Medium-dependent control of the bacterial growth rate

Biochimie xxx (2012) 1e16

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Review

Medium-dependent control of the bacterial growth rate Måns Ehrenberg b, *, Hans Bremer c, Patrick P. Dennis a a

Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA, USA Department of Cell and Molecular Biology, BMC, Uppsala University, Box 596, S-751 24 Uppsala, Sweden c Department of Molecular and Cell Biology, University of Texas at Dallas, Richardson, TX 75083-0688, USA b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 31 July 2012 Accepted 22 November 2012 Available online xxx

By combining results from previous studies of nutritional up-shifts we here re-investigate how bacteria adapt to different nutritional environments by adjusting their macromolecular composition for optimal growth. We demonstrate that, in contrast to a commonly held view the macromolecular composition of bacteria does not depend on the growth rate as an independent variable, but on three factors: (i) the genetic background (i.e. the strain used), (ii) the physiological history of the bacteria used for inoculation of a given growth medium, and (iii) the kind of nutrients in the growth medium. These factors determine the ribosome concentration and the average rate of protein synthesis per ribosome, and thus the growth rate. Immediately after a nutritional up-shift, the average number of ribosomes in the bacterial population increases exponentially with time at a rate which eventually is attained as the final post-shift growth rate of all cell components. After a nutritional up-shift from one minimal medium to another minimal medium of higher nutritional quality, ribosome and RNA polymerase syntheses are co-regulated and immediately increase by the same factor equal to the increase in the final growth rate. However, after an up-shift from a minimal medium to a medium containing all 20 amino acids, RNA polymerase and ribosome syntheses are no longer coregulated; a smaller rate of synthesis of RNA polymerase is compensated by a gradual increase in the fraction of free RNA polymerase, possibly due to a gradual saturation of mRNA promoters. We have also analyzed data from a recent publication, in which it was concluded that the macromolecular composition in terms of RNA/protein and RNA/DNA ratios is solely determined by the effector molecule ppGpp. Our analysis indicates that this is true only in special cases and that, in general, medium adaptation also depends on factors other than ppGpp. Ó 2012 Elsevier Masson SAS. All rights reserved.

Keywords: E. coli Ribosomes RNA polymerase rrn ppGpp Fis

1. Introduction Understanding how bacteria adapt to different nutritional environments and achieve an optimization of their growth rate remains a major challenge in microbial physiology. Previously we used a systems biology approach to analyze the control of ribosomal RNA (rRNA) synthesis and its relation to growth rate in the model bacterium Escherichia coli [1]. In that review we described the factors and effectors that interact with the rRNA (rrn) promoter region or the RNA polymerase to affect the rate of rRNA synthesis. However, the mechanisms whereby the bacteria sense the nutritional content of the growth medium and connect this to the activity of the factors and effectors regulating the synthesis of ribosomes are complex and remain partly obscure. One way to

* Corresponding author. Tel.: þ46 18 47 14 213. E-mail addresses: [email protected] (M. Ehrenberg), attglobal.net (H. Bremer), [email protected] (P.P. Dennis).

bremer3@

interrogate the connections within this sensing and control network is to monitor over time the macromolecular adjustments that occur as bacteria transit from one particular nutritional environment to a second that causes a change in their rate of growth. The responses to the nutrient changes that occur during this transition begin immediately upon entering the new environment and continue over an extended period of time until a new steadystate of exponential growth is achieved. Below we describe and analyze these macromolecular adjustments following a nutritional up-shift into a growth medium with higher nutritional quality to gain a deeper understanding of the mechanisms that allow bacteria to adapt to different nutrient environments. 2. Relationship between macromolecular cell composition and bacterial growth rate A widely accepted concept of bacterial physiology, known as “growth rate-dependent control” of physiological parameters was first introduced 40 years ago by Maaløe [2]. Recently this concept

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M. Ehrenberg et al. / Biochimie xxx (2012) 1e16

has been redefined as “growth medium-dependent control” and expanded to incorporate the observation that macromolecular composition and growth rate are also affected by the physiological history of a bacterial culture [3]. In the following, the major parameters and relationships affecting bacterial growth are explained within the context of these new concepts. 2.1. Definition of balanced, nonsynchronous, steady-state exponential growth When bacteria of a given genetic background are brought into a medium containing all nutrients including oxygen (provided by aeration or shaking) at saturating, non-limiting concentrations, the culture gradually assumes a constant rate of nonsynchronous exponential growth, which can continue indefinitely as long as the culture is periodically diluted into fresh medium. Under such conditions, defined as “balanced, steady-state exponential growth” [2], the amount of every cellular component per unit volume of culture, measured in samples containing a large number of cells at

varying stages of the cell cycle, increases with the same exponential function of time. This function defines the growth rate, given either as m in doublings per hour, or by its reciprocal, the doubling time s expressed in minutes (m ¼ 60/s). When biological problems are analyzed today from a biophysical perspective, i.e. “using mathematical tools to integrate experimental data into a logically consistent framework” [1], it is sometimes preferred to substitute the definitions of s and m, introduced by Maaløe, with se and me, respectively, where se is the time required for an e-fold (2.71-fold) increase and the growth rate me is defined as the reciprocal, 1/se. Similarly, one might use s2 and m2 to represent the 2-fold increase that defines bacterial growth; se ¼ s2/ln2 and me ¼ m2$(ln2/60). In the following whenever s and m are used without subscript (e.g., in Table 1 below), it always refers to the standard s2 and m2. During exponential growth, the fractional increase per unit of time remains constant for any cell component X in the culture and equals me, i.e. (dX/dt)/X ¼ me. For example, if time is measured in minutes, then 100me represents the percent increase per minute of

Table 1 Parameters pertaining to the synthesis rates of ribosomes and RNA polymerase in exponentially growing E. coli B/r as a function of growth rate at 37  C. At s (min) and m (doublings/h): Parameter

Symbol

Units

RNAP synthesizing stable RNA RNAP synthesizing rRNA rRNA chain elong. RNAP activity RNAP/total protein Peptide chain elong. Ribosome activity Ribos. prot/tot. prot. Ribosomes/cell RNAP molec./cell RNAP/ribosome RNAP prot/rib.prot. Factor (Equation (1a)) Factor (Equation (2a)) Calc. growth rate Change in a Change in b Change in m

