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J Bacteriol. 2009 Jun; 191(11): 3740–3746.
Published online 2009 Mar 27. doi:  10.1128/JB.00128-09
PMCID: PMC2681913

Varying Rate of RNA Chain Elongation during rrn Transcription in Escherichia coli


The value of the rRNA chain elongation rate in bacteria is an important physiological parameter, as it affects not only the rRNA promoter activity but also the free-RNA polymerase concentration and thereby the transcription of all genes. On average, rRNA chains elongate at a rate of 80 to 90 nucleotides (nt) per s, and the transcription of an entire rrn operon takes about 60 s (at 37°C). Here we have analyzed a reported distribution obtained from electron micrographs of RNA polymerase molecules along rrn operons in E. coli growing at 2.5 doublings per hour (S. Quan, N. Zhang, S. French, and C. L. Squires, J. Bacteriol. 187:1632-1638, 2005). The distribution exhibits two peaks of higher polymerase density centered within the 16S and 23S rRNA genes. An evaluation of this distribution indicates that RNA polymerase transcribes the 5′ leader region at speeds up to or greater than 250 nt/s. Once past the leader, transcription slows down to about 65 nt/s within the 16S gene, speeds up in the spacer region between the 16S and 23S genes, slows again to about 65 nt/s in the 23S region, and finally speeds up to a rate greater than 400 nt/s near the end of the operon. We suggest that the slowing of transcript elongation in the 16S and 23S sections is the result of transcriptional pauses, possibly caused by temporary interactions of the RNA polymerase with secondary structures in the nascent rRNA.

When Escherichia coli bacteria grow rapidly in rich media, 90% of all transcription is stable rRNA and tRNA and only about 10% is mRNA (6). Under these conditions, the activity of rRNA promoters is determined mainly by the concentration of free RNA polymerase, which, in part, depends on the velocity with which the RNA polymerase transcribes DNA (7). The transcription velocity, in addition to determining the number and spacing of RNA polymerases within an active gene, also determines the speed with which the RNA polymerase moves away from the promoter and makes room for the binding of the next RNA polymerase to the previously occupied promoter. In this way, transcription elongation affects the promoter activity (10, 22). For these reasons, the in vivo elongation rates of transcripts, including the potential variability of the rate of elongation during the transcription of various genes, is of special importance.

In the following, we analyze the distribution of RNA polymerase molecules over the rrn operon in fast-growing wild-type bacteria as visualized by electron microscopy (EM) and reported by Quan et al. (17). The distribution indicates that the transcription velocity at the beginning and end of the rrn operon is much higher than the previously determined average and that the polymerases slow down in the 16S and 23S regions of the operon. We suggest that the retardation in these later sections is caused by transcriptional pausing, either at secondary structures in the nascent rRNA transcript (12) or due to DNA sequence-related variations of the standard free energy of the moving transcription elongation complex (2).

Transcription of rrn operons. (i) Determination of the average rrn chain elongation rate.

Values of the rrn chain elongation rate, cr, are generally obtained as an average over the entire rrn transcription unit by measuring the accumulation of tRNAs from tRNA genes at the 3′ ends of rrn operons after stopping transcript initiation with rifampin (rifampicin). For rrn transcripts in E. coli K-12 grown in LB-glucose medium, Condon et al. (8) observed a transcription time of 60 s for the rrnC operon, with a length of 5,450 base pairs, corresponding to an average rRNA chain elongation rate of 91 nucleotides [nt]/s (5,450/60 = 91). This value is similar to data from most other laboratories (89 nt/s for bacteria in glucose-amino acids medium and 79 nt/s in glycerol minimal medium [18]; 86 nt/s in glucose minimal medium [17a]).

