Mathematical Models of Biochemical Switch Networks
Mohr, Cassandra A., 1997--
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This project centers on mathematical applications to biochemistry. Specifically, the use of a dynamical system to model a special type of biochemical network and determine the effect of initial concentrations on the existence of several constant solutions. Many biochemical networks act as biological switches that are responsible for important biological functions such as cell differentiation and cell death; consequentially, the ability to better predict and manipulate their outcome is of great importance. One particularly insightful and relatively simple form of biochemical mechanism is that of the reversible substrate inhibition reaction. Utilizing basic principles of mathematics and chemistry, it is possible to convert a biochemical network into a system of differential equations; this in turn permits further in-depth analysis of the original chemical reaction in order to determine its projected outcomes. Using the Jacobian and its characteristic polynomial as well as analysis of the system itself, we can gain enhanced comprehension into the effect initial concentration has on the eventual outcome of the overall system of biochemical reactions. Specifically, it is possible to determine what limitations must be imposed on the initial network in order to guarantee fixed points.