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

Abstract

The small (1 mm) nematode Caenorhabditis elegans (Corsi [1], wormbook.org) has become widely used as a model organism; in particular the C. elegans connectome has been completely mapped, and C. elegans locomotion has been widely studied. We describe a minimal reaction-diffusion model for the locomotion of 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 [2]). 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 C. elegans undulation, and thus locomotion, yielding a minimal, biomimetic model as a building block for further exploring C. elegans locomotion.