Growth-rate-dependent partitioning of RNA polymerases in bacteria

Abstract

Physiological changes that result in changes in bacterial gene expression are often accompanied by changes in the growth rate for fast adapting enteric bacteria. Because the availability of RNA polymerase (RNAP) in cells depends on the growth rate, transcriptional control involves not only the regulation of promoters, but also depends on the available (or free) RNAP concentration, which is difficult to quantify directly. Here, we develop a simple physical model describing the partitioning of cellular RNAP into different classes: RNAPs transcribing mRNA and ribosomal RNA (rRNA), RNAPs nonspecifically bound to DNA, free RNAP, and immature RNAP. Available experimental data for Escherichia coli allow us to determine the 2 unknown parameters of the model and hence deduce the free RNAP concentration at different growth rates. The results allow us to predict the growth-rate dependence of the activities of constitutive (unregulated) promoters, and to disentangle the growth-rate-dependent regulation of promoters (e.g., the promoters of rRNA operons) from changes in transcription due to changes in the free RNAP concentration at different growth rates. Our model can quantitatively account for the observed changes in gene expression patterns in mutant E. coli strains with altered levels of RNAP expression without invoking additional parameters. Applying our model to the case of the stringent response after amino acid starvation, we can evaluate the plausibility of various scenarios of passive transcriptional control proposed to account for the observed changes in the expression of rRNA and biosynthetic operons.

Fig. 1.

Model for the partitioning of RNAPs. In exponentially growing cells all RNAPs are taken to fall into 5 classes, RNAPs transcribing mRNA (N_m) and rRNA (N_r), RNAPs nonspecifically bound to DNA (N_ns), free RNAPs (N_free), and RNAP assembly intermediates (immature RNAPs, N_interm). The total number of RNAPs per cell (N_RNAP) is the sum of the number of RNAPs in these classes. Our model describes the numbers of RNAPs in each class by equations that link them to measured biophysical parameters of the cell (see SI Text for a detailed description and Tables S1 and S2 for the parameter values, many of which are growth-rate dependent). The numbers of transcribing RNAPs (N_r and N_m) are both described by a microscopic model Eqs. 1a, 2a, and estimated directly from measured RNA synthesis rates Eqs. 1b and 2b.

Fig. 2.

Partitioning of RNAPs at different growth rates. (A) Total number of RNAPs per cell and numbers of RNAPs in the different classes as predicted by our model. (B) Concentrations of total RNAP and RNAPs in the different classes.

Fig. 3.

Growth-rate-dependent transcription from constitutive promoters. Growth-rate dependence of the transcription rates from several constitutive promoters and the rrn promoter P2. Data are taken from ref. and have been normalized to the maximal value per promoter. (For P2 we also included corresponding data from ref. .) The black curve indicates the free RNAP concentration from Fig. 2, which is proportional to the predicted transcription rate from an unsaturated constitutive promoter.

Fig. 4.

Consequences of the predicted free RNAP concentration. (A) Growth-rate-dependent regulation of the rrn promoters: Effective promoter strengths for the rrn promoters P1 (black), P2 (gray), and the pair P1-P2 (white) as calculated from the transcription rates measured in ref. . (B) Predicted mRNA expression for over- and under expression of RNAP and comparison with data from ref. . (C) Passive control during the stringent response: Concentration of free RNAPs during the stringent response relative to the concentration during the exponential growth (with a rate of 2.5 doublings per hour) before starvation.