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Microbiology and Molecular Biology Reviews, December 2004, p. 639-668, Vol. 68, No. 4
1092-2172/04/$08.00+0     DOI: 10.1128/MMBR.68.4.639-668.2004
Copyright © 2004, American Society for Microbiology. All Rights Reserved.

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

Patrick P. Dennis,1* Mans Ehrenberg,2 and Hans Bremer3

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

   SUMMARY
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The first part of this review contains an overview of the various contributions and models relating to the control of rRNA synthesis reported over the last 45 years. The second part describes a systems biology approach to identify the factors and effectors that control the interactions between RNA polymerase and rRNA (rrn) promoters of Escherichia coli bacteria during exponential growth in different media. This analysis is based on measurements of absolute rrn promoter activities as transcripts per minute per promoter in bacterial strains either deficient or proficient in the synthesis of the factor Fis and/or the effector ppGpp. These absolute promoter activities are evaluated in terms of rrn promoter strength (Vmax/Km) and free RNA polymerase concentrations. Three major conclusions emerge from this evaluation. First, the rrn promoters are not saturated with RNA polymerase. As a consequence, changes in the concentration of free RNA polymerase contribute to changes in rrn promoter activities. Second, rrn P2 promoter strength is not specifically regulated during exponential growth at different rates; its activity changes only when the concentration of free RNA polymerase changes. Third, the effector ppGpp reduces the strength of the rrn P1 promoter both directly and indirectly by reducing synthesis of the stimulating factor Fis. This control of rrn P1 promoter strength forms part of a larger feedback loop that adjusts the synthesis of ribosomes to the availability of amino acids via amino acid-dependent control of ppGpp accumulation.


   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 Vmax and Km (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.

Primary Control of Ribosomal Protein Synthesis

The first model to explain the control of ribosome synthesis was proposed by Maaloe (83), who made two ad hoc assumptions; one about the factor controlling rRNA synthesis and another about the growth rate-dependent control of this factor: (i) the rate of rRNA transcription is positively controlled by one of the r-proteins and is thereby adjusted to the rate of synthesis of the primarily controlled r-protein and (ii) r-protein promoters are constitutive, and in rich media their activity increases passively due to the repression of amino acid and other biosynthetic operons by exogenous nutrients, which increases the concentration of free RNA polymerase.

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.

Stringent and Relaxed Responses

The real start and experimental basis for a solution of the problems related to the control of rRNA synthesis was the discovery of the relA gene, followed by the elucidation of its function as a ppGpp synthetase. The first important observation was reported over 40 years ago in a study of a bacterial mutant that responds abnormally to amino acid starvation (123). In wild-type bacteria, the accumulation of rRNA immediately ceases if any one amino acid is in short supply. Stent and Brenner (123) concluded that RNA synthesis (actually stable RNA, i.e., rRNA and tRNA synthesis) has a stringent requirement for the presence of all 20 amino acids. Accordingly, the cessation of rRNA synthesis under these conditions became known as the stringent response. In contrast, in the mutant strain, stable RNA accumulation continues for some time during the starvation until it also ceases; i.e., the stringent amino acid requirement was apparently relaxed. This became known as the relaxed response.

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).

Control by Amino Acids

A stimulation of rRNA synthesis, as observed in the relaxed response, can also be induced in wild-type (relA+) bacteria by any inhibition of protein synthesis, e.g., by the antibiotic chloramphenicol (56, 69, 72) or by the inhibition of translation initiation (26). At least a partial explanation for this stimulation was suggested by the finding that the average charging of tRNAs with amino acids actually increases during deprivation for a single amino acid (138); i.e., any inhibition of ribosome function produces a rise in amino acid pools comparable to a nutritional shift-up from a minimal to an amino acid-supplemented medium. This suggested that amino acids play an essential role in the control of rRNA synthesis: the higher the rate of amino acid supply in relation to the capacity of ribosomes to consume amino acids in protein synthesis, the greater the stimulation of rRNA synthesis. However, if all amino acid levels are high except for the one amino acid that is missing, then it is not judicious for the bacteria to make more ribosomes. The mechanism that prevents this involves the function of RelA, which overrides the stimulation by amino acids and inhibits rRNA synthesis under such conditions.

