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

0440828 - MÚ 2015 RIV CZ eng J - Journal Article
Vejchodský, Tomáš
Accurate reduction of a model of circadian rhythms by delayed quasi steady state assumptions.
Mathematica Bohemica. Roč. 139, č. 4 (2014), s. 577-585. ISSN 0862-7959
Grant - others:European Commission(XE) StochDetBioModel(328008)
Program: FP7-PEOPLE
Institutional support: RVO:67985840
Keywords : biochemical networks * gene regulatory networks * oscillating systems * periodic solution
Subject RIV: BA - General Mathematics
http://hdl.handle.net/10338.dmlcz/144135

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.
Permanent Link: http://hdl.handle.net/11104/0243931