Bridging the microscopic and the hydrodynamic in active filament solutions

TL;DR

This paper derives hydrodynamic equations for active filament solutions from a microscopic model, highlighting the importance of motor stepping rate spatial dependence and anisotropic diffusion in filament dynamics.

Contribution

It introduces a microscopic derivation of hydrodynamics for active filaments, emphasizing the role of motor stepping rate spatial variation and anisotropic diffusion effects.

Findings

Motor stepping rate spatial dependence drives bundle formation

Anisotropic filament diffusion enables net filament motion

New terms affect the stability of homogeneous states

Abstract

Hydrodynamic equations for an isotropic solution of active polar filaments are derived from a microscopic mean-field model of the forces exchanged between motors and filaments. We find that a spatial dependence of the motor stepping rate along the filament is essential to drive bundle formation. A number of differences arise as compared to hydrodynamics derived (earlier) from a mesoscopic model where relative filament velocities were obtained on the basis of symmetry considerations. Due to the anisotropy of filament diffusion, motors are capable of generating net filament motion relative to the solvent. The effect of this new term on the stability of the homogeneous state is investigated.