Systems level analysis of action potential firing in neuronal networks

Action-potential-mediated release of neurotransmitters at chemical synapses is fundamental to interneuronal communication. More specifically, presynaptic Action Potentials (APs) trigger the fusion of docked vesicles which subsequently empty their neurotransmitter content into the synaptic cleft and drive transient changes in the postsynaptic membrane potential. An excitatory synaptic connection leads to depolarization of the membrane potential, and a postsynaptic AP is elicited when it reaches a critical threshold level. Such postsynaptic AP ``firings" are classically modeled using the integrate-and-fire model, where the threshold is fixed. In the paper we consider a revised model where the threshold changes in response to recent firing activity. Our analysis reveals that the adaptive threshold can lead to a band-pass effect where the postsynaptic AP frequency is maximized to an intermediate presynaptic AP frequency. Next we analyze a cascade of synaptically connected neurons of arbitrary lengths with a particular focus on understanding how AP firing time statistics is altered along the cascade. Our results show that generally AP firings become consistent with a Poisson rate (exponentially-distributed inter AP times) for downstream neurons, but in some cases, such as a pure (non-leaky) integrate-and-fire model, the firing time statistics remains hypo-exponentially distributed throughout the cascade.