Js Jr

% % Nucl./s % % aa resid./s % % 103 Ribos./cell 103 RNAP/cell Factor Factor See text See text Doublings/h Factor Factor Factor

cr

bp ap

cp

br ar

Nr Np Np/Nr ap/ar a b

m fa fb fm

s / 100

60

40

30

24

20

m / 0.6

1.0

1.5

2.0

2.5

3.0

24 21 85 15.5 0.90 13 85 7.7 8.0 1.8 0.23 0.12 0.030 0.0016 0.6 1.0 1.0 1.0

36 31 85 16.8 1.10 18 85 9.2 14.9 3.5 0.24 0.12 0.049 0.0027 1.0 1.6 1.7 1.7

56 48 85 17.6 1.30 21 85 11.6 25.9 5.7 0.22 0.11 0.078 0.0038 1.5 2.6 2.4 2.5

69 59 85 21.9 1.45 22 85 15.0 43.9 8.4 0.19 0.10 0.121 0.0044 2.0 4.0 2.8 3.3

79 68 85 28.2 1.55 22 85 18.8 61.4 10.0 0.16 0.08 0.177 0.0047 2.5 5.9 2.9 4.2

86 74 85 36.2 1.60 22 85 22.7 72.9 10.2 0.14 0.07 0.248 0.0048 3.0 8.3 3.0 5.0

Observed parameter(s)

Footnote

rs/rt, cs, cm

a

Js, ft

Indirect rs, rm, cs, cm, Np

ap

b c d e

Indirect Indirect

f

ar

h

RC, fs, ft

ap, PC

Np, Nr

ap, ar Jr, cr, bp ap, cp, br a, b a, a1 b, b1 m, m1

g

i j k l m n o p q r

Fraction of active RNA polymerase synthesizing stable RNA (from Table 3 in [3], originally calculated: Js ¼ 1/{1 þ [1/(rs/rt)  1] (cs/cm)}, using values for rs/rt, cs and cm shown in the same Table). b Fraction of active RNA polymerase synthesizing rRNA, Jr ¼ (1  ft) Js, where ft is the fraction of stable RNA that is tRNA ¼ 0.14 (Table 1 in [3]). c Stable RNA (or rRNA) chain elongation rate (from Table 3 in [3]; originally determined from the accumulation rrn-terminal 5S-rRNA or tRNA after stopping transcription initiation with rifampicin). d Fraction of total RNA polymerase that is actively transcribing (from Table 3 in [3]; originally calculated using the relationship: bp ¼ (rs/cs þ rm/cm)/Np, using values for rs, rm, cs, cm, and Np in the same Table). e Fraction of total protein that is core RNA polymerase (from Table 3 in [3]; determined from the b and b0 subunit content measured after sodium dodecyl sulfate-gel electrophoresis). f Peptide chain elongation rate (from Table 3 in [3]; calculated from the amount of protein per cell, PC, and the number of active ribosomes per cell, br Nr, using the relationship cp ¼ (ln2/s)$PC/(br$Nr), as explained in the same table). g Fraction of total ribosomes active in polypeptide synthesis (from Table 3 in [3], originally measured as fraction of ribosomes in polysomes, with a correction for active 70S ribosomes, as explained in the same table). h Fraction of total protein that is ribosomal protein (from Table 3 in [3], originally determined as the fraction of labeled protein in 30S and 50S ribosomal particles). i Number of ribosomes per cell (from Table 3 in [3], determined from the amount of total RNA per cell, RC, the fraction of total RNA that is stable RNA, fs ¼ 0.98, the fraction of stable RNA that is tRNA, ft ¼ 0.14 and the number of RNA nucleotides per 70S ribosome, nucl./rib ¼ 4566: Nr ¼ RC fs (1 e ft)/(nucl./rib). j Number of core RNA polymerase per cell [from Table 3 in [3], calculated from the amount of protein per cell, PC,the fraction of total protein that is RNA polymerase, ap (this table, footnote e), and the number of amino acid residues per core RNA polymerase, aa/pol ¼ 3707: Np ¼ PC ap/(aa/pol)]. k Number of RNA polymerase molecules per ribosome, Np/Nr, using the values for Np and Nr in this table (footnotes i and j). l RNA polymerase protein per ribosomal protein, ap/ar, using the values for ap and ar in this table (footnotes e and h). m Factor a in Equation (1a): a ¼ (Jr cr bp)/(nuc/rib), using the values for Jr, cr and bp in this table (footnotes b, c, and d) and the number of nucleotides per 70 ribosome, (nuc/ rib) ¼ 4566. n Factor b in Equation (2a): b ¼ (ap cp br)/(aa/pol), using the values for ap, cp and br in this table (footnotes e, f, and g) and the number of amino acid residues per core RNA polymerase, (aa/pol) ¼ 3707. o Calculated growth rate (doublings/h), using Equation (7): m ¼ (60/ln2)Oab with the values for a and b in this table (footnotes m and n). p Change in a, fa ¼ a(m > 0.6)/a (m ¼ 0.6). q Change in b, fb ¼ b(m > 0.6)/b (m ¼ 0.6). r Change in m, fm¼(m > 0.6)/0.6. a

