Modeling of Long-Distance Backward Swimming in Paramecia Based on the Relaxation Process of Chemical Gradients

Abstract

This study aims to model the spatial adaptive behavior of Paramecium based on the relaxation process of chemical gradients. Paramecium exhibits a behavior in which it repeats short-distance backward swimming upon collision with obstacles in narrow spaces, thus gradually increasing the distance of its backward swimming until it exhibits long-distance backward swimming. This behavior arises from the changes in the membrane potential induced by intracellular and extracellular chemical gradients, which control the direction and frequency of ciliary movement. To replicate this behavior, a mathematical model was developed by integrating an electrophysiological model of membrane potential with a motility model that formalizes the relationship between membrane dynamics and ciliary motion. Numerical simulations successfully reproduced the transition from short-distance to long-distance backward swimming and revealed that, in addition to the slow response of calcium ion channels, a dynamically changing threshold of calcium current for inducing backward swimming is essential. These findings suggest that Paramecium possesses an adaptive capability driven not only by passive responses to chemical gradients but also by an intrinsic control mechanism mediated through the dynamics of membrane potential and ciliary motion.