Phase plane dynamics of ERK phosphorylation

Stanislav Y. Shvartsman, Sarah McFann, Martin Wühr, Boris Y. Rubinstein

Research output: Contribution to journalArticlepeer-review


The extracellular signal–regulated kinase (ERK) controls multiple critical processes in the cell and is deregulated in human cancers, congenital abnormalities, immune diseases, and neurodevelopmental syndromes. Catalytic activity of ERK requires dual phosphorylation by an upstream kinase, in a mechanism that can be described by two sequential Michaelis-Menten steps. The estimation of individual reaction rate constants from kinetic data in the full mechanism has proved challenging. Here, we present an analytically tractable approach to parameter estimation that is based on the phase plane representation of ERK activation and yields two combinations of six reaction rate constants in the detailed mechanism. These combinations correspond to the ratio of the specificities of two consecutive phosphorylations and the probability that monophosphorylated substrate does not dissociate from the enzyme before the second phosphorylation. The presented approach offers a language for comparing the effects of mutations that disrupt ERK activation and function in vivo. As an illustration, we use phase plane representation to analyze dual phosphorylation under heterozygous conditions, when two enzyme variants compete for the same substrate.

Original languageEnglish (US)
Article number105234
JournalJournal of Biological Chemistry
Issue number11
StatePublished - Nov 2023

All Science Journal Classification (ASJC) codes

  • Molecular Biology
  • Biochemistry
  • Cell Biology


  • dual phosphorylation
  • enzyme kinetics
  • heterozygosity
  • mitogen-activated protein kinase (MAPK) signaling
  • modeling and simulation
  • parameter estimation
  • phase plane analysis


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