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every cell component. The increase of a cell component in a given volume of exponential culture, also called its “accumulation”, equals the difference “rate of synthesis minus rate of degradation”. If the component is stable or its degradation is negligible, then (dX/dt) measures its synthesis rate, which is found from its amount X by multiplication with me. 2.2. Range of growth rates of E. coli observed with different exogenous nutrients For simplicity we focus only on aerobic growth. In minimal media with different single carbon sources, like acetate, succinate, glycerol, or glucose and, in addition to salts, including phosphate, nitrogen and sulfur sources, all at saturating concentrations, bacteria assume different growth rates. Acetate with the poorest nutritional quality results in a growth rate (for wild-type E. coli B/r at 37  C) of about 0.5 doublings/h. Glucose with the highest nutritional quality results in a growth rate of about 1.4 doublings/h. These carbon compounds are used by the bacteria partly as substrates to synthesize the various cytoplasmic molecules, and partly as a source of energy to drive the biochemical reactions within the cells. This energy is obtained predominantly by “burning” part of the carbon source or its derivatives in a series of reactions in a process called respiration, which utilizes oxygen from the environment as the terminal electron acceptor and releases carbon dioxide and water. When the growth medium with a single carbon source is supplemented with amino acids and/or nucleosides, a higher growth rate is achieved than with the carbon source alone. The fastest growth is observed in glucose-supplemented Luria-Bertani broth (LB medium), with rates at 37  C of 3.0 doublings/h for wild-type E. coli B/r, and 2.5 doublings/h for wildtype E. coli K-12. The 20% slower growth of K-12 compared to B strains appears to result from a lower average rate of ribosome function, since both strains show the same amounts of RNA and protein per mass during growth in LB medium [Fig. 4 of ref. [4]], suggesting the same ribosome concentrations (see following section). The reason for this strain difference in ribosome function is not known. 2.3. Dependence of the growth rate on the ribosome concentration and function Since the bacterial (dry) mass consists mostly of proteins and proteins are made by ribosomes, studies of bacterial growth have centered on the study of the synthesis and function of ribosomes. The cytoplasmic concentration of ribosomes in an average cell of a given exponential culture is defined here as the number of ribosomes per amount of protein (in amino acid residues) present in that culture, Nr/P. The rate of ribosome function, or “ribosome efficiency”, is given as the number of amino acid residues polymerized per unit of time per average ribosome, er ¼ (dP/dt)/Nr [2]. Since the Nr factors cancel in the product, (Nr/P)$er, it equals (dP/dt)/ P, the rate of protein synthesis relative to the amount of protein present (the unit for the protein readout cancels in this quotient). Since most E. coli proteins are stable, this quotient represents the exponential rate of protein accumulation, me. Therefore, the exponential growth rate of a non-synchronous bacterial culture equals the product of its ribosome concentration (Nr/P) and ribosome function (er): me ¼ (ln2/60)$m2 ¼ (Nr/P)$er. Obviously there are other factors in addition to translation that have impact on bacterial growth in a given environment, but all such contributing factors must ultimately affect either the concentration and/or function of ribosomes. In the definition of er ¼ (dP/dt)/Nr the value of Nr includes both protein elongation-active mono-and polysomes as well as

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elongation-inactive 50S and 30S ribosomal particles. If br is the fraction of elongation-active ribosomes and cp is the peptide chain elongation rate in amino acids polymerized per unit time per average elongating ribosome (for values of br and cp at different growth rates see Table 1 above), then er equals the product br$cp. 2.4. Growth medium-dependent versus growth rate-dependent control of the cell composition When parameters defining the macromolecular composition (like RNA per mass, DNA per cell, etc.) are plotted as functions of growth rate, different sets of curves may be obtained, depending on the particular choice of media that was made to obtain the different growth rates [3]. This is illustrated by the following example. When two exponential cultures of E. coli B/r are compared, one grown in glycerol minimal medium and the other in a medium containing succinate plus all 20 amino acids, it is found that they grow at the same rate of about 1.0 doubling/h (at 37  C). However, the culture with all 20 amino acids shows a lower ribosome concentration (lower Nr/P) and a correspondingly higher efficiency of ribosome function (higher er), so that the product of these two parameters, which equals the growth rate (me ¼ er$Nr/P), is the same for both growth media despite their different values for ribosome concentration and function. Furthermore, in bacteria growing in the presence of all amino acids (i.e. when the genes for amino acid-biosynthetic enzymes are repressed) the RNA polymerase synthesizes relatively less mRNA and more stable RNA (rRNA and tRNA) in comparison to bacteria growing at the same rate in minimal media without amino acids [5]. These observations show that in different media the same value for the product (Nr/P)$er and thus the same growth rate can be obtained at different macromolecular compositions. This demonstrates that the growth rate does not uniquely determine the macromolecular composition of the bacteria; but rather vice versa, the macromolecular composition, in particular the product (Nr/P)$ er, determines the growth rate. The growth rate is, in other words, not an independent variable which defines the cytoplasmic concentrations of cellular components, although, for historical reasons, such a relation is often assumed. Therefore, we prefer the term “growth medium-dependent” control of physiological parameters to the term growth rate-dependent control [3]. The implications of this novel view of “growth medium-dependent control” as opposed to “growth rate-dependent control” have not yet garnered complete recognition or appreciation from the bacterial physiology community (e.g. ref. [6]). In the above example the growth medium unambiguously defines the growth rate, but also this assumption is but an approximation as will be described next. 2.5. Initial conditions of a bacterial culture affecting its subsequent growth Since Maaløe’s studies 50 years ago, it has been generally assumed that the growth rate is fully determined by the nutrient composition of the growth medium [7,8]. However, even this assumption is only approximately correct. Generally, the poorer the nutritional quality of the growth medium, the greater the variations in the growth rate found when cultures of the same bacterial strain are prepared on different days from different “overnight” starter cultures in the same growth medium. For example, for E. coli B/r in succinate minimal medium, nearly twofold differences in the steady-state exponential growth rate have been observed with doubling times varying between 67 and 113 min [9e11]. The different growth rates are maintained as long as growth remains exponential. However, when several

