In a dynamic far-field diffraction experiment, we calculate the largest
Lyapunov exponent of a time series obtained from the optical
fluctuations in a dynamic diffraction pattern. The time series is used
to characterize the locomotory predictability of an oversampled
microscopic species. We use a live nematode, Caenorhabditis elegans, as a model organism to demonstrate
our method. The time series is derived from the intensity at one point
in the diffraction pattern. This single time series displays chaotic
markers in the locomotion of the Caenorhabditis
elegans by reconstructing the multidimensional phase space.
The average largest Lyapunov exponent (base e) associated with the
dynamic diffraction of 10 adult wildtype (N2) Caenorhabditis elegans is
1.27
±
0.03
s
−
1
.
The small (1 mm) nematode Caenorhabditis elegans (Corsi [1], wormbook.org) 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. We describe a minimal reaction-diffusion model for the locomotion of C. elegans, using as a framework a simplified, stylized "descending pathway" of neurons as central pattern generator (CPG) (Xu et al., Proceedings of the National Academy of Sciences 115, 2018 [2]). Finally, we realize a model of the required oscillations and coupling with a network of coupled Keener (IEEE Transactions on Systems, Man, and Cybernetics SMC-13, 1983 [3]) analog neurons. Note that Olivares et al. (BioRxiv 710566, 2020 [4]) present a likely more realistic model more distributed CPG. We use the simpler simulation to show that a small network of FitzHugh-Nagumo neurons (one of the simplest neuronal models) can generate key features of C. elegans undulation, and thus locomotion, yielding a minimal, biomimetic model as a building block for further exploring C. elegans locomotion.
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