Modulation of Chemical Composition and Other
Parameters of the Cell by Growth Rate
HANS BREMER AND PATRICK P. DENNIS
97
HISTORY
Schaechter et al. (121) first demonstrated that the macromolecular composition of the bacterial cell was
related to its metabolic activity and that RNA-containing particles were involved in the synthesis of protein.
When they examined the variations in growth and composition of Salmonella typhimurium cultures in
different media, they realized that the cellular contents of DNA, RNA, and protein at a given temperature
depended only on the growth rate and not on the nutrient supplement in the growth medium used to achieve
that growth rate. They also found (i) that fast-growing bacteria are larger and contain more DNA, RNA,
and protein than slow-growing bacteria, (ii) that the amounts of these macromolecules are exponential
functions of growth rate, and (iii) that the exponents of these functions are different for different
macromolecules. The last implies that the relative proportions of the different macromolecules change with
growth rate; at a given temperature, RNA and ribosome concentration increase with increasing growth rate,
DNA concentration decreases, and protein concentration remains almost constant. When the growth rate
was varied by changing the temperature rather than the nutrient content of the growth medium, the DNA,
RNA, and protein concentrations remained invariant.
These early studies of bacterial physiology are documented by Maaløe and Kjeldgaard (95). The
statement of observations in terms of simple mathematical relationships was characteristic for the
“Copenhagen approach,” in which calculated constants, proportionalities, and quadratic or exponential
functions suggested special control mechanisms. Many of these relationships later turned out to be more
complex than originally imagined. Nevertheless, these propositions have stimulated thought and led to
more sophisticated observations; the book continues to be provocative, as many of the fundamental
problems posed in it are still far from being solved.
A theoretical basis for explaining the empirical relationships of the early Copenhagen school was not
available until Cooper and Helmstetter (32) derived a formula for determining the average amount of DNA
per cell in an exponential culture as a function of C (the time required to replicate the chromosome), D (the
time period between termination of a round of replication and the following cell division), and τ (the
culture doubling time). This theory also included the important concept of overlapping rounds of
chromosome replication, where a round of replication is initiated before the previous round is completed.
This occurs when τ is less than C and explains how bacteria are able to grow with a doubling time shorter
than the time required for chromosome replication.
Donachie (51) extended this theory by introducing the concept of the “initiation mass” (the cell mass
per replication origin at the time of initiation) and derived the average mass per cell, or amount of protein
per cell, as a function of C, D, τ, and an additional parameter, mass or protein per replication origin (MO or
PO , respectively). The Cooper-Helmstetter equation predicts the amount of DNA per cell as a function of
C, D, and τ; the additional parameter, PO , links the amount of protein to the amount of DNA.
At about the same time, Schleif (122) and Maaløe (93) began to establish a theoretical relationship
between the amounts of protein and RNA in the cell and the two parameters, cp and βr , which define
ribosome function (βr is the fraction of total ribosomes actively engaged in peptide chain elongation; cp is
the rate of peptide chain elongation). Based on these relationships, Churchward et al. (27) were able to
describe the global cell composition in terms of DNA, RNA, and protein content as a function of the
doubling time, τ, and five additional parameters, C, D, PO, βr, and cp.
(It is noteworthy that these parameters include the peptide and DNA chain elongation rates [C period],
but not the RNA chain growth rate. Intuitively it would seem that all three chain elongation rates should be
equally important and contribute to the DNA, RNA, and protein content. The explanation for this paradox
is that the RNA chain elongation rate is implicit in the value of τ; if one asks for the composition as a
function of growth rate, one assumes τ as a given parameter without asking how its value was achieved.
Thus the cell composition is indeed determined by all three macromolecular chain elongation rates.)
OBSERVED CELL COMPOSITION OF E. COLI B/r
Cell Growth-Related Parameters
In Table 1, a number of growth-related parameters are listed that are generally useful in describing or
establishing the macromolecular composition of bacterial cultures. These parameters can be divided into
five classes: (i) structural parameters that are inherently constant and do not vary with the growth rate, like
the number of rRNA nucleotides in a 70S ribosome; (ii) partition factors which are essentially invariant
and growth rate independent, like the fraction of total RNA that is stable rRNA; (iii) other partition
parameters which change as a function of the exponential growth rate and have substantial effects on cell
composition, like the fraction of active RNA polymerase synthesizing rRNA and tRNA; (iv) kinetic
parameters describing functional activities (the values of some of the parameters are essentially invariant,
whereas others appear to approach a maximum or biological limit value, like the peptide chain elongation
rate); (v) chromosome replication and cell division parameters that in general do not limit the exponential
growth rate, like the C period.
Reference Units
Physiological parameters describing cell composition, like the amount or synthesis rate of a particular
component, require a reference unit such as “per cell,” “per cell mass,” “per amount of protein,” “per
microgram of dry weight,” etc. Except for studies dealing with the cell cycle, we recommend in most cases
the use of cell mass (e.g., “per OD460” [unit of optical density at 460 nm]) as a reference unit because its
determination is simpler, faster, and more accurate than that of other units. The per-mass values may also
be used to estimate the intracellular concentrations because the average cell volume per mass unit changes
very little with growth conditions. In many cases the concentration is more relevant than the amounts of
components per genome equivalent of DNA or per cell. Since the reference parameters are themselves
subject to growth rate-dependent regulation, no single reference unit is ideal or more natural than another.
There has been a tendency in the recent literature for authors to state that rRNA or ribosomes
accumulate in proportion to the square of the growth rate. This, of course, is incorrect because the unit of
reference is undefined. As first pointed out by Maaløe (93), the rate of RNA accumulation per genome does
increase with the square of the growth rate, µ. This reflects the fact that the amount of RNA per genome is
proportional to the growth rate (at least above growth rates of 0.5 doubling per h). Since in any exponential
system the synthesis rate is proportional to the amount, and the amount is already proportional to µ, it
follows that the rate must be proportional to µ2. However, since the ratio RNA/DNA reflects both
chromosome replication and RNA synthesis control, this square relationship has no particular significance
for ribosome control itself; the relationship no longer holds in certain replication control mutants which
alter DNA content but show no change in rRNA control (27, 28).
Macromolecular Composition as a Function of Growth Rate
For physiological studies, Escherichia coli B/r has several advantages over other E. coli strains. Due to a
special property of its outer membrane, this strain can be age-fractionated by the membrane elution
technique (71) and used to measure cell cycle-related parameters. Helmstetter and Cooper (70) used this
strain to measure the C and D periods and deduced from these measurements the relationships between
chromosome replication and the cell division cycle. This strain also (i) has a lesser tendency for clumping
and “snake” formation than other strains of E. coli, (ii) grows well in minimal media, and (iii) is free of
mutations which might otherwise influence the growth rate or composition. A disadvantage is that the
strain is genetically incompatible with K-12 strains because of the B and K restriction systems. Mutants
deficient in B restriction or with K-12 restriction and modification are available from the authors. For these
reasons, E. coli B/r is the preferred choice for physiological studies and composition measurements.
Table 2 lists the amounts of protein, RNA, and DNA and related physiological parameters for cultures
of E. coli B/r growing exponentially at 37°C in different growth media at rates between 0.6 and 2.5
doublings per h. The per-mass values (top section) represent averages obtained from curves drawn as a best
fit through individually measured points (28). The actual measurements fluctuate by about 15% around
these curves. Most of this scatter represents a true variation from culture to culture (the contribution due to
measuring errors is about ±6%, 2.5%, 5%, and 5% for protein, RNA, DNA, and cell number, respectively).
Protein, RNA, and DNA were measured colorimetrically, and cell numbers were determined with an
electronic particle counter as indicated in Table 2. From the per-mass values, protein and RNA per genome
and protein, RNA, and DNA per cell were calculated.
The sums of the weights of protein, RNA, and DNA are proportional to the mass in OD460 units and
correspond to 75 to 91% of the dry weight; lipids, carbohydrates, soluble metabolites, and salts represent
the remaining 9 to 25% of the total dry mass. The relative proportions of the macromolecules at the
different growth rates are illustrated in the bar graphs of Fig. 1. The greatest relative change is found in the
RNA sector, reflecting the increasing concentration of ribosomes at higher growth rates. More ribosomes
are required to support the higher rate of protein synthesis in rapidly growing cells.
The growth rate-dependent changes in the relative proportions of DNA, RNA, and protein can be described
by the two ratios, RNA/protein and DNA/protein. With increasing growth rate, RNA/protein increases and
DNA/protein decreases (Fig. 2a and b). The increasing RNA/protein ratio reflects the control of ribosome
synthesis (see equation 18 in Table 6 below), and the decreasing DNA/protein ratio reflects the control of DNA
replication (see legend to Fig. 2j). The RNA/protein ratio is proportional to the number of ribosomes per amount
of protein and, therefore, is a measure for the cytoplasmic ribosome concentration. The growth rate of an
exponential culture is equal to the product of ribosome concentration times the rate of ribosome function (i.e.,
the protein synthesis rate per average ribosome or the ribosome efficiency; 74, 122). Therefore, at a given
growth rate, the protein synthesis rate per ribosome can be calculated from the RNA/protein ratio. When the
growth rate increases, the rate of ribosome function approaches a maximum value, corresponding to 21 amino
acids polymerized per second per active ribosome (Fig. 2c, right ordinate scale).
The number of replication origins in a culture was obtained by measuring the amount of DNA that had
accumulated 50 to 80 min after treatment of a culture with rifampin. Rifampin stops initiation of
replication, but allows the ongoing rounds of replication to go to completion, so that the number of
completed chromosomes becomes equal to the number of functional origins present at the time of rifampin
addition (128, 129). The mass per origin, MO, was then obtained by dividing this number of completed
chromosomes by the OD460 observed at the time of rifampin addition. The amount of protein per origin, PO,
was found from MO by multiplication with the amount of protein per mass, PM (Table 2).
Protein per origin, PO, is a formal measure for the control of replication initiation; it has a meaning
similar to cell mass per origin, MO, which is proportional to the “initiation mass” defined by Donachie (51).
The initiation mass is the cell mass at the time of initiation, divided by the number of replication origins at
which initiation occurs, i.e., Mi/Oi (Fig. 2j), whereas MO is the total mass in a given volume of exponential
culture, divided by the number of copies of oriC present in that volume. Both PO and MO increase with
growth rate and approach a constant value at growth rates above 1.5 doublings per h (Fig. 2j; PO = 4 × 108
amino acids per oriC). The exact growth rate dependence of PO (or MO) may depend on the strain used. A
decreasing initiation mass with increasing growth rate has been reported for a K-12 strain of E. coli (130).
The parameter PO links DNA replication to protein synthesis and growth. Whereas the time intervals
between consecutive cell divisions vary considerably, the time intervals between consecutive initiations of
rounds of replication vary very little (83). This is presumed to reflect the accumulation of a hypothetical
protein that triggers initiation at a certain threshold value (17). This putative initiation protein would be
made as a constant fraction of total protein synthesis, thereby linking chromosome replication to protein
synthesis.
The numbers of replication termini and of forks on the chromosome were calculated from the values of
the C and D periods (taken from Table 3, below). These numbers relate to the extent of chromosome
branching as a result of increasing overlap in rounds of replication as the cells grow faster (Fig. 1).
Parameters Pertaining to the Macromolecular Synthesis Rates
The rates of accumulation of protein, RNA, and DNA or the rate of cell division (or of any other extensive
property, X, of the system) can be calculated using the first-order rate equation dX/dt = Xkµ = X(ln2)/τ,
where µ is in doublings per hour, τ is in minutes, and k = (ln2)/60; the rate is per minute.
