Solution of the Michaelis-Menten equation using the decomposition
method
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1.
Department of Radiological Sciences, University of Oklahoma Health Sciences Center, Oklahoma City, OK 73190
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2.
Cell Culture Development, Global Biologics Development, Bayer HealthCare, 800 Dwight Way, Berkeley, CA 94710
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Received:
01 December 2007
Accepted:
29 June 2018
Published:
01 December 2008
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MSC :
Primary: 34A05, 34A55; Secondary: 92C45
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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 decompositionmethod[J]. Mathematical Biosciences and Engineering, 2009, 6(1): 173-188. doi: 10.3934/mbe.2009.6.173
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Abstract
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.
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