Modulation of Chemical Composition and Other Parameters of the Cell at Different Exponential Growth Rates

HANS BREMER^1* AND PATRICK P. DENNIS^2*

[SECTION EDITOR: ELIO SCHAECHTER]

Posted October 7, 2008

Department of Molecular and Cell Biology, University of Texas at Dallas, Richardson, TX 75083-0688,¹ and Department of Biochemistry and Molecular Biology, University of British Columbia, Vancouver, British Columbia V6T 1Z3, Canada²

*Corresponding authors. Mailing address for Hans Bremer: Department of Molecular and Cell Biology, University of Texas at Dallas, Richardson, TX 75083-0688. E-mail, This e-mail address is being protected from spambots. You need JavaScript enabled to view it . Mailing address for Patrick P. Dennis: National Science Foundation; Division of Molecular and Cellular Biosciences, 4201 Wilson Blvd, Arlington, VA 22230. Phone: (703) 292-7145, Fax (703) 292-9061, E-mail, This e-mail address is being protected from spambots. You need JavaScript enabled to view it

HISTORY

Schaechter et al. (167) 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 exponential Salmonella enterica serovar 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 defined the exponential growth rate, μ, in doublings per hour. The growth rate μ is proportional to the reciprocal of the culture doubling time, τ, which is usually expressed in minutes, so that μ = 60/τ. 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 per cell are exponential functions of growth rate, and (iii) that the exponents of these functions are different for different macromolecules. The last finding implies that the relative proportions of the different macromolecules change with growth rate; at a given temperature, RNA and ribosome concentrations increase with increasing growth rate, the DNA concentration decreases, and the protein concentration remains almost constant. When changing the temperature rather than the nutrient content of the growth medium, the DNA, RNA, and protein concentrations remained invariant at varying growth rates.

These early studies of bacterial physiology are documented by Maaløe and Kjeldgaard (132). 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 stimulated thought and led to more sophisticated observations. Many of the fundamental problems posed by the Copenhagen group 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 (52) derived a formula for determining the average amount of DNA per cell in an exponential culture as a function of the time required to replicate the chromosome (C), the time period between termination of a round of replication and the following cell division (D), and the culture doubling time (τ). This theory also included the important concept of overlapping rounds of chromosome replication, where a new round of replication is initiated before the previous round is completed. This occurs when C is greater than τ and explains how bacteria are able to grow with a doubling time shorter than the time required to replicate their chromosome.

Donachie (74) extended this theory by introducing the concept of the "initiation mass," which he defined as the cell mass per replication origin at the time of initiation. Based on this idea, he derived a formula for 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 (M_O or P_O, respectively). The Cooper-Helmstetter equation predicts the amount of DNA per cell as a function of C, D, and τ, and the additional parameter, P_O, links the amount of DNA to the amount of protein in the cell.

At about the same time, Schleif (168) and Maaløe (130) began to establish a theoretical relationship between the amounts of protein and RNA in the cell and the two parameters, c_p and β_r, which define the function of ribosomes: β_r is the fraction of total ribosomes actively engaged in peptide chain elongation; c_p is the rate of peptide chain elongation. Based on these relationships, Churchward et al. (47) 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 the five additional parameters, C,D,P_o, β_r, and c_p. These mathematical relationships define the connections between the various physiological parameters, but do not explain the underlying biological process, since the relationships are derived entirely from the definition of the exponential growth function and of the parameters used, without requiring any observed data. Therefore, the relationships do not help to understand how the parameters are determined in the cell.

Despite almost 50 years of intensive study in many different laboratories, the mechanisms by which the growth medium affects the synthesis of ribosomes and their rate of function (i.e., the two factors that determine the growth rate; see "Growth rate dependency of the macromolecular composition," below), are not yet understood. This means that the important problem of the control of bacterial growth is far from being solved. However, considerable progress has been made during the past 10 years in the determination of absolute promoter activities (in transcripts initiated per minute per promoter) for ribosomal RNA (rRNA) and ribosomal protein (r-protein) genes at different growth rates. This determination requires a combination of transcription and replication information. Such studies have allowed us to determine the in vivo strength of promoters and to define the promoter control in terms of changing Michaelis-Menten constants, which, in turn, allows one to distinguish between factor-dependent transcriptional control of the promoter and changes in promoter activity due to changes in the concentration of free functional RNA polymerase associated with different growth conditions. The latter affects all unsaturated promoters, both controlled and constitutive, to the same extent. These new developments have been recently reviewed (72).

GROWTH RATE DEPENDENCY OF THE MACROMOLECULAR COMPOSITION

Relationship between Macromolecular Composition and Growth Rate

The total, or bulk, amounts of RNA and protein are linked to the growth rate, because most bacterial RNA is ribosomal RNA (rRNA). Since ribosomes are required for protein synthesis, their number and their rate of function determine the rate of protein synthesis and cytoplasmic mass accumulation. Mathematically, the exponential growth rate equals the product of the number of ribosomes per amount of total protein present (N_r/P, representing the ribosome concentration) times the rate of protein synthesis per average ribosome, known as "ribosome efficiency" (e_r; see equation 18 in Table 6).

Table 6Basic parameters determining the bacterial growth rate

The idea that the exponential growth rate, μ, is limited by only two factors, N_r/P and e_r, might seem overly simplistic, as one can think of many other potential bottle necks besides translation that could limit the growth rate. However, the relationship between N_r/P, e_r, and μ (see equation 18 in Table 6) is not based on any "model" or assumption (other than that most Escherichia coli proteins are stable). Instead it follows directly from the definition of exponential functions. As long as steady-state exponential cultures are considered, the relationship is necessarily correct (for details in the derivation of the formula, see reference 72). The values of N_r/P and e_r, of course, depend on many physiological factors which, in turn, depend at least in part on the composition of the growth medium.

In the original work by Schaechter et al. (167) the ribosome efficiencies observed during growth in different media were quite similar, especially during growth in amino acid-supplemented media, when ribosomes are assumed to function at or near their maximum rate (see "Peptide chain elongation rate," below). Therefore, Schaechter et al. (167) assumed a general "constancy of the rate of protein synthesis/particle," i.e., a constant value of e_r. Under such conditions the growth rate is fully determined by the value of N_r/P, which reflects the ratio of total RNA/total protein. Therefore, when (at constant e_r) a particular growth medium produces a particular value of N_r/P, this value also "sets" the growth rate. This is the main reason for Maaløe’s conclusion that the macromolecular composition depends only on the growth rate, and not on the growth medium. In the following we suggest that the situation is more complex and that this idea is not universally applicable.

Growth Medium-Dependent Control

Since the macromolecular composition of bacteria appeared to depend only on the growth rate (see above), observed parameters pertaining to the physiology of bacterial cultures were most often expressed as functions of the growth rate. However, in some instances this can be misleading. For example, the synthesis of many bacterial mRNAs and enzymes can be induced by exogenous nutrients without producing a significant change in the growth rate or in the general physiology and macromolecular composition of the bacterial culture. Evidently, the growth rate does not determine the physiological parameters of the bacteria; rather vice versa, certain physiological parameters determine the growth rate. Therefore, instead of using the term "growth rate-dependent control" (e.g., of the synthesis of ribosomes or of other components), we prefer to use the term "growth medium-dependent control."

An important observation in this context is the following. When the rate of mRNA synthesis (per genome equivalent of DNA) was compared in six cultures, three in minimal media with different carbon sources (succinate, glycerol, and glucose) and the other three cultures in the same media supplemented with all 20 amino acids, the mRNA synthesis rates could not be plotted as a single function of growth rate, but only as two separate curves, one for the three minimal media, and a second curve for the three amino acid-supplemented media (170). In another study cultures were grown in two sets of media, one with both different carbon sources and amino acid content as in the experiments on which and below are based, and the other with different carbon sources in the presence of all amino acids. Here the strength and activity of a ribosomal RNA (rRNA) promoter, plotted as function of growth rate, gave a different curve for each set (206). For cultures grown in the presence of all amino acids, it was found that, independent of the growth rate, (i) the rate of ribosome function is near maximal (16), (ii) the accumulation of the effector ppGpp (an inhibitor of rRNA synthesis; see also section about RNA polymerase activity below) is close to zero, and (iii) the rRNA promoters have their maximum strength (72, 206). (Promoter strength is defined as the promoter activity per free RNA polymerase concentration under conditions when the promoter is far from being saturated with polymerase.)

These observations show that two cultures grown in different media may produce the same growth rate but have different macromolecular compositions; this conflicts with Maaløe’s conclusion above. One might argue that mRNA represents only a few percent of total RNA, so that different rates of mRNA synthesis do not significantly affect the overall composition of the bacteria. However, all mRNAs compete for ribosome binding. Many mRNAs made in the presence of amino acids (i.e., when the mRNAs for amino acid biosynthesis are repressed) have strong ribosome binding sites whose presence reduces the expression of all other active genes (see "Translation frequency of mRNA," below, and the discussion of Fig. 3 in reference 72). This implies that there can be profound differences in the spectrum of gene activities in cultures grown in different media that produce the same growth rate.

Different Compositions in Cultures Growing at the Same Rate in Different Media

Why did we find differences in the macromolecular composition of cultures growing at equal rates but in different growth media when the "Copenhagen school" did not observe this result? There are several possible reasons; the most apparent are as follows. (i) In part, the difference reflects the choice of media. Schaechter et al. (167) used mostly media that contained only amino acids as nutrients. We have not used media that contain only amino acids, because the amino acids preferentially used as a carbon source (i.e., serine or aspartate) might become exhausted, so that the bacteria have to switch to another amino acid for a carbon source, which makes it impossible to maintain prolonged balanced growth. (ii) In the original work only four parameters (expressed "per cell") were measured: mass (optical density units), RNA, DNA, and "nuclei." We have also measured mRNA, RNA polymerase, peptide chain elongation, as well as DNA replication and other cell division parameters. This leads to a more complete description of the composition, where differences will become apparent that are not necessarily apparent when only the four original parameters are observed. (iii) There also seems to be a difference in the growth rates observed by Schaechter et al. (167) for Salmonella and our results obtained with E. coli B/r. We found a growth rate of 1.0 doubling/h in a medium with all amino acids plus succinate as a carbon source (170), whereas Schaechter et al. (167) found almost twice that growth rate in a medium containing all amino acids but without an additional carbon source (their Table 1: μ = 2.0 for Casamino acids medium and μ = 1.83 for 20 amino acids medium). We cannot explain this difference; perhaps some amino acid used as a carbon source by the bacteria in the experiments of Schaechter et al. was superior to succinate.

Growth Medium-Dependent and Growth Rate-Dependent Control

Since our aim is to understand the control of the bacterial growth rate, it is apparent from the above discussion that we cannot logically make the growth rate an independent, freely chosen parameter. Nevertheless, for both historical and practical reasons, we have kept the tradition in Table 2 and Table 3 below to describe physiological parameters "as functions of growth rate." The observations mentioned above indicate that the single functions of growth rate represented by the data in these tables were only possible by the particular choice of media used: minimal media with different carbon sources (succinate, glycerol, glucose) with glucose producing the fastest growth, followed by media containing glucose and amino acids, and additional supplements (glucose-amino acids, and LB-glucose) resulting in higher growth rates than obtained with glucose alone. The data in the tables were then obtained by drawing smoothed best-fit curves through the points from particular sets of published experiments (indicated in the footnotes to the tables), so that they appear to represent continuous functions of growth rate. Actual data, even if precisely determined, generally deviate somewhat from those values and do not necessarily produce a smooth curve.

Since the tables are based on a selective choice of media, the interpretation of the values in these tables requires some caveats. As an example, if we consider two cultures, one in glycerol minimal medium, the other one in succinate-amino acids medium, both grow at a rate of approximately 1.0 doubling/h. In the first case, about 50% of the total rate of RNA synthesis is mRNA, and it the second case it is only about 20% (from Fig. 9 in reference 170). The data for μ = 1.0 doubling/h in Table 2 and Table 3 below refer only to cultures grown in glycerol minimal medium; i.e., they are not valid for cultures in succinate-amino acids medium that grow at the same rate.

To bridge the discrepancy between more complex multifactorial control and growth rate-dependent control inherent in these tables, we suggest that the growth rate values in the tables should be understood as representing particular media that produce growth rates close to the values shown. Since the growth rate values in the tables were rounded to constant intervals of 0.5 doubling/h which do not exactly match the observed growth rates in the media used, most of the parameter values shown had to be obtained by interpolation. For this purpose, smooth functions of growth rate were assumed for the growth media chosen. Partly because of the "history effect" described below, and partly because different growth media reflect qualitative, rather than gradually changing quantitative, differences in the nutrients, this assumption may be only approximately correct.

The Physiological History of a Culture Affects Its Growth and Composition

Even a given growth medium does not fully determine the growth rate and macromolecular composition of a bacterial culture. In addition, effects of the history of the particular starter culture that is used to inoculate an experimental culture can be of importance. Certain physiological controls are apparently "set" shortly after an experimental culture is started by dilution from another, generally stationary ("overnight") culture; these controls lead to a certain exponential growth rate associated with a certain macromolecular composition after at least 10 generations (see "Exponential growth," below). This particular "balanced" physiological state is maintained as long as the culture is kept under nonrestricting conditions, meaning that all nutrient factors in the medium, including oxygen, are present at nonlimiting concentrations, and it may be prolonged indefinitely by dilutions with fresh (prewarmed) medium (38). The effects of the history of the starter cultures from which experimental cultures are prepared have hardly been studied in the past and are at present somewhat beyond the control of the experimenter.

This history effect causes variations in the data, i.e., both in the exponential growth rate and in the macromolecular composition, from cultures prepared on different days, i.e., with different overnight starter cultures. This is especially true for cultures grown in nutritionally poor media, as observed variations in the growth rate for a given medium tend to increase with decreasing nutritional value of the carbon source used in minimal media. For example, doubling times were found to vary between 42 and 48 min in glucose minimal medium, or between 55 and 70 min in glycerol minimal medium, and between 67 and 113 min in succinate minimal medium (38, 173). An average growth rate for a given minimal medium cannot be clearly defined, because both the observed average and extent of variation in the growth rate may depend on particular ways different experimenters prepare their overnight cultures. In one study with four succinate cultures (173), the ribosome concentration (N_r/P) for the fastest growing culture (0.90 doubling/h) was lower than the values observed in the other, more slowly growing cultures, but the lower ribosome concentration was balanced by a higher rate of ribosome function (e_r), which was close to the value normally found only in cultures growing in amino acid-supplemented media. The varying growth rates in minimal media imply varying rates (per total amount of protein, or per cell volume) of amino acid biosynthesis, of importing and processing the exogenous carbon source, and of respiration. This raises the (unanswered) question: what limits the growth rate of a particular culture in a particular medium?

An implication of these observations is that bacteria in nutritionally poor media generally do not grow at their maximum possible rate, i.e., they appear to partly downregulate their potential growth rate. Why this could be advantageous for the bacteria is discussed in the section "Optimal cell composition for maximal growth," below.

Cultures grown in minimal media may not only show variable growth rates, but also somewhat different macromolecular compositions at the same growth rate. This latter variability relates to the fact that the growth rate equals the product of the two factors, ribosome concentration and function (N_r/P and e_r; see above and equation 18 in Table 6 below). During fast growth in rich media, ribosomes function at or near their maximum, so that the only variable factor that determines the growth rate is the ribosome concentration, N_r/P. In contrast, during slow growth in poor media, the rate of ribosome function is generally submaximal, so that different pairs of N_r/P and e_r may produce the same growth rate, i.e., either fewer ribosomes that function somewhat faster or more ribosomes that function more slowly. Either combination requires the same rate of amino acid biosynthesis and leads to the same rate of protein synthesis and growth.

