This study aims to represent the fundamental principles of information processing systems that generate flexible behaviors in organisms using a mathematical model based on chemical gradients. Biological experiments were conducted to study the behavioral responses of the ciliate Paramecium, a unicellular organism, to collisions with obstacles. The results showed that Paramecium exhibited two distinct behaviors: one in which it changed direction immediately after the collision and another in which it moved along the obstacle before changing direction. While both behaviors had the same angle and speed at the time of collision, the sign of the angle changed before the collision. The behavior of Paramecium is controlled by the movement of cilia on its surface, which is regulated by membrane excitation dynamics driven by chemical gradients inside and outside the cell. We developed a mathematical model that links membrane excitation dynamics to observed behaviors and performed numerical simulations. The results showed that, similar to the experimental results, the two behaviors could be replicated based on the difference in the sign of the angle change before the collision. In other words, Paramecium exhibits flexibility in its behavior, producing different responses based on its motion history, even under the same chemical gradient conditions.

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.