Stochastic analysis of frequency bandwidth and noise attenuation in neurotransmission

Action potential (AP)-triggered neurotransmitter release forms the key basis of inter-neuronal communication. We present a stochastic hybrid system model that captures the release of neurotransmitter-filled vesicles from a presynaptic neuron. More specifically, vesicles arrive as a Poisson process to attach at a given number of docking sites, and each docked vesicle has a certain probability of release when an AP is generated in the presynaptic neuron. The released neurotransmitters enhance the membrane potential of the postsynaptic neuron, and this increase is coupled to the continuous exponential decay of the membrane potential. The buildup of potential to a critical threshold level results in an AP firing in the postsynaptic neuron, with the potential subsequently resetting back to its resting level. Our model analysis develops formulas that quantify the fluctuations in the number of released vesicles and mechanistically connects them to fluctuations in both the postsynaptic membrane potential and the AP firing times. Increasing the frequency of APs in the presynaptic neuron leads to saturation effects on the postsynaptic side, resulting in a limiting frequency range of neurotransmission. Interestingly, AP firing in the postsynaptic neuron becomes more precise with increasing AP frequency in the presynaptic neuron. We also investigate how noise in AP timing varies with different parameters, such as the probability of releases, the number of docking sites, the voltage threshold for AP firing, and the timescale of voltage decay. In summary, our results provide a systematic understanding of how stochastic mechanisms in neurotransmission enhance or impinge the precision of AP fringing times.