On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle

Author ORCID Identifier

Tomoyuki Shibata:https://orcid.org/0000-0001-6056-9547

Publication Title

Mathematical Biosciences and Engineering

ISSN

15471063

E-ISSN

15510018

Document Type

Article

Abstract

Protein phosphorylation cycles are important mechanisms of the post translational modification of a protein and as such an integral part of intracellular signaling and control. We consider the sequential phosphorylation and dephosphorylation of a protein at two binding sites. While it is known that proteins where phosphorylation is processive and dephosphorylation is distributive admit oscillations (for some value of the rate constants and total concentrations) it is not known whether or not this is the case if both phosphorylation and dephosphorylation are distributive. We study simplified mass action models of sequential and distributive phosphorylation and show that for each of those there do not exist rate constants and total concentrations where a Hopf bifurcation occurs. To arrive at this result we use convex parameters to parametrize the steady state and Hurwitz matrices.

First Page

494

Last Page

513

Publication Date

1-1-2020

DOI

10.3934/mbe.2020027

PubMed ID

31731363

Keywords

Chemical reaction networks, Convex parameters, Hopf bifurcation, Oscillations, Phosphorylation networks

Department

Department of Mathematical Sciences

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