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Control of rRNA Synthesis in Escherichia coli: a Systems Biology Approach

Division of Molecular and Cellular Biosciences, National Science Foundation, Arlington, Virginia,¹ Department of Cell and Molecular Biology, BMC, Uppsala University, Uppsala, Sweden,² Department of Molecular and Cell Biology, University of Texas at Dallas, Richardson, Texas³

SUMMARY

INTRODUCTION

HISTORICAL OVERVIEW

Primary Control of Ribosomal Protein Synthesis

Stringent and Relaxed Responses

Control by Amino Acids

Discovery of ppGpp Synthetase I

Differential Inhibition of rrn P1 and P2 Promoters by ppGpp

Discovery of ppGpp Synthetase II

RNA Polymerase Partitioning by ppGpp

Ribosome Feedback Models

Passive Control by Free RNA Polymerase Concentration

Control of rRNA Synthesis in the Absence of ppGpp

NTP Substrate Model

New ppGpp Model

Kinetic Constants of rrn Promoters

Current Status of the Field

SYSTEMS BIOLOGY APPROACH

Relationship between rRNA Synthesis and Growth Rate

Definition of balanced steady-state exponential growth.

Physiological balance of the controls of rRNA synthesis and ribosome activity.

Square relationship between rRNA synthesis and growth rate.

Theory of Transcript Initiation under In Vivo Conditions

Reactions involved in transcript initiation.

Promoter activity under steady-state conditions.

Effects of varying free RNA polymerase concentrations.

Effects of varying promoter concentrations.

Rate constants for the reactions involved in transcript initiation.

Transcriptional Control of Gene Expression

Constitutive and regulated promoters.

Control of promoter strength.

Control by exogenous and endogenous effectors.

Gene expressions observed with translation or transcription assays.

Transcriptional Activity of rrn Operons

Rationale for the method.

Measurement of protein and nucleic acids.

Calculation of rrn transcriptional activities.

The Fis paradox.

Relative Expression from rrn P1 and P2 Promoters

Use of translation and transcription assays.

Absolute Transcriptional Activities of rrnB P1 and P2

rrn P2 promoter occlusion.

Free RNA Polymerase Concentration in the Bacterial Cytoplasm

Methods for determination of free RNA polymerase concentration.

Constitutivity of the rrn P2 promoter.

rrn P1 Promoter Strength at Different Growth Rates

Control of rRNA Synthesis by ppGpp and Fis

Mathematical Modeling of the Control of rrn Transcript Initiation

Reactions involved in transcript initiation.

Rate of transcript initiation.

Maximum activity, Vmax.

Free RNA polymerase concentration at half-maximal activity, Km.

Michaelis-Menten relationship for promoter activity.

Rate constants for rrn promoters.

Reduction of P1 promoter strength by ppGpp.

PERSPECTIVE AND OUTLOOK

ADDENDUM

ACKNOWLEDGMENTS

REFERENCES

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INTRODUCTION

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An important problem of bacterial physiology is how bacteria adapt and optimize their rate of growth in response to different environments. Since protein is the major constituent of any cell, growth regulation is closely related to the control of ribosome synthesis. In fact, the number of ribosomes per amount of total protein present in a growing culture of Escherichia coli increases in nearly direct proportion to the growth rate (67, 112). The proportionality would be exact if a constant fraction of ribosomes were elongating proteins at a constant rate (83). Ribosomes are composed of RNA (rRNA) and protein (r-protein). The rate of r-protein synthesis is negatively controlled by free r-proteins, in that excessive accumulation of free r-proteins causes a reduction in the translation and lifetime of r-protein mRNA (38, 39, 63, 77, 81, 84) and thereby reduced synthesis of r-protein. Since the concentration of free r-proteins depends on the concentration of free or nascent rRNA, which titrates r-proteins, this mechanism adjusts the synthesis of r-proteins to the synthesis of rRNA. For this reason, the study of the control of ribosome synthesis centers on the control of rRNA synthesis.

The E. coli genome has seven rRNA (rrn) operons, each with two tandem promoters, P1 and P2, from which the 16S, 23S, and 5S rRNA transcripts are expressed. The P1 promoters of all seven rRNA operons have the same discriminator sequence, GCGC, bordering identical TATAAT –10 regions (63, 139, 140). Upstream of each of these P1 promoters, there is an activator region with three binding sites for the protein factor Fis (48, 74). Binding of Fis to these sites stimulates expression from P1 (reviewed in reference 63). In addition, rRNA synthesis is inhibited by the nucleotide effector ppGpp (reviewed in reference 23). After correction for position effects in the E. coli chromosome, all rrn operons are similarly expressed (27; reviewed in reference 63).

Numerous and often conflicting hypotheses about the control of rRNA synthesis in bacteria have been proposed during the last 20 years (see the following section). This control involves a feedback loop that operates in two consecutive steps. First, transcription factors (repressors or activators) and effectors (corepressors, inducers, or molecules binding to RNA polymerase, like ppGpp and nucleoside triphosphate [NTP] substrates) control the activity of rrn promoters. Second, the overall activity of these factors and effectors is controlled in response to the balance of the supply of amino acids against the consumption imposed by ribosomal function. In this review, we address the first problem, identification of the factors and effectors that directly interact with either the rrn promoter region or the RNA polymerase in a promoter-specific manner. Only when these directly interacting factors and effectors have been clearly identified can one begin to clarify the mechanisms by which the composition of the growth medium affects the activity of these factors. When this second goal is achieved as well, the control of ribosome synthesis can be said to be understood (see the section Perspective and Outlook at the end of this review).

