2007/01/31 by Liming Wang, Eduardo D. Sontag, Eduardo Sontag
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Convergence (economics) #Dynamical systems theory #Feedback loop #Gene Regulatory Network Analysis #Monotone polygon #Monotonic function #Negative feedback #Nonlinear Dynamics and Pattern Formation #Strongly monotone #math.CA #math.DS #msc:34D15 #msc:37C65 #stochastic dynamics and bifurcation
paper · pdf · doi:10.1007/s00332-008-9021-2
21 pages, 3 figures, corrected typos, references removed
arxiv created 2007/03/07 · openalex publication_date 2008/03/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.