For DNA, ribosomes, and protein, the rates of synthesis during periods of balanced growth are
essentially equal to the rates of accumulation since their turnover is negligible (37, 38). For total RNA,
however, the instantaneous synthesis rate is substantially higher than the accumulation rate because of the
instability of mRNA and of spacer sequences in the primary rRNA and tRNA transcripts.
In Table 3, physiological parameters related to the macromolecular synthesis rates have been divided
into three groups: parameters pertaining to (i) RNA polymerase synthesis and function, (ii) ribosome
synthesis and function, and (iii) DNA synthesis and cell division. Some of these parameters were observed,
and others were calculated as indicated (see Table 3 footnotes).
FIGURE 1 Relationships between growth rate, cell size, chromosome replication, transcription, and
macromolecular composition. (Left column) Average cell size (mass per cell, Table 2) for E. coli B/r
growing with a doubling time,τ, ranging from 100 to 24 min is depicted by the shaded ovals. An idealized
cell cycle with the major cell cycle events, ranging from cell age 0.0 (a newborn daughter cell) to 1.0 (a
dividing mother cell), is presented for each growth rate. The position of an average cell of age 0.41
(defined so that 50% of the cells in the population are younger and 50% are older) is indicated by A. The
cell ages at initiation (I) and termination (T) of chromosome replication are also indicated. The dashed
portion of the age axis indicates a period during which there is no DNA replication (no replication forks on
the chromosome). The line portions represent periods where there are two forks per chromosome structure,
and the heavy bar portions indicate the age periods during which there are six forks per chromosome
structure. After termination, there are two chromosome structures per cell which are segregated to the
daughter cells at the subsequent cell division (at age 1.0). (Center column) Structure of the replicating
chromosome or chromosomes in the average cell of age 0.41. For a 24-min cell cycle (τ = 24 min), the
chromosome pattern indicates that replication is being initiated and that each of these chromosome
structures has multiple (six) replication forks. The amount of DNA in these structures in genome
equivalents (G) is indicated (calculated from C, D, and τ in Table 2 for a cell of age 0.41). The number of
origins (O), termini (T), and forks (F) in this average cell are also indicated. (Right columns) The synthesis
rates of rRNA (rR), tRNA (tR), r-protein mRNA (rpm), and other mRNA (om), expressed as a percent of
total transcription, and the macromolecular composition are illustrated in bar graph form. The stable RNA
fraction of the total transcription increases with increasing growth rate, the r-protein mRNA fraction
remains essentially constant, and the total mRNA fraction decreases. The proportion of the total mRNA
that is r-protein mRNA clearly increases, approximately in parallel with the increase in αr, the fraction of
the total protein synthesis that is r-protein, implying that there is transcriptional control of r-protein operons
(the transcription values are adapted from references 42 63, 89 and P. Dennis, unpublished data). Relative
amounts of protein (P), DNA (D), RNA (R), and other components (O) as percent of the total cell mass are
from the data in Table 2.
FIGURE 2 Amounts and synthesis rates of molecular components in bacteria growing exponentially at
rates between 0.6 and 2.5 doublings per h. The values of the RNA-to-protein (R/P; panel a) and DNA-to-
protein (G/P; panel b) ratios were calculated from lines 1, 2, and 3 in Table 2. The ribosome efficiency
(i.e., the protein synthesis rate per average ribosome; panel c, left ordinate) was calculated from the number
of ribosomes per cell (line 15, Table 3) and the rate of protein synthesis per cell. The latter was obtained
from the amount of protein per cell (line 10, Table 2) using the first-order rate equation. The peptide chain
elongation rates (panel c, right ordinate) are 1.25-fold higher than the ribosome efficiency values and
account for the fact that only about 80% of the ribosomes are active at any instant. The fraction of the total
RNA synthesis rate that is stable RNA or mRNA (rs or rm; panel d) is from line 5, Table 3. The rates of
stable RNA and mRNA synthesis per amount of protein (rs/P or rm/P; panel e) were calculated from lines 9
and 10, Table 3, divided by the amount of protein per cell (line 10, Table 2). The ppGpp per protein value
(ppGpp/P; panel f) is from line 11, Table 3. The cell age at which chromosome replication is initiated at
oriC (ai in fractions of a generation; panel g) is calculated from C and D (lines 23 and 24, Table 3) and
equation 14 in Table 5. The protein (or mass) per cell at replication initiation (panel h) was calculated from
the initiation age (ai, panel g) and the cell mass immediately after cell division (age zero; i.e., a = 0), using
equation 17 in Table 5. The latter was obtained from the average protein or mass content of cells (lines 10
or 13, respectively, Table 2), using equation 16 of Table 5. The number of replication origins at the time of
replication initiation (Oi, panel i) was obtained from the values of C and D (Table 3), using equation 15 of
Table 5. The initiation mass (panel j), given as protein (or mass) per replication origin at the time of
replication initiation, was obtained as the quotient of the values for Pi (or Mi) and Oi shown in panels h and
i.
RNA Polymerase Synthesis and Function.
RNA polymerase concentration. The instantaneous rate of transcription in the cell depends on the
concentration of RNA polymerase, αp, measured as the fraction of total protein that is RNA polymerase
core enzyme (three subunits, α2, β, and β′). The values of αp increase with the growth rate and reflect the control of
the synthesis of the β and β′ subunits of RNA polymerase. Since the α subunit is in excess in E. coli (see Table 4),
the amount of core enzyme would seem to be limited by the amount of β and β′ subunit polypeptides. The
synthesis of these subunits is under dual transcriptional control (i) at the level of initiation at an upstream promoter
and (ii) at the level of termination-antitermination at an attenuator in front of the rpoB gene (6, 7, 40–42, 52). Both
controls are growth rate dependent, but the mechanisms mediating these controls are poorly understood. The
initiation control might involve the effector nucleotide guanosine tetraphosphate (ppGpp), whereas the read-
through at the attenuator might involve an autoregulation by free or active RNA polymerase (40, 52, 96).
There is also translational control of the rpoBC mRNA (43, 47, 48). Combining the observed αp values
with the protein per cell values of Table 2, the number of RNA polymerase molecules per cell has been
calculated and was found to increase from 1,500 to 11,400 between growth rates of 0.6 and 2.5 doublings
per h.
RNA polymerase activity. The total complement of RNA polymerase enzyme in the cell can be
partitioned into active RNA polymerase (enzymes engaged in RNA chain elongation) and inactive RNA
polymerase (DNA-bound, idling polymerase; unbound, free enzyme, ready to bind to a promoter; and truly
inactive, e.g., immature enzyme). The active enzyme is determined from the rate of transcription and the
RNA chain elongation rate. Due to a difference in the chain elongation rates for mRNA and rRNA (see
below), the calculation contains separate components for mRNA and stable RNA. The calculation shows
that only 17 to 30% of the RNA polymerase enzyme is active at any instant; this fraction, βp, is seen to
increase with growth rate (125). In ppGpp-deficient strains, up to 60% of the total RNA polymerase was
found to be active; this has suggested that part of the inactive polymerase is transiently stalled at
ppGpp-dependent pause sites during the synthesis of mRNA (74). Most of the remaining inactive RNA
polymerase might be involved in ppGpp-independent transcriptional pausing.
Within the cell, it seems that active RNA polymerase limits the rate of transcription and that the DNA
template is in excess. This was demonstrated using a mutant bacterial strain that exhibits altered DNA
replication control which results in a lower DNA concentration. In spite of the lower DNA concentration
there was no change in the level of transcription, implying that the total rate of transcription is regulated at
the level of active RNA polymerase in the cell and not the level of available DNA template (28).
What is the state of inactive RNA polymerase within the cell? Experiments with a minicell strain
indicate that most of the (core) RNA polymerase is sequestered with the DNA (N. Shepherd, Ph.D. thesis,
University of Texas, Dallas, 1979). This enzyme might either be bound nonspecifically to DNA (21), or,
alternatively, it might have initiated transcription but is halted at some pausing site (81, 100), perhaps
associating with termination-antitermination factors (66). It remains unclear why there is such a large
excess of inactive RNA polymerase, and whether and how the partition between active and inactive
enzyme is maintained.
Partitioning between stable RNA and mRNA synthesis. The active RNA polymerase enzyme can be
further partitioned into the fractions engaged in the synthesis of stable RNA species (rRNA, tRNA, and
their spacers; ψs) and of mRNA (ψm = 1 – ψs). This partitioning is strongly correlated with, and possibly
controlled by, the nucleotide effector ppGpp (119). During periods of amino acid insufficiency, ppGpp is
derived from the relA-dependent system and elicits the well-characterized stringent response (40, 49, 69).
During exponential growth at different rates, ppGpp is derived from a relA-independent system (3, 56, 117)
that involves a product of the spoT gene (73, 141).
Nomura and his coworkers have suggested that free ribosomes rather than ppGpp regulate transcription
of rrn operons (77, 105). However, when free ribosomes were allowed to accumulate by limiting the
concentration of the translation initiation factor IF2, rRNA synthesis was stimulated (30), not inhibited as
predicted by the free ribosome feedback hypothesis. At the same time, ppGpp levels were reduced. Thus,
limitation of IF2, like treatment with chloramphenicol, induces the equivalent of the relaxed response (39,
72, 84). Furthermore, in strains unable to synthesize ppGpp due to deletions in the genes for the two
separate ppGpp synthetases, ψs was found to be growth rate-invariant (74). This observation supports the
idea that ppGpp is involved in the partitioning of RNA polymerase into stable RNA- and mRNA-
synthesizing fractions. In an in vitro system with purified RNA polymerase, ppGpp has been found to
preferentially inhibit rRNA synthesis (e.g., references 136 and 137), whereas attempts to find a similar
effect by free ribosomes have failed (77).
The levels of ppGpp listed in Table 3 are seen to decrease from 55 to 10 pmol per OD460 when the
growth rate increases from 0.6 to 2.5 doublings per h. At the same time, the transcription from rRNA and
tRNA genes, expressed as the fraction of the total instantaneous rate of transcription, rs/rt, increases from
40 to 85%. The parameters ψs and rs/rt both express the same ppGpp-correlated partitioning of RNA
polymerase; the difference between these two parameters reflects the difference in the chain elongation
rates for rRNA and mRNA. Since rRNA chains grow faster than mRNA chains, it follows that for equal
numbers of polymerase-transcribing stable RNA and mRNA genes (ψs = 0.5), the rate of stable RNA
synthesis must be somewhat greater than the rate of mRNA synthesis (i.e., rs/rt > 0.5).
Rates of stable RNA and mRNA synthesis per cell. The rate of stable RNA synthesis was calculated
from the amount of RNA, determined from its UV absorbance (Table 2). The rate of mRNA synthesis was
found from its relative rate (rm/rt = 1 – rs/rt) and the absolute rate of stable RNA synthesis. It is seen that the
stable RNA synthesis rate per cell, in particular, increases dramatically with growth rate, which accounts
for the higher RNA content in rapidly growing bacteria (see Fig. 1). The same relationships are apparent
when rates of stable RNA and mRNA synthesis are expressed per amount of protein (Fig. 2e).
Chain elongation rates of stable RNA and mRNA. Whereas the chain elongation rate of stable RNA is
independent of the growth rate and equal to 85 nucleotides per s (99, 120, 124, 139), the chain elongation
rate of mRNA appears to increase somewhat and approaches a maximum value of 55 nucleotides per s at
high growth rates (19, 139). The reason for this velocity difference is not known, although it may be related
to polymerase pausing or stuttering during chain elongation. The leader regions of rrn transcription units
are known to contain strong Nus factor-dependent antitermination sites (85, 103). As a consequence,
transcripts initiated at rrn promoters are able to transcribe through Rho protein-dependent transcription
terminators and can reverse transposon-induced polarity (1, 127). Thus, for rRNA transcripts this pausing
or stuttering may be minimized by the antitermination state of the RNA polymerase and account for the
increased stable RNA chain elongation rate.
