Vesicular mechanisms and estimates of firing probability in a network of spiking neurons

A neural network with mutual excitatory connections and external stimulation is investigated. The units of the network are Morris–Lecar neurons. The synaptic transmission is described at the vesicular level. Random number of activated vesicles at synaptic contacts and random quanta of released transmitter are considered. These fluctuations are applied in a form of inhomogeneous Poisson processes, at the time scale of the spike duration. The parameters of these processes depend on the presynaptic spiking activity and on the strength of afferent connections. It is shown how synchronization of the activity in the network appears. A statistical analysis of spiking times is performed, showing smooth mean behavior of response frequencies. A diffusion approximation of the network Poissonian process is derived from which an analytical formula for firing probability is calculated.