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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.
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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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.
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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 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."
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).
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.
relA
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
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).
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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.
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.
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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) |
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,
Nr, the following relationship between growth rate
and ribosome concentration is obtained:
![]() | (2) |
) 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) |
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.
|
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 |
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):
![]() |
![]() |
(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/(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/kIII 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) |
, 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) |
![]() | (6) |
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).
![]() View larger version (14K): [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).
|
![]() View larger version (17K): [in a new window] |
FIG. 2. Effect
of varying gene concentration on the total rate of RNA synthesis, rate
of transcription per gene, and concentration of free RNA polymerase
(data from reference 19).
The relationships are derived from an idealized cell, in which all
promoters are identical and the transcription times of all genes are
equal. The volume of the cell is 1 unit, and concentrations are given
as numbers of molecules per cell. The cell contains 2,000 RNA
polymerase molecules, and the number of promoters per cell
[Pt] is varied between 0 and 400
(abscissa in all panels). Vmax = 30
initiations/minute per promoter, and Km =
200 molecules/cell. All transcripts are 1,500 nucleotides long, and the
RNA chain elongation rate is 50 nucleotides/s. (c) The ordinate is the
total steady-state rate of transcription, i =
V · [Pt],
measured as transcripts per minute per cell. (b) The ordinate is the
steady-state rate, V, of transcription for one promoter
measured as transcripts per minute per promoter and calculated from
equation 4. (a) The ordinate is the free RNA polymerase concentration,
[Rf], calculated from equation 7 in
reference 19. For panels
b and c, the ordinates are shown in log scale to illustrate how
V and [Rf] approach zero as
[Pt] increases and the total rate of
transcription per cell, i, approaches its plateau
value.
|
Rate constants for the reactions involved in transcript initiation.
The two time parameters on the
right side of equation 6, tmin and
tb, are related to the eight rate constants of the
reactions involved in transcript initiation (above) as follows
(78) (also see
Mathematical Modeling of rrn Transcript Initiation
below):
![]() | (7) |
![]() | (8) |
![]() | (9) |
The values of kIV and kV depend on the RNA chain elongation rate and on the number of nucleotides, n, that an initiating RNA polymerase has to move away from the promoter to allow the next RNA polymerase to bind. The nascent rRNA chains are known to be elongated at a rate of about 5,400 nucleotides/min (134), and a realistic value for n is 50 nucleotides (142). Accordingly, we find for the reciprocal of the sum 1/kIV + 1/kV [i.e. kIVkV/(kIV + kV)] a value of about 110 initiations/min (5,400/50). Since the observed rRNA promoter activities approach this value during growth in rich media (see Fig. 7 below), we have argued that, for rRNA promoters, the values for kII and kIII are small compared to kIV + kV, so that for rRNA promoters, Vmax corresponds to about 110 initiations/min (142).
![]() View larger version (22K): [in a new window] |
FIG. 7. Growth
rate dependence of transcriptional activities and strength of the
rrnB P1 and P2 promoters in the absence of Fis. Data on
transcriptional activity (upper panels) and promoter strength
(Vmax/Km, lower panels) for
rrnB P1 () and P2 ( ) in
fis strains in the absence (left panels) and presence
(right panels) of ppGpp (data from reference
143). The P2 promoter
strength values ( ) in the lower panels are assumed to be
always constant (Km = 1.0,
Vmax = 110,
Vmax/Km = 110; see the
text).
|
Control of promoter strength.
At very low, nonsaturating
concentrations of free RNA polymerase
([Rf]
0), a given promoter
shows a certain rate of transcript initiation, V. The greater
this rate at a given [Rf], the stronger
the promoter. For small values of [Rf]
([Rf] << Km),
the Michaelis-Menten equation 4 above becomes
![]() | (10) |
This definition of promoter strength differs from the definition given by McClure (85): "The term promoter strength refers to the relative rate of synthesis of full-length RNA product from a given promoter, and initiation frequency expresses the same idea in absolute units of reciprocal time (e.g., 10 chains/min, once/generation, etc.)." According to that definition, promoter strength equals V, or Vmax if the promoters are saturated with polymerase, rather than Vmax/Km.
Control by exogenous and endogenous effectors. Promoters may be controlled by exogenous and endogenous effectors. For example, the lac operon and amino acid biosynthetic operons are controlled by exogenous lactose or amino acids, respectively, in the growth medium. Lactose acts as an inducer and the amino acids as corepressors. The control can in these and similar cases be studied by varying the concentration of the effector in the growth medium, often with very small effects on the growth rate or on the general physiology of the cells. This is the case when induction or repression involves only one or a few operons, e.g., when lactose or a single amino acid is added to a culture growing in glucose minimal medium or, in the classical example, when the lac operon is controlled by the concentration of the gratuitous inducer isopropylthiogalactopyranoside (IPTG) in the growth medium. Under these conditions the concentration of free RNA polymerase in the bacterial cytoplasm can be assumed to remain essentially constant, i.e., unaffected by the effector concentration in the medium, so that the observed changes in gene expression reflect a specific control of the promoter. Here the changing gene expression at increasing concentration of the exogenous effector shows a control of Vmax that depends on the probability that an effector is bound to the repressor.
Genes controlled by endogenously generated signals include the operons for rRNA, r-proteins, RNA polymerase subunits, ribosomal factors, and others. In general, these endogenous signals can only be varied by changing the composition of the growth medium, which also changes the growth rate. In these cases, any observed changes in gene activity may reflect either a specific control of the promoter or changes in free RNA polymerase concentration associated with changes in the growth rate. In addition, the observed gene expression is affected by the control of the reference unit used, total protein or total RNA. For example, growth rate-dependent control might be observed as a change in the amount of enzyme per total protein (enzyme specific activity) or in the amount of specific mRNA per total RNA with quite different results (see the following section). These complications make it difficult to interpret expression data from endogenously controlled genes.
Gene expressions observed with translation or transcription assays. An example of the ambiguities associated with the study of endogenously controlled promoters is illustrated in Fig. 3, which shows the growth rate-dependent control of ß-galactosidase expressed from the constitutive ribosomal protein promoter Pspc (78). With a translational or enzyme activity assay, lacZ expression from Pspc is seen to decrease with increasing growth rate (Fig. 3a). In contrast, with a transcriptional assay based on hybridization with a probe specific for lacZ mRNA, the proportion of lacZ mRNA per total mRNA is seen to increase with increasing growth rate (Fig. 3b). This discrepancy is not apparent when only one or the other kind of assay is used. How, then, can the discrepancy be explained? One possibility seems to be that there is translational control of lacZ mRNA. However, this is ruled out by experiments showing that the rate of translation of lacZ mRNA is almost constant and independent of the growth rate (Fig. 3c).