Some reported data showed significantly lower values; e.g., an elongation rate of 73 nt/s (a transcription time for rrnC of 75 s) was found in a mutant strain which in LB medium grew at only half the rate of wild-type K-12 strains (Fig. 6 of Voulgaris et al. [20]), and an exceptionally low value of 42 nt/s was found by directly observing by EM the emptying of rrn operons from RNA polymerases after transcript initiation was stopped with rifampin (Fig. 2 of Gotta et al. [14]). In those experiments, rifampin might not have instantly stopped transcript initiation.

On average, rrn transcripts elongate at a rate (cr) that is greater than that of mRNA transcripts (cm). In addition, cr is nearly constant at different growth rates, whereas cm increases with increasing growth rate (18). The higher chain elongation rate for rRNA is the result of the presence of special antitermination features located in the rrn operon leader region (1). When the antitermination sequences near the rrn promoters are removed, the rrn transcript elongation rate is reduced, and when these sequences are inserted at the front of an mRNA gene, the mRNA elongation rate is increased (19, 21). This antitermination mechanism is essential for efficient rrn transcription presumably because of the lack of coupled translation and because of the extensive secondary structures present in rRNA transcripts. At least in vitro, and probably also in vivo, transcript elongation occurs in fast spurts followed by short transcriptional pauses, perhaps on the order of a few seconds (see, e.g., Kingston and Chamberlin [15] and Bai et al. [3]). These pauses are sometimes related to the presence of secondary structures formed in the nascent transcripts that can interact with the RNA polymerase and temporarily interfere with its function (12).

Transient transcriptional arrests are also caused by reverse sliding of the elongation complex for one or more nucleotide (“backtracking”), which temporarily inactivates the elongation complex (11). Reactivation of the elongation complex occurs both spontaneously (by reversal of the backtracking) and by special factors (GreA, GreB) that induce a cleavage of the nascent transcript to create a new 3′ end at the catalytic site (16). It is not known whether significant backtracking also occurs in the presence of antitermination mechanisms.

(ii) Distribution of RNA polymerase molecules along the rrn operon.

Quan et al. (17) determined the distribution of transcribing RNA polymerase molecules along the rrn operon by EM for bacteria growing at 2.5 doublings/h. For this purpose, they approximated the length of an rrn operon as 6,000 bp, divided it into 20 sections of 300 bp, and counted the number of RNA polymerase molecules with an attached nascent rrn transcript in each section; the data were averaged from a total of 11 rrn operons counted and were then plotted as percentages of total RNA polymerase molecules per section. If rRNA chains were initiated at constant time intervals and elongated at a constant rate, and if there were no premature transcript terminations, then the RNA polymerase molecules would be evenly distributed along the operon, so that each of the 20 sections would show 5% of the total number of polymerases transcribing the operon. The total number of RNA polymerase molecules per average rrn operon was 51.5, so that the average number of polymerase molecules under conditions of uniform distribution should be 2.6 RNA polymerases per section (0.05·51.5 = 2.58); this corresponds to an average distance between adjacent polymerases of 116 bp (6,000/51.5 = 300/2.58 = 116). However, a uniform distribution was not found; instead, the distribution exhibits two peaks of higher polymerase density centered within the 16S and 23S rRNA genes (Fig. 4a of reference 17, reproduced in Fig. Fig.1b1b below). The left ordinate in Fig. Fig.1b1b shows the RNA polymerase density as a percentage of the total in each section, varying between 0.1 and 8% per section (from Quan et al. [17]); the right ordinate is recalibrated as the (average) number of polymerase molecules per 300-bp section and varies between 0.1 and about 4.0 polymerases per section. The two peaks in the distribution are statistically significant by a number of criteria (see Appendix).

FIG. 1.
Flow of RNA polymerase molecules through an rrn operon of E. coli K-12 during exponential growth at 2.5 doublings/h in LB-glucose medium. The evaluation is based on distributions of RNA polymerase molecules along the rrn operon observed by EM (17). The ...

(iii) Factors affecting the RNA polymerase density on the DNA template.

