Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism

Krishnan Lakshmi Narayanan; Velmurugan Meena; Lakshman Rajendran; Jianqiang Gao; Subbiah Parathasarathy Subbiah

doi:doi:10.11648/j.acm.20170603.13

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Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism

Krishnan Lakshmi Narayanan, Velmurugan Meena, Lakshman Rajendran, Jianqiang Gao, Subbiah Parathasarathy Subbiah

Published in Applied and Computational Mathematics (Volume 6, Issue 3)

Received: 5 April 2017 Accepted: 18 April 2017 Published: 21 June 2017

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Abstract

In this paper, mathematical models of immobilized enzyme system that follow the Michaelis-Menten mechanism for both reversible and irreversible reactions are discussed. This model is based on the diffusion equations containing the non-linear term related to Michaelis-Menten kinetics. An approximate analytical technique employing the modified Adomian decomposition method is used to solve the non-linear reaction diffusion equation in immobilized enzyme system. The concentration profile of the substrate is derived in terms of all parameters. A simple expression of the substrate concentration is obtained as a function of the Thiele modulus and the Michaelis constant. The numerical solutions are compared with our analytical solutions for slab, cylinder and spherical pellet shapes. Satisfactory agreement for all values of the Thiele modulus and the Michaelis constant is noted. Graphical results and tabulated data are presented and discussed quantitatively to illustrate the solution.

Published in	Applied and Computational Mathematics (Volume 6, Issue 3)
DOI	10.11648/j.acm.20170603.13
Page(s)	143-160
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Mathematical Modeling, Nonlinear Differential Equations, Modified Adomian Decomposition Method, Michaelis-Menten Kinetics, Immobilized Enzyme

References

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Krishnan Lakshmi Narayanan, Velmurugan Meena, Lakshman Rajendran, Jianqiang Gao, Subbiah Parathasarathy Subbiah. (2017). Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism. Applied and Computational Mathematics, 6(3), 143-160. https://doi.org/10.11648/j.acm.20170603.13

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ACS Style

Krishnan Lakshmi Narayanan; Velmurugan Meena; Lakshman Rajendran; Jianqiang Gao; Subbiah Parathasarathy Subbiah. Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism. Appl. Comput. Math. 2017, 6(3), 143-160. doi: 10.11648/j.acm.20170603.13

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AMA Style

Krishnan Lakshmi Narayanan, Velmurugan Meena, Lakshman Rajendran, Jianqiang Gao, Subbiah Parathasarathy Subbiah. Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism. Appl Comput Math. 2017;6(3):143-160. doi: 10.11648/j.acm.20170603.13

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@article{10.11648/j.acm.20170603.13,
  author = {Krishnan Lakshmi Narayanan and Velmurugan Meena and Lakshman Rajendran and Jianqiang Gao and Subbiah Parathasarathy Subbiah},
  title = {Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {3},
  pages = {143-160},
  doi = {10.11648/j.acm.20170603.13},
  url = {https://doi.org/10.11648/j.acm.20170603.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170603.13},
  abstract = {In this paper, mathematical models of immobilized enzyme system that follow the Michaelis-Menten mechanism for both reversible and irreversible reactions are discussed. This model is based on the diffusion equations containing the non-linear term related to Michaelis-Menten kinetics. An approximate analytical technique employing the modified Adomian decomposition method is used to solve the non-linear reaction diffusion equation in immobilized enzyme system. The concentration profile of the substrate is derived in terms of all parameters. A simple expression of the substrate concentration is obtained as a function of the Thiele modulus and the Michaelis constant. The numerical solutions are compared with our analytical solutions for slab, cylinder and spherical pellet shapes. Satisfactory agreement for all values of the Thiele modulus and the Michaelis constant is noted. Graphical results and tabulated data are presented and discussed quantitatively to illustrate the solution.},
 year = {2017}
}

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TY  - JOUR
T1  - Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism
AU  - Krishnan Lakshmi Narayanan
AU  - Velmurugan Meena
AU  - Lakshman Rajendran
AU  - Jianqiang Gao
AU  - Subbiah Parathasarathy Subbiah
Y1  - 2017/06/21
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170603.13
DO  - 10.11648/j.acm.20170603.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
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EP  - 160
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20170603.13
AB  - In this paper, mathematical models of immobilized enzyme system that follow the Michaelis-Menten mechanism for both reversible and irreversible reactions are discussed. This model is based on the diffusion equations containing the non-linear term related to Michaelis-Menten kinetics. An approximate analytical technique employing the modified Adomian decomposition method is used to solve the non-linear reaction diffusion equation in immobilized enzyme system. The concentration profile of the substrate is derived in terms of all parameters. A simple expression of the substrate concentration is obtained as a function of the Thiele modulus and the Michaelis constant. The numerical solutions are compared with our analytical solutions for slab, cylinder and spherical pellet shapes. Satisfactory agreement for all values of the Thiele modulus and the Michaelis constant is noted. Graphical results and tabulated data are presented and discussed quantitatively to illustrate the solution.
VL  - 6
IS  - 3
ER  -