Ribosome Synthesis and Function.
Ribosomal components and their control. The ribosome consists of three species of RNA (16S, 23S, and
5S) and 52 species of protein. The three rRNAs are processed from a 35S primary transcript derived from
seven unlinked rrn transcription units. The 52 different ribosomal proteins (r-proteins) are encoded by
genes in about 20 different transcription units located at 14 different positions on the E. coli chromosome
(4). The primary regulation of ribosome synthesis is most likely the ppGpp-correlated partitioning of RNA
polymerase which, at a given concentration and activity of RNA polymerase, sets the rate of transcription
of rRNA and tRNA genes (36, 119; see also Fig. 1). However, even in the absence of ppGpp in bacterial
strains deleted for both ppGpp synthetases (141), the stable RNA gene activity increases with increasing
growth rate, apparently as a result of only an increase in the concentration of active RNA polymerase (74).
There is the additional possibility that ppGpp might also influence either directly or indirectly the
transcription of r-protein operons within the mRNA sector to achieve an approximate balance between the
production of the rRNA and r-protein components of the ribosome (40, 49, 50). This is the transcriptional
control of r-protein operons (35, 42, 63, 87, 89). It is clear from Fig. 1 that the promoter activities of rRNA
operons and of r-protein operons do not respond coordinately to changes in the steady-state growth rate.
Coordination is neither expected nor required if the ratio of r-protein mRNA to total mRNA is important in
determining αr.
A second mechanism in addition to the transcriptional control, used to accurately balance or fine tune
the translation frequency of the 20 different mono- and polycistronic r-protein mRNAs to the availability of
free rRNA, involves an autogenous translational control: specific regulatory r-proteins bind to the leader
regions of their own mRNAs and inhibit further translation when they are not rapidly incorporated into
assembling ribosomes (47, 55, 78, 88, 105).
During exponential growth at moderate to fast rates, turnover of ribosomal components appears to be
negligible. During slow growth, some excess of newly made rRNA is degraded (63, 106); this results in a
slight increase in the proportion of tRNA to rRNA during slow growth (124).
r-Protein synthesis. A measure for the synthesis of r-protein is its proportion of total protein, αr.
Values of αr have been determined (i) from the protein content of ribosomes and (ii) from the RNA-to-
protein ratio. Both methods give essentially identical values. The proportion of r-protein increases with
growth rate from 9% at 0.6 to 21% at 2.5 doublings per h. It has been reported that the r-protein mRNA
synthesis per total RNA synthesis rate is nearly invariant with growth rate, but, when expressed as a
fraction of the rate of (total) mRNA synthesis, it increases with growth rate like αr or rRNA synthesis (Fig.
1; 42, 63, 89). These observations support the idea that, to a first approximation, r-protein production is
matched to rRNA production at the level of transcription.
Ribosomes and tRNA per cell. Given that r-protein matches rRNA and that rRNA and tRNA are
synthesized in constant proportions, corresponding to nine tRNA molecules per 70S ribosome (37, 54, 124,
143), the numbers of ribosomes and of tRNA molecules per cell were calculated from the total amount of
RNA. In the growth range considered, the number of ribosomes per average cell was seen to increase 10-
fold from 6,700 to 71,000. This reflects both an increasing ribosome concentration (ribosomes per OD460
unit of cell mass) and increasing cell size (OD460 units per cell). For achieving rapid growth, only the
ribosome concentration is relevant.
Ribosome activity. The fraction of ribosomes engaged in peptide chain elongation at any instant, βr ,
has been estimated from the ribosome content of polysomes and was found to be about 80% and
independent of the growth rate (57). Since the assembly and maturation of ribosomes takes about 5 min
(86), it appears that, at least in fast-growing bacteria, the major portion of inactive ribosomes are particles
in the final stages of ribosome assembly.
Peptide chain elongation rate. The peptide chain elongation rate has been estimated (i) from pulse-
labeling kinetics of nascent polypeptides of given length (111, 142) and (ii) from the first appearance of β-
galactosidase activity after induction (33, 61, 110, 111, 142). These measurements indicate that the peptide
chain elongation rate increases with growth rate from about 13 to 20 amino acid residues per s between 0.6
and 2.5 doublings per h. These values are in agreement with the values calculated in Table 3 from the
RNA-to-protein ratio under the assumption that 80% of the ribosomes are active at any instant.
What limits the peptide chain elongation rate during slow growth? During fast growth when the peptide
chain elongation rate is maximal (20 amino acids per s; Table 3), ribosomes seem to be saturated with
substrates (elongation factor Tu-GTP-aminoacyl-tRNA ternary complex), implying that the peptide chain
elongation rate is limited by the rate of peptide bond formation or ribosome translocation on the mRNA.
During slow growth, the (submaximal) peptide chain elongation rate is probably limited by the extent of
tRNA charging (i.e., by the ratio of charged to uncharged tRNA) and to some extent by the types of codons
being employed, rather than by the absolute concentration of charged tRNA. This is suggested by the
observation that in a nutritional shift-up from a minimal medium to an amino acid-supplemented medium
the protein synthesis rate per average ribosome increases immediately in a stepwise fashion, before the
concentrations of tRNA and EF-Tu have increased (20). During further postshift growth, the
concentration of tRNA, and thus presumably also of charged tRNA, increases severalfold (e.g., about
threefold in a shift from succinate minimal to glucose amino acids medium) without further increasing
ribosome activity (126). It is also unlikely that ppGpp binds to and thereby inhibits elongation factor Ts
function during slow growth since the peptide chain elongation rate was unaffected in a ribosome control
mutant with 10-fold reduced level of ppGpp (90).
It is conceivable that in poor media, the greater proportion or abundance of mRNAs with hard-to-read
codons might contribute to the reduced peptide chain elongation rate. It is well established that the utilization of
codons in the genes of E. coli is not random (113, 123, 138). Genes expressed from strong promoters tend to
contain a higher proportion of major codons, whereas genes expressed from weak promoters contain a lower
proportion of major codons. With some exceptions, major codons are recognized by abundant tRNA species and
minor codons are recognized by rare tRNA species (76). However the concentration of minor tRNAs is probably
not limiting the rate of peptide chain elongation. Instead, each codon probably has a specific transit time for
progressing through the A- and P-sites of the ribosome that depends upon the physical-chemical nature of the
tRNA-mRNA (anticodon-codon) interaction. As an example, the GAA and GAG glutamic acid codons are both
recognized by the abundant tRNAGlu2, but decoding of the prevalent GAA triplet involving strict Watson-Crick
base pairing occurs threefold more rapidly than the decoding of the GAG triplet involving wobble base pairing
(110, 131, 132).
Ribosomal gene dosage and gene activity. There are seven rrn genes on the E. coli chromosome;
most of them map near the chromosomal origin of replication (4). The actual number of rrn genes per
(average) cell is much greater than 7, ranging from 12 to 36, depending on the extent of chromosome
branching (see Fig. 1). From this number and the rate of rRNA synthesis, the rate of initiation of rRNA
chains at each rrn gene was calculated and was found to increase with increasing growth rate from 4/min to
61/min. These are the average values in an exponential culture. Measurements of DNA and RNA synthesis
rates in age-fractionated cultures indicate that replication causes the number of rrn genes to fluctuate nearly
twofold during the cell cycle without abrupt or concomitant changes in the rate of rRNA synthesis (36).
Instead, the rate of rRNA synthesis increases by a factor of 2 in a slow and continuous manner, without
perturbation, as cells progress through the division cycle; this pattern is followed regardless of when the rrn
genes are replicated (36, 37). This implies that the rate of transcription initiation at rrn genes changes (i.e.,
decreases) nearly twofold at the time the rrn genes are duplicated. Accordingly, the average rate of 61
initiations per min per gene means a fluctuation from about 40 to 80 initiations per min per gene during the
cell cycle for a bacterium with a 24-min doubling time (actually the fluctuation is somewhat less because
rRNA genes are not all clustered at exactly the same map position). Therefore the copy number of rrn
genes does not limit the rate of rRNA synthesis under conditions of exponential growth. In addition, if
there are up to 80 initiations per min per gene in rapidly growing bacteria, the time for the formation of the
open promoter complex must be less than 1 s.
TABLE 4 Stoichiometric content of transcription-translation
proteins in E. coli
Protein Mol wt
(103)αia
(t = 40 min)
(%)
Molecules (τ = 40 min) Reference(s)
Per OD460
(1012)Per ribosome
r-Protein 850 13.5 10.2 1.00 38, 44
L7/L12 12 0.81 40.8 4.00 134
EF-Tu 42 5.55 55.1 5.40 112
EF-G 84 1.66 8.2 0.80 112
EF-Ts 31 0.13 1.8 0.18 112
IF1 8 0.04 2.5 0.25 75
IF2 115 0.52 3.1 0.30 75
IF3 20 0.07 2.0 0.20 75
Leu S 100 0.12 0.5 0.05 112
Phe S-β 94 0.21 1.0 0.10 112
Lys S 58 0.11 0.8 0.08 112
Arg S 58 0.08 0.6 0.06 112
Gly S 77 0.17 0.9 0.09 112
Val S 106 0.14 0.6 0.06 112
Glu S-β 48 0.10 0.9 0.09 112
Ile S 107 0.24 1.0 0.10 112
Phe S-α 36 0.11 1.2 0.12 112
Gln S 61 0.11 0.8 0.08 112
Thr S 65 0.09 0.6 0.06 112
RNA polymerase β150 0.52 1.4 0.14 112
RNA polymerase α 39 0.37 3.8 0.37 112
RNA polymerase, core 375 1.30 1.9 0.19 125
00aαi, synthesis rate of the protein as a percentage of total protein synthesis rate.
These conclusions have been further corroborated by the observation that the rRNA synthesis rate is
not reduced in bacteria with a mutational defect in the control of chromosome replication that leads to a
40% reduction in the concentration of all genes, including rrn genes (28). Furthermore, up to three rrn
genes may be deleted from the E. coli chromosome without much change in the growth rate, again
suggesting that the rrn gene dosage does not limit the rate of rRNA synthesis (31; it is to be noted,
however, that contrary to the authors’ interpretation, we believe that the rRNA synthesis rate per gene was
not suitably measured because of the use of inappropriate reference units).
Translation frequency of mRNA. With increasing growth rate the average mRNA becomes more and
more crowded with ribosomes, i.e., the average spacing of ribosomes on mRNA decreases from 120
nucleotides to 60 nucleotides in the range of growth rates considered. Here again, there is no indication that
mRNA is a limiting factor for protein synthesis. Immediately after a nutritional shift-up the concentration
of mRNA decreases temporarily because the increased rate of rRNA synthesis occurs partly at the expense
of mRNA synthesis; at the same time, the protein synthesis rate increases (45, 102, 126). The increased
spacing of ribosomes during slow growth could potentially cause some mRNA instability or premature
termination of transcription (polarity), but whether this is indeed the case has not been established.
Component proteins of the transcription-translation apparatus. The protein composition of the
ribosome is essentially invariant with the growth rate, and each of the 52 different r-proteins is present in
one copy per 70S particle (38, 68). The only exception to this is protein L7/L12, which is present in four
copies per ribosome (134). This implies that the synthesis rate of each r-protein is strictly coordinate with
the synthesis of rRNA and also tRNA at growth rates above 0.5 doublings per h. At slower growth rates
there appears to be a slight excess in the synthesis rate of stable RNA (62, 63, 106); the excess rRNA is
rapidly degraded, whereas the tRNA accumulates.