The explanation for the discrepancy is found from a fourth type of measurement; the rate of translation per average bulk mRNA increases steeply with increasing growth rate (Fig. 3d). This shows that the constitutive mRNAs made during fast growth in rich media have more efficient ribosome-binding sites than the average repressible mRNAs made during slow growth in poor media. As a result, the bulk mRNAs made during fast growth compete more efficiently for ribosome binding and translation, so that, despite the increasing abundance of lacZ mRNA (Fig. 3b), the translation products of lacZ mRNA become a decreasing proportion of total protein (Fig. 3a).
Such difficulties in the interpretation of gene expression data obtained at different growth rates, as illustrated in Fig. 3, are a primary reason for the continuing uncertainty about the growth rate-dependent control of rRNA synthesis in E. coli. This dilemma can only be resolved by determination of the absolute activities of rRNA promoters (initiations per minute per promoter) as functions of growth rate. In the following, it is described how this can be done.
Rationale for the method.
The in vivo rate of transcription
from the promoter of any chosen gene X can be found in
absolute units (transcripts per minute per promoter) from two kinds of
measurement. First, it is necessary to find the absolute activity of a
suitable reference gene or operon with a stable transcript that can be
accurately quantified. For this purpose we have chosen the rrn
operons, since rRNA is stable under most conditions of exponential
growth. Then, relative expressions from the promoters of gene
X and from the reference (rrn) operon have to be
determined. To this end, we have used
Px-lacZ and
Prrn-lacZ fusions with either
transcription or translation assays for lacZ
(78,
141). The absolute
activity of gene X, Vx, in transcripts per
minute per promoter, is then found as the product of the absolute
activity of the rrn reference operon,
Vrrn, and the quotient of the relative expression
values, Ex-lac/Errn-lac as
follows:
![]() | (11) |
Measurement of protein and nucleic acids. The transcriptional activity of an average rrn operon (Vrrn in equation 11 above, measured in transcripts per minute per promoter) was obtained from four kinds of primary measurements, each in absolute units per mass unit of culture (Fig. 4): (i) total protein (amino acid residues per unit of optical density at 600 nm [OD600]); (ii) total RNA (RNA nucleotides per OD600); (iii) total DNA (genome equivalents per OD600; 1 genome equivalent = 4.2 Mbp); (iv) number of copies of the replication origin (oriC copies per OD600). The determination of protein is not directly required for finding the rrn gene activity, but it is useful in interpreting observations when the growth rate is changed (e.g., as a result of Fis deficiency) or when enzyme activity data are evaluated. Since the methods used for these determinations, essential for analysis of gene expression in general and growth medium control in particular, have not been generally employed in other laboratories, they are summarized here for convenience.
![]() View larger version (15K): [in a new window] |
FIG. 4. Protein,
RNA, DNA, and oriC content in exponential cultures. The
amounts of protein, RNA, and DNA and the number of replication origins
(oriC) per mass unit of bacterial culture (OD600)
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). The
cultures were grown in glycerol minimal, glucose minimal, glucose amino
acids, and LB media (with increasing growth rate; see the text for
details).
|
The results of such measurements, plotted as functions of growth rate, are illustrated in Fig. 4 (from reference 142) for two isogenic strains; one wild type and the other carrying a deletion in the gene for the factor, Fis, that stimulates transcription from the P1 promoters of rrn operons. Each strain was grown in four different media (glycerol minimal, glucose minimal, glucose amino acids, and Luria-Bertani [LB] medium) to obtain a range of growth rates between approximately 0.7 and 3.0 doublings/h. The absence of Fis is seen to have little effect on the accumulation of protein and RNA at a given growth rate but leads to significantly lower DNA and oriC concentrations at all growth rates, reflecting a stimulating effect of Fis on the initiation of DNA replication at oriC that affects the rrn gene dosage (see below).
Calculation of rrn transcriptional activities. From the primary data of total protein, RNA, DNA, and replication origins (as in Fig. 4), four further parameters were calculated (Fig. 5): (i) the quotient RNA per protein (RNA nucleotides in total RNA per amino acid residue in total protein); (ii) the peptide chain elongation rate (amino acids polymerized per second per active ribosome); (iii) protein per oriC (amino acids/oriC); and (iv), the (wanted) rrn gene activity in absolute units (initiations per minute per rrn operon). The first two parameters are related to ribosome concentration and function (see equation 2a above). Protein per origin, also called initiation mass, is a measure for the control of DNA replication (13, 36). The rrn transcription activity was obtained by four sequential conversions from RNA, DNA, and oriC per OD600 (Fig. 4b to d) as follows:
(i) The number of rrn transcripts per OD600 of culture mass, r/OD600 = RNA/OD600 x 0.98 x 0.86/4,566, where RNA/OD600 was taken from Fig. 4b, 0.98 is the fraction of total RNA that is stable RNA (about 2% is mRNA), 0.86 is the fraction of total stable RNA that is rRNA (14% is tRNA), and 4,566 is the number of rRNA nucleotides in the 16S, 23S, and 5S transcripts stemming from one transcription of an rrn operon (see reference 16 for more explanations).
(ii) The number of rrn transcripts
initiated per minute per OD600,
(dr/dt)/OD600 =
r/OD600 x ln2/
, where
is
the culture doubling time (in minutes) (equation 1 above).
(iii) The number of rrn transcripts initiated per minute per number of oriC copies, (dr/dt)/ori = (dr/dt)/OD600/oriC/OD600, where oriC/OD600 is taken from Fig. 4d.
(iv) The number of rrn transcripts initiated per minute per rrn operon, (dr/dt)/rrn = [(dr/dt)/oriC]/(rrn/oriC). Here rrn/oriC is the number of rrn operons per oriC, which is obtained from the DNA replication velocity, the culture doubling time, and the map locations of the seven rrn operons on the E. coli chromosome, as explained in Table 1.