What causes the cell to choose a particular pair of values for N_r/P and e_r in a given minimal medium is not known. However, when several experimental cultures are started at the same time from the same stationary overnight culture, they generally behave identically; i.e., they assume the same exponential growth rate and show the same macromolecular composition. Apparently certain physiological parameters are affected by events during the preceding stationary phase (38). As a result, N_r/P and e_r values observed in a particular experiment might differ from the values observed in a similar study on another day. The product of N_r/P and e_r may either remain similar to produce a similar growth rate, or within certain limits, differ to produce a different growth rate. In general, longer durations in stationary phase are associated with a longer initial lag before growth resumes after inoculation of an experimental culture and with a somewhat lower final growth rate. The reason for this is not known since these effects have never been systematically studied. The most reproducible results are obtained when the duration of the stationary phase in the starter culture used to inoculate the experimental culture is kept at a minimum. This can be achieved in various ways, for example by minimizing the inoculum used for the overnight starter culture, so that it reaches stationary phase only a few hours before it is used to inoculate the experimental cultures.

When stationary cultures in different media are incubated for several days and monitored by flow cytometry, the average size of their cells and the chromosome number per cell is found to gradually decrease. For example, a stationary culture in LB medium contains initially large cells with four or eight chromosomes, but after further incubation, different subpopulations arise with smaller cells containing only one or two chromosome(s) (1). It is not surprising, therefore, that the condition of a particular stationary culture affects the subsequent growth of an experimental culture derived from it. A systematic study of these effects will be necessary in the future to fully understand the control of bacterial growth. A further discussion about the control of the bacterial growth rate is found in "Mathematical description of cell composition and growth," below.

The observations described above might suggest that the growth rate is perhaps not the only factor that determines the macromolecular composition, but at least it is one among other factors. However, the causal arrow can only go in one direction, from the cell environment via genetic background (species, strain) and initial conditions ("history") to composition and growth rate, and not in the opposite direction. The following analogy might help to clarify this idea: a unique relationship exists between the volume of the mercury within a thermometer and the temperature surrounding it. However, to say that the volume of mercury in the thermometer "determines" the temperature is ambiguous, because causally the weather produces the outside temperature which, in turn, determines the volume of the mercury, not the other way around.

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 that are essentially invariant and growth rate independent, like the fraction of total RNA that is stable rRNA and tRNA; (iii) other partition parameters that 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 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.

Table 1Parameters related to the growth and macromolecular composition of bacterial cells

The values of the fraction of total RNA that is stable RNA (f_s) and the fraction of total stable RNA that is tRNA (f_t) in class ii need some comment. The value of f_s = 0.98 means that 98% of all bacterial RNA is rRNA and tRNA, whereas 2% is mRNA. The value of 98%, which cannot be measured with the precision necessary to distinguish it from 100% (total RNA), was obtained instead as the difference between measurements of total RNA (100%) and mRNA. Since there is no hybridization probe for total mRNA, the 2% value for mRNA was estimated indirectly from the rate of mRNA synthesis and the average mRNA lifetime. The rate of mRNA synthesis was found from the (observable) rate of stable RNA accumulation and from the fraction of the total RNA synthesis rate that is stable RNA, r_s/r_t (see Table 3 ; obtained by hybridization of pulse-labeled RNA to an rDNA hybridization probe, taking into account the hybridization efficiency and the fraction of total stable RNA that is tRNA, f_t). The proportion of the mRNA synthesis rate is then equal to the difference (1 − r_s/r_t). To obtain the amount of mRNA, the "average lifetime of an average mRNA" must also be determined. This was done by a complex evaluation of the pulse-labeling kinetics of total RNA and rRNA for bacteria grown in glucose minimal medium at 1.3 doublings/h: under those conditions, 60% of the total RNA synthesis was mRNA synthesis, the average life of mRNA was 1.0 ± 0.2 min, and the amount of mRNA was calculated to be 2.3% of the total RNA (8). Thus, f_s is equal to about 98%, as given in Table 1. In another approach based on measurements of the average life of lacZ mRNA at different growth rates, the relative abundance of mRNA has been estimated to decrease from about 2.2% at μ = 0.6 to 1.1% at μ = 3.0 (121). This suggests that f_s may increase slightly with growth rate from 0.98 to 0.99.

The value f_t = 0.14 in Table 1 means that 14% of the total stable RNA is tRNA and 86% is rRNA. Stable RNA refers to the sum of 23S, 16S, and 5S rRNA and all tRNA species, excluding unstable spacers in the primary rRNA and tRNA transcripts. The value of f_t = 0.14 corresponds to about 9 tRNA molecules per ribosome. During slow growth in nutritionally poor media, the number of tRNA molecules per ribosome is somewhat higher, and this number was found to decrease from about 12 at μ = 0.4 to a constant plateau of about 7 at growth rates faster than 1.0 doubling/h (75). The higher tRNA values during slow growth can be attributed to two growth rate-related phenomena—an instability of some newly made rRNA at slow growth rates and a slight increase in the ratio of rRNA to tRNA genes at fast growth rates due to increased chromosome "branching" associated with shorter intervals between initiations of chromosome replication (see Fig. 1). In the first instance, at the very low growth rate of 1 doubling/10 h, 70% of newly made rRNA was found to be degraded (91); this unstable fraction diminishes as cells grow faster and at growth rates above 1 doubling/h, virtually all of the newly made rRNA is believed to be stable. In the second instance, an analysis of the location of seven rrn transcription units and 81 different tRNA genes on the E. coli chromosome indicates that the average rrn unit is located about 10 min (using the 100-minute genetic scale) from the origin of replication, oriC, whereas the average tRNA gene is located about 20 min from oriC. This means that with increasing growth rate, the dosage of rrn genes increases slightly faster than the dosage of tRNA genes due to the increase in the degree of chromosome branching (between μ = 0.6 and 3.0 the ratio of gene dosages, rRNA/tRNA, is expected to increases by about 15%). During growth in succinate minimal medium at a rate of 0.67 doubling/h, the accumulation of tRNA relative to that of rRNA was 10 to 15% higher than during twofold faster growth in glucose minimal medium (57), so that perhaps for the lowest growth rate of 0.6 doubling/h in Table 2 and Table 3 below, a 10 to 15% upward correction would need to be made for the value of f_t.

Fig. 1Relationships between growth rate, cell size, chromosome replication, transcription, and macromolecular composition. (Left) Average cell size (mass per cell, Table 2) for E. coli B/r growing with a doubling time, τ, ranging from 100 to 20 min (growth rate, μ, ranging from 0.6 to 3.0 doublings/h) 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 light line portions represent periods where there are two forks per chromosome structure, and the heavy line 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) Average structure of the replicating chromosome or chromosomes in the culture. For 24- and 20-min cell cycles (τ = 24 or 20 min; bottom portion), the chromosome pattern indicates that replication has reinitiated 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 (values from Table 2). The numbers of origins (O), termini (T), and forks (F) in this average genome are also indicated (from Table 2). (Right) 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 increases as a fraction of the total mRNA synthesis rate. 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.

We assume that the bulk of tRNA is coregulated with rRNA transcription. This notion, primarily based on the observed constancy of f_t at higher growth rates, is further supported by observations that the rates of rRNA and bulk tRNA transcription decrease coordinately in the presence of extra rrn genes (106) and increase coordinately during chloramphenicol treatment, which mimics the relaxed response or an internal nutritional shift-up (59, 170). Furthermore, most (although not all) tRNA genes have P1 and P2 promoters similar to those of the rrn genes and are subject to stringent control like rRNA genes (39). Therefore, f_t in Table 1 could also be defined as the fraction of the stable RNA synthesis rate that is tRNA synthesis, which would then be valid for all growth rates.

In this context, it should be noted that Emilsson and Kurland (80) have measured the abundance of five leucine and three methionine isoacceptor tRNAs as a function of growth rate. They found that the ratios of Leu1 and Leu3, and fMet1, fMet2, and Met3 tRNAs to ribosomes remained relatively constant between growth rates of 0.5 and 2.1 doublings/h. The Leu1 tRNA reads the major CUG codon and is encoded by four identical genes whereas the Leu3 tRNA reads the minor codon CUA as well as the major CUG codon (through wobble base pairing) and is encoded by a single-copy gene. In contrast, the ratios of Leu2, Leu4, and Leu5 tRNAs to ribosomes decrease five- to eightfold as the growth rate is increased from 0.5 to 2.1 doublings/h. These three tRNAs read the minor CUU, CUC, UUG, and UUA leucine codons that are infrequent in highly expressed proteins. Each of the three tRNAs is encoded by single-copy genes. These results demonstrate that the synthesis of at least some of the tRNAs reading the most abundant codons is coordinate with the synthesis of ribosomes, whereas at least some of the tRNAs reading minor codons are more highly expressed at slow growth rates where they would be required for the synthesis of proteins containing a higher frequency of minor codons.

Reference Units

Physiological parameters describing the cell composition, like the amounts or synthesis rates of particular components, require a reference unit such as "per cell," "per cell mass," "per amount of protein," "per genome," "per microgram of dry weight," etc. This means that for any quantitative measurement of a particular cell component, at least two parameters have to be quantitatively measured, representing the desired component of interest and the reference unit. Therefore, the accuracy of any physiological measurement is also affected by the accuracy with which the reference unit can be determined.

The primary reference unit for our measurements from exponential cultures is the cell mass density, given in units of turbidity of the culture, i.e., "per OD₄₆₀" (optical density unit at 460 nm), because determination of the optical density is simpler, faster, and more accurate than that of other units. For E. coli B/r bacteria grown in glycerol minimal medium at 1.0 doubling/h and in glucose-amino acids medium at 2.1 doublings/h, we found their dry weight (after washing them free of adhering growth medium) to be 173 and 172 μg, respectively, per OD₄₆₀ unit of culture (38). For the calculations of cell mass in micrograms in Table 2 below, we have therefore used a constant value of 173 μg/OD₄₆₀ for all media (see Table 2 , footnote r).

The per mass values have also been used to express approximate relative intracellular concentrations, because the average cell volume per mass unit changes relatively little with growth conditions. For E. coli B/r growing in glucose minimal medium (at 1.33 doublings/h) and in glucose-amino acids medium (at 2.14 doublings/h) average cell volumes of 0.35 and 0.29 μl per OD₄₆₀ unit, respectively, were found (Table 1 in reference 43). This corresponds to a 17% decrease in volume per mass for a 1.6-fold increase in the growth rate. However, using data from cultures grown under similar conditions, volume/mass values of 0.32 and 0.25 μl per OD₄₆₀ unit, respectively, have been estimated for these two growth rates (34), corresponding to a 22% difference. The reason for the different results is the variability of the average cell size in cultures grown on different days under seemingly identical conditions (see "Cell volumes and cytoplasmic concentrations," below).

When parameters are to be expressed with other reference units, they are found from additional measurements of the wanted reference parameter "per mass." For example, the amount of protein per average cell is obtained by dividing the amount of "protein/mass" by the number of "cells/mass."

There has been a tendency in the literature for authors to state that rRNA or ribosomes accumulate in proportion to the square of the growth rate. This, of course, is unsuitable because the unit of reference is not specified. As first pointed out by Maaløe (130), the rate of RNA accumulation "per genome equivalent of DNA" does increase with the square of the growth rate, μ (67). This reflects the fact that the amount of RNA per genome is proportional to the growth rate (at least above growth rates of 0.6 doubling/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 controls of chromosome replication and RNA synthesis, this square relationship has no particular significance for ribosome control itself; the relationship no longer holds in certain replication control mutants that alter DNA content but show no change in the growth rate or rRNA control (47, 48).

In the following, the limitations in the accuracy of measurements of the three most frequently used reference units, i.e., per mass, per cell, and per cell volume, are discussed.

Optical density of bacterial cultures.

In contrast to normal absorbance measurements of solutions, measurements of the OD of a bacterial culture (i.e., of the turbidity caused by scattering of light by bacterial cells), depend somewhat on the particular spectrophotometer used (i.e., features of the light beam and the measuring cuvette), so that OD measurements from different laboratories do not always reflect exactly the same culture densities. The amounts of macromolecules per OD₄₆₀ unit in Table 2 below are based on newer data (16) that deviate somewhat from the values given in previous editions of this table. This is partly due to the use of different spectrophotometers and partly due to a refinement of the method to determine the OD.

The OD of a culture is not always an exact measure of the cell mass density: the higher the cell density, the greater the deviation of the "observed OD" from the "true OD" because of cell shadowing and backscattering. In earlier work, this effect was partly taken into account by measuring the OD of diluted culture samples. This causes some inaccuracies due to variation in pipetting volumes associated with the dilution and because the lower OD values measured (closer to the background OD) have inherently a greater variability. For the new data in Table 2 below, the relationship between observed and true OD was first independently determined for the bacterial strain used; it was found that the deviation from the true OD increases in proportion to the square of the true OD. Using this mathematical relationship, the corrected OD (including subtraction of the background OD of the cell-free growth medium) was calculated by a computer spreadsheet (see reference 16 for details). From these corrected values, the spreadsheet calculated the best-fit exponential growth function. The corrected OD values from samples taken over two to three doubling times deviated by less than 1% from this exponential function. The best-fit function thus provided an accurate value for the growth rate (μ). For determinations of particular cell components, like protein, RNA, or DNA, the exact OD at the sampling times calculated from the best-fit exponential growth function was used to obtain macromolecular amounts "per OD-unit of culture mass" (16).

We have now extended the data range in Table 2 and Table 3 from the maximum growth rate of 2.5 doublings/h in the previous edition up to 3.0 doublings/h in this edition. The previous data were based on experiments in which glucose-amino acids was the most nutritious growth medium used. That medium typically gives a growth rate of 2.14 doublings/h for E. coli B/r, so that the values given for 2.5 doublings/h were actually obtained by extrapolation. The inclusion of values for a growth rate of 3.0 doublings/h in the new tables was possible by using experimental cultures grown in Luria-Bertani (LB) medium (supplemented with 0.2% glucose; reference 16). In this medium the bacteria grow at what appears to be their maximum rate of 3.0 doublings/h (at 37°C). However, this cannot be done by following the OD at 460 nm, because of the high background absorbance of the LB medium alone, without bacteria, at this wavelength. Therefore, OD₆₀₀ units were used as a reference for cultures grown in LB medium. By monitoring both the OD₄₆₀ and the OD₆₀₀ of cultures growing in different media, parallel growth curves were obtained, differing by a factor of 1.60 ± 0.03 (OD₄₆₀/OD₆₀₀). This factor was then used to convert OD₆₀₀ units into OD₄₆₀ units for cultures in LB medium. The use of LB medium excludes the use of radioactive assays because the nutrients in the medium dilute by an unknown factor the specific radioactivity of the base, nucleoside, or amino acid precursor used to label the macromolecules in the cell. For that reason nonradioactive colorimetric assays were used for the basic measurements of DNA, RNA, or protein.

Cell numbers.

A seemingly "natural" reference is the "average cell." When it was first observed in Maaløe’s laboratory that fast-growing cells are much larger than slowly growing cells (reference 167; see also the next section), Maaløe proposed not to use "per cell," but instead to use a "genome equivalent of DNA" (per genome) as the standard reference unit for physiological data from bacteria. He thought that DNA was somehow limiting reactions that were important for determining the growth rate and macromolecular composition. The per genome reference is no longer used, since later studies have shown that DNA is generally not limiting the rate of transcription (see below). For historical reasons per genome values for the cell composition are still shown in Table 2 below.

The per cell values in Table 2 and Table 3 below were obtained from the primary values determined per OD by division with the cell numbers per OD. An "average cell" refers to a particular size between two cell divisions, which is found by taking the so-called "age distribution" into account (23) (see "Cell composition at a defined cell age," below). Because of relatively large variations of the times between consecutive cell divisions, the actual predivision and postdivision cell volumes in a culture vary by more than a factor of two in a non-Gaussian fashion (23, 24).

