A minimal reaction-diffusion neural model generates $\textit{C. elegans}$ undulation

TL;DR

This paper presents a minimal reaction-diffusion neural model using FitzHugh-Nagumo neurons to replicate extit{C. elegans} undulatory locomotion, providing a simplified biomimetic framework for studying nematode movement.

Contribution

It introduces a minimal, reaction-diffusion neural model based on FitzHugh-Nagumo neurons that captures key features of extit{C. elegans} locomotion.

Findings

A small neural network can generate extit{C. elegans} undulation patterns.

The model demonstrates key locomotion features with simplified neuron dynamics.

Provides a minimal framework for future studies of nematode movement.

Abstract

The small (1 mm) nematode $\textit{Caenorhabditis elegans}$ (Corsi [1], wormbook.org) has become widely used as a model organism; in particular, the $\textit{C. elegans}$ connectome has been completely mapped, and $\textit{C. elegans}$ locomotion has been widely studied. We describe a minimal reaction-diffusion model for the locomotion of $\textit{C. elegans}$, using as a framework a simplified, stylized "descending pathway" of neurons as central pattern generator (CPG) (Xu et al., Proceedings of the National Academy of Sciences 115, 2018). Finally, we realize a model of the required oscillations and coupling with a network of coupled Keener (IEEE Transactions on Systems, Man, and Cybernetics SMC-13, 1983 [3]) analog neurons. Note that Olivares et al. (BioRxiv 710566, 2020 [4]) present a likely more realistic model more distributed CPG. We use the simpler simulation to show that a small network of FitzHugh-Nagumo neurons (one of the simplest neuronal models) can generate key features of $\textit{C. elegans}$ undulation, and thus locomotion, yielding a minimal, biomimetic model as a building block for further exploring $\textit{C. elegans}$ locomotion.