A minimal neural reaction-diffusion model which generates <i>C. elegans</i> undulation

The small (1 mm) nematode Caenorhabditis elegans 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 (c.f. http://www.wormbook.org/). We describe a minimal reaction-diffusion model for the C. elegans central pattern generator (CPG) (c.f. Xu et al. 2018, Wen et al. 2012). We use simulation methods to show that a small network of FitzHugh (1961)-Nagumo (et al. 1962) neurons (one of the simplest neuronal models) can generate key features of C. elegans undulation (c.f. Magnes et al. 2017) and thus locomotion. Compare the neuromechanical model of Izquierdo and Beer (2015). We also investigate dynamics and stability of the model.
References
FitzHugh R. 1961. Biophysical J. 1, 445.
Izquierdo EJ and Beer RD. 2015 Proc. European Conference on Artificial Life, p. 219.
Magnes J et al. 2017. JoVE. 2017, 127.
Nagumo J et al. 1962. Proc IRE 50, 2061.
Wen Q et al. 2012. Neuron 76, 750.
Xu T et al. 2018. PNAS USA 115 E4493.