Development of equation of motion deciphering locomotion including omega turns of Caenorhabditis elegans

Abstract

Locomotion is a fundamental behavior of Caenorhabditis elegans (C. elegans). Previous works on kinetic simulations of animals helped researchers understand the physical mechanisms of locomotion and the muscle-controlling principles of neuronal circuits as an actuator part. It has yet to be understood how C. elegans utilizes the frictional forces caused by the tension of its muscles to perform sequenced locomotive behaviors. Here, we present a two-dimensional rigid body chain model for the locomotion of C. elegans by developing Newtonian equations of motion for each body segment of C. elegans. Having accounted for friction-coefficients of the surrounding environment, elastic constants of C. elegans, and its kymogram from experiments, our kinetic model (ElegansBot) reproduced various locomotion of C. elegans such as, but not limited to, forward-backward-(omega turn)-forward locomotion constituting escaping behavior and delta-turn navigation. Additionally, ElegansBot precisely quantified the forces acting on each body segment of C. elegans to allow investigation of the force distribution. This model will facilitate our understanding of the detailed mechanism of various locomotive behaviors at any given friction-coefficients of the surrounding environment. Furthermore, as the model ensures the performance of realistic behavior, it can be used to research actuator-controller interaction between muscles and neuronal circuits.