A proof of bistability for the dual futile cycle. (August 2015)

• Record Type: Journal Article
• Authors: Hell, Juliette; Rendall, Alan D.
• Is Part Of: Nonlinear analysis. Volume 24(2015)
• Page Start: 175
• Page End: 189
• Publication Date: 2015-08
• Subjects: MAPkinase cascade -- Multiple futile cycle -- Cusp bifurcation -- Geometric singular perturbation theory -- Bistability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.02.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The multiple futile cycle is an important building block in networks of chemical reactions arising in molecular biology. A typical process which it describes is the addition of n phosphate groups to a protein. It can be modelled by a system of ordinary differential equations depending on parameters. The special case n = 2 is called the dual futile cycle. The main result of this paper is a proof that there are parameter values for which the system of ODE describing the dual futile cycle has two distinct stable stationary solutions. The proof is based on bifurcation theory and geometric singular perturbation theory. An important entity built of three coupled multiple futile cycles is the MAPK cascade. It is explained how the ideas used to prove bistability for the dual futile cycle might help to prove the existence of periodic solutions for the MAPK cascade.