding proteins. This problem was raised first by Civelekoglu and Edelstein-Keshet [Bull. Math. Biol., 56 (1994), pp. 587-616]. When restricted to a two-dimensional configuration, the mathematical model consists of a single Boltzmann-like integrodifferential equation for the one-dimensional angular distribution. Linear stability analysis, asymptotic analysis, and numerical results reveal that at certain parameter values of actin-actin interactions, spontaneous alignment of filaments in the form of unipolar or bipolar bundles or orthogonal networks can be expected.