Rotation Dynamics of Flexible Active Filaments with Chiral Self-Propulsion

The variety of active phases formed by self-propelled, elongated particles is greatly enriched by the introduction of a finite bending rigidity, but this complicates the motions of even individual active filaments. Of particular interest are findings of both bulk rotation amongst interacting filaments, such as in microtubule-kinesin gliding assay experiments, as well as a distinct individual rotation of filaments when the bending rigidity is small. Numerical simulations of semi-flexible filaments driven by active forces acting at a fixed angle to the filaments' tangent vectors have successfully reproduced the collective bulk rotation of interacting filaments. Accordingly, to study the behaviour of semi-flexible individual filaments, we develop a time-dependent nonlinear continuum model for an elastic one-dimensional curve segment which is self-propelled by such an active force. By deriving differential equations for the time evolution of the filament curvature and tangent vectors, we analytically obtain the nonequilibrium steady state shape of such filaments and analyse the stability of these solutions thereby clarifying the connection between chiral self-propulsion and filament rotation. We test our analytical predictions with numerical simulations.