Pattern formation driven by nematic ordering of assembling biopolymers

TL;DR

This paper investigates how the nematic ordering of assembling biopolymers like actin and microtubules leads to spatial patterns, highlighting nonlinear effects and a discontinuous transition between states.

Contribution

It introduces a continuum model linking pattern formation to nematic transition theory, emphasizing nonlinear effects and a discontinuous transition.

Findings

Pattern formation depends on nonlinear effects.

Wave number decreases with assembly/disassembly rate.

Transition between nematic and periodic states is discontinuous.

Abstract

The biopolymers actin and microtubules are often in an ongoing assembling/disassembling state far from thermal equilibrium. Above a critical density this leads to spatially periodic patterns, as shown by a scaling argument and in terms of a phenomenological continuum model, that meets also Onsager's statistical theory of the nematic--to--isotropic transition in the absence of reaction kinetics. This pattern forming process depends much on nonlinear effects and a common linear stability analysis of the isotropic distribution of the filaments is often misleading. The wave number of the pattern decreases with the assembling/disassembling rate and there is an uncommon discontinuous transition between the nematic and the periodic state.