Conceived and designed the experiments: AZ UA SI. Performed the experiments: AZ SI. Analyzed the data: AZ SI. Contributed reagents/materials/analysis tools: AZ SK AB AJ AM ED UA SI. Wrote the paper: AZ UA SI.
The authors have declared that no competing interests exist.
Cells need to allocate their limited resources to express a wide range of genes. To understand how
Cells respond to a changing environment by regulating the activity of genes. Here, we sought to understand how
Bacteria face an interesting optimization problem: How to allocate limited transcriptional resources among thousands of different promoters. Beginning with the pioneering work of the Copenhagen school, several studies have measured the composition of the bacterial cell at different growth rates. Precise measurements were made of RNA, DNA, cell mass and size, as well as ribosome content
Here we study the transcriptional resource allocation in
We find that the distribution of promoter activities at a given growth rate is invariant to growth conditions. This distribution shows a heavy-tail, with promoter activities that span nearly four orders of magnitude. The distribution shape depends somewhat on growth rate: The higher the growth rate the more skewed the distribution. The distribution can be decomposed into at least two distinct classes of promoters showing different behavior between conditions: ribosomal promoters and metabolic promoters. The class of ribosomal promoters is invariably highly expressed in a correlated manner between conditions, while the promoters of metabolic proteins are expressed at low-intermediate levels and vary between different growth conditions. Fractional ribosomal promoter activity closely follows growth rate in the non-balanced growth conditions studied. We also study a simple optimization model for resource allocation, which suggests that the observed invariant distribution can maximize the growth rate.
We sought to measure the activity of
To obtain high-throughput measurements of the entire library under different growth conditions, we developed a new method using robotics. We used a robotic liquid handling system to inoculate the cells in 384-well plates, grow them in an automated incubator, and periodically transfer them to a multi-well fluorimeter/photometer. Cell density and fluorescence were measured at a 16 min resolution over 14 h of growth. In the resulting dataset, each promoter was assayed at 52 time points over the growth curve, which spanned exponential phase and entrance into stationary phase. Reproducibility of fluorescence at a given growth rate was high (coefficient of variance ∼20%,
The experiment was performed under several growth conditions (
Conditions | Maximal OD | Maximal growth rate (cell divisions per hour) |
Glucose | 0.343 (2) | 0.92(1) |
Glycerol | 0.199(1) | 0.76(1) |
No amino-acids | 0.145(1) | 0.54(1) |
Phosphate limitation | 0.139(1) | 0.76(1) |
Nitrogen limitation | 0.129(1) | 0.65(1) |
Ethanol 4% | 0.137(1) | 0.76(1) |
Numbers in parentheses are standard errors in last digit.
Maximal growth rate is the maximal growth rate which was reached by 90% of the strains.
We studied the distribution of promoter activities under diverse conditions and growth rates. We find that the distributions are heavy-tailed and approximately follow a power law P(x)∼x−2 over two decades (
The observed power-law tail is similar to that found in microarray studies that measured the distribution of gene expression
To begin to analyze this distribution, we focused on the distribution of promoter activities of two classes of genes: Ribosomal and metabolic genes. We find that ribosomal promoters are always at the high end of the distribution, whereas metabolism-related promoters are found at the low to mid ranges of the distribution (
Distributions of additional functional classes of genes also generally display defined scales at the low to mid ranges of the distribution (
Interestingly, we find that a superposition of two log-normal distributions of promoters, one with low and one with high average intensities, gives rise to a combined distribution that resembles a power-law in a log-log plot over two to three decades (
The finding that the distribution of promoter activities at a given growth rate does not depend on growth conditions may be counter-intuitive, because each condition is expected to require a different set of genes to be expressed. Indeed, we find differences in the relative compositions of expressed genes under the different growth conditions (
Shown are the rank-rank plots of ribosomal component genes
Not only is the total distribution invariant, but also the distributions of ribosomal and metabolic promoter activities are nearly invariant across different conditions (
Previous studies, conducted under balanced growth (deep exponential phase), demonstrated that total ribosomal fraction in bacteria cells increases linearly with growth rate
Shown is the sum of promoter activities of the 19 ribosomal promoters (corresponding to 63 ribosomal genes) divided by the total promoter activity of all 1,920 promoters in the library for six different conditions at 30°C. Linear regression of the data is also shown (R2 = 0.97±0.03). Note that at different environmental conditions the cells reach different maximal growth rates (highest in the glucose condition and lowest in the condition with no amino acids). Standard errors are shown for three representative growth rates for each condition.
