Characterizing neuronal synaptic transmission using stochastic hybrid systems

Action potential-triggered release of neurotransmitters at chemical synapses forms the key basis of communication between two neurons. To quantify the stochastic dynamics of the number of neurotransmitters released, we investigate a model where neurotransmitter-filled vesicles attach to a finite number of docking sites in the axon terminal, and are subsequently released when the action potential arrives. We formulate the model as a Stochastic Hybrid System (SHS) that combines three key noise mechanisms: random arrival of action potentials, stochastic refilling of docking sites, and probabilistic release of docked vesicles. This SHS representation is used to derive exact analytical formulas for the mean and noise (as quantified by Fano factor) in the number of vesicles released per action potential. Interestingly, results show that in relevant parameter regimes, noise in the number of vesicles released is sub-Poissonian at low frequencies, super-Poissonian at intermediate frequencies, and approaches a Poisson limit at high frequencies. In contrast, noise in the number of neurotransmitters in the synaptic cleft is always super-Poissonian, but is lowest at intermediate frequencies. We further investigate changes in these noise properties for non-Poissonian arrival of action potentials, and when the probability of release is frequency dependent. In summary, these results provide the first glimpse into synaptic parameters not only determining the mean synaptic strength, but also shaping its stochastic dynamics that is critical for information transfer between neurons.