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 yields expected scalings. Namely, 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.