The density of the RNA polymerases in sections across the operon as seen by EM varies from nearly four polymerases per section in the 16S and 23S peaks to two or fewer in the intergenic space and at the beginning and ends of the operon. The polymerase density along the operon is determined by three factors: (i) the frequency of transcript initiations at the promoter, (ii) transcript terminations that might have occurred as the polymerase moves along the operon, and (iii) the speed with which polymerases elongate the nascent RNA through various sections of the operon. In the following, we ask which of these factors contributes to the observed two-peak density distribution.

Frequency of transcript initiations at the promoter.

To create two density peaks of polymerase molecules along the rrn operon as a result of a varying rate of transcript initiation, one would have to assume short cyclic fluctuations on the order of about 0.5 min in the rate of initiation; i.e., a higher rate of initiation would create higher polymerase densities and a lower rate correspondingly lower densities. If the polymerases then move after transcript initiation with about equal speeds along the DNA of the operon (at 91 nt/s [see above]), any density peak created by temporarily more rapid initiations would move as a wave along the operon, and at a particular instance one peak might happen to be in the 16S region and another one in the 23S region, as observed. However, this particular picture could not be the average from many different EM pictures originating from different cells; therefore, short cyclic fluctuations in the initiation rate to create the two density peaks in the 16S and 23S regions can be ruled out.

We note, however, that fluctuations in the rate of initiation resulting in irregular spacing of groups of RNA polymerase on the rrn operons have been observed when the number of rrn operons was increased by adding extra rrn operons on multicopy plasmids (20). The reason for these apparent bursts and pauses in transcript initiation under such conditions is not known. It might indicate temporary shortages of RNA polymerases at the artificially high copy numbers of rrn promoters that are located both on the plasmids and within the nucleoid.

In addition, three different kinds of temporary changes in RNA polymerase densities along the rrn operon are caused by replication of the operons, but none of these could produce the observed two-peak distribution. (i) During the time the replication fork moves through the operon (about 5 s), the polymerase density behind the fork corresponds to half the density in front of it; however, such (rare) images of “forked” rrn operons are not included in the evaluation. (ii) During a period of 1 min (the time needed to transcribe the operon) immediately following replication of an operon, the polymerase density near the beginning of the operon produced by newly initiated transcripts equals twice the lower density left behind by the passing replication fork; such images would persist for about 1 min and be present with about 4% probability (1 min/24-min doubling time = 0.04). (iii) The rate of rrn transcript initiation and average polymerase densities on the rrn operons vary nearly twofold during the cell cycle due to the clustering of five of the seven rrn genes per genome near the replication origin (10; see also Appendix). Although these cell cycle-dependent effects could be expected to be averaged in the 11 operons analyzed, preferential lysis of larger cells late in the cell cycle during preparation of the cells for EM imaging may greatly attenuate the impact of these effects on the EM pictures (see Appendix).

Premature terminations of rrn transcripts.

In the distribution of polymerase densities (Fig. 4a of reference17), the average densities correspond to somewhat above 5% per section in the whole 16S region and to somewhat below 5% in the whole 23S region. This might suggest the occurrence of some terminations during rrn transcription. However, since the ratio of free 30S to 50S ribosomal subunits was equal to 1 (Table 2 of Quan et al. [17]), this possibility seems unlikely. Since the vast majority of ribosome subunits were in 70S particles and polysomes (Fig. 5 of reference 17), the ratio for all ribosome subunits is clearly very close or equal to 1.0. This agrees with previous observations for wild-type E. coli after all ribosomes had been dissociated into their subunits (by dialysis against low Mg buffer; see, e.g., Bremer and Berry [5] and Dennis and Bremer [9]). Finally, observations that the density of polymerase is very low at the beginning of the 16S region and at the end of the 23S region are inconsistent with the polarity of transcription and the fact that 23S and 5S rRNAs are made in amounts equal to that of 16S rRNA. In other words, in wild-type E. coli bacteria, there is no compelling evidence for premature termination during rRNA transcription as the cause of the observed two-peak distribution in polymerase density.

