Reexamining Michaelis-Menten enzyme kinetics for xanthine oxidase

Abbreviated expressions for enzyme kinetic expressions, such as the Michaelis-Menten (M-M) equations, are based on the premise that enzyme concentrations are low compared with those of the substrate and product. When one does progress experiments, where the solute is consumed during conversion to form a series of products, the idealized conditions are violated. Here, we analyzed data of xanthine oxidase in vitro from Escribano et al. (Biochem J 254: 829, 1988) on two conversions in series, hypoxanthine to xanthine to uric acid. Analyses were done using four models: standard irreversible M-M reactions (model 1), Escribano et al.'s M-M forward reaction expressions with product inhibition (model 2), fully reversible M-M equations (model 3), and standard differential equations allowing forward and backward reactions with mass balance accounting for binding (model 4). The results showed that the need for invoking product inhibition vanishes with more complete analyses. The reactions were not quite irreversible, so the backward reaction had a small effect. Even though the enzyme concentration was only 1-2% of the initial substrate concentrations, accounting for the fraction of solutes bound to the enzyme did influence the parameter estimates, but in this case, the M-M model overestimated Michaelis constant values by only about one-third. This article also presents the research and models in a reproducible and publicly available form.