Microbiology (2003), 149, 729–737
DOI 10.1099/mic.0.25645-0
Correlation of the rate of protein synthesis and the
third power of the RNA : protein ratio in
Escherichia coli and Mycobacterium tuberculosis
Robert A. Cox
Division of Mycobacterial Research, National Institute for Medical Research, London NW7 1AA, UK
Correspondence
Robert A. Cox
[email protected]
Received 3 April 2002
Revised
21 October 2002
Accepted 12 November 2002
In order to further understand the different physiological states of the tubercle bacillus, a frame of
reference was sought by first correlating the macromolecular compositions of Escherichia coli with
specific growth rates and also with the rates of protein synthesis. Data for DNA : protein : RNA were
converted to the average amounts of DNA [mDNA(av)], protein [mp(av)] and RNA [mRNA(av)] per cell.
The specific growth rate m was found to be directly proportional to mRNA(av)/mp(av). The specific
protein synthesis rate per average cell [vp(av)] was shown to be directly proportional to the third
power of the ratio mRNA(av)/mp(av) which reflects the ribosome concentration. The equations derived
were shown apply to both E. coli (m=1?73 h21) and Mycobacterium bovis BCG (m=0?029 h21).
INTRODUCTION
Why does Mycobacterium tuberculosis require 24 h to divide
when Mycobacterium smegmatis only takes 2 h? (Jacobs,
2000)
Mycobacteria are aerobic, non-motile, rod-shaped bacteria
that are Gram-positive and acid-fast. Mycobacterium leprae
and M. tuberculosis are human pathogens; their slow growth
[generation times of 12 days (Shepard, 1960) and approaching 1 day (Wayne, 1994), respectively] is a notable property.
The emergence of drug-resistant strains of M. tuberculosis
has led to tuberculosis again becoming a threat to world
health. Pathogenic mycobacteria have challenging properties such as an ability to survive within host cells. They are
engulfed by host macrophages but survive and grow within
phagosomes (Armstrong & D’Arcy-Hart, 1971; Ferrari et al.,
1999). Treatment of tuberculosis is lengthy because bacilli
persist despite chemotherapy, allowing the illness to resume
its course if drug treatment is stopped prematurely. In the
persistent state of the bacillus, drug resistance appears physiological rather than genetic in origin. It is known that,
under hypoxic conditions, M. tuberculosis can exist in a
dormant state that is resistant to standard antimycobacterial
drugs. Tubercle bacilli can encounter hypoxic conditions
in vivo (Weber et al., 2000) and oxygen starvation is thought
to halt growth and lead to dormancy (Wayne & Hayes,
1996). Reactivation of dormant cells is thought to be the
cause of the disease appearing many years after the exposure
to the tubercle bacillus.
A knowledge of mycobacterial physiology during exponential growth in vitro and in vivo, within macrophages,
adaptation to oxygen starvation and of the dormant state,
Abbreviations: BCG, bacillus Calmette–Guérin.
0002-5645 G 2003 SGM
Printed in Great Britain
would further our understanding of the course of tuberculosis. Current knowledge has been limited by technical problems such as slow growth and cell aggregation (for review
see Ratledge, 1982; Wheeler & Ratledge, 1994). For example,
the macromolecular compositions of M. tuberculosis grown
under different conditions have not been reported.
Proteins comprise approximately one half of the dry mass of
a bacterial cell (Bremer & Dennis, 1996). Ninety-five per
cent of the energy used by the cell to synthesize macromolecules is devoted to the synthesis of proteins and 5 % is
used to synthesize DNA, RNA, peptidoglycan, phospholipid,
lipopolysaccharides and polysaccharides (Ingraham et al.,
1983). The RNA content of a cell, of which approximately
83 % is rRNA (Bremer & Dennis, 1996; Butcher et al., 1999),
reflects the number of ribosomes per cell. The central role
played by ribosomes in protein biosynthesis suggests that
there is a relationship between protein content, the rate of
protein synthesis and RNA content.