Recently, we addressed the question about the factors controlling the interaction between RNA polymerase and the promoters of the rrnB operon with a Michaelis-Menten kinetic approach (143). The underlying rationale for this approach is the fact that any factor that affects these interactions can be defined and measured as a change in the Michaelis-Menten parameters V_max and K_m (maximum promoter activity and RNA polymerase concentration at half-maximal activity, respectively). To determine values for these parameters requires a systems biology approach, i.e., the use of mathematical tools to integrate experimental data into a logically consistent conceptional framework.

This review has two parts. First we review the various models for the control of rRNA synthesis in E. coli which have been proposed over a period of 45 years. This historical overview is unusually complex because the research that it describes has produced different and often mutually exclusive interpretations of experimental data.

The second part represents an alternative way to describe the same observations from a mathematical rather than historical perspective. This part begins with a description of the theory of transcript initiation, which forms the basis for our kinetic approach to the question of rRNA control. The following sections contain the experimental data used to estimate absolute rrn gene activities, an evaluation of the gene activity data in terms of the kinetic properties of rrn promoters, and the conclusions from these studies with regard to the control of rRNA synthesis by ppGpp and Fis. At the end, we present a kinetic model for the subreactions involved in rrn transcript initiation and the effect of ppGpp in terms of changing rate constants for these different subreactions. It is our hope that this systems biology approach will establish the necessary conceptual framework to resolve the controversies and misunderstandings that have confounded the subject area during past decades.

HISTORICAL OVERVIEW

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The control of bacterial ribosome synthesis has been an evolving topic for more than 40 years, beginning in 1958 with the classical work in Maaloe's laboratory that described the changing macromolecular composition of the bacterial cell during growth in different media (67, 112). The various hypotheses that have been proposed over the years about the identity of factors controlling rRNA synthesis as well as about the growth rate-dependent control of the concentration or activity of such factors have recently been described and discussed (143) and are here recapitulated and extended. Because of the importance of the topic, and because of the complexity of the problems involved, the contributions that have been made to this topic from many different laboratories over decades of study are so numerous that it was impossible for us to describe them all. Here we wish to acknowledge our appreciation of the work of a generation of scientists whose contributions to the field, even if not specifically mentioned in our review below, are included in a background of fundamental facts that are often taken for granted.

Several features implicit in this proposal have been verified: (i) r-protein promoters are constitutive (78); (ii) r-protein promoters are not always saturated with RNA polymerase, so that their activity depends, indeed, on the extent of repression of other genes (78); (iii) specific r-proteins participate in the regulation of ribosome synthesis (63); and (iv) synthesis of rRNA is specifically regulated (see below). However, the constitutivity of r-protein promoters does not imply that r-protein synthesis is unregulated because the mRNAs of r-protein operons contain internal elements that control their elongation, translation, and lifetime (38, 39, 63, 77, 81, 84, 118). The regulatory r-proteins specific to each operon that are not rapidly incorporated into assembling ribosomes bind to these elements, which are often structural mimics of their binding sites on rRNA, and cause transcript attenuation or rapid degradation of the entire mRNA, called retroregulation (77, 84, 118). Since the concentrations of free r-proteins depend on the concentration of free or nascent rRNA, this mechanism adjusts r-protein synthesis to rRNA synthesis, in contrast to the assumption underlying Maaloe's model.

When the mutation was mapped (4), the gene was named relA. Later, it was found that rRNA synthesis is actually stimulated during the relaxed response but this is obscured because free rRNA becomes unstable in the absence of free r-proteins, so that rRNA accumulation reaches a plateau at a steady state of breakdown and resynthesis (71, 119). An important further step in the elucidation of the amino acid requirement for rRNA synthesis was the finding that not the amino acids themselves are required, but rather the charging of all transfer RNAs with amino acids (90).

Overexpression of relA in a strain carrying a relA gene linked to the isopropylthiogalactopyranoside (IPTG)-inducible lac promoter causes an accumulation of ppGpp accompanied by a rapid decline in rRNA synthesis and growth (126). Mutants with partial resistance to this growth inhibition phenotype were found to have a mutation in the gene for the RNA polymerase ß-subunit (126). This suggested that RNA polymerase could be the target for ppGpp action. With biochemical methods, the binding site specific for ppGpp (i.e., for which GDP or GTP do not compete) on the RNA polymerase has now been located by cross-linking at the interface between the ß and ß' subunits (112, 129). Recently, the ppGpp-RNA polymerase complex from Thermus thermophilus has been studied by X-ray crystallography, where it was found that ppGpp binds near the active center with base-specific contacts between ppGpp and specific cytosine residues in the non template DNA during both transcription initiation and elongation (6).

Based on the term stringent response, reduced promoter activity at elevated levels of ppGpp is now often described as stringent control. However, this term is not clearly defined because, during the stringent response, rRNA synthesis is further inhibited by a greatly reduced RNA polymerase activity (106), presumably due to ppGpp-dependent transcriptional pausing that reduces the concentration of free RNA polymerase (64, 68) and thereby the activity of all unsaturated promoters. Therefore, stringent control may or may not include the effects of specific promoter control by ppGpp.

