2007/03/31 by Liming Wang, Eduardo D. Sontag, Wang, Liming +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #FOS: Biological sciences #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Microtubule and mitosis dynamics #Molecular Networks (q-bio.MN) #Quantitative Methods (q-bio.QM) #q-bio.MN #q-bio.QM
paper · pdf · doi:10.48550/arxiv.0704.0036
Resubmit with new results on the upper bound of the number of steady states. 20 pages, 2 figures, See http://www.math.rutgers.edu/~sontag/PUBDIR/index.html for online preprints and reprints of related work
openalex publication_date 2007/03/31 · arxiv created 2007/07/20 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The multisite phosphorylation-dephosphorylation cycle is a motif repeatedly used in cell signaling. This motif itself can generate a variety of dynamic behaviors like bistability and ultrasensitivity without direct positive feedbacks. In this paper, we study the number of positive steady states of a general multisite phosphorylation-dephosphorylation cycle, and how the number of positive steady states varies by changing the biological parameters. We show analytically that (1) for some parameter ranges, there are at least n+1 (if n is even) or n (if n is odd) steady states; (2) there never are more than 2n-1 steady states (in particular, this implies that for n=2, including single levels of MAPK cascades, there are at most three steady states); (3) for parameters near the standard Michaelis-Menten quasi-steady state conditions, there are at most n+1 steady states; and (4) for parameters far from the standard Michaelis-Menten quasi-steady state conditions, there is at most one steady state.