Fig 1.
Illustration of the flux-sum coupling concept. A. A toy network representation consisting of six metabolites, denoted by A - G, and nine reactions, depicted in the box. B. Illustration of flux-sum couplings on the toy network. Nodes represent metabolites A-F, and labeled edges represent coupling relations (see legend). C. Classification of flux-sum couplings of metabolites and j. Flux-sums of metabolites i and j are denoted as
and
, respectively. The coupling classes are assigned based on the minimum and maximum flux-sum ratios,
and
, which can be achieved at steady state.
Fig 2.
Flux-sum coupling and mutual metabolic pathway types across three metabolic models. Models of three organisms were used to compare the fraction of particular flux-sum coupling types, namely the iML1515 model of E. coli, the iMM904 model of S. cerevisiae, and the AraCore model of A. thaliana. A. Fraction of pairs that belong to the particular flux-sum coupling type, namely: fully, partially, directionally coupled metabolites in the three metabolic models. B. Representation of particular flux-sum couplings in selected metabolic pathways. This bar chart illustrates the percentage of coupling types in selected metabolic pathways across the three metabolic models. The fully, partially, and directionally coupled pairs were found to be most related to Lipopolysaccharide Biosynthesis/Recycling, Glycerophospholipid Metabolism, Histidine Synthesis, and Tyrosine, Tryptophan, and Phenylalanine Metabolism. Within each model, the coupling types are represented with hues, from darkest to lightest: full coupling (FC), partial coupling (PC), and directional coupling. (DC) (see legend).
Fig 3.
Network representation of metabolites with fully coupled flux-sums in the iML1515 model. Nodes represent metabolites, and edges depict the mutual pathways in which pairs of metabolites participate. Nodes with a degree smaller than 1 have been removed from the graph to improve visualization. Abbreviations for metabolites are used in the figure. The full names of the metabolites are given in Table A in S2 Table.
Fig 4.
Distribution of correlations of measured metabolite levels across flux-sum coupling types in E. coli. Boxplots comparing Pearson correlations of measured metabolite levels for fully coupled (FC), partially coupled (PC), directionally coupled (DC), and uncoupled (UC) pairs in the iML1515 model of E. coli.