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## Section: New Results

### Knowledge-based generalization of metabolic models

Participants : David James Sherman [correspondant] , Pascal Durrens, Razanne Issa, Anna Zhukova.

Large metabolic networks are hard to understand and curate, because the large number of detailed reactions, which are needed for accurate modeling and simulation, obscure the high-level structure of the reaction network. We defined knowledge-based methods that factor similar reactions into “generic” reactions in order to visualize a whole pathway or compartment, while maintaining the underlying model so that the user can later “drill down” to the specific reactions if need be[15] , [16] An implementation of this method is available as a Python library (see paragraph 5.3 ).

Figures 2 and 3 illustrate model generation for Yarrowia lypolitica fatty acid oxidation in the peroxisome. Molecular species are represented using SBGN notation: as circular nodes, and the reactions as square ones, connected by edges to their reactants and products. Ubiquitous species are of smaller size and colored gray. Non-ubiquitous species are divided into six equivalence classes, and coloured accordingly. The size of the model does not allow for readability of the species labels, thus we do not show them (figure 2 ).

The specific model is appropriate for simulation, because it contains all of the precise reactions. The generalized model is suited for a human, because it reveals the main properties of the model and masks distracting details. For example, the generalized model highlights the fact that there is a particularity concerning C24:0-CoA (stearoyl-CoA) (yellow): there exists a "shortcut" reaction (orange), producing it directly from another fatty acyl-CoA (yellow), avoiding the usual four-reaction beta-oxidation chain, used for other fatty acyls-CoA. This shortcut is not obvious in the specific model, because it is hidden among a plethora of similar-looking reactions.

We formally defined the generalization method in [15] and showed how to calculate it using a good approximation to an NP-complete set cover problem. The method was further validated in a collection of 1283 inferred models and revealed, on the one hand, a number of probable errors in the inferred models, and on the other hand, that there exist different families of generalization with a plausible link to different adaptive responses.

Figure 2. Yarrowia lypolitica fatty acid oxidation model before generalization. Reactions of the specific model are divided into fifteen equivalence classes, represented by different colours. Generally speaking, $\beta$-oxidation is a transformation of fatty acyl-CoA (yellow) into dehydroacyl-CoA (violet), then into hydroxyacy fatty acyl-CoA (dark green), 3-ketoacyl-CoA (magenta), and back to fatty acyl-CoA (with a shorter carbon chain); while the specific model describes the same process in more details, specifying those reactions for each of the fatty acyl-CoA species presented in the organisms' cell (e.g. decanoyl-CoA, dodecanoyl-CoA, etc.). This high-level, repetitive structure is obscured by the detail of the individual reactions.
Figure 3. Generalization of the Yarrowia lypolitica fatty acid oxidation model, described as a transformation of fatty acyl-CoA (yellow) into dehydroacyl-CoA (violet), then into hydroxyacy fatty acyl-CoA (dark green), 3-ketoacyl-CoA (magenta), and back to fatty acyl-CoA with a shorter carbon chain. The generalization algorithm identifies equivalent molecular species using an ontology, and groups together reactions that operate on the same abstract species. It finds the greatest generalization the preserves stoichiometry. The generalized model represents quotient species and reactions. For example, the violet dehydroacyl-CoA node is a quotient of hexadec-2-enoyl-CoA, oleoyl-CoA, tetradecenoyl-CoA, trans-dec-2-enoyl-CoA, trans-dodec-2-enoyl-CoA, trans-hexacos-2-enoyl-CoA, trans-octadec-2-enoyl-CoA, and trans-tetradec-2-enoyl-CoA (colored violet in figure 2 ). In a similar manner, the light-green acyl-CoA oxidase quotient reaction, that converts fatty acyl-CoA (yellow) into dehydroacyl-CoA (violet), generalizes six corresponding light-green reactions of the initial model (figure 2 ).