Discovery of ppGpp Synthetase I

The observations described above made it clear that relA function is involved in the control of rRNA synthesis. In an attempt to link the reduction in rRNA synthesis during the stringent response to a reduction in the nucleoside triphosphate (NTP) concentrations, Cashel and Gallant discovered instead two new kinds of nucleotides that they named magic spots I and II (MSI and MSII). These nucleotides are formed during amino acid starvation in relA+ but not in relA mutant bacteria (21). MSI and MSII were later identified as guanosine tetra- and pentaphosphate (ppGpp and pppGpp, respectively) (22). Following this discovery, it was soon found that relA codes for a ribosome-associated guanosine tetra- and pentaphosphate synthetase (PSI) that converts GDP or GTP in vitro to ppGpp and pppGpp, respectively, when ribosomes are idling at A-site codons in a reaction that depends on the presence of cognate deacylated tRNA (52). In vivo, pppGpp is rapidly converted to ppGpp by a pppGpp-5'-phosphohydrolase (51). These and further observations suggested that ppGpp is involved in the control of rRNA synthesis. Subsequently, it was observed that ppGpp specifically inhibits rRNA synthesis in vitro (50, 65, 66 130-132), presumably by reducing the affinity of the RNA polymerase to stable RNA promoters (50, 53, 65, 66, 98). Thus, unless these in vitro effects are artifactual, they indicate that ppGpp is a direct effector and responsible for at least part of the in vivo inhibition of rRNA synthesis during the stringent response.

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.

Differential Inhibition of rrn P1 and P2 Promoters by ppGpp

As was mentioned above (see Introduction), all seven rRNA (rrn) genes of E. coli have two similar promoters, about 120 nucleotides apart, called P1 and P2 (46). It was found that ppGpp preferentially inhibits transcription from P1 (35, 47, 62, 73, 110, 111, 141) in a way that depends on the presence of a discriminator sequence (GCGC) bordering the –10 (TATAAT) recognition sequence of P1 but not P2 promoters (139, 140).

Discovery of ppGpp Synthetase II

The observations described above can explain the inhibition of rRNA synthesis during the stringent response as a result of a relA-dependent accumulation of ppGpp. However, the situation during normal exponential growth was unclear, since the growth rate-dependent control of rRNA synthesis is more or less the same in relA+ and relA bacteria. Since relA+ and relA bacteria produce similar low basal levels of ppGpp during exponential growth, it was suspected that the relA1 mutation used in those earlier studies was leaky. However, this idea did not fit the observation that the basal level of ppGpp in relA bacteria drops and essentially disappears during the relaxed response. For these and other reasons, it was suggested that E. coli might have a second ppGpp synthetase (PSII) that is active during exponential growth (40, 42, 72, 86, 103, 104, 125).

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.

RNA Polymerase Partitioning by ppGpp

The ratio rs/rt between the synthesis rates of stable tRNA and rRNA (rs) and of total RNA (rt) decreases monotonically with increasing levels of ppGpp. At near zero levels of ppGpp, during growth in amino acid-supplemented media or during the relaxed response, rs/rt has a value greater than 0.9, i.e., more than 90% of all RNA made in the bacteria is stable rRNA and tRNA and less than 10% is mRNA. In contrast, at increasingly higher levels of ppGpp during growth in minimal media or during the stringent response, rs/rt approaches a smallest value of 0.25; i.e., 25% of all RNA synthesized at any instant is stable RNA and 75% is mRNA (8, 17, 107). The residual rRNA synthesized under the latter conditions originates almost exclusively at the P2 promoters of rrn genes (141). It was therefore proposed that ppGpp determines the partitioning of RNA polymerase into stable RNA- and mRNA-synthesizing fractions (17, 107).

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 rs/rt, 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 rs/rt maintained under all conditions supports the idea that ppGpp controls rs/rt 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."

