ArticleJournal of mathematical biology2017
Intermediates, catalysts, persistence, and boundary steady states.
Article in Journal of mathematical biology, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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Who cites it
6 citing papers in PubMed.
- Maximum likelihood estimation of log-affine models using detailed-balanced reaction networks.Journal of mathematical biology · 2025Article
- Connectivity of Parameter Regions of Multistationarity for Multisite Phosphorylation Networks.Bulletin of mathematical biology · 2024Article
- Topological descriptors of the parameter region of multistationarity: Deciding upon connectivity.PLoS computational biology · 2023Article
- Oscillations and bistability in a model of ERK regulation.Journal of mathematical biology · 2019Article
- Dynamics of Posttranslational Modification Systems: Recent Progress and Future Directions.Biophysical journal · 2018Review
- Identifying parameter regions for multistationarity.PLoS computational biology · 2017Article
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Authors and funding
3 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
For dynamical systems arising from chemical reaction networks, persistence is the property that each species concentration remains positively bounded away from zero, as long as species concentrations were all positive in the beginning. We describe two graphical procedures for simplifying reaction networks without breaking known necessary or sufficient conditions for persistence, by iteratively removing so-called intermediates and catalysts from the network. The procedures are easy to apply and, in many cases, lead to highly simplified network structures, such as monomolecular networks. For specific classes of reaction networks, we show that these conditions for persistence are equivalent to one another. Furthermore, they can also be characterized by easily checkable strong connectivity properties of a related graph. In particular, this is the case for (conservative) monomolecular networks, as well as cascades of a large class of post-translational modification systems (of which the MAPK cascade and the n-site futile cycle are prominent examples). Since one of the aforementioned sufficient conditions for persistence precludes the existence of boundary steady states, our method also provides a graphical tool to check for that.
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Registered trials
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