title: On the number of steady states in a multiple futile cycle.
abstract: 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.
authors.affiliation: Department of Mathematics, Rutgers University, New Brunswick, NJ, USA.
authors.forename: Liming
authors.initials: L
authors.lastname: Wang
authors.forename: Eduardo D
authors.initials: ED
authors.lastname: Sontag
mesh_terms: D000818:Animals; D019295:Computational Biology / Q000379:methods*; D025461:Feedback, Physiological / Q000502:physiology; D006801:Humans; D007700:Kinetics; D020935:MAP Kinase Signaling System; D053858:Metabolic Networks and Pathways; D008954:Models, Biological; D010766:Phosphorylation; D015219:Substrate Cycling