Resource allocation to cell envelopes and the scaling of bacterial growth rate

Although various empirical studies have reported a positive correlation between the specific growth rate and cell size across bacteria, it is currently unclear what causes this relationship. We conjecture that such scaling occurs because smaller cells have a larger surface-to-volume ratio and thus have to allocate a greater fraction of the total resources to the production of the cell envelope, leaving fewer resources for other biosynthetic processes. To test this theory, we developed a coarse-grained model of bacterial physiology composed of the proteome that converts nutrients into biomass, with the cell envelope acting as a resource sink. Assuming resources are partitioned to maximize the growth rate, the model predicts that the growth rate and ribosomal mass fraction scale negatively, while the mass fraction of envelope-producing enzymes scales positively with surface-to-volume. These relationships are compatible with growth measurements and quantitative proteomics data reported in the literature.