Ribosome Feedback Models

Before describing the ribosome feedback models, a clarification of the terminology is required. The term feedback regulation (more precisely negative feedback) implies that the value of a controlled parameter is kept nearly constant by a mechanism that senses deviations from the controlled value and generates a signal that leads to an adjustment of this value. This is to be distinguished from a biochemical equilibrium, in which the accumulation of a product inhibits the net rate of the reaction. Since at different growth rates neither the concentrations of total or translating ribosomes nor the rate of ribosome synthesis is constant, it can be asked whether there is any evidence that feedback regulation is involved in the control of ribosome 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 rs/rt 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, rs/rt, 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).

Passive Control by Free RNA Polymerase Concentration

Whereas the RNA polymerase partitioning model described above assumed that ppGpp was a direct effector in the control of rRNA synthesis, the proponents of the ribosome feedback models excluded such a direct effector role of ppGpp. As a possible way out of this dilemma, Jensen and Pedersen (59) proposed a model of global transcriptional control of stable RNA and mRNA synthesis that followed the ideas of the first Maaloe model described above except that now rRNA promoters, not r-protein promoters, were assumed to be constitutive. They made the following additional assumptions: (i) mRNA promoters have high Vmax/Km ratios but low values of Vmax and Km; (ii) stable RNA promoters have low Vmax/Km ratios but high Vmax and Km values; (iii) the Michaelis-Menten parameters of mRNA and stable RNA promoters are unchanged by ppGpp; (iv) elevated levels of ppGpp induce frequent pausing during the transcription of both mRNA and stable RNA genes; (v) ppGpp-dependent transcriptional pausing decreases the free RNA polymerase concentration; and (vi) all ppGpp, including basal levels, originates from PSI as a result of ribosome idling when uncharged tRNA binds to ribosomal A-sites.

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.

Control of rRNA Synthesis in the Absence of ppGpp

The construction of {Delta}relA {Delta}spoT double deletion (double null) strains devoid of measurable ppGpp was first reported from the Cashel laboratory in 1991 (137). Already a year earlier, the Gourse laboratory had determined the expression of lacZ driven by the rrnB P1 promoter on a lysogenic {lambda} phage integrated into the chromosome of one of the Cashel double null strains (43). They found that, in the absence of ppGpp, lacZ expression increases with growth rate in a manner similar to that in ppGpp-proficient strains. Accordingly, they concluded that "guanosine 3'-diphosphate 5'-diphosphate is not required for growth rate-dependent control of rRNA synthesis in Escherichia coli" (43).

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, rs/rt, 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 rs/rt values remained approximately constant in the ppGpp-deficient strains (58), whereas they increased with growth rate in ppGpp-proficient strains (107).



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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).

 
Since it had been shown previously that the cytoplasmic level of ppGpp causally determines rs/rt (8), the constancy of rs/rt in the absence of ppGpp was taken as support for the previous conclusion that ppGpp is involved in the control of rRNA synthesis (58). Furthermore, the original isolation of mutations in the gene for PSII was based on the idea that reduced basal levels of ppGpp should stimulate P1-lacZ expression and thereby provide a selectable marker for a mutationally defective PSII gene (57). The fact that this strategy was successful and led to the correct identification of spoT as the PSII gene provides strong support for the conclusion that ppGpp is involved in the control of P1. Today, this idea is shared by Gourse and collaborators (see section about New ppGpp Model below).

NTP Substrate Model

Gourse and collaborators measured relative NTP concentrations in bacteria growing at different rates and, in addition, in vitro rrn transcription rates at different NTP concentrations. By comparing the in vivo and in vitro observations, they concluded that initiation at rrn promoters is controlled by growth rate-dependent changes in the concentrations of the initiating NTPs (44). This became known as the NTP model for the control of rRNA synthesis. As mentioned above, it was proposed that initiating NTPs were the controlling signals in the translational ribosome feedback model and that increased consumption of NTPs during increased translation might reduce the NTP pools, so that initiation at rrn promoters is selectively reduced (44).

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 Km 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 (Vmax = 83 nucleotides/s, Km = 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 ([NTPf] > 4 Km), still above 80% saturation for initiation.

