Simultaneous estimation ofV max, K m, and the rate of endogenous substrate production (R) from substrate depletion...

Area of Science:

• Biochemistry
• Enzyme Kinetics
• Mathematical Modeling

Background:

• Estimating enzyme kinetic parameters like Vmax and Km is crucial for understanding biological processes.
• Linearized forms of the Michaelis-Menten equation are commonly used but can be sensitive to errors in initial substrate concentration (S0).

Purpose of the Study:

• To evaluate the reliability of nonlinear and linearized forms of the integrated Michaelis-Menten equation for estimating kinetic parameters when initial substrate concentration (S0) is not error-free.
• To propose a new equation for kinetic studies in natural habitats with endogenous substrate production.

Main Methods:

• Comparison of three linearized forms and one nonlinear form of the integrated Michaelis-Menten equation.
• Evaluation of parameter estimation accuracy and sensitivity to ±1% errors in initial substrate concentration (S0).
• Development and application of a new equation for estimating kinetic parameters and endogenous substrate production (R) using nonlinear regression.

Main Results:

• One specific linearized form (t/(S0-S) vs. ln(S0/S)/(S0-S)) provided the closest estimates to true population means for Vmax and Km.
• This linearization was least sensitive to ±1% errors in S0 among the tested linearized forms.
• Nonlinear regression analysis of progress curve data was superior to all linearized forms when S0 was error-prone.
• The integrated Michaelis-Menten equation is unsuitable for estimating Vmax and Km when substrate production occurs concurrently with consumption.

Conclusions:

• Relying on r(2) values to choose among linearized forms can be misleading.
• Nonlinear regression is the preferred method for estimating kinetic parameters from progress curve data, especially with uncertain initial substrate concentrations.
• A new equation and nonlinear regression are necessary for accurate kinetic studies involving endogenous substrate production in natural samples.