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 : values was made by comparing them with highly accurate solutions
obtained using the Lambert 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 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
Related Papers:
[1]
Karl Peter Hadeler .
Michaelis-Menten kinetics, the operator-repressor system, and least squares approaches. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1541-1560.
doi: 10.3934/mbe.2013.10.1541
Min Hou, Tonghua Zhang, Sanling Yuan .
Stability and Hopf bifurcation of an intraguild prey-predator fishery model with two delays and Michaelis-Menten type predator harvest. Mathematical Biosciences and Engineering, 2024, 21(4): 5687-5711.
doi: 10.3934/mbe.2024251
[4]
Peter Rashkov, Ezio Venturino, Maira Aguiar, Nico Stollenwerk, Bob W. Kooi .
On the role of vector modeling in a minimalistic epidemic model. Mathematical Biosciences and Engineering, 2019, 16(5): 4314-4338.
doi: 10.3934/mbe.2019215
[5]
Tewfik Sari, Frederic Mazenc .
Global dynamics of the chemostat with different removal rates and variable yields. Mathematical Biosciences and Engineering, 2011, 8(3): 827-840.
doi: 10.3934/mbe.2011.8.827
[6]
Agustín Gabriel Yabo, Jean-Baptiste Caillau, Jean-Luc Gouzé .
Optimal bacterial resource allocation: metabolite production in continuous bioreactors. Mathematical Biosciences and Engineering, 2020, 17(6): 7074-7100.
doi: 10.3934/mbe.2020364
[7]
Xiaoling Han, Xiongxiong Du .
Dynamics study of nonlinear discrete predator-prey system with Michaelis-Menten type harvesting. Mathematical Biosciences and Engineering, 2023, 20(9): 16939-16961.
doi: 10.3934/mbe.2023755
[8]
Christopher M. Kribs-Zaleta .
Sharpness of saturation in harvesting and predation. Mathematical Biosciences and Engineering, 2009, 6(4): 719-742.
doi: 10.3934/mbe.2009.6.719
[9]
Linard Hoessly, Carsten Wiuf .
Fast reactions with non-interacting species in stochastic reaction networks. Mathematical Biosciences and Engineering, 2022, 19(3): 2720-2749.
doi: 10.3934/mbe.2022124
[10]
Adélia Sequeira, Rafael F. Santos, Tomáš Bodnár .
Blood coagulation dynamics: mathematical
modeling and stability results. Mathematical Biosciences and Engineering, 2011, 8(2): 425-443.
doi: 10.3934/mbe.2011.8.425
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 : values was made by comparing them with highly accurate solutions
obtained using the Lambert 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 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.
This article has been cited by:
1.
Xiaotian Wu, Jun Li, Fahima Nekka,
Closed form solutions and dominant elimination pathways of simultaneous first-order and Michaelis–Menten kinetics,
2015,
42,
1567-567X,
151,
10.1007/s10928-015-9407-3
2.
Alejandro Pérez Paz,
Analytical solution to the simultaneous Michaelis-Menten and second-order kinetics problem,
2024,
1878-5190,
10.1007/s11144-024-02703-0
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
Jagadeesh R. Sonnad, Chetan T. Goudar. Solution of the Michaelis-Menten equation using the decomposition
method[J]. Mathematical Biosciences and Engineering, 2009, 6(1): 173-188. doi: 10.3934/mbe.2009.6.173