The synthesis rates of other components of the transcription-translation apparatus also appear to be
subject to growth rate-dependent regulation (59, 65, 75, 112, 125). These components include translation
initiation and elongation factors, the subunits of RNA polymerase, and the aminoacyl-tRNA synthetases
(Table 4). From the available data it seems clear that the concentration of all these components increases
with growth rate, but the increases might not be—and for at least some of the proteins such as RNA
polymerase, for example, are not—strictly parallel with the increase in ribosome (and r-protein)
concentration. In Table 4 we list the proteins which have been examined in this context and give the αi
values for each (i.e., the synthesis rate of the protein as a percent of the total protein synthesis rate) at a
growth rate of 1.5 doublings per h (τ equals 40 min). In addition, the numbers of molecules of each protein
per unit of mass and per ribosome are also indicated. In compiling the information in this table we have had
to reinterpret or extrapolate some of the original measurements in the cited references. If the synthesis of
these proteins were strictly coordinate with synthesis of ribosomes, the listed number of molecules per
ribosome would remain constant and not change with changes in the steady-state growth rate.
The r-protein operons also encode the genes specifying the α, β, β′, and σ subunits of RNA
polymerase and the protein synthesis elongation factors Tu, Ts, and G (for review see reference 88). There
is a second gene for Tu on the E. coli chromosome which is not in an r-protein operon; presumably two
copies of this gene are required to produce the six molecules of Tu per ribosome at high growth rates. The
β and β′ RNA polymerase subunit genes, although cotranscribed with the L10 and L12 r-protein genes, are
regulated somewhat independently by a transcription attenuator located between the upstream r-protein
genes and the downstream RNA polymerase genes (see RNA polymerase synthesis and function, above).
There are about nine tRNA molecules per ribosome in exponentially growing E. coli, and this ratio
shows little variation for growth rates above 0.5 doublings per h (Table 3). Since the peptide chain
elongation rate approaches 20 amino acids per s, each tRNA is required to cycle through the ribosome on
average about two times per second. Ikemura (76) has quantitated over 70% of the total tRNA population
into 26 separate species, at least one for each amino acid except for proline and cysteine. For each of these
18 different amino acids there is at least one major isoacceptor which is present at a molar ratio of 0.15 to
0.60 copy per ribosome. The aminoacyl-tRNA synthetases are present at about 0.1 copy per ribosome; each
synthetase molecule is therefore required to aminoacylate about 10 molecules of its cognate tRNA every
second to sustain protein synthesis.
The elongation factor Tu is required for the GTPase-dependent deposition of aminoacylated tRNA into
the A-site of the translating ribosome. The charging level of tRNA is about 75 to 90%. There are between
two and three tRNA molecules bound to each translating ribosome (98, 116). The six copies of Tu are
available for ternary complex formation with GTP and the remaining aminoacylated tRNAs. The
concentration of the ternary complex required to initiate the process of amino acid addition on the
translating ribosome is thus maximized.
During periods of amino acid insufficiency the synthesis of r-protein, like that of rRNA and tRNA, is
subject to stringent regulation; this control is exerted at the level of transcription (40, 49, 50). Many of the
genes that are cotranscribed with r-protein genes are also, as expected, stringently regulated. These include
the genes encoding the elongation factors G, Tu, and Ts (8, 60, 115). In contrast, the genes encoding the β,
β′, and σ subunits of RNA polymerase are not stringently regulated (8). The nonstringent regulation of
transcription of the β and β′ genes is mediated by control at the attenuator in the L10 (rplJL rpoBC) operon
(96). In the case of the rpoD (σ) gene, a new promoter signal is utilized (C. Gross, personal
communication). With respect to aminoacyl-tRNA synthetases, the data on their stringent regulation are
equivocal (8).
DNA Replication and Cell Division.
Chromosome replication time. The C period is the time interval required for the replication forks to
move from the origin (oriC, at 84 min on the E. coli genetic map) to the terminus (terC, approximately at
36 min on the genetic map; 91). Pulse-labeling of the terminus in cells with synchronized replication has
indicated that both replication forks created at every initiation event move with equal speed (65
kilobases/min for wild-type strains) clockwise and counterclockwise, respectively, with very little variation
from cell to cell (9, 10). In addition, the time intervals between consecutive replications of any given
section of the chromosome are very constant and equal to the mass doubling time (83, 97, 101). This
suggests that both the times between consecutive initiations of rounds of replication and the replication
velocities themselves are constant within a cell population.
The C period has been measured by Helmstetter and Cooper (70) in age-fractionated cells. Due to the
considerable variability from cell to cell in the duration of the D period (see below), the initiation age,
termination age, and interdivision interval all vary (12). This makes the determination of C (and D) from
age-fractionated or synchronous cultures somewhat inaccurate. The C period has also been measured in
exponential cultures (i) from the relative frequencies of genes at given map locations (equation 9, Table 5
below; reference 22) and (ii) from the increase in DNA after stopping of initiation (26, 114, 144). Cooper
and Helmstetter (32) estimated that the C period was constant (41 min) for growth rates above 1 doubling
per h and increased in proportion to τ at lower growth rates. Measurements of the increase in DNA after a
replication stop (26) suggest that the C period decreases gradually with increasing growth rate, approaching
a value of 40 min in rapidly growing bacteria (Table 3).
Chromosome segregation and cell division. The D period is the time between termination of a round
of replication and the following cell division. The cell division is believed to require the action of a protein
synthesized at the time of termination of replication (79). During the D interval the completed
chromosomes are segregated. The length of time between the completion of replication and the onset of
constriction is subject to a stochastic process (13, 14). This results in a (non-Gaussian) fluctuation in the
length of the D interval, which is the major factor contributing to cell cycle variability including (i) the
variability of the initiation age (the time after cell division at which a round of chromosome replication is
initiated) and (ii) the variability of the time intervals between consecutive divisions (12).
Helmstetter and Cooper (70) estimated the average D to be about 22 min for growth rates above 1
doubling per h and to increase as a constant fraction of the doubling time for growth rates below 1 doubling
per h. The average D period has also been determined in exponential cultures from the increase in the cell
number after a replication stop by thymine starvation or by the addition of sodium azide (14). Cells that do
not terminate replication due to an experimentally induced replication stop will not divide, whereas cells
that have already terminated and have made termination protein, i.e., cells in the D period, divide once
(79). These experiments suggest that the D period decreases from about 30 min during slow growth to
about 22 min during rapid growth.
The average C and D intervals have also been obtained by the method of flow cytometry, which
measures the distribution of the amounts of DNA (labeled with a fluorescent dye) per cell in exponential
cell populations (frequency of cells as a function of DNA per individual cell). In this manner, values of C
equal to 42 min and D equal to 22 to 24 min were found for E. coli B/r A during balanced growth with a
27-min doubling time (129).
At a given doubling time, the C and D periods determine the initiation age, ai, and the termination age, at
(Fig. 1; see Table 5 below). Depending on the values of the three parameters, C, D, and τ, rounds of
replication may be initiated at the beginning, in the middle, or near the end of the cell cycle (Fig. 1). If
initiation occurs on average at the beginning of the cell cycle, it means that initiation actually occurs shortly
before division in some cells of the population and shortly after in others.
In thymine-requiring bacteria, where the DNA replication velocity can be altered by changing the
thymine concentration in the growth medium, the C period, and thus the initiation age, can be
experimentally changed. This has no effect on cell growth rate or on the control of replication initiation.
When the C period is extended, the time of the cell division, which occurs C plus D min after initiation,
is delayed. As a consequence, cells are larger than normal, but their ribosome concentration is unaltered
(28).
Replication initiation control depends on PO, i.e., the amount of protein per origin. Changes in PO (e.g.,
by mutation) do not affect the initiation age (24). This apparent paradox reflects the fact that a change in
the initiation time (without a change in C and D) causes an equal change in the time of division so that the
initiation age remains unaltered.
Macromolecular Composition during Growth at Different Temperatures
At 20, 25, 30, 35, and 40°C the growth rates of E. coli B/r in glucose minimal medium were 0.41, 0.65,
0.91, 1.18, and 1.35 doublings per h, respectively. At these temperatures the rRNA chain elongation rates
were 30, 45, 59, 76, and 103 nucleotide residues per s, and the peptide chain elongation rates were 5, 8,
11, 14, and 16 amino acid residues per s, respectively (120). Most of the other physiological parameters
are essentially unaltered by a change in temperature. In particular, the relative proportions of mRNA and
stable RNA synthesis are the same, suggesting that the chain elongation rates of stable RNA and mRNA
have equal temperature coefficients. The growth rate is expected to change as the square root of the
changes in the product of the peptide and RNA chain elongation rates (equation 19, Table 6 below),
which is, indeed, observed.
The C period changes with temperature in proportion to the doubling time (i.e., the ratio C/τ is
constant; 24, 58), which implies identical replication fork patterns at different temperatures. The chain
elongation rates for DNA, RNA, and polypeptides have thus about equal temperature coefficients, which in
the absence of further regulation results in a temperature independence of the macromolecular cell
composition. During the first 30 min after a temperature upshift, extensive temporary changes in the
macromolecular synthesis rates have been observed (e.g., reference 120) and a new RNA polymerase
sigma subunit is induced (67). These temporary perturbations constitute the heat shock response and reflect
active regulation and adjustment to the postshift temperature.
MATHEMATICAL DESCRIPTION OF CELL COMPOSITION AND GROWTH
Cell Composition as a Function of the Culture Doubling Time
A number of equations have been reported that describe the macromolecular composition of an average cell
in an exponential culture as a function of the culture doubling time and five additional parameters: the C
and D periods, protein per origin (PO), ribosome activity (βr), and peptide chain elongation rate (cp) (see
History, above; 27, 32, 51, 122). These equations, reproduced in Table 5, are useful for work dealing with
the cell composition and have been used for the calculation of many of the parameters in Table 3.
Additional equations in Table 5 can be used to calculate the copy number of genes per cell or per genome
as a function of their map location. All equations in Table 5 follow from the definitions of their constituent
parameters without special, simplifying assumptions or hypotheses.
Age Distribution and the Concept of the Average Cell
The average number of a component per cell has to be distinguished from the number of that component
per average cell. The first is obtained as the number per unit volume of culture, divided by the number of
cells in that volume. This quotient can be any noninteger number. The latter refers to a particular average
cell, which is defined by the fact that 50% of all cells in the population are younger and 50% are older.
Because young cells are more frequent than old cells in an exponential population, the average cell has an
age of 0.41, rather than 0.50. The number of any component in the average cell is always an integer; for
example the number of chromosome replication origins in the average cell is equal to 2, 4, or 8,
depending on the growth rate (see Fig. 1). In contrast, the average number of origins per cell (given by
equation 7 in Table 5) may have any noninteger value, such as 2.43 for a growth rate of 1 doubling per h
(Table 2), implying that some cells in the population have four origins, while others have only two.
These average numbers of components per cell are identical to the values calculated from the
formulas in Table 5.
To calculate a population average, the equation for the “ideal age distribution” (135) (meaning that all
cells divide in exactly equal time intervals) has been used in the past, with integration over different age
intervals. For example, the Cooper-Helmstetter equation and Donachie’s equation for the average amounts
of DNA and protein, respectively, per cell (equations 3 and 1 of Table 5) were originally derived under the
assumption of an ideal age distribution. However, a reexamination of these equations has indicated that they
are independent of any assumptions, including the assumptions of an ideal age distribution and of
synchronous initiation at all origins in the cell at a given initiation age (15, 18). The formulas in Table 5
give correct values irrespective of the age distribution. In fact, the cell cycle variability has no effect on
the average cell composition.
