Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches

Area of Science:

• Biochemistry
• Enzyme kinetics
• Mathematical modeling

Background:

• The Michaelis-Menten (MM) function is fundamental in enzyme kinetics.
• Estimating MM parameters using nonlinear or linear least squares can be problematic.
• Nonlinear methods may fail to find a minimizer, while linear methods can yield non-positive parameters.

Purpose of the Study:

• To establish sufficient conditions for successful nonlinear Michaelis-Menten parameter estimation.
• To define conditions ensuring positive parameter estimates from linear least squares methods.
• To extend these findings to operator-repressor systems, MM with leakage, and reversible MM kinetics.

Main Methods:

• Analysis of nonlinear least squares fitting for Michaelis-Menten kinetics.
• Investigation of linear least squares fitting for Michaelis-Menten kinetics.
• Development of sufficient conditions for positive parameter estimates.
• Application to operator-repressor systems, MM with leakage, and reversible MM kinetics.

Main Results:

• Sufficient conditions are provided for nonlinear methods to yield at least one positive minimizer.
• Conditions are derived for linear methods to produce a positive minimizer.
• The importance of data with a concavity property (chemically feasible data) is highlighted.

Conclusions:

• Chemically feasible data is critical for robust Michaelis-Menten parameter estimation.
• The derived conditions enhance the reliability of both nonlinear and linear fitting approaches.
• The methodology is applicable to various biological regulatory models.