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View this table: [in a new window] |
TABLE 1. Map
locations and relative frequencies of the seven rrn operons in
E. coli growing exponentially at 1.0 and at 2.5
doublings/h
|
The Fis paradox. An unexpected result seen in Fig. 5d is that the rrn gene activity at a given growth rate is higher in the absence than in the presence of Fis. It is known that Fis stimulates transcription from rrn P1 promoters (48, 91, 93, 105, 133). How then can the results in Fig. 5d be correct?
To understand this, it should first be noticed that, in rich media, bacteria without Fis grow more slowly than bacteria with Fis. Therefore, what looks in Fig. 5d like a stimulation of rrn gene activity in the absence of Fis at a given growth rate (y arrow) should be viewed as an unchanged rrn gene activity at a reduced growth rate (x arrow) (92). The question then becomes why rrn gene activity is unchanged by the removal of Fis and not reduced, as was expected. There are several reasons for this. (i) Due to a reduced DNA concentration (compare DNA/OD600 for the two strains in Fig. 4c), the free RNA polymerase concentration in Fis-deficient bacteria is increased, and this increased free RNA polymerase concentration partly compensates for the lack of Fis stimulation of P1. (ii) Due to control of the ppGpp synthetase activity, Fis-deficient strains accumulate less ppGpp (see Fig. 9a below); this stimulates expression from rrn P1 promoters. (iii) Finally, Fig. 5d shows transcription from both promoters of rrn operons; generally the activity of the downstream P2 promoter is reduced by the activity of the upstream P1 promoter by an effect known as promoter occlusion (142). When P1 activity is reduced due to the absence of Fis, P2 activity increases due to the reduced promoter occlusion. Together these three effects, i.e., increased free RNA polymerase, decreased inhibition by ppGpp, and reduced P2 promoter occlusion, completely compensate for the lack of Fis stimulation of P1 with respect to rrn operon activity.
![]() View larger version (20K): [in a new window] |
FIG. 9. Effect
of ppGpp accumulation on rrnB P1 promoter strength.(a) The accumulation of ppGpp was measured during exponential growth at
different rates in the Fis-proficient () and Fis-deficient
( ) strains (data from reference
143). The results of two
determinations from the same preparation of nucleotides are shown. (b)
The promoter strength (Vmax/Km)
of rrnB P1 as a function of ppGpp in Fis-proficient
() and Fis-deficient ( ) strains was obtained by
combining the data in panel a with the data in Fig.
7d and
8d (circles),
respectively.
|
. This was important because it has been observed that
the translation of lacZ is frequently affected by structures
in the 5'-terminal mRNA immediately downstream of the
transcription start and upstream of the ribosome-binding site for
lacZ (76). In
the rrnB promoter fusions used (Fig.
6), the region immediately upstream of the lacZ translation start
was always the same
DNA, independent of the cloned promoter,
so that promoter effects on lacZ translation were absent
(76). In addition, all
fusions contained the rrn antitermination sequences
(3,
75).
![]() View larger version (31K): [in a new window] |
FIG. 6. Activity
of the P1, P2, and P1-P2 promoters. (a) and (d) ß-galactosidase
specific activity expressed from rrnB P1, P2, and the tandem
P1-P2 promoters in wild-type and Fis-deficient E. coli strains
as a function of growth rate (data from reference
142). (b and e) Ratios
of ß-galactosidase specific activities expressed from
rrnB P1 and P1-P2 and from P2 and P1-P2, respectively. (c and
f) Absolute activities of the tandem P1-P2 promoters (from Fig.
5d), of the isolated P1
and P2 promoters, and of the P2 promoter when it is in tandem,
downstream of P1. The points are plotted at the average growth rate for
the three cultures used in the fis+ and
fis strain backgrounds, i.e., carrying the
P1-lacZ, P2-lacZ, and P1-P2-lacZ fusions,
respectively. In panels c and f, the absolute activities for the P1-P2
strains (square symbols) taken from Fig.
5d are plotted at the
(slightly different) growth rates observed for the cultures used for
the ß-galactosidase determinations in panels a and d,
respectively (see the text for further
explanations).
|
fis (right panels) strains. In
fis+ bacteria, the expression from P1
increases with growth rate (Fig.
6a, circles), whereas the
enzyme specific activity expressed from P2 is nearly constant (Fig.
6a, triangles). In the
past, such lacZ expression data from rrn P1 and P2
promoters have been interpreted as an indication that the P1 promoters
are controlled by the growth rate, whereas the P2 promoters lack a
growth rate-dependent control
(49,
61). However, as was
shown above (Fig. 3),
unambiguous conclusions about promoter control cannot be drawn from
enzyme expression data at different growth rates without further
considerations. Figures 6b and e show P1 and P2 expression relative to expression from the reference P1-P2. Again, these ratios cannot be interpreted in terms of promoter activities or control; they are but a part of the total information that is required to estimate the absolute promoter activities.
Use of translation and transcription assays. The results from transcriptional or translational assays of gene expressions from endogenously controlled promoters observed at different growth rates show large quantitative discrepancies as a result of the different reference units used for the assays (Fig. 3). However, the expression ratios P1/(P1-P2) and P2/(P1-P2) are the same when they are obtained from either transcription (hybridization) assays by measuring lacZ mRNA or from ß-galactosidase activity measurements, as long as the samples for preparing RNA for hybridization assays are taken from the same cultures that are used for the enzyme activity measurements (76). This is because all effects of the different reference units cancel in the ratios. Therefore, the following determination of absolute promoter activities is independent of the type of assay (mRNA or enzyme activity) used for obtaining the expression ratios.
The rRNA chain elongation rate sets a maximum limit of about 110 initiations/minute for the rate of transcript initiation at an rRNA promoter (see the section Transcript Initiation under In Vivo Conditions above and the section Mathematical Modeling of rrn Transcript Initiation below). The initiation rate approaches 80% of this maximal value at high growth rates, and there is little indication of promoter saturation (Fig. 6c and f). For this reason we have previously concluded that Vmax for rRNA promoters is limited by the chain elongation steps that occur after transcript initiation and are required for promoter clearance and regeneration, so that Vmax is assumed to be close to 110 initiations/minute (142, 143).
