Computation of the explicit solution to the Michaelis-Menten equation

Area of Science:

• Biochemistry
• Pharmacokinetics
• Mathematical Modeling

Background:

• The Michaelis-Menten equation is fundamental in enzyme kinetics.
• Solving this differential equation with complex input conditions (bolus, zero-order) can be challenging.
• Existing methods may lack efficiency or accessibility for certain functions.

Purpose of the Study:

• To derive an explicit analytical solution for the Michaelis-Menten equation under bolus and zero-order input.
• To develop efficient computational methods for functions required by the solution.
• To provide practical implementation tools (FORTRAN code) for researchers.

Main Methods:

• Derivation of an explicit solution to the Michaelis-Menten differential equation.
• Development of numerical algorithms for computing specific, non-trivial functions.
• Implementation of these algorithms in FORTRAN for practical application.

Main Results:

• An explicit mathematical solution for the Michaelis-Menten model with bolus and zero-order input has been obtained.
• Efficient algorithms capable of computing required function values to arbitrary precision are presented.
• FORTRAN source codes are provided for direct implementation in pharmacokinetic and biochemical modeling.

Conclusions:

• The derived explicit solution simplifies the analysis of enzyme kinetics under specific input conditions.
• The provided algorithms and code enhance the practical utility and accuracy of Michaelis-Menten modeling.
• This work offers a valuable computational tool for researchers in biochemistry and pharmacokinetics.