Determination of accurate KI values for tight-binding enzyme inhibitors: an in silico study of experimental error and assay design

Determination of accurate K(I) values for tight-binding enzyme inhibitors is important from both a basic biochemistry point of view (understanding the differences in affinity of related molecules) and a medicinal chemistry vantage (developing structure-activity relationships (SAR)). It is advantageous to directly fit the quadratic equation describing tight-binding behavior, known commonly as the Morrison equation, to obtain these K(I) values. The results of simulated experiments that examine the effect of assay design and experimental error on the ability to accurately determine K(I) values at several [E]0/K(I-app) ratios are described. Input ("true") values of the uninhibited velocity, inhibition constant, and total enzyme concentration were used to calculate the velocity at various inhibitor concentrations. Gaussian error was introduced into the velocities and the simulated reactions were fit to estimate upsilon0, K(I), and [E]0. Recommendations for optimizing the inhibitor dilutions within the context of a 96-well-plate format and simple serial dilution steps are made. These include using three points to determine the enzyme concentration ([I]=0, 0.5[E]0, and [E]0), using a narrow dilution series with only two or three points to determine the asymptote at high inhibitor concentration, and avoiding fixing [E]0 to a constant value in the fitting if at all possible. The risks and rewards of fixing [E]0 to a constant value, especially the effect on SAR, are also examined.