Bifurcations and nonlinear dynamics of the follower force model for active filaments

TL;DR

This paper investigates the bifurcations and nonlinear dynamics of the follower force model for active filaments, revealing new quasiperiodic states and the influence of filament slenderness using computational dynamical systems techniques.

Contribution

It provides a comprehensive analysis of bifurcations in the follower force model, identifying new states and effects of filament slenderness on filament dynamics.

Findings

Identification of bifurcations leading to different filament states

Discovery of quasiperiodic states in the model

Effect of filament slenderness on bifurcation behavior

Abstract

Biofilament-motor protein complexes are ubiquitous in biology and drive the transport of cargo vital for many fundamental cellular processes. As they move, motor proteins exert compressive forces on the filaments to which they are attached, leading to buckling and a subsequent range of dynamics. The follower force model, in which a single compressive force is imposed at the filament tip, is the standard and most basic model for an elastic filament, such as a microtubule, driven by a motor protein. Depending on the force value, one can observe different states including whirling, beating and writhing, though the bifurcations giving rise to these states are not completely understood. In this paper, we utilise techniques from computational dynamical systems to determine and characterise these bifurcations. We track emerging time-periodic branches and identify new, quasiperiodic states. We investigate the effect of filament slenderness on the bifurcations and, in doing so, present a comprehensive overview of the dynamics which emerge in the follower force model.