The significance of the relationship between the specific
growth rates and the protein and RNA contents of
Mycobacterium bovis bacillus Calmette–Guérin (BCG), a
close relative of M. tuberculosis (Brosch et al., 2000), is the
subject of this study. Two questions were formulated. First,
how is the average ribosome concentration of a bacterial
culture related to m, the specific growth rate? Second, how is
the average ribosome concentration related to the average
rate of protein synthesis?
Three concepts are implicit in the questions posed. First, the
principal features of protein synthesis are thought to be
common to all bacteria irrespective of growth rate (Maaløe
& Kjelgaard, 1966). Second, the concentrations of reactants
strongly influence the rate of a chemical reaction. Third, the
729
R. A. Cox
ratio of RNA : protein is thought to be directly proportional
to the concentration of ribosomes (Bremer & Dennis, 1996).
Progress was made by first analysing definitive data for the
macromolecular compositions of cells of Escherichia coli
grown optimally in five media (doubling time, tD, 0?4–
1?67 h). The macromolecular composition of M. bovis BCG
was calculated from its chemical composition (Winder &
Rooney, 1970). The relationships established for E. coli were
then shown to apply to M. bovis BCG.
Theoretical section
Definition of slow growth. Traditionally (see, for example, Wayne & Kubica, 1986) mycobacteria are classified as
either fast-growing or slow-growing according to whether
colonies appear on a solid medium within 5 days (fastgrowers) or longer than 5 days (slow-growers). Bacteria
growing optimally are defined according to m, their specific growth rate (Fig. 1); slow growth spans the range
m¡0?14 h21 (tD¢5 h), fast growth span the range
m>0?14 h21<0?7 h21 (tD 1–5 h). Faster-growing bacteria
(m>0?7 h21 tD<1 h) are classified as ultra-fast growers.
A feature of ultra-fast growth is that genome replication
spans more than one cell division cycle (Cooper &
Helmstetter, 1968; Helmstetter & Cooper, 1968) giving
rise to newborn cells that have more than one genome
equivalent per cell. In contrast, newborn cells of fast- and
slow-growing bacteria, including mycobacteria (Hiriyanna
& Ramakrishnan, 1986), are thought to have a single
genome that is replicated within the cell division cycle.
When growth conditions are less favourable (m<0?7 h21),
ultra-fast-growers resemble fast-growers and slow-growers,
with genome replication being started and completed within
the cell division cycle (Fig. 1).
Definitions, axioms and assumptions. The analysis pre-
sented below concerns exponentially growing cell cultures
of E. coli for which it is known that the conditions of
growth govern both the specific growth rate m and macromolecular composition (DNA : protein : RNA). Specifically,
different growth rates correlate with different macromolecular compositions of cell cultures (see, for example,
Bremer & Dennis, 1996). In contrast, when the specific
growth rate was 0?2 h21 or less, it was noted that the
macromolecular content changed very little. Cultures had
minimal contents of protein and RNA as judged by the
DNA : protein and DNA : RNA ratios (Jacobsen, 1974
cited by Ingraham et al., 1983). For cells of minimal protein and RNA contents, the growth rates are designated
mmin; the subscript min denotes that protein and RNA contents are minimal. These cells are thought to have an
excess of ribosomes over the apparent demand for protein
synthesis, as was shown for a Vibrio sp. by Flärdh et al.
(1992). Cultures characterized by mmin are not included in
the analysis. However, the concept of minimal cells could
be relevant to dormant mycobacterial cells. (Symbols are
defined in Table 1).
730
Fig. 1. Definition of slow, fast and ultra-fast growth. Each category is defined by the range of maximum growth rates shown
by the labelled, double-headed arrows. All bacteria are capable
of growing at less than maximum rates when conditions are
less favourable; that is, all bacteria are capable of slow growth.
When the generation time, tD, is more than 1 h the genome is
usually replicated within the cell division cycle (see text); in
other words, tD exceeds the period, C, required for DNA replication (tD>C) and each newborn cell has a single genome.
Usually, when tD is less than 1 h (hatched bars) the replication
of the genome takes place over more than one cell division
cycle (C>tD) so that each newborn cell has more than one
genome equivalent, this property defines ultra-fast growth.
