Structural Anisotropy Stabilises Asymmetric Beating in Instability Driven Filaments

TL;DR

This study investigates how structural anisotropy and intrinsic curvature influence filament dynamics, revealing that anisotropy can stabilize asymmetric beating patterns in three-dimensional models, which are otherwise unstable.

Contribution

It demonstrates that combining intrinsic curvature with anisotropic bending stiffness stabilizes asymmetric beating in filaments, advancing understanding of ciliary motion.

Findings

Intrinsic curvature induces asymmetric beating in planar motion.

Anisotropy suppresses out-of-plane instabilities and stabilizes beating.

Low stiffness ratios combined with anisotropy stabilize asymmetric patterns.

Abstract

Asymmetries and anisotropies are widespread in biological systems, including in the structure and dynamics of cilia and eukaryotic flagella. These microscopic, hair-like appendages exhibit asymmetric beating patterns that break time-reversal symmetry needed to facilitate fluid transport at the cellular level. The intrinsic anisotropies in ciliary structure can promote preferential beating directions, further influencing their dynamics. In this study, we employ numerical simulation and bifurcation analysis of a mathematical model of a filament driven by a follower force at its tip to explore how intrinsic curvature and direction-dependent bending stiffnesses impact filament dynamics. Our results show that while intrinsic curvature is indeed able to induce asymmetric beating patterns when filament motion is restricted to a plane, this beating is unstable to out of plane perturbations. Furthermore, we find that a 3D whirling state seen for isotropic filament dynamics can be suppressed when sufficient asymmetry or anisotropy are introduced. Finally, for bending stiffness ratios as low as 2, we demonstrate that combining structural anisotropy with intrinsic curvature can stabilise asymmetric beating patterns, highlighting the crucial role of anisotropy in ciliary dynamics.