ArticlePLoS computational biology2017
Identifying parameter regions for multistationarity.
Article in PLoS computational biology, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 17 papers.
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17 citing papers in PubMed.
- Positive equilibria in mass action networks: geometry and bounds.Journal of mathematical biology · 2026Article
- CRITERIA: A network decomposition and elementary flux mode translation-based tool for computing equilibria of biochemical systems.PLoS computational biology · 2026Article
- Parametrized systems of generalized polynomial inequalities via linear algebra and convex geometry.Positivity · 2026Article
- Uncovering bifurcation behaviors of biochemical reaction systems from network topology.Scientific reports · 2025Article
- Connectivity of Parameter Regions of Multistationarity for Multisite Phosphorylation Networks.Bulletin of mathematical biology · 2024Article
- A framework for deriving analytic steady states of biochemical reaction networks.PLoS computational biology · 2023Article
- Topological descriptors of the parameter region of multistationarity: Deciding upon connectivity.PLoS computational biology · 2023Article
- Network regulation meets substrate modification chemistry.Journal of the Royal Society, Interface · 2023Article
- A numerical approach for detecting switch-like bistability in mass action chemical reaction networks with conservation laws.BMC bioinformatics · 2022Article
- Symmetry breaking meets multisite modification.eLife · 2021Article
- Dynamics of ERK regulation in the processive limit.Journal of mathematical biology · 2021Article
- Robustness and parameter geography in post-translational modification systems.PLoS computational biology · 2020Article
- Oscillations and bistability in a model of ERK regulation.Journal of mathematical biology · 2019Article
- A Deficiency-Based Approach to Parametrizing Positive Equilibria of Biochemical Reaction Systems.Bulletin of mathematical biology · 2019Article
- Regions of multistationarity in cascades of Goldbeter-Koshland loops.Journal of mathematical biology · 2019Article
- Dynamics of Posttranslational Modification Systems: Recent Progress and Future Directions.Biophysical journal · 2018Review
- Core signalling motif displaying multistability through multi-state enzymes.Journal of the Royal Society, Interface · 2016Article
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4 authors.
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Abstract
Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce a procedure to partition the parameter space of a parameterized system of ordinary differential equations into regions for which the system has a unique or multiple equilibria. The procedure is based on the computation of the Brouwer degree, and it creates a multivariate polynomial with parameter depending coefficients. The signs of the coefficients determine parameter regions with and without multistationarity. A particular strength of the procedure is the avoidance of numerical analysis and parameter sampling. The procedure consists of a number of steps. Each of these steps might be addressed algorithmically using various computer programs and available software, or manually. We demonstrate our procedure on several models of gene transcription and cell signalling, and show that in many cases we obtain a complete partitioning of the parameter space with respect to multistationarity.
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