Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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STOCHASTIC DIFFERENTIAL EQUATION MODELS FOR EXTRACELLULAR SIGNAL-REGULATED KINASE PATHWAYS

  • Choo, S.M. (Department of Mathematics, University of Ulsan) ;
  • Kim, Y.H. (Department of Mathematics, University of Ulsan)
  • Received : 2013.01.09
  • Accepted : 2013.03.08
  • Published : 2013.05.30
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Abstract

There exist many deterministic models for signaling pathways in systems biology. However the models do not consider the stochastic properties of the pathways, which means the models fit well with experimental data in certain situations but poorly in others. Incorporating stochasticity into deterministic models is one way to handle this problem. In this paper the way is used to produce stochastic models based on the deterministic differential equations for the published extracellular signal-regulated kinase (ERK) pathway. We consider strong convergence and stability of the numerical approximations for the stochastic models.

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References

  1. S.M. Choo, Finite difference schemes for calcium diffusion equations, J. Appl. Math. Informatics 26(2008), 299-306.
  2. P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, New York, 1988.
  3. B. Oksendal, Stochastic Differential Equations, 6th ed. Springer, New York, 2010.
  4. S.Y. Shin, O. Rath, S.M. Choo, F. Fee, B. McFerran, W. Kolch, and K.H. Cho, Positive- and negative-feedback regulations coordinate the dynamic behavior of the Ras-Raf-MEK-ERK signal transduction pathway, J Cell Sci. 122(2009), 425-435. https://doi.org/10.1242/jcs.036319