Parametric analysis of the errors associated with the Michaelis-Menten equation

Area of Science:

• Biochemical Engineering
• Enzyme Kinetics
• Chemical Reaction Engineering

Background:

• Michaelis-Menten kinetics is fundamental to enzyme-catalyzed reactions.
• Simplified rate expressions are often preferred for practical applications like reactor design.
• Assumptions in simplified models can lead to inaccuracies.

Purpose of the Study:

• To evaluate the accuracy of simplified Michaelis-Menten kinetic models against the exact solution.
• To determine the conditions under which simplified models are suitable for reactor design.
• To provide guidelines for selecting the appropriate kinetic model based on system parameters.

Main Methods:

• Developed three rate expressions: exact solution (Model 1), pseudo-steady-state assumption (Model 2), and further simplification (Model 3).
• Utilized dimensionless forms of the models for error analysis.
• Compared model predictions across a wide range of parameter values, including initial substrate to enzyme ratio (α(0)) and the ratio of Michaelis-Menten constant to enzyme concentration (σ).

Main Results:

• Model 1 (exact solution) is the most precise but requires numerical integration and three parameters.
• Models 2 and 3 are simpler, requiring only two parameters, but introduce errors.
• Established specific criteria for α(0) and σ to determine the adequacy of Model 2 and Model 3, with a 2% error tolerance.

Conclusions:

• Model 3 is adequate when α(0) > 15 or σ ≥ 100.
• Model 2 is suitable for 5 < α(0) < 15 or σ ≥ 10.
• Model 1 is necessary for α(0) < 5 and σ < 10 to ensure accuracy in reactor design.