# American Institute of Mathematical Sciences

2009, 6(1): 173-188. doi: 10.3934/mbe.2009.6.173

## Solution of the Michaelis-Menten equation using the decomposition method

 1 Department of Radiological Sciences, University of Oklahoma Health Sciences Center, Oklahoma City, OK 73190, United States 2 Cell Culture Development, Global Biologics Development, Bayer HealthCare, 800 Dwight Way, Berkeley, CA 94710, United States

Received  December 2007 Revised  August 2008 Published  December 2008

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.
Citation: Jagadeesh R. Sonnad, Chetan T. Goudar. Solution of the Michaelis-Menten equation using the decomposition method. Mathematical Biosciences & Engineering, 2009, 6 (1) : 173-188. doi: 10.3934/mbe.2009.6.173
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