Modeling the Mitogen Activated Protein (MAP)-Kinase Pathway Using Ordinary Differential Equations

Sharadwata Pan; Sameer E. Mhatre

doi:doi:10.11648/j.cbb.20130102.11

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Modeling the Mitogen Activated Protein (MAP)-Kinase Pathway Using Ordinary Differential Equations

Sharadwata Pan, Sameer E. Mhatre

Published in Computational Biology and Bioinformatics (Volume 1, Issue 2)

Received: 30 April 2013 Published: 10 June 2013

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Abstract

Mitogen Activated Protein (MAP) Kinase pathway is central to comprehend the key cellular signal transduction mechanisms in animal physiology, including human beings. Modeling MAP Kinase pathway has two main applications: deciphering a transient response of three main components (MAPKKK, MAPKK and MAPK) to regulate signaling and utilizing the models to make it behave as a potential drug target. The current study develops a mathematical representation for this transient cell-signaling pathway, based on a simple modular approach to structure and model a three-tier cascade. Based on assumptions from existing literature, ordinary differential equations have been formulated to express the concentrations of MAPKKK, MAPKK and MAPK as a function of time. Finally, the transient responses of the deduced concentrations of these components are analyzed to understand the pathway behavior and some interesting results are obtained by analyzing the temporal evolutions of the concentrations of the six components involved in the pathway. We conclude that the transient behaviour of MAPKKK can be captured with first order ordinary differential equations. Some anomalous behavior is observed in case of MAPKK and MAPK. In this perspective, future work can be designed to regulate the MAP Kinase signaling by taking Michaeli-Menten kinetics into consideration and make complex models to get more accurate results.

Published in	Computational Biology and Bioinformatics (Volume 1, Issue 2)
DOI	10.11648/j.cbb.20130102.11
Page(s)	6-9
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), 2013. Published by Science Publishing Group

Keywords

Modeling, MAP-Kinase, MAPKKK, MAPKK, MAPKK, Cascade, Differential Equation

References

[1]	Cobb, M. H.: MAP Kinase Pathways; Prog. Biophys. Mol. Biol.; vol. 71, pp. 479–500. (1999)
[2]	Orton, R. J., Sturm, O. E., Vyshemirsky, V., Calder, M., Gilbert, D. R., and Kolch, W.: Computational modelling of the receptor-tyrosine-kinase-activated MAPK pathway; Biochem. J.; vol. 392; pp. 249–261.(2005)
[3]	Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., and Walter, P.: Molecular Biology of the Cell (1st edition), Chapter 15, Garland Science: New York. p. 948. (1982)
[4]	Huang, C. Y. F., and Ferrell (Jr.), J. E.: Ultrasensitivity in the mitogen-activated protein kinase cascade; Proc. Natl. Acad. Sci.; vol. 93; pp. 10078-10083.(1996)
[5]	Widmann, C., Gibson, S., Jarpe, M. B., and Johnson, G. L.: Mitogen-Activated Protein Kinase: Conservation of a Three-Kinase Module From Yeast to Human; Physiol. Rev.; vol. 79; pp. 143–180.(1999)
[6]	Chang, L., and Karin, M.: Mammalian MAP kinase signalling cascades; Nature (London); vol. 410; pp. 37–40.(2001)
[7]	Rodriguez, J. S., Kremling, A., Conzelmann, H., Bettenbrock, K., and Gilles, E. D.: Modular Analysis of Signal Transduction Networks (Feature Article); IEEE Control Systems Magazine; vol. 24; pp. 35-52.(2004)
[8]	Hornberg, J. J., Heinrich, R., Bruggeman, F. J., Binder, B., Geest, C. R., Marjolein Bij de Vaate, A. J., Lankelma, J., and Westerhoff, H.V.: Principles behind the multifarious control of signal transduction; FEBS Journal; vol. 272; pp. 244-258.(2005)
[9]	Schoeberl, B., Eichler-Jonsson, C., Gilles, E. D., and Muller, G.: Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors; Nat. Biotechnol.; vol. 20; pp. 370–375.(2002)

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Sharadwata Pan, Sameer E. Mhatre. (2013). Modeling the Mitogen Activated Protein (MAP)-Kinase Pathway Using Ordinary Differential Equations. Computational Biology and Bioinformatics, 1(2), 6-9. https://doi.org/10.11648/j.cbb.20130102.11