The values for "mass per cell" (i.e., the reciprocal of cell numbers per OD) in Table 2 were obtained in two ways. First, the number of cells at a given OD was determined with an electronic particle counter equipped with a 20-μm orifice, which allows the counting of small cells present in nutritionally poor media. The size distribution displayed by the particle counter helps to visualize and to avoid counting the background from debris in the growth or dilution medium (each has to be carefully filtered). The size distribution also indicates when newly divided cells are temporarily sticking together to form "snakes." This degree of stickiness often depends on uncontrolled conditions within a particular culture, so that measured cell numbers per OD unit may vary from culture to culture. The E. coli strain B/r used for the data in Table 2 and Table 3 below exhibits a relatively tight size distribution and is less prone to stickiness than many of the more widely used K-12 strains (see below).

A second, indirect method consists of calculating cells/mass as the quotient DNA/mass and DNA/cell, where DNA/mass is measured directly and DNA/cell is obtained from the C- and D-periods (Table 3 ), using the Cooper-Helmstetter formula (see above; equation 3 in Table 5 below). This latter method has been used for the data in Table 2 and Table 3 to make all values in the tables consistent with the theoretical relationships connecting them in various ways.

Table 5Equations relating the cell composition in exponential cultures to basic cell cycle parameters

Cell volumes and cytoplasmic concentrations.

For biochemical studies the most relevant reference seems to be the average cell volume, because this allows one to estimate intracellular molar concentrations by division of the average per cell values of a given compound with the "volume per average cell." The average cell volume has been determined in two ways: first, from the volume distribution obtained with a particle size analyzer calibrated with latex spheres of known volume (49), and second, by measuring the cell dimensions in electron microscopic pictures (24).

The particle counter equipped with a size analyzer (made by Coulter Electronics) that has been used for our studies with E. coli B/r measures the temporary reduction in the electric conductivity between two volumes of salt solution separated by a small hole ("orifice") through which the particles are being sucked; i.e., while a particle passes through the hole, the electrical resistance of the solution in the narrow channel formed by the orifice temporarily increases. The electronic "pulse" generated in this manner is assumed to be proportional to the volume of the passing particle, i.e., to the volume of the solution displaced by the particle. These counters were originally developed for much larger eukaryotic cells; to sufficiently increase their sensitivity for much smaller bacteria, the orifice had to be reduced to the smallest available size of 20 μm diameter. This is still much wider than the bacteria with dimensions of about 1 μm, and it is not clear how accurately the electronic pulses generated in this manner reflect exact cell volumes, and to what extent the difference in the shapes of the elongated bacteria and the round latex spheres used for calibration might affect these distributions.

The volume distributions of bacteria are highly asymmetric, with a peak close to the minimum volume and a longer trail toward larger size bacteria. This reflects the age distribution of the cells, i.e., the average young cell just after division is half the size and twice as frequent as the average older cell before division. The volume distributions for cultures grown at 1.30 doublings/h in glucose minimal medium and at 2.14 doublings/h in glucose amino acids-medium were found to have peaks at 0.60 and 0.81 μm³ (Fig. 4 in reference 49). Assuming that these peaks represent the most frequent cells just after division, their cell volumes were multiplied with the factor 2 • ln2 (= 1.39) to obtain the average cell volume, i.e. by taking the age distribution into account (see "Age distribution and the concept of the average cell," below). With this factor, average cell volumes for E. coli B/r in these two media were estimated to be 0.83 and 1.12 μm³, respectively (Table 1 of reference 49).

By use of the method of electron microscopy for bacteria grown in glucose minimal medium at 1.33 doublings/h and fixed with formaldehyde, a similar volume distribution was obtained from measurements of the widths and lengths (and assuming half-spherical ends) of 959 cells (Fig. 8 in reference 24); the average volume was 0.73 μm³; i.e., somewhat smaller than the value of 0.83 μm³ obtained with the particle counter. Because of distortions of the shape of the bacteria during the preparation for the electron microscopy, such volume determinations might also be not entirely accurate.

By using the data above, approximate cell volumes for E. coli B/r growing at 1.0 and 2.5 doublings/h have been estimated by extrapolation (34). For this purpose, the cell volumes of 0.83 μm³ and 1.12 μm³ for μ = 1.33 and 2.14 doublings/h (see above) were first divided by the mass/cell values to calculate volume per mass ratios (0.32 and 0.25 μl, respectively), which were then linearly extrapolated to 1.0 and 2.5 doublings/h to give 0.34 and 0.22 μl, respectively, of combined cell volumes per OD₄₆₀ unit of culture mass. Multiplication with the averaged mass/cell values for these two growth rates (1.84 and 5.47 OD₄₆₀ units per 10⁹ cells, calculated indirectly from protein/mass, protein/oriC, and oriC/cell, setting 1 μm³ = 10⁻⁹ μl) gave 0.63 and 1.20 μm³ for the average cell volume in exponential cultures growing at 1.0 and 2.5 doublings/h, respectively (34).

The average cell volumes estimated in this manner may not be precise because average cell sizes vary considerably for cultures grown under the same conditions on different days, presumably reflecting a variability in the average D-period (see "DNA replication and cell division," below). As described below ("Exponential growth"), flow-cytometric data indicate that the average cell sizes may begin to decrease in exponential cultures at very low cell densities, long before the exponential accumulation of mass and major macromolecules begins to decrease during the approach to stationary phase (1).

Since a substantial fraction of the cell volume is taken up by the nucleoid, the actual space available for most biochemical reactions within the cell is much smaller than the total cell volume, and the macromolecular concentrations calculated from the total cell volume are correspondingly underestimated (see below).

The cell volume appears to be largely determined by its protein content. At the two growth rates of 1.0 and 2.5 doublings/h, where the average volume increases from 0.63 to 1.20 μm³ (see above), the average amounts of protein per cell correspond to 1.2 · 10⁹ and 2.4 · 10⁹ amino acid residues, respectively (see Table 2 ). This means that, at least within this 2.5-fold range of growth rates, every cubic micrometer of (total) cell volume is associated with about 2 · 10⁹ amino acid residues in protein.

The average amount of protein per cell (P_C) (and thus also the average cell volume) increases with increasing growth rate in proportion to the average number of replication origins per cell. This is seen as follows: protein per cell equals the product of protein per replication origin (P_O) times the number of origins per cell (O_C). Thus, the volume of an average cell in a culture of the E. coli strain B/r (Vol_C) can be described by the formula: Vol_C = (P_O · O_C/2 · 10⁹) μm³, where the values for P_O and O_C at different growth rates can be found in Table 2 .

P _O expresses the control of initiation of replication (see above) and is approximately constant for E. coli B/r during exponential growth at different rates (reference 16; Table 2 ), whereas O_C depends on the C- and D-periods and on the doubling time: O_C = 2^(C+D)/τ (see equation 7 in Table 5). Substituting the original data of Helmstetter and Cooper (where the sum of C and D was found to be equal to about 60 min at growth rates above 1.0 doubling/h; reference 99), we obtain O_C = 2^60/τ = 2^μ. This implies that the average cell volume increases nearly exponentially with increasing growth rate, approximated by the function 2^μ.

If μ approaches zero, the values for O_C in Table 2 extrapolate to 1.0 (i.e., 2⁰ = 1). This would mean that most cells at μ close to zero are expected to have one nonreplicating chromosome with one origin. However, determinations of C and D for very slowly growing E. coli B/r suggest that O_C approaches a lowest value of about 1.25, which was observed at 0.08 doubling/h (rather than 1.06 = 2^0.08; reference 137). Assuming further that the amount of protein per origin remains approximately constant under these conditions, equal to about 4 · 10⁸ amino acid residues (Table 2 ), the formula above gives an approximate minimum volume of (B/r) bacteria growing very slowly in poor media (but still exponentially under balanced conditions), equal to 0.25 μm³.

Although our data showed that C and D decrease somewhat with increasing growth rate (see Table 3 ), these considerations show that the increasing cell volumes with increasing growth rate are the result of the controls of DNA replication and cell division and an implication of the exponential growth function. Therefore, any parameter (like protein, RNA, or DNA, or their rates of synthesis) observed under different growth conditions and expressed "per cell" reflects not only the specific control of the parameter under study but also the control of DNA replication and cell division and the exponential growth function in general. This justifies Maaløe’s concern about the use of the "per cell" reference and his search for a more suitable reference unit. However, now we see that his proposal to use per genome as a standard reference is subject to similar deficiencies (see above).

In the tables below, molar concentrations were not calculated. Because of the high component densities within the cytoplasm, and because a substantial fraction of the total cell volume is occupied by the densely packed chromosomal DNA in the nucleoid, most cell components are not expected to be evenly distributed throughout the cell volume. As was pointed out by Maaløe and Kjeldgaard (132), large enzyme complexes, including RNA polymerase and ribosomes, might not move freely between the DNA strands within the nucleoid. Therefore, local concentrations of many (especially larger) cellular compounds are expected to differ from the cellular average. This makes estimates of molar concentrations within the cell (and, in some instances, the extrapolation from in vitro data to the in vivo situation) somewhat tenuous. These effects, known as "crowding," may be taken into account by estimating a "volume fraction" that is available for most biochemical reactions in the cell (14).

The following observed example illustrates the uneven distribution of molecules within the cells. When radioactive uracil is used to label RNA, the UMP residues in the newly synthesized RNA have a much higher specific radioactivity than the simultaneously determined (average) specific radioactivity of the UTP precursor pool (140). Apparently most transcriptionally active sections on the DNA are located close to the sites for UTP synthesis, presumably near the cell periphery where uracil transport from the growth medium involves a conversion to UMP which is quickly phosphorylated to UDP and UTP.

Use of the amount of protein as a reference unit.

Since average cell volumes for given exponential cultures are difficult to determine and since values per cell, per genome, or per mass (i.e., per turbidity unit of culture) have little physiological significance, one might ask: is there any better choice? We believe that the use of total protein as a standard reference (see also Fig. 2) has several advantages: (i) as was seen above, the amount of protein per cell volume is approximately constant, so that the amounts of cellular components "per amount of protein" closely reflect cellular concentrations; (ii) two parameters referring to total protein, the ribosome concentration (ribosomes per protein, N_r/P) and the "initiation mass" (P/oriC, reciprocal of oriC concentration) have a special significance for bacterial physiology (see "History" and "Relationship between macromolecular composition and growth rate," above); and (iii) the protein reference is already used as the fraction of total protein that is ribosomal protein (α_r) or RNA polymerase (α_p; see Table 3 ) and as specific enzyme activities for gene products with enzymatic function.

Fig. 2Amounts and synthesis rates of molecular components in bacteria growing exponentially at rates between 0.6 and 2.5 doublings/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 (Table 3) and the rate of protein synthesis per cell. The latter was obtained from the amount of protein per cell (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 (r_s or r_m; panel d) is from line 5, Table 3. The rates of stable RNA and mRNA synthesis per amount of protein (r_s/P or r_m/P; panel e) were calculated from the data in Table 3, divided by the amount of protein per cell (Table 2). The ppGpp per protein value (ppGpp/P; panel f) is from Table 3. The cell age at which chromosome replication is initiated at oriC (a_i in fractions of a generation; panel g) is calculated from C and D (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 (a_i; 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 (O_i; 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 P_i (or M_i) and O_i shown in panels h and i.

Macromolecular Composition at Different Growth Rates

Exponential growth.

The parameter values in the tables below refer to the condition of "balanced, steady-state exponential growth." "Balanced" means that every component in the medium (including oxygen provided by aeration or shaking) is present at saturating, nonlimiting concentrations; and "steady state" means that the bacteria have grown for at least ten generations in a given medium (i.e., at least a 1,000-fold dilution from an overnight culture). In this condition, the rate of accumulation of every component relative to its total amount in the culture is constant in time and its value is the same for every component. If the growth conditions for bacteria are changed, e.g., by dilution of a stationary culture into fresh medium, or after a nutritional shift-up, then the new steady state is approached with the function (1 − 2^−t/τ), which means it takes ten doubling times until all parameters have reached 99.9% of the change to their final new steady-state value (38), although some parameters may reach their final value immediately after a medium shift (see "Control of the growth rate," below).

The above definition of exponential growth refers to cultures containing large numbers of asynchronously growing cells. Components within single cells that increase stepwise during the cell cycle, like the copy number of a particular gene, can be assumed to increase exponentially when a significant volume of culture is considered. If a single cell were isolated from such an exponential culture and cultured separately under the same conditions, the cellular mass would continue to increase exponentially, but the cell number would at first double in a stepwise manner. Moreover, rounds of replication in the initial daughter cells would be initiated synchronously. It is unclear how long this synchrony would persist. As far as we are aware, parameters that vary and contribute to the gradual loss of synchrony in a culture started from a single exponentially growing cell, and the length of time it would take until the culture could be considered truly exponential and asynchronous has never been studied in detail. One possible factor contributing to asynchrony might be the positioning of the division plane; if the division is somewhat imprecise, the daughter cells would have slightly different initial masses and the triggering of the subsequent initiation of rounds of replication would be slightly out of phase.

In some published experimental work, authors have diluted their overnight culture much less than 1,000-fold, so that the culture begins to approach the new stationary phase before reaching true steady-state exponential growth. The term "midlog phase" is frequently used to indicate the time when samples were taken for measurement (i.e., the time at which the mass density plotted on a log scale changes from increasing to decreasing). This inflection point does not define steady-state exponential growth, and the use of the term midlog phase is misleading, because once the steady state is reached, it should remain in that state for a finite period of time as required for the analysis. The period of exponential growth can be extended either by a greater initial dilution of the overnight culture, or later, before oxygen becomes limiting, by successive dilutions with prewarmed, conditioned medium (38).

Åkerlund et al. (1) have diluted stationary E. coli bacteria 10⁻⁵- to 10⁻⁷-fold into fresh media and measured, in addition to mass accumulation (OD₅₅₀), cell sizes and DNA content per cell, using flow cytometry. They found that a truly steady state of balanced growth occurs only as long as the OD₅₅₀ is kept below 0.01; at higher mass densities, size and DNA content of the cells began to decrease gradually, suggesting a shortening of the D-period as a result of the oxygen limitation that leads to stationary phase growth. However, mass accumulation still remained exponential up to an OD₅₅₀ of about 0.8, suggesting that reactions other than those involved in cell division are not significantly affected until mass densities much higher than 0.01 (OD₅₅₀) are reached.

Bacterial strain.

For physiological studies, E. coli B/r has several advantages over other E. coli strains. Due to a special property of its outer cell surface, this strain can be age-fractionated by the membrane elution technique (100) and used to measure cell cycle-related parameters. Helmstetter and Cooper (99) 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 sticking or clumping and "snake" formation than many other strains of E. coli, (ii) grows well in minimal media, and (iii) is free of mutations that might otherwise influence the growth rate or composition; for example, its maximum growth rate in Luria-Bertani medium (3.0 doublings/h) and its growth rate in glucose minimal medium (1.3 doublings/h) is about 20% higher than the growth rates of the standard K-12 strains in these media. For these reasons, E. coli B/r is the preferred choice for physiological studies and composition measurements. A disadvantage is that the strain is genetically incompatible with K-12 strains because of the B and K restriction systems. B/r mutants deficient in B restriction or with K-12 restriction and modification have been used by the authors.

Growth media.

As has been discussed in the beginning of this chapter, the amounts and synthesis rates of the major macromolecules (including DNA, rRNA, tRNA, mRNA, protein) can be plotted as approximately single functions of growth rate only for a selected choice of growth media. The media used for the data in Table 2 and Table 3 below include, with increasing growth rate, succinate minimal medium, glycerol minimal medium, glucose minimal medium, glucose-amino acids medium, and glucose-supplemented Luria-Bertani broth (LB medium). The growth rates observed in these media range between 0.6 and 3.0 doublings/h. As explained above, exact growth rates in a given medium vary somewhat, depending on the history of the overnight starter culture used to inoculate the experimental cultures.