Mycobacterium chelonae (M. C. Nuñez & M. J. Garcia,
Univerisidad Autonoma, Madrid, Spain. unpublished work);
M. tuberculosis (Wayne, 1994); M. smegmatis (Gonzalez-yMerchand et al., 1999); Pseudomonas aeruginosa (Yoshimura
& Nikaido, 1982); Proteus vulgaris (Schaechter et al., 1962);
Salmonella typhimurium (Schaechter et al., 1962); Escherichia
coli (Koch, 1979).
At any time, t, during the exponential growth of a culture
the mass of protein, pt, is given by equation (1) where p0 is
the mass of protein at t=0.
pt ~p0 emt
ð1Þ
The mass of protein, pt, is the product of the number of cells,
nt, present at time t and the average mass of protein mp(av)
Microbiology 149
RNA : protein ratio and the rate of protein synthesis
Table 1. Definitions of symbols
Symbol
a
b
mDNA(av)
mdc(av)
mp(a)
mp(a=0)
mp(av)
mp(t)
mRNA(av)
na
na=0
naa(av)
nR(av)
nt
p0
pt
t
tD
v(av)
a
baq
bm
h
m
mmin
r
vp(av)
Definition
Age of a cell (a=t/tD); a ranges from a=0 for a newborn cell
to a=1 for a cell about to divide
Gradient (h21) in equation (11)
Average mass (fg) of DNA per cell
Average dry cell mass (fg) per cell
Mass (fg) of protein per cell aged a
Mass (fg) of protein per newborn cell
Average mass (fg) of protein per cell
Mass (fg) of protein per cell at time t (t¡tD)
Average mass of RNA (fg) per cell
Number of cells per culture aged a
Number of cells per culture aged a=0
Average amount of protein (number of amino acids) per cell
Average number of ribosomes per cell
Number of cells per culture at time t
Mass (fg) of protein per culture at time t=0
Mass (fg) of protein per culture at time t
Time (h)
Doubling or generation time (h)
Average cell volume (fl or mm3)
Gradient [(fg protein)21 h21] in equation (10)
Fraction of cell mass that is water
Fraction of dry cell mass that is protein
Gradient (fg protein synthesized h21) in equation (12)
Specific growth rate (h21)
Specific growth rate (h21) for minimal cells (see text for definition)
Buoyant density of a bacterium [g cell mass (ml cell volume)21 (or pg fl21, or mm3)]
Specific protein synthesis rate (fg protein synthesized per cell per hour) [equation (5)]
per cell. Although the number of cells per culture increases
exponentially their age distribution remains unchanged
(Powell, 1956). A cell’s age, a, ranges from a=0 (a newborn cell) to a=1 (a cell about to divide), where a=t/tD;
t=0 for newborn cells and t=tD for cells about to divide.
Hence, the average amount of protein per cell is given by
equation (2).
ð1
ð1
ð2Þ
mp(av) ~pt =nt ~ na mp(a) da= na da
0
dpt =dt~pt •m
ð3Þ
Substitution for pt=ntNmp(av) on the right-hand side of
equation (3) leads to equation (4)
dpt =dt~nt •mp(av) •m
ð4Þ
0
where na is the number of cells aged a; na=0 is the number of
cells aged a=0; mp(a) is the amount of protein per cell aged
a. Evaluation of equation (2) reveals (Ingraham et al., 1983)
that mp(av) is equal to mp(a=0)/ln2 [1?4 mp(a=0)] where
mp(a=0) is the mass of protein per newborn cell. Other
average cell properties are similarly defined; for example,
v(av) (fl or mm3), average dry cell mass mdc(av), average dry
cell mass RNA mRNA(av) and average dry cell mass DNA
mDNA(av). In each case, mass is measured in femtograms (fg).
Each of these properties, which serve to define an ‘average’
cell, has a constant value for a particular set of growth
conditions because the age distribution of cells remains
unchanged throughout exponential growth.
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A culture, which at time t comprises nt cells, accumulates
protein at an instantaneous rate specified by equation (3),
which is the differential of equation (1).