There are several options to explain the varying rrn promoter activities. For example, Barker et al. (10, 11) proposed that rrn promoters are saturated, so that changes in the free RNA polymerase concentration do not contribute to the changing rrn promoter activities, and therefore both promoters must be under some form of specific growth medium-dependent control. To distinguish between this and other possibilities, it is necessary to obtain information about the concentration of free RNA polymerase in the bacterial cytoplasm. How this is done is explained in the sections below.
rrn P2 promoter occlusion. In addition to the activity of the P2 promoter when it is isolated from P1, Fig. 6c and f also show the activity of the P2 promoter when it is in tandem with and downstream of the P1 promoter (P2-tand; diamonds). These curves were obtained as the difference in activities P1-P2 (tandem) minus P1 (separated). At high growth rates, the activity of the tandem P2 promoter is seen to be reduced in comparison to the activity of the separated P2 promoter. This reduction in activity when P2 is located downstream of an active P1 promoter is known as promoter occlusion. The probability that the P2 promoter is occluded can be predicted by a theory that takes into account the transcriptional activity of the P1 promoter, the length of DNA required for promoter binding, and the length of DNA covered by a transcribing RNA polymerase. The theoretical prediction agrees well with the observed extent of occlusion (142).
Methods for determination of free RNA polymerase concentration. Three methods are available to determine the free RNA polymerase concentration in the bacterial cytoplasm.
(i) The most direct way consists of determination of the concentration of total cytoplasmic RNA polymerase, which consists of free functional and immature nonfunctional RNA polymerase. The total free RNA polymerase has been estimated from the amount of RNA polymerase subunits in DNA-free minicells of certain mutant bacterial strains (122); the immature RNA polymerase can be found from the maturation time of RNA polymerase, observed as the time lag between the synthesis of RNA polymerase subunits and their appearance in the nucleoid (109). By subtracting the immature from the total cytoplasmic polymerase, it was estimated that [Rf] is 1.2 µM for bacteria growing at 2.5 doublings/h in rich media (19). This value corresponds to 9% of the total RNA polymerase in the cell and is consistent with other available data. However, this estimate was based on experiments done in different laboratories with nonisogenic strains, and it is too complex to be readily applicable to different growth conditions and strains.
(ii) Another method consists of probing
the free functional RNA polymerase with a suitable constitutive,
unsaturated promoter that is linked to a reporter sequence. For this
purpose we have chosen the rrnB P2 promoter linked to
lacZ. The Km for RNA polymerase binding to
this promoter under in vivo conditions is not known, but one can obtain
relative values, [Rf]rel, with
this method, i.e., the free RNA polymerase concentration in the
cytoplasm relative to the free RNA polymerase concentration at which
the rrn P2 promoter shows half-maximal activity (set equal to
one concentration unit). By applying the Michaelis-Menten relationship
(equation 4 above) and setting Vmax to 110
initiations/minute (see above),
[Rf]rel (i.e., the quotient
[Rf]/Km) is found
from the rrn P2 promoter activity,
VP2:
![]() | (12) |
In contrast to these findings, it has been proposed recently that the free RNA polymerase concentration should decrease with increasing growth rate as a consequence of the increased induction of rRNA transcription at higher growth rates and the resulting sequestering of large numbers of RNA polymerase molecules on the rrn operons (10, 11). However, the results of a computer simulation of global transcriptional activities at different growth rates (19) confirmed that the free RNA polymerase concentration can be expected to increase, not decrease, with increasing growth rate (see the following paragraph).
(iii) The concentration of free RNA polymerase can also be determined from the observable concentration of total RNA polymerase, the concentration and properties of all promoters in the cell, and their associated transcript lengths and transcription velocities. Since kinetic parameters are unknown for most mRNA promoters, this method can only be applied to a simplified model by grouping all bacterial promoters into a small number of different classes with assumed average promoter properties. These average classes are based on the observed properties of certain promoters that are assumed to be typical of their class. The results of such modeling of global transcription in E. coli showed that free RNA polymerase is indeed a small fraction of the total RNA polymerase concentration and that this fraction increases with increasing growth rate as a result of the increased synthesis of total RNA polymerase (120, 121) and increased repression of mRNA genes by nutrients present in rich growth media (19).
Constitutivity of the rrn P2 promoter. Before the method to find [Rf]rel, described in the preceding section ii, was applied to observed rrn P2 promoter activities, the question as to whether the P2 promoter is constitutive had to be answered. The answer to this question is controversial. Recently, it was reported that "rrnB P2 is regulated: it displays clear responses to amino acid availability (stringent control), rRNA gene dose (feedback control) and changes in growth rate (growth rate-dependent control)" (87). However, this question depends, first, on the definition of control. In the definition used by those authors, changes in gene expression caused by changes in free RNA polymerase concentrations would be included in the term control, whereas we exclude such effects. Second, those authors define changes in enzyme expression from a given promoter as changes in gene activities, which is incorrect for changing growth conditions (see Fig. 3 above).
These issues have been addressed previously in detail
(143). In summary, the
answer is that no control or factor binding sites are known for the
rrn P2 promoter and that, under various conditions, P2 behaves
in every respect like a constitutive, unsaturated promoter. For
example, at low growth rates, P2 promoter activity increases with
growth rate in parallel with the activity of a number of other
promoters that are generally assumed to be constitutive, including the
ß-lactamase promoter Pbla and the
PL promoter of phage
(78). Furthermore,
changes in DNA concentration, e.g., in replication-defective mutants
(25), affect the
concentration of free RNA polymerase (see Fig.
2) and change P2 promoter
activity in exactly the way that would be expected for unsaturated,
uncontrolled promoters. An alternative hypothesis is that
all bacterial promoters previously considered constitutive are in fact
subject to a nonspecific and growth medium-dependent control that
results in exactly the same activity changes as would be expected for
constitutive promoters subject to varying concentrations of free RNA
polymerase. This is logically possible but appears
unlikely.
Based on the observation that rrn P2 promoter activity is reduced during the stringent response, it has been concluded previously that rrn P2 promoters are subject to stringent control (45). However, the authors did not consider the effects of free RNA polymerase. The severely reduced concentration of free RNA polymerase associated with the stringent response (106) affects all unsaturated promoters, constitutive and regulated. This effect needs to be distinguished from that of ppGpp accumulation during the stringent response, which reduces the strength of the P1 promoter but not that of the constitutive P2 promoter.