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experimental cultures are started at the same time from the same stationary overnight culture, they assume the same exponential growth rate and show the same macromolecular composition, including the same values for the growth-determining parameters Nr/P and er. This shows that the history of the particular starter culture used to inoculate an experimental culture affects the physiological parameters in the following generations of bacteria that determine their growth rate during steady-state exponential growth. This raises the conundrum: what limits the growth rate in a particular bacterial culture? These effects of the history of the starter cultures from which experimental cultures are prepared have hardly been studied in the past. When a “stationary” culture in a given medium is further incubated and kept in this condition for several days, the average size of the cells and the chromosome number per cell gradually decrease [12], which implies that the stationary condition is not uniform over time. Rather, the cells in a stationary culture undergo internal changes, including cell divisions and cell death, such that their total (combined) mass remains approximately constant. Generally, the longer a starter culture is kept in stationary phase, the lower the number of viable cells, the longer the initial lag before growth resumes after inoculation into fresh medium, and the greater the chance that the final growth rate will be somewhat reduced (unpublished observations from the laboratory of HB). Thus, the growth rate and macromolecular composition of an exponential culture depend on both, the growth medium and the initial condition given by the history of the bacteria used to inoculate and start an experimental culture. To summarize, the macromolecular composition of an exponentially growing bacterial culture depends on (i) its genetic background (i.e. the strain used), (ii) the physiological history of the bacteria used for inoculation of a given growth medium, and (iii) the kind of nutrients in the growth medium. It is, however, always true that the ribosome concentration (Nr/P) and ribosome function (er) determine the growth rate (for more details see ref. [3]). 3. Evaluation of medium shifts to study the control of bacterial growth 3.1. Definition of nutritional shifts The first systematic study of the relationship between bacterial growth in different media and the macromolecular composition of the growing cells was reported 50 years ago from Maaløe’s laboratory [7]. However, as has been pointed out above, a given bacterial strain of E. coli may grow at somewhat different rates in a given nutritional environment, especially during growth under submaximal conditions in minimal media, depending on the physiological history of the bacteria used to inoculate an experimental culture. Without further studies of these “history effects” our understanding of the optimization of the bacterial growth rate remains incomplete. It appears that enteric bacteria like E. coli do not necessarily maximize their growth rate in a nutrient-limited environment (which in nature is encountered in sewage or lake water), but rather optimize a physiological state which allows rapid resumption of maximal growth when improved nutrient conditions are encountered (see Section “Optimal cell composition for maximal growth” in ref. [3]). How bacteria establish a particular growth rate in a given nutritional environment with minimal effects of undefined factors associated with their history can be studied in “shifts” from nutrient-poor to nutrient-rich growth media or vice versa. For such shift experiments, a bacterial culture is initially maintained in steady-state exponential growth in a defined pre-shift medium; i.e., essential components of the cell, like total DNA, RNA, and

protein, all increase in parallel with the same exponential function that defines their growth rate. At a point along a time line (time t ¼ 0), the medium is altered either by addition of nutrients to obtain a medium of higher quality and a faster growth, or by removing or changing nutrients to obtain a medium of lower quality and a slower growth. The two experimental procedures are termed nutritional up-shift or down-shift, respectively [2]. In the past, most studies of bacterial growth control have involved nutritional up-shifts, since down-shifts are often associated with long lag periods without any net growth [8]. Broda [13] found that this lag is caused by a temporary depletion of the cellular pools of isoleucine and valine, and when these two amino acids are provided in the post-shift medium the growth lag is prevented. Unfortunately, this result has never been explored further, most likely because it was never widely circulated. Clearly, future studies that focus on nutritional down-shifts in the absence of prolonged amino acid starvation have the potential of providing additional valuable information relating to growth rate adaptation. The following analysis of the reactions controlling bacterial growth is based on earlier studies involving: (i) a determination of macromolecular synthesis rates (DNA, RNA, protein) after an upshift from succinate minimal to glucose-amino acids medium [9]; (ii) measurements of RNA polymerase synthesis and the distribution of transcribing RNA polymerase between stable RNA and mRNA genes after similar medium shifts [11]; (iii) newer results on the control of rRNA and mRNA promoter activities in different growth media and the role of the effector ppGpp (reviewed in ref. [1]); and (iv) a theoretical analysis of the mutual effects of RNA polymerase and ribosome synthesis on their accumulation during exponential growth and after medium shifts [14]. 3.2. Stable RNA synthesis after an up-shift A decisive event after bacteria are brought into an improved nutritional environment was observed 50 years ago in Maaløe’s laboratory [8]: the exponential accumulation of stable RNA (Rs, measured per unit volume of culture) consisting of rRNA and tRNA, changes abruptly, i.e. within about a minute after the medium shift (at time t ¼ 0), to a higher value which “sets” the new growth rate in the post-shift medium. Mathematically, this can be expressed as a step-wise increase in the quotient [(dRs/dt)/Rs]. As was explained above, during steady-state exponential growth, the “rate-peramount” quotient has the same value for the accumulation of all cell components and remains constant in time, equal to ln2/s, which defines the growth rate. In a nutritional up-shift, the value of (dRs/dt)/Rs increases at t ¼ 0 from ln2/s1 to ln2/s2, where s1 is the (longer) pre-shift doubling time of the culture and s2 is the (shorter) post-shift doubling time of stable RNA. For other cell components, including protein, the rate-per-amount quotient approaches this higher value of ln2/s2 only gradually, so that it takes hours of post-shift growth before a constant macromolecular composition and a new steady-state of exponential growth is reached. This prolonged transition occurs even though stable RNA begins immediately to accumulate exponentially with the new doubling time s2 (Fig. 5b in [9], Fig. 1a taken from Fig. 7 of ref. [9]). If the amounts of RNA and protein accumulation are measured one or 2 min after an up-shift, the increases are too small to allow the drawing of any conclusion about changes in their rates of synthesis. Moreover, direct measurements of the rate of RNA synthesis (e.g. by pulse-labeling) are virtually impossible in this time interval because of changes in the mRNA synthesis and degradation rates and fluctuations in the precursor pools. However, if one measures total RNA accumulation (consisting of 98% stable rRNA and tRNA) in 5-to 10-min intervals before and after an upshift and the results are plotted on a semilog scale, the post-shift

