On the number of steady states in a multiple futile cycle |
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Authors: | Liming Wang Eduardo D Sontag |
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Institution: | (1) Department of Mathematics, Rutgers University, New Brunswick, NJ, USA |
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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.
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Keywords: | Futile cycles Bistability Signaling pathways Biomolecular networks Steady states |
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