The conclusion, that the cell cycle variability has no effect on the composition and growth
parameters, has been disputed by Alberghina and Mariani (2). These authors have not distinguished
the doubling time, τ, defined as cell number doubling time in an exponential culture (equal to the mass
doubling time), from the average interdivision interval, denoted by τ. The latter may be determined
from growth curves of synchronous cultures (13) and depends on the particular subpopulation of cells
for which individual division intervals are measured. Although synchronous cells have the same
division age, they are generally somewhat out of phase with respect to their replication cycles. This
means that a zero-age population may contain a large number of subpopulations in which the cells are
in step, only in different phases, with respect to their last round of chromosome replication. Each of
these subpopulations (with different phase relationships between their replication age and division
age) would give a different synchronous growth curve and a different average interdivision interval
despite an equal mass doubling time (12). For these reasons, τ and τ (and, similarly, C and C, and D
and D) must be distinguished in theory (15, 27); only with C, D, and τ are the relationships in Table 5
strictly valid. However, the extent of variability in the cell cycle is such that the differences between τ
and τ, etc., amount to only a few percent (12) and, in practice, are negligible.
TABLE 5 Equations relating the cell composition in exponential
cultures to basic cell cycle parametera
Parameter Symbol Equation Equation no. Reference(s)
Protein/cell PCPC = PO ⋅ 2(C+D)/τ 1 51
RNA/cell RCRC = K′(PO/cp)(1/τ)2(C+D)/τ, where K′ = (nucl./rib) ⋅ ln2/[fs ⋅ (1 – ft) ⋅ βr ⋅ 60] 2 27
DNA/cell GCGC = [τ/(C ⋅ ln2)] ⋅ [2(C+D)/τ – 2D/τ] 3 32
Mass/cell MCMC = k1 ⋅ PC + k2 ⋅RC + k3 ⋅ GC, where:
k1 = 1.35 ⋅ 10–18 OD460 units per amino acid residue
k2 = 4.06 ⋅ 10–18 OD460 units per RNA nucleotide residue
k3 = 3.01 ⋅ 10–11 OD460 units per genome equivalent of DNA
4 27
Peptide chain elongation cpcp = K′/[(R/P) ⋅ τ] 5 44, 122
Ribosomal protein/total protein αrαr = (R/P) ⋅ [(aa/ribosome) ⋅ fs ⋅ (1–ft)/(nucl./rib)] 6 44, 122
Origins/cell OCOC = 2(C + D)/τ 7 15, 23
Termini/cell TCTC = 2D/τ 8 15, 23
No. of gene X/cell XCXC = 2[C(1 – m′) + D]/τ, where:
m′ = map location of gene X relative to location or replication origin
= (m + 16)/50 for map locations (m) between 0 and 36 min
= (84 – m)/50 for map locations between 36 and 84 min
= (m – 84)/50 for map locations between 84 and 100 min
9 15, 23
Replication forks/cell FCFC = 2 ⋅ [2(C+D)/τ – 2D/τ 10 15, 23
Origins/genome OGOG = (C/τ) ⋅ ln2/(1–2–C/τ) 11 15, 23
No. of gene X/genome XGXG = (O/G) ⋅ 2–m′C/τ 12 15, 23
Initiation age aiai = 1 + n – (C + D)/τ
where n is the next lower integer value of [(C + D)/τ];
i.e., n = int[(C + D)/τ]
13 32
Termination age atat = 1 – D/τ 14 32
Origins per cell at initiation OiOi = 2n; for a definition of n, see equation 13 15 32
Cell mass after division (a0) MdMd = MC/(2 ⋅ ln2) 16 18
Cell mass at initiation (ai) MiMi = Md ⋅ 2ai 17 18
aSee Tables 1 and 2 for definitions.
Cell Composition at a Defined Cell Age
In some instances the cell composition at certain cell ages becomes important; in particular, at the time of
cell division (either shortly before or shortly after) or at the time of initiation of chromosome replication. In
these cases, it is also not necessary to use the age distribution formula. Instead, the following relationships
can be used. (i) The average amount of a component in the subpopulation of zero-age cells (immediately
after division) is 1/(2⋅ln2) times the average amount of that component in the population as a whole
(obtained as described above). Correspondingly, the factor to obtain the average amount of the component
in the cells immediately before division has twice that value, i.e., 1/(ln2). (ii) The amount of protein (or cell
mass) per replication origin in a cell at the time of initiation (“initiation mass” defined by Donachie [51]) is
PO/ln2 (or MO/ln2), where PO (or MO) is the total protein (or cell mass) divided by the total number of
chromosomal replication origins in a unit volume of exponential culture. (Table 2 shows only PO, but MO
may be calculated from the data in the Table.) For the mathematical relationships dealing with the age
distribution, see references 12, 15, and 16.
Parameters Determining Bacterial Growth Rate
In the preceding discussion, the cell composition was expressed as a function of the growth rate. This
suggests that the composition is determined by the growth rate. In reality, the nutrients and other
components in the medium, together with genetically determined structural and kinetic constants of cellular
components, determine both the biochemical reaction rates (and thus the growth rate) and the cell
composition. It seems likely that only a few physiological parameters limit cell growth, whereas other
physiological parameters and most of the reaction rates and concentrations in a bacterium are probably not
growth limiting.
The DNA concentration is not growth limiting. Maaløe and Kjeldgaard (94, 95) have discussed the
idea that the amount of protein per DNA is constant and that the amount of RNA per DNA increases in
direct proportion to the growth rate. These relationships seem to suggest a limitation by DNA, for example,
that mRNA synthesis is limited by DNA and protein synthesis is limited by mRNA, which then results in a
constant ratio of protein to DNA. Maaløe (94) argued that the apparent and exact proportionality of the
ratio of RNA to DNA reflected the control of growth. Similarly, Koch (82) and Daneo-Moore and
Schockman (34) have used rate constants of RNA synthesis per DNA in models for the control of RNA
synthesis or growth. However, a DNA replication (initiation) mutant which has a reduced DNA
concentration and therefore an increased ratio of RNA to DNA at all growth rates (because the
denominator, DNA, is reduced) has an unaltered growth rate (24, 28, 29). The reduced DNA concentration
is the result of an increased initiation mass (protein per oriC, PO). This mutant shows that RNA synthesis
and growth are not normally limited by the concentration of DNA; in the mutant, the ratio of RNA to DNA
is no longer exactly proportional to the growth rate. Moreover, the amount of protein per DNA is generally
not constant, even in wild-type cells (see Fig. 2b).
TABLE 6 Basic parameters determining the bacterial growth ratea
Parameter Symbol EquationbEquation
no.
Growth rate (doublings/h) µµ = (60/ln2) ⋅ (Nr/P) ⋅ er, where the ribosome efficiency, er = βr ⋅ cp18
Growth rate (doublings/h) µµ = (60/K) ⋅ [ψs ⋅ αp ⋅ βp ⋅ βr ⋅ cs ⋅ cp]0.5,
where K = ln2 ⋅ [(nucl./prib)(aa/pol)/(1–ft)]0.5 19
acs and cp in these equations should be expressed as rates per minute to obtain the growth rate in doublings per
hour. For definitions, see Table 1. (The equation 19 is from reference 11.)
bFor a definition or explanation of symbols, see Tables 1 and 3.
The ribosome concentration (measured as number of ribosomes per protein) and the protein synthesis
rate per ribosome are growth limiting in any living cell whose protein turnover is negligible. These two
factors determine the exponential growth rate (equation 18, Table 6). Equation 18 is identical to the one
used by Schleif (122) to evaluate the RNA-to-protein ratio as a function of growth rate (see also equation 5,
Table 5). In his case, however, the growth rate, µ, was the independent variable and R/P was the dependent
variable. By making µ the dependent parameter, we have here exchanged the roles of the two variables.
For any growth equation to be meaningful, the parameters must be constant in time. For example, in
equation 18 (Table 6), both the ribosome concentration and activity must be constant. If they changed, µ
would have a changing value and growth would not be exponential. A constant and given ribosome
concentration results from the regulation of ribosome synthesis, which in turn involves the regulation of
RNA polymerase synthesis and its partitioning into rRNA and mRNA-synthesizing enzyme (see above).
These additional concepts have been taken into account in the more complex growth equation 19 (Table 6),
which contains six factors: RNA polymerase concentration (αp), RNA polymerase activity (βp),
partitioning of active RNA polymerase into stable RNA and mRNA-synthesizing enzyme (ψs), ribosome
activity (βr), and the chain elongation rates for stable RNA and polypeptides (cs, cp).
In equation 19 the parameters must again be constant in time to produce exponential growth. In the
preceding discussion (see above, Observed Cell Composition of E. coli B/r), the constancy of physiological
parameters during exponential growth was implicit in the definition of exponential growth, but if one asks
for the conditions that lead to exponential growth, then this constancy cannot be taken for granted. A full
explanation of why these parameters have certain, constant values under given growth conditions would solve
the problem of growth control. Growth equations such as those in Table 6 identify growth-limiting
parameters and predict their effect on the growth rate
Optimal Cell Composition for Maximal Growth
Maaløe and Kjeldgaard (94, 95) have pointed out that the protein synthesis rate per average ribosome in
bacteria is constant and presumably maximal under most growth conditions and, further, that this constancy
is economically advantageous for the cell. Since ribosomes are more expensive than their substrates, they
should always work at their maximum rate and therefore be saturated with substrates. Thus, the increased
demand for protein synthesis at higher growth rates can only be achieved by increasing the ribosome
concentration, since the rate of protein synthesis per ribosome is already maximal. Similarly, the increases
in αr and ψs with increasing growth rate can then be understood as consequences of the constant ribosome
function. These arguments try to explain the changing cell composition as an expression of an optimization
principle which allows the cell to achieve maximum growth at a minimum expenditure of energy.
Ehrenberg and Kurland (53) have theoretically analyzed how metabolic pathways should be designed
for maximum energy efficiency. With regard to ribosomes, they concluded that an optimal utilization of
energy would be achieved if both the substrate and ribosome concentration were to increase with increasing
demand for protein synthesis (substrates for the ribosome are the different elongation factor Tu-aminoacyl-
tRNA-GTP ternary complexes.) This can be understood as follows. At high ribosome concentrations, the
substrate pools, even at saturating concentrations, would represent only a small fraction of the total mass of
the protein-synthesizing system. At low ribosome concentrations the same pool would constitute a greater
fraction of the total system mass, and the energy required to produce that substrate pool would no longer be
negligible. The cells would then save energy by reducing the concentration of substrates, especially when
this concentration is above the Km for substrate binding, such that substantial reductions in substrate
concentrations can be compensated for by only small increases in ribosome number. In support of the
conclusion of Ehrenberg and Kurland, it should be noted that the ribosome function (cp) does, indeed,
increase with growth rate (Table 3). Also, the concentrations of tRNA and elongation factors Tu and Ts are
not constant but increase in proportion to the ribosome concentration (Table 4). If these concentrations
were above the Km at fast growth rates, their reduction during slow growth should save energy.
It is likely that energy efficiency has played a major role in the evolution of the regulatory parameters that
determine the macromolecular composition and growth rate of the cell. In addition, other principles, like
rapid adaptability to a changing growth environment, have evolved at the expense of energy efficiency. In
some instances an inefficiency might be a necessary byproduct of control mechanisms; for example, the
“stuttering” and pausing RNA polymerase might be the result of controls that depend on the secondary
structure of mRNA, like RNA chain termination, attenuator control, or control of mRNA stability.
ACKNOWLEDGMENTS
We thank Sharon Krowchuk for her role in preparing and typing this manuscript. This work was
supported by grants MT6340 from the Medical Research Council of Canada to P.P.D. and R01 GM1542
from the National Institutes of Health to H.B. P.P.D. is a Fellow in the Evolutionary Biology program of
the Canadian Institute for Advanced Research.
LITERATURE CITED
1. Aksoy, S., C. L. Squires, and C. Squires. 1984. Evidence for antitermination in Escherichia coli
rRNA transcription. J. Bacteriol. 159:260–264.
