An Asynchronous Discrete Model of Chemical Interactions in Simple Neuronal Systems

Abstract

An asynchronous discrete model of nonsynaptic chemical interactions between neurons is proposed. The model significantly extends the previous work [1, 2] by novel concepts that make it more biologically plausible. In the model, neurons interact by emitting neurotransmitters to the shared extracellular space (ECS). We introduce the dynamics of membrane potentials that comprises two factors: the endogenous rates of change depending on the neuron’s firing type and the exogenous rates of change depending on the concentrations of neurotransmitters that the neuron is sensitive to. The neuron’s firing type is determined by the individual composition of endogenous rates. We consider three basic firing types: oscillatory, tonic, and reactive. Each firing type is essential for modeling central pattern generators—neural ensembles that generate rhythmic activity in the absence of external stimuli. Differences in endogenous rates of different neurons lead to asynchronous neural interactions and significant variability of phase durations in the activity patterns present in simple neural systems. The algorithm computing the behavior of the proposed model is provided.