American Institute of Mathematical Sciences

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

Solution of the Michaelis-Menten equation using the decomposition method

Jagadeesh R. Sonnad 1, and  Chetan T. Goudar 2,

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.
Keywords: Michaelis-Menten equation, enzyme kinetics, decomposition method.
Mathematics Subject Classification: Primary: 34A05, 34A55; Secondary: 92C45.
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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