A New Nonlinear Optimization Method for Parameter Estimation in Enzyme Kinetics

Abstract

A new nonlinear optimization method for parameter estimation in Michaelis-Menten equation has been developed. This method is based on a special mathematical form of the Michaelis-Menten equation to finding the best fit of the linear plot of R versus S/(S + Km) where R, S, and Km are the reaction rate, concentration of substrate, and the Michaelis-Menten constant, respectively. By setting the intercept of this line to zero, the proper Km will be obtained and the slope would give the saturation rate, Vmax. As a result, a nonlinear, two-parameter optimization is simplified into finding the roots of a nonlinear equation. Generated data sets were used to illustrate this new method, and data sets from the literature were used to demonstrate the accuracy and convergence of the method in comparison with graphical methods, genetic algorithm, particle swarm optimization, Excel’s Solver add-in, and some other optimization methods. It was found that the new method was very fast in comparison with common numerical optimization techniques. Results showed that accuracy of the method was better than the Lineweaver-Burk and Hanes methods, and was in good agreement with genetic algorithm, particle swarm optimization, and Excel’s Solver.