ArticleJournal of mathematical biology2017
Graphical reduction of reaction networks by linear elimination of species.
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.
- The linear framework: using graph theory to reveal the algebra and thermodynamics of biomolecular systems.Interface focus · 2022Review
- A structural property for reduction of biochemical networks.Scientific reports · 2021Article
- Maximization of information transmission influences selection of native phosphorelay architectures.PeerJ · 2021Article
- Joining and decomposing reaction networks.Journal of mathematical biology · 2020Article
- 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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3 authors.
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Abstract
The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are assumed effectively to be at steady state with respect to the "slow" species. Under this assumption the steady state equations can be used to eliminate the "fast" variables and a new ODE system with only the slow species can be obtained. We interpret a reduced system obtained by time-scale separation as the ODE system arising from a unique reaction network, by identification of a set of reactions and the corresponding rate functions. The procedure is graphically based and can easily be worked out by hand for small networks. For larger networks, we provide a pseudo-algorithm. We study properties of the reduced network, its kinetics and conservation laws, and show that the kinetics of the reduced network fulfil realistic assumptions, provided the original network does. We illustrate our results using biological examples such as substrate mechanisms, post-translational modification systems and networks with intermediates (transient) steps.
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