Abstract
Fractal scaling is a common property of temporal change in various modes of animal behavior. The molecular mechanisms of fractal scaling in animal behaviors remain largely unexplored. The nematode C. elegans alternates between swimming and resting states in a liquid solution. Here, we report that C. elegans episodic swimming is characterized by scale-free kinetics with long-range temporal correlation and local temporal clusterization, namely consistent with multifractal kinetics. Residence times in actively-moving and inactive states were distributed in a power law-based scale-free manner. Multifractal analysis showed that temporal correlation and temporal clusterization were distinct between the actively-moving state and the inactive state. These results indicate that C. elegans episodic swimming is driven by transition between two behavioral states, in which each of two transition kinetics follows distinct multifractal kinetics. We found that a conserved behavioral modulator, cyclic GMP dependent kinase (PKG) may regulate the multifractal kinetics underlying an animal behavior. Our combinatorial analysis approach involving molecular genetics and kinetics provides a platform for the molecular dissection of the fractal nature of physiological and behavioral phenomena.