The most direct experimental support for the constitutivity of the rrn P2 promoter comes from experiments in which the nutritional quality of the growth medium was improved minimally by the addition of single amino acids to cultures growing in minimal medium. In such single-amino-acid upshifts, transcription from rrn P1 promoters increases up to 100% depending on the particular amino acid added to the medium, but the activity of the P2 promoter and the growth rate remain essentially unchanged (X. Zhang et al., unpublished data). Since the rate of total transcription increases by only a few percentage points in such single-amino-acid upshifts, no significant change in the free RNA polymerase concentration, and therefore no change in the activity of constitutive promoters, is to be expected. This agrees with the observed absence of stimulation for P2 by the single-amino-acid upshifts despite the clear stimulation of P1.
relA
spoT) and ppGpp-proficient
(relA+ spoT+)
bacteria (from reference
143) and for
Fis-deficient (
fis) and Fis-proficient
(fis+)
strains are illustrated (Fig. 7
and
8).
![]() View larger version (23K): [in a new window] |
FIG. 8. Growth
rate dependence of transcriptional activities and strength of the
rrnB P1 and P2 promoters in the presence of Fis. Data on
transcriptional activity (upper panels) and promoter strength
(Vmax/Km, lower panels) for
rrnB P1 () and P2 ( ) in
fis+ strains in the absence (left
panels) and presence (right panels) of ppGpp (data from reference
143). The P2 promoter
strength values ( ) in the lower panels are assumed to be
always constant (Km = 1.0,
Vmax = 110,
Vmax/Km = 110; see the
text).
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In Fig. 9b, the results of the ppGpp determinations in Fig. 9a are combined with the promoter strength determinations in Fig. 7 and 8. P1 promoter strength is seen to decrease with increasing cytoplasmic levels of ppGpp. In the absence of ppGpp or at low concentrations of ppGpp during growth in rich media, Fis stimulates the P1 promoter threefold (Fig. 9b). The extent of this stimulation decreases with the increasing level of ppGpp, until it is totally absent at high levels of ppGpp during slow growth in poor media. This can be explained by the negative control of Fis synthesis by ppGpp, which is expected to prevent Fis activation of P1 during slow bacterial growth (7, 93, 94).
During fast growth at very low levels of ppGpp in ppGpp-proficient strains, P1 promoter strength has the same highest value as at any growth rate in the total absence of ppGpp in ppGpp-deficient strains (compare circles in panels c and d of Fig. 7 and 8). These observations, taken together with those in Fig. 9, clearly implicate ppGpp as a negative effector in the control of P1 promoter strength. However, the results do not indicate if the control is direct or indirect. Rather than acting directly by reducing the RNA polymerase-P1 promoter interaction, ppGpp could positively control the synthesis of an inhibitory factor that binds to rrn P1 promoters. A potential candidate for such an inhibitor is H-NS, a factor that appears to inhibit transcription from the P1 promoter in vitro (2, 127, 128). However, no difference in the in vivo activity of P1 was found between hns+ and hns strains (Fig. 4b of reference 1).
The observation that ppGpp binds to RNA polymerase (24, 102, 129) suggests that this binding directly affects transcript initiation at the promoters of genes assumed to be regulated by ppGpp, including rrn P1, fis, and genes of additional unidentified factors that might affect P1 promoter strength. All such effects, direct and indirect, on P1 promoter strength are included in the ppGpp effects seen in Fig. 9b.
The question remains how it can be proved that ppGpp controls rrn P1 promoter strength directly by changing the interaction of RNA polymerase with the P1 promoter and not indirectly by controlling the synthesis or activity of another factor that binds to the P1 promoter region. It might appear that such a proof can only come from in vitro experiments. Numerous research groups have shown in vitro inhibition of P1 activity by ppGpp (10, 50, 53, 65, 66, 98). However, depending on the assay conditions (including the degree of superhelicity of the templates), the in vitro results have differed quantitatively from in vivo observations, presumably because complex in vivo conditions cannot yet be reproduced in vitro. For example, a recent study (10) found that ppGpp inhibits the formation of the open complex at P1 (see Historical Overview above, new ppGpp model), but in that study the Vmax for P1 was at least 100 times lower than was observed in vivo (143). Therefore, interpretation of existing in vitro data relating to the in vivo effects of ppGpp at the P1 promoter remains problematic.
A potential solution to this dilemma may already exist. As mentioned earlier (Historical Overview), ppGpp-dependent in vivo inhibition of the P1 promoter can be abolished by a base change in the GCGC discriminator region bordering the 10 TATAAT region of the rrn P1 promoter (139, 140). Since this region is known to be contacted only by the RNA polymerase, it is very likely that rrn P1 promoter strength is subject to a direct inhibition resulting from ppGpp binding to the RNA polymerase. Once this result is confirmed and becomes more firmly established, the further question about the molecular mechanism of P1 inhibition by ppGpp can be addressed (see Mathematical Modeling of the Control of rrn Transcript Initiation below for a step in that direction).
If we assume that ppGpp is a direct effector of transcript initiation at rrn P1, the half-maximal reduction in P1 promoter strength by ppGpp occurs at a level of ppGpp corresponding to approximately 20 pmol/OD460 (Fig. 9b). Previously, it was found that the fraction of total RNA (mRNA + tRNA + rRNA) synthesis that is stable RNA (tRNA + rRNA), rs/rt, decreases with increasing cytoplasmic level of ppGpp from a value greater than 0.9 at near zero levels of ppGpp to a minimum value of 0.25 at high levels of ppGpp (17, 107). The 25% residual rRNA synthesized at high levels of ppGpp originates predominantly at the rrn P2 promoters that are not specifically inhibited or controlled by ppGpp (141). In those previous experiments, the half-maximal reduction in rs/rt occurred at 20 pmol/OD460 (8, 17, 107), i.e., the same value as found for the half-maximal reduction in P1 promoter strength (Fig. 9b). The value of 20 pmol/OD460 corresponds to a molar concentration of about 50 µM (143). We suggest that RNA polymerase is half-saturated with ppGpp at this concentration, which then would be equal to the dissociation constant (Kd) for ppGpp binding to RNA polymerase. Bacteria growing in glucose minimal medium contain approximately 20 pmol/OD460 (Fig. 9a); therefore, we suggest that under those conditions, about half of all RNA polymerase molecules have ppGpp bound.
