| The regulation of gene expression is essential for the maintenance of homeostasis within an organism. Thus, the ability to predict which genes are expressed and which are silenced based on the cellular environment is highly desired by molecular biologists. Mathematical models of gene regulatory networks have frequently been given in terms of systems of differential equations, which although useful for understanding the mechanisms of regulation, are not always as interpretable as discrete models when one wishes to analyze the global-level dynamics of the system. In particular, Boolean network models have been previously shown to be simple yet effective tools for modeling operons such as the lactose operon in Escherichia coli. In this thesis, we propose a Boolean model of a similar nature for the arabinose operon. While this operon is also used by E. coli to regulate sugar metabolism, it contains several unique biological features such as a positive inducible control mechanism that distinguish it from previously modeled gene networks. By treating the network model as a polynomial dynamical system, analysis of the system dynamics shows that our model accurately captures the biological behavior of the operon and also provides insight into interactions within the network. |
