Response of Worm-like Chains to Traveling-Wave Active Forces

TL;DR

This paper develops a simplified theoretical model of semiflexible flagella as worm-like chains subjected to traveling-wave active forces, aiming to understand how these forces induce beating patterns similar to biological flagella.

Contribution

It introduces a systematic analysis of how traveling-wave perturbations influence worm-like chains, highlighting key parameters that shape flagellar beating dynamics.

Findings

Identification of parameters influencing flagellar shape

Demonstration of active forces inducing beating patterns

Insights into the interplay between rigidity and external perturbations

Abstract

We present a simplified theory for semiflexible flagella under the action of a traveling-wave perturbation that emulates the organized active forces generated by molecular motors, capable of inducing beating patterns to the filament. By modeling the flagellum as a worm-like chain (WLC), we explore the interplay (competition) between the externally applied perturbation and the intrinsic bending rigidity of the filament. Our analysis aims to understand how this interplay can lead to a selection of conformations with the spatiotemporal behavior resembling the beating dynamics of axonemes such as those in sperm tails, in Chlamydomonas cilia, or eukaryotic flagella in general. Through a systematic analysis of the WLC's response to traveling-wave perturbations, we try to identify the key parameters that mostly influence the flagellar motion and shape its beating-like profiles.