2. Alberghina, L., and L. Mariani. 1980. Analysis for a cell model for Escherichia coli. J. Math. Biol.
9:389.
3. Atherly, A. 1979. Deletion of relA and relX has no effect on basal or carbon-downshift ppGpp
synthesis, p. 53–66. In G. Koch and D. Richter (ed.), Regulation of Macromolecular Synthesis by
Low Molecular Weight Mediators. Academic Press, Inc., New York.
4. Bachmann, B. 1990. Linkage map of Escherichia coli K-12, edition 8. Microbiol. Rev. 54:130–197.
5. Baracchini, E., and H. Bremer. 1987. Determination of synthesis rate and lifetime of bacterial
mRNAs. Anal. Biochem. 167:245–260.
6. Barry, G., C. Squires, and C. L. Squires. 1980. Attenuation and processing of RNA from the rplJL-
rpoBC transcription unit of Escherichia coli. Proc. Natl. Acad. Sci. USA 77:3331–3335.
7. Barry, G., C. L. Squires, and C. Squires. 1979. Control features within the rplJL-rpoBC
transcription unit of Escherichia coli. Proc. Natl. Acad. Sci. USA 76:4922–4926.
8. Blumenthal, R., P. Lemaux, F. Neidhardt, and P. Dennis. 1976. The effects of the relA gene on the
synthesis of amino acyl tRNA synthetase and other transcription-translation proteins in Escherichia coli
B. Mol. Gen. Genet. 149:291–296.
9. Bouché, J. P. 1982. Physical map of a 470 kbase-pair region flanking the terminus of DNA replication
in the Escherichia coli K12 genome. J. Mol. Biol. 154:1–20.
10. Bouché, J. P., J. P. Gelugne, J. Louarn, J. M. Louarn, and K. Kaiser. 1982. Relationship between
the physical and genetic maps of a 470 kbase-pair region around the terminus of K12 DNA replication.
J. Mol. Biol. 154:21–32.
11. Bremer, H. 1975. Parameters affecting the rate of synthesis of ribosomes and RNA polymerase in
bacteria. J. Theor. Biol. 53:115–124.
12. Bremer, H. 1982. Variation in the generation times in Escherichia coli populations: its cause and
implications. J. Gen. Microbiol. 128:2865–2876.
13. Bremer, H., and L. Chuang. 1981. The cell cycle in Escherichia coli B/r. J. Theor. Biol. 88:47–81.
14. Bremer, H., and L. Chuang. 1981. The cell division cycle after inhibition of chromosome replication
in Escherichia coli. J. Theor. Biol. 93:909–926.
15. Bremer, H., and G. Churchward. 1977. An examination of the Cooper-Helmstetter theory of DNA
replication and its underlying assumptions. J. Theor. Biol. 69:645–654.
16. Bremer, H., and G. Churchward. 1978. Age fractionation of bacteria by membrane elution: relation
between age distribution and age profile. J. Theor. Biol. 74:69–81.
17. Bremer, H., and G. Churchward. 1990. Control of cyclic chromosome replication in Escherichia
coli. Microbiol. Rev. 55:459–475.
18. Bremer, H., G. Churchward, and R. Young. 1979. Relation between growth and replication in
bacteria. J. Theor. Biol. 81:533–545.
19. Bremer, H., and D. Yuan. 1968. RNA chain growth rates in Escherichia coli. J. Mol. Biol. 38:163–
180.
20. Brunschede, H., T. L. Dove, and H. Bremer. 1977. Establishment of exponential growth after a
nutritional shift-up in Escherichia coli B/r: accumulation of deoxyribonucleic acid, ribonucleic acid, and
protein. J. Bacteriol. 129:1020–1033.
21. Chamberlin, M. J. 1976. Interactions of RNA polymerase with the DNA template, p. 159–191. In R.
Losick and M. Chamberlin (ed.), RNA Polymerase. Cold Spring Harbor Laboratory, Cold Spring Harbor,
N.Y.
22. Chandler, M., R. Bird, and L. Caro. 1975. The replication time of Escherichia coli K12
chromosome as a function of the cell doubling time. J. Mol. Biol. 94:127–132.
23. Chandler, M. G., and R. H. Pritchard. 1975. The effect of gene concentration and relative gene
dosage on gene output in Escherichia coli. Mol. Gen. Genet. 138:127–141.
24. Choung, K.-K., E. Estiva, and H. Bremer. 1981. Genetic and physiological characterization of a
spontaneous mutant of Escherichia coli B/r with aberrant control of deoxyribonucleic acid replication. J.
Bacteriol. 145:1239–1248.
25. Chow, J., and P. P. Dennis. 1994. Coupling between mRNA synthesis and mRNA stability in
Escherichia coli. Mol. Microbiol. 11:919–932.
26. Churchward, G., and H. Bremer. 1977. Determination of deoxyribonucleic acid replication time in
exponentially growing Escherichia coli B/r. J. Bacteriol. 130:1206–1213.
27. Churchward, G., H. Bremer, and R. Young. 1982. Macromolecular composition of bacteria. J.
Theor. Biol. 84:651–670.
28. Churchward, G., H. Bremer, and R. Young. 1982. Transcription in bacteria at different DNA
concentrations. J. Bacteriol. 150:572–581.
29. Churchward, G., E. Estiva, and H. Bremer. 1981. Growth rate-dependent control of chromosome
replication initiation in Escherichia coli. J. Bacteriol. 145:1232–1238.
30. Cole, J. R., C. L. Olsson, J. W. B. Hershey, M. Grunberg-Monago, and M. Nomura. 1987.
Feedback regulation of rRNA synthesis in Escherichia coli. Requirement for initiation factor IF2. J. Mol.
Biol. 198:383–392.
31. Condon, C., S. French, C. Squires, and C. L. Squires. 1993. Depletion of functional ribosomal
RNA operons in Escherichia coli causes increased expression of the remaining intact copies. EMBO J.
12:4305–4315.
32. Cooper, S., and C. Helmstetter. 1968. Chromosome replication and the division cycle of Escherichia
coli B/r. J. Mol. Biol. 31:519–540.
33. Dalbow, D., and R. Young. 1975. Synthesis time of b-galactosidase in Escherichia coli B/r as a
function of growth rate. Biochem. J. 150:13–20.
34. Daneo-Moore, L., and G. D. Schockman. 1976. The bacterial cell surface in growth and cell
division, p. 653–715. In G. Poste and G. L. Nicholson (ed.), The Synthesis, Assembly and Turnover of
Cell Surface Components. Elsevier/North-Holland Biomedical Press, Amsterdam.
35. Delcuve, G., and P. P. Dennis. 1981. An amber mutation in a ribosomal protein gene: ineffective
suppression stimulates operon-specific transcription. J. Bacteriol. 147:997–1001.
36. Dennis, P. P. 1971. Regulation of stable RNA synthesis in Escherichia coli. Nature (London) New
Biol. 232:43–47.
37. Dennis, P. P. 1972. Regulation of ribosomal and transfer ribonucleic acid synthesis in Escherichia
coli B/r. J. Biol. Chem. 247:2842–2845.
38. Dennis, P. P. 1974. In vivo stability, maturation and relative differential synthesis rates of individual
ribosomal proteins in Escherichia coli. J. Mol. Biol. 88:24–41.
39. Dennis, P. P. 1976. Effects of chloramphenicol on the transcriptional activities of ribosomal RNA and
ribosomal protein genes in Escherichia coli. J. Mol. Biol. 108:535–546.
40. Dennis, P. P. 1977. Influence of the stringent control system on the transcription of ribosomal
ribonucleic acid and ribosomal protein genes in Escherichia coli. J. Bacteriol. 129:580–588.
41. Dennis, P. P. 1977. Regulation of the synthesis and activity of a mutant RNA polymerase in
Escherichia coli. Proc. Natl. Acad. Sci. USA 74:5416–5420.
42. Dennis, P. P. 1977. Transcription patterns of adjacent segments of Escherichia coli containing genes
coding for four 50S ribosomal proteins and the β and β′ subunits of RNA polymerase. J. Mol. Biol.
115:603–625.
43. Dennis, P. P. 1984. Site specific deletion of regulatory sequences in a ribosomal protein-RNA
polymerase operon in E. coli: effects on β and β′ gene expression. J. Biol. Chem. 259:3203–3209.
44. Dennis, P. P., and H. Bremer. 1974. Differential rate of ribosomal protein synthesis in Escherichia
coli B/r. J. Mol. Biol. 84:407–422.
45. Dennis, P. P., and H. Bremer. 1974. Regulation of ribonucleic acid synthesis in Escherichia coli B/r:
an analysis of a shift up. III. Stable RNA synthesis rate and ribosomal RNA chain growth rate following
a shift up. J. Mol. Biol. 89:233–239.
46. Dennis, P. P., and H. Bremer. 1974. Macromolecular composition during steady-state growth of
Escherichia coli B/r. J. Bacteriol. 119:270–281.
47. Dennis, P. P., and N. Fiil. 1979. Transcriptional and post-transcriptional control of RNA polymerase
and ribosomal protein genes cloned on composite ColE1 plasmids in the bacterium Escherichia coli. J.
Biol. Chem. 254:7540–7547.
48. Dennis, P. P., V. Nene, and R. E. Glass. 1985. Autogenous post-transcriptional regulation of RNA
polymerase β and β′ subunit synthesis in Escherichia coli. J. Bacteriol. 161:803–806.
49. Dennis, P. P., and M. Nomura. 1974. Stringent control of ribosomal protein gene expression in
Escherichia coli. Proc. Natl. Acad. Sci. USA 71:3819–3823.
50. Dennis, P. P., and M. Nomura. 1975. Stringent control of the transcriptional activities of ribosomal
protein genes in E. coli. Nature (London) 255:460–465.
51. Donachie, W. 1968. Relationships between cell size and time of initiation of DNA replication. Nature
(London) 219:1077–1079.
52. Downing, W., and P. P. Dennis. 1991. RNA polymerase activity may regulate transcription initiation
and attenuation in the rplKAJL rpoBC operon in E. coli. J. Biol. Chem. 266:1304–1311.
53. Ehrenberg, M., and C. Kurland. 1984. Costs of accuracy determined by a maximal growth rate
constraint. Q. Rev. Biophys. 17:45–82.
54. Emilsson, V., and C. G. Kurland. 1990. Growth rate dependence of transfer RNA abundance in
Escherichia coli. EMBO J. 9:4359–4366.
55. Fallon, A. M., C. S. Jinks, M. Yamamoto, and M. Nomura. 1979. Expression of ribosomal protein
genes cloned in a hybrid plasmid in Escherichia coli: gene dosage effects on synthesis of ribosomal
proteins and ribosomal protein messenger ribonucleic acid. J. Bacteriol. 138:383–396.
56. Fehr, S., and D. Richter. 1981. Stringent response of Bacillus stearothermophilus: evidence for the
existence of two distinct guanosine 3′,5′-polyphosphate synthetases. J. Bacteriol. 145:68–73.
57. Forchhammer, J., and L. Lindahl. 1971. Growth rate of polypeptide chains as a function of the cell
growth rate in a mutant of Escherichia coli 15. J. Mol. Biol. 55:563–568.
58. Frey, J., M. Chandler, and L. Caro. 1981. The initiation of chromosome replication in a dnaAts46
and dnaA+ strain at various temperatures. Mol. Gen. Genet. 182:364–366.
59. Furano, A. 1975. Content of elongation factor Tu. Proc. Natl. Acad. Sci. USA 72:4780–4784.
60. Furano, A., and F. Wittel. 1976. Syntheses of elongation factors Tu and G are under stringent control
in Escherichia coli. J. Biol. Chem. 251:898–901.
