ArticleFrontiers in genetics2016
Elementary Vectors and Conformal Sums in Polyhedral Geometry and their Relevance for Metabolic Pathway Analysis.
Article in Frontiers in genetics, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 16 papers.
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16 citing papers in PubMed, 6 citations in OpenAlex.
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- A mathematically rigorous algorithm to define, compute and assess relevance of the probable dissociation constants in characterizing a biochemical network.Scientific reports · 2024Article
- Topological descriptors of the parameter region of multistationarity: Deciding upon connectivity.PLoS computational biology · 2023Article
- ReDirection: an R-package to compute the probable dissociation constant for every reaction of a user-defined biochemical network.Frontiers in molecular biosciences · 2023Article
- What makes a reaction network "chemical"?Journal of cheminformatics · 2022Article
- Elementary vectors and autocatalytic sets for resource allocation in next-generation models of cellular growth.PLoS computational biology · 2022Article
- EFMlrs: a Python package for elementary flux mode enumeration via lexicographic reverse search.BMC bioinformatics · 2021Article
- Understanding FBA Solutions under Multiple Nutrient Limitations.Metabolites · 2021Article
- Unlocking Elementary Conversion Modes: ecmtool Unveils All Capabilities of Metabolic Networks.Patterns (New York, N.Y.) · 2021Article
- MCS2: minimal coordinated supports for fast enumeration of minimal cut sets in metabolic networks.Bioinformatics (Oxford, England) · 2019Article
- Flux tope analysis: studying the coordination of reaction directions in metabolic networks.Bioinformatics (Oxford, England) · 2019Article
- OptMDFpathway: Identification of metabolic pathways with maximal thermodynamic driving force and its application for analyzing the endogenous CO2 fixation potential of Escherichia coli.PLoS computational biology · 2018Article
- A mathematical framework for yield (vs. rate) optimization in constraint-based modeling and applications in metabolic engineering.Metabolic engineering · 2018Article
- From elementary flux modes to elementary flux vectors: Metabolic pathway analysis with arbitrary linear flux constraints.PLoS computational biology · 2017Review
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2 authors at 1 institution in 1 country.
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Abstract
A fundamental result in metabolic pathway analysis states that every flux mode can be decomposed into a sum of elementary modes. However, only a decomposition without cancelations is biochemically meaningful, since a reversible reaction cannot have different directions in the contributing elementary modes. This essential requirement has been largely overlooked by the metabolic pathway community. Indeed, every flux mode can be decomposed into elementary modes without cancelations. The result is an immediate consequence of a theorem by Rockafellar which states that every element of a linear subspace is a conformal sum (a sum without cancelations) of elementary vectors (support-minimal vectors). In this work, we extend the theorem, first to "subspace cones" and then to general polyhedral cones and polyhedra. Thereby, we refine Minkowski's and Carathéodory's theorems, two fundamental results in polyhedral geometry. We note that, in general, elementary vectors need not be support-minimal; in fact, they are conformally non-decomposable and form a unique minimal set of conformal generators. Our treatment is mathematically rigorous, but suitable for systems biologists, since we give self-contained proofs for our results and use concepts motivated by metabolic pathway analysis. In particular, we study cones defined by linear subspaces and nonnegativity conditions - like the flux cone - and use them to analyze general polyhedral cones and polyhedra. Finally, we review applications of elementary vectors and conformal sums in metabolic pathway analysis.
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