Age-dependent Dynamics of Locomotion in <em>Caenorhabditis elegans</em>: A Lyapunov Exponent Analysis

This study investigates the influence of age on the mobility of Caenorhabditis elegans (C. elegans) by employing Dynamic Optical Diffraction (DOD) to estimate the Largest Lyapunov Exponent (LLE). The LLE, a key metric in dynamical systems, quantifies the rate of divergence or convergence of trajectories in phase space, indicating the predictability and chaos in the system's dynamics, in this case, the locomotive behaviors of the worm. 632 nm laser light diffracts off the swimming worm in a water column, forming a diffraction pattern. A photodiode detects the light at a single point within the diffraction pattern, capturing a one-dimensional time series as the worm undulates. This time series serves as a composite representation of the entire worm's motion, encapsulating its locomotion dynamics since one point in the diffraction pattern is a superposition of all points on the worm. The time series is then embedded into a higher-dimensional phase space to calculate the LLE. C. elegans typically live for around 14 days, following a pattern of increasing and declining motor control with age. To isolate age-specific effects, worms were transferred to fresh agar plates containing E. coli every two days, ensuring they were appropriately aged (3 to 12 days old). Analysis of a cohort of 13 C. elegans revealed that the LLE peaked at five days post-hatching, at a rate of 1.34 ± 0.03 1/s. This peak signifies a critical point in development where the worms' locomotion displays the highest complexity and chaotic behavior. The observed LLE values align with the Moore equation, a well-established model that describes age-related changes in voluntary activity, linking decreasing motor control and activity levels with increasing age in C. elegans.