Hydrodynamics of isotropic and liquid crystalline active polymer solutions

TL;DR

This paper develops a hydrodynamic model for active polymer solutions, capturing how crosslinkers induce filament alignment, lead to various ordered states, and cause instabilities like bundling, with results linked to physical parameters.

Contribution

It introduces a continuum hydrodynamic framework for active polymer solutions, connecting microscopic interactions to large-scale collective behaviors and instabilities.

Findings

Mobile crosslinkers induce filament bundling and instability.

The model predicts stable polar and nematic states.

Parameters can be estimated from physical properties of crosslinkers.

Abstract

We describe the large-scale collective behavior of solutions of polar biofilaments and both stationary and mobile crosslinkers. Both mobile and stationary crosslinkers induce filament alignment promoting either polar or nematic order. In addition, mobile crosslinkers, such as clusters of motor proteins, exchange forces and torques among the filaments and render the homogeneous states unstable via filament bundling. We start from a Smoluchowski equation for rigid filaments in solutions, where pairwise crosslink-mediated interactions among the filaments yield translational and rotational currents. The large-scale properties of the system are described in terms of continuum equations for filament and motor densities, polarization and alignment tensor obtained by coarse-graining the Smoluchovski equation. The possible homogeneous and inhomogeneous states of the systems are obtained as stable solutions of the dynamical equations and are characterized in terms of experimentally accessible parameters. We make contact with work by other authors and show that our model allows for an estimate of the various parameters in the hydrodynamic equations in terms of physical properties of the crosslinkers.