With lacZ expression from rrnB P1 in a relA1 strain background as a selectable indicator for PSII-derived basal levels of ppGpp, a search for mutations in the PSII gene was initiated. This search resulted in the isolation of mutants with reduced levels of ppGpp at 30°C and no detectable ppGpp at 43°C. Surprisingly, these mutations mapped in spoT (57), a gene that was already known to be coding for the major ppGpp (i.e., magic spot) hydrolase (5, 54, 70, 124), "suggesting that spoT encodes both ppGpp degradation and synthesis activities and that these two functions can be independently affected by mutation" (57). This idea was supported by the simultaneous findings in another laboratory that (i) cells with relA deletions (i.e., not only the relA1 mutants) still produce basal levels of ppGpp (137); (ii) cells with relA spoT double deletions produce no detectable ppGpp (137); and (iii) relA and spoT have extensive amino acid sequence similarity (86). Thus, either SpoT is a bifunctional enzyme or the spoT polypeptide exists in two different versions that cannot interconvert, i.e., either as a ppGpp synthetase (PSII) or as a ppGpp hydrolase. How the switch between the two activities might be mediated or how the distinct enzymatic activities might be produced is still unknown (see the section Perspective and Outlook at the end of this review).

The basal levels of ppGpp produced during exponential growth in relA⁺ and relA bacteria vary with growth rate: the poorer the medium and the slower the growth, the higher the basal (PSII-derived) level of ppGpp (107). By measuring both synthesis and degradation of ppGpp during growth in different media and under different conditions, it could be shown that the PSII activity is highly unstable (40 s average life) and requires continuous protein synthesis (89). Furthermore, the greater the number of different amino acids in the medium, the lower the PSII activity (89). These observations suggest that both PSI and PSII activities are controlled by amino acids, and that both of these enzymes are involved in the control of rRNA synthesis.

The fact that the levels of ppGpp could be experimentally controlled by changing the extent of amino acid starvation in relA⁺ and relA bacterial strains (8) shows that ppGpp levels causally affect r_s/r_t, in contrast to a mere correlation between the two. Furthermore, the fact that the ppGpp levels could be continuously varied from near zero (as observed during growth in amino acid-supplemented media) up to the highest levels (as observed during the stringent response) with the same relationship between ppGpp level and r_s/r_t maintained under all conditions supports the idea that ppGpp controls r_s/r_t not only during the stringent response but also during exponential growth in different media (8). These results identified ppGpp as a direct or indirect effector involved in the control of rRNA synthesis.

This conclusion about the control by ppGpp did not address the question of or provide a model for the initial signals involved in this control. This latter issue was addressed by the ribosome feedback models described below, as stated by Cole et al. (26): "Instead of attempting to isolate effectors acting directly on rRNA transcription, our research has concentrated on defining the initial signals leading to regulation of rRNA synthesis."

In considering feedback regulation, four basic questions should be addressed. First, which parameter is controlled and held constant? Is it total ribosomes? Or is it only translating ribosomes? Or is it something else? Only once this question is answered can one address the next three questions: What signal is generated when the parameter deviates from its controlled value? How do the deviations produce that signal? And how does that signal adjust the controlled parameter? These questions have generally not been systematically considered in the models described below. For this reason the implied meaning of ribosome feedback has changed several times during the last 20 years, each time with a somewhat different role proposed for ppGpp.

At about the time that the measurements of r_s/r_t and the basal levels of ppGpp during exponential growth at different rates were reported, Nomura and colleagues reported the effect of increased rrn gene dosage on rrn gene activity by using multicopy plasmids carrying cloned rrn operons (60). The increased rrn gene dosage was found to reduce the transcriptional activity per rrn gene present in the cell. To explain this observation, they suggested that (i) the increased rrn gene dosage leads to an excess of nontranslating ribosomes in the cell and (ii) "free, nontranslating ribosomes (i.e., in excess of the amount needed for protein synthesis) inhibit rRNA synthesis." They called this the ribosome feedback regulation model. To distinguish between the possibilities that either (i) some product of rrn operons feedback-inhibits rRNA synthesis or (ii) some factor essential for rRNA and tRNA operon transcription (for example, RNA polymerase) is limiting, the authors employed plasmids carrying a deletion in the rrn operon leading to the expression of truncated versions of 16S and 23S rRNAs. Using these rrn deletion plasmids, they did not observe an inhibition of transcription from the chromosomal rrn operons. From this observation, they concluded that the feedback involves products of intact rrn operons.

The authors indicated that their efforts to show any possible direct regulatory effects of ribosomes on the transcription from ribosomal promoters in vitro had been negative. Therefore, they considered the possibility that the apparent feedback regulation by free ribosomes is achieved indirectly. To explain the role of RelA, the authors reasoned that "a major effect of ppGpp during amino acid starvation is to inhibit the initiation of protein synthesis" (95). Accordingly, "this inhibition would lead to accumulation of free nontranslating ribosomes in stringent strains which could in turn cause the inhibition of rRNA synthesis." Thus, ppGpp was thought to be an initial effector controlling rRNA synthesis, at least at the high levels of ppGpp accumulating during the stringent response, and free ribosomes would be an additional, either direct or intermediate effector in this control.

With the same rrn plasmids as employed by Nomura and coworkers, the effects of rrn gene dosage were reinvestigated in greater detail by measuring not only rrn transcription in a given medium but also ppGpp accumulation, r_s/r_t, protein synthesis, and plasmid copy numbers during growth in different media (9). Those results indicated that increased rrn gene dosage or the presence of plasmids with deletions in their rrn operons has complex regulatory effects that involve global changes in growth rate, ppGpp accumulation, mRNA synthesis, and ribosome function that complicate the interpretation of such observations. In contrast to free ribosomes acting as inhibitors, the alternative suggestion was made that increased rrn gene dosage would reduce the concentration of free RNA polymerase and thereby reduce the transcription rate per rrn gene (19).