Rearrangement of equation (4) leads to the identities shown
in equation (5), which also defines vp(av), the specific
protein synthesis rate (fg protein synthesized per cell per
hour).
vp(av) ~(1=nt )•(dpt =dt)~mp(av) •m
ð5Þ
In other words, dpt/dt is equal to the product of nt and
vp(av).
It is thought that the amount of protein per cell increases
exponentially over the range t=0 for a newborn cell to t=tD
when the cells divide (Cooper, 1988). Hence, mp(t), the
amount of protein per cell at time t, is given by equation (6)
731
R. A. Cox
where mp(t=0) is the amount of protein per newborn cell.
mp(t) ~mp(t~0) e
mt
ð6Þ
Over the same period (t=0 to t=tD) the specific protein
synthesis rate [vp(t)] at time t is given by equation (7).
vp(t) ~mp(t) •m
ð7Þ
When mp(t)=mp(av), equation (7) may be written as
equation (8).
vp(av) ~mp(av) •m
ð8Þ
Thus, equations (3) and (8) are related through nt [equation
(5)], which further illustrates the notion that the properties
of a cell culture are determined by the properties of average
cells. Thus, both mp(av) and vp(av) are parameters that
usefully describe the exponential growth of a cell culture.
Macromolecular composition of E. coli as a function of
the specific growth rate. For cells growing at a rate in
the range 0?42–1?73 doublings h21 (Table 2), the mass of
protein [mp(av)] and dry cell mass [mdc(av)] increase concomitantly with growth rate; that is, mp(av) appears to be
in constant proportion, bm, of mdc(av). The average cell
volume [v(av)] will be directly proportional to mdc(av) and
hence, to mp(av) if the fraction of cell mass due to water,
baq, and the buoyant density, r, are independent of
growth rate. A value for baq of 0?7 was established for
E. coli growing optimally in glucose minimal medium
(Ingraham et al., 1983); this value appears to be accepted
for E. coli cells in general. The buoyant density, r, of E. coli
was found to lie within the range 1?09±0?015 g cell mass
(ml cell volume)21 [or pg fl21 (or mm3)] for cells with
growth rates of 0?4–3?0 h21 and to remain constant
during the growth cycle (Woldringh et al., 1981); and was
found to be independent of the composition of the
growth medium below 1000 mosM (Baldwin et al., 1994).
Thus, as a first approximation, r may be regarded as a
constant. The parameters r, mdc(av) (or mp(av)/bm) and
v(av) are related by equations (9a) and (9b).
v(av) ~mdc(av) •10{3 =½(1{baq )•r
(9a)
ð9aÞ
v(av) ~mp(av) •10{3 =½bm •(1{baq )•r
(9b)
ð9bÞ
The concentration of protein [mp(av)/v(av)], which was estimated to be 0?16 pg fl21 (or mm3), is thought to be not
only constant during the growth cycle but also to be independent of growth rate (see also Bremer & Dennis, 1996);
that is, both bm and baq are also thought to be independent of growth rate.
Table 2. Properties of E. coli B/r growing exponentially at different growth rates at 37 ˚C
Properties
tD (min)*
m (h21)*
Protein per cell*
naa(av) (amino acids 61028)
mp(av) (fg)
RNA per cell*
Nucleotides 61027
mRNA(av) (fg)
Ribosomes, nR(av), per cell 61023*
Number, x, tRNAs per ribosome*
Number, y, EF-Tu copies per ribosome3
Dry cell mass (fg)*
mdc(av) (fg)4
Cell volume (fl or mm3)1
v(av)
Concentration of ribosomes per cell (particles fl21)61023
nR(av)/v(av)
RNA : protein [mRNA(av)/mp(av)]
Results
100
0?42
60
0?69
40
1?04
30
1?39
24
1?73
5?6
100
8?7
156
13?0
234
18?9
340
25?0
450
3?7
20
6?8
9?3
6?7
148
204
7?3
39
13?5
9?3
6?3
258
318
14?3
77
26?3
9?3
5?6
433
677
24?4
132
45?1
9?3
5?2
641
694
39?0
211
72?0
9?3
5?0
865
918
0?62
0?97
1?46
2?12
2?80
11?0
0?20
13?9
0?25
18?0
0?33
21?3
0?39
25?7
0?47
*Data compiled by Bremer & Dennis (1996).