61. Gausing, K. 1972. Efficiency of protein and messenger RNA synthesis in bacteriophage T4 infected
cells of Escherichia coli. J. Mol. Biol. 71:529–545.
62. Gausing, K. 1974. Ribosmal protein in E. coli: rate of synthesis and pool size at different growth
rates. Mol. Gen. Genet. 129:61–75.
63. Gausing, K. 1977. Regulation of ribosome production in Escherichia coli: synthesis and stability of
ribosomal RNA and ribosomal protein mRNA at different growth rates. J. Mol. Biol. 115:335–354.
64. Gauss, D., and M. Sprinzl. 1983. Compilation of tRNA sequences. Nucleic Acids Res. 11:r1-r53.
65. Gordon, J. 1970. Regulation of the in vivo synthesis of polypeptide chain elongation factors in
Escherichia coli. Biochemistry 9:912–917.
66. Greenblatt, J. 1984. Regulation of transcription termination in E. coli. Can. J. Biochem. 62:79–88.
67. Grossman, A. D., J. W. Erickson, and C. Gross. 1984. The htpR gene product of E. coli is a sigma
factor for heat-shock promoters. Cell 38:383–390.
68. Hardy, S. 1975. The stoichiometry of ribosomal proteins of Escherichia coli. Mol. Gen. Genet.
140:253–274.
69. Haseltine, W., R. Block, W. Gilbert, and K. Weber. 1972. MSI and MSII made on ribosomes in
the idling step of protein synthesis. Nature (London) 238:381–384.
70. Helmstetter, C., and S. Cooper. 1968. DNA synthesis during the division cycle of rapidly growing
E. coli B/r. J. Mol. Biol. 31:507–518.
71. Helmstetter, C. E., and D. J. Cummings. 1964. An improved method for the selection of bacterial
cells at division. Biochim. Biophys. Acta 82:608–610.
72. Hernandez, V. J., and H. Bremer. 1990. Guanosine tetraphosphate (ppGpp) dependence of the
growth rate control of rrnB P1 promoter activity in Escherichia coli. J. Biol. Chem. 265:11605–11614.
73. Hernandez, V. J., and H. Bremer. 1991. Escherichia coli ppGpp synthetase II activity requires spoT.
J. Biol. Chem. 266:5991–5999.
74. Hernandez, V. J., and H. Bremer. 1993. Characterization of Escherichia coli devoid of ppGpp. J.
Biol. Chem. 268:10851–10862.
75. Howe, J., and J. Hershey. 1983. Initiation factor and ribosome levels are coordinately controlled in
Escherichia coli growing at different rates. J. Biol. Chem. 258:1954–1959.
76. Ikemura, T. 1981. Correlations between the abundance of Escherichia coli transfer RNAs and the
occurrence of the respective codons in its mRNA genes. J. Mol. Biol. 146:1–21.
77. Jinks-Robertson, S., R. Gourse, and M. Nomura. 1983. Expression of rRNA and tRNA genes in
Escherichia coli: evidence for feedback regulation by products of rRNA operons. Cell 33:865–876.
78. Johnsen, M., T. Christiansen, P. Dennis, and N. Fiil. 1982. Autogenous control: ribosomal protein
L10-L12 complex binds to the leader region of its mRNA. EMBO J. 1:999–1004.
79. Jones, N. C., and W. D. Donachie. 1973. Chromosome replication, transciption and control of cell
division in Escherichia coli B/r. Nature (London) New Biol. 243:100–103.
80. Kennel, D. 1968. Titration of the gene sites on DNA by DNA-RNA hybridization. II. The Escherichia
coli chromosome. J. Mol. Biol. 34:85–103.
81. Kingston, R., W. Nierman, and M. Chamberlin. 1981. A direct effect of guanosine tetraphosphate
on pausing of Escherichia coli RNA polymerase during RNA chain elongation. J. Biol. Chem.
256:2787–2797.
82. Koch, A. 1970. Overall control on the biosynthesis of ribosomes in growing bacteria. J. Theor. Biol.
28:203–231.
83. Koppes, L., and K. Nordstrom. 1986. Insertion of an R1 plasmid into the origin of replication of the
E. coli chromosome: random timing of replication of the hybrid chromosome. Cell 44:117–124.
84. Lagosky, P., and F. N. Chang. 1980. Influence of amino acid starvation on guanosine 5′-diphosphate
3′-diphosphate basal level synthesis in Escherichia coli. J. Bacteriol. 144:499–508.
85. Li, S., C. L. Squires, and C. Squires. 1984. Antitermination of E. coli rRNA transcription is caused
by a control region segment containing a nut-like sequence. Cell 38:851–860.
86. Lindahl, L. 1975. Intermediates and time kinetics of the in vivo assembly of Escherichia coli
ribosomes. J. Mol. Biol. 92:15–37.
87. Lindahl, L., R. Archer, and J. Zengel. 1983. Transcription of the S10 ribosomal protein operon is
regulated by an attenuator in the leader. Cell 33:241–248.
88. Lindahl, L., and J. Zengel. 1982. Expression of ribosomal genes in bacteria. Adv. Genet. 21:53–121.
89. Little, R., and H. Bremer. 1984. Transcription of ribosomal component genes and lac in a relA+/relA
pair of Escherichia coli strains. J. Bacteriol. 159:863–869.
90. Little, R., J. Ryals, and H. Bremer. 1983. Physiological characterization of Escherichia coli rpoB
mutants with abnormal control of ribosome synthesis. J. Bacteriol. 155:1162–1170.
91. Louarn, J., J. Patte, and J. M. Louarn. 1979. Map position of the replication terminus on the
Escherichia coli chromosome. Mol. Gen. Genet. 172:7–11.
92. Lowry, O. H., N. J. Rosebrough, A. L. Farr, and R. J. Randall. 1951. Protein measurement with
the Folin phenol reagent. J. Biol. Chem. 193:265–275.
93. Maaløe, O. 1969. An analysis of bacterial growth. Dev. Biol. 3(Suppl.):33–58.
94. Maaløe, O. 1979. Regulation of the protein synthesizing machinery—ribosomes, tRNA, factors and
so on, p. 487–542. In R. Goldberger (ed.), Biological Regulation and Development, vol. 1. Plenum
Publishing Corp., New York.
95. Maaløe, O., and N. O. Kjeldgaard. 1966. Control of Macromolecular Synthesis. W. A. Benjamin,
New York.
96. Maher, D., and P. Dennis. 1977. In vivo transcription of E. coli genes coding for rRNA, ribosomal
proteins and subunits of RNA polymerase: influence of the stringent control system. Mol. Gen. Genet.
155:203–211.
97. Meselson, M., and F. Stahl. 1958. The replication of DNA in Escherichia coli. Proc. Natl. Acad. Sci.
USA 44:671–682.
98. Moazed, D., and H. Noller. 1989. Intermediate states in the movement of transfer RNA in the
ribosome. Nature (London) 342:142–148.
99. Molin, S. 1976. Ribosomal RNA chain elongation rates in Escherichia coli. Alfred Benzon Symp.
9:333–339.
100. Müller, K., and H. Bremer. 1969. Heterogeneous initiation and termination of enzymatically
synthesized ribonucleic acid. J. Mol. Biol. 43:89–107.
101. Newman, C., and H. Kubitschek. 1978. Variations in periodic replication of the chromosome in
Escherichia coli B/r TT. J. Mol. Biol. 121:461–471.
102. Nierlich, D. P. 1972. Regulation of ribonucleic acid synthesis in growing bacterial cells. II. Control over
the composition of newly made RNA. J. Mol. Biol. 7:765–777.
103. Nodell, J. R., and J. Greenblatt. 1993. Recognition of box A antitermination RNA by E. coli
antitermination factor NusB and ribosomal protein S10. Cell 72:261–268.
104. Noller, H. F. 1984. Structure of ribosomal RNA. Annu. Rev. Biochem. 53:119–162.
105. Nomura, M., R. Gourse, and G. Baughman. 1984. Regulation of the synthesis of ribosomes and
ribosomal components. Annu. Rev. Biochem. 53:75–117.
106. Norris, T., and A. Koch. 1972. Effect of growth rates on the relative rates of messenger, ribosomal and
transfer RNA in Escherichia coli. J. Mol. Biol. 64:633–649.
107. Ovchinnikov, Y., V. Lipkin, N. Modzanov, O. Chestov, and Y. Smirnov. 1977. Primary structure
of the α subunit of DNA dependent RNA polymerase from Escherichia coli. FEBS Lett. 76:108–111.
108. Ovchinnikov, I., G. Monastyrskaia, U. Gubanov, S. Guriev, O. Chertov, N. Modisnov, V.
Grinkevich, I. Makarova, T. Marchenko, I. Polovnikova, V. Lipkin, and E. Sverdlov. 1980. Primary
structure of RNA polymerase of Escherichia coli: nucleotide sequence of gene rpoB and amino acid
sequence of β-subparticle. Dokl. Akad. Nauk SSSR 253:994–999.
109. Ovchinnikov, I., G. Monastyrskaia, U. Gubanov, S. Guriev, and I. Salomatina. 1981. Primary
structure of RNA polymerase of Escherichia coli: nucleotide sequence of gene rpoC and amino acid
sequence of β′-subparticle. Dokl. Akad. Nauk SSSR 261:763–768.
110. Pedersen, S. 1984. Escherichia coli ribosomes translate in vivo with variable rate. EMBO J. 3:2895–
2898.
111. Pedersen, S. 1984. In Escherichia coli individual genes are translated with different rates in vivo.
Alfred Benzon Symp. 19:101–107.
112. Pedersen, S., P. Bloch, S. Reeh, and F. Neidhardt. 1978. Patterns of protein synthesis in E. coli: a
catalogue of the amount of 140 individual proteins at different growth rates. Cell 14:179–190.
113. Post, L. E., G. D. Strycharz, M. Nomura, H. Lewis, and P. P. Dennis. 1979. Nucleotide sequence
of the ribosomal protein gene cluster adjacent to the gene for RNA polymerase subunit β in Escherichia
coli. Proc. Natl. Acad. Sci. USA 76:1697–1701.
114. Pritchard, R. H., and Z. Zaritsky. 1970. Effect of thymine concentration on the replication velocity of
DNA in a thymineless mutant of E. coli. Nature (London) 226:126–131.
115. Reeh, S., S. Pedersen, and J. Friesen. 1976. Biosynthetic regulation of individual proteins in relA+
and relA– strains of Escherichia coli during amino acid starvation. Mol. Gen. Genet. 149:279–289.
116. Rheinberger, H.-J., H. Sternbach, and K. Nierhaus. 1981. Three tRNA bonding sites on
Escherichia coli ribosomes. Proc. Natl. Acad. Sci USA 78:5310–5314.
117. Richter, D. 1979. Synthesis and degradation of the pleiotropic effector guanosine 3,5′-
bis(diphosphate) in bacteria, p. 85–94. In G. Koch and D. Richter (ed.), Regulation of Macromolecular
Synthesis by Low Molecular Weight Mediators. Academic Press, Inc., New York.
118. Rosset, R., J. Julian, and R. Morier. 1966. Ribonucleic acid composition of bacteria as a function
of growth rate. J. Mol. Biol. 18:308–320.
119. Ryals, J., R. Little, and H. Bremer. 1982. Control of rRNA and tRNA synthesis in Escherichia coli
by guanosine tetraphosphate. J. Bacteriol. 151:1261–1268.
120. Ryals, J., R. Little, and H. Bremer. 1982. Temperature dependence of RNA synthesis parameters in
Escherichia coli. J. Bacteriol. 151:879–887.
121. Schaechter, E., O. Maaløe, and N. O. Kjeldgaard. 1958. Dependence on medium and temperature
of cell size and chemical composition during balanced growth of Salmonella typhimurium. J. Gen.