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ACS Style

Sharadwata Pan; Sameer E. Mhatre. Modeling the Mitogen Activated Protein (MAP)-Kinase Pathway Using Ordinary Differential Equations. Comput. Biol. Bioinform. 2013, 1(2), 6-9. doi: 10.11648/j.cbb.20130102.11

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AMA Style

Sharadwata Pan, Sameer E. Mhatre. Modeling the Mitogen Activated Protein (MAP)-Kinase Pathway Using Ordinary Differential Equations. Comput Biol Bioinform. 2013;1(2):6-9. doi: 10.11648/j.cbb.20130102.11

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@article{10.11648/j.cbb.20130102.11,
  author = {Sharadwata Pan and Sameer E. Mhatre},
  title = {Modeling the Mitogen Activated Protein (MAP)-Kinase Pathway Using Ordinary Differential Equations},
  journal = {Computational Biology and Bioinformatics},
  volume = {1},
  number = {2},
  pages = {6-9},
  doi = {10.11648/j.cbb.20130102.11},
  url = {https://doi.org/10.11648/j.cbb.20130102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cbb.20130102.11},
  abstract = {Mitogen Activated Protein (MAP) Kinase pathway is central to comprehend the key cellular signal transduction mechanisms in animal physiology, including human beings. Modeling MAP Kinase pathway has two main applications: deciphering a transient response of three main components (MAPKKK, MAPKK and MAPK) to regulate signaling and utilizing the models to make it behave as a potential drug target. The current study develops a mathematical representation for this transient cell-signaling pathway, based on a simple modular approach to structure and model a three-tier cascade. Based on assumptions from existing literature, ordinary differential equations have been formulated to express the concentrations of MAPKKK, MAPKK and MAPK as a function of time. Finally, the transient responses of the deduced concentrations of these components are analyzed to understand the pathway behavior and some interesting results are obtained by analyzing the temporal evolutions of the concentrations of the six components involved in the pathway. We conclude that the transient behaviour of MAPKKK can be captured with first order ordinary differential equations. Some anomalous behavior is observed in case of MAPKK and MAPK. In this perspective, future work can be designed to regulate the MAP Kinase signaling by taking Michaeli-Menten kinetics into consideration and make complex models to get more accurate results.},
 year = {2013}
}

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TY  - JOUR
T1  - Modeling the Mitogen Activated Protein (MAP)-Kinase Pathway Using Ordinary Differential Equations
AU  - Sharadwata Pan
AU  - Sameer E. Mhatre
Y1  - 2013/06/10
PY  - 2013
N1  - https://doi.org/10.11648/j.cbb.20130102.11
DO  - 10.11648/j.cbb.20130102.11
T2  - Computational Biology and Bioinformatics
JF  - Computational Biology and Bioinformatics
JO  - Computational Biology and Bioinformatics
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EP  - 9
PB  - Science Publishing Group
SN  - 2330-8281
UR  - https://doi.org/10.11648/j.cbb.20130102.11
AB  - Mitogen Activated Protein (MAP) Kinase pathway is central to comprehend the key cellular signal transduction mechanisms in animal physiology, including human beings. Modeling MAP Kinase pathway has two main applications: deciphering a transient response of three main components (MAPKKK, MAPKK and MAPK) to regulate signaling and utilizing the models to make it behave as a potential drug target. The current study develops a mathematical representation for this transient cell-signaling pathway, based on a simple modular approach to structure and model a three-tier cascade. Based on assumptions from existing literature, ordinary differential equations have been formulated to express the concentrations of MAPKKK, MAPKK and MAPK as a function of time. Finally, the transient responses of the deduced concentrations of these components are analyzed to understand the pathway behavior and some interesting results are obtained by analyzing the temporal evolutions of the concentrations of the six components involved in the pathway. We conclude that the transient behaviour of MAPKKK can be captured with first order ordinary differential equations. Some anomalous behavior is observed in case of MAPKK and MAPK. In this perspective, future work can be designed to regulate the MAP Kinase signaling by taking Michaeli-Menten kinetics into consideration and make complex models to get more accurate results.
VL  - 1
IS  - 2
ER  -

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Author Information

Sharadwata Pan

Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai - 400076, India
Sameer E. Mhatre

Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai - 400077, India

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Plain Text BibTeX RIS

APA Style

Sharadwata Pan, Sameer E. Mhatre. (2013). Modeling the Mitogen Activated Protein (MAP)-Kinase Pathway Using Ordinary Differential Equations. Computational Biology and Bioinformatics, 1(2), 6-9. https://doi.org/10.11648/j.cbb.20130102.11

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ACS Style

Sharadwata Pan; Sameer E. Mhatre. Modeling the Mitogen Activated Protein (MAP)-Kinase Pathway Using Ordinary Differential Equations. Comput. Biol. Bioinform. 2013, 1(2), 6-9. doi: 10.11648/j.cbb.20130102.11

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AMA Style

Sharadwata Pan, Sameer E. Mhatre. Modeling the Mitogen Activated Protein (MAP)-Kinase Pathway Using Ordinary Differential Equations. Comput Biol Bioinform. 2013;1(2):6-9. doi: 10.11648/j.cbb.20130102.11

Copy | Download

@article{10.11648/j.cbb.20130102.11,
  author = {Sharadwata Pan and Sameer E. Mhatre},
  title = {Modeling the Mitogen Activated Protein (MAP)-Kinase Pathway Using Ordinary Differential Equations},
  journal = {Computational Biology and Bioinformatics},
  volume = {1},
  number = {2},
  pages = {6-9},
  doi = {10.11648/j.cbb.20130102.11},
  url = {https://doi.org/10.11648/j.cbb.20130102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cbb.20130102.11},
  abstract = {Mitogen Activated Protein (MAP) Kinase pathway is central to comprehend the key cellular signal transduction mechanisms in animal physiology, including human beings. Modeling MAP Kinase pathway has two main applications: deciphering a transient response of three main components (MAPKKK, MAPKK and MAPK) to regulate signaling and utilizing the models to make it behave as a potential drug target. The current study develops a mathematical representation for this transient cell-signaling pathway, based on a simple modular approach to structure and model a three-tier cascade. Based on assumptions from existing literature, ordinary differential equations have been formulated to express the concentrations of MAPKKK, MAPKK and MAPK as a function of time. Finally, the transient responses of the deduced concentrations of these components are analyzed to understand the pathway behavior and some interesting results are obtained by analyzing the temporal evolutions of the concentrations of the six components involved in the pathway. We conclude that the transient behaviour of MAPKKK can be captured with first order ordinary differential equations. Some anomalous behavior is observed in case of MAPKK and MAPK. In this perspective, future work can be designed to regulate the MAP Kinase signaling by taking Michaeli-Menten kinetics into consideration and make complex models to get more accurate results.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Modeling the Mitogen Activated Protein (MAP)-Kinase Pathway Using Ordinary Differential Equations
AU  - Sharadwata Pan
AU  - Sameer E. Mhatre
Y1  - 2013/06/10
PY  - 2013
N1  - https://doi.org/10.11648/j.cbb.20130102.11
DO  - 10.11648/j.cbb.20130102.11
T2  - Computational Biology and Bioinformatics
JF  - Computational Biology and Bioinformatics
JO  - Computational Biology and Bioinformatics
SP  - 6
EP  - 9
PB  - Science Publishing Group
SN  - 2330-8281
UR  - https://doi.org/10.11648/j.cbb.20130102.11
AB  - Mitogen Activated Protein (MAP) Kinase pathway is central to comprehend the key cellular signal transduction mechanisms in animal physiology, including human beings. Modeling MAP Kinase pathway has two main applications: deciphering a transient response of three main components (MAPKKK, MAPKK and MAPK) to regulate signaling and utilizing the models to make it behave as a potential drug target. The current study develops a mathematical representation for this transient cell-signaling pathway, based on a simple modular approach to structure and model a three-tier cascade. Based on assumptions from existing literature, ordinary differential equations have been formulated to express the concentrations of MAPKKK, MAPKK and MAPK as a function of time. Finally, the transient responses of the deduced concentrations of these components are analyzed to understand the pathway behavior and some interesting results are obtained by analyzing the temporal evolutions of the concentrations of the six components involved in the pathway. We conclude that the transient behaviour of MAPKKK can be captured with first order ordinary differential equations. Some anomalous behavior is observed in case of MAPKK and MAPK. In this perspective, future work can be designed to regulate the MAP Kinase signaling by taking Michaeli-Menten kinetics into consideration and make complex models to get more accurate results.
VL  - 1
IS  - 2
ER  -

Copy | Download