According to Cole et al. (26), the observations described above (60) suggested that "the rRNA synthesis rate is modulated through feedback to give the proper rate of ribosome accumulation, as determined by growth conditions." To investigate the next step in this feedback loop, the authors asked whether either free or translating ribosomes influence the RNA synthesis rate. To answer this question, they inhibited the initiation of translation by limiting the cellular concentration of IF2, which results in rapid accumulation of free, nontranslating ribosomes. The expected inhibition of rRNA synthesis was not observed; instead, rRNA synthesis was stimulated. The authors therefore proposed that translating rather than free, nontranslating ribosomes inhibit rRNA synthesis: "In other words, excess ribosomes cause a small increase in translation which in turn generates a signal leading to an eventual decrease in rRNA synthesis." This became known as the translating ribosome feedback model. Thus, whereas free ribosomes were at first thought to be both the controlled parameter and the controlling signal (i.e., ppGpp was only thought to create free ribosomes during the stringent response [60]), now translating ribosomes were thought to be the controlled parameter, but the question about the nature of the controlling signal was left open; it could have been ppGpp or some other, unknown factor (26).

Ten years later, when initiating nucleoside triphosphates were proposed to be direct effectors controlling rRNA synthesis (44) (see NTP substrate model below), that idea was linked to the translating ribosome feedback model by suggesting that initiating NTPs were the controlling signals: the increased consumption of NTPs during increased translation might reduce the NTP pools, so that rRNA synthesis is reduced (44). However, this cannot explain the increased rRNA synthesis at increased growth rates.

Recently the term feedback has received a new meaning: it was redefined as the specific effects on rrn expression associated with changes in rrn gene dosage (114). Although the original feedback models addressed the growth rate-dependent control of rRNA synthesis, it was later reported that "the feedback response of E. coli rRNA synthesis is not identical to the mechanism of growth rate-dependent control" (135). In that work feedback response and growth rate-dependent control were defined by the changes in LacZ enzyme expression from rrn P1resulting from changes in either rrn gene dosage or growth medium, respectively (see the section Current Status of the Field, below). It was then suggested that the gene dosage effects result from associated changes in NTP and ppGpp levels (114).

With regard to this latest use of the term feedback, we note that rrn gene dosage is not a parameter that is controlled by or related to feedback. Increased rrn gene dosages were only first used, unsucessfully, to generate an excess of free ribosomes. Furthermore, absolute promoter activities were measured in enzyme specific activity units (114), but enzyme expression values obtained from a promoter under different growth conditions do not reflect gene activities (see section below on Gene Expression Observed with Translation or Transcription Assays). The term absolute promoter activity needs to be defined unambiguously as the number of transcripts initiated per unit of time per promoter, not as enzyme specific activity.

At the end of this review, we propose a new feedback model, based on the principles outlined at the beginning of this section. In this new model, the feedback-regulated parameter that is held approximately constant is the function, not the concentration, of ribosomes, and the feedback signal is ppGpp (see Perspective and Outlook, below, for more details).

Their model implies that mRNA promoters are favored when the concentration of free RNAP in the cell is low and that stable RNA promoters are favored when it is high. When there is excess capacity for protein synthesis in the cell, this will lead to amino acid deprivation and elevated synthesis of ppGpp (by PSI). When the concentration of ppGpp is high, this slows down the rate of transcription of RNA polymerase molecules so that they become sequestered on DNA. This lowers the concentration of free RNA polymerase so that mRNA synthesis is favored in relation to transcription of stable RNA genes. In contrast, when amino acid supply is in excess, the level of ppGpp is low and there is little sequestering of RNA polymerase on DNA. The higher concentration of free RNA polymerase favors transcription of stable RNA genes.

There is support for several but not all of these assumptions (78; see Discussion in reference 18). In particular, their model appears to be valid for the P2 promoters of rrn operons (78). However, rrn P1 promoters are not constitutive and were later shown to be specifically regulated by ppGpp (56). Furthermore, not all ppGpp is derived from PSI (see above).

The Jensen-Pedersen model was subsequently obscured by the discovery of PSII (see above), by the associated observations on ppGpp-deficient bacteria, and by the NTP substrate model that began to dominate the discussion about the control of rRNA synthesis.

With the same double null strains from Cashel but a different rrnB P1-lacZ fusion, our laboratory later undertook a characterization of RNA and DNA synthesis in E. coli strains devoid of ppGpp (58). This consisted of a detailed study of the physiology of ppGpp-deficient strains, including measurements of ribosome concentrations and function, RNA polymerase concentrations and function, chromosome replication data, bulk mRNA gene activities and rrn gene activities (in absolute units), mRNA synthesis rates, r_s/r_t, and lacZ expression from rrnB P1, all as functions of growth rate. Direct measurements of ribosome synthesis rates were found to increase with growth rate identically in both ppGpp-proficient and ppGpp-deficient strains, which seemed to agree with the conclusion from the earlier study of Gourse's laboratory (based on lacZ expression from rrnB P1 [43]). However, identical ribosome synthesis rates at a given growth rate between the two strains were expected on theoretical grounds, given that ribosomes in the two strains are equally efficient. This follows from the definition of exponential growth and is independent of any other observations (for an explanation, see equation 3 below under Systems Biology Approach). Therefore, rrn gene activity data alone are not sufficient to draw conclusions about the control of rRNA synthesis.

In contrast to the earlier findings (43), our study (58) showed that lacZ expression from rrnB P1 was approximately constant in ppGpp-deficient strains. The reasons for this discrepancy remain unclear. It was suggested that perhaps differences in the P1-lacZ fusion constructs were responsible for it, although a later study with a different P1-lacZ fusion ruled this out (141). However, since gene expression data obtained under different growth conditions from a given promoter do not reflect the promoter activities (see Fig. 3 and text below), no conclusion about the control of the promoter was drawn from those lacZ expression data. Of more significance was the observation that r_s/r_t values remained approximately constant in the ppGpp-deficient strains (58), whereas they increased with growth rate in ppGpp-proficient strains (107).