3Data of Pedersen et al. (1978). The values cited are average values relative to proteins S1 and EF-G as the reference species; S1 and EF-G are
thought to be present as one copy and 0?8 copies per ribosome, respectively (Bremer & Dennis, 1996).
4The values of dry cell mass cited by Bremer & Dennis (1996) were not measured directly but were calculated on the basis of the assumption that
one OD460 unit of culture is equivalent to 173 mg of dry cell mass. The equation relating mp(av) and mdc(av), which was found to be mp(av)=0?49
mdc(av)+25, is anomalous because it signifies that a cell containing 25 fg protein has no dry cell mass. To avoid this anomaly, mdc(av) was
calculated from mp(av) on the basis of the assumption that mp(av)=0?49 mdc(av).
1Cell volume calculated by means of equation (9b).
732
Microbiology 149
RNA : protein ratio and the rate of protein synthesis
Whereas the concentration of protein appears to be independent of the specific growth rate, the mass of protein per
cell is not. The relationship between mp(av) and m [equation
(10)] is illustrated in Fig. 2.
ð10Þ
m~a•mp(av)
where a=4?1610
23
(fg protein)
21
21
h .
The plot of RNA : protein ratios [mRNAav/mp(av)] against m
(Fig. 3) has features in common with the plot of mp(av)
against m (Fig. 2). A linear correlation [equation (11)] of m
with mRNA(av)/mp(av) was found (see data of Table 2).
m~½b•mRNA(av) =mp(av) {0:34
ð11Þ
21
where b=4?37 h . The intercept on the abscissa raises the
possibility that there is a limiting value of mRNAav/
mp(av)<0?08 for viable cells.
Whereas the RNA : protein ratio was found to be directly
proportional to the specific growth rate when cells were
grown optimally, the specific protein synthesis rate vp(av)
[equation (5)] was not (Fig. 4). Both the specific protein
synthesis rate and, hence, the associated rate of consumption of energy were found to increase as the specific growth
rate increased. The dependence of the specific protein
synthesis rate on the RNA : protein ratio (Fig. 5a) was
similar to the plot shown in Fig. 4; the similarities in the two
graphs are to be expected since m and mRNAav/mp(av) are
linearly related [equation (11)]. The specific protein
synthesis rate was found to increase approximately eightfold for a doubling of the RNA : protein ratio (Fig. 5a),
which suggests that vp(av) is proportional to the third power
of the ratio mRNA(av)/mp(av). This conclusion is supported by
the plot of log [vp(av)] against log [mRNA(av)/mp(av)], which
was found to have a slope of 3?2 (Fig. 5b), in accord with a
third power relationship. The plot of the specific protein
synthesis rate against the third power of the RNA : protein
ratio (Fig. 5c) was found to be linear [equation (12)] with a
Fig. 2. Relationship between specific growth rate, m, average
protein content, trun -1mp(av) and average cell volume, v(av). The
average cell volume was calculated by means of equation (9b),
Table 2. #, Data for E. coli (Table 2); &, datum for M. bovis
BCG (Table 3); solid line, empirical plot; broken line, linear plot
for E. coli (curve I) and M. bovis BCG (curve II).
Fig. 4. Correlations between vp(av), the concomitant rate of
energy consumption and specific growth rate. The rate of
energy consumption needed to maintain the rate of protein biosynthesis was calculated on the basis of the assumption that
4?2 high energy phosphate bonds (~P) are required for the formation of one peptide bond (Ingraham et al., 1983). #, Data
for E. coli calculated by means of equation (4) using the information given in Table 2; &, datum for M. bovis (Table 3).
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Fig. 3. Specific growth rate, m, is directly proportional to the
RNA : protein ratio. For average ribosome concentrations see
Tables 2 and 3. #, Data for E. coli; &, datum for M. bovis
BCG; broken line, extrapolation of curve for m against mRNA(av)/
mp(av).
