MATHEMATICAL-MODELING OF THE ENTERIC NERVOUS NETWORK-1 - CHOLINERGIC NEURON

A mathematical model is proposed to describe the coupled electrochemic al mechanisms of nerve-pulse transmission via cholinergic synapse. Bas ed on pharmacological and morphophysiological data, the model describe s the dynamics of the propagation of the electric signal along the unm yelinated geometrically non-uniform axon of the neuron and the chemica l mechanisms of the transformation of the electrical signal in the syn aptic 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 functio n of the cholinergic neuron quantitatively and qualitatively describe the dynamics of Ca2+ ions influx into the terminal, acetycholine relea se from the vesicles, accumulation of its free fraction, diffusion int o the synaptic cleft, and binding with the receptors on the postsynapt ic structures with the generation of the fast excitatory postsynaptic potential. They are in good agreement with the observed experimental f indings.