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

Carsten Conradi; Elisenda Feliu; Maya Mincheva

doi:10.3934/mbe.2020027

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

Carsten Conradi, Elisenda Feliu, Maya Mincheva

Institut for Matematiske Fag

3 Citationer (Scopus)

2 Downloads (Pure)

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 four 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 parameterize the steady state and Yang's Theorem.

Originalsprog	Udefineret/Ukendt
Tidsskrift	Mathematical Biosciences and Engineering
Vol/bind	17
Udgave nummer	1
Sider (fra-til)	494-513
ISSN	1547-1063
DOI	https://doi.org/10.3934/mbe.2020027
Status	Udgivet - 2020

Emneord

q-bio.MN
math.AG
math.DS
37N25

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10.3934/mbe.2020027Licens: Ikke-specificeret

OA-On the existence of Hopf bifurcations in the sequential and distributivedouble phosphorylation cycleForlagets udgivne version, 750 KBLicens: Ikke-specificeret

Citationsformater

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TY - JOUR

T1 - On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle

AU - Conradi, Carsten

AU - Feliu, Elisenda

AU - Mincheva, Maya

PY - 2020

Y1 - 2020

N2 - 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 four 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 parameterize the steady state and Yang's Theorem.

AB - 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 four 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 parameterize the steady state and Yang's Theorem.

KW - q-bio.MN

KW - math.AG

KW - math.DS

KW - 37N25

U2 - 10.3934/mbe.2020027

DO - 10.3934/mbe.2020027

M3 - Tidsskriftartikel

C2 - 31731363

SN - 1547-1063

VL - 17

SP - 494

EP - 513

JO - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

IS - 1

ER -