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RNA points lie quite precisely on a straight line that intersects the RNA curve from the pre-shift samples (also linear on the log scale) within the first minute after the shift. (Fig. 1a; these plots of RNA accumulation could also be consistent with a short lag, followed by short temporary overshoot, so that after 5 or 10 min the result would be the same as in the absence of a lag plus overshoot, as seen in Fig. 8b of ref. [9]). Since the rate of chain elongation of nascent stable RNA shows little dependency on the growth rate [15], the rapid increase in Rs after the nutritional up-shift must reflect an increase in the frequency of initiation of transcription at stable RNA promoters. If this increase were abrupt and occurred within seconds of the upshift, it would produce an elevated step of polymerase density traversing along the rrn operons and reaching the end after a transcription time of about 1 min [16]. Therefore, even with the fastest response, the rate of stable RNA accumulation would only gradually increase to its higher value during the first minute of post-shift growth, whereas the rate of production of finished 16S, and 23S plus 5S rRNAs would increase abruptly at about 20 s and 60 s, respectively, after the up-shift. 3.3. Protein synthesis after an up-shift When the amounts of protein (P) and stable RNA (Rs) per unit volume of culture are measured at different time points before and after an up-shift, Rs is initially a linear function of P. The slope increases abruptly to a higher (constant) value within the first minute following the medium shift. This is seen as the intersection between the linear pre- and post-shift curves at the time of the medium shift (Fig. 1b, from Fig. 6 of ref. [9]). The slopes of these linear functions represent the differential quotient dRs/dP, and are equal to the ratio of the accumulation rates of stable RNA and protein, (dRs/dt)/(dP/dt). The post-shift constancy of this ratio indicates that the protein synthesis rate increases in parallel with the exponentially increasing amount of stable RNA. This has several implications: (i) after the up-shift a constant proportion of the newly made stable RNA must result in active ribosomes which immediately participate in protein synthesis; (ii) to produce functioning ribosomes, the synthesis of ribosomal proteins must be controlled in parallel with the rate of stable RNA (including rRNA) synthesis; i.e. the ratio of the synthesis rates of r-protein to total protein (ar) must also increase stepwise to its final value at the time of the shift [17,18]. The rate of synthesis of ribosomal proteins is autogenously regulated by the availability of newly synthesized ribosomal RNA [19e21]. The differential rates of synthesis of individual ribosomal proteins have been measured during the first few minutes following a nutritional up-shift from succinate minimal medium to glucose plus amino acids medium. The individual proteins exhibit complex patterns of inductions and oscillations that in part reflect the positions of their encoding genes within r-protein operons [17]. Induction of the earliest proteins is already apparent within the first minute following the up-shift and the new steady-state is reached for all r-proteins within about 5 min [17,18]. It is unclear if the induction of r-proteins requires new elevated transcription of rprotein operons or whether it occurs on preexisting mRNAs and reflects translational control at the 50 -end of the mRNA and coupled translation of down-stream genes. In any case the induction is likely to be coupled to increased availability of rRNA transcripts (see Section 5 below). From the step-wise changes in dRs/dP and dRs/dt (slopes of the RNA curves in Fig. 1a and b, respectively) the rate of ribosome function, i.e. the stepwise increase in the value for the rate of protein synthesis per average ribosome [er ¼ (dP/dt)/Nr] can be found (see Appendix in ref. [9] for details). Thus, from the observed

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accumulation of RNA and protein in a culture subjected to a nutritional up-shift, the kinetic functions describing the synthesis of ribosomes and protein, as well as the parameters (Nr/P), er and ar, can be obtained without any assumptions other than implied in the definitions of the parameters used [9]. These functions describe in mathematical terms the immediate and gradual changes in the macromolecular composition caused by the medium shift, but they do not explain the underlying control that causes the constant exponential increase in the number of ribosomes during post-shift growth. 3.4. DNA synthesis after an up-shift Immediately after a nutritional up-shift the rate of DNA synthesis per unit volume of culture increases exponentially, with the new, larger post-shift growth rate, in parallel with the similarly increasing rate of protein synthesis (i.e. after the rapid, initial increase in the rate of protein synthesis due to a rapid increase in the rate of peptide chain elongation). Thus, the rate of DNA synthesis remains proportional to the rate of protein synthesis, but the factor of proportionality is 30% smaller after than before the shift (straight line in Fig. 1b, circles, with a 0.7-fold reduced slope). The reduced rate of DNA to protein synthesis after the up-shift gradually decreases the cytoplasmic DNA concentration (amount of DNA per amount of protein) to a 30% lower steady-state level (Fig. 1a). The control of bacterial chromosome replication depends on the “initiation mass”, defined as the amount of mass or protein per replication origin at the time of initiation of a new round of replication which occurs once per doubling time. The initiation mass is approximately the same during growth in different media [22], as is the time required to replicate the chromosome [40-minute Cperiod, ref. [23]). Because of this, chromosomes become increasingly branched at higher growth rates, when new rounds of replication are initiated before the previous round is terminated. This produces 2, 4, or maximally 8 replication origins per replication terminus [23] and results in a decrease of the amount of DNA per replication origin. Therefore, at constant initiation mass (protein per replication origin), the DNA concentration (DNA per protein) must decrease like the amount of DNA per origin, as observed (Fig. 1a). Newer measurements of the initiation mass and the Cperiod in E. coli at different growth rates show that these parameters do change somewhat with growth rate [4], but the outcome a decreased DNA concentration at higher growth rates (as seen in Fig. 1a and implied in Fig. 1b), reflecting a decreased concentration of genes distal from the origin of replication e remains unchanged. The decreased gene concentrations at higher growth rates raise the question whether DNA might become limiting for the rate of RNA synthesis and, in particular, whether the number of rrn genes in the cell might limit the rate of rRNA synthesis after a nutritional up-shift. Since most rrn genes are clustered near the origin of replication, it follows from the approximate constancy of the initiation mass that the rrn gene dosage (here defined as rrn genes per amount of protein) decreases only slightly with increasing growth rate. Since the rate of rRNA synthesis increases rapidly after the up-shift (Fig. 1a), it appears that this rate is not limited by the rrn gene dosage. This has been shown more directly in studies of a mutant with a defective replication control gene (dnaA, ref. [24]). This mutant has a 0.6-fold higher initiation mass and thus a 0.6-fold lower concentration of all genes in comparison to the wild-type, but the synthesis rates of RNA polymerase, stable RNA (rRNA and tRNA) and mRNA were unchanged [24]. This implies that the transcriptional activities of all genes in the mutant were almost twice as high as the activities of the corresponding genes in the wild type. It was concluded that the bacteria normally contain an

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Fig. 1. Accumulation of RNA, protein and DNA in E. coli B/r after a nutritional up-shift from succinate minimal medium at 90 min doubling time to glucose amino acid medium at 28 min doubling time. (a) Calculated accumulation of RNA, protein, DNA and mass (sum of the weights of RNA, protein and DNA) from Fig. 7 of Brunschede et al. [9]. The data are illustrated for the initial post-shift period of 2 h. It should be noted that the slopes of the protein, DNA and mass curves after 2 h are still increasing and have not reached their final post-shift value, whereas the RNA curve reaches the post-shift value within the first few minutes. True exponential growth is achieved only after an about 100-fold increase in mass. (b) Relative amounts of RNA (triangles) and DNA (circles) in the shifted culture as a function of the relative amount of protein (Fig. 6a of ref. [9]); Copyright Ó 1977 American Society for Microbiology). The equations used to calculate the accumulation curves in panel (a) from the data presented in panel (b) are derived and explained in greater detail in the Appendix of ref. [9].

excess of DNA, so that the rate of transcription is limited by the RNA polymerase concentration, and not by the DNA concentration. This means that the actively transcribing fraction of DNA-bound RNA polymerase is much larger than the fraction of free RNA polymerase and implies that most promoters are far from being saturated with polymerase. If under such conditions the concentration of all genes is reduced, e.g. to one half, then the concentration of free RNA polymerase would be expected to double, so that all genes become twice as active, but with half the number of genes the total rate of transcription remains unchanged, as observed. In the following, quoted rrn gene activities observed at different growth rates were obtained by taking changing replication parameters and rrn gene dosage into account. However, since the rrn genes are generally far from being saturated with RNA polymerase, the control of DNA replication was not considered as of great importance for the control of growth and rRNA synthesis after a medium shift.

