Schaechter et al. [6] proposed that for exponentially growing cells an average number (n _x(av)) of constituent, x, per cell may be defined as the number of x per ml of culture divided by the number of cells per ml of culture. The population-average cell defined in this way reflects the properties of the entire cell population, which includes cells of all ages, a, ranging from newborn cells (a = 0) to cells about to divide (a = 1). Quantities measured by qRT-PCR in the study of an RNA fraction isolated from a cell culture may now be defined in terms of parameters of population-average cells which are denoted by the subscript (av) [10], [11].

Bacterial ribosome synthesis is governed by a co-ordinated production of individual ribosomal components. Synthesis of rRNA is a highly regulated response to the nutrients available to the cell (for review see [22]). The synthesis of ribosomal proteins (r-proteins) is tightly linked to rRNA synthesis by feedback inhibition, termed autogenous control (for reviews see [7], [29], [30], [31]). Autogenous control of r-protein synthesis suggests that within the cell r-proteins are located mainly in the ribosomes. This expectation was shown to be correct [32]; apart from rpsA and rpsB, pools of free r-proteins were found to be less than 7% of the total number of copies. Furthermore, the pool size of rpsL was found to be within background levels whereas the pool size of rplL was 0.5% and of rplJ was 3.5%. Pools sizes can be taken into account by the inclusion of an appropriate factor (for example, 1.035 in the case of rplJ) in equation (8) below.

Ribosomes are stable enzymes catalyzing sequential peptide bond formation with lifetimes that exceed the lifespan of individual cells. The pool sizes of free component proteins are small (see the preceding Section), r-protein synthesis is subject to autogenous control (see references 7,29–31), newly synthesized component proteins are free to interact with nascent precursor 16S rRNA and 23S rRNA to form nascent 30S and 50S ribosomal subunits; in contrast, ribosomes are abundant within the cell. For these reasons we concluded that degradation of r-proteins is not a significant factor in the measurement of their polypeptide chain elongation rates.

The mathematical analysis below is based on the assumption that pools of ribosomal proteins are small so that the numbers of copies per cell of the three components studied (16S rRNA, rpsL and rplL) are each equal to the product of the number of ribosomes per cell and the number of copies of the component per ribosome.

M. fortuitum has two rRNA operons (rrnA and rrnB). The promoter regions and the 5′-ends of the 16S rRNA (rrs) genes of the two operons are shown in (Figure 2). Each operon has the classical structure of leader region, 16S rRNA coding region, Internal Transcribed Spacer region 1 (ITS1), 23S rRNA coding region, Internal Transcribed Spacer region 2 (ITS2), 5S rRNA coding region and trailer region [2], [3]. The above-mentioned studies show that the leader regions contained a highly conserved sequence motif Conserved Leader 2 (CL2) which is implicated in both antitermination of transcription and the formation of precursor-16S rRNA (pre-16S rRNA). A complementary sequence cCL2 is located downstream from the 3′-end of the 16S rRNA coding region. The interaction of CL2 and cCL2 sequence motifs leads to the formation of a double-helical stem structure that contains an RNAaseIII processing site. Cleavage at this site generates pre-16S rRNA [3]. The study of the transcription of E. coli rrn operons by electron microscopy [33] revealed a double ‘Christmas tree’ effect that showed that cleavage of the pre-16S rRNA gene took place before the transcription of the 23S rRNA gene began. This information, together with the axiom [34] that each “RNA polymerase (RNAP) complex synthesizing RNA generates a single RNA chain”, provides the basis for the measurement of ε _rrs nucleotides h⁻¹, the 16S rRNA chain elongation rate, by qRT-PCR.

