Invariant Distribution of Promoter Activities in Escherichia coli
Cells need to allocate their limited resources to express a wide range of genes. To understand how Escherichia coli partitions its transcriptional resources between its different promoters, we employ a robotic assay using a comprehensive reporter strain library for E. coli to measure promoter activity on a genomic scale at high-temporal resolution and accuracy. This allows continuous tracking of promoter activity as cells change their growth rate from exponential to stationary phase in different media. We find a heavy-tailed distribution of promoter activities, with promoter activities spanning several orders of magnitude. While the shape of the distribution is almost completely independent of the growth conditions, the identity of the promoters expressed at different levels does depend on them. Translation machinery genes, however, keep the same relative expression levels in the distribution across conditions, and their fractional promoter activity tracks growth rate tightly. We present a simple optimization model for resource allocation which suggests that the observed invariant distributions might maximize growth rate. These invariant features of the distribution of promoter activities may suggest design constraints that shape the allocation of transcriptional resources. Cells respond to a changing environment by regulating the activity of genes. Here, we sought to understand how E. coli cells distribute their limited transcriptional resources among their target genes, and how this allocation varies with growth rate and growth conditions. To achieve this, we assayed the expression of a comprehensive library of transcriptional reporter strains under different conditions. High-temporal resolution measurements of promoter activities were obtained for different growth rates spanning recovery from stationary phase into exponential phase and eventually deep stationary phase again. We find that the genome-wide promoter activity follows a power-law distribution, which depends solely on growth rate and is independent of the specific growth conditions. Moreover, we find that the power-law distribution can be decomposed into two log-normal distributions: metabolic promoters that make up the low end of the distribution, and ribosomal promoters that make up the high end of the distribution. While distributions remained constant for a given growth rate, the ranked expression of metabolic promoters differed according to the specific condition. Thus, the invariant distribution may suggest optimal resource allocation under constrained resources. A mathematical theory is presented to explain these results.