733
R. A. Cox
Fig. 5. vp(av) Is a function of the RNA : protein ratio.#, Data for E. coli, Table 2; &, datum for M. bovis BCG, Table 3. (a)
vp(av)=mp(av)Nm as a function of mRNA(av)/mp(av); (b) log [vp(av)] as a function of log [mRNA(av)/mp(av)]; (c) vp(av) is directly
proportional to the third power of the RNA : protein ratio.
gradient h=7?56103 fg protein synthesized h21.
3
vp(av) ~h•½mRNA(av) =mp(av) ð12Þ
Growth and macromolecular composition of M.
tuberculosis. The era of the study of the macromolecular
composition of bacteria (see, for example, Maaløe &
Kjeldgaard, 1966) was centred around 1960–1970 and such
studies are now unfashionable. The only study of the chemical composition of a mycobacterium was carried out by
Winder & Rooney (1970), who reported a careful and
comprehensive study of Mycobacterium bovis BCG, a
member of the M. tuberculosis complex that is very closely
related to M. tuberculosis (Brosch et al., 2000). The mycobacterium was grown in a standard medium and the generation time was approximately 24 h. The results presented
in Table 3 were obtained from the data of Winder &
Rooney (1970) by making a number of simple calculations based on the definitions of the units used, and current data for the size of the genome, the average number
of genomes per cell (footnote * of Table 3) and the size of
the rRNA moiety of ribosomes (Cole et al., 1998). The
numbers of cells per millilitre, mDNA(av), mRNA(av), mp(av)
and v(av) were calculated. Thus, Table 3 summarizes all
the information that is available for the macromolecular
composition of a member of the M. tuberculosis complex in
particular and mycobacteria in general.
The limited data for M. bovis BCG are presented in Figs 2–5.
In Fig. 2, a plot of m against mp(av), the datum for M. bovis
BCG (curve II) does not conform with the data for E. coli
(curve I). More data were needed for M. bovis in order to
explain why this should be the case. In contrast, in Figs 3–5
data for the mycobacterium were found to form a smooth
curve with data for E. coli, suggesting that the associated
equations (11) and (12) may also apply to M. bovis BCG
growing optimally. This was confirmed, as may be seen
from the following example. Very similar protein contents
[mp(av)<156 fg] were reported for E. coli (tD=1 h) grown in
a glycerol medium (Table 2) and for M. bovis BCG
734
(tD=24 h) growing exponentially (Table 3). In contrast,
the corresponding RNA : protein ratios of E. coli (Table 2)
and M. bovis BCG (Table 3) were found to be 0?25
and 0?085, respectively, almost a three-fold difference.
Substitution of the RNA : protein ratios in equation (11)
yielded values of m of 0?73 and 0?025 h21, respectively, for
E. coli and M. bovis BCG; the observed values were 0?69 and
0?029 h21, respectively. The RNA : protein ratios were also
substituted in equation (12) in order to calculate the specific
protein synthesis rate [vp(av)]. The calculated specific protein
synthesis rates were 117 and 4?6 fg protein synthesized
per cell per hour, respectively, for E. coli and M. bovis
BCG; the observed values, calculated by means of equation
(5), were 108 and 4?5 fg protein synthesized per cell per
hour, respectively. Thus, equations (11) and (12) which
were derived for E. coli apply also to M. bovis BCG.
The ability of these equations to describe both E. coli and
M. bovis BCG emphasizes that the concentration of RNA
which is measured by RNA : protein ratio is an informative
cell parameter.
The macromolecular composition of stationary phase cells
(day 8 of Table 3) provides a guide to the properties of
minimal cells of the mycobacterium. When appropriate conversion factors (Table 3) were applied to data for M. bovis
BCG as to data for E. coli, the following picture emerged.
Minimal cells of E. coli were estimated to have an average
of 6200 ribosomes, a concentration of 8200 ribosomes per
femtolitre of cell volume. In contrast, minimal cells of
M. bovis BCG were estimated to have an average of 2200
ribosomes per cell, a concentration of approx. 4500 ribosomes per femtolitre of cell volume, which is close to the
limit inferred for viable cells from the intercept on the
RNA : protein axis in Fig. 3.