Importantly, nearly the same linear curve is found for different growth conditions and phases of growth (
The fact that the fraction of ribosomal promoter activities increases linearly with increasing growth rates can explain the more skewed distribution at higher growth rates (
We present a simple model that can explain the invariance of the fractional ribosomal promoter activities under a framework of optimal resource allocation. We follow the pioneering work of Ehrenberg and Kurland
Consider a cell that has two types of proteins: ribosomal proteins
To proceed, note that cell growth under most conditions is limited by the rate of protein production. Thus one seeks to increase
The resource
The three equations can be united to a single equation for the growth rate as a function of the fraction of ribosomal proteins,
Scaled growth rate (α/
Maximizing the growth rate with respect to
Thus the optimal fraction of ribosomes out of the total amount of proteins
The model can be extended to include, in addition to
This study used a comprehensive library of reporter strains together with a robotic assay to examine the effect of growth rate on the genome-wide distribution of promoter activities in
The finding that the distribution of promoter activities does not change in different conditions is perhaps surprising, because one might expect different sets of genes to be turned ON and OFF in each condition. We find that indeed genes are differentially expressed in each condition, but that their expression levels still fall within the same distribution.
The distribution is scale-rich
In the present study we use promoter activity measurements as indicators for allocation of transcriptional resources, where high transcription rates necessitate more transcriptional resources to be allocated. Since our experimental approach is based on measuring plasmid-based fluorescence, the copy number of virtually all of the promoters is equal. This, however, is not the case when considering ribosomal RNA genes which are clustered on the chromosome in seven copies. Moreover, this cluster is in proximity to the origin of replication which suggests that more than seven copies are likely to be found during exponential growth. Thus, when considering the multiple copy number of these genes, the distribution observed in
To understand the invariance in the observed scale-rich distribution we also studied the total fraction of promoter activities allocated to ribosomal promoters. We find that the fraction of ribosomal promoter activity in
We present a simple model that explains the invariance of the promoter activity distributions by accounting for the invariant fraction of resources allocated to the ribosomal components. The model predicts that in order to maximize growth rate, resource allocation at the optimal growth rates yields a linear relation between the fraction of ribosome components and the optimal growth rate, independently of the details of the environmental conditions. It is important to note that the model considers protein concentration units while our measurements are of promoter activity levels. This is a simplification as promoter activities should not correlate precisely with protein concentrations when considering possible post-transcriptional regulation.
Promoter activities were calculated based on measurements of growth (od) and fluorescence (GFP). In particular, the usage of a stable GFP enabled us to calculate the rate at which GFP accumulates in the cells by taking the time derivative of the fluorescence measurements. By doing so, we assumed that regulatory processes downstream to transcription (e.g. mRNA degradation, translation) are at a constant rate. While such processes may vary when conditions change throughout growth, the invariant distribution observed across all conditions suggests that such variability is minimal. Moreover, the distributions among the different conditions are always compared at a specific growth rate; thus, possible variability due to different growth conditions is probably negligible.
