The Michaelis-Menten Reaction at Low Substrate Concentrations: Pseudo-First-Order Kinetics and Conditions for...

Area of Science:

• Biochemistry
• Chemical Kinetics
• Mathematical Biology

Background:

• The Michaelis-Menten model is fundamental in enzyme kinetics.
• Accurate mathematical modeling is crucial for understanding biochemical reactions.
• Simplifying complex reaction mechanisms aids experimental analysis.

Purpose of the Study:

• To approximate the Michaelis-Menten reaction mechanism using a linear system.
• To establish conditions for pseudo-first-order kinetics at low substrate concentrations.
• To derive a closed-form solution for accurate rate constant estimation.

Main Methods:

• Utilized a monotonicity property of the reaction system.
• Applied Kamke's comparison theorem for mathematical proof.
• Investigated timescale separation within the linear approximation.

Main Results:

• Demonstrated accurate approximation of Michaelis-Menten kinetics by a linear system for low initial substrate concentrations.
• Established pseudo-first-order kinetics, simplifying calculations.
• Derived a closed-form solution independent of initial enzyme concentration, with validity condition $$ related to the Van Slyke-Cullen constant.

Conclusions:

• The linear approximation provides a robust method for analyzing enzyme kinetics under specific conditions.
• Pseudo-first-order kinetics simplify experimental data analysis and model parameter estimation.
• Identified conditions for timescale separation, leading to reduced dimensionality models.