Reduction of a kinetic model of active export of importins

Sarbaz H. A.  Khoshnaw

doi:10.3934/proc.2015.0705

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2015, Volume 2015: 705-722. Doi: 10.3934/proc.2015.0705 open access

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Reduction of a kinetic model of active export of importins

Sarbaz H. A. Khoshnaw^1,

1.
Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH

Received: August 2014

Revised: February 2015

Published: November 2015

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Abstract

We study a kinetic model of active export of importins. The kinetic model is written as a system of ordinary differential equations. We developed some model reduction techniques to simplify the system. The techniques are: removal of very slow reactions, quasi-steady state approximation and simplification of kinetic equations based on stoichiometric conservation laws. Local sensitivity analysis is used for the identification of critical model parameters. After model reduction, the numbers of reactions and species are reduced from $28$ and $29$ to $20$ and $20$, respectively. The reduced model and original model are compared in numerical simulations using SBedit tools for Matlab, and the methods of further model reduction are discussed. Interestingly, we investigate an iterative algorithm based on the Duhamel iterates to calculate the analytical approximate solutions of the complex non--linear chemical kinetics. This technique plays as an explicit formula that can be studied in detail for wide regions of concentrations for optimization and parameter identification purposes. It seems that the third iterative solution of the suggested method is significantly close to the actual solution of the kinetic models in most cases.

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Mathematics Subject Classification: Primary: 92C42, 92C45; Secondary: 92B05.

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