Variable speeds of RNA polymerases.

The supposition that there are no cyclic variations in rRNA transcript initiation or premature transcript termination leaves variable polymerization speeds as the only way to explain the observed density distribution of polymerases over the rrn operon; i.e., the polymerases must temporarily slow down when they transcribe the 16S and 23S regions. This is similar to traffic situations in which cars get closer together in highway sections where traffic is slow and get further apart when traffic speeds up again. In the following, the variation in the speeds of polymerases as they traverse the rrn operon is examined.

Variable rate of rRNA chain elongation during transcription of an rrn operon.

The average distribution of RNA polymerases over the rrn operon (Fig. (Fig.1b)1b) obtained by examination of 11 individual operons represents a steady state, which means that the distribution remains constant in time; for every new RNA polymerase entering the operon at the 5′ end, another polymerase terminates at the 3′ end and every polymerase on the DNA moves forward to the (average) position that was previously occupied by the preceding polymerase. An exact constancy applies only to the average, not to an individual, rrn operon at a given time. The varying rates of transcript elongation along the rrn operon can then be found from this distribution in the following way.

Since “speed” is defined as “distance traveled per unit of traveling time,” the rRNA chain elongation rate within a given section, j, of the rrn operon, crj, equals the average distance, dj (in bp), between adjacent RNA polymerases in that section (Fig. (Fig.1a,1a, right ordinate) divided by the average time interval, τi, between two consecutive initiations; i.e., crj = dji. The average distance between adjacent polymerases in each section equals 300 bp/section (assuming that the rrn operon is 6,000 bp long, as in Fig. 4 of reference 17; the actual value is somewhat less [see Appendix below]) divided by the average number of RNA polymerase molecules in that section, nj (Fig. (Fig.1b,1b, right ordinate scale): dj = 300/nj. The average time interval between transcript initiations is the inverse of the average rate of transcript initiation at the rrn promoters, Vrrn: τi = 1/Vrrn. Values of Vrrn at different growth rates have been obtained from measurements of the rate of rRNA synthesis and of the number of rrn genes (per unit volume of exponential culture; see Dennis et al. [10]), and particular values of Vrrn can also be found from the total number of RNA polymerases seen on rrn operons in EM images (e.g., 51.5; see “Distribution of RNA polymerase molecules along the rrn operon” above) and the total time it takes to transcribe the operon (i.e., 60 s; see “Determination of the average rrn chain elongation rate” above and Appendix for further details). Thus, crj = dji = dj/(1/Vrrn) = 300·Vrrn/nj. For the 11 operons examined in this study, Vrrn equals 51.5 transcript initiations per minute or 0.86 initiation per second. Both Vrrn and nj vary during the cell cycle and at different growth rates but presumably in parallel so that their quotient and, thus, the transcription velocities along the rrn operon remain constant. A more rigorous derivation of this relationship, including determination of Vrrn and nj, is described in the Appendix.

According to these calculations, the polymerases begin transcription of an rrn operon at a rate of about 230 nt per second (±30%; one RNA polymerase per 300 bp in the first section of the rrn operon). It is unclear how this high rate relates to the polymerase passing through the first antitermination site in the rrn leader (note that a second antitermination site is located between the 16S and 23S sections). As the polymerase enters the 1,500-bp region of the 16S gene, the rRNA chains grow at a reduced rate of about 65 nt per second (3.6 RNA polymerases per 300 bp) and the polymerases become more closely spaced (83-bp average distance between adjacent polymerases, or 3.6 polymerases per section). Next, in the spacer region between the 16S and 23S sections, the polymerases speed up again to about 90 nt per second before slowing down a second time to 65 nt per second in the 23S region (the second peak in the polymerase density distribution). Near the end of the operon, the polymerase speeds up gradually to rates of >400 nt per second. The average rate over the whole operon is 91 nt per second (see above). Thus, the two peaks with maximum densities in the 16S and 23S regions (about 3.6 RNA polymerases per 300-bp section) (Fig. (Fig.1b)1b) correspond to two valleys with minimum average velocities of RNA chain growth (about 65 nt/s) and minimum average distances between adjacent polymerases (about 83 bp) (Fig. (Fig.1a1a).

