Temporal Analysis of Stochastic Turning Behavior of Swimming C. elegans

Abstract

Caenorhabditis elegans exhibits spontaneous motility in isotropic environments, characterized by periods of forward movements punctuated at random by turning movements. Here, we study the statistics of turning movements—deep \(\Omega\)-shaped bends—exhibited by swimming worms. We show that the durations of intervals between successive \(\Omega\)-turns are uncorrelated with one another and are effectively selected from a probability distribution resembling the sum of two exponentials. The worm initially exhibits frequent \(\Omega\)-turns on being placed in liquid, and the mean rate of \(\Omega\)-turns lessens over time. The statistics of \(\Omega\)-turns is consistent with a phenomenological model involving two behavioral states governed by Poisson kinetics: a “slow” state generates \(\Omega\)-turns with a low probability per unit time; a “fast” state generates \(\Omega\)-turns with a high probability per unit time; and the worm randomly transitions between these slow and fast states. Our findings suggest that the statistics of spontaneous \(\Omega\)-turns exhibited by swimming worms may be described using a small number of parameters, consistent with a two-state phenomenological model for the mechanisms that spontaneously generate \(\Omega\)-turns.