Estimation of Ki in a competitive enzyme-inhibition model: comparisons among three methods of data analysis

Abstract

There are a variety of methods available to calculate the inhibition constant (Ki) that characterizes substrate inhibition by a competitive inhibitor. Linearized versions of the Michaelis-Menten equation (e.g., Lineweaver-Burk, Dixon, etc.) are frequently used, but they often produce substantial errors in parameter estimation. This study was conducted to compare three methods of analysis for the estimation of Ki: simultaneous nonlinear regression (SNLR); nonsimultaneous, nonlinear regression, "KM,app" method; and the Dixon method. Metabolite formation rates were simulated for a competitive inhibition model with random error (corresponding to 10% coefficient of variation). These rates were generated for a control (i.e., no inhibitor) and five inhibitor concentrations with six substrate concentrations per inhibitor and control. The KM/Ki ratios ranged from less than 0.1 to greater than 600. A total of 3 data sets for each of three KM/Ki ratios were generated (i.e., 108 rates/data set per KM/Ki ratio). The mean inhibition and control data were fit simultaneously (SNLR method) using the full competitive enzyme-inhibition equation. In the KM,app method, the mean inhibition and control data were fit separately to the Michaelis-Menten equation. The SNLR approach was the most robust, fastest, and easiest to implement. The KM,app method gave good estimates of Ki but was more time consuming. Both methods gave good recoveries of KM and VMAX values. The Dixon method gave widely ranging and inaccurate estimates of Ki. For reliable estimation of Ki values, the SNLR method is preferred.