Analysis, Simulation, and Optimization of Stochastic Vesicle Dynamics in Synaptic Transmission

Synaptic transmission is the mechanism of information transfer from one neuron to another (or from a neuron to a muscle or to an endocrine cell). An important step in this physiological process is the stochastic release of neurotransmitter from vesicles that fuse with the presynaptic membrane and spill their contents into the synaptic cleft. We are concerned here with the formulation, analysis, and simulation of a mathematical model that describes the stochastic docking, undocking, and release of synaptic vesicles and their effect on synaptic signal transmission. The focus of this talk is on the parameter p_0, the probability of release for each docked vesicle when an action potential arrives. We study the influence of this parameter on the statistics of the release process and on the theoretical capability of the model synapse in reconstructing various desired outputs based on the timing and amount of neurotransmitter release. This theoretical capability is assessed by formulating and solving an optimal filtering problem. Methods for parameter identification are proposed and applied to simulated data. This is joint work done in collaboration with Charles S. Peskin at the Courant Institute, New York University.