Biological modeling the undulatory locomotion of C. elegans using dynamic neural network approach

This paper provides an undulatory locomotion model of C. elegans to achieve the chemotaxis behaviors based on the biological neuronal and neuromuscular structure. The on-cell and off-cell mechanism, as well as the proprioceptive mechanism is incorporated into the locomotion model. The nervous system of C. elegans is modeled by a dynamic neural network (DNN) that involves two parts: head DNN and motor neurons. The head DNN perceives the outside concentrations and generates the undulatory wave to the body. The motor neurons are responsible for transiting the undulatory wave along the body. The body of C. elegans is represented as a multi-joint rigid link model with 11 links. The undulatory locomotion behavior is achieved by using the DNN to control the lengths of muscles on ventral and dorsal sides, and then using the muscle lengths to control the angles between two consecutive links. In this work, the relations between the outputs of DNN and muscle lengths, as well as the muscle lengths and the angles between two consecutive links, are determined. Furthermore, owing to the learning capability of DNN, a set of nonlinear functions that are designed to represent the chemotaxis behaviors of C. elegans are learned by the head DNN. The testing results show good performance of the locomotion model for the chemotaxis behaviors of finding food and avoiding toxin, as well as slight and Ω turns. At last, quantitative analyses by comparing with the experiment results are provided to verify the realness and effectiveness of the locomotion model, which could serve as a prototype for other footless animals.