Activity in sparsely connected excitatory neural networks: effect of connectivity

The Nucleus Tractus Solitarius (NTS) of the brainstem contains a neural circuit with only excitatory connections displaying a spontaneous activity involved in the control of respiration. A model of a network with random connections is presented and is used to investigate a possible mechanism of spontaneous activity generation consisting of the amplification of a low-background activity by the excitatory connections. First, the steady states of the network model and its ability to amplify the activity are studied. Then, a low-background activity is introduced, and dynamics of simulated networks are examined. Low-tonic, slow-phasic and fast-tonic activities are successively observed when the mean number K of connections per neuron increases. The transition between the two first types of activity is progressive whereas the transition from slow-phasic to fast-tonic activity is sharp. Simulation results show that activities of low frequency can be obtained with the proposed mechanism of spontaneous activity generation only if the network connectivity is low.