Coarse-graining metabolic networks via feature learning reveals cross-species growth laws

Bacterial growth and the underlying metabolic networks are highly dissimilar across species, posing a fundamental challenge for bioengineering tasks involving diverse species. For a given species across nutrient environments, growth is regulated via proteome allocation, which gives rise to linear relationships between growth and the sizes of coarse-grained proteome sectors. However, whether and how coarse-grained growth predictors generalize across species remain unclear. Here, using genome-scale metabolic models, we discover a simple cross-species trend in which the monoculture growth of a species is proportional to the number of nutrients it utilizes, indicating that the latter is a regulatory feature that is conserved across species. By coarse-graining metabolic networks using feature learning, we identify novel proteome sectors whose sizes exhibit cross-species correlations with growth in wide-ranging experiments, suggesting that these sectors are also conserved regulatory features. We further show that the sectors enable a predictive encoding of proteome costs and growth benefits, thereby providing a potential explanation for how coarse-grained network features emerge to be simple determinants of growth across diverse metabolic networks.