3.5. Two-step process involved in the approach to a higher growth rate The observations in Fig. 1 pose two questions about the establishment of a particular growth rate in a given environment: (i) What causes the first, rapid increase in (dRs/dt)/Rs just after the addition of superior nutrients to the growth medium? (ii) What keeps (dRs/dt)/Rs constant during the following growth period, during which every cell component will eventually increase with the same exponential function and establish the steady-state growth rate in the new environment? In the following the

reactions relating to these two processes and their control are articulated. 4. Initial stepwise increase in the stable RNA synthesis rate after an up-shift The rapid increase in the rate of stable RNA synthesis after bacteria enter an enriched nutritional environment results from a complex cascade of interrelated reactions. These reactions are briefly summarized in the context of a specific up-shift of E. coli B/r from succinate minimal to glucose-amino acids medium: (i) The presence of exogenous amino acids in the post-shift medium rapidly raises the supply flow of free amino acids in the cytoplasm, resulting in a rapid rate of tRNA charging by the aminoacyl-tRNA-synthetases and an increased rate of ribosome function. Direct measurement of the peptide elongation rate has revealed that it increases by about 25% upon the medium shift, to near the maximum value of 22 amino acid residues polymerized per second per active ribosome (Table 1), and results in a corresponding 25% increase in the rate of protein synthesis [9]. (ii) The increased rate of ribosome function inactivates the ppGpp synthetase of the spoT gene product [25,26], leading to a rapid decrease of the concentration of ppGpp by degradation in the absence of synthesis [27]. (iii) Before the up-shift, the ppGpp concentration is high, which enhances the interaction between ppGpp and RNA polymerase [28]. This interaction restricts polymerase binding on ppGpp-dependent promoters such as the fis gene promoter

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and the P1 promoters of stable RNA genes. After the up-shift, when the concentration of ppGpp drops precipitously, these ppGpp-repressed promoters become active. The derepression of fis results in a rising level of the Fis factor, which binds to an activator region of the rrn P1 promoters. Together, the redirection of polymerase and the FIS activation increases the combined P1eP2 promoter strength about two-fold [1,29]. (iv) The increased cellular pools of amino acids and glycolytic intermediates during growth in the post-shift medium repress the genes involved in their biosynthesis, and reduce the rate of total mRNA synthesis by about 40%. (v) The lower level of ppGpp results in a suppression of transcriptional pausing and a corresponding increase in the fraction of active RNA polymerase. (vi) Together, the activation of RNA polymerase and the repression of mRNA synthesis result in an about 1.6-fold increase of the concentration of free RNA polymerase. (vii) The combination of the twofold increased average strength of the stable RNA promoters and the 1.6-fold increased concentration of free RNA polymerase produces the 3.2-fold increase in the rate of transcript initiation at the stable RNA promoters immediately after the medium shift. This starts the 3.2-fold increase in the exponential rate of stable RNA synthesis that leads to the 3.2-fold increase the growth rate, from 0.67 doublings per hour in succinate minimal medium to 2.14 doublings per hour in glucose-amino acids medium. The reactions in this cascade of events will now be discussed in more detail.

4.1. Acceleration of ribosome function One of the first effects of a nutritional up-shift that triggers the further steps leading to an increased stable RNA synthesis is the stimulation of ribosome function due to the increased supply flows of cytoplasmic amino acids and nucleotides, greatly increasing the charging level of all cognate tRNAs. In the up-shift from succinate minimal to glucose-amino acids medium, the ribosome efficiency (er) increases 1.25-fold, which causes a 25% increase in the rate of protein accumulation in the culture within the first minute (Fig. 8 in ref. [9]). During the following post-shift growth, er remains about constant at this higher level, whereas the ribosome concentration (Nr/P) gradually approaches its final higher value over a prolonged period of time (as evidenced by the gradual narrowing in the vertical distance between the protein and RNA curves after the upshift in Fig. 1a). When the steady-state is reached in the new medium, the product (Nr/P)$er equals the “immediate” post-shift value of the quotient (dRs/dt)/Rs. Accordingly, the greater the initial increase of er at the time of the shift the lower the following increase in (Nr/P). The rapid acceleration of the peptide chain growth after the upshift occurs before any significant increase in the concentrations of tRNAs, tRNA charging enzymes and translation elongation factors. This means, in particular, that the rates of charging of all aminoacyltRNAs increase abruptly in response to the increased supply flows of all amino acids. This raises three questions: (i) Why are the rates of amino acid supply flows limiting for ribosome function in minimal media? In other words why are the concentrations of ribosomes (demand) and the activity of amino acid synthetic enzymes (supply) not balanced to each other during growth in poor media? (ii) Why is this limitation expressed in the rate of protein elongation and not in a reduced fraction of elongating ribosomes? (iii) Why are tRNAs and ribosomal factors synthesized at higher rates in rich media, leading to higher concentrations, when they are