By connecting the points in the transcription velocity distribution of Fig. Fig.1a1a to a continuous curve, one might assume that there are smooth transitions between the varying velocity points that have been plotted. However, an exact “local speed” would be the reciprocal of the translocation time of the polymerase at a particular nucleotide within the rrn transcript. As far as we are aware, translocation times have not been determined for any in vivo transcription. The individual points on the curve in Fig. Fig.1a1a still represent averages within each section, not individual translocation rates within the section. As shown below, there is reason to believe that actual translocation rates are much higher than any observed average but that the process of transcript elongation is intermittently interrupted by temporary pauses which reduce the average speed.

RNA polymerase pausing during transcription of the 16S and 23S rrn regions.

As far as we are aware, the data by Quan et al. (17) allow for the first time an estimate of varying instantaneous polymerization velocities during the in vivo synthesis of an rRNA precursor. An unexpected result of these observations is that rRNA transcripts made in the presence of the Nus antitermination factors on the RNA polymerase can apparently grow at speeds exceeding 200 nt per second, i.e., much faster than assumed from the previously determined ensemble averages. If the polymerization of RNA chains can be that fast, then the question becomes what causes the RNA polymerases to slow down to a rate of only 65 nt per second in the 16S and 23S regions of the operon? As was mentioned above, secondary structures forming in the nascent transcripts are known to lead to transcriptional pauses, and it is also known that 16S and 23S rRNA molecules immediately fold into complex higher-order structures that are binding targets for the r proteins; as is seen in the EM pictures, the proteins are already assembling into the preribosomal particles as the rRNA is being synthesized. Therefore, it seems reasonable to suggest that the RNA polymerase molecules seen in the 16S and 23S regions of the rrn operons are prone to pausing, possibly at the 3′ end to stem-loops in the nascent transcript. The pausing may then cause the reduction in the average chain elongation rate to 65 nt per second in the 16S and 23S sections and concomitant crowding of polymerase. This rate is significantly below the average rate of 91 nt per second measured over the entire operon. An alternative possibility is that the varying transcriptional speed is the result of DNA sequence-related variations of the standard free energy of the moving transcription elongation complex (2).

Computer simulation of the observed RNA polymerase density distribution.

If RNA polymerases pause during transcription, then one might expect to find queues of polymerases piling up behind pausing polymerases. Such queues are not seen in the electron micrographs from wild-type bacteria. However, queues are apparent at higher rates of rrn transcript initiation in pictures from rrn operons of strains with rrn deletions (Fig. 5 of reference 8). The probabilities of queue formation and the reasons for their absence in wild-type bacteria and their presence in rrn deletion strains will be detailed in a separate analysis to be reported in the future. To illustrate the principle, we have performed Monte-Carlo simulations based on the Gillespie (13) algorithm to derive the average densities of RNA polymerase in the different sections of the rrn operon as observed by Quan et al. (17) and here reproduced in Fig. Fig.1b.1b. For this, we assumed ideal steady-state conditions with no consideration of cell cycle variations or other external factors. The polymerase step times per base were assumed to be exponentially distributed and chosen so that, conditionally on the absence of queuing, the average time to transcribe each section corresponds to the experimental estimates in Fig. Fig.1a.1a. In the simulations, we assumed “passive queuing,” i.e., that a polymerase that touches a preceding polymerase cannot move forward and does not affect the rate constant by which the polymerase ahead steps forward. The special case with uniform step times per base in each section is shown in Fig. Fig.2,2, along with Monte-Carlo simulation-estimated standard deviations of the densities in the different sections. It is seen that the standard deviations in the different sections are about 10%, in line with our estimate below (see “Significance of the two-peak density distribution within the rrn operon” in the Appendix). The similarity between the observed distribution, representing no queuing, and the Monte-Carlo simulation distribution (Fig. (Fig.2)2) demonstrates queuing to be insignificant in this special case with uniform step times in each section. In reality, fewer but longer pauses may occur and alter the queuing propensity.

