Stochastic perturbations of biochemical reaction systems

Recent work in mathematical biology has pointed out the need for a theory of biochemical reaction systems subjected to random and ongoing perturbations. While tools such as metabolic control analysis have been successful in finding how small, specific changes in a network affect the equilibrium values of concentrations and fluxes, there has not been a theory developed which considers large scale fluctuations in parameters and inputs that do not allow a system to ever reach a state of equilibrium. We consider biochemical reaction systems equipped with an input subjected to stochastic fluctuations and prove how different geometric and algebraic properties of biochemical reaction systems suppress, magnify, or otherwise shape the fluctuations. In particular, we prove a number of results for systems such that each complex is a single species and the kinetics is mass action. We find that for a reaction chain with monotone, but otherwise arbitrary kinetics the variances of the fluxes will decrease as one moves down the chain. We also give a number of results that explain how fluctuations through a system travel when one or more of the kinetics is "fast" as compared to the others. The results of this thesis are biologically useful for two reasons: (i) They demonstrate a possible reason for why some biochemical reaction systems are organized the way they are. (ii) They give tools for investigating particular biochemical reaction systems.