A suitable parameterization of the Michaelis-Menten enzyme reaction

Area of Science:

• Biochemistry
• Enzyme kinetics
• Statistical modeling

Background:

• The Michaelis-Menten model is fundamental for simple enzymic reactions.
• Standard formulations can lead to parameter estimation bias and non-normality.
• Accurate statistical inference is crucial for understanding enzyme mechanisms.

Purpose of the Study:

• To identify a suitable form of the Michaelis-Menten model for improved parameter estimation and statistical inference.
• To demonstrate the advantages of the parameters-in-denominator approach for enzyme kinetic modeling.
• To extend this principle to more complex catalytic models.

Main Methods:

• Reformulation of the Michaelis-Menten equation with parameters in the denominator.
• Application of the Gauss-Newton method for least-squares estimation.
• Utilizing generalized linear model (GLM) frameworks like GENSTAT and GLIM for model fitting.

Main Results:

• The parameters-in-denominator form ensures convergence for least-squares estimates using the Gauss-Newton method.
• Models fitted in this form are members of the generalized linear models class, compatible with standard statistical packages.
• Least-squares estimators derived from this form exhibit near-unbiasedness and normal distribution.

Conclusions:

• The parameters-in-denominator formulation offers a robust approach for Michaelis-Menten model analysis.
• This method enhances the reliability of parameter estimation and statistical inference in enzyme kinetics.
• The principle is adaptable to more complex enzymatic and catalytic reaction models.