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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AIMS Press
2008-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.173 |
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| author | Jagadeesh R. Sonnad Chetan T. Goudar |
| author_facet | Jagadeesh R. Sonnad Chetan T. Goudar |
| author_sort | Jagadeesh R. Sonnad |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-03c41ba886da4547aa19cb4912b741dc |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2008-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-03c41ba886da4547aa19cb4912b741dc2025-01-24T01:58:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182008-11-016117318810.3934/mbe.2009.6.173Solution of the Michaelis-Menten equation using the decompositionmethodJagadeesh R. Sonnad0Chetan T. Goudar1Department of Radiological Sciences, University of Oklahoma Health Sciences Center, Oklahoma City, OK 73190Department of Radiological Sciences, University of Oklahoma Health Sciences Center, Oklahoma City, OK 73190We 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.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.173michaelis-menten equationenzyme kineticsdecomposition method |
| spellingShingle | Jagadeesh R. Sonnad Chetan T. Goudar Solution of the Michaelis-Menten equation using the decompositionmethod Mathematical Biosciences and Engineering michaelis-menten equation enzyme kinetics decomposition method |
| title | Solution of the Michaelis-Menten equation using the decompositionmethod |
| title_full | Solution of the Michaelis-Menten equation using the decompositionmethod |
| title_fullStr | Solution of the Michaelis-Menten equation using the decompositionmethod |
| title_full_unstemmed | Solution of the Michaelis-Menten equation using the decompositionmethod |
| title_short | Solution of the Michaelis-Menten equation using the decompositionmethod |
| title_sort | solution of the michaelis menten equation using the decompositionmethod |
| topic | michaelis-menten equation enzyme kinetics decomposition method |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.173 |
| work_keys_str_mv | AT jagadeeshrsonnad solutionofthemichaelismentenequationusingthedecompositionmethod AT chetantgoudar solutionofthemichaelismentenequationusingthedecompositionmethod |