Discrete Modeling of Neuronal Interactions in Multi-Transmitter Networks

Abstract

This paper presents a discrete model of non-synaptic interactions between neurons, which are performed by special chemical agents, neurotransmitters. In this model, all signals are broadcast: each neuron’s activity can be perceived by all other neurons that are sensitive to its neurotransmitter. The purpose of leaving synapses out is to demonstrate the importance of heterochemical¹ interactions in the nervous system. Transmitter-specific neurons are described as finite automatons, which are a generalization of the traditional formal neuron. In a network consisting of such neurons, all connections are functional and not structural. This feature makes it possible to explain rapid reconfigurations of activity patterns in the generation of different rhythms by neuron ensembles, which are observed in living systems. We discuss and justify the choice of a discrete mathematical framework for simulation of heterochemical interactions.