Macromolecular composition.

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 3.0 doublings per h. The per mass values (top section) represent averages obtained from curves drawn as a best fit through individually measured points (16). Actual measurements may deviate by as much as ±15% around these curves (see Fig. 4 in reference 12). Most of this "scatter" does not represent random variations in the accuracy of measurements, but true variations from culture to culture, reflecting differences in the "history" of the overnight starter culture used (see above). The contribution due to measuring errors was minimized by taking four to five samples over one to two generations and is generally less than 5%. Protein and DNA were measured colorimetrically after appropriate calibration, and RNA was determined from the A₂₆₀ of an RNA hydrolysate. Cell numbers per mass in Table 2 were calculated from the DNA/cell values as explained in footnote e.

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 65 to 73% of the dry weight. Lipids, carbohydrates, soluble metabolites, and salts represent the remaining 27 to 35% of the total dry mass. The relative proportions of the macromolecules at the different growth rates are illustrated in the composition bar graphs of Fig. 1. The greatest relative change is found in the RNA sector (increase from 10 to 21%), 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 is therefore an approximate measure for the cytoplasmic ribosome concentration. As explained above, 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; references 72, 103, and 168). 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 about 22 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 (16, 176, 177). The number of replication origins per genome (O_G) was then obtained from the factor increase in the amount of DNA in a culture after stopping replication initiation by the addition of rifampin, and by measuring and taking into account the delay in the action of rifampin (16).

The number of replication origins per genome depends on the C-period; therefore, the observed values for O_G have been used to calculate the C-period values given in Table 3 . It turned out that the best-fit curve for C as a function of the growth rate was a simple exponential (i.e., empirical) function (reference 16; see footnote x), that has been used to obtain the "smoothed" values of C in Table 3 . These values have then been used in a reversed procedure to obtain the smoothed values of O_G in Table 2 (see footnote i). Furthermore, we note that the values calculated for C in Table 3 , i.e., from the empirical function, have been rounded to the nearest full minute, but for the parameters in Table 2 obtained from C (i.e., replication origins and forks), the calculated exact (nonrounded) values for C were used. This would cause some deviations in the last decimal point if the number of replication origins or forks were recalculated from the rounded C values shown in Table 3 .

The initiation mass, expressed as protein per origin, P_O (Table 2 ; Fig. 2j), is a formal measure for the control of replication initiation; it has a meaning similar to cell mass per origin, M_O. M_O is proportional (factor ln2) to the "initiation mass," defined by Donachie (74) as the cell mass at the time of initiation, divided by the number of replication origins at which initiation occurs (i.e., M_i/O_i). In contrast, M_O is the total mass in a given volume of exponential culture, divided by the number of copies of oriC present in that volume (Fig. 2j). Both P_O and M_O are approximately constant (Table 2 , P_O = 4 × 10⁸ amino acids per oriC). The exact growth rate dependence of P_O (or M_O) depends on the strain used (12). A decreasing initiation mass with increasing growth rate has been reported for K-12 strains of E. coli (16, 178, 194).

The time intervals between consecutive initiations of rounds of replication show little cell-to-cell variation, whereas the time intervals between consecutive cell divisions vary considerably because of (non-Gaussian) variations in the D-period (23, 114). The tight control on initiation is presumed to reflect the accumulation of a hypothetical protein that triggers initiation at a certain threshold value (31). This putative initiation protein would be made as an about constant fraction of total protein synthesis, thereby linking chromosome replication to protein synthesis. The numbers of replication origins, termini, and replication forks on the chromosome (Table 2 ) were calculated from the values of the C- and D-periods (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 by using the first-order rate equation dX/dt = Xkμ = X(ln2)/τ, where X is the measured amount of the component, μ is in doublings per hour, τ is in minutes, and k = (ln2)/60; the rate is per minute (for more details, see reference 72).

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 (57, 58). 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). In the following the parameters in these three groups and the way they were either measured or calculated are discussed.

RNA Polymerase Synthesis and Function

RNA polymerase concentration.

The rate of transcription in the cell depends on the concentration of RNA polymerase. The fraction of total protein that is RNA polymerase core enzyme (three subunits, α₂, β, and β'), α_p, has been determined after electrophoretic separation of E. coli proteins (172). Since the α₂ ?subunit is in excess in E. coli (see Table 4), the amount of core enzyme was assumed to be limited by the amount of β and β' subunit polypeptides. Between 0.6 and 3.0 doublings/h the fraction of RNA polymerase core enzyme increases from 0.9 to 1.6% of total protein. Recently, it has been established that a further small subunit ω is part of the core enzyme and involved in the maintenance of the conformation of the large β' subunit (135).

Table 4Stoichiometric content of transcription-translation proteins in E. coli

For glucose minimal and glucose-amino acids media with 1.3 and 2.2 doublings/h, the α_p values would be about 1.2 and 1.5%, respectively, which may be compared with independently reported α_p values for a strain of K12 growing in these two media, equal to 0.5 and 1.8%, respectively (95). The experimental variation in the higher value (1.8%) observed by those authors (about 30%; Table 1 in reference 95) makes this value consistent with our somewhat lower value of 1.5%. The α_p value of 0.5% for glucose minimal medium was associated with a culture doubling time of 133 min (0.45 doubling/h), whereas our B/r strain has a doubling time of 45 min (1.3 doublings/h) in this medium. The dramatic difference in growth rates in glucose minimal medium makes the strain difference a major factor in the different values of α_p that are observed.

The synthesis of the β and β' subunits is transcriptionally controlled at least in part at the level of termination-antitermination at an attenuator in front of the rpoB gene. Under most conditions, this attenuator stops about 80% of the transcripts coming from the upstream L11 and L10 r-protein operons (11, 12, 45, 55, 61, 62, 76). In the past, it has been thought that the control of r-protein promoters might involve the effector nucleotide guanosine tetraphosphate, ppGpp (60, 70, 71, 107), but at least for the r-protein spc operon it has been shown that its promoter, P_spc, is constitutive, without specific control (118, 119, 120). The apparent correlation of the accumulation of spc-mRNA with the stringently controlled rRNA transcripts is now assumed to be the result of a control of spc-mRNA degradation, which depends on the accumulation of r-protein S8. This protein binds to the spc-mRNA and inhibits its translation, which, in turn, makes the mRNA accessible to endonucleolytic cleavage followed by exonucleolytic degradation. Thus, when rRNA synthesis is inhibited by ppGpp during the stringent response, free S8 accumulates and causes a reduction in the accumulation of spc-mRNA (for details, see references 109 and 121). We suspect that other r-protein promoters, including the promoters for the L11 and L10 operons, are similarly constitutive. The main regulation of the rpoBC gene expression might therefore be the readthrough control at the attenuator, perhaps involving an autoregulation by free RNA polymerase and/or cleavage of the transcript by RNaseIII (60, 76, 133). There is also translational control of the rpoBC mRNA (63, 68, 69, 77).

Combining the observed α_p values with the protein per cell values of Table 2 , the average numbers of core RNA polymerase molecules per cell, N_p, have been calculated in Table 3 and were found to increase from about 1,800 to 10,200 between growth rates of 0.6 and 3.0 doublings/h. These values differ somewhat from the values in the previous edition of this chapter (1,500 to 11,400 at 2.5 doublings/h). The main reason for this is the use of newer and presumably more accurate values of "cells per mass" (Table 2 ) to calculate the numbers of polymerase per cell. The previous cell numbers for the different cultures were determined directly with an electronic particle counter, whereas the new numbers used here were obtained indirectly from DNA replication and cell division data to make all parameter values consistent with one another (see "Cell numbers," above).

The amount of σ⁷⁰, the housekeeping sigma factor that is employed for most transcription initiation during exponential phase growth, is present in excess over the amount of free (and even total) core RNA polymerase (95, 174).

RNA polymerase activity.

The total complement of RNA polymerase enzyme in the cell can be partitioned into active RNA polymerase engaged in RNA chain elongation and inactive RNA polymerase. The inactive polymerase includes promoter-bound enzyme (especially at mRNA promoters with long promoter clearance times), DNA-bound polymerase idling during transcription, nonspecifically DNA-bound polymerase, free holoenzyme, ready to bind to a promoter; and newly synthesized immature enzyme. The fraction of enzyme actively engaged in RNA chain elongation, β_p, was determined from the total 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 calculations in Table 3 show that β_p increases with growth rate (172) and that only 15 to 36% of the RNA polymerase enzyme is transcriptionally active, i.e., involved in RNA chain elongation, at any instant.

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 (174). This enzyme might either be bound nonspecifically to DNA (40, 95), or, alternatively, it might have initiated transcription but is halted at some pausing site (111, 141), perhaps associating with termination-antitermination factors (94). It remains unclear why there is such a large excess of inactive RNA polymerase, how the partition between active and inactive enzyme is maintained, what fraction of the inactive RNA polymerase is nonspecifically bound to DNA, and to what extent such nonspecifically bound RNA polymerase equilibrates with free RNA polymerase.

In ppGpp-deficient strains, up to 60% of the total RNA polymerase is active (103), which has suggested that part of the inactive polymerase (i.e., 27 to 46% of the total polymerase) in ppGpp-proficient bacteria is transiently stalled at ppGpp-dependent pause sites during the synthesis of mRNA (103, 111). Of the remaining inactive RNA polymerase in ppGpp-deficient cells (i.e., 40% of total), about one half consists of the fractions of total RNA polymerase that are either free functional or free nonfunctional (immature) or promoter-bound before promoter clearance; these three forms have been estimated to represent 5.1, 3.5, and 10.0%, respectively, of the total polymerase at μ = 1.0 doubling/h and 7.8, 9.1, and 1.9%, respectively, at μ = 2.5 doublings/h (see Table 4 in reference 34). The sum of these fractions is about 19% of total polymerase at either growth rate. The other half (about 20% of total RNA polymerase) seems to be involved in ppGpp-independent transcriptional pausing or might be nonspecifically bound to DNA. As mentioned above, the σ⁷⁰ subunit is in excess over free, functional core enzyme (95, 174), suggesting that essentially all free enzyme is functional holoenzyme.

The total rate of transcription in E. coli is not limited by the DNA concentration but is limited by the concentration of free functional RNA polymerase (34). This is perhaps surprising in view of the fact that only a small fraction of the polymerase is actively engaged in transcript elongation at any instant. The condition of excess DNA was demonstrated in various ways, for example, by using a mutant bacterial strain with altered DNA replication control, which results in a lower DNA concentration. Despite the lower DNA concentration there was no change in the level of total RNA accumulation, i.e., mainly of stable RNA (48). This means that the DNA template is in excess, at least for the transcription of stable RNA.

The concentration of free functional RNA polymerase depends on the cytoplasmic concentration of total RNA polymerase (α_p) and on the concentrations of all promoters in the cell, their kinetic constants, state of repression, associated transcript lengths, and transcription velocities (for details, see reference 34). The constitutive promoters of many mRNA genes are saturated at growth rates above 1.5 doublings/h (120), so that their transcription at higher growth rates is limited by their gene dosage, rather than by free RNA polymerase.

The basic concepts relating to an excess or limitation in free RNA polymerase on the transcription from a particular promoter are illustrated by considering an idealized cell with a given concentration of total RNA polymerase (2,000 molecules per cell) and a variable number of mRNA genes (0 to 400 per cell, with a length of 1,500 nucleotides and typical V_max and K_m values). From this example, the following relationships become apparent (Fig. 3). (i) At low DNA concentrations (below 50 genes per cell), the increasing concentration of genes and promoters causes an increasing rate of total transcription (Fig. 3c). The rate of total transcription is then limited by the total DNA available, and all promoters are nearly saturated with polymerase and active at near their maximum rate (Fig. 3b). In addition, most of the total polymerase is in the form of free RNA polymerase (Fig. 3a). This condition may be described as excess RNA polymerase. (ii) When the DNA and gene concentrations are gradually increased to above 200 genes per cell, the total rate of transcription reaches a plateau (Fig. 3c), but the free RNA polymerase concentration (Fig. 3a) and the activity per promoter (Fig. 3b) continue to decrease. Such conditions, when the total rate of transcription is limited by the total RNA polymerase, may be described as excess DNA. Under these conditions, free RNA polymerase is only a small fraction of the total, and the major fraction of RNA polymerase is either bound to a promoter or involved in transcript elongation. Excess DNA appears to be the typical in vivo condition in bacterial cells.

Fig. 3Effect of varying gene concentration on the total rate of RNA synthesis, the rate of transcription per gene, and the concentration of free RNA polymerase (from reference 34). The relationships are derived from an idealized cell, where all promoters are identical and the transcription times of all genes are equal. The volume of the cell is one unit and concentrations are given as numbers of molecules per cell. The cell contains 2,000 RNA polymerase molecules, and the number of promoters per cell [P_t] is varied between 0 and 400 (abscissa in all panels). V_max is set at 30 initiations per minute per promoter, and K_m is set at 200 RNA polymerase molecules per cell. All transcripts are 1,500 nucleotides long, and the RNA chain elongation rate is 50 nt/s. (a) The ordinate is the total steady-state rate of transcription, i = V · [P_t], measured as transcripts/min per cell. (b) The ordinate is the steady state rate, V, of transcription for one promoter measured as transcripts/min per promoter, calculated from equation 4 in reference 72. (c) The ordinate is the free RNA polymerase concentration, [R_f], calculated from equation 7 in reference 34. For panels b and c the ordinates are shown in log scale to illustrate how V and [R_f] approach zero as [P_t] increases and the total rate of transcription per cell, i, approaches its plateau value.

In this idealized cell (Fig. 3), we have assumed that the cell volume is constant. In an actual cell, the addition of extra genes might cause additional "crowding"; i.e., it might reduce the available reaction space and thereby cause some increase in the concentration of free RNA polymerase.

Partitioning between stable RNA and mRNA synthesis.

The actively transcribing RNA polymerase enzyme can be further partitioned into the fractions engaged in the synthesis of stable RNA species (rRNA, tRNA, and their spacers; ψ_s) and of mRNA (ψ_m = 1 − ψ_s). The term ψ_s was originally introduced by Maaløe and coworkers in their early studies of the control of ribosome and tRNA synthesis (152). ψ_s reflects the controls of both the rates of stable RNA and of mRNA synthesis, and the term is useful in certain formulas related to the control of the growth rate (e.g., equation 19 in Table 6 below). Determinations of ψ_s are based on the determinations of the rate of stable RNA synthesis relative to the total RNA synthesis rate, r_s/r_t, and of the chain elongation rates of mRNA and stable RNA (see formula in footnote e of Table 3 ).

The quotient r_s/r_t was first estimated by Pato and von Meyenburg in Maaløe’s laboratory from the kinetics of radioactive uridine incorporation into RNA after stopping initiation of transcription with rifampin (152). Because of the instability of some rRNA made in the presence of rifampin (due to the inhibition of r-protein mRNA synthesis), this method was not accurate, but the error could be corrected by a complex extension of the method of measurements (25, 64, 66). Later, when cloned rRNA genes became available as hybridization probes for rRNA transcripts, determination of r_s/r_t became easier and more direct (165, 173). At growth rates between 0.6 and 3.0 doublings/h, r_s/r_t increases a little over twofold, from 41 to 90%, implying that the fraction of mRNA synthesis decreases about sixfold from 59 to 10% (Table 3 , values from reference 165).

