| Abstract: |
| Synapses play a major role in neuron communications in the brain. The synapses act through a chemical process called synaptic fusion between pre-synaptic and post-synaptic terminals. In the paper, we develop a mathematical model in 3-D to emulate spontaneous and evoked neurotransmissions resulted from glutamate release within a single synapse. We propose numerical methods for solving piecewise continuous heat diffusion equation, estimate and verify its errors of second order accuracy. In order to identify the spatial relation between spontaneous and evoked glutamate releases, we consider quantitative factors, such as the size of synapses, inhomogeneity of diffusion coefficients, the geometry of synaptic cleft, and the release rate of neurotransmitter, that will affect postsynaptic currents. The computed results match well with existing experimental findings and provide a quantitative map of boundaries of physical constraints for having independent synaptic fusion events. |
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