FIG. 2.
Polymerase density and standard deviation estimates from Monte-Carlo simulations of rrn transcription. The solid line represents the mean polymerase densities obtained as an average of 10,000 simulation samples, with a sampling frequency of 0.01/s; i.e., ...

For the simulation, the rate of transcript initiation was assumed to be 0.74 rrn transcript per second, which resulted in a mean number of polymerases on the operon equal to 51.8, similar to what was observed (51.5 [see above]). The rate of 0.74 (transcript/s) is somewhat less than the value of 0.86 (transcript/s) calculated above (see “Variable rate of rRNA chain elongation during transcription of an rrn operon”). This reflects mainly the difference in the assumed lengths of the rrn operon, which, for the simulation, was based on the value 6,000 bp (17), rather than 5,450 bp, the value on which the determination of the average rRNA chain elongation rate was based (cr = 91 nt/s [8]); this value for cr was used to calculate the transcription velocities in each section as plotted in Fig. Fig.1a1a (from equation 3d in Appendix). To some extent, the difference in transcript initiation rates also reflects the small amount of queuing occurring in the simulation. The rather complex questions about pausing and queuing and their relationship to the rate of transcript initiation will be addressed in the future work mentioned above.

To summarize, the density distribution of transcribing RNA polymerase molecules along the rrn operon observed in the EM pictures by Quan et al. (17) indicates that the translocation rates of RNA polymerases on rrn operons in the presence of Nus antitermination factors can be much greater, i.e., >200 nt/s, than the previously assumed average of about 90 nt/s, based on measurements of the time it takes to transcribe the whole rrn operon. However, the polymerases slow down during the transcription of the 16S and 23S rRNA genes, presumably as a result of transcriptional pauses. These pauses could be caused either by temporary inhibitory interactions of the polymerase with secondary structures in their nascent transcript or by DNA sequence-related variations of the standard free energy of the moving transcription elongation complex. Both these transcriptional pause mechanisms have been found to be at work during transcription in vitro, but current evidence is insufficient to decide if one of these mechanisms is responsible for the variable rate of rrn transcription in vivo or if yet another explanation has to be given.


We thank Karin Nilsson, Cathy Squires, Ciaran Condon, Terry Hwa, and Arbel D. Tadmor for suggestions and comments.

This material was based on work supported by the National Science Foundation while P.P.D. was working at the Foundation.

The opinions, findings and conclusions expressed in this publications are ours and do not necessarily reflect the views of the National Science Foundation.


Significance of the two-peak density distribution within the rrn operon.

It might be argued that the two peaks in the 16S and 23S regions of the distribution are the accidental result of statistical fluctuations due to the low number of RNA polymerase molecules per 300-bp section and due to other uncertainties in the EM pictures, including determination of the exact positions of the transcription start and end points. However, the observed heights in the two peaks correspond to about 7% of the total, or 3.6 RNA polymerase molecules per section (51.5·0.07 = 3.6). Since the numbers are based on the evaluation of 11 rrn operons, they represent a total of 40 (= 3.6·11) RNA polymerase molecules counted for each 300-bp peak section. This gives a standard deviation of about 16% (√40 = 6.3; 6.3/40 = 0.16), assuming Poisson statistics. Since the maximum number of polymerase molecules per 300-bp section is limited (perhaps to about six, assuming a minimum distance of about 50 bp), the average deviations should actually be somewhat less than 16%, which is consistent with the observed 10% differences in the heights of neighboring sections within the peaks. Therefore, the distribution in the rrn operons with two peaks of increased RNA polymerase density, one in the 16S region and the other in the 23S region, is assumed to be essentially correct and typical for the strain and conditions used. A similar distribution with two peaks based on the evaluation of 27 rrn operons was found for a strain deficient in the antitermination factor NusB (Fig. 4b of reference 17). It is extremely unlikely that both distributions with two peaks are accidental results from statistical fluctuations.