Determinations of r_s/r_t are also needed for finding the synthesis rates of total RNA and mRNA. The stable RNA synthesis rate, r_s, can be found from the amount of stable RNA, R_s (using any reference unit, like per mass or per cell), and the growth rate (see the next section). The total rate of RNA synthesis, r_t, then equals the quotient r_s/(r_s/r_t), and the mRNA synthesis rate, r_m, equals the difference r_t − r_s. These values were further used to find the fraction of total RNA polymerase that is actively engaged in RNA chain elongation at any instant (see "RNA polymerase activity," above).

When r_s/r_t is plotted as a function of the intracellular concentration of the effector ppGpp, a unique relationship is obtained, independent of whether concentrations of ppGpp are varied by using growth media with different nutritional values, or by inducing partial amino acid starvation in either wild-type (relA⁺) bacteria (triggering the "stringent response" with high levels of ppGpp) or in relA mutant bacterial strains (triggering the "relaxed response" with low levels of ppGpp). When the concentration of ppGpp is close to zero, r_s/r_t is close to 1.0 (i.e., almost no mRNA synthesis in relation to stable RNA synthesis). As the concentration of ppGpp gradually increases the values of r_s/r_t gradually decrease; at high concentrations of ppGpp generated during the stringent response, the value of r_s/r_t reaches a minimum plateau of 0.25 (9). This unique function is surprising, since r_s/r_t depends in a complex manner on the controls of mRNA and stable RNA promoters, and on the concentration of free RNA polymerase, as described below.

By combining measurements of transcription from specific promoters and of DNA replication to find gene dosages under different growth conditions, it is possible to determine absolute in vivo activities of specific promoters in transcript initiations per minute per promoter, and to define the in vivo control of stable RNA and mRNA promoters in biochemical (Michaelis-Menten) terms (72, 120). "Promoter strength" is defined as the promoter activity (measured in transcripts per unit time per promoter) per free RNA polymerase concentration (given in either molar or relative units) under conditions of low RNA polymerase concentration (so low that it does not saturate any of the promoters considered). Mathematically, the promoter strength equals the ratio of the Michaelis-Menten parameters V_max and K_m (maximum promoter activity at saturation with RNA polymerase and RNA polymerase concentration at half-maximal activity). If V_max /K_m for a given promoter remains constant under different growth conditions, the promoter is said to be "constitutive." If V_max and/or K_m changes, it means that the promoter is subject to control. Control occurs either through the action of a repressor or activator that binds to the DNA near the promoter, or by an effector like ppGpp that binds to the RNA polymerase and thereby changes the promoter–polymerase interactions. As long as the promoter is not saturated with RNA polymerase, its activity also depends on the free RNA polymerase concentration as illustrated in Fig. 3.

Of the two tandem promoters of the rRNA (rrn) genes, transcription from the upstream P1 promoter is inhibited by the nucleotide effector ppGpp and is controlled, whereas the downstream P2 promoter is constitutive (for a review of the controversial issue of rrn P2 control, see reference 72). However, within the context of the rrn operon, P2 is subject to "promoter occlusion" by transcribing RNA polymerase molecules coming from the upstream P1 promoter and temporarily blocking the access of RNA polymerase to the downstream P2 (204). Both rrn P1 and P2 have short promoter clearance times (= 1/V_max = 0.52 s) in vivo, so that they are not saturated with polymerase under most growth conditions; therefore, their activities increase with increasing concentrations of free RNA polymerase at increasing growth rates (10, 72, 120, 204). In contrast, most mRNA promoters, because of their slow clearance, become saturated with polymerase so that their activities reach maximum levels at growth rates above 1.5 doublings/h (120).

The strength of rRNA (and tRNA) promoters is actually lower than the strength of many mRNA promoters (e.g., r-protein mRNA promoters; reference 120). However, since the mRNA promoters, but not stable RNA promoters, become saturated, the stronger mRNA promoters have a higher activity than the stable RNA promoters during growth in nutritionally poor media, but at the higher concentrations of free RNA polymerase during growth in rich media, the stable RNA promoters have a higher activity, despite their lower strength (72, 120). Thus, stable RNA and mRNA promoter controls, as well as changing free RNA polymerase concentrations, contribute to the values of ψ_s and r_s/r_t observed under different growth conditions. The higher concentration of free RNA polymerase at higher growth rates results both from an increased concentration of total RNA polymerase (Table 3 , α_p) and from the repression of mRNA genes by exogenous nutrients (34).

The effect of exogenous nutrients on the relative synthesis of mRNA is seen from the following example. In a culture grown in succinate minimal medium at 0.6 doublings/h, r_s/r_t equals about 0.4 (Table 3 ). If the exogenous succinate is substituted by glycerol, the growth rate increases to about 1.0 doubling/h and r_s/r_t increases by about 20% to 0.5 (Table 3 ). At the same time the rrn gene activities increase more than twofold from 4 to 10 initiations/min per rrn gene (Table 3 ), reflecting both the control of stable RNA promoters by ppGpp and the increased free RNA polymerase concentration resulting from a control of RNA polymerase synthesis (increased α_p, Table 3 ) (34). But the mRNA gene activities also increase as a result of increased free RNA polymerase concentration, only somewhat less than the stable RNA gene activities, which yields the 20% increase in r_s/r_t. When, instead of replacing succinate by glycerol, the growth rate is increased (also to 1.0 doubling/h) by adding 20 amino acids to the succinate medium, r_s/r_t doubles to about 0.8 (Fig. 9 in reference 170), implying a threefold decrease in the fraction of mRNA synthesis (i.e., from 0.6 to 0.2). This decreased mRNA synthesis must reflect the repression of amino acid biosynthetic enzymes in the amino acid-supplemented medium. As was explained above, the values in Table 2 and Table 3 for the growth rate of 1.0 doubling/h refer only to cultures grown in glycerol minimal medium, not to succinate-amino acids media that produce the same growth rate.

In view of the complexity of regulations involving the values of r_s and r_m, it is not clear why r_s/r_t becomes a single function of ppGpp levels under seemingly all conditions (i.e., not only during exponential growth at different rates in the chosen selection of media), and also independent of the absolute values of r_s and r_m (9). Understanding of this phenomenon requires further analysis.

Rates of stable RNA and mRNA synthesis per cell.

The rate of stable RNA synthesis per cell (r_s) was calculated from the amount of total RNA per cell, determined from the UV absorbance of RNA hydrolysates (Table 2 ), after a small correction for the presence of mRNA (using the factor f_s = fraction of total RNA that is stable RNA; see Table 1). The value of r_s is seen to increase dramatically with growth rate, which reflects both the increasing ribosome concentration and the increasing cell size.

The synthesis rates and amounts of mRNA per cell (r_m, R_m) were found from r_s and r_s/r_t (see above). Both r_m and R_m increase about fourfold in the range of growth rates considered (Table 3 ), which mainly reflects the increasing cell size; i.e., r_m and R_m per mass remain approximately constant. A comparison of the values of total RNA per cell (Table 2 ) and mRNA per cell (Table 3 ) shows that the fraction of total RNA that is mRNA (1 − f_s) decreases from about 2% at a growth rate of 0.6 doubling/h to only 1% at 3.0 doublings/h.

Chain elongation rates of stable RNA and mRNA.

Whereas mRNA transcripts elongate at a rate (c_m) that increases somewhat with increasing growth rate and approaches a maximum value of about 56 nucleotides per second (56 nt/s) at high growth rates (29, 178, 192), transcripts of the rrn operons elongate at a rate (c_r) that is nearly constant and equal to about 85 nucleotides (nt)/s (139, 166, 190, 191, 192). For rrn transcripts in bacteria grown in glucose-amino acids medium a transcription time of 60 s has been observed for an rrn operon with a length of 5,450 bp (51), corresponding to an rRNA chain elongation rate of 91 nt/s (5,450/60 = 91). This value is similar to data from other laboratories: 89 nt/s for bacteria in glucose amino acids medium, 79 nt/s in glycerol minimal medium (190), and 78 nt/s in glucose minimal medium (166). For the range of growth rates between 0.6 and 3.0 doublings/h we have here assumed a constant value of 85 nt/s for all stable RNA transcription (c_s, Table 3 ). However, the constancy might not be exact, because some increase in c_r with increasing growth rate has been reported (139, 190).

The leader regions of rrn transcription units contain strong Nus factor-dependent antitermination sites (4, 117, 145). As a consequence, transcripts initiated at rrn promoters are able to transcribe through Rho protein-dependent transcription terminators and can reverse transposon-induced polarity (2, 175). Thus, for rRNA transcripts, pausing or stuttering is minimized by the antitermination state of the RNA polymerase, which accounts in part for the increased stable RNA chain elongation rate (191, 192). When the antitermination sequences at the rrn promoters are removed, the rrn transcript elongation rate is reduced, and when these sequences are inserted at the front of a mRNA promoter, then the mRNA elongation rate is increased (192). This antitermination mechanism is essential for efficient rrn transcription because of the lack of coupled translation and because of the extensive secondary structures present in rRNA transcripts.

Accumulation of the effector ppGpp.

The accumulation of ppGpp at different growth rates has been determined from the A₂₆₀ of the ppGpp peak after separation of the bacterial nucleotides by reversed-phase high-pressure liquid chromatography (165). The role of ppGpp in the control of stable RNA synthesis has been controversial since the publication of a proposal that free or translating ribosomes, rather than ppGpp, regulate transcription of rrn operons (50, 106, 147). Today however, the predominant importance of ppGpp in the control of rRNA synthesis in vitro (186, 188) and during exponential growth (101, 125, 165) is established and generally accepted (reviewed in reference 72). During periods of amino acid insufficiency, ppGpp is derived from the relA-dependent system and elicits the well-characterized stringent response (39, 60, 98, 116). During exponential growth at different rates, the "basal levels" of ppGpp are derived mainly from a relA-independent system (6, 84, 162) that involves a product of the spoT gene (102, 142, 196). The basal levels of ppGpp listed in Table 3 are seen to decrease from about 55 to 6 pmol/OD₄₆₀ when the exponential growth rate increases from 0.6 to 3.0 doublings/h. These values refer to balanced, steady-state exponential growth in the selected choice of media (see above). If growth is limited by the supply of some amino acid during chemostat growth where the growth rate is determined by the dilution rate of the culture (in the original studies of the Maaløe laboratory these were called "continuous culture experiments"; e.g., in Fig. 1 and 2 of reference 167), the RelA ppGpp synthetase is presumably activated and produces higher levels of ppGpp (70).

The growth medium-dependent control of the SpoT-dependent synthesis of ppGpp, which adjusts the synthesis of ribosomes during exponential growth and thereby partly determines the growth rate, is still a mystery (142). It might involve the GTPase CgtA_E that cofractionates with the 50S ribosomal subunit and interacts with SpoT (195), or the acyl carrier protein ACP that interacts with SpoT (13). It has been proposed that this control might involve a feedback control of the peptide chain elongation rate (72): whenever c_p has a submaximal value, i.e., when it drops below 22 amino acid residues polymerized per minute per active ribosome during growth in minimal media, then the ppGpp synthesis activity of SpoT is stimulated to reduce the synthesis of ribosomes and thereby the consumption of amino acids. Such a mechanism would minimize the reduction in c_p and save energy by reducing any excessive synthesis of ribosomes (see "Optimal cell composition for maximal growth").

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 (7). During exponential growth at moderate to fast rates, turnover of ribosomal components is negligible, but during slow growth, some excess of newly made rRNA is degraded (91, 148), which contributes to the slight increase in the proportion of tRNA to rRNA (57, 75, 171).

The primary regulation of ribosome synthesis occurs at the level of rRNA synthesis; the synthesis of r-proteins is then adjusted to the accumulating rRNA. Any excessive accumulation of free r-proteins causes a reduction in the synthesis and lifetimes of r-protein mRNA (82, 107, 109, 119, 123) and thereby reduces the synthesis of r-protein (see below).

Each of the seven rRNA (rrn) operons has two tandem promoters, P1 and P2, from which the rRNA transcripts are expressed. After correction for position effects on the E. coli chromosome, all rrn operons are similarly expressed (reference 51, reviewed in reference 109). The P1 promoters of all seven rrn operons have the same discriminator sequence, GCGC, bordering similar TATAAT –10 regions (109, 200, 201). Upstream of each of these P1 promoters are three binding sites for the protein factor Fis; the binding of Fis to these sites stimulates expression from P1. In addition, P1 is negatively controlled by ppGpp, which binds to the interface of the β and β' subunits of the RNA polymerase (43, 159, 185) near the active site (5). In the presence of the adaptor protein DksA (153), this binding of ppGpp to RNA polymerase reduces the strength of the P1 promoter directly, and also indirectly by reducing expression of Fis (72). The rrn promoter strength is given as V_max/K_m for the RNA polymerase promoter interaction (see "Partitioning between stable RNA and mRNA synthesis," above)

In the absence of both ppGpp and Fis, the (isolated) P1 and P2 promoters have about equal activities that only increase with increasing free RNA polymerase concentration. Their activities then increase in parallel with increasing growth rate, and, before they become saturated, also in parallel with the activity of constitutive mRNA promoters (see "Partitioning between stable RNA and mRNA synthesis," above). Under such conditions the strength of the rrn promoters remains constant at different growth rates, i.e., P1 and P2 are both constitutive (204, 205).

In the absence of ppGpp, but the presence of Fis, the strength of P1 still remains constant, but due to Fis, about twofold higher than the strength of the P2 promoter, and the activities of P1 and P2 also increase in parallel (i.e., by the same factor) with increasing growth rate, again reflecting only the increasing concentration of free RNA polymerase (205).

r-Protein synthesis.

A measure used for the synthesis of r-protein is the proportion of total protein that is r-protein, α_r. Values of α_r have been determined (i) directly from the protein content of ribosomes after separation from other proteins by sucrose gradient centrifugation (65, 168), and (ii) indirectly from the RNA-to-protein ratio (see footnote m in Table 3 ). Both methods give similar values. The proportion of r-protein increases from about 8% of total protein at a growth rate of 0.6 doubling/h to 23% at 3.0 doublings/h (Table 3 ). The mRNAs of r-protein operons contain internal elements that control their elongation, translation and lifetime. The regulatory r-proteins specific to each operon that are not rapidly incorporated into assembling ribosomes bind to these elements, which are often structural mimics of their binding sites on rRNA, and may cause transcript attenuation or rapid degradation of the entire mRNA; this has been called retroregulation (reviewed in reference 109). In this manner, r-protein synthesis is adjusted and matched to rRNA synthesis.

Ribosomes and tRNA per cell.

Given that r-protein matches rRNA and that rRNA and tRNA are synthesized in a nearly constant proportion, corresponding to about nine tRNA molecules per 70S ribosome (57, 80, 171, 199; see "Cell growth-related parameters," above), the numbers of ribosomes (N_r) and of tRNA molecules per cell (N_t) were calculated from the total amount of RNA per cell (RC; Table 2 ) after subtraction of the small amount of mRNA (only 1 to 2% of the total RNA; see above). In the growth range considered, the average number of ribosomes per cell (N_r) is seen to increase about 10-fold from 8,000 to 73,000 (Table 3 ). This reflects both an increasing ribosome concentration (ribosomes per OD₄₆₀ unit of cell mass, or per total amount of protein) and the increasing cell size (OD₄₆₀ units or protein 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, β_r, has been estimated from the ribosome content of polysomes and was found to be about 80% and independent of the growth rate (85).

Here we have assumed a slightly higher value of 85% (from Table 2 in reference 121), based on the assumption that the maximum value for the rate of peptide chain elongation in vivo is 22 amino acid residues per second (see the next section). The relative constancy of β_r may only be approximate, mainly indicating that the fraction of inactive ribosomes (the difference 1 − β_r) is relatively small, probably between 10 and 20%, which includes both mature "free" 30S and 50S particles ready to initiate translation, and immature particles. Since the assembly and maturation of ribosomes takes about 5 min (122), it appears that, at least in fast-growing bacteria, immature subunits in the final stages of assembly constitute the major portion of the inactive ribosomes.

