Solution of the Michaelis-Menten equation using the decomposition method.
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.
Sonnad
Jagadeesh R
JR
Department of Radiological Sciences, University of Oklahoma Health Sciences Center, Oklahoma City, OK 73190, United States. jsonnad@ouhsc.edu
Goudar
Chetan T
CT
D000465:Algorithms; D002384:Catalysis; D003198:Computer Simulation; D004798:Enzymes / Q000737:chemistry*; D008956:Models, Chemical; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D012984:Software
D004798:Enzymes