The K-12 strains (MC1400, W1485, and AB1157) used in this and previous work grow at a rate of 2.5 doublings/h in LB medium (4, 8, 17). We therefore assume that the polymerase distribution with two peaks along the rrn operon (Fig. (Fig.1b)1b) is typical for most K-12 strains grown under these conditions. We note, however, that strain HB101 (genotype pro leu lacY hsdR hsdM endA recA rpsL20 ara-14 galK2 xyl-5 mtl-1 supE44) containing a pBR322 plasmid, which grows poorly in LB medium, exhibits a different RNA polymerase density distribution along rrn operons without any clear peaks in the 16S and 23S regions (20). That strain showed a number of other abnormalities; e.g., it grew only at 1.3 doublings/h in LB medium but slightly faster in the nutritionally poorer glucose-amino acids medium, and it had a higher rate of rrn transcript initiation than observed in wild-type strains despite its slower growth (20). Without further data on the physiology of HB101, it is not clear what causes these differences in rrn transcription and growth from those of other K-12 strains.

Derivation of changing rRNA chain elongation rates along the rrn operon.

The parameters used for the following derivation of the polymerization velocity from the observed density distribution are explained in the text below. For easier reference, they are listed here: j, section number of rrn operon, from 1 to 20; Nrrn, length of rrn operon (bp); Nj, length of section j (bp); nrrn, average number of RNA polymerase molecules per rrn operon; nj, average number of RNA polymerase molecules in section j; njrel, relative number of RNA polymerase molecules in section j (% of total per operon); τrrn, average time for an RNA polymerase to transcribe the rrn operon (s); τj, average time for an RNA polymerase to transcribe section j (s); Vrrn, rate of rrn transcript initiation at one rrn operon (transcripts/s); fj, flow of RNA polymerase molecules through section j (RNA polymerase molecules/s); cr, average rRNA chain elongation rate along the whole rrn operon (nt/s); and crj, average rRNA chain elongation rate in section j of the operon (nt/s).

In Fig. 4 of reference 17, the total length of the rrn operon, Nrrn (bp), was divided into 20 sections, j (j = 1, 2, 3,…20) of equal lengths [Nj = Nrrn/20 [bp]). The operon length was approximated by assuming that Nrrn was equal to 6,000 bp, so that each of the 20 sections was assumed to have a length (Nj) of 300 bp. We note, however, that actual lengths of rrn operons are somewhat shorter; e.g., for rrnC, Nj is equal to 5,450 bp (8), so that a more accurate value for Nj would be 5,450/20, or 273 bp. In Fig. 4a of reference 17, the relative RNA polymerase densities observed in segment j, njrel (%), for a wild-type E. coli K-12 strain (MC4100) growing at 2.5 doublings/h in LB medium are plotted versus the distance (in bp) from the operon start site (from 0 to 6,000). The relative polymerase densities were obtained from the average number of polymerases with an attached nascent rRNA, nj, observed in that segment (from a total of 11 rrn operons evaluated), divided by the average total number of RNA polymerases per rrn operon, which was 51.5 (polymerases/rrn); i.e., averaged from 11 operons:

equation M1

The distribution from Fig. 4a of reference 17, njrel, as a function of the distance in bp (midpoint of section j) from the operon start site, is here reproduced in Fig. Fig.1b,1b, left ordinate scale. Resolving equation 1a for nj,

equation M2

allows the average number of polymerases in section j, nj, to be calculated from njrel. This relationship (equation 1b) was here used to recalibrate the right ordinate scale of Fig. Fig.1b1b.