View larger version (17K): [in this window] [in a new window]   FIG. 3. Growth rate dependence of the ß-galactosidase specific activity expressed from Pspc in E. coli and of transcription and translation parameters that determine this specific activity (data from reference 76); see the text for further explanations. (a) ß-Galactosidase specific activity. (b) Relative abundance of lacZ mRNA in total mRNA. (c) Rate of translation initiation of lacZ mRNA in relative units. (d) Average rate of translation initiation of total (bulk) mRNA in translations per minute per average mRNA molecule. This rate canbe found either from the total rate of protein synthesis per amount of mRNA [(dP/dt)/Rm] or from the peptide chain elongation rate and the average distance of ribosomes on the mRNA (see Table 3 in reference 16).

In contrast to these results, another study showed no apparent growth rate-dependent variations of NTP concentrations in E. coli (96). Whereas Gourse's laboratory used alkali for nucleotide extraction after fixation with formaldehyde (44), the other laboratory used formic acid (96). To check whether the different methods might have caused the different results, Schneider et al. (113) compared both formic acid and KOH extraction. They reported that "Although formic acid extraction resulted in higher NTP yields than those obtained by the formaldehyde/alkaline extraction method, relative changes in NTP levels (between strains or between the same strain grown under the different conditions used here) were virtually identical with both extraction methods." Thus, in their hands, NTP levels increased with growth rate independently of the method used. From these and further data, they concluded that NTP sensing by E. coli promoters is direct.

However, a repeat of these experiments by Schneider and Gourse (117) gave a contradictory result: "Extraction with formic acid indicated that ATP concentration did not change with growth rate, whereas formaldehyde treatment followed by extraction with alkali indicated that ATP concentration increased proportionally to the growth rate." Sixfold less ATP was found with alkali than with formic acid at a growth rate of 0.8 doubling/h, and threefold less was found during maximal growth in rich medium. Accordingly, the original in vivo NTP concentrations on which the NTP model was based (44) were underestimated in a growth rate-dependent manner. The authors stated: "Because ATP concentrations do not change with growth rate in cells unable to make ppGpp and rrn P1 core promoters continue to display growth rate-dependent regulation under these conditions, we conclude that at least one more regulator of rrn P1 core promoter activity (in addition to changing concentrations of initiating NTPs and ppGpp) remains to be identified."

The two methods of nucleotide extraction had also been compared previously in connection with the development of a method for quantifying ppGpp in absolute (molar) units (82). In that study, the alkali method was found to be superior to formic acid extraction and apparently 100% efficient. This is to be expected because alkali solubilizes (i.e., saponifies) the lipid membrane and completely lyses the bacteria, so that no extraction is necessary. Apparently, in the Gourse laboratory, the cells were not completely lysed during the alkali treatment, perhaps because insufficient time was allowed for the KOH to work before the sample was neutralized with phosphoric acid. Generally, whenever lysis is incomplete, large cells (which dominate in fast-growing cultures) are preferentially lysed. As a result, the ATP losses were likely to be greatest for slow-growing bacteria, as observed.

To decide finally the question of whether or not intracellular ATP concentrations increase with growth rate, the formic acid and alkali methods used by Schneider and Gourse (117) were complemented with a luciferase assay for determination of the in vivo concentration of ATP under various growth conditions. These measurements of relative ATP concentrations also suggested that the ATP concentration does not vary with the growth rate. However, this assay is associated with a number of caveats. The entry of luciferin into E. coli cells was achieved by polymyxin B treatment of the cell populations. Polymyxin B is a bactericidal antibiotic (30) that opens the cell wall for luciferin entry and ATP exit. Since cellular ATP is rapidly turning over and the luminescence assay was performed in the minute time range, it cannot be excluded that the polymyxin B treatment significantly perturbs the rates of synthesis and intracellular consumption of ATP as well as the ATP-ADP ratio. This problem is aggravated by the proposed adjustment of the luminescence peak time to the same value for all bacterial samples by variation of the concentration of added polymyxin B. Moreover, the cytoplasmic ATP concentrations (see following paragraph) are so much higher than the K_m for ATP interaction with their luciferase mutant (0.83 mM) that the assay is expected to be nearly saturated by ATP under the conditions used. In that case, the observed constant luminescence values may not reflect the cellular ATP concentrations.

In summary, it is not yet certain whether the NTP pools are constant or show variations under changing growth conditions. To decide this question, measurements of absolute intracellular concentrations of ATP (in molar units) are needed. This should not be difficult, because the high intracellular ATP concentrations make the UV absorption peak of ATP easily visible (and thus measurable) in chromatographic distributions of cellular nucleotides (82). However, even variable NTP concentrations would not significantly affect the frequency of rrn transcript initiation, because they were found to be far above the saturation level for rrn transcript initiation (in vitro, 0.8 mM [(44]). This was seen by converting the relative in vivo concentrations obtained by Gaal et al. (44) to absolute concentrations, which ranged from 4 to 10 mM (78). With a different approach, the in vivo concentrations of free NTPs can be estimated from a comparison of the RNA chain elongation rates observed in vitro (V_max = 83 nucleotides/s, K_m = 0.63 mM [14, 15]) and in vivo (85 nucleotides/s at all growth rates studied [108, 134]). This comparison suggests a lower limit of 2.5 mM for free NTPs in vivo ([NTP_f] > 4 K_m), still above 80% saturation for initiation.

