Mathematical modelling of the enteric nervous network. 1: Cholinergic neuron.

A mathematical model is proposed to describe the coupled electrochemical mechanisms of nerve-pulse transmission via cholinergic synapse. Based on pharmacological and morphophysiological data, the model describes the dynamics of the propagation of the electric signal along the unmyelinated geometrically non-uniform axon of the neuron and the chemical mechanisms of the transformation of the electrical signal in the synaptic zone into the postsynaptic output. The combined nonlinear system of partial and ordinary differential equations has been obtained and solved numerically. The results of numerical simulation of the function of the cholinergic neuron quantitatively and qualitatively describe the dynamics of Ca2+ ions influx into the terminal, acetylcholine release from the vesicles, accumulation of its free fraction, diffusion into the synaptic cleft, and binding with the receptors on the postsynaptic structures with the generation of the fast excitatory postsynaptic potential. They are in good agreement with the observed experimental findings.