ArticleJournal of mathematical biology2012
Multistationarity in mass action networks with applications to ERK activation.
Article in Journal of mathematical biology, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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9 citing papers in PubMed.
- In distributive phosphorylation catalytic constants enable non-trivial dynamics.Journal of mathematical biology · 2024Article
- Article
- Gain and loss of function mutations in biological chemical reaction networks: a mathematical model with application to colorectal cancer cells.Journal of mathematical biology · 2021Article
- When More Is Less: Dual Phosphorylation Protects Signaling Off State against Overexpression.Biophysical journal · 2018Article
- Dynamics of Posttranslational Modification Systems: Recent Progress and Future Directions.Biophysical journal · 2018Review
- Identifying parameter regions for multistationarity.PLoS computational biology · 2017Article
- Investigating the Role of TNF-α and IFN-γ Activation on the Dynamics of iNOS Gene Expression in LPS Stimulated Macrophages.PloS one · 2016Article
- Catalytic constants enable the emergence of bistability in dual phosphorylation.Journal of the Royal Society, Interface · 2014Article
- Modeling approaches for qualitative and semi-quantitative analysis of cellular signaling networks.Cell communication and signaling : CCS · 2013Article
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2 authors.
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Abstract
Ordinary Differential Equations (ODEs) are an important tool in many areas of Quantitative Biology. For many ODE systems multistationarity (i.e. the existence of at least two positive steady states) is a desired feature. In general establishing multistationarity is a difficult task as realistic biological models are large in terms of states and (unknown) parameters and in most cases poorly parameterized (because of noisy measurement data of few components, a very small number of data points and only a limited number of repetitions). For mass action networks establishing multistationarity hence is equivalent to establishing the existence of at least two positive solutions of a large polynomial system with unknown coefficients. For mass action networks with certain structural properties, expressed in terms of the stoichiometric matrix and the reaction rate-exponent matrix, we present necessary and sufficient conditions for multistationarity that take the form of linear inequality systems. Solutions of these inequality systems define pairs of steady states and parameter values. We also present a sufficient condition to identify networks where the aforementioned conditions hold. To show the applicability of our results we analyse an ODE system that is defined by the mass action network describing the extracellular signal-regulated kinase (ERK) cascade (i.e. ERK-activation).
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