Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

Details Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles

2007-01-20

arxiv.org/abs/math/0701575v2

Mathematics

Dynamical Systems

21 pages, 3 figures, corrected typos, references removed

Scientific paper

10.1007/s00332-008-9021-2

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comparatively fast time scale, the main dynamical property of (strongly) monotone systems, convergence to steady states, is still valid. An application is worked out to a double-phosphorylation ``futile cycle'' motif which plays a central role in eukaryotic cell signaling.

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