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. Author summary It is widely known that smaller eukaryotes tend to grow faster. However, this trend does not hold in bacteria, where small-celled species grow slower. We propose that small bacteria – compared to their larger counterparts – have to invest a greater fraction of the total resources to cell envelope owing to their large surface-to-volume ratio, leaving fewer resources to internal biosynthetic processes that build the cell. By representing the cell as being composed of proteins (that convert nutrients into biomass), and cell envelope, we find that cells with large surface-to-volume ratio grow more slowly because they have to invest resources in the production of the cell envelope and the enzyme machinery that builds this structure, thus leaving fewer resources to ribosomes that replicate the cell. These predictions are corroborated by comparison with growth rate data across more than 200 bacterial species. ### Competing Interest Statement The authors have declared no competing interest.