Parameter estimation using a direct solution of the integrated Michaelis-Menten equation

Area of Science:

• Biochemistry
• Enzyme kinetics
• Mathematical modeling

Background:

• Enzyme kinetic parameter estimation is crucial for understanding enzyme mechanisms.
• Traditional methods often involve complex root-solving or numerical integration of the Michaelis-Menten equation.
• These methods can be computationally intensive and prone to inaccuracies.

Purpose of the Study:

• To introduce a novel method for estimating enzyme kinetic parameters using the Lambert omega function.
• To simplify the process of parameter estimation by avoiding root-solving and numerical integration.
• To demonstrate the accuracy and efficiency of the omega function approach.

Main Methods:

• Utilized the Lambert omega function to derive explicit expressions for substrate and product concentrations in the integrated Michaelis-Menten equation.
• Applied nonlinear regression coupled with the omega function for parameter estimation.
• Validated the method using progress curve data from five different experimental systems.

Main Results:

• The omega function provided highly accurate (order of 10(-16)) expressions for substrate and product concentrations.
• Kinetic parameters estimated using the omega function were nearly identical to those obtained via conventional root-solving techniques.
• The computation of omega was found to be simpler and more efficient than traditional methods.

Conclusions:

• The Lambert omega function offers an accurate and simplified approach to enzyme kinetic parameter estimation.
• This method avoids the need for computationally intensive root-solving and numerical integration.
• The omega function presents an attractive and efficient alternative for analyzing enzyme kinetics data.