The head leads the body: a curvature-based kinematic description of C. elegans

TL;DR

This paper introduces a curvature-based model for C. elegans locomotion, showing that complex body shapes and trajectories can be described by simple harmonic functions propagating from the head, simplifying the understanding of worm movement.

Contribution

The study presents a novel analytical curvature model that captures diverse worm shapes and trajectories using simple harmonic functions with abrupt parameter changes.

Findings

Curvature wave generated in the head explains body shapes.

Piecewise sinusoidal curvature models worm trajectories.

Simple harmonic functions effectively describe undulatory movement.

Abstract

Caenorhabditis elegans, a free-living soil nematode, propels itself by producing undulatory body motion and displays a rich variety of body shapes and trajectories during its locomotion in complex environments. Here we show that the complex shapes and trajectories of C. elegans have a simple analytical description in curvature representation. Our model is based on the assumption that the curvature wave is generated in the head segment of the worm body and propagates backwards. We have found that a simple harmonic function for the curvature can capture multiple worm shapes during the undulatory movement. The worm body trajectories can be well represented in terms of piecewise sinusoidal curvature with abrupt changes in amplitude, wavevector, and phase.