Peptide chain elongation rate.

The average peptide chain elongation rate, c_p, has been estimated directly from (i) pulse-labeling kinetics of nascent polypeptides of given length (155, 198), and (ii) the first appearance of β-galactosidase activity after induction (53, 89, 154, 155) and indirectly (iii) from calculations based on the RNA-to-protein ratio under the assumption that 85% of the ribosomes are active at any instant. All three methods give similar values; the values in Table 3 were calculated from the RNA-to-protein ratio. These measurements indicate that the average peptide chain elongation rate increases with growth rate from about 13 amino acid residues per second at 0.6 doubling/h to a maximum value of 22 amino acid residues per second at growth rates above 1.5 doublings/h.

The chain elongation rate of β-galactosidase in serovar Typhimurium has also been measured at different growth rates between 0.5 and 1.9 doublings/h by measuring the time from the entry of labeled threonine into the pool of threonyl-tRNA until the label appears in the N-terminal threonine residues in the free, completed β-galactosidase tetramers (81). With this method, the chain growth rate was found to be 16 to 20 amino acids per second at 37°C, and independent of the growth rate. It is not clear why the chain growth rate in those experiments did not increase with the growth rate.

What limits the peptide chain elongation rate? The answer to this question is still controversial. During fast growth, i.e., in media supplemented with all 20 amino acids, the peptide chain elongation rate was found to have essentially the same, apparently maximal value of 22 amino acid residues polymerized per second (Table 3 ). We assume, therefore, that ribosomes are saturated with substrates (elongation factor Tu-GTP-aminoacyl-tRNA ternary complex) under such conditions, implying that the peptide chain elongation rate is limited by structural rearrangements within the ribosome (17, 18), the rate of peptide bond formation, or ribosome translocation on the mRNA. Furthermore, we assume that the submaximal chain elongation rates during slow growth are probably limited by the smaller size of the amino acid pools and reduced tRNA charging (i.e., by the ratio of charged to uncharged tRNA [163]) and to some extent by the types of codons being employed.

An alternative interpretation of the growth-medium-dependent changes in the rate of ribosome function has been proposed in a theoretical study by Elf and Ehrenberg (79), who suggest that in any particular cell at any given time, only one amino acid can be limiting, so that the cell then undergoes a type of temporary single amino acid deprivation, with ribosomes halted at the codons for the limiting amino acid. This temporary pause in protein synthesis should allow a maximal charging of the tRNAs for all other amino acids, while the depletion of the pool for the limiting amino acid causes a derepression of the corresponding biosynthetic operons. The ensuing amino acid synthesis allows the ribosomes in that particular cell to resume function until some other amino acid becomes limiting. For the whole culture, this kind of "stuttering" ribosome function produces an average reduction in c_p.

The question, whether it is possible to deplete the pools for more than one amino acid, has been addressed in Stents’s laboratory by Broda (36), who found that on simultaneous starvation for arginine and histidine, neither amino acid could be detected in the pool. That study also found that, in a shift-down from an amino acid-supplemented to a minimal medium, both isoleucine and valine pools were depleted. In addition, we note that stuttering ribosomes cause premature terminations of polypeptides, e.g., during single amino acid deprivation (37), or during treatment with ribosome inhibitors (like puromycin) that induce the heat shock response (187). Since premature termination of peptides has not been observed during growth of bacteria in minimal media, we suggest that such long translational pauses do not occur under these conditions, and that several tRNA species may be submaximally charged in a given cell at the same time.

In this context, an unanswered question is how polypeptides elongate in single cells, especially during growth in minimal media, when the average value of c_p is reduced below the maximum. For example, one could ask whether there is always a small fraction of cells in which all peptide chain elongation is temporarily halted, because the pool for a limiting amino acid is totally (but temporarily) depleted, or whether such a situation never arises. As far as we are aware, experiments addressing this issue have not been done.

Another explanation for the reduced ribosome function at low growth rates has been proposed by Ehrenberg and Kurland (78) and Lovmar and Ehrenberg (128), based on their "maximum fitness theory" (see "Optimal cell composition for maximal growth," below). According to that theory, the peptide chain elongation rate during exponential growth in different media is not limited by amino acids or tRNA charging, but by the concentration of ternary complex substrates, i.e., the complex of elongation factor Tu (EF-Tu), GTP, and aminoacyl-tRNA. Furthermore, based on in vitro measurements of peptide chain elongation rates and in vivo measurements of diffusion rates, the maximum in vivo chain elongation rate was calculated to be 50 (rather than 22) amino acids per second, implying that in vivo ribosomes are never saturated with substrates, even at the highest growth rates. In support of this idea, Kruger et al. (115) have observed that the in vivo translation rate of the GAA by tRNA^Glu lacking the 5-methylaminomethyl modification at U34 was 47 codons per second compared with a rate of 18 codons per second for the fully modified tRNA. In contrast the translation rate of the GAG codon by the unmodified tRNA was only 1.9 codons per second compared with a rate of 7.7 codons per second for the fully modified tRNA.

After a nutritional shift-up, the peptide chain elongation rate increases to the postshift steady-state rate, apparently within the first minute (38), well before there is any significant additional accumulation of the macromolecular components of the ternary complex (i.e., EF-Tu and tRNA). Therefore, we suggest that the reduced peptide chain elongation during growth in minimal media reflects the reduced sizes of several, if not most, amino acid pools, which causes a reduced tRNA charging (197) and a more or less evenly reduced rate of ribosome function without significant stuttering. In amino acid-supplemented media the increased amino acid pools, in turn, are assumed to produce a maximal charging of tRNA and thereby a maximum rate of ribosome function.

It has been reported that ppGpp-EF-Tu complexes bind to ribosomes where they reduce the peptide chain growth rate and increase the fidelity of proofreading by inhibiting the binding of the ternary complex substrate and the formation of peptide bonds (73). Since the ppGpp levels are increased in slow-growing bacteria and decrease rapidly after a nutritional shift-up, this effect might contribute to the reduced ribosome function during growth in minimal media and to its rapid increase in the presence of exogenous amino acids. However, it is unlikely that the low basal levels of ppGpp during exponential growth have this effect, since the peptide chain elongation rate is apparently unaffected in a ribosome control mutant with 10-fold reduced levels of ppGpp (126). Moreover Sorensen at al. (180) have shown that ppGpp does not affect the peptide chain elongation rate.

The utilization of codons in the genes of E. coli is not random (157, 169, 189). It is conceivable that, in poor media, the greater proportion or abundance of mRNAs with hard-to-read codons might contribute to the reduced average peptide chain elongation rate. 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 (105). However, the concentration of minor tRNAs is probably not limiting the rate of peptide chain elongation. Instead, each codon–cognate tRNA pair probably has a specific transit time for progressing through the A and P sites of the ribosome that depends on the physical-chemical nature of the tRNA–mRNA (anticodon–codon) interaction; the limiting step is the initial codon-dependent interaction of the ternary complex and the deposition of the tRNA into the A site of the ribosome (189). As an example, the GAA and GAG glutamic acid codons are both recognized by the abundant tRNA^Glu2, 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 (154, 179, 181).

Ribosomal RNA gene dosage and activity.

Most of the seven rrn genes on the E.coli chromosome map near the chromosomal origin of replication (7). The number of rrn genes per average cell (N_rrn) in an exponential culture is much greater than 7, ranging from 12 to 38, depending on the extent of chromosome branching (see Fig. 1). From the number of rrn genes and the rate of rRNA synthesis, the average rate of initiation of rRNA chains at each rrn gene (i_rrn) was calculated and was found to increase with increasing growth rate from 4 transcripts per minute to 68 transcripts per minute per gene (Table 3 ).

During the cell cycle the number of rrn genes per cell doubles through a series of incremental steps occurring each time an rrn transcription unit is replicated. Since in a given cell new rounds of replication are initiated synchronously at all origins and the replication forks move with about equal speed (see "DNA replication and cell division," below), and since 5 of the 7 rrn genes are clustered near oriC, the number of rrn genes per cell is expected to almost double in a series of closely spaced steps shortly after a new round of replication is initiated. Despite this near doubling of rrn genes, measurements of DNA and RNA synthesis rates in age-fractionated cultures indicate that replication of the rrn genes causes no abrupt or concomitant increase in the rate of rRNA synthesis (56). Instead, as cells progress through the division cycle, the rate of rRNA synthesis increases by a factor of 2 in a slow, uniform, and continuous manner, without perturbation, regardless of the cell age at which the rrn genes are replicated (56, 57). This implies that the rate of transcript initiation at rrn genes decreases nearly twofold when the rrn genes located near the origin of replication are duplicated. During growth in rich media, when 90% of all transcription comes from stable RNA genes (Table 3 : r_s/r_t at μ = 3.0), initiation of replication occurs at eight origins (Fig. 1), so that 40 (i.e., 8 × 5) rrn genes double to 80 within a short interval of time without causing any noticeable change the rate of total rRNA synthesis in the cell. Thus, the copy number of rrn genes does not limit the rate of rRNA synthesis during the cell cycle.

This conclusion has 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 (48). 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 normally limit the rate of rRNA synthesis during exponential growth (57).

The reason for the rrn gene dosage independence of total rRNA synthesis is assumed to be the condition of DNA excess in the bacteria (see discussion of Fig. 3 above in connection with the RNA polymerase activity). The replication of long transcription units with strong promoters such as rrn operons (i.e., increase in the DNA concentration) under the condition of DNA excess is expected to cause a corresponding reduction in the concentration of free RNA polymerase such that the initiation frequency at all unsaturated promoters is reduced.

These observations indicate that an average rate of 68 initiations per minute per rrn operon at the maximum growth rate of 3.0 doublings/h (Table 3 ) involves a fluctuation in the range between 45 and 90 initiations per minute per rrn gene during the cell cycle (actually the fluctuation is somewhat less because rRNA genes are not all clustered at exactly the same map position). A rate of 90 initiations per minute implies that the in vivo time for the formation of the open promoter complex at the rrn promoters must be less than 1 second (for details about reactions and rate constants involved in rrn transcript initiation, see reference 72).

Translation frequency of mRNA.

The average mRNAs made during growth in rich media at higher growth rates are more crowded with ribosomes than mRNAs made at low growth rates; i.e., the average spacing of ribosomes on the average mRNA, d_r, decreases from 142 nucleotides to 69 nucleotides in the range of growth rates considered (Table 3 ). 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 the synthesis of mRNAs that are repressed in the more nutritious postshift medium (38); at the same time, the protein synthesis rate increases due to an increased rate of peptide chain elongation (66, 144, 173). The greater spacing of ribosomes on mRNAs made 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.

The rate of initiation of translation of lacZ mRNA has been found to be nearly independent of the growth rate, which has suggested that the concentration of free, translation-ready ribosomes is approximately constant (121). This means that the decreasing value of d_r during fast growth in rich media reflects the different composition of mRNA; i.e., mRNAs made predominantly in rich media (including mRNA for r-proteins) have apparently stronger ribosome binding sites than the average mRNAs made predominantly during slow growth in minimal media (including the mRNAs for amino acid biosynthesis). An average mRNA molecule made at a growth rate of 0.6 doublings/h is translated about once every 4 seconds, whereas an average mRNA molecule made at a growth rate of 3.0 doublings/h is translated four times faster, about once every second (see Table 2 in reference 121).

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 (58, 97). The only exception to this is protein L7/L12, which is present in four copies per ribosome (183). 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 0.6 /h. At slower growth rates there appears to be a slight excess in the synthesis rate of stable RNA (90, 91, 148); 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 medium-dependent regulation (31, 41, 87, 93, 104, 156). 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, are not—strictly parallel with the increase in ribosome (and r-protein) concentration. Table 4 lists the proteins that have been examined in this context and gives the α_i 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/h (τ = 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 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. It is surprising, considering the recent emphasis on systems biology, that there has not been a systematic and comprehensive proteomic effort to measure the relative or absolute amounts of individual E. coli proteins even at a single 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 a review, see reference 124). There is a second gene for Tu on the E. coli chromosome that 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 and RNaseIII processing site located between the upstream r-protein genes and the downstream RNA polymerase genes (see "RNA polymerase synthesis and function," above).

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% (197). There are between two and three tRNA molecules bound to each translating ribosome (138, 161). 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.

It has been reported that during periods of amino acid insufficiency the synthesis of r-protein, like that of rRNA and tRNA, is subject to stringent regulation at the level of transcription (60, 70, 71). Many of the genes that are cotranscribed with r-protein genes appeared also to be stringently regulated, but the regulation is likely to be at the level of mRNA degradation (see below). These include the genes encoding the elongation factors G, Tu, and Ts (19, 88, 160). In contrast, the genes encoding the β, β', and σ subunits of RNA polymerase were not found to be stringently regulated (19). The regulation of transcription of the β and β' genes is mediated by control at the attenuator in the L10 (rplJL rpoBC) operon (133). With respect to aminoacyl-tRNA synthetases, the data on their stringent regulation were equivocal (19).

The stringent regulation of r-protein genes has come under question after a thorough investigation of the control of the promoter of the spc operon, P_spc. This investigation showed that the promoter is constitutive. At low growth rates, its rate of transcript initiation first increases with increasing growth rate due to the increasing concentration of free RNA polymerase and then approaches a constant level of about 25 transcript initiations per minute per promoter at growth rates above 1.5 doublings/h, reflecting saturation with RNA polymerase (120). The previously observed apparent stringent control of the amount of spc mRNA can now be explained as the result of a regulation of spc mRNA decay in response to ppGpp-dependent changes in rRNA synthesis (119, 121).

Synthesis and function of tRNA.

There are about nine tRNA molecules per ribosome in exponentially growing E. coli, and this ratio shows little variation for growth rates above 0.6 doubling/h (Table 3 ). Since the peptide chain elongation rate approaches 22 amino acids per second, each tRNA is required to cycle through the ribosome on average about two times per second. Ikemura (105) 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 tRNA 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 (= 1 cognate tRNA per second per ribosome) to sustain protein synthesis at a rate of about 20 amino acids per second per ribosome.

DNA Replication and Cell Division

Chromosome replication and segregation.

The C-period is the time interval required for the replication forks to move from the origin (oriC, at 84.6 min on the E. coli genetic map) to the terminus (terA-F, multiple sites centered near 36 min on the genetic map; 15, 127). 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 (0.6 to 1.2 kb/min for wild-type strains) clockwise and counterclockwise, respectively, with very little variation from cell to cell (20, 21). 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 (114, 136, 143). This suggests that both the times between consecutive initiations of rounds of replication and the replication velocities themselves are constant within an exponentially growing cell population.

The C-period was first measured by Helmstetter and Cooper (99) in exponential cultures that were age fractionated. Because of the considerable variability from cell to cell in the duration of the D-period (see below), the initiation age, termination age, and interdivision intervals all vary (19). 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 without age fractionation from (i) the relative frequencies of genes at given map locations (equation 9, Table 5 below; reference 35), (ii) the increase in DNA after stopping initiation of replication (14, 46, 158, 202), and (iii) flow cytometry (137, 177). Cooper and Helmstetter (52) estimated that the C-period was constant (41 min) for growth rates above 1 doubling/h and increased in proportion to τ at lower growth rates. Measurements of the increase in DNA after a stop in initiation of replication (16, 46) suggest that the C-period decreases gradually with increasing growth rate, from about 67 min at 0.6 doubling/h to 33 min in bacteria growing at 3.0 doublings/h (Table 3 ). It is not known what causes this increase in the average speed of the replication forks at higher growth rates.