In the steady state, the flow rate of polymerases, fj, through the operon and through every section is given as the number of RNA polymerases that enter as well as exit every segment of the operon per time unit; it is the same through all sections and must be equal in number to the rate of transcript initiation at the rrn promoters, Vrrn (number of transcripts/s):

equation M3

Since the flow rate is independent of the length of the section considered, it also equals the total number of polymerases per rrn operon, nrrn, divided by the total time, τrrn, to transcribe the whole operon, i.e., nrrnrrn. With nrrn equal to 51.5 polymerases (17) and τrrn equal to 60 s (8), we obtain the equation Vrrn = 51.5/60 = 0.86 (transcripts/s), or a flow rate of 0.86 polymerases/s through the operon under the conditions used by Quan et al. (17). The constant flow rate of polymerases through the operon has to be distinguished from the local speed of the polymerases, which varies along the operon. This may be visualized by considering a river passing through a narrow gorge: the flow of the amount of water through the river is everywhere the same, but when the river narrows, the speed with which the water moves increases, and when the river widens it slows down again.

Resolving equation 2a for τj, we obtain the average time a polymerase spends in section j:

equation M4

The rate of transcription averaged over the whole rrn operon, i.e., the average rRNA chain elongation rate, cr (nt/s), is defined by the average time, τrrn, for a polymerase to transit the whole operon of length Nrrn; i.e., cr = Nrrnrrn (nt/s). With Nrrn equal to 5,450 bp and τrrn equal to 60 s (8), one obtains the formula cr = (5,450/60) = 91 nt/s. In the same manner, the average transcription rate, crj (nt/s), in section j is defined by the average time, τj, that a polymerase spends in section j of bp length Nj:

equation M5

Combining equations 3a and 2b gives

equation M6

This is the relationship derived in the text above. Further, setting Nj as equal to Nrrn/20 (see above), Vrrn as equal to nrrnrrn (equation 2a), and nj as equal to njrel·nrrn/100 (equation 1b) gives the average polymerase speed in section j as

equation M7

equation M8

With cr equal to Nrrnrrn (5,450/60 or 91 nt/s [see above]), we obtain

equation M9

This relationship with njrel values from Fig. 4a of reference 17 was used to calculate the average rRNA elongation rates in each section (Fig. (Fig.1a,1a, left ordinate scale).

Under true steady-state conditions in the absence of premature termination events, equation 3 is always valid. One potential complication is that Vrrn and nj vary through the cell cycle as a result of the replication of the rrn operons. However, the observation that cr is nearly invariant with the growth rate (19) suggests that Vrrn and nj vary in parallel, so that their quotient in equation 3b remains constant.

The value of Vrrn as 51.5/60 or 0.86 transcript per second (see above), or 51.5 transcripts initiated per minute per rrn operon, obtained here from the data of Quan et al. (17) and Condon et al. (8), is significantly below values of about 67 transcripts/min initiated per rrn operon obtained from measurements of rRNA synthesis rates and rrn gene copy numbers in an average cell for E. coli growing exponentially at 2.5 doublings/h (reviewed by Dennis et al. [10], with data from B/r strains and with application of data for K-12 strains). This suggests that the EM technique used by Quan et al. (17) might have preferentially lysed larger, more-fragile cells during the later part of the cell cycle, with higher-than-average rrn gene copy numbers and therefore lower rates of transcript initiation. However, as pointed out above, this is unlikely to significantly affect the validity of equation 3d and the calculated values of crj, because the values of njrel (%) in equation 3d are independent of the cell cycle. According to equation 1a, njrel is given by the quotient nj/nrrn, where the numbers of polymerases in each section, nj, vary during the cell cycle to the same extent as the numbers in the whole operon, nrrn, so that their quotient remains constant.


Published ahead of print on 27 March 2009.


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