Victor Matveev: Deterministic vs. Stochastic Simulation of First-Passage Time to Synaptic Neurotransmitter Release

Most physiological mechanisms exhibit high variability due to the fundamental stochasticity of biochemical reaction pathways. Quantifying the impact of stochastic effects is necessary for a deeper understanding of physiological processes and their regulation, and helps in the choice of an efficient approach for their computational modeling. This is especially true in the case of synaptic neurotransmitter release, which is caused by the fusion of the secretory vesicle membrane with the cell membrane in response to calcium ion binding. Although stochastic calcium channel gating is one of the primary source of this stochasticity, it can be implemented in a computationally inexpensive way in combination with deterministic simulation of the downstream calcium diffusion and binding reactions. Another fundamental reason for the high variability of synaptic response is that only a small number of calcium ions enter the synaptic terminal through a single channel during an action potential. This fact entails large fluctuations due to calcium diffusion and its binding to calcium 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 calcium-dependent cell processes. 

However, several comparative studies show a surprising close agreement between deterministic and trial-averaged stochastic simulations of calcium dynamics, as long as calcium channel gating is not calcium-dependent. This result deserves careful investigation. This talk will focus on further analysis and comparison of stochastic and mass-action modeling of vesicle release, showing that the discrepancy between deterministic and stochastic approaches remains 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 calcium concentration and the state of the vesicle release sensor, rather than fluctuation amplitude. Whereas diffusion and buffering increases fluctuation size, the same processes appear to de-correlate fluctuations in calcium concentration from fluctuations in calcium sensor binding state. Finally, contrary to naïve intuition, the mass action / mean-field reaction-diffusion description allows an accurate estimate of the probability density of vesicle release latency (first-passage time), 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.