MATHEMATICA BOHEMICA, Vol. 139, No. 4, pp. 577-585, 2014

Accurate reduction of a model of circadian rhythms by delayed quasi-steady state assumptions

Tomáš Vejchodský

Tomáš Vejchodský, University of Oxford, Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom, and Institute of Mathematics, Academy of Sciences, Žitná 25, Praha 1, CZ-115 67, Czech Republic, e-mail: vejchod@math.cas.cz

Abstract: Quasi-steady state assumptions are often used to simplify complex systems of ordinary differential equations in the modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original system and to have a small number of variables. This enables to use the stability and bifurcation analysis to reveal a deeper structure in the dynamics of the original system. This contribution shows that introducing delays to quasi-steady state assumptions yields a simplified system that accurately agrees with the original system not only qualitatively but also quantitatively. We derive the proper size of the delays for a particular model of circadian rhythms and present numerical results showing the accuracy of this approach.

Keywords: biochemical networks; gene regulatory networks; oscillating systems; periodic solutions; model reduction; accurate approximation

Classification (MSC 2010): 92C45, 92B25, 80A30, 34C15, 34C23


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