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A global convergence result for processive multisite phosphorylation systems. (English) Zbl 1334.92169
Summary: Multisite phosphorylation plays an important role in intracellular signaling. There has been much recent work aimed at understanding the dynamics of such systems when the phosphorylation/dephosphorylation mechanism is distributive, that is, when the binding of a substrate and an enzyme molecule results in the addition or removal of a single phosphate group and repeated binding therefore is required for multisite phosphorylation. In particular, such systems admit bistability. Here, we analyze a different class of multisite systems, in which the binding of a substrate and an enzyme molecule results in the addition or removal of phosphate groups at all phosphorylation sites, that is, we consider systems in which the mechanism is processive, rather than distributive. We show that in contrast to distributive systems, processive systems modeled with mass-action kinetics do not admit bistability and, moreover, exhibit rigid dynamics: each invariant set contains a unique equilibrium, which is a global attractor. Additionally, we obtain a monomial parametrization of the steady states. Our proofs rely on a technique of Johnston for using “translated” networks to study systems with “toric steady states,” recently given sign conditions for the injectivity of polynomial maps, and a result from monotone systems theory due to D. Angeli and E. D. Sontag [Nonlinear Anal., Real World Appl. 9, No. 1, 128–140 (2008; Zbl 1401.92086)].

MSC:
92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
92C42 Systems biology, networks
Software:
CoNtRol; crntwin
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References:
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