An interesting question is the origin of the invariant distribution of promoter activities within the class of metabolic genes. It seems that a fixed range of resources (in terms of total promoter activity) is allocated to the metabolic class of promoters. Within this fixed range of allocated resources, the relative rank of the promoters varies according to the growth condition. A model by Furusawa et al
The present experimental approach, using a robotic system to assay a comprehensive library of reporter strains, opens the way for large-scale measurements of promoter activities in
The platform used in this study measures the averaged promoter activity in a population of cells. An outstanding question is how the distribution of single cells within a population of a given reporter strain varies in different growth rates across different conditions
All media were based on M9 defined medium (0.6% Na2HPO4, 0.3% KH2PO4, 0.05% NaCl, 0.01% NH4Cl, 0.1 mM CaCl2, 1 mM MgSO4, 5·10−4% Thiamin). The media used in this study are: Gluocse (M9 minimal medium +0.5% glucose +0.1% Amino Acids (AA, Casein peptone, Pronadisa Ltd) +50 µg/ml kanamycin); Glycerol (M9 minimal medium +0.5% glycerol +0.1% AA +50 µg/ml kanamycin); No amino-acids (M9 minimal medium +0.5% glucose +50 µg/ml kanamycin); Phosphate limitation (M9 minimal medium diluted 1∶5 into M9 minimal medium lacking Na2HPO4 and KH2PO4 +0.5% glucose +0.1% AA +50 µg/ml kanamycin. pH was corrected to 7 using MOPS); Nitrogen limitation (M9 minimal medium diluted 1∶5 into M9 minimal medium lacking NH4Cl +0.5% glucose+50 µg/ml kanamycin); Ethanol (Glucose medium +4% absolute ethanol +50 µg/ml kanamycin). We chose the 4% ethanol condition since preliminary assays showed that
The library of reporter strains, each bearing a low-copy plasmid with a promoter of interest controlling fast-folding GFP (GFPmut2
We note that anaerobic conditions may arise when growing cells in small tubes (384-well plates). However, the fact that a power law distribution, in which ribosomal genes make up the higher end, is observed during well-aerated balanced growth as well (
Although changes in growth rate affect the plasmid copy number in the reporter strains
To ensure that reporter strains with high GFP expression do not show slower growth rate we analyzed the correlation between growth rate and GFP expression levels for individual strains. We find no correlation between maximal growth rate and maximal promoter activity of the strains (correlation coefficient = −0.007, p = 0.75). Furthermore,
Data was automatically obtained from the robot software (Evoware, Tecan) and processed using custom Matlab software. All OD and GFP measurements were background subtracted separately for each overnight 96-well plate cultures. Outlier cultures in which OD curves deviated more than three standard deviation of the mean OD curve for the plate, were discarded (less than 5% of cultures). For each 96-well plate, a background GFP curve was constructed by the mean of the 15% of the cultures with lowest GFP readings. These bottom 15% usually included the two strains with promoterless vector used as controls in each 96-well plate. Strains whose GFP curve was below 2 standard deviations above this background curve were considered to have undetectable promoter activity. Promoter activity was calculated as the temporal derivative of the background subtracted GFP intensity divided by the OD, PA = dGFP/dt/OD
Error bars were estimated as follows – given the standard error of 20%, estimated from the repeated strains(
We chose a subset of reporter strains with different promoter activities that together span the entire range of the power law distribution as observed during non-balanced growth in 384-well plates. This subset included 4 ribosomal genes and 28 metabolic genes. We measured promoter activity in these strains under two conditions: (1) glucose condition and (2) no amino acids condition, as described for the assays done with 384-well plates. To achieve well-aerated balanced growth, over night cultures were diluted 1∶400 and grown in wide-mouth glass tubes (15 mm width) with vigorous shake (250 rpm, 30°C). Growth was monitored by OD (600 nm) and both OD and GFP (485/535 nm) measurements were taken during exponential growth. OD and GFP were measured by removing 150 µl from the batch culture and placing in 96-well plates (Nunc) which were then assayed using Victor3 plate reader (Perkin Elmer). Promoter activity was measured by taking the time derivative of the GFP divided by OD PA = dGFP/dt/OD
Reproducibility of promoter activity measurements. Shown are the Promoter activities of 21 identical repeats of two control strains -
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Total promoter activity is relatively constant between growth conditions but strongly dependent on growth rate. Shown is the average over all growth conditions of the sum of the promoter activities at different growth rates. (a) All promoters. (b) Metabolism related promoters. Standard errors are over the different growth conditions.
