Discrete Model of Asynchronous Multitransmitter Interactions in Biological Neural Networks

An asynchronous discrete model of nonsynaptic chemical interactions between neurons is proposed. The model significantly extends the previous work [5,6] 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 dynamics of membrane potentials that comprises two factors: the endogenous currents depending on the neurons of firing type, and the exogenous current, depending on the concentrations of neurotransmitters that the neuron is sensitive to. The firing type of a neuron is determined by the individual composition of endogenous currents. We consider three basic firing types: oscillatory, tonic and reactive. Each of them is essential for modeling central pattern generators, i. e. neural ensembles generating rhythmic activity in the absence of external stimuli. Variability of endogenous currents of different neurons leads to asynchronous neural interactions and significant fluctuations of phase durations in the activity patterns present in simple neural systems. An algorithm computing the behavior of the proposed model is provided.