During exponential growth ω _rrs the specific synthesis rate of pre-16S rRNA is given by equation (1) where n _R(av) is the number of ribosomes per population-average cell, l _p-rrs is the length (nucleotides) of pre-16S rRNA and μ is the specific growth rate.(1)However, ω _rrs is also the product of n _RNAP(rrs) the number of RNAPs synthesizing pre-16S rRNA and ε _rrs the rate of 16S rRNA chain elongation (see equation 2)(2)Equating the right hand sides of equations (1) and (2) and making ε _rrs the subject leads to equation (3).(3)Equation (4) applies because a ribosome has a single copy of 16S rRNA and one RNAP has a single transcript.(4)Both n*_c-rrs and n*_tr(rrs), respectively the number of copies of 16S rRNA and the number of transcripts of precursor-16S rRNA per ng RNA substrate for cDNA synthesis, can be measured by qRT-PCR.(5)Equation (5) is a formal statement of the requirement that the composition of the cDNA used in qRT-PCR experiments must accurately reflect the composition of the RNA component of the population-average cell. Provided that equation (5) applies ε _rrs may be evaluated by means of equation (6).(6)

Coupling between the processes of bacterial transcription and translation has long been accepted [35], [36]. A snapshot of an ORF undergoing transcription/translation was obtained by electron microscopy of lysates of fragile E. coli cells [33]. RNA polymerase complexes (RNAPs) were shown at intervals along the gene, with nascent mRNA transcripts increasing in size according to the position of the RNAP; and a proportionate number of ribosomes attached to each nascent mRNA. Understanding the snapshot provided by electron microscopy in quantitative terms is key to analysing the results obtained by qRT-PCR. It is not known how the bacterial cell achieves transcription/translation coupling although the transcription elongation factors NusA and NusG may play a role (for review see [37]). However, the rate of transcription must limit the rate of translation. Specifically, the rate of codon synthesis (ε _mRNA(i)/3; where ε _mRNA(i) is the rate mRNA_(i) of chain elongation) must be less than the rate limiting step in peptide bond formation [38], [39]. When ribosomes translate a previously synthesized mRNA the rate limiting step is the interaction of a ternary complex of aminoacyl-tRNA, elongation factor EF-Tu and GTP with the A-site of the ribosome [40].

The transcription/translation of a particular ORF (ORF_(i)) is represented schematically by the fibril diagram shown in Figure 3. The ORF is shown to be fully loaded with RNAPs and transcripts loaded with ribosomes. A population-average cell is representative of a very large number of cells of different ages [10]. For a single copy gene the number of fibrils per population-average cell will depend on age of the cell when the ORF_(i) is replicated; this number cannot exceed two and is more likely to approximate to 1.5. Thus, there is an upper limit per cell for both n _tr(i)(av) the number of transcripts of ORF_(i) and n _R(i)(av) the number of ribosomes synthesizing the encoded protein p _(i).

The specific synthesis rate, ω _p(i), of protein p _(i) is given by equation (7) where n _c-p(i)/c is the number of copies of p _(i) per cell and l _aa(i) amino acids is the length of p _(i).

The number of copies of protein p_(i) per population-average cell is affected by the extent to which the protein is either degraded or exported. Thus, it is necessary to distinguish between the gross value n _c-p(i)(av), the net value n^# _c-p(i)(av) and the empirical value n ^* _c-p(i)(av) of the number of copies of protein p _(i) per cell. When there is neither degradation nor export of the protein the gross, net and empirical values are equivalent. When the protein is degraded or is exported the gross value is greater than the net value which is equal to the empirical value of the number of copies per cell.(7)The number of copies of p _(i) per cell is the product of n _R(av) and n _c-p(i)/R the gross number of copies of protein p _(i) per ribosome. Substitution for n _c-p(i)(av) in equation (7) leads to equation (8).(8)The specific protein synthesis rate of p _(i) is also equal to the product of n _R(i)(av) the number of ribosomes per cell synthesizing p _(i) and ε _aa(i) the rate at which the peptide chain is elongated (see equation 9).(9)Equating the right hand sides of equations (8) and (9) and making ε _aa(i) the subject leads to equation (10).(10) ε _aa(i) may be calculated by qRT-PCR in the following way: The number n _R(av) of ribosomes per cell is equal to n _c-rrs the number of copies of 16S rRNA per cell. The number n _R(i)(av) of ribosomes synthesising p _(i) per cell can be evaluated through the parameter n _R(i)/tr(i) which relates n _R(i)(av) to n _tr(i)(av) the number of transcripts of ORF_(i) per population-average cell (see equation 11).(11)The experimentally accessible parameters are n*_c-rrs and n*_tr(i) which are respectively the numbers of copies of 16S rRNA and numbers of transcripts of ORF_(i) per ng of RNA used as the substrate for cDNA synthesis. Thus, ε _aa(i) may be evaluated provided that the composition of the cDNA substrate for qRT-PCR accurately reflects the composition of the RNA component of the population-average cell, as stated in equation (12).(12)Hence equation (13), which links the number of transcripts of a particular ORF that are needed for protein synthesis with the gross number of copies of the encoded protein per ribosome, allows the polypeptide chain elongation rate to be evaluated.(13)

