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

Tomáš Vejchodský

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 4, page 577-585
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Vejchodský, Tomáš. "Accurate reduction of a model of circadian rhythms by delayed quasi-steady state assumptions." Mathematica Bohemica 139.4 (2014): 577-585. <http://eudml.org/doc/269834>.

@article{Vejchodský2014,
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.},
author = {Vejchodský, Tomáš},
journal = {Mathematica Bohemica},
keywords = {biochemical networks; gene regulatory networks; oscillating systems; periodic solutions; model reduction; accurate approximation; biochemical networks; gene regulatory networks; oscillating systems; periodic solutions; model reduction; delay differential equations; accurate approximation},
language = {eng},
number = {4},
pages = {577-585},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Accurate reduction of a model of circadian rhythms by delayed quasi-steady state assumptions},
url = {http://eudml.org/doc/269834},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Vejchodský, Tomáš
TI - Accurate reduction of a model of circadian rhythms by delayed quasi-steady state assumptions
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 4
SP - 577
EP - 585
AB - 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.
LA - eng
KW - biochemical networks; gene regulatory networks; oscillating systems; periodic solutions; model reduction; accurate approximation; biochemical networks; gene regulatory networks; oscillating systems; periodic solutions; model reduction; delay differential equations; accurate approximation
UR - http://eudml.org/doc/269834
ER -

References

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  8. Verdugo, A., Rand, R., 10.1016/j.cnsns.2006.05.001, Commun. Nonlinear Sci. Numer. Simul. 13 (2008), 235-242. (2008) Zbl1134.34325MR2360687DOI10.1016/j.cnsns.2006.05.001
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