To summarize our conclusions about the control of rRNA synthesis: rrn P1 activity increases about 50-fold when the growth rate of a wild-type strain increases about fourfold (Fig. 8b) as a result of the combined effects of decreasing inhibition by ppGpp, increasing stimulation by Fis, and increasing concentration of free RNA polymerase. In contrast, transcription coming from the (tandem) P2 promoters of rrn operons decreases to near zero at the higher end of the growth rate range as a result of increasing P2 promoter occlusion by increasing P1 activity upstream of P2 (Fig. 6c, diamonds).
![]() |
![]() |
at
m nucleotides when the transition from initiation to
elongation is complete and 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 bp (i.e., 51 bp) away from the
promoter. The rate constants associated with these reactions are defined by their reciprocals as follows: 1/(kI[Rf]) is the average time required to bind once to the promoter (or 1/kI is the average time required to bind once to the promoter at [Rf] = 1 unit; in the following, 1 unit is assumed to be 1 µM); 1/kII is the average time to go once from RPc1 to RPo2; 1/kIII is the average time to go once from RPo2 to RPinit(1); 1/kIV is the time required 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 RNA polymerase remains in RPc1 before dissociating; 1/kII is the average time the RNA polymerase remains in RPo2 before reverting to RPc1; and 1/kIII is the average time the RNA polymerase remains in RPinit(1) before reverting to RPo2.
Rate of transcript initiation.
The average time
between two transcript initiations,
ini, equals the
sum of the times required for all five reactions involved in transcript
initiation:
![]() | (A1) |
c1 is the average
time required to form RPc1 per
initiation, including repeats due to reversibility; this time equals
the average time per initiation that the promoter stays free or the
average time required for the polymerase to bind
[
c1 equals
tb in equation 6 and in Fig.
1b and c above).
o2 is the average time per
initiation required to form RPo2 from
RPc1, including repeats; this time
equals the average time per initiation that the promoter stays in the
closed complex.
init is the average time per
initiation required to form RPinit(1) from
RPo2, including repeats; this time
equals the average time per initiation that the promoter stays in the
open complex.
TC10 is the average time
the polymerase stays in RPinit(1, m) before
the release of
; and
TC50 is
the average time the polymerase stays in
TC(m + 1, n)
after the release of
. These times equal the product of the
time required for one occurrence of the reaction (see definitions of
reciprocals of rate constants above), and the number of times,
n, the reaction is repeated for one successful
initiation:
![]() | (A2) |
![]() | (A3) |
![]() | (A4) |
![]() | (A5) |
![]() | (A6) |
![]() | (A7) |
![]() | (A8) |
![]() | (A9) |
Maximum activity, Vmax.
The maximum
promoter activity (initiations per minute) at promoter saturation is
referred to as Vmax. Its reciprocal, the minimum
average time between transcript initiations,
min = 1/Vmax, equals
the sum of the four times required for the reactions
occurring after the initial binding:
![]() | (A10) |
values above (equations A3 to
A6):
![]() | (A10a) |
min also
equals the average time per initiation that the promoter is occupied by
an RNA polymerase.
Free RNA polymerase concentration at half-maximal activity, Km.
The concentration
of free RNA polymerase at which the promoter activity is half-maximal
is referred to as Km. At this concentration, the
promoter is free 50% of the time and occupied by an RNA
polymerase 50% of the time. The half-maximal rate is obtained
when
ini = 2
min, or
when the average total time required for promoter binding, including
repeats of binding required for one successful initiation, equals the
total average time required for all reactions occurring after the
initial binding, including possible repeats of these reactions, i.e.,
if
c1 =
min. Substituting equation A2 in this identity
gives
![]() |
![]() | (A11) |
![]() | (A11a) |
Michaelis-Menten relationship for promoter activity.
With
equations A1, A2, A10, and A11a, the average time between two
initiations becomes
![]() | (A12) |
![]() | (A12a) |
Rate constants for rrn promoters. In the following, the Michaelis-Menten analysis derived above is applied to the rrn P1 promoter in the absence of both Fis and ppGpp. Under such conditions, the rrn P1 promoter resembles the constitutive rrn P2 promoter (see Fig. 7a), for which approximate values for Vmax = 110 initiations/minute and Km = 4.35 µM have been estimated (19, 143).
The last two
steps in the five-step initiation reaction scheme above require RNA
chain elongation until the RNA polymerase has moved 50 bp away from the
promoter (i.e., an rrn transcript of 50 nucleotides must be
synthesized) before a free promoter is regenerated and a new RNA
polymerase can bind. The rRNA chain elongation rate has been determined
to be 90 nucleotides per second
(134). Therefore, the
sum (
TC10 +
TC50) in equation A3 is assumed to equal
to 50/90 = 0.55 s. This gives an upper limit for
Vmax: if the times for open complex and initiation
complex formation,
o2 and
init, were negligibly small compared to
0.55 s, then Vmax would be 1.8
(= 1/0.55) initiations per second, or 108
initiations per minute. Since rrn promoter activities of 80 to
90 initiations/minute have been observed without evidence for promoter
saturation (Fig. 7b and
8b), we concluded
previously that
o2 and
init are very much smaller than 0.55 s
and in the millisecond range, so that Vmax for
rrn promoters equals about 110 initiations per
minute.
It is also known that the closed and open complexes for rrn promoters are extremely unstable, so that the existence of these complexes cannot be demonstrated by DNA footprinting (9). In contrast, the initiation complex with the first two nucleotides of the transcript, RPinit(2), is very stable and can be detected by footprinting. With the observed estimate for Km (4.35 µM), the following set of rate constants for the rrn P2 promoter and the rrn P1 promoter in the absence of Fis and ppGpp may be assumed: 1/kI = 0.35 s per [Rf], 1/kII = 0.002 s, 1/kIII = 0.002 s, 1/kIV = 0.11 s, 1/kV = 0.44 s, 1/kI = 0.01 s, 1/kII = 0.01 s, and 1/kIII = 100 s.
When these values are entered into a computer spreadsheet
which also contains the equations above to calculate the various
parameters characterizing transcript initiation, one obtains
o2 = 0.06 s,
init = 0.02 s,
TC10 = 0.11 s,
TC50 = 0.44 s, and
min = 0.56 s, corresponding to
Vmax = 106 initiations/minute; for
Km, a value of 4.35 µM is calculated, as
observed. Furthermore, in glucose minimal medium, a relative value for
[Rf] was found to be 0.19 (Fig.
