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

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Standard

On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle. / Conradi, Carsten; Feliu, Elisenda; Mincheva, Maya.

I: Mathematical Biosciences and Engineering, Bind 17, Nr. 1, 2020, s. 494-513.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Conradi, C, Feliu, E & Mincheva, M 2020, 'On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle', Mathematical Biosciences and Engineering, bind 17, nr. 1, s. 494-513. https://doi.org/10.3934/mbe.2020027

APA

Conradi, C., Feliu, E., & Mincheva, M. (2020). On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle. Mathematical Biosciences and Engineering, 17(1), 494-513. https://doi.org/10.3934/mbe.2020027

Vancouver

Conradi C, Feliu E, Mincheva M. On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle. Mathematical Biosciences and Engineering. 2020;17(1):494-513. https://doi.org/10.3934/mbe.2020027

Author

Conradi, Carsten ; Feliu, Elisenda ; Mincheva, Maya. / On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle. I: Mathematical Biosciences and Engineering. 2020 ; Bind 17, Nr. 1. s. 494-513.

Bibtex

@article{22e57363fc8a4d1ca07616b8542d3a61,
title = "On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle",
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. ",
keywords = "q-bio.MN, math.AG, math.DS, 37N25",
author = "Carsten Conradi and Elisenda Feliu and Maya Mincheva",
year = "2020",
doi = "10.3934/mbe.2020027",
language = "English",
volume = "17",
pages = "494--513",
journal = "Mathematical Biosciences and Engineering",
issn = "1547-1063",
publisher = "American Institute of Mathematical Sciences",
number = "1",

}

RIS

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 - Journal article

C2 - 31731363

VL - 17

SP - 494

EP - 513

JO - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

SN - 1547-1063

IS - 1

ER -

ID: 225521928