New ppGpp Model

In recent in vitro studies, Gourse and collaborators showed that (i) the rate of initiation of transcription at the rrnB P1 promoter saturates at a much lower concentration of RNA polymerase than the rate of initiation at a promoter for amino acid biosynthetic enzymes; (ii) the rate of open complex formation at rrnB P1 but not at the amino acid promoter is reduced by ppGpp; and (iii) the open complex is destabilized at all studied promoters by the action of ppGpp (10, 11). From these data and additional in vivo experiments, they suggested that, in contrast to amino acid promoters, rRNA promoters are always saturated with RNA polymerase. According to this model, an increasing level of ppGpp in the cell reduces the Vmax for initiation of transcription of rRNA operons, which results in an increased concentration of free RNA polymerase in the cell. This, in turn, enhances the activities of promoters for amino acid biosynthesis and other unsaturated promoters.

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).

Kinetic Constants of rrn Promoters

Our approach to studying the in vivo control of rRNA synthesis during exponential growth (78, 143) is related to the ideas expressed by Jensen and Pedersen (59) (see above). It is based on a determination of the Michaelis-Menten parameters of RNA polymerase-rrn promoter interaction, Vmax and Km. If these parameters are constant, the promoter is defined as constitutive, and if they change, the promoter is defined as regulated. The values of Vmax and Km include all contributions caused by specific regulatory proteins and effectors as well as general conditions for transcription, such as superhelicity of DNA templates (74, 100, 136) and NTP substrate concentrations (44). Any changes in the values of Vmax and/or Km with different growth conditions define promoter-specific control in an unambiguous manner. In this way the previously suggested roles of Fis and ppGpp have been confirmed and quantitated. The results indicate that, during steady-state exponential growth, ppGpp (and its influence on the synthesis and activity of the transcriptional activator Fis) is the only factor involved in the growth medium-dependent control of rrn promoter strength (Vmax/Km).

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.

Current Status of the Field

Despite over four decades of research in numerous laboratories, the problem of the control of ribosome synthesis has remained controversial. Most recently, rRNA promoters were proposed to be subject to three different kinds of control: stringent control as a response to amino acid availability, feedback control as a response to changes in gene dosage, and growth rate-dependent control as a response to changes in the growth medium (88, 115-117). These controls were assumed to involve the effectors ppGpp, initiating NTPs, and others yet to be discovered. The conclusions were based on observed correlations between relative ppGpp or ATP levels, respectively, and relative rrnB P1 promoter activities. However, the interpretation of these observations is ambiguous because the various relative values for the concentrations of ppGpp, NTPs, and promoter activities were measured with different reference units that themselves change during the medium shift conditions studied. Since changing rrn gene dosages were not taken into account, relative promoter activities (i.e., reflecting rates of transcript initiation per rrn promoter) were actually not measured. Furthermore, to show the in vivo effects of initiating NTPs and ppGpp, it is necessary to measure absolute cytoplasmic concentrations of NTPs and to separate the effects of changing free RNA polymerase concentrations from the effects of ppGpp on RNA polymerase-rrn promoter interactions.

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.

Relationship between rRNA Synthesis and Growth Rate

Before describing the theory of transcript initiation, three related background issues are addressed that deal with the relationships between rRNA synthesis and growth rate: (i) the definition of balanced, steady-state exponential growth; (ii) the physiological balance of ribosome concentration and activity that determines the exponential growth rate; and (iii) the so-called square relationship between rRNA synthesis and growth rate.

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 {tau} is the doubling time in minutes, ln2/{tau} is the exponential growth rate per minute (the reciprocal, {tau}/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/{tau}). 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, Nr, 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/{tau}) equals the product of the ribosome concentration, given as the number of ribosomes per amount of protein (Nr/P), times the rate of protein synthesis per average ribosome [(dP/dt)/Nr]. 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, er (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 ßr and the protein synthesis rate per average active ribosome is defined as the peptide chain elongation rate, cp, then it follows that er = ßr · cp, 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 (Nr/P), or the proportion of ribosomes actively engaged in translation (ßr; active ribosomes per total number of ribosomes), or the peptide chain elongation rate (cp; amino acid residues polymerized per minute per active ribosome), or by any combination of changes in these factors. ßr 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 (Nr/P) and peptide chain elongation rate (cp). 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 cp. If the conditions are such that this is not possible, then cp 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.



