Solution of the Michaelis-Menten equation using the decompositionmethod
We present a low-order recursive solution to the Michaelis-Menten equationusing the decomposition method. This solution is algebraic in nature andprovides a simpler alternative to numerical approaches such as differentialequation evaluation and root-solving techniques that are currently used tocompu...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2008-11-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.173 |
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| Summary: | We present a low-order recursive solution to the Michaelis-Menten equationusing the decomposition method. This solution is algebraic in nature andprovides a simpler alternative to numerical approaches such as differentialequation evaluation and root-solving techniques that are currently used tocompute substrate concentration in the Michaelis-Menten equation. A detailedcharacterization of the errors in substrate concentrations computed fromdecomposition, Runge-Kutta, and bisection methods over a wide range of $s_{0}$:$K_{m}$ values was made by comparing them with highly accurate solutionsobtained using the Lambert $W$ function. Our results indicated thatsolutions obtained from the decomposition method were usually more accuratethan those from the corresponding classical Runge-Kutta methods. Moreover,these solutions required significantly fewer computations than theroot-solving method. Specifically, when the stepsize was 0.1% of the totaltime interval, the computed substrate concentrations using the decompositionmethod were characterized by accuracies on the order of 10$^-8$ or better.The algebraic nature of the decomposition solution and its relatively highaccuracy make this approach an attractive candidate for computing substrateconcentration in the Michaelis-Menten equation. |
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| ISSN: | 1551-0018 |