Propagation of the nerve-impulse within a neuronal chain

A mathematical model of a hypothetical “cholinergic chain” has been developed, based on the actual morphological data of its organization. The neuronal chain is composed of excitatory (cholinergic) neurones interconnected by polysynaptic channels, in a form of the geometrically non-uniform unmyelinated nerve axons. The synaptic zones are modelled as a three-compartment open pharmacokinetic system, i.e., presynaptic terminal, synaptic cleft and postsynaptic membrane where the pharmacokinetic mechanisms of electrochemical coupling are considered. All the chemical reactions of transformation of acetylcholine within them are described by first order Michaelis-Menten kinetics. The propagation of the electrical impulse along the axons and in the vicinity of the nerve terminal is described by the modified Hodgkin-Huxley equations. The results of numerical simulation of the propagation of excitation within the neuronal chain, under normal physiological conditions and after treatment with cholinergic/adrenergic agonists and antagonists are presented. The model predicts the dose-dependent influence of pharmacological agents on the neural chain function