We define the conversion factor n _R(i)/tr(i) as n _R(i)/ORF the number of ribosomes translating transcripts of ORF_(i) divided by n _tr(i)/ORF the number of transcripts per ORF_(i). There is one transcript per RNAP so that n _R(i)/tr(i) the number of ribosomes per transcript is equal to the number of ribosomes per RNAP (see equation 14).(14)ORF_(i) will be fully loaded with RNAPs when, on average, there is one RNAP per α base-pairs of ORF_(i) (see equation 15).(15)The maximum number of RNAPs per ORF is determined by the footprint of the initiating RNAP at the promoter. Krummel & Chamberlin [41] found that the initiating complex of an RNAP at the promoter had a footprint of about 80 base-pairs; that is, α approximately 80 base-pairs.

Furthermore, the lengths of transcripts associated with adjacent RNAPs will differ by α base-pairs. Suppose that there is one ribosome per β nucleotides of mRNA: then the number of ribosomes per transcript will increase according to an arithmetic progression. The sum of the progression yields n _R(i)/ORF which is given by equation (16).(16)Rearrangement of equation (16) leads to equation (17).(17)Thus, by definition (see equation 14) n _R(i)/tr(i) is given by the right hand side of equation (17). Substitution for n _RNAP(i)/ORF (see equation 15) on the right hand side of equation (17), followed by simplification leads to equation (18).(18)The diameter of a bacterial ribosome [28] is 25 nm (250 Å). Neglecting secondary structure this dimension correspond the length of 74 nucleotides. It is inferred that, to a first approximation, β = 80 nucleotides [10]. Hence, n _R(i)/tr(i) can be evaluated by means of equation (18). Errors in the values of α and β are likely to be small so that values of n _R(i)/tr(i) are expected to be better than plus or minus 20%.

Data for the macromolecular compositions of E. coli B/r [15] and our knowledge of the E. coli genome provide sufficient information for the evaluation of parameters such as n _RNAP(rrs) (hence n _tr(rrs)(av)) and n _R(i)(av) (hence n _tr(i)(av)) to be achieved by means of the equations presented in Table 2. The theoretical values obtained provide a frame of reference for testing the validity of the results obtained by qRT-PCR for M. fortuitum.

Data for E. coli B/r (μ = 0.42 h⁻¹) grown in succinate medium [15] were chosen because the genome is then replicated once only during the cell division cycle [15]. The relevant data are: μ = 0.42h⁻¹; n _R(av) = 6800 ribosomes; n _aa(av) = 5.6×10⁸ amino acid residues; ε _aa(av) = 43,200 amino acid residues h⁻¹; the lengths of rpsL, and rplL respectively are 124 and 121 amino acid residues.

For E. coli (μ = 0.42 h⁻¹), ε _aa(av) the average rate of polypeptide chain elongation was estimated to be 43,200 amino acid residues h⁻¹ (12 amino acid residues s⁻¹) [17]. Several proteins involved in protein synthesis were found to have peptide chain elongation rates similar to the above-mentioned average value; the proteins studied were infB [14], tuf, rpsA (the largest r-protein) and fus [23]. These data suggest that at least to a first approximation of ε _aa(av) the average rate for the protein fraction may be assigned to all r-proteins present as a single copy per ribosome; as shown in Supplementary Data (see Tables S1 (proteins of the 30S ribosomal subunit) and S2 (proteins of the 50S ribosomal subunit)).