DISCUSSION
This study contributes towards establishing a theoretical
framework for further understanding the growth of
Microbiology 149
RNA : protein ratio and the rate of protein synthesis
Table 3. Properties of M. bovis BCG (Glaxo) during growth (at 37 ˚C) in batch cultures
Properties were calculated from the data of Winder & Rooney (1970). Medium A contained (l21) 75?5 g glycerol, approx. 0?5 g ammonium
ions, 4 g asparagine and 3 g pancreatic casein hydrolysate.
Properties*
Period of growth in shaken cultures (days)3
tD (h)
m (h21)
Cell mass (mg insoluble nitrogen ml21)
Number of cells (61028) per ml4
DNA per cell1
Genome equivalents
Megabase-pairs
mDNA(av)(fg)
RNA per cell1
Megabases
mRNA(av) (fg)
Ribosomes (nR(av)61023) per cell||
Protein per cell"
naa(av) (amino acids61028)
mp(av) (fg)
RNA : protein [mRNA(av)/mp(av)]
Cell volume (fl or mm3)
v(av)#
Concentration of ribosomes (particles per femtolitre61023)
nR(av)/v(av)
Medium A
2
3
4
r————— 24 —————R
r—————0?029————R
7?9
17?1
32?0
2?5
6?3
10?8
5
6
8
51?3
18?9
72?5
29?2
135?2
92?8
r——————————1?45±0?25——————–—––—––––––R
r——————————6?38±1?10–———————–—–––––––R
r–––––————————6?9±1?2–——————————–––––R
25?6
14?1
4?4
23?5
12?9
4?1
23?0
12?7
4?0
23?8
13?1
4?1
19?4
11?1
3?4
12?7
7?0
2?2
9?4
167
0?084
8?0
143
0?090
8?9
158
0?080
8?1
144
0?090
7?7
138
0?080
4?3
76
0?092
1?04
0?89
0?99
0?90
0?86
0?47
4?2
4?6
4?1
4?6
4?0
4?7
*The average number, G, of genomes per cell was calculated by means of the equation (Helmstetter & Cooper, 1968)
G~(tD =Cln2)f½2(CzD) =tD {2(D=tD ) g. A value of G=1?45±0?25 was obtained for a generation time, tD, of 24 h, a period, C, of DNA
replication of 10?33 h and an interval, D, between the completion of DNA synthesis and cell division of 6 h. The range indicated in the number
of genomes per cell reflects uncertainty in the length of the D period and is based on the extreme values D=1 h and D=13 h (Colston & Cox,
1999). The size of the genome was taken as 4?4 megabase-pairs (Cole et al., 1998). Hence, mDNA(av)=mgNG, where mg is the mass (fg) of the
genome. Values of mp(av) and mRNA(av) were calculated from the ratios DNA : protein : RNA=1NhNi, as follows: mp(av)=hNmDNA(av);
mRNA(av)=iNmDNA(av).
3Inoculated cultures were left to stand for 4 days and were then shaken for the period shown.
4The yield of cells was calculated from the equation x=FNyNz, where x is the number of cells per ml, y is the yield (mg) of acid-insoluble N per ml,
z is the appropriate amount of DNA (number of mg atoms P per mg insoluble N) and F, which is equal to 4?761010, is the number of
‘1?45 genome’ equivalents per mg atoms P.
1The amounts of RNA and DNA were originally expressed as mg atoms P; 1 mg atom of DNA P is equivalent to 4?761010 cells each containing
1?45 genome equivalents.
||The numbers of ribosomes were calculated on the basis of the assumption that rRNA comprises 83 % of total RNA, and that the RNA moiety of
a ribosome (16S rRNA, 23S rRNA and 5S rRNA) comprises 4700 nucleotides.
"Amounts of protein were originally expressed as g N; 85 % of total N was shown to be protein. Protein g N was converted to g protein by the
factor 1g N;6?23 g protein. This factor was computed for a protein having the composition of total E. coli protein. The data given in Arnstein &
Cox (1992) were used. The yield of cells was reported as the amount (mg) of insoluble N.
#v(av) Was calculated by means of equation (9b).
