Applied Interdisciplinary Mathematics (AIM) Seminar

Biochemical reactions are continuously taking place in all living organisms and most of them involve molecules called enzymes, which act as remarkably efficient catalysts. Enzymes react selectively on specific substrates to accelerate reactions, and regulate cellular processes. To understand their role, we investigate enzyme kinetics which is mainly the study of rates of reactions, and temporal behavior of reactants and the conditions which influence them. The governing differential equations of enzyme catalyzed reactions are nonlinear, and present disparate timescales allowing for the systematic simplification of these equations through singular perturbation methods. The simplification is of critical importance for biomedical scientists as they used these equations to measure the rates of enzyme catalyzed reactions in the laboratory. In this talk, we will illustrate how Tikhonov-Fenichel parameters, in conjunction with scaling methods from the analysis of ordinary differential equations, are used to derive the enzyme kinetic equations approximations used in the laboratory. We will also show how we derive the conditions for the validity of those equations to capture the temporal dynamics of the enzyme catalyzed reactions. Interestingly our research of enzyme catalyzed reactions shows that the conditions for the derivation of the simplified equations are not the same conditions under which these equations can be used to estimate parameters accurately. Understanding the conditions for which the parameter estimation with simplified equations is well posed remains a challenge in the field, and is crucial for the effective and efficient design of experiments. Speaker(s): Santiago Schnell (University of Michigan)