Development of equation of motion deciphering locomotion including omega turns of <i>Caenorhabditis elegans</i>.

Abstract

Locomotion is a fundamental behavior of <i>Caenorhabditis elegans</i> (<i>C. elegans</i>). 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 <i>C. elegans</i> 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 <i>C. elegans</i> by developing Newtonian equations of motion for each body segment of <i>C. elegans</i>. Having accounted for friction-coefficients of the surrounding environment, elastic constants of <i>C. elegans</i>, and its kymogram from experiments, our kinetic model (ElegansBot) reproduced various locomotion of <i>C. elegans</i> 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 <i>C. elegans</i> 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.