Some Mathematical Models in Neuroscience Applications

Document Type

Presentation Abstract

Presentation Date

12-4-2014

Abstract

A neuron is an electrically excitable cell that processes and transmits information through electrical and chemical signals. Neurons connect and pass signals to other cells through the structure called synapse. We focus on synapses through which the signals are transferred by signaling molecules called neurotransmitters. One of the predominant excitatory neurotransmitters in the central nervous system of the mammals, including humans, is glutamate. It is directly or indirectly involved in most brain functions. However, the excessive stimulation of the glutamate receptors is toxic to neurons, therefore it is important to rapidly clear the glutamate from the extracellular space and keep its concentration low. Glutamate transporters play a crucial role in regulating glutamate concentration in synaptic clefts. Thus, it is important to understand the mechanisms underlying this process.

We describe measurement of the glutamate concentration in the extracellular space. It is important to estimate the baseline glutamate concentration to use it in future models and studies. However, two existing methods of measuring the glutamate concentration in the extracellular space give inconsistent results with about 100—fold difference. We construct the model of the process of the glutamate concentration measurement in order to explain that discrepancy.

Also, we consider an experiment, derive a model for it, and use the data from the experiment for estimation of some important constants of glutamate dynamic process in a brain.

Additional Details

Master’s Thesis Defense.

Thesis Committee: Dr. Leonid Kalachev (Mathematical Sciences), Dr. Emily Stone (Mathematical Sciences), Dr. Michael Kavanaugh (Center for Structural and Functional Neuroscience)

Thursday, December 4th, 2014 at 3:00 p.m. in Skaggs 117

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