ArticleJournal of mathematical biology2019
Oscillations and bistability in a model of ERK regulation.
Article in Journal of mathematical biology, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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Who cites it
10 citing papers in PubMed.
- CRITERIA: A network decomposition and elementary flux mode translation-based tool for computing equilibria of biochemical systems.PLoS computational biology · 2026Article
- Mathematical Modeling for Oscillations Driven by Noncoding RNAs.Methods in molecular biology (Clifton, N.J.) · 2025Article
- The Inheritance of Local Bifurcations in Mass Action Networks.Journal of nonlinear science · 2025Article
- Widespread biochemical reaction networks enable Turing patterns without imposed feedback.Nature communications · 2024Article
- Catalyst: Fast and flexible modeling of reaction networks.PLoS computational biology · 2023Article
- Topological descriptors of the parameter region of multistationarity: Deciding upon connectivity.PLoS computational biology · 2023Article
- Nonmodular oscillator and switch based on RNA decay drive regeneration of multimodal gene expression.Nucleic acids research · 2022Article
- Collective Oscillations in Coupled-Cell Systems.Bulletin of mathematical biology · 2021Article
- Dynamics of ERK regulation in the processive limit.Journal of mathematical biology · 2021Article
- Inference of Multisite Phosphorylation Rate Constants and Their Modulation by Pathogenic Mutations.Current biology : CB · 2020Article
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Authors and funding
4 authors.
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Abstract
This work concerns the question of how two important dynamical properties, oscillations and bistability, emerge in an important biological signaling network. Specifically, we consider a model for dual-site phosphorylation and dephosphorylation of extracellular signal-regulated kinase (ERK). We prove that oscillations persist even as the model is greatly simplified (reactions are made irreversible and intermediates are removed). Bistability, however, is much less robust-this property is lost when intermediates are removed or even when all reactions are made irreversible. Moreover, bistability is characterized by the presence of two reversible, catalytic reactions: as other reactions are made irreversible, bistability persists as long as one or both of the specified reactions is preserved. Finally, we investigate the maximum number of steady states, aided by a network's "mixed volume" (a concept from convex geometry). Taken together, our results shed light on the question of how oscillations and bistability emerge from a limiting network of the ERK network-namely, the fully processive dual-site network-which is known to be globally stable and therefore lack both oscillations and bistability. Our proofs are enabled by a Hopf bifurcation criterion due to Yang, analyses of Newton polytopes arising from Hurwitz determinants, and recent characterizations of multistationarity for networks having a steady-state parametrization.
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