locomotion in three dimensions

We characterize some key features of the locomotion of Caenorhabditis elegans (C. elegans) in its natural (3D) environment. C. elegans, a small (1 mm) nematode is widely studied and used as model organism in the neuroscience community (“Wormbook,”http://www.wormbook.org) because it is a “complete microorganism” with a relatively small, fully described nervous system.The locomotion of C. elegans in 2D environments has been widely studied (19,600 references in Google Scholar search on 10/02/2020) and well understood since Pierce-Shimomura, Morse and Lockery (1999). The motion of C. elegans is captured with diffraction microscopy (Magnes, Susman and Eells, 2012). In particular, diffraction imaging responds to changes in the shape of C. elegans. The diffraction signal at one point yields a time series, and thus an attractor in typically 4D space (using mutual information and false nearest neighbors techniques for Takens embedding). We find a positive Lyapunov exponent of 1.3/ s, a marker of deterministic chaos, larger than the value of 0.7/ s found by Ahamed, Costa and Stephens (2019) for motion in 2D. Finally, we see complex dynamics on multiple time scales in recurrence plots of 3D motion, as seen earlier for 2D motion by Stephens et al. (2011).