The D-period is the time between termination of a round of replication and the following cell division when the replicated chromosomes are segregated. Helmstetter and Cooper (99) estimated the average D to be about 22 min for growth rates above 1 doubling/h and to increase as a constant fraction of the doubling time for growth rates below 1 doubling/h. The average D-period has also been determined in exponential cultures again without age fractionation from the increase in the cell number after a replication stop by thymine starvation (27). 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 (108). These experiments suggest that the average D-period decreases from about 30 min during slow growth (0.67 doubling/h) to about 22 min during rapid growth (3.0 doublings/h).

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 during balanced growth at a 27-min doubling time (177). For a similar doubling time (30 min), our data in Table 3 show C = 44 min and D = 24 min, i.e., about the same values. However, a recent investigation based on a new method to evaluate flow cytometric data ("precise determinations of C and D periods"), Michelsen et al. (137) reported C = 39 min and D = 13 min for a 30-min generation time. On average, the C-period measured in that work was concluded to be constant, equal to about 40 min, at generation times below 60 min; above 60 min it increased linearly with increasing generation time. The D-periods showed a similar behavior, with an average value approximately half the average value of C. Those findings seem to support the conclusions of Helmstetter and Cooper of constant C- and D-periods mentioned above (99). However, due to the considerable scatter in those data (two- to fivefold variations in the values for a given generation time) our gradually changing values of C and D in Table 3 obtained with different methods are generally consistent with the flow cytometric measurements.

At a given doubling time, the average C- and D-periods determine the average initiation age, a_i, and the average termination age, a_t (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 cell division, which occurs C plus D min after initiation, is delayed. As a consequence, cells are larger than normal, but their ribosome concentration (N_r/P) is unaltered (48).

The control of replication initiation depends on the amount of protein per oriC, P_O. Changes in P_O (e.g., by mutation) do not affect the initiation age (44). 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, but the greater P_O, the larger the cells.

Chromosome segregation and cell division.

The D-period is the time between termination of a round of replication and the following cell division. Recent advances in cell imaging coupled with genetic and biochemical measurement have begun to reveal a complex mechanism whereby cells sense when chromosome replication and segregation are completed and where to form the plane for the upcoming cell division (reference 134 and references therein). At the core of this mechanism is the formation of a ring structure composed of the tubulin homolog FtsZ, near the midpoint of the cell at about the time that replication is complete. The positioning of the Z ring is determined by two separate systems. The Min system is composed of three proteins that cycle between the poles of the cell and prevent the assembly of the FtsZ ring. As a consequence of Min cycling, the Z ring is directed to the midpoint of the cell where the concentration of the Min proteins is lowest. The second system, nucleoid occlusion, is mediated by the SlmA protein in E. coli. This protein binds to sites on the chromosome and prevents FtsZ from forming a ring that would lead to "guillotining" of the partially replicated chromosome. When chromosome replication is completed and the nucleoids begin to separate the Z ring can then form at the cell midpoint region that has been vacated. Once the Z ring is formed, the linear recruitment of a host of additional membrane-associated proteins that are essential for cell division begins. The earliest proteins added to the complex contribute to stabilizing the ring, whereas the later additions function in septum formation. The temporal controls of these complex processes are not well understood.

Variability of the D-period.

The cell division is believed to require the action of a protein synthesized at the time of termination of replication (108). During the D-interval the completed chromosome structures (Fig. 1) are segregated and a cell constriction is formed near the center of the elongated bacterium, which gradually deepens until it separates the two daughter cells. The time until the onset of constriction after of a round of replication is completed varies from cell to cell, but minimally it takes about 8 min, whereas the time between the onset of constriction and final cell separation (T-period) has a constant duration of about 9 min (24, 26, 27, 28).

To visualize the variability of D in different cells of an exponential culture, one may consider a subpopulation of cells which have just terminated a round of replication. Although no simple method exists to obtain cells synchronized with respect to their last termination of replication, the kinetics of cell divisions in such a hypothetical culture can be derived indirectly from (i) studies of cultures synchronized with respect to their last cell division; (ii) cultures in which replication has been retarded or stopped by partial or full thymine starvation, respectively; and (iii) the cell size distribution (including cells showing a constriction) of an exponential culture, using electron microscopic data (24, 26, 27, 28). If the relative cell number in such a (hypothetical) cell population is set equal to 1.0 at the beginning of the D-period (t = 0), then this number doubles to 2.0 when all cells have ended the D-period. For the first 17 min no divisions are expected to occur in this culture (i.e., the first constrictions form at t = 8 min, followed 9 min later by the first divisions; see above), so that the relative cell number remains constant at 1.0 until t = 17 (D₀ = minimum D-period). At this time the rate of division abruptly increases from zero to a value given by 1/τ_avg, where τ_avg is the average length of time after D₀ until division occurs. The rate of cell division then decreases exponentially, (1/e)-fold for every τ_avg period passed after t = 17. The average length of the D-period, D_avg, equals the sum, D₀ + τ_avg. For a culture growing in glucose minimal medium at 1.3 doublings/h, the average D-period was found to be 29 min (reference 27; i.e., somewhat longer than the value of 26 min obtained by interpolation from the values of D in Table 3 ), so that τ_avg = 12 min (= 29 – 17) for that particular culture.

At t = D_avg , 37% (= 1/e = 0.37) of the cells have not yet divided, and 63% have divided, so that the relative cell number in the hypothetical culture synchronized at termination of replication (set at t = 0) has increased to 1.63 at t = 29 min, i.e., after an average D-period has elapsed. During the next three τ_avg periods the fraction of undivided cells decreases to 14, 5, and 1%, respectively (= 1/eⁿ; n = number of τ_avg periods elapsed after t =17). In other words, with an average D-period of 29 min, it takes 65 min (17 + 4τ_avg) until 99% of all cells in the initial population have ended their D-period and divided.

These observations suggest that the D-period has three phases: (i) a period of about 8 min preparing for the formation of the constriction; (ii) a period of variable length during which constriction begins with a constant probability per unit of time (= 1/τ_avg); and (iii) a T-period of about 9 min, during which the constriction is completed and the two daughter cells are separated. The first period would correspond to the assembly and stabilization of the FtsZ ring on the inner surface of the cytoplasmic membrane, the second to the addition and activation of several transmembrane proteins that have domains in the periplasmic space and function to build the septum, and the third to the building and completion of the septum and the separation of the daughter cells (reference 134 and references therein).

It might be argued that this stochastic behavior in the cell division process is based on a model that might not be correct. However, the variability of D was established from observed data which showed a clear exponential decrease in the number of remaining undivided cells after a replication stop (see Fig. 5c in reference 27). It is not known what might cause this stochastic variation in the time until the onset of constriction. The variation is independent of the growth of the cells during the D-period; i.e., when the rate of mass accumulation was varied after a replication stop, either increased by adding amino acids to the minimal medium, or reduced by the addition of sodium azide; the resulting changes in cell growth had no significant effect on the pattern of cell divisions during the D-period (28).

Variable cell cycle.

The exponential fluctuation in the length of the D-period affects a number of cell cycle-related parameters, including (i) the size of the newborn daughter cells at the time of division, (ii) the age at which the newborn daughter cells initiate the next round of replication (i.e., the age at which the critical initiation mass is reached), and (iii) the duration of the subsequent cell cycle (23).

The time between two divisions, i.e., the duration of a particular cell cycle, is affected by the variations of D both at the end of the preceding cycle and also at the end of the current cycle. This produces a symmetrical (non-Gaussian) frequency distribution of cell cycle periods (frequency as a function of cell cycle duration) with a sharp peak at the average doubling time and two exponentially decreasing trails extending to either side of the peak, determined by τ_avg as defined above (see Fig. 12e in reference 26). The integral of this distribution can be directly observed as the gradually increasing cell number in a synchronous culture (e.g., Fig. 2 of reference 26). In such synchronous cultures where all cells have divided at t = 0, the next division occurs over a wide range of times, some within minutes after t = 0, others long after the average doubling time. One might ask: how can the time between two divisions last only a few minutes when the doubling time of the culture is 45 min and the average D-period is 29 min, as in the example above?

The answer to this paradox is seen as follows: with an average D-period of 29 min, the actual D-period for a few cells (i.e., 1%) may last 65 min or longer (see above). Since rounds of chromosome replication in cells with a 45-minute mass doubling time are initiated and terminated in regular intervals of 45 min, it means that during a 65-minute D-period (in that 1% of the cells), a next round of replication must have terminated 20 min before the previous D-period ends at t = 65; this results in an overlap between the previous D-period and the newly initiated D-periods. If this "nested" D-period for the next cycle happens to be short (e.g., minimally 17 min), then the daughter cells from a division occurring after a long D-period might divide again immediately thereafter, if not even a few minutes earlier. In such (rare) cases the large cells before division would contain three constrictions: the center one leading to the first division at t = 0 and the other two producing the next divisions that follow shortly thereafter.

When the D-period is extended in a particular cell (i.e., division is delayed), the mass of the daughter cells is proportionately increased, the age (in minutes after division) at which the daughter cells initiate the next round of DNA replication is proportionately reduced and the cell cycle in the daughters is likely to be shortened (depending on the same stochastic variation in the length of the daughter cell D-period). Similarly, when the D-period is shortened in a particular cell (i.e., division occurs earlier than the average), the mass of the daughter cells is proportionately decreased, the age (in minutes after division) at which the daughter cells initiate the next round of DNA replication is proportionately extended, and the cell cycle in the daughters is likely to be extended (depending on the same stochastic variation in the length of the daughter cell D-period). This implies that any particularly long cell cycles are followed by shorter-than-average cell cycles and vice versa. This also produces the perhaps unexpected feature of synchronous cultures that the large extent of asynchrony observed for the first division after the synchronous division at zero time (see above) does not lead to a further increase in the extent of asynchrony during the following cell cycles.

Macromolecular Composition during Growth at Different Temperatures

Between 20°C and 37°C the growth rate of E. coli B/r in glucose minimal medium linearly increases about threefold from 0.4 to 1.3 doublings/h; above 38°C the growth rate begins to decrease again (166). In this temperature range, protein and RNA per mass (P_M, R_M), the fraction of total protein that is RNA polymerase (α_p), and the fractions of total RNA synthesis corresponding to stable RNA and mRNA synthesis (r_s/r_t, r_m/r_t) remain constant (166). At least in the medium range between 25 and 37°C, the peptide and RNA chain elongation rates increase in proportion to the growth rate (166). The C period also changes with temperature in proportion to the doubling time (i.e., the ratio C/τ is constant; references 44 and 86), which implies identical replication fork patterns and gene dosages at different temperatures. Thus, in this medium range, the chain elongation rates for DNA, RNA, and polypeptides have about equal temperature coefficients. In the absence of further regulation, this 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 166) and a new RNA polymerase sigma subunit is induced (96). These temporary perturbations constitute the heat- or cold-shock response and reflect active regulation and adjustment to the postshift temperature. At higher temperatures, between 38 and 42°C, more complex changes occur, including protein degradation, which causes a reduction in the growth rate (83).

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 (P_O), ribosome activity (β_r), and peptide chain elongation rate (c_p) (see "History," above) (33, 38, 57, 131). These equations, reproduced in Table 5, follow from the definitions of their constituent parameters without special, simplifying assumptions or hypotheses. The equations are useful for work dealing with the cell composition and were 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 equivalent of DNA as a function of their map location. These latter equations are needed to find the concentrations of particular genes in a bacterial culture, which is necessary for the determination of their absolute transcriptional activities. A knowledge of absolute gene activities, in turn, allows one to define the transcriptional control of the gene in biochemical (Michaelis-Menten) terms and thereby distinguish the specific promoter control from changes in gene activity due to changes in the free RNA polymerase concentration (72). Moreover, this distinction helps to identify effectors involved in the promoter-specific control occurring under different growth conditions.

Age Distribution and the Concept of the Average Cell

The age of a given cell, a, is defined as the time elapsed since the last division relative to the mass or culture doubling time τ. Thus, a newly born cell has the age zero and when that cell is about to divide again after τ minutes it has the age 1.0. If all cells would divide regularly in exactly the same intervals, equal to one mass doubling time, then the oldest cells in the population would have the age 1.0 and the age distribution would end abruptly at age 1.0. The age distribution from such a hypothetical exponential culture (without a spread in generation times) is called "ideal age distribution" and is given by the formula n(a) = ln2 • 2^1−a for ages between 0 and 1.0 and n(a) = 0 for a >1, where n(a) is the differential frequency (dN/da) of cells in the population having the age a. The formula shows that, in an exponential, nonsynchronous population, zero-age cells are twice as frequent as cells of the age 1.0, because every dividing cell gives rise to two newly born cells of age zero. However, due to the spread of generation times reflecting the variability of the D-period (see above), the ideal age distribution does not occur in reality. Rather, some cells divide before reaching the age 1.0 and others divide later at an age greater than 1.0 (23, 27). Consequently, the actual age distribution deviates from the ideal age distribution by not abruptly ending at age 1.0, but rather by gradually decreasing to zero at ages above 1.0 (for details, see Fig. 5 in reference 23).

The averagenumber 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 of the component per unit volume of culture, divided by the number of cells in that volume, whereas the latter refers to a particular average cell. This is a cell at an average age, 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, this 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 2.7 for a growth rate of 1.0 doubling/h (Table 2 ), implying that some cells in the population have four origins, while others have only two. The average numbers of components per cell are calculated from the formulas in Table 5.

To calculate a subpopulation average for a certain age range, the equation for the "ideal age distribution" (184) 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 assumption of an ideal age distribution and of synchronous initiation at all origins in the cell at a given initiation age (29, 32). 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 (3). 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 bar. The latter may be determined from growth curves of synchronous cultures (26) 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 (23). For these reasons, τ and τ bar (and, similarly, C and C bar and D and D bar) must be distinguished in theory (29, 47); 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 bar, etc., amount to only a few percent (23) and, in practice, are negligible.

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 [68]) is P_O/ln2 (or M_O/ln2), where P_O (or M_O) 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 P_O, but M_O may be calculated from the data in the table.) For the mathematical relationships dealing with the age distribution, see references 23, 29, and 30.

Control of the Growth Rate

In previous editions of this chapter, we treated the growth rate as a given parameter to describe the "Modulation of chemical composition and other parameters of the cell by growth rate." Since we no longer assume the growth rate to be an independent variable, we have now altered the title to "Modulation ...at different exponential growth rates." This might not seem to be much different, but the word "by" growth rate implies a causal relationship, whereas "at" different growth rates only means a description without further implications, not even that of a correlation between growth rate and composition or parameter values. Therefore, instead of asking how the growth rate determines the macromolecular composition, we may ask the reverse question: how does the composition determine the growth rate? Or, more accurately, how do the three factors (i) genetic background of the particular strain used, (ii) initial conditions (the history as discussed in the introduction), and (iii) the nutritional environment determine the cell composition and the growth rate? In the following section this question is discussed.

Parameters limiting the bacterial growth rate.

Only a few physiological parameters in a bacterium limit cell growth, whereas most physiological parameters and reaction rates are not directly growth limiting. The DNA concentration is not growth limiting. Maaløe and Kjeldgaard (131, 132) 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 seemed to suggest a limitation by DNA, such that DNA limits mRNA synthesis and mRNA limits protein synthesis. This would result in a constant ratio of protein to DNA. Maaløe argued that the apparent proportionality of the ratio of RNA to DNA reflected the control of growth (131). Similarly, Koch (113) and Daneo-Moore and Schockman (54) used rate constants of RNA synthesis per DNA in models for the control of RNA synthesis or growth. However, a DNA replication (initiation) mutant that 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 (44, 48, 49). The reduced DNA concentration is the result of an increased initiation mass (protein per oriC, P_O). 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 exactly constant, even in wild-type cells (see Table 2 and Fig. 2b).

