Multichannel measurements of C. elegans largest Lyapunov exponents using optical diffraction.

Dynamic diffraction (DOD) is a form of microscopy that allows the dynamic tracking of changing shapes in a 1D time series. DOD can capture the locomotion of a nematode while swimming freely in a 3D space, allowing the locomotion of the worm to more closely mimic natural behavior than in some other laboratory environments. More importantly, we are able to see markers of chaos as DOD covers dynamics on multiple length scales. This work introduces a multichannel method to measure the dynamic complexity of microscopic organisms. We show that parameters associated with chaos, such as the largest Lyapunov exponent (LLE), the mean frequency, mutual information (MI), and the embedding dimension, are independent of the specific point sampled in the diffraction pattern, thus demonstrating experimentally the consistency of our dynamic parameters sampled at various locations (channels) in the associated optical far-field pattern.

Dynamic Markers for Chaotic Motion in C. elegans.

We describe the locomotion of Caenorhabditis elegans (C. elegans) using nonlinear dynamics. C. elegans is a commonly studied model organism based on ease of maintenance and simple neurological structure. In contrast to traditional microscopic techniques, which require constraining motion to a 2D microscope slide, dynamic diffraction allows the observation of locomotion in 3D as a time series of the intensity at a single point in the diffraction pattern. The electric field at any point in the far-field diffraction pattern is the result of a superposition of the electric fields bending around the worm. As a result, key features of the motion can be recovered by analyzing the intensity time series. One can now apply modern nonlinear techniques; embedding and recurrence plots, providing valuable insight for visualizing and comparing data sets. We found significant markers of low-dimensional chaos. Next, we implemented a minimal biomimetic simulation of the central pattern generator of C. elegans with FitzHugh-Nagumo neurons, which exhibits undulatory oscillations similar to those of the real C. elegans. Finally, we briefly describe the construction of a biomimetic version of the Izquierdo and Beer robotic worm using Keener's implementation of the Nagumo et al. circuit.