Data for S. coelicolor A3(2) [10], [20] and M. bovis BCG [18] were also used to provide reference data for the synthesis of rpsL and rplL of M. fortuitum. The data [10], [20] for S. coelicolor A3(2) are: μ = 0.024h⁻¹; n _R(av) = 10500 ribosomes; n _aa(av) = 7.8×10⁸ amino acid residues; ε _aa(av) = 2,200 amino acid residues h⁻¹; the lengths of rpsL and rplL respectively 123 and 124 amino acid residues. The data [18] for M. bovis BCG are: μ = 0.03h⁻¹; n _R(av) = 3900 ribosomes; n _aa(av) = 4.03×10⁸ amino acid residues; ε _aa(av) = 3,900 amino acid residues h⁻¹; the lengths of rpsL and rplL respectively 125 and 131 amino acid residues. In each case equation (13) was applied on the basis of the assumption that ε _aa(av) = ε _aa(i) and 2ε _aa(av) = ε _aa(j).

M. fortuitum ATCC 6841^T was grown at 37°C until exponential phase in medium Middlebrook 7H9 supplemented with Tween80 and ADC (Albumin, Dextrose and Catalase. Difco).

Mycobacterial cultures were collected, and total RNA isolated as described previously [42]. Standard precautions were undertaken to avoid contamination with RNases during the purification of total RNA [43]. Precautions taken in the manipulation of RNA included separate equipment and materials to be used only for experiments with RNA as well as the use of Diethylpyrocarbonate (Sigma) and RNasin (Promega). The integrity of the isolated RNA was checked by gel electrophoresis and RNA was quantified by spectrophotometry [43].

One hundred ng of the mycobacterial RNA isolated was reverse transcribed by using 30 U AMV reverse transcriptase and random primer hexamers (Promega). After DNase treatment the absence of DNA was confirmed by performing conventional PCR using the primers FoPCL1 and cKK4 [44].

Two independent cDNA preparations were obtained from individual samples of the same RNA isolate. For each cDNA preparation at least two independent qRT-PCR experiments were carried out usually in triplicate. Each qRT-PCR measurement cited in the Tables is the average of four or more determinations.

Real-time PCR was carried out using a capillary PCR instrument (Light Cycler; Roche). The oligonucleotides used in qRT-PCR are indicated in the Table 7. The amplification of the target sequence was detected using SYBR green. Conditions were used as follows: LightCycler Fast Start DNA master SYBR Green I reagent (1µl) was supplemented with 3.5 mM (final concentration) MgCl₂ and 0.5 mM of each primer in 7µl of volume. Sample cDNA (3 µl) was added to the mix. The PCR cycling programme was as follows: denaturizing, 1 cycle of 95°C for 10 min with a transition rate of 20°C/s; amplification, 45 cycles at 95°C for 0 s, the corresponding annealing temperature for each product for 5 s and an extension at 72°C for 10 s with a single fluorescence acquisition, in all the cases the transition rate was 20°C/s. Specificity of the reaction was checked by analysis of the melting curve of the final amplified product. All PCR experiments were stopped before fluorescence was detected in the control negative capillaries.

The qRT-PCR data were plotted as the fluorescence signal versus the cycle number. An arbitrary threshold was set at the midpoint of the log of fluorescent level versus cycle number plot. The Ct value is defined as the cycle number at which the fluorescent level crosses this threshold.

Nucleotide sequence data for rrn operons were obtained as follows: gene bank entry accession number X99775 (rrnA) and see Menendez et al. [3] for rrnB. The lengths of rpsL and rplL were assigned values of 125 and 131 amino acid residues respectively by comparison to M. tuberculosis because these values are highly conserved within Mycobacterium.