Graduation Semester and Year

2015

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Jianzhong Su

Abstract

As synapses are responsible for the majority of neuron communications in the brain, the events of evoked and spontaneous synaptic vesicle release/fusion are key features of all synaptic current. These release events typically activate receptors within a single postsynaptic site and give rise to miniature postsynaptic currents through activations of $N$-methyl-$D$-asparate (NMDA) and $\alpha$-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors, and therefore, they have been extremely instrumental in neurotransmissions. In this paper we will use a mathematical model to simulate spontaneous and evoked neurotransmission resulted from glutamate release within a synapse. Among several issues that modeling can provide quantitative assessment, the issue of independent signaling of spontaneous and evoked neurotransmission has been prominent. Our main goal is to determine the necessary conditions synapses to obtain independent signaling. We examine how different factors, including the release rate of the neurotransmitter, size and geometry of synaptic cleft, and diffusion coefficient will affect post-synaptic currents and which of these are instrumental in obtaining independent signaling.

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

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Mathematics Commons

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