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already close to saturating at lower concentrations during growth in minimal media? With regard to the first two questions, Maaløe (in a 1968 seminar) compared bacteria brought into a poor growth medium with a factory that has to reduce its output, e.g. by 50%, when the supply for its manufactured product has suddenly become limiting. In this comparison Nr/P and er correspond, respectively, to the number of factory workers and the speed at which they work. Maaløe argued that, under a socialist system, the factory manager would keep all employees and tell them to work half as fast, but under a capitalist system the manager would fire half his employees and tell those remaining to work as fast as usual. Since the latter is obviously more efficient, Maaløe concluded by analogy that bacterial ribosomes must always function at their maximum speed and that published evidence of reduced peptide chain elongation rates during growth in poor media was thus likely to be experimentally flawed [30]. However, a theoretical analysis by Ehrenberg and Kurland [31] showed that the amount of tRNA charging enzymes and other factors required to keep the ribosomal function at a maximum level in poor growth media was not negligible with respect to the cost of ribosome synthesis. Consequently, the best efficiency at limiting availability of nutrients would be achieved by a partial reduction of both, Nr/P and er, to an extent very similar to what has been observed. Even if bacteria were able to reduce their rate of ribosome synthesis and increase the activity of amino acid producing enzymes to achieve a higher growth rate, this would not necessarily be advantageous because the time it takes for bacteria to maximize their growth (rate of protein accumulation) after a media up-shift is reduced by an increased ribosome concentration in the pre-shift medium. Accordingly, the average growth over long periods of time of bacteria living under changing conditions will be maximized by a seemingly too high ribosome concentration for cells growing in poor media. The third question, why the synthesis of tRNAs and ribosomal factors should increase during growth in rich media when these molecules are at close to saturating concentrations for their functions during growth in minimal media, has not been experimentally addressed, as far as we are aware. However, the higher concentration of ribosomes (Nr/P) during growth in rich media is likely to keep relatively more tRNAs and ribosomal factors temporarily bound to ribosomes, so that they are not available for maintaining the ribosome substrates (the ternary complex of EFTu, charged tRNA, and GTP) at saturating levels. This is probably one reason for the (approximate) co-regulation of tRNAs and ribosomal factors with the synthesis of ribosomes. This coregulation is not always tight, especially for some of the aa-tRNA synthetases; also the tRNA population changes somewhat in fast growth and may reflect the position of tRNAs genes on the chromosome relative to oriC (reviewed in ref. [3], see also ref. [32]). In addition to this relief of tRNA sequestering, the rate of ribosome association with ternary complex and elongation factor G is expected to increase with increased concentrations of free EF-Tu, aminoacyl-tRNAs and EF-G. This could lead to a further and slow increase in the protein elongation rate, too small to be observed in the type of experiment performed by Brunschede et al. [9], yet in accordance with theory [31] and significant in an evolutionary perspective [33]. We have assumed that the reduced rate of ribosome function during growth in poor media is due to a limiting synthesis of amino acids and thus to a limited supply of charged tRNAs. A different type of explanation has been proposed by Rojani et al. [34]; they suggested that uncharged tRNA inhibits ribosome function, based on experiments in which the concentrations of total tRNATrp and of Trp-tRNATrp were independently varied. The

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rate of protein synthesis was found to depend on the ratio of charged to uncharged tRNATrp, independent of the absolute concentration of Trp-tRNATrp. An inhibition by uncharged tRNA cannot be ruled out, but their conclusion is not entirely compelling since they find that the rate and extent of protein synthesis are similar with and without induction of tRNATrp synthesis (their Fig. 2c and d). The induction of tRNATrp synthesis largely increases the concentration of deacylated tRNATrp and it also increases the absolute concentration of charged tRNATrp, although it keeps its fraction (of total tRNATrp) reduced. These changes in tRNA concentrations do not affect the rate of protein synthesis which, under their conditions, is limited by the rate of aminoacylation of tRNATrp. As long as charging of tRNATrp remains rate limiting for bulk protein synthesis, which seems to be the case, a putative inhibition of ribosome function by uncharged tRNATrp would just raise the fraction of charged tRNATrp at an unchanged total rate of protein synthesis. 4.2. Repression of mRNA genes A second, immediate effect caused by the increased pools of amino acids, aminoacyl-tRNAs and glycolytic intermediates associated with an up-shift is the repression of mRNA genes for enzymes involved in the biosynthesis of amino acids and gluconeogenesis. After an up-shift from succinate minimal to glucoseamino acids medium, the total rate of mRNA synthesis decreases abruptly by about 40% (see Fig. 2 from Fig. 7 in ref. [11]). This decrease is rapidly followed by an exponentially increasing rate of mRNA synthesis, in parallel with the exponentially increasing rate of stable RNA synthesis (dRs/dt), with a doubling time equal to the final post-shift doubling time s2 (Fig. 2). The increasing post-shift mRNA synthesis rate reflects the increasing transcription from mRNA promoters that are not repressed, i.e. those for ribosomal proteins, RNA polymerase, as well as ribosomal and other factors needed to keep up with the increased synthesis and function of ribosomes. The increasing rate of mRNA synthesis following its abrupt initial decrease requires an increased rate of RNA polymerase synthesis. The latter is caused

by an increased rate of total protein synthesis and an increased value of the fraction of total protein that is RNA polymerase, ap (see Section 5 below). 4.3. Activation of stable RNA genes The initial increase of the quotient (dRs/dt)/Rs after the upshift must reflect an increase in the numerator, dRs/dt, since the amount of stable RNA, Rs, in the denominator cannot rapidly change. Similarly, neither the amount of RNA polymerase nor the stable RNA gene dosage, two factors that might affect the synthesis of stable RNA, can change abruptly. Therefore, the initial step-wise increase in (dRs/dt) that eventually determines the final growth rate reflects a redistribution of RNA polymerase molecules from the transcription of mRNA to stable RNA genes. The distribution of RNA polymerases between mRNA and stable RNA transcription (86% of which is rRNA and 14% is tRNA) is given by the parameter Js, the fraction of actively transcribing RNA polymerase that is synthesizing stable RNA. This parameter is experimentally determined from the proportion of the total RNA synthesis rate that is stable RNA, rs/rt, by taking the different average chain elongation rates of stable RNA and mRNA into account [Table 1, reproduced from ref. [3]). In the up-shift from succinate minimal to glucose-amino acids medium, when the growth rate increases 3.2-fold from 0.67 to 2.14 doublings/h, there is initially a 3.2-fold increase in rs ¼ (dRs/dt) at t ¼ 0 [9]. In this case, Js increases about 2.5-fold from 28 to 71% (values obtained for 0.67 and 2.14 doublings/h by interpolation of the Js data in Table 1, from ref. [3]). This means that about 43% (71e 28 ¼ 43) of the RNA polymerase molecules transcribing mRNA at the time of the up-shift rapidly move to transcription of stable RNA genes and this abrupt redistribution of RNA polymerase activity brings about the 3.2-fold increase in the rate of stable RNA synthesis, rs. The 2.5-fold increase in Js creates a 3.2-fold increase in rs because the rate of chain elongation of stable RNA is larger than that of mRNA. The change in Js reflects the controls of both mRNA (see above) and stable RNA synthesis (see below).