In any living cell where protein turnover is negligible the ribosome concentration (measured as number of ribosomes per amount of protein, N_r/P) and the protein synthesis rate per average ribosome [e_r = dP/dt)/N_r] are growth limiting. The product of these two factors is equal to the rate of protein synthesis per amount of protein [(dP/dt)/P] because the number of ribosomes, N_r, cancels in the product. The rate per amount of any stable component in the cell defines the exponential growth function; i.e., the value of μ (equation 18, Table 6). Equation 18 is identical to the one used by Schleif (168) 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.

A given ribosome concentration results from the regulation of ribosome synthesis, which in turn involves the regulation of RNA polymerase synthesis and function, and the regulation of rRNA genes. These additional concepts have been taken into account in the more complex growth equation 19 (Table 6), which contains six factors: RNA polymerase concentration (α_p), RNA polymerase activity (β_p), partitioning of active RNA polymerase into stable RNA and mRNA-synthesizing enzyme (ψ_s), ribosome activity (β_r), and the chain elongation rates for stable RNA and polypeptides (c_s, c_p). As was discussed in the beginning (see "Growth rate dependency of the macromolecular composition of E. coli"), the particular values of these growth-limiting parameters, and thus the growth rate of a given culture, depend not only on the composition of the growth medium, but also on the history of the stationary starter culture that is used to inoculate an experimental culture.

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 during the exponential growth phase of a culture. If they changed in time growth would not be exponential. In the preceding discussion (see "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 one has to explain why these parameters have certain constant values under given conditions. Equations such as those in Table 6 only identify growth-limiting parameters and predict their effect on the growth rate, but they do not explain the mechanisms involved in their control. Further insights into these questions are found by observing the changes of macromolecular synthesis rates when bacteria are shifted to a different nutritional environment.

Establishment of exponential growth after medium shifts.

The parameter values that determine the growth of a bacterial culture under "balanced" conditions (meaning that all exogenous nutrients are at saturating concentrations) are "reset" within minutes after bacteria enter a new, more nutritious environment, hours before a new steady-state of exponential growth and macromolecular composition is reached. It had already been observed 40 years ago that a key element in the adaptation to a new growth medium is the control of the stable rRNA and tRNA synthesis rate (25, 132). For example, in a shift from a minimal to an amino acid-supplemented medium, stable RNA (R_s) in the culture begins abruptly, within a minute after the time of the shift, to accumulate at the new, higher exponential rate that is to become the final postshift steady-state growth rate (μ) of the bacteria in the new medium (33, 38, 132, 173). Mathematically, this can be expressed as a stepwise increase in the quotient [(dR_s/dt)/R_s], which defines the exponential growth function. Since rRNA is synthesized as a constant fraction of stable RNA (see "Cell growth-related parameters," above) and r-protein matches rRNA (58, 109), the faster exponential accumulation of stable RNA after the shift-up produces an equally faster exponential accumulation of ribosomes and an exponentially increasing rate of protein synthesis (33, 38, 173).

In addition to the stepwise increase in the rate of ribosome synthesis, the rate of ribosome function (e_r) and the synthesis of RNA polymerase as a proportion of the total protein synthesis rate (α_p; see Table 3 ) also increase stepwise to their final values at the time of the medium shift (173). The RNA polymerase subunit genes are cotranscribed with ribosomal protein genes, and at lower growth rates in minimal media, the number of RNA polymerase molecules per ribosome remains about constant (0.22 to 0.24; Table 3). However, at increasing growth rates in amino acid-supplemented media, the number of RNA polymerase molecules per ribosome becomes increasingly reduced (see Table 3 ).

As explained above, the bacterial growth rate equals the product of ribosome concentration and function, N_r/P · e_r (equation 18, Table 6). The value of e_r increases rapidly to its final value, but N_r/P approaches its final value only gradually over several hours of postshift growth, even though its final value is already determined at the time of the shift by the changed ratio of the stable RNA and protein synthesis rates (38). Since the rate per amount of stable RNA synthesis [(dR_s/dt)/R_s] determines the final growth rate, any accompanying increase in the rate of ribosome function, e_r, reduces the final ribosome (and tRNA) concentration, N_r/P, so that the product N_r/P · e_r remains the same, i.e., equal to (dR_s/dt)/R_s.

How bacterial growth and the macromolecular composition respond to the opposite situation, when the nutritional environment suddenly deteriorates, is less well known. A shift-down from an amino acid-supplemented to a minimal medium produces an instant growth lag that may last several hours (112). This lag is caused by a disappearance of isoleucine and valine from the cellular amino acid pools and can be prevented when these two amino acids are kept in the growth medium (36). As far as we are aware, neither the cause for this amino acid deficiency, nor the control of macromolecular synthesis rates after a shift-down in the presence of these two amino acids has been investigated. In the latter case, stable RNA synthesis might decrease immediately to its lower exponential rate, without any lag.

Control of growth and macromolecular composition after medium shifts.

The relationships between macromolecular composition of bacteria and growth rate and the effects of medium shifts were described in mathematical terms by Maaløe and coworkers nearly 50 years ago (112, 167), and those earlier analyses were later extended (e.g., reference 47), as described in "History," above. In the following, new results and data on the control of rRNA synthesis are applied to those earlier analyses.

Based on studies of the control of rrn promoter activities (reviewed in reference 66), the initial stimulation of stable RNA synthesis after a nutritional shift-up can now be explained as follows. The exogenous nutrients added to the growth medium cause a shift of RNA polymerase molecules in the bacteria from mRNA to stable RNA genes in two ways: (i) they repress mRNA genes for the biosynthesis of these nutrients, which increases the concentration of free RNA polymerase. (ii) They increase the bacterial amino acid pools and tRNA charging, which increases the rate of ribosome function (e_r). This causes a reduced accumulation of the effector ppGpp (206), which increases the strength of stable RNA promoters (206). The increases in free RNA polymerase and in the strength of stable RNA promoters produce the initial stepwise increase in the stable RNA synthesis rate, i.e., in the value of (dR_s/dt)/R_s.

The subsequent exponential accumulation of stable RNA at the new rate [i.e., the maintenance of (dR_s/dt)/R_s at a constant level] involves the control of RNA polymerase synthesis (22). The synthesis rate of ribosomes depends on a mutual relationship between ribosomes and RNA polymerase: the rate of ribosome synthesis is proportional (factor a) to the number of RNA polymerase molecules, and the rate of RNA polymerase synthesis is proportional (factor b) to the number of ribosomes. The two factors reflect the controls of rRNA synthesis and of RNA polymerase synthesis, respectively (each factor is a product of several component parameters). If a and b remain constant in time, then both ribosomes and RNA polymerase increase exponentially at a rate equal to the square root of the product ab [μ = (60/ln2)√ab; equation 19 of Table 6, which contains the component parameters of a and b: ψ_s, α_p, β_r, β_p, c_s, c_p, defined in Table 3 ].

If a and b increase stepwise by the same factor f, the theory predicts that stable RNA and ribosomes should immediately begin to increase exponentially at an f-fold increased rate and produce an f-fold increased growth rate, as observed after a nutritional shift-up. From the data in Table 3 , we have calculated a and b for different growth rates, using the formulas given in reference 18. We then considered a preshift culture growing at μ = 0.6 doubling/h (the lowest growth rate in Table 3 , approximated by growth in succinate minimal medium), to find out what would happen if this culture were shifted to a number of hypothetical media with higher nutritional contents, producing growth rates of 1.0, 1.5, 2.0, 2.5, and 3.0 doublings/h (i.e., the higher growth rates shown in Table 3 ). For each of these five (hypothetical) shifts, the factor changes in a and b (f_a and f_b) were calculated from the data in Table 3 . For shifts to media producing 1.0 and 1.5 doublings/h, f_a and f_b were, indeed, the same and equal to f_μ, the factor increase in the growth rate, i.e., f_μ = (1.0/0.6) = 1.7 and f_μ = (1.5/0.6) = 2.8, respectively. This means that the ratio of RNA polymerase molecules to ribosomes remains unchanged under these conditions (equal to about 0.23; see Table 3 ), and that the initial controls in the synthesis of stable RNA and RNA polymerase suffice to explain the observed constancy of (dR_s/dt)/R_s during postshift growth.

For shifts to increasingly more nutritious (i.e., amino acid-supplemented) growth media that produce growth rates between 2.0 and 3.0 doublings/h, f_a is increasingly greater than f_μ and f_b is correspondingly smaller than f_μ, implying that the ratio of RNA polymerase molecules to ribosomes decreases during postshift growth. In these cases a cannot immediately increase to its final value, because that would cause an overshoot in the exponential accumulation of stable RNA, but later f_a must become greater than f_μ to compensate for the lower value of f_b, reflecting a lesser accumulation of RNA polymerase.

A major component factor defining a is the distribution of transcribing RNA polymerase between stable RNA and mRNA genes, measured by the parameter ψ_s (fraction of active polymerase engaged in stable RNA synthesis; see Table 3 ). In shifts from succinate to glucose-amino acids medium, ψ_s approaches its final value gradually after the shift (173), i.e., with increasing postshift time, relatively more RNA polymerase molecules transcribe stable RNA genes and relatively less transcribe mRNA genes. This gradual redistribution of RNA polymerase between mRNA and stable RNA genes keeps (dR_s/dt)/R_s constant during postshift growth when f_a > f_b.

The gradual rise in ψ_s during postshift growth is assumed to be caused, at least in part, by a saturation of mRNA promoters, which occurs when the concentration of total RNA polymerase increases during growth in rich media (120). The saturation of mRNA promoters raises the concentration of free RNA polymerase, which stimulates transcription from unsaturated stable RNA promoters (72). Changes in the abundance of ppGpp or in the ppGpp-dependent accumulation of Fis (a factor stimulating the strength of stable RNA promoters) are likely to participate in this adjustment. However, the levels of ppGpp during growth in media supplemented with all amino acids are so low that the strength of rrn promoters is near maximal (204, 205). Therefore, postshift adjustments in the rate of stable RNA synthesis result mainly from an increasing concentration of free RNA polymerase.

Optimal Cell Composition for Maximal Growth

Two attempts have been made in the past to explain the changing cell composition in different nutritional environments as an expression of an optimization principle that allows the cell to achieve a maximum growth rate under given conditions.

The first such proposal was made by Maaløe (131), who pointed out that the protein synthesis rate per average ribosome in bacteria should be constant and maximal under most growth conditions and 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, higher growth rates can only be achieved by increasing the ribosome concentration, since the rate of protein synthesis per ribosome is already maximal. The increase in α_r in proportion to the increasing growth rate can then be understood as a consequence of the constant and maximal rate of ribosome function.

A different proposal was made by Ehrenberg and Kurland (78) based on their "maximal fitness theory." That theory predicts that an optimal utilization of nutrients would be achieved if both the substrates for ribosome function and the ribosome concentration would increase with increasing growth rate (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 cost required to produce that substrate pool would no longer be negligible. The cells would then save resources and energy by reducing the concentration of substrates, especially when this concentration is above the K_m for substrate binding, such that substantial reductions in substrate concentrations can be compensated for by only small increases in ribosome number. These predictions were refined by Lovmar and Ehrenberg (128), who combined new data on the peptide chain elongation rate measured in vitro under optimal conditions with measurements of in vivo diffusion rates within the bacterial cell. From those data, they calculated a V_max value of c_p in vivo equal to 50 amino acid residues per second (about twice the observed maximum of 22 amino acid residues per second in Table 3 ) and concluded that the substrate concentrations for ribosome function are always limiting in vivo, so that even at the highest observed growth rates, c_p has only reached its half-maximal value.

How are these proposals supported by observations? If c_p were always kept constant and maximal as proposed by Maaløe (131), then the ribosome concentration should extrapolate to zero at zero growth rate, i.e., bacteria in nutritionally very poor media or in stationary phase should have a near-zero number ribosomes. Actually the ribosome concentration, as approximated by the RNA/protein ratio, is seen to extrapolate to a positive value at μ = 0 (Fig. 2a). This indicates submaximal values of c_p and an "overproduction" of ribosomes during growth in poor media.

The reduction in c_p at low growth rates (Table 3 ) is consistent with the maximal fitness theory. However, the value of c_p reaches a maximum plateau at growth rates above 1.5 doublings/h (Table 3 ), in contrast to the prediction from the maximal fitness theory that c_p should continue to increase with increasing growth rate. Furthermore, after a nutritional shift-up, c_p increases immediately (stepwise) close or equal to its final postshift value, but the concentrations of the macromolecular component requirements for the ternary complex (tRNA, elongation factors, charging enzymes) are expected to increase only gradually over several generations to their final values (reference 38; see "Peptide chain elongation rate," above). For these and other reasons we suggest that (i) the value of 22 amino acid residues polymerized per second per active ribosome represents the V_max value for c_p under in vivo conditions; and (ii) the lower c_p values observed at lower growth rates result from reduced levels of tRNA charging in bacteria grown in the absence of exogenous amino acids. The value of 22 amino acids per second is an average over all codons being translated; the step times for individual codons may vary from this average (154, 179, 181).

It might seem plausible that during growth in nutritionally poor media the biosynthesis of amino acids cannot keep up with the demand for protein synthesis and would thus cause the submaximal charging of tRNA and reduction in c_p. However, it would be equally plausible if the bacteria had evolved an alternative strategy to keep c_p maximal without the need for increased amino acid biosynthesis, by appropriately down-regulating the synthesis of ribosomes and thereby reducing the ribosome concentration (N_r/P). This would lead to the same product (N_r/P) · β_r · c_p, and thus to the same growth rate (equation 18 in Table 6) and rate of amino acid consumption. In other words, the rate of amino acid biosynthesis does not have to become a limiting factor to keep the ribosome function maximal if the ribosome concentration could be sufficiently lowered.

This again raises the question: why do bacteria overproduce ribosomes and reduce c_p during growth in poor media instead of down-regulating ribosome synthesis to keep c_p maximal, as postulated by Maaløe? As an alternative to Maaløe’s proposal and to the maximal fitness theory, we propose that the evolutionary selection for an overproduction of ribosomes and their substrates at low growth rates lies in the advantage for the bacteria to rapidly adapt to changing growth conditions; i.e., to restart protein synthesis and growth immediately when conditions improve; for example, when they are coming from a nutritionally poor medium, like lake water in nature, into a nutritionally rich environment, like an animal intestine. During evolution the advantage of being able to rapidly resume fast growth under improved conditions might have outweighed the greater expense caused by the overproduction of ribosomes and substrates during growth in nutritionally poor media. This might reflect the fact that under natural conditions enteric bacteria are subject to frequent changes in their nutritional environment.

This raises a new question: how do the bacteria control the overproduction of ribosomes during slow growth? As was explained above, the bacteria adjust the synthesis of ribosomes during exponential growth by controlling the ppGpp synthesis activity of the spoT gene product (142); the mechanism of this control is still not understood. During growth in minimal media, the basal levels of ppGpp are so high, that the P1 promoters of the rrn genes are nearly turned off (205). However, rRNA synthesis still continues from the constitutive P2 promoters that are not subject to a control by ppGpp. As a result, when intracellular levels of ppGpp continue to increase, the fraction of the total RNA synthesis that is stable RNA (r_s/r_t) reaches a 25% lowest value (165), and the 25% residual rRNA and tRNA transcripts originate at the P2 promoters of stable RNA genes (203, 204). Even during the most severe repression of rRNA synthesis, during the stringent response to amino acid starvation, 25% of the residual RNA synthesis is rRNA and tRNA transcribed from the P2 promoters (9). Thus, the presence of an additional constitutive P2 promoter for stable RNA genes may have evolved to guarantee that ribosome synthesis is never completely turned off during growth in a nutritionally poor environment.

ACKNOWLEDGMENTS

This work was supported by the National Science Foundation.

The opinions, findings, and conclusions expressed in this publication and those cited are those of the authors and do not necessarily reflect the views of the National Science Foundation.