In judging the significance of these in vitro observations, we note that the rate of open complex formation is not limiting the P1 promoter activity in vivo and that the free RNA polymerase concentration increases, rather than decreases, with increasing growth rate (see section below on Kinetic Properties of rrn Promoters).

The in vitro measurements of Gourse and collaborators (10, 11) were complemented by in vivo measurements of relative P1 promoter activities following nutritional shifts (88). From these experiments, they concluded that "rapid changes in the concentrations of initiating NTPs and ppGpp account for the rapid changes in rRNA expression" after the shift and "changes in initiating NTP concentration dominate regulation during outgrowth from stationary phase, whereas changes in ppGpp concentration are responsible for regulation...during exponential phase." This latter statement agrees with the conclusions from earlier studies that established a causal relationship between levels of ppGpp and the rate of rRNA synthesis relative to the total rate of RNA synthesis during exponential growth (8, 17, 107, 108) (see section above on RNA polymerase partitioning by ppGpp).

The identification of ppGpp as the only effector involved in the control of rrn promoter strength does not imply that the growth medium-dependent control of ribosome synthesis is completely understood. The most important questions remaining involve the controls of the ppGpp synthetase activities and of RNA polymerase synthesis in response to changing growth media. However, these questions are usually not addressed in the models about the control of rRNA synthesis, and they are not included in this review.

The systems biology approach to these problems described in the second part of this review unifies the description of these controls. It is shown that the growth rate-dependent control of the rrn P1 promoter is not different from stringent control or the control associated with changing rrn gene dosage. The changing P1 promoter strength depends only on the changing cytoplasmic level of ppGpp. In addition, rrn gene activities are affected by interdependent changes in RNA polymerase synthesis, free RNA polymerase concentration (depending on the concentrations and activities of all genes in the cell), and chromosome replication-dependent changes in rrn gene dosage. It is hoped that the mathematical analysis applied to these problems leads to a better understanding of transcriptional regulation in general and of the control of rrn transcription in particular.

SYSTEMS BIOLOGY APPROACH

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The main reason for the continuing controversy about the control of bacterial rRNA synthesis is the complexity of the problem that defies traditional molecular biology approaches. In this systems biology approach, we provide a theoretical framework that integrates the experimental data into a consistent picture that should finally help to resolve the controversies and misunderstandings in this field.

For this analysis, it is first necessary to develop the theory and obtain the data to which the theory can be applied. Accordingly, the first three sections below describe the theory of transcript initiation under conditions of balanced, steady-state exponential growth, and the next three sections describe how the absolute activities of the rrn P1 and P2 promoters were determined under different growth conditions. Then, in two further sections, the theory is applied to the promoter activity data to find the free RNA polymerase concentrations and kinetic constants of the RNA polymerase-rrn promoter interaction. Finally, the meaning of these results with regard to the control of rRNA synthesis is discussed. Based on these results, we present a mathematical model of the process of RNA polymerase binding to rrn promoters and the ensuing reactions that lead to transcript initiation, including the effect of ppGpp on these reactions.

Definition of balanced steady-state exponential growth. Our work on the growth rate-dependent control of bacterial rRNA synthesis applies to the physiological condition of balanced steady-state exponential growth. Balanced growth means that every component in the medium is present at saturating, nonlimiting concentrations, in contrast to chemostat growth, when one component is growth limiting (83). Steady state means that the bacteria have grown for at least 10 generations in a given medium (i.e., at least a 1,000-fold increase in mass after dilution of an overnight culture). In this condition, the rate of accumulation of every component relative to its total amount in the culture is constant in time. That is, when X is the amount of component X in a culture at time t, then the fractional increase in X per unit time, (dX/dt)/X, defines the exponential growth rate:

(1)

Here is the doubling time in minutes, ln2/ is the exponential growth rate per minute (the reciprocal, /ln2, is the time required for an e-fold increase), and µ is the growth rate in doublings per hour (equal to 60 min per h/). Equation 1 is the basis for several fundamental relationships that define the properties of exponential-phase cultures.

Physiological balance of the controls of rRNA synthesis and ribosome activity. If component X is the total protein P in the cell population, then its amount P (counted as the number of amino acids in peptide chains) can be put into equation 1 instead of X. If, furthermore, the numerator and denominator in the equation are multiplied by the number of ribosomes, N_r, the following relationship between growth rate and ribosome concentration is obtained:

(2)

This relationship says that the growth rate of an exponential-phase culture (ln2/) equals the product of the ribosome concentration, given as the number of ribosomes per amount of protein (N_r/P), times the rate of protein synthesis per average ribosome [(dP/dt)/N_r]. This expression represents the total rate of protein synthesis (number of peptide bonds made per time unit) divided by the total number of 70S ribosome equivalents in a bacterial culture and has been named ribosome efficiency, e_r (83). The total number of ribosomes includes actively translating ribosomes, free, functional ribosomes, and nonfunctional, immature ribosomes. If the fraction of actively translating ribosomes is defined as ß_r and the protein synthesis rate per average active ribosome is defined as the peptide chain elongation rate, c_p, then it follows that e_r = ß_r · c_p, and equation 2 can be rewritten (33) as

(2a)

This says that bacteria can increase their exponential growth rate by increasing either the concentration of ribosomes (N_r/P), or the proportion of ribosomes actively engaged in translation (ß_r; active ribosomes per total number of ribosomes), or the peptide chain elongation rate (c_p; amino acid residues polymerized per minute per active ribosome), or by any combination of changes in these factors. ß_r has been found to be approximately constant during exponential growth between 0.6 and 3.0 doublings/h, equal to about 0.8 (41). This means that 80% of all ribosomes are present in polysomes, whereas about 20% represent either free functional or immature nonfunctional 30S and 50S ribosomal particles (80). Therefore, the bacterial growth rate is essentially determined by the two variable factors, ribosome concentration (N_r/P) and peptide chain elongation rate (c_p). Either parameter has limit values, e.g., the bacteria cannot use more than about 25% of their total protein for ribosomal protein, and individual ribosomes cannot synthesize protein faster than at about 21 amino acids per second at saturation with their substrates (16). Below such limits, however, bacteria must balance their metabolic activities between the production of either ribosomes or factors and substrates involved in ribosome function.

