Determination of the best-fit values of kinetic parameters of the Michaelis-Menten equation by the method of least squares with the Taylor expansion

Abstract

The best-fit values of the Michaelis constant (Km) and the maximum velocity (V) in the Michaelis-Menten equation can be obtained by the method of least squares with the Taylor expansion for the sum of squares of the absolute residual, i.e., the difference between the observed velocity and the corresponding velocity by calculation. This method makes it possible to determine the values of Km and V not in a trial-and-error manner but in a deductive and unique manner after some iterative procedures starting from arbitrary approximate values of Km and V. These values can be said to be uniquely determined for a set of data as the finally converged values are no longer dependent upon the initial approximate values of Km and V. It is also very important to obtain initial approximate values of parameters for the application of the method described above. A simple method is proposed to estimate the approximate values of parameters involved in fractional functions. The method of rearrangement after canceling of denominator of a fractional function can be utilized to obtain approximate values, not only for cases of two unknown parameters such as the Michaelis-Menten equation, but also for cases with more than two unknowns.