Theory of the locomotion of nematodes

For agar, the tangential drag coefficient C||,agar is 3.2 × 10−3 kg·s−1, as estimated by Niebur and Erdös (1991) from Wallace's measurement.

“For agar, Wallace estimated the tangential drag coefficients C||,agar by directly measuring the force required to pull glass fibers of similar dimension to C. elegans across the surface (Wallace, 1969). Based on this measurement, Niebur and Erdös (1991) estimated C||,agar = 3.2 × 10−3 kg·s−1.”

Previous models of locomotion have typically assumed graded potential neurons, in line with available data at the time.

“Previous models of locomotion have typically assumed graded potential neurons (Niebur and Erdös, 1991; Karbowski et al., 2006; Bryden and Cohen, 2008), in line with available data at the time (Goodman et al., 1998; Nickell et al., 2002; Francis et al., 2003; O’Hagan et al., 2005).”

The normal drag coefficient for agar C⊥,agar is 128 × 10−3 kg·s−1, obtained by taking Kagar = 40 and Niebur and Erdös' estimate for C||,agar.

“We previously estimated the normal drag coefficient C⊥,agar from recordings of wild type worms using our motion simulator (Berri et al., 2009). Briefly, we found the ratio of drag coefficients to be in the range Kagar ≈ 30–40; taking a value of Kagar = 40 and Niebur and Erdös’ estimate for C||,agar gives C⊥,agar = 128 × 10−3 kg·s−1, which will be used in what follows.”

The model requires integration of proprioceptive inputs over up to half a body length.

“Previously, the necessary extent of proprioceptive receptive fields has been considered only for crawling-like motor patterns (Niebur and Erdös, 1991; Bryden and Cohen, 2008), but we find that our model requires integration of proprioceptive inputs over up to half a body length.”