ArticleProceedings of the National Academy of Sciences of the United States of America2017
Maximal aggregation of polynomial dynamical systems.
Article in Proceedings of the National Academy of Sciences of the United States of America, 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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6 citing papers in PubMed.
- Quantifying and comparing causal patterns in stochastic chemical reaction networks.NPJ systems biology and applications · 2026Article
- Reducing Boolean networks with backward equivalence.BMC bioinformatics · 2023Article
- Exploring the link between chronobiology and drug delivery: effects on cancer therapy.Journal of molecular medicine (Berlin, Germany) · 2021Review
- Modeling cell line-specific recruitment of signaling proteins to the insulin-like growth factor 1 receptor.PLoS computational biology · 2019Article
- Computing with biological switches and clocks.Natural computing · 2018Article
- Maximal aggregation of polynomial dynamical systems.Proceedings of the National Academy of Sciences of the United States of America · 2017Article
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4 authors.
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Abstract
Ordinary differential equations (ODEs) with polynomial derivatives are a fundamental tool for understanding the dynamics of systems across many branches of science, but our ability to gain mechanistic insight and effectively conduct numerical evaluations is critically hindered when dealing with large models. Here we propose an aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion). A key feature of our proposal is to encode a polynomial ODE system into a finitary structure akin to a formal chemical reaction network. This enables the development of a discrete algorithm to efficiently compute the largest equivalence, building on approaches rooted in computer science to minimize basic models of computation through iterative partition refinements. The physical interpretability of the aggregation is shown on polynomial ODE systems for biochemical reaction networks, gene regulatory networks, and evolutionary game theory.
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