Microbiol. 19:592–606.
122. Schleif, R. 1967. Control of the production of ribosomal protein. J. Mol. Biol. 27:41–55.
123. Sharp, P. M., and W. Li. 1986. Codon usage in regulatory genes in Escherichia coli does not reflect
selection for rare codons. Nucleic Acids Res. 14:7737–7749.
124. Shen, V., and H. Bremer. 1977. Rate of ribosomal ribonucleic acid chain elongation in Escherichia
coli B/r during chloramphenicol treatment. J. Bacteriol. 130:1109–1116.
125. Shepherd, N. S., G. Churchward, and H. Bremer. 1980. Synthesis and activity of ribonucleic acid
polymerase in Escherichia coli. J. Bacteriol. 141:1098–1108.
126. Shepherd, N. S., G. Churchward, and H. Bremer. 1980. Synthesis and function of ribonucleic acid
polymerase and ribosomes in Escherichia coli B/r after a nutritional shift-up. J. Bacteriol. 143:1332–
1344.
127. Siehnel, R. J., and E. A. Morgan. 1983. Efficient read-through of Tn9 and IS1 by RNA polymerase
molecules that initiate at rRNA promoters. J. Bacteriol. 153:672–684.
128. Skarstad, K., E. Boye, and H. B. Steen. 1986. Timing of initiation of chromosome replication in
individual Escherichia coli cells. EMBO J. 5:1711–1717.
129. Skarstad, K., H. Steen, and E. Boye. 1985. Escherichia coli DNA distributions measured by flow
cytometry and compared with theoretical computer simulations. J. Bacteriol. 163:661–668.
130. Skarstad, K., H. B. Steen, T. Stokke, and E. Boye. 1994. The initiation mass of Escherichia coli K-12
is dependent on growth rate. EMBO J. 13:2097–2102.
131. Sorensen, M. A., C. G. Kurland, and S. Pedersen. 1989. Codon usage determines translation rate in
Escherichia. J. Mol. Biol. 207:365–377.
132. Sorensen, M. A., and S. Pedersen. 1991. Absolute in vivo translation rates of individual codons in
Escherichia coli. Two glutamic acid codons GAA and GAG are translated with a threefold difference in rate.
J. Mol. Biol. 222:265–280.
133. Spahr, P. R. 1962. Amino acid composition of ribosomes from Escherichia coli. J. Mol. Biol. 4:395–406.
134. Subramanian, R. 1975. Copies of protein L7 and L12 and heterogeneity of the large subunit of
Escherichia coli ribosomes. J. Mol. Biol. 95:1–8.
135. Sueoka, N., and Y. Yoshikawa. 1965. The chromosome of Bacillus subtilis. I. The theory of
marker frequency analysis. Genetics 52:747–757.
136. Travers, A. 1976. Modulation of RNA polymerase specificity by ppGpp. Mol. Gen. Genet.
147:225–232.
137. van Ooyen, A., M. Gruber, and P. Jorgensen. 1976. The mechanism of action of ppGpp on
rRNA synthesis in vitro. Cell 8:123–128.
138. Varenne, S., J. Bue, R. Llouber, and C. Lazdunski. 1984. Translation is a non-uniform process:
effect of tRNA availability on the rate of elongation of nascent polypeptide chains. J. Mol. Biol.
180:549–576.
139. Vogel, U., and K. F. Jensen. 1994. The RNA chain elongation rate in Escherichia coli depends
on the growth medium. J. Bacteriol. 176:2807–2813.
140. Wittmann, H. G. 1982. Components of the bacterial ribosome. Annu. Rev. Biochem. 51:155–183.
141. Xiao, H., M. Kalman, K. Ikehara, S. Zemel, G. Glaser, and M. Cashel. 1991. Residual
guanosine 3′,5′-bispyrophosphate synthetic activity of relA null mutants can be eliminated by spoT
null mutations. J. Biol. Chem. 266: 5980–5990.
142. Young, R., and H. Bremer. 1976. Polypeptide chain elongation rate in Escherichia coli B/r as
a function of growth rate. Biochem. J. 160: 185–194.
143. Yuan, D., and V. Shen. 1975. Stability of ribosomal and transfer ribonucleic acid in Escherichia
coli B/r after treatment with ethylenedinitrilotetraacetic acid and rifampin. J. Bacteriol. 122:425–432.
144. Zaritsky, A., and R. H. Pritchard. 1971. Replication time of the chromosome in thymineless
mutants of Escherichia coli. J. Mol. Biol. 60:65–74.
- CitationsCitations629
- ReferencesReferences154
- The cost of replacement for a ribosome, β ribosome , is given by the cost of remaking both the rRNA and the ribosomal proteins, where there are 4566 ribonucleotides and 7336 amino acids per ribosome (Bremer and Dennis, 1996) and the respective polymerization energiers are described above. Likewise, β tRNA is found by considering that the average length of a tRNA is 80 nucleotides (Bremer and Dennis, 1996) and again using the above RNA polymerization ATP requirements. It has been demonstrated (Kempes et al., 2012) that the metabolic scaling relationship for active and endogenous metabolism can be used to derive growth rate, µ (s −1 ), following the relationship
[Show abstract] [Hide abstract] ABSTRACT: Microbes maintain themselves through a variety of processes. Several of these processes can be reduced or shut down entirely when resource availability declines. In pure culture conditions with ample substrate supply, a relationship between the maximum growth rate and the energy invested in maintenance has been reported widely. However, at the other end of the resources spectrum, bacteria are so extremely limited by energy that no growth occurs and metabolism is constrained to the most essential functions only. These minimum energy requirements have been called the basal power requirement. While seemingly different from each other, both aspects are likely components of a continuum of regulated maintenance processes. Here, we analyze cross-species tradeoffs in cellular physiology over the range of bacterial size and energy expenditure and determine the contributions to maintenance metabolism at each point along the size-energy spectrum. Furthermore, by exploring the simplest bacteria within this framework– which are most affected by maintenance constraints– we uncover which processes become most limiting. For the smallest species, maintenance metabolism converges on total metabolism, where we predict that maintenance is dominated by the repair of proteins. For larger species the relative costs of protein repair decrease and maintenance metabolism is predicted to be dominated by the repair of RNA components. These results provide new insights into which processes are likely to be regulated in environments that are extremely limited by energy.- mRNAs are then translated by ribosomes (z) to produce protein (x i ). At a constant growth rate, the total amount of ribosomes are conserved [7]. Assuming that binding reactions are much faster than transcription and translation [14], and thus can be set to quasi-steady state, each node can be described by its mRNA and protein concentrations:
- Cellular composition across diverse bacteria CP Kempes et al tracks, but is consistently smaller than the observed volume of ribosomes from our cross-species compilation of published data, which includes Bremer et al. (1996), Fegatella et al. (1998), Seybert et al. (2006) and Luef et al. (2015. We also find a relationship for the number of ribosomes using a best fit of the degradation rates with the power-law approximation of μ (see Supplementary Information), which accurately captures the crossspecies trends in ribosome volume in Figure 2c.
[Show abstract] [Hide abstract] ABSTRACT: One of the most important classic and contemporary interests in biology is the connection between cellular composition and physiological function. Decades of research have allowed us to understand the detailed relationship between various cellular components and processes for individual species, and have uncovered common functionality across diverse species. However, there still remains the need for frameworks that can mechanistically predict the tradeoffs between cellular functions and elucidate and interpret average trends across species. Here we provide a comprehensive analysis of how cellular composition changes across the diversity of bacteria as connected with physiological function and metabolism, spanning five orders of magnitude in body size. We present an analysis of the trends with cell volume that covers shifts in genomic, protein, cellular envelope, RNA and ribosomal content. We show that trends in protein content are more complex than a simple proportionality with the overall genome size, and that the number of ribosomes is simply explained by cross-species shifts in biosynthesis requirements. Furthermore, we show that the largest and smallest bacteria are limited by physical space requirements. At the lower end of size, cell volume is dominated by DNA and protein content—the requirement for which predicts a lower limit on cell size that is in good agreement with the smallest observed bacteria. At the upper end of bacterial size, we have identified a point at which the number of ribosomes required for biosynthesis exceeds available cell volume. Between these limits we are able to discuss systematic and dramatic shifts in cellular composition. Much of our analysis is connected with the basic energetics of cells where we show that the scaling of metabolic rate is surprisingly superlinear with all cellular components.- During conditions of rapid growth there are as many as 70,000 ribosomes in a cell. To keep up with high demand for ribosomes, 90% of transcription in fast growing E.coli produces rRNA and tRNA, and only 10% produces mRNA [15] . As a result, there is a high density of RNAPs on all rrn operons and a high transcription completion rate is imperative.
[Show abstract] [Hide abstract] ABSTRACT: In fast-transcribing prokaryotic genes, such as an rrn gene in Escherichia coli, many RNA polymerases (RNAPs) transcribe the DNA simultaneously. Active elongation of RNAPs is often interrupted by pauses, which has been observed to cause RNAP traffic jams; yet some studies indicate that elongation seems to be faster in the presence of multiple RNAPs than elongation by a single RNAP. We propose that an interaction between RNAPs via the torque produced by RNAP motion on helically twisted DNA can explain this apparent paradox. We have incorporated the torque mechanism into a stochastic model and simulated transcription both with and without torque. Simulation results illustrate that the torque causes shorter pause durations and fewer collisions between polymerases. Our results suggest that the torsional interaction of RNAPs is an important mechanism in maintaining fast transcription times, and that transcription should be viewed as a cooperative group effort by multiple polymerases.- For wild-type E. coli, this argument holds true when additional ATP costs for translation are considered, and it was estimated that on average an additional 31% of ATP maintenance was required. Since one mRNA was assumed to be translated up to 11 times (calculated from Bremer and Dennis (1996)), the ATP costs for protein formation are about 5-fold higher than those for mRNA formation. Wild-type E. coli could still endure these costs.
- First, taxa that are rare in the rDNA community have been observed to be disproportionately active relative to abundant members (Campbell et al., 2011; Hugoni et al., 2013; Hunt et al., 2013). Second, it is more difficult to detect rare taxa in the total (rDNA) community compared to the active community because metabolically active cells may contain 100s–1000s of ribosomes (Bremer and Dennis, 1996; Fegatella et al., 1998) but only 1–15 rDNA gene copies (Klappenbach et al., 2001). These factors – in isolation or in combination – could contribute to the observation of phantom taxa.
[Show abstract] [Hide abstract] ABSTRACT: Bacterial metabolisms are responsible for critical chemical transformations in nearly all environments, including oceans, freshwater, and soil. Despite the ubiquity of bacteria in the atmosphere, little is known about the metabolic functioning of atmospheric bacterial communities. To gain a better understanding of the metabolism of bacterial communities in the atmosphere, we used a combined empirical and model-based approach to investigate the structure and composition of potentially active bacterial communities in air sampled at a high elevation research station. We found that the composition of the putatively active bacterial community (assayed via rRNA) differed significantly from the total bacterial community (assayed via rDNA). Rare taxa in the total (rDNA) community were disproportionately active relative to abundant taxa, and members of the order Rhodospirillales had the highest potential for activity. We developed theory to explore the effects of random sampling from the rRNA and rDNA communities on observed differences between the communities. We found that random sampling, particularly in cases where active taxa are rare in the rDNA community, will give rise to observed differences in community composition including the occurrence of “phantom taxa”, taxa which are detected in the rRNA community but not the rDNA community. We show that the use of comparative rRNA/rDNA techniques can reveal the structure and composition of the metabolically active portion of bacterial communities. Our observations suggest that metabolically active bacteria exist in the atmosphere, and that these communities may be involved in the cycling of organic compounds in the atmosphere.
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