Several significant chemical reactions include molecules called enzymes which act as catalysts for product formation. Mathematical models have been developed to study such enzyme kinetics to understand the behavior of chemical species involved and the conditions which influence them. Singular perturbation methods can be applied to further simplify the governing differential equations of the reactions. In this talk, we will discuss one such significant system in chemical kinetics called the Michaelis-Menten reaction. We will introduce Fenichel theory and apply it to the system to obtain approximations. We will also talk about the validity of these approximations in stochastic environments. The talk will include brief introductions to the theory of perturbation problems, dynamic bifurcations and stochastic simulation algorithms.
Speaker(s): Kashvi Srivastava (University of Michigan)