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