A minimal, biomimetic, add-on model for C. elegans swimming in a natural environment

The small (1 mm) nematode Caenorhabditis elegans (C. elegans) is widely used as a model organism; in particular its connectome has been completely mapped and its locomotion widely studied (c.f. http://www.wormbook.org/). In order to better understand C. elegans locomotion, we develop a minimal “add-on” model (the opposite of a knockout model) for the C. elegans central pattern generator (CPG) (c.f. Xu et al. 2018, Wen et al. 2012).  This model consists of a small network of simulated FitzHugh-Nagumo neurons, coupled by diffusion, whose topology is based on the Xu et al. connectome (Singhvi et al. 2021).  Here we show that the model admits traveling wave solutions corresponding to forward and backward locomotion, as well as phenomenological omega turns, and that these modes can be largely represented by the first three “eigenworms” of Stephens et al. (2008) and Ahamed et al. (2021). We also show that incorporating a simple Markov model (c.f. Roberts et al. 2016) for translating sensory inputs into dynamics of this simple model generates the observed random searching behavior (Calhoun et al. 2014).  Finally, we compare the locomotion of simulated worms to our (JM and HMH) lab’s experimental results (Magnes et al. 2020). (AS and CEL contributed equally to this work.)