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Rank-frequency plots of promoter activities for the six growth conditions of
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Rank-frequency plots of promoter activities for the six growth conditions of
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Growth rate of two representative reporter strains during balanced growth (a) in GLU condition (b) in no amino acids condition. Blue, promoterless strain; Red,
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Rank-frequency plots of promoter activities for 32 reporter strains in two conditions (a) GLU conditions (b) in no amino acids condition. The strains were grown in well-aerated glass tubes so that balanced growth was reached. The distributions were fitted to a power law distribution and the best fit results in the following exponents: (a) GLU condition; α = −1.87. (b) No amino acids condition; α = −2.2. These values are very similar to the values that best fit the distribution observed during non-balanced growth using 384-well plates (α∼−2).
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Rank frequency plot of motility, chemotaxis, energytaxis genes. Blue - glucose medium, green - ethanol, red - glycerol, cyan - no amino-acids, magenta - Phosphate limitation, black - Nitrogen limitation.
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Rank frequency plot of SOS response genes. Blue - glucose medium, green - ethanol, red - glycerol, cyan - no amino-acids, magenta -Phosphate limitation, black - Nitrogen limitation.
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Rank frequency plot of TCA cycle genes. Blue - glucose medium, green - ethanol, red - glycerol, cyan - no amino-acids, magenta -Phosphate limitation, black - Nitrogen limitation.
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Rank frequency plot of drug response/sensitivity genes. Blue - glucose medium, green - ethanol, red - glycerol, cyan - no amino-acids, magenta -Phosphate limitation, black - Nitrogen limitation.
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Rank frequency plot of cell division genes. Blue - glucose medium, green - ethanol, red - glycerol, cyan - no amino-acids, magenta -Phosphate limitation, black - Nitrogen limitation.
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Rank frequency plot of house keeping genes. These are genes that had an expression level above background in all six conditions studied (ribosomal components were excluded). Blue - glucose medium, green - ethanol, red - glycerol, cyan - no amino-acids, magenta -Phosphate limitation, black - Nitrogen limitation.
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Rank frequency plot of anaerobic respiration genes. Blue - glucose medium, green - ethanol, red - glycerol, cyan - no amino-acids, magenta -Phosphate limitation, black - Nitrogen limitation.
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Rank frequency plot of aerobic respiration genes. Blue - glucose medium, green - ethanol, red - glycerol, cyan - no amino-acids, magenta -Phosphate limitation, black - Nitrogen limitation.
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Rank frequency plot of transport genes. Blue - glucose medium, green - ethanol, red - glycerol, cyan - no amino-acids, magenta -Phosphate limitation, black - Nitrogen limitation.
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Promoter activities of ribosomal components are more correlated between conditions than metabolic promoters. Average over all pairs of conditions between the correlation coefficient of ranks for metabolic promoters (814 promoters) and ribosomal and tRNA promoters (19 promoters constituting 63 genes, making up ∼70% of known ribosomal-related promoters including ribosomal RNA and ribosomal proteins).
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Fractional promoter activity vs. growth rate of (a) the sum C′ of ribosomal promoters R and promoters of metabolic proteins P (as defined in Ecocyc
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Growth curves of
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Examples of OD measurements and calculated growth rates for six representative genes, demonstrating a plateau during exponential phase.
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Normalized promoter activities sorted according to maximal level. Each row holds the promoter activities of one promoter (normalized between 0 and 1) as in
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All promoter activities and OD at each condition.
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All of the data at α = 0.8 and α = 0.25 divisions per hour, including mean, standard deviation and CV for all values greater than zero.
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Annotation classes of each gene.
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We thank Paul Sternberg for providing lab space and resources. We also thank Eran Segal, Naama Barkai and Arbel Tadmor for valuable comments.