Thermosensitive double-membrane neurons and their network dynamics

Abstract

Cell membrane of biological neurons has distinct geometric structure, and involvement of diffusive term is suitable to estimate the spatial effect of cell membrane on neural activities. The gradient field diversity between two sides of the cell membrane can be approached by using a double-layer membrane model for the neuron. Therefore, two capacitive variables and diffusive terms are used to investigate the neural activities of cell membrane, and the local kinetics is described by a functional circuit composed of two capacitors. The voltages for the two parallel capacitors describe the inner and outer membrane potentials, and the diffusive effect of ions is considered on the membrane surface. The results reveal that neural activities are relative to the capacitance ratio between the inside and outside of the membrane and diffusive coefficient. High-energy periodic external stimulation induces the target waves to spread uniformly, while low-energy chaotic stimulation results in wave fragmentation. Furthermore, when the capacitance ratio exhibits exponential growth under an adaptive control law, the resulting energy gradient within the network induces stable target waves. That is, energy distribution affects the wave propagation and pattern formation in the neuron. The result indicates that the spatial diffusive effect and capacitance diversity between outer and inner cell membranes are important for selection of firing patterns and signal processing during neural activities. This model is more suitable to estimate neural activities than using generic oscillator-like or map neurons without considering the spatial diffusive effect.