Nonlinear competition between asters and stripes in filament-motor-systems

TL;DR

This paper models filament-motor systems to understand how patterns like asters and stripes emerge from nonlinear interactions, revealing bifurcations driven by motor and filament concentrations.

Contribution

It introduces a bifurcation analysis of filament-motor interactions predicting pattern formation and stability ranges for asters and stripes.

Findings

Homogeneous filament distributions can become unstable, leading to pattern formation.

Pattern selection depends on motor and filament concentrations.

Numerical simulations confirm analytical predictions.

Abstract

A model for polar filaments interacting via molecular motor complexes is investigated which exhibits bifurcations to spatial patterns. It is shown that the homogeneous distribution of filaments, such as actin or microtubules, may become either unstable with respect to an orientational instability of a finite wave number or with respect to modulations of the filament density, where long wavelength modes are amplified as well. Above threshold nonlinear interactions select either stripe patterns or periodic asters. The existence and stability ranges of each pattern close to threshold are predicted in terms of a weakly nonlinear perturbation analysis, which is confirmed by numerical simulations of the basic model equations. The two relevant parameters determining the bifurcation scenario of the model can be related to the concentrations of the active molecular motors and of the filaments respectively, which both could be easily regulated by the cell.