Accuracy of deterministic vs. stochastic modeling of Ca2+-dependent vesicle release

High degree of variability is a characteristic feature of synaptic neurotransmitter release, which is important to consider in our  understanding and modeling of this fundamental physiological process. Although stochastic Ca2+ channel gating is one of the primary source of this variability, it can be easily implemented in a computationally inexpensive way in combination with deterministic simulation of the downstream Ca2+ diffusion and binding. A more fundamental reason for the high variability of synaptic response is that only a small number of Ca2+ ions enter the synaptic terminal through a single channel during an action potential. This fact entails large fluctuations due to Ca2+ diffusion and its binding to Ca2+ buffers and vesicle release sensors, leading to a widely-held view that solving continuous deterministic reaction-diffusion equations does not provide high accuracy when modeling Ca2+-dependent cell processes. However, several comparative studies show a surprising close agreement between deterministic and trial-averaged stochastic simulations of Ca2+ dynamics, as long as Ca2+ channel gating is not Ca2+-dependent. This is a surprising result, deserving careful investigation. In this talk I will present further analysis and comparison of stochastic and mass-action modeling of vesicle release, showing that the discrepancy between deterministic and stochastic approaches can be surprisingly small even when only as few as 40-50 ions enter per single channel-vesicle complex. The reason for the close agreement between stochastic and mass-action simulations is that the discrepancy between the two approaches is determined by the size of the correlation between the local Ca2+ concentration and the state of the vesicle release sensor, rather than the fluctuation amplitude. Although diffusion and buffering increases fluctuation amplitude, it has an effect of averaging out the correlations between reactant fluctuations. Finally, contrary to naïve intuition, the mass action / mean-field reaction-diffusion description allows an accurate estimate of the entire probability distribution of vesicle release latency, rather than providing information about trial-averaged quantities only. These results may help in the choice of appropriate and efficient tools for the modeling of this and other fundamental biochemical cell processes.