M. tuberculosis in two ways. First, an upper limit was placed
on the protein and RNA contents for minimal cells of M.
bovis BCG. Second, the correlations observed between
specific growth rates and macromolecular compositions of
an ultra-fast-growing organism (E. coli) can be extrapolated
to a very-slow-growing organism (M. tuberculosis). The
RNA : protein ratio was found to be a key property of the
bacterial cells studied. For cells growing optimally, the
specific growth rate was found to be linearly related to the
http://mic.sgmjournals.org
RNA : protein ratio [equation (11)] and the specific protein
synthesis rate was found to be directly proportional to the
third power of the RNA : protein ratio [equation (12)].
The significance of the correlations specified in equations
(11) and (12) lies in the relationship between the RNA :
protein ratio and ribosome concentration. A simple proportionality between the RNA : protein ratio and ribosome
concentration requires mRNA(av) to be directly proportional
735
R. A. Cox
to the average number of ribosomes, which seems likely
because rRNA and tRNA are thought to account for 98 %
or so of the RNA fraction. Furthermore, mp(av) is required to
be directly proportional to cell volume, or, more specifically,
to the volume in which protein synthesis takes place. In
other words, the concentration of protein is required to have
a constant value that is independent of growth rate. The
available data for E. coli (Table 2) indicate that protein
constitutes a fixed proportion, bm, of dry cell mass that is
independent of the specific growth rate; there are no data
reported for M. tuberculosis.
On the basis of the assumption that the RNA : protein ratio
is proportional to ribosome concentration, equation (12)
may be revised to relate the specific protein synthesis rate
directly to the third power of the ribosome concentration.
This proposed relationship can be shown to be in accord
with our knowledge of mRNA-directed protein synthesis.
The exponential increases in mass, volume, RNA content
and protein content during growth ensure that the concentrations of RNA and protein are kept constant and
require that the amounts of substrates, enzymes and products increase concomitantly to maintain constant concentrations. The balance between components of the machinery
for protein synthesis is maintained if the proportions of
individual components such as tRNA and protein
factors such as elongation factor EF-Tu, etc., are kept in
balance with the number of ribosomes. For example,
9?26–9?29 tRNAmolecules per ribosome and five to seven
copies of EF-Tu were reported for E. coli independently
of growth rate (Table 2).
Protein synthesis involves many steps and many components (for review see Al-Karadagh et al., 2000). The ratelimiting step in peptide bond formation is the interaction
of a ternary complex (tc) composed of aminoacyl tRNA
(aatRNA), elongation factor EF-Tu and GTP with the A-site
of the ribosome (Pape et al., 1998). The overall reaction is
given by equation (13).
A-siteztc?A-site•aatRNAzEF-Tu•GDPzPi
ð13Þ
The reaction involves ribosomes, aatRNA and EF-Tu. The
concentrations of the latter two components may be directly
related to ribosome concentration (Table 2), suggesting that
the rate of peptide bond formation is a function of the third
power of the ribosome concentration. Two further factors
apply to protein synthesis during cell growth; namely, the
concentration of protein remains constant, whereas the cell
volume increases exponentially.
The correlation observed between specific growth rates and
macromolecular compositions of both an ultra-fast and a
very-slow grower reflects the importance of both protein
concentration and the rate of protein biosynthesis in cell
growth. For example, the protein content reflects cell
volume, the RNA : DNA ratio reflects the number of
ribosomes per cell and the RNA : protein ratio reflects the
concentration of ribosomes and hence, the specific protein
736
synthesis rate. Finally, the ability to measure the ratios
DNA : protein : RNA simply and accurately, using a minimal
number of cells, would be advantageous; flow cytometry
may offer this potential (Diaper & Edwards, 1994: Turner
et al., 2000).
ACKNOWLEDGEMENTS
I thank Simon A. Cox for his help in the preparation of this manuscript,
my colleague Dr I. D. J. Burdett for his expert advice and constant
encouragement and my colleague Dr J. Ecclestone for advice on
nomenclature. I thank Dr R. Rosenberger of the National Institute for
Biological Standards and Control, South Mimms, UK, for his interest
and Professor C. Ratledge of the Department of Biological Sciences,
The University of Hull, UK, for his invaluable advice on mycobacterial
metabolism.
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