Active Curved Polymers Form Vortex Patterns on Membranes.

Jonas Denk,Lorenz Huber,Emanuel Reithmann,Erwin Frey

doi:10.1103/physrevlett.116.178301

Abstract

Recent invitro experiments with FtsZ polymers show self-organization into different dynamic patterns, including structures reminiscent of the bacterial Z ring. We model FtsZ polymers as active particles moving along chiral, circular paths by Brownian dynamics simulations and a Boltzmann approach. Our two conceptually different methods point to a generic phase behavior. At intermediate particle densities, we find self-organization into vortex structures including closed rings. Moreover, we show that the dynamics at the onset of pattern formation is described by a generalized complex Ginzburg-Landau equation.

Highlights

Recent in vitro experiments with FtsZ polymers show self-organization into different dynamic patterns, including structures reminiscent of the bacterial Z ring
Motivated by these experimental findings, we have studied pattern formation in a class of active systems, where particles move on circular tracks and interact only via steric repulsion
To assess the dynamics of this class, we consider two conceptually different models: First, we emulate active particles as elastic polymers with fixed intrinsic curvature that move with a constant tangential velocity [Fig. 1(a)] and perform Brownian dynamics simulations

Summary

Introduction

Recent in vitro experiments with FtsZ polymers show self-organization into different dynamic patterns, including structures reminiscent of the bacterial Z ring. For dilute systems ρ ≪ 1, our simulations show that each polymer is propelled on a circular path and collisions between polymers are infrequent; see Fig. 2(a) and Movie 1 in Supplemental Material [12]. It describes the dynamics of the density of particles in phase-space element drdθ which is being convected due to particle self-propulsion and which undergoes rotational diffusion and binary particle collisions, as given by the collision integrals Id1⁄2f and Ic1⁄2f; f, respectively; for explicit expressions, please see Supplemental Material

Results

Conclusion