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Author Information

Krishnan Lakshmi Narayanan

Department of Mathematics, Sethu Inistitute of Technology, Kariapatti, India
Velmurugan Meena

Department of Mathematics, Madurai Kamaraj University Constitutional College, Madurai, India
Lakshman Rajendran

Department of Mathematics, Sethu Inistitute of Technology, Kariapatti, India
Jianqiang Gao

Department of Computer Information, Hohai University, Nanjing, China
Subbiah Parathasarathy Subbiah

Mannar Thirumalai Naiker College, Pasumalai, Madurai, India

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APA Style

Krishnan Lakshmi Narayanan, Velmurugan Meena, Lakshman Rajendran, Jianqiang Gao, Subbiah Parathasarathy Subbiah. (2017). Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism. Applied and Computational Mathematics, 6(3), 143-160. https://doi.org/10.11648/j.acm.20170603.13

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ACS Style

Krishnan Lakshmi Narayanan; Velmurugan Meena; Lakshman Rajendran; Jianqiang Gao; Subbiah Parathasarathy Subbiah. Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism. Appl. Comput. Math. 2017, 6(3), 143-160. doi: 10.11648/j.acm.20170603.13

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AMA Style

Krishnan Lakshmi Narayanan, Velmurugan Meena, Lakshman Rajendran, Jianqiang Gao, Subbiah Parathasarathy Subbiah. Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism. Appl Comput Math. 2017;6(3):143-160. doi: 10.11648/j.acm.20170603.13

Copy | Download

@article{10.11648/j.acm.20170603.13,
  author = {Krishnan Lakshmi Narayanan and Velmurugan Meena and Lakshman Rajendran and Jianqiang Gao and Subbiah Parathasarathy Subbiah},
  title = {Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {3},
  pages = {143-160},
  doi = {10.11648/j.acm.20170603.13},
  url = {https://doi.org/10.11648/j.acm.20170603.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170603.13},
  abstract = {In this paper, mathematical models of immobilized enzyme system that follow the Michaelis-Menten mechanism for both reversible and irreversible reactions are discussed. This model is based on the diffusion equations containing the non-linear term related to Michaelis-Menten kinetics. An approximate analytical technique employing the modified Adomian decomposition method is used to solve the non-linear reaction diffusion equation in immobilized enzyme system. The concentration profile of the substrate is derived in terms of all parameters. A simple expression of the substrate concentration is obtained as a function of the Thiele modulus and the Michaelis constant. The numerical solutions are compared with our analytical solutions for slab, cylinder and spherical pellet shapes. Satisfactory agreement for all values of the Thiele modulus and the Michaelis constant is noted. Graphical results and tabulated data are presented and discussed quantitatively to illustrate the solution.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism
AU  - Krishnan Lakshmi Narayanan
AU  - Velmurugan Meena
AU  - Lakshman Rajendran
AU  - Jianqiang Gao
AU  - Subbiah Parathasarathy Subbiah
Y1  - 2017/06/21
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170603.13
DO  - 10.11648/j.acm.20170603.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 143
EP  - 160
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20170603.13
AB  - In this paper, mathematical models of immobilized enzyme system that follow the Michaelis-Menten mechanism for both reversible and irreversible reactions are discussed. This model is based on the diffusion equations containing the non-linear term related to Michaelis-Menten kinetics. An approximate analytical technique employing the modified Adomian decomposition method is used to solve the non-linear reaction diffusion equation in immobilized enzyme system. The concentration profile of the substrate is derived in terms of all parameters. A simple expression of the substrate concentration is obtained as a function of the Thiele modulus and the Michaelis constant. The numerical solutions are compared with our analytical solutions for slab, cylinder and spherical pellet shapes. Satisfactory agreement for all values of the Thiele modulus and the Michaelis constant is noted. Graphical results and tabulated data are presented and discussed quantitatively to illustrate the solution.
VL  - 6
IS  - 3
ER  -

Copy | Download