Graphic mathematical modelling of calcium ion binding dependent vesicle exocytosis in the presynaptic terminal of a central synapse

Abstract

A fundamental aspect of neuroscience is understanding the function of the chemical synapse. To relay electrical signals from neuron to neuron, synaptic vesicles fuse with the presynaptic terminal, undergoing exocytosis to release neurotransmitters into the synaptic cleft. Vesicle exocytosis is a stochastic process which relies on the presence, diffusion, and chelation of calcium ions (Ca²⁺). These ions enter the presynaptic terminal upon depolarization by action potentials. Accordingly, this study used graphic modelling in Python to examine the spatial and temporal interactions of Ca²⁺, chelators, and synaptic vesicles in the presynaptic terminal to determine the effects of Ca²⁺ binding to vesicleassociated Ca²⁺ binding targets on the release probability of synaptic vesicles. A twodimensional model of the presynaptic terminal was constructed, employing the Monte Carlo Method to represent the probabilistic nature of Ca²⁺ conductance and vesicle fusion in the terminal. For observable effect, the model was animated and the initial locations of Ca²⁺ and chelators were allowed to vary randomly while controlling the initial conditions of Ca²⁺, chelator, and vesicle counts. This model found a positive correlation between Ca²⁺ count and vesicle exocytosis, and a negative correlation between buffer count and vesicle exocytosis. This allowed important microscopic trends to be observed in a physiologically accurate macroscopic way.

Key words: synaptic vesicle, chelator, neurotransmission, chemical synapse, graphic modelling, Monte Carlo Method, Brownian motion, exocytosis