Mathematical Modeling of the Chemical Reaction Network that Protects Mitochondria in Human Neural Cells Following Traumatic Brain Injury
Burns, Dustin Ray
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Following traumatic brain injury, human neural cells experience an increase in reactivity between peroxynitrite and superoxide dismutase. This reaction prevents superoxide dismutase from performing its essential role in the cell, which is to act as a catalyst in a reaction which protects mitochondria in the cell from damage (Bayir, 2007). Since mitochondria are vital to a cell’s survival, it is desirable to understand the mechanism that a cell uses to protect itself from harm when these reactions occur. The goal of this research is the mathematical development of these processes using the techniques of chemical kinetics, so that we may gain understanding of the complicated system of chemical reactions governing this mechanism. This mathematical development includes analyzing the concentration versus time of all reactants, discovering the time scales when they react, and analyzing which reactions in particular influence the tendency of the concentration of a particular reactant to reach equilibrium. This analysis and the interpretation of the results will provide mathematical support for the proposed protection mechanism, furthering our understanding of how the brain cell behaves under the stress of traumatic head injuries. We find that this system can indeed be modeled by a system of ordinary differential equations, whose solution can be interpreted to accurately describe the system. The oxidation percentages and ratios of the different enzymes involved can be plotted and interpreted, and the amount that each reaction forces the concentration of each reagent to change at turning points can be determined.
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