An explicit solution for progress curve analysis in systems characterized by endogenous substrate production.

Area of Science:

• Biochemistry
• Chemical Kinetics
• Mathematical Modeling

Background:

• The Michaelis-Menten equation is fundamental in enzyme kinetics.
• Accurate estimation of kinetic parameters is crucial for understanding biological processes.
• Modeling endogenous substrate production complicates traditional kinetic analyses.

Purpose of the Study:

• To develop an explicit solution for the modified Michaelis-Menten equation incorporating endogenous substrate production.
• To simplify kinetic parameter estimation using progress curve analysis.
• To validate the explicit formulation with both synthetic and experimental data.

Main Methods:

• The Lambert W function was employed to derive an explicit solution relating substrate concentration to time and kinetic parameters.
• Synthetic data with controlled parameters and added noise were generated.
• Experimental substrate depletion data from published studies were utilized for validation.

Main Results:

• The explicit solution accurately described synthetic substrate depletion data with 5% error.
• The method effectively modeled experimental hydrogen depletion data from multiple systems.
• The Lambert W function approach eliminated the need for differential equation solving and iterative estimation.

Conclusions:

• The explicit formulation provides a simplified and accurate method for progress curve analysis.
• This approach is particularly beneficial for biological systems with endogenous substrate production.
• The study demonstrates a significant advancement in kinetic parameter estimation techniques.