Markers of Chaotic Locomotion of C. elegans Swimming in Three Dimensions*

Caenorhabditis elegans, more commonly known as C. elegans, are transparent nematodes approximately 1 mm long that inhabit soil in temperate environments. C. elegans have 302 neurons that are similar in form and function to that of humans, which has spiked the interest of neurological and biological communities. Time-dependent diffraction by oversampling provides information about the locomotion in the form of a single time-series. Several markers of chaos are calculated such as a broad frequency spectrum, a positive Largest Lyapunov Exponent (LLE), and the time evolution of the locomotion as visualized by Recurrence Plots (RP). The recurrence matrix is also used to visualize switching behavior time scales and to calculate Recurrence Quantification Analysis (RQA) values for comparison between different data sets. Surrogate data analysis further proves the presence of nonlinearity in the time-series. In comparison to the real worm dynamics, a simulated worm is made using a descending chain of  FitzHugh-Nagumo neurons (Singhvi, Lee et al. in our labs). Repeating the previous analysis method on the simulated worm time-series could validate the model and range of parameters necessary to invoke similar chaotic markers.