1a, second data point from
the left), corresponding to 0.83 µM (= 0.19 x
4.35). With [Rf] = 0.83
µM and the values for the eight rate constants as above, the
spreadsheet calculates an initiation rate at the isolated rrn
P2 of V = 17 transcripts/minute, as observed (Fig.
6c, triangles, second
point from the left), and an average time required for promoter
binding,
c1 =
3.0 s, also as observed (Fig.
1c, second point from the
right, value above the dotted line). It should be noted that the
equations above and the spreadsheet based on them are applicable to any
promoter under any conditions.
The assumed values for kII, kIII, kI, and kII are lower limit values; these rates might be faster without much change in the promoter properties. For example, if these four rates were increased 10-fold, the promoter strength (Vmax/Km) would remain unchanged; also, the number of times the closed and open complexes have to be formed per initiation would remain unchanged.
The rate involved in promoter binding, kI, is determined by the observed Km value as long as the ratio kI/kII is not changed. Furthermore, kIII might be lower, i.e., the initiation complex might be stable for several minutes rather than for only 100 s, as assumed above, but again, this would have little effect on the promoter properties; i.e., the formation of the transcription complex is essentially irreversible, so that it is formed only once per initiation event. The reversion rates kI and kII could not be too much larger, because too many repeats of the open complex formation would reduce Vmax below the observed value unless the forward rates are also assumed to be faster. If the reversion rates kI and kII are increased fivefold in comparison to the model above, so that 1/kI = 0.0002 s and 1/kII = 0.0002 s, then 1/kI would have to be shortened to 0.022 s to obtain the observed Km value, and closed and open complex formation would have to be repeated 111 and 11 times (rather than 7 and 3 times) per initiation event, but Vmax and promoter strength would remain nearly unchanged. However, it is not clear whether such fast polymerase binding and the associated 111 repeats of the binding are compatible with actual diffusion rates within the cytoplasm, which set an upper limit to those rates.
Thus, the assumed values for the rate constants above give approximately correct Vmax and Km values and reflect the instabilities of the closed and open complexes and the stability of the initiation complex. These values are adjustable within broad limits without much change in the promoter properties and are consistent with observations. This set of values is considered a first attempt to model the process of rrn transcript initiation; this model can be expected to be refined in the future as more observational data become available.
Reduction of P1 promoter strength by ppGpp. In the absence of Fis, ppGpp reduces the strength of the rrn P1 promoter maximally about fivefold (Fig. 7d) (143). This might be entirely a direct effect of ppGpp binding to the RNA polymerase. However, as was mentioned above, it cannot be excluded that part of this reduction in promoter strength reflects the effect of a still-unidentified inhibitor that binds to the upstream region of the P1 promoters and whose synthesis is stimulated by ppGpp. In that case, the direct reduction in P1 promoter strength caused by ppGpp binding to the RNA polymerase would be less than fivefold.
For the lambda pR promoter it was found that ppGpp inhibits the formation of the initiation complex or, more specifically, the formation of the first nucleotide bond of the emerging transcript (97). For this reason (see also reference 53), we assume that ppGpp reduces kIII for the rrn P1 promoter. If we assume an eightfold reduction in kIII and leave the other rate constants in the model above unchanged, we find that the promoter strength is reduced about fivefold, as observed in Fig. 7d. This is due to a fivefold increase in Km from 4.35 to 24.4 and a modest 7% reduction in Vmax from 106 to 99 initiations/minute. The effect of ppGpp might be amplified by a greater reversibility of open complex formation and promoter binding. For example, if we assume fivefold-increased reversibility with 1/kI = 0.0002 s and 1/kII = 0.0002 s discussed above, then a fivefold reduction in kIII would have sufficed to reduce the promoter strength about fivefold, again mainly by an increase in Km.
From in vitro measurements of the time it takes to form the open complex at rrnB P1 at different ppGpp concentrations, Barker et al. (10, 11) recently concluded that ppGpp reduces the Vmax of the P1 promoter (see Historical Overview above). However, the theoretical analysis presented here shows that in vivo Vmax is essentially determined by the values for kIV and kV, which depend on the rRNA chain elongation rate. The rRNA chain elongation rate is independent of the growth rate (108, 134), presumably reflecting the combined effects of the antitermination sites of rrn operons and saturation with NTP substrates (see Historical Overview above). This makes it unlikely that, under in vivo conditions, ppGpp controls Vmax at different growth rates.
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The available evidence suggests that the peptide chain elongation rate is monitored directly to activate PSII (Zhang et al., unpublished data). As a possible model, we have suggested that a low rate of translation of spoT mRNA favors a different folding of the SpoT polypeptide, so that it becomes the highly unstable ppGpp synthetase (40-s average life [89]) rather than the stable ppGpp hydrolase. In this manner, the synthesis of ribosomes could be adjusted to the capacity of the cellular metabolism to provide sufficient substrates for the ribosomes to function efficiently. These ideas are schematically illustrated in Fig. 10.
![]() View larger version (20K): [in a new window] |
FIG. 10. Ribosome
synthesis and growth rate. The states of the feedback loop that
connects ribosome function and ribosome production to achieve an
optimal growth rate in minimal (A) and rich (B)
nutrient environments are illustrated. When the system is in balance,
expanded growth and the rate of production of new ribosomes are tuned
to the cellular capacity to increase the supply of amino acids and
other substrates required to support protein synthesis. In the two
examples, the concentrations of cellular components within the feedback
circuit (amino acids, ppGpp, free RNA polymerase, and Fis) are
indicated by the sizes of the ovals. The fluxes at different steps in
the circuit (supply of amino acids, production of ppGpp, interaction of
free RNA polymerase with the rrn P1 and P2 promoters, and
ribosome biogenesis pathway) are indicated by the sizes of the arrows.