It has been argued on theoretical grounds that the observed balance (see Fig. 5a and b below) serves to maximize the growth rate in different media (37). It appears that the whole bacterial metabolism is geared to supply activated amino acids (aminoacyl-tRNAs) at a rate sufficient for the ribosomes to function at nearly maximal c_p. If the conditions are such that this is not possible, then c_p drops below its maximal value. This stimulates the activities of the ppGpp synthetases (see Historical Overview, above), which produce the signal molecule ppGpp (22, 57, 137), which specifically reduces transcription of rrn operons (23, 143). The ensuing reduced ribosome synthesis leads to a new balance at which fewer ribosomes function at only a slightly reduced but still nearly maximal rate. In this manner, ribosome function is monitored to achieve the particular balance between ribosome synthesis and function that maximizes the fitness of bacterial populations.

View larger version (16K): [in this window] [in a new window]   FIG. 5. Activity of rrn operons. Ratio RNA per protein, peptide chain elongation rate, protein per oriC (initiation mass [36]), and rate of transcription per average rrn operon in wild-type and Fis-deficient E. coli strains as a function of growth rate are shown in panels a to d, respectively (data from reference 142). This figure is an evaluation of the data in Fig. 4; see the text for details. The peptide chain elongation rate is related to ribosome efficiency (see equation 2) by the factor 0.8 (the fraction of ribosomes that are engaged in translation; the remaining fraction, 0.2, are either ribosome assembly intermediates or ribo-somes between rounds of translation, as discussed in reference 16). In panel d, the vertical arrow (y) shows the apparent stimulation in rrn gene activity at a given growth rate resulting from the absence of Fis; the horizontal arrow (x) shows the reduction in growth rate at a constant rrn gene activity caused by the absence of Fis.

Square relationship between rRNA synthesis and growth rate. To define the control of rRNA synthesis, it is frequently stated that rate of rRNA synthesis increases with the square of the growth rate (60, 111), or most recently, "rRNA synthesis is proportional to the square of the culture's growth rate. The molecular basis for this phenomenon, called growth rate-dependent control, still remains unresolved, however" (117). In all these cases, the reference unit needed to define the rate of rRNA synthesis was not given (e.g., rate per gene, per cell, per mass unit, or per culture volume). However, the authors consistently cite Maaloe's work for their statement. Since both cell size and DNA content increase dramatically with growth rate (112), Maaloe suggested using the reference unit per genome equivalent of DNA (also referred to as per genome for short) rather than per cell to measure macromolecular components (83).

During moderate to fast growth, the amount of RNA per genome in Salmonella spp. and in E. coli B/r was found to increase in direct proportion to the growth rate (33, 112). This proportionality implies that the rate of RNA accumulation per genome [(dr/dt)/G] increases with the square of the growth rate, i.e., with µ² (see equation 1 above). However, this reflects the control of both RNA and DNA synthesis, i.e., the initiation and velocity of chromosome replication (13, 16, 55). Therefore, the relationship is altered in bacterial mutants that exhibit aberrant control of DNA replication but have normal control of rRNA synthesis (25), so that this square relationship is unsuited to define the growth rate-dependent control of rRNA synthesis.

The relationship has been restated with the reference per amount of protein, e.g., "the synthesis of rRNA per unit amount of protein increases with the square of the growth rate and this phenomenon is called growth rate-dependent control of rRNA synthesis" (135). This statement derives from equation 2 above as follows. Each ribosome contains the equivalent of one rrn transcript, so that N_r/P equals the number of rRNA transcripts per amount of protein, r/P. When r is used instead of X in equation 1 and instead of N_r in equation 2a, these two expressions together with the definition e_r = (dP/dt)/N_r can be used to write the rRNA synthesis rate per amount of protein as

3

Thus, if e_r were constant and independent of the growth rate, then the rate of rRNA synthesis per amount of protein, (dr/dt)/P, would indeed be proportional to µ². However, e_r has been determined from measurements of RNA and protein in absolute units; all such measurements have indicated that e_r is not constant but increases with increasing growth rate and approaches a maximum value (20, 33, 142) (see Fig. 5 below). Therefore, the square relationship does not hold. Moreover, the relationship (3) is based entirely on equation 1, which is only a logical consequence of exponential growth and therefore cannot reflect the workings of a control mechanism. Rather, the analysis of this control needs to be developed from the theory of transcript initiation applied to in vivo conditions (see below).

