Novel form of the Michaelis–Menten equation that enables accurate estimation of (kcat/KM)*KI with just two rate measurements; utility in directed evolution

One of applications of directed evolution is to desensitize an enzyme to an inhibitor. kcat,1/KM and KI are three dimensions that when multiplied measure an enzyme's intrinsic capacity for catalysis in the presence of an inhibitor. The ideal values for the individual dimensions depend on substrate and inhibitor concentrations under the conditions of the application. When attempting to optimize those values by directed evolution, (kcat/KM)*KI can be an informative parameter for evaluating libraries of variants, but throughput is limited. We describe a manipulation of the Michaelis-Menten equation for competitive inhibition that isolates (kcat/KM)*KI on one side of the equation. If velocity is measured at constant enzyme and substrate concentrations with two different inhibitor concentrations (one of which can be 0), the data are sufficient to calculate (kcat/KM)*KI with just two rate measurements. The procedure is validated by correlating values obtained by the rapid method with those obtained by substrate saturation kinetics.