During growth in minimal medium, where ribosome function is suboptimal,
both ppGpp hydrolyase and ppGpp synthetase activities are produced from
expression of the spoT gene, and ppGpp accumulates. During
growth in rich medium, where ribosome function is optimal, only ppGpp
hydrolyase is produced, and ppGpp does not accumulate. The relative
strengths of the rrn P1 and P2 promoters
(Vmax/Km) are illustrated by
the sizes of the promoter rectangles. Important interactions are
illustrated as solid lines connecting components. For example, during
slow growth in nutritionally poor medium, the high concentration of
ppGpp binds to the RNA polymerase and (i) inhibits the production of
the rrn P1 transcriptional activator Fis and (ii) reduces the
rrn P1 promoter strength
(Vmax/Km). During rapid growth
in rich medium, where the ppGpp concentration is low, Fis accumulates
and activates the P1 promoter. For details, see the text. The ppGpp
hydrolyase and PSII ppGpp synthetase are alternative activities encoded
by the spoT
gene.
|
Any control that involves the generation of a signal that adjusts the controlled parameter, as opposed to a simple reaction equilibrium, can be referred to as feedback control (see section Ribosome Feedback Models above). Therefore, the control of rRNA synthesis as proposed above can be referred to as ribosome feedback. Several other ribosome feedback hypotheses have been proposed previously involving free ribosomes (60), translating ribosomes (26), or rrn gene dosage (114). Since neither free nor translating ribosomes accumulate to higher levels during slow growth in comparison to fast growth, the mechanism must have a more complex response pattern than envisioned initially. The new ribosome feedback proposed here differs from the previous hypotheses in that it assumes that the velocity of translation by ribosomes, not the concentration of free or translating ribosomes, is the controlled parameter, deviations from which generate the controlling signal ppGpp.
With a role for ppGpp in the growth medium-dependent control of rRNA synthesis now well supported, the question is what remains for the future? One of the most important problems with respect to the control of ribosome synthesis and growth is to establish the mechanism of the growth medium-dependent control of ppGpp accumulation that involves the enzymatic ppGpp synthetase and ppGpp hydrolase activities of the spoT gene. Does this control indeed involve spoT mRNA translation as proposed above, or is SpoT a bifunctional enzyme whose activity is controlled by metabolic signals related to ribosome function? In addition, several more complex questions remain unanswered. One of these returns us to the balance between ribosome synthesis and function. According to equation 2a above, the same rate of protein synthesis and growth rate (i.e., where growth rate is equivalent to protein production) can be achieved with different pairs of values for ribosome synthesis (i.e., number of ribosomes per amount of protein) and function (i.e., the rate of peptide chain elongation) as long as the product of these parameters remains unchanged. The question is, what determines the fine tuning of the particular set of values for these parameters? Only if we understand how these parameters remain in metabolic balance under a given condition can we say that the problem of the control of ribosome synthesis and bacterial growth is solved.
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We also note that the interpretation of the data from P1 expression and the RNA/protein ratio (R/P) is more complex than assumed by the authors. In wild-type bacteria growing in rich, glucose-amino acids medium, R/P equals 6 (µg/µg), and the absence of DksA does not change this ratio. In contrast, in glucose minimal medium, the absence of DksA increases R/P nearly twofold, from 3.5 to 6 (µg/µg). This seems to suggest that the absence of DksA increases the rate of rRNA synthesis during growth in minimal media, when ppGpp levels are high, but not in rich media when ppGpp levels are close to zero. Although intuitively plausible, this interpretation may not be correct. Based on the definition of exponential growth (equation 1 above), R/P, together with the growth rate, determines the rate of rRNA synthesis per amount of protein and the rate of protein synthesis per ribosome ("ribosome efficiency"). The calculation shows that the absence of DksA reduces the rRNA synthesis rate per amount of protein by 33% in glucose-amino acids medium and by 15% in glucose minimal medium, in contrast to the intuitive appearance. In addition, the absence of DksA reduces the ribosome efficiency in the two media by 30 and 15% and the growth rate by 33 and 50%, respectively. These considerations highlight the complexities in interpreting the effects of DksA on the bacterial physiology; clearly, further analysis will be required for a complete understanding.
In another paper (H. D. Murray and R. L. Gourse, Mol. Microbiol. 52:1375-1387, 2004), the authors reiterate earlier conclusions (87) that the rrn P2 promoter is regulated by ppGpp and iNTP's. In vitro transcription from rrn P2 was 50% inhibited by ppGpp; but no inhibition occurred with a mutant promoter P2(dis). In addition, relative amounts of P2 reporter transcripts and of NTPs were measured in vivo after transitions from stationary to exponential phase and vice versa, and after nutritional upshifts. The in vivo experiments are difficult for us to interpret, since neither the absolute P2 promoter activities, nor the cytoplasmic NTP concentrations were determined; i.e., none of the changes associated with the shifts that alter cell volumes (for cytoplasmic NTP concentrations), DNA replication (to determine activities per promoter), reporter transcript turnover, and free RNA polymerase were measured and taken into consideration. In vitro, ppGpp decreases the formation and stability of the open complex, but since open complex formation at rrn promoters is more than 100 times faster in vivo than in vitro and therefore not limiting the rate of initiation, ppGpp is not expected to measurably affect the P2 activity in vivo. In fact, previous results showed no significant differences in the growth rate-dependent regulation of the absolute activity of rrn P2 promoters in the presence or absence of ppGpp (78). Thus, the new in vitro results do not invalidate previous in vivo observations that showed the activity of the isolated rrn P2 promoter to be unaffected by ppGpp during exponential growth at different rates.
Finally, we acknowledge a publication by L. Jöres and R. Wagner (J. Biol. Chem. 278:16834-16843, 2003) that suggests that essential steps in the ppGpp-dependent regulation of bacterial rRNA promoters can be explained by substrate competition. Those results support our conclusion that ppGpp reduces the rate constant kIII for the formation of the initiation complex (see "Mathematical modeling of the control of rrn transcript initiation" above). This is in contrast to other proposals that ppGpp exerts its effect by reducing kII, the rate of open complex formation (10, 11).
The opinions, findings, and conclusions expressed in this publications are those of the authors and do not necessarily reflect the views of the National Science Foundation.
We
dedicate this review in gratitude to Gunther S. Stent, who set the
field about the control of ribosome synthesis and growth of bacteria in
motion 45 years ago, when he and Sidney Brenner initiated the study of
a mutant with an unusual response of RNA synthesis to amino acid
starvation. Without his initial stimulus and the experience gained by
trainees in the Stent laboratory, this review would not have been
possible. ![]()
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C. Neidhardt, R. Curtiss III, J. L. Ingraham, E.
C. C. Lin, K. B. Low, B. Magasanik, W. S.
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