Environment-specificity and universality of the microbial growth law

As the nutrient quality changes, the fractions of ribosomal proteins in the proteome are usually positively correlated with the growth rates due to the auto-catalytic nature of ribosomes. While this growth law is observed across multiple organisms, the relation between the ribosome fraction and growth rate is often more complex than linear, beyond models assuming a constant translation speed. Here, we propose a general framework of protein synthesis considering heterogeneous translation speeds and protein degradations. We demonstrate that the growth law curves are generally environment-specific, e.g., depending on the correlation between the translation speeds and ribosome allocations among proteins. Our predictions of ribosome fractions agree quantitatively with data of Saccharomyces cerevisiae. Interestingly, we find that the growth law curve of Escherichia coli nevertheless appears universal, which we prove must exhibit an upward bending in slow-growth conditions, in agreement with experiments. Our work provides insights on the connection between the heterogeneity among genes and the environment-specificity of cell behaviors.