A proof of bistability for the dual futile cycle

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....

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2015-08, Vol.24, p.175-189
Main Authors: Hell, Juliette, Rendall, Alan D.
Format: Article
Language:English
Subjects:
Bifurcation theory
Bistability
Cascades
Chemical reactions
Cusp bifurcation
Differential equations
Geometric singular perturbation theory
MAPkinase cascade
Mathematical models
Molecular biology
Multiple futile cycle
Proving
Singular perturbation
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Summary: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.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2015.02.004