Author

Sat Byul Seo

ORCID Identifier(s)

0000-0002-9110-271X

Graduation Semester and Year

2017

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Jianzhong Su

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. Presynaptic terminals release neurotransmitters either in response to action potential or spontaneously independent of presynaptic activity. In the case of glutamate, released neurotransmitters acivate N-methyl-D-asparate (NMDA) receptors within a single postsynaptic site and give rise to miniature postsynaptic currents. In this dissertation, 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 post-synaptic currents. We conclude quantitatively that as a synapse's size is smaller and if the synaptic cleft space is less diffusive in the peripheral area than the center area, then there is high a possibility of having crosstalk between two signals from spontaneous and evoked releases. On the other hand, when a synaptic size is larger, the cleft space is less diffusive in the central area than the edge area, if the geometry synaptic cleft has a narrower gap in the center and if glutamate release is slower, then there is a better chance for independence of two modes of currents from spontaneous and evoked release. 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.

Keywords

Mathematical modeling, Numerical methods

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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