Solution of the Michaelis-Menten equation using the decomposition method

Math Biosci Eng. 2009 Jan;6(1):173-88. doi: 10.3934/mbe.2009.6.173.

Abstract

We present a low-order recursive solution to the Michaelis-Menten equation using the decomposition method. This solution is algebraic in nature and provides a simpler alternative to numerical approaches such as differential equation evaluation and root-solving techniques that are currently used to compute substrate concentration in the Michaelis-Menten equation. A detailed characterization of the errors in substrate concentrations computed from decomposition, Runge-Kutta, and bisection methods over a wide range of s(0) : K(m) values was made by comparing them with highly accurate solutions obtained using the Lambert W function. Our results indicated that solutions obtained from the decomposition method were usually more accurate than those from the corresponding classical Runge-Kutta methods. Moreover, these solutions required significantly fewer computations than the root-solving method. Specifically, when the stepsize was 0.1% of the total time interval, the computed substrate concentrations using the decomposition method were characterized by accuracies on the order of 10(-8) or better. The algebraic nature of the decomposition solution and its relatively high accuracy make this approach an attractive candidate for computing substrate concentration in the Michaelis-Menten equation.

MeSH terms

  • Algorithms*
  • Catalysis
  • Computer Simulation
  • Enzymes / chemistry*
  • Models, Chemical*
  • Nonlinear Dynamics
  • Numerical Analysis, Computer-Assisted*
  • Software*

Substances

  • Enzymes