Model Reduction and Analysis for ERK Cell Signalling Pathway Using Implicit-Explicit Rung-Kutta Methods

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science and Health, Koya University, Koya KOY45, Kurdistan Region - F.R. Iraq

2 Department of Mathematics, Faculty of Science and Health, Koya University, Koya KOY45, Kurdistan Region - F.R. Iraq.

3 Department of mathematics Education, Faculty of Education, Tishk International University, Erbil, Iraq

Abstract

Many complex cell signalling pathways and chemical reaction networks include many variables and parameters; this is sometimes a big issue for identifying critical model elements and describing the model dynamics. Therefore, model reduction approaches can be employed as a mathematical tool to reduce the number of elements. In this study, we use a new technique for model reduction: the Lumping of parameters for the simple linear chemical reaction network and the complex cell signalling pathway that is extracellular-signal-regulated kinase (ERK) pathways. Moreover, we propose a high-order and accurate method for solving stiff nonlinear ordinary differential equations. The curtail idea of this scheme is based on splitting the problem into stiff and non-stiff terms. More specifically, stiff discretization uses the implicit method, and nonlinear discretization uses the explicit method. This is consequently leading to a reduction in the computational cost of the scheme.
The main aim of this study is to reduce the complex cell signalling pathway models by proposing an accurate numerical approximation Runge-Kutta method. This improves one's understanding of such behaviour of these systems and gives an accurate approximate solution. Based on the suggested technique, the simple model's parameters are minimized from 6 to 3, and the complex models from 11 to 8. Results show that there is a good agreement between the original models and the simplified models.

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Volume 4, Special issue
This special issue is related to the 9th Scientific Conference of University of Garmian: Pure Sciences and Technology Applications (SCUG-PSTA-2022) October 26–27, 2022. (All the manuscripts have been peer-reviewed.)
November 2022
Pages 160-178