Author

Maisha Zahed

Date of Award

2018

First Advisor

Harold Hastings

Second Advisor

Erin McMullin

Third Advisor

Patty Dooley

Abstract

The Belousov-Zhabotinsky (BZ) reaction has been studied as a model for the dynamics of neural networks because both display similar excitable dynamics: a local stimulus can generate outgoing waves of activation. Both the BZ reaction and the brain can also support globally synchronous oscillations, a characteristic of the diseased state of epilepsy in the brain. In this analogy, a spike in the concentration of bromous acid corresponds to the action potential generated when a neuron fires. My thesis proposes a basic chemical model for epilepsy by investigating the transition from pacemaker-generated local oscillations to global, synchronous oscillations in the BZ reactions. My experiments may provide insights into abnormal patterns of excitability in the brain, called “dynamical disease” by Leon Glass (1995) and other researchers. The BZ reaction leads to the production of bromous acid from hydrogen and bromate ions. In order to emulate the oscillatory behavior of GABA and glutamate, the concentrations of the aforementioned ions along with the bromide ion was used as analogies of these neurotransmitters. The effect of hydrogen and bromate ions, which together control excitability in the BZ reaction, appears to correspond to the effect of glutamate which increases excitability in the brain. Similarly, the concentration of brominated malonic acid, which determines the rate of production of bromide ions (the inhibitor in the BZ reaction), may correspond to the concentration of GABA, which inhibits neuronal activity. The objective was to emulate the effect of GABA and glutamate upon the nature of oscillations by studying the effects of concentrations of chemicals in the BZ reaction. These effects can be simulated using mathematical models (the FitzHugh-Nagumo neuronal model and a related model for BZ reactions, the Oregonator) in order to further understand details of the dynamics.

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