Discrete Modeling of Multi-transmitter Neural Networks with Neuronal Competition

We propose a novel discrete model of central pattern generators (CPG), neuronal ensembles generating rhythmic activity. The model emphasizes the role of nonsynaptic interactions and the diversity of electrical properties in nervous systems. Neurons in the model release different neurotransmitters into the shared extracellular space (ECS) so each neuron with the appropriate set of receptors can receive signals from other neurons. We consider neurons, differing in their electrical activity, represented as finite-state machines functioning in discrete time steps. Discrete modeling is aimed to provide a computationally tractable and compact explanation of rhythmic pattern generation in nervous systems. The important feature of the model is the introduced mechanism of neuronal competition which is shown to be responsible for the generation of proper rhythms. The model is illustrated with an example of the well-studied feeding network of a pond snail. Future research will focus on the neuromodulatory effects ubiquitous in CPG networks and the whole nervous systems.