Reactions involved in transcript initiation. The reactions involved in the initiation of transcripts at a given promoter can be described by the following scheme (78):

In this scheme, R is the free RNA polymerase, P is the free promoter, RPc₁ is the closed complex, RPo₂ is the open complex, RP_{init(1, m)} is the initiation complex, including abortive initiations, when the transcript has a length of less than m nucleotides (m = 10), TC_{(m + 1, n)} is the transcription complex after the release of (i.e., completion of the transition between initiation and elongation) at m nucleotides when the transcript has a length of between m + 1 and n nucleotides (n = 50), and TC_{(n + 1)} is the transcription complex after promoter regeneration when the polymerase has moved n + 1 nucleotides away from the promoter. The first four reactions are described by Record et al. (101). They were originally derived for the in vitro transcription of promoter fragments, where the polymerase falls off at the end of the template immediately after the release of the factor. Reaction 5 has been added by Liang et al. (78) to describe the in vivo situation, where the RNA polymerase has to move at least 50 nucleotides away from the promoter to make sufficient room for binding of the next polymerase to the promoter. This last kinetic step limits the maximal activity of rRNA promoters and other promoters with very short promoter clearance times.

The rate constants associated with these reactions can be understood from their reciprocals. Thus, 1/(k_I[R_f]) is the average time required for an RNA polymerase with free concentration [R_f] to bind the promoter, 1/k_II is the average time for the RNA polymerase to go once from RP_c1 to RP_o2, 1/k_III is the average time for it to go once from RP_o2 to RP_init(1), 1/k_IV is the time required for it to go from RP_init(1) to TC_{(m + 1)}, 1/k_V is the time required to sufficiently elongate the transcript to regenerate a free promoter, 1/k_–I is the average time the polymerase remains in the closed complex before dissociating again from the promoter, 1/k_–II is the average time the open complex exists before reverting to the closed complex, and 1/k_–III is the average time the initiation complex exists before reverting to the open complex.

These eight rate constants (i.e., five forward and three backward reactions) determine the activity of a promoter under a given condition. The values for some of these rate constants have been estimated in vitro but are often incompatible with the situation in vivo. For example, in vitro, the time required for the formation of the open complex at the rrnB P1 promoter at saturation with RNA polymerase has recently been found to be 25 s (10). In vivo, this reaction needs to be at least 100 times faster in order to account for the rate of initiation at rrn promoters in rapidly growing cells (143) (see Mathematical Modeling rrn Transcript Initiation at the end of this review). For these reasons, we have argued that, in vivo, the reactions leading to promoter clearance and promoter regeneration rather than those leading to open complex and initiation complex formation (see the scheme above) become limiting for rrn promoter activity. In the following, we define the RNA polymerase-promoter interactions in terms of Michaelis-Menten parameters and use the scheme above as a support for interpretations and, in some cases, to constrain the parameter values.

Promoter activity under steady-state conditions. Under steady-state in vivo conditions, the activity, V, of a given promoter depends on the promoter-specific Michaelis-Menten parameters V_max and K_m and the concentration of free RNA polymerase, [R_f]:

(4)

V is the rate of transcript initiation at the promoter (initiations/minute), V_max is the maximum activity at promoter saturation (initiations/minute), [R_f] is the concentration of free RNA polymerase, and K_m is the concentration of free RNAP at half-maximal rate. The factor on the right side, 1/(1 + K_m/[R_f]), represents the probability that the promoter is occupied by an RNA polymerase. For [R_f] , this factor approaches 1.0, so that V approaches V_max. The values for V_max and K_m include the effects of all rate constants involved in transcript initiation (see below). In the following, it is explained how the values for V, V_max, K_m, and [R_f] can be estimated under in vivo conditions.

Effects of varying free RNA polymerase concentrations. The effects of a changing free RNA polymerase concentration on the rate of transcript initiation at a given promoter are seen best by writing equation 4 in its reciprocal form:

(5)

Defining t_i as the average time between two transcript initiations and equal to 1/V, t_min as the average minimum time between two transcript initiations and equal to 1/V_max, and t_b as the average time required for RNA polymerase binding per transcript and equal to (K_m/V_max) · 1/[R_f] gives

(6)

Relationship 6 implies that the average time between two transcript initiations equals the sum of the average minimum time, t_min, between initiations observed under conditions of promoter saturation with polymerase plus the average time t_b required for RNA polymerase binding. The time t_b is proportional to the reciprocal of the free RNA polymerase concentration [R_f] and is zero when the RNA polymerase concentration saturates the promoter.

This is illustrated in Fig. 1 for two constitutive E. coli promoters, ribosomal protein promoter P_spc and the P2 promoter of rrnB (78); how the values used in this figure were obtained will be explained in the sections below. P_spc is one of the strongest mRNA promoters (78) and t_min for P_spc is seen to be about 2 s. In contrast, t_min for the rRNA P2 promoter is four times less, i.e., about one initiation every 0.5 s. However, at a given nonsaturating concentration of free RNA polymerase, the binding times for P_spc are shorter (3 s during growth in glycerol minimal medium; last point on the curve) than for rrn P2 (7 s). This means that at low concentrations of free RNA polymerase, i.e., during slow growth in poor media, P_spc activity is greater than rrn P2 activity, whereas at high RNA polymerase concentrations during fast growth in rich media, P2 activity is greater. This implies that the activity of a promoter under a given condition does not always measure its strength (see the definition of the term promoter strength below in the section Control of Promoter Strength), as assumed by McClure (85). In general, rRNA promoters appear to be binding limited with fast promoter clearance times, so that they are only saturated at high concentrations of free polymerase (34). In contrast, mRNA promoters have long promoter clearance times and become saturated at lower concentrations of polymerase (78).

View larger version (14K): [in this window] [in a new window]   FIG. 1. Relative cytoplasmic concentration of free RNA polymerase [Rf] as a function of growth rate (a) and average time between two transcript initiations ti at the promoters Pspc (b) and P2rrnB (c) as a function of 1/[Rf] (data from reference 78). Dotted line, tmin at [Rf] = ; arrowheads, average RNA polymerase binding times tb at 1/[Rf] = 8 (relative value, shown as an example).