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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.

 
The following review of our analysis of the growth rate-dependent control of rRNA synthesis describes only the in vivo effects of ppGpp and ppGpp-dependent Fis synthesis on the initiation of transcription from rrn promoters and excludes a discussion of the control of ppGpp levels by the growth medium. The latter involves complex controls of cytoplasmic amino acid levels, of ribosome function, and of the synthesis and turnover rates of ppGpp. These phenomena are not yet fully understood and must await further studies before they can be brought into a full picture of the control of ribosome synthesis by the growth medium (see the section about Perspective and Outlook at the end of this review).

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 Nr/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 Nr in equation 2a, these two expressions together with the definition er = (dP/dt)/Nr can be used to write the rRNA synthesis rate per amount of protein as

3
Thus, if er 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, er has been determined from measurements of RNA and protein in absolute units; all such measurements have indicated that er 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).

Theory of Transcript Initiation under In Vivo Conditions

The theory of transcript initiation has been derived in the past from in vitro transcription studies with purified RNA polymerase and promoter-carrying DNA fragments (see the review by Record et al. [101]). In the following, an extended version of this theory that applies to the in vivo situation is presented (78). During exponential growth in vivo, the transcription of a given gene is initiated and terminated at a constant rate, and the concentration of free RNA polymerase is maintained at a steady-state level in a manner that has not been possible to duplicate in vitro.

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, RPinit(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 {sigma} (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 {sigma} 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/(kI[Rf]) is the average time required for an RNA polymerase with free concentration [Rf] to bind the promoter, 1/kII is the average time for the RNA polymerase to go once from RPc1 to RPo2, 1/kIII is the average time for it to go once from RPo2 to RPinit(1), 1/kIV is the time required for it to go from RPinit(1) to TC(m + 1), 1/kV is the time required to sufficiently elongate the transcript to regenerate a free promoter, 1/kI is the average time the polymerase remains in the closed complex before dissociating again from the promoter, 1/kII 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 Vmax and Km and the concentration of free RNA polymerase, [Rf]:

(4)
V is the rate of transcript initiation at the promoter (initiations/minute), Vmax is the maximum activity at promoter saturation (initiations/minute), [Rf] is the concentration of free RNA polymerase, and Km is the concentration of free RNAP at half-maximal rate. The factor on the right side, 1/(1 + Km/[Rf]), represents the probability that the promoter is occupied by an RNA polymerase. For [Rf] -> {infty}, this factor approaches 1.0, so that V approaches Vmax. The values for Vmax and Km include the effects of all rate constants involved in transcript initiation (see below). In the following, it is explained how the values for V, Vmax, Km, and [Rf] 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 ti as the average time between two transcript initiations and equal to 1/V, tmin as the average minimum time between two transcript initiations and equal to 1/Vmax, and tb as the average time required for RNA polymerase binding per transcript and equal to (Km/Vmax) · 1/[Rf] gives

(6)
Relationship 6 implies that the average time between two transcript initiations equals the sum of the average minimum time, tmin, between initiations observed under conditions of promoter saturation with polymerase plus the average time tb required for RNA polymerase binding. The time tb is proportional to the reciprocal of the free RNA polymerase concentration [Rf] 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 Pspc and the P2 promoter of rrnB (78); how the values used in this figure were obtained will be explained in the sections below. Pspc is one of the strongest mRNA promoters (78) and tmin for Pspc is seen to be about 2 s. In contrast, tmin 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 Pspc 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, Pspc 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).



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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] = {infty}; arrowheads, average RNA polymerase binding times tb at 1/[Rf] = 8 (relative value, shown as an example).

 
Effects of varying promoter concentrations. The cytoplasmic concentrations of all bacterial promoters vary during the cell cycle as a result of DNA replication and during growth in