Fig. 2. Kinetic changes in the rates of stable RNA (solid curve) and mRNA synthesis (circles), and in the number of functioning (triangles) and total (squares) RNA polymerase molecules after an up-shift of E. coli B/r from succinate minimal medium to glucose amino acids medium in three different experiments (panels a, b and c) done on different days; ordinate values normalized to 1.0 at t ¼ 0, except for mRNA synthesis. A value of 4.0 for the zero-time rate of mRNA synthesis means that during preshift growth the rate of mRNA synthesis is four-times greater than the rate of stable RNA synthesis. After the up-shift the rate of mRNA synthesis becomes smaller than the rate of stable RNA synthesis (mRNA curve below stable RNA curve) [from Fig. 7 of ref. [11], Copyright Ó 1980 American Society for Microbiology].

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4.4. Change in ppGpp accumulation The accelerated ribosome function after the up-shift decreases the accumulation of the effector ppGpp, that controls the rate of stable RNA synthesis. The accumulation of ppGpp in exponentially growing bacteria depends on the activities of the spoT gene product, the SpoT protein. SpoT has two independently controlled enzymatic activities: a ppGpp synthetase that produces ppGpp [35,36] and a ppGpp hydrolase that degrades ppGpp and limits its accumulation [37,38]. During exponential growth at different rates in different media the hydrolase activity of SpoT is about constant, resulting in a 0.7-min average lifetime of ppGpp, determined from the exponential decrease in (high) ppGpp levels produced by the RelA ppGpp synthetase during amino acid starvation after terminating the starvation [27,39]. In contrast, the synthetase activity of SpoT varies with the growth medium to produce the varying “basal” levels of ppGpp [27]. The SpoT synthetase activity requires ongoing protein synthesis at a submaximal rate of ribosome function [27,40], but the mechanism by which the rate of ribosome function controls this activity has remained obscure. During growth in the nutritionally poorer pre-shift medium, the tRNAs are submaximally charged [41] and ribosomes function at a submaximal rate [4,42]. This activates the ppGpp synthetase activity of SpoT and results in an accumulation of ppGpp to a relatively high “basal” level (i.e. still much lower than the very high RelA-produced ppGpp levels observed during the stringent response). In contrast, during growth in the amino acids-containing post-shift medium when the ribosomes function at near their maximum rate, the ppGpp synthetase activity of SpoT nearly disappears, which results in barely detectable levels of ppGpp [27,43]. Because of the rapid increase in the rate of ribosome function after the up-shift, the SpoT-dependent accumulation of ppGpp decreases rapidly to its low post-shift levels through SpoTdependent degradation. 4.5. Control of stable RNA promoter activity by ppGpp The stable RNA genes, including the rRNA operons (rrn), have two promoters, P1 and P2, about 120 bp apart [44]. The strength of the upstream P1 promoters is regulated by the effector ppGpp and the protein factor Fis. In contrast, the strength of the downstream P2 promoters is constant, defining them as constitutive. Neither the P1 nor the P2 promoter is saturated by RNA polymerase (reviewed in ref. [1]). This implies that their varying activities depend on the concentration of free RNA polymerase. In the absence of both Fis and ppGpp (Dfis DrelA DspoT strains) the P1 promoter behaves like a constitutive promoter with activities identical to those observed for P2 [45]. The promoter strength (S) is defined as its activity, V (initiations per promoter per time), normalized to the free RNA polymerase concentration, [Rf], when the promoter is far from being saturated with polymerase. By this definition, S is equal to the kcat/Km-value for the interaction between free RNA polymerase and promoter [46]. The effector ppGpp binds to RNA polymerase and thereby reduces the polymerase-P1 promoter interaction and thus the promoter strength, S. In addition, ppGpp reduces expression of the Fis protein factor from the fis promoter. Fis binds to an activator region on the DNA upstream of the rrn P1 promoters and thereby increases their strength nearly 3-fold (ref. [45], reproduced in Figs. 7c and 8c of ref. [1]). In this manner, high levels of ppGpp during slow growth in poor media reduce the rrn P1 promoter strength both directly through binding to RNA polymerase, and indirectly through the inhibition of Fis synthesis (see review in ref. [1]). As a result, in the pre-shift succinate minimal medium at high basal levels of ppGpp the P1 promoters of stable RNA genes are

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almost completely repressed. Under this condition, most of the stable RNA transcription originates at the constitutive P2 promoters. In contrast, in the post-shift glucose-amino acids medium the situation is reversed: nearly all transcription comes from the maximally up-regulated P1 promoters, whereas the downstream P2 promoters are “occluded” by the high density transcription from the upstream P1 promoters (45, reviewed in ref. [1]). Since the maximal strength of the P1 promoters is about twice that of the P2 promoters, the combined strength of the P1 and P2 promoters increases about twofold by the up-shift (45, reproduced in Fig. 8d of ref. [1]). Together with a 1.6-fold increased free RNA polymerase concentration (see the following section), this causes the observed 3.2-fold rapid increase in the stable RNA promoter activity at the time of the up-shift. It is not known how fast the concentration of Fis increases after a nutritional up-shift and how many minutes it takes until the P1 promoters of stable RNA genes achieve their maximum strength due to binding of Fis. Most likely, immediately after the shift transcription will come from both P1 and P2 promoters, and as transcription from P1 increases due to activation by Fis, transcription from P2 decreases correspondingly due to increased occlusion from upstream P1 transcription. Alternative interpretations of rrn promoter control [6,47] are discussed in Section 6 below. 4.6. Increased concentration of free RNA polymerase As mentioned above (Section 3.4), DNA is generally in excess for transcription within E. coli bacteria, implying that the rate of transcription is limited by the amount of active RNA polymerase, rather than by the amount of DNA [24]. This further implies (i) that most active promoters are not saturated with polymerase, so that they respond to changes in the concentration of free, functional RNA polymerase holoenzyme [Rf]; and (ii) that free RNA polymerase (Rf) is only a small fraction of the total cellular RNA polymerase (Rt). If under such conditions the amount of DNA in the cell with all its active genes were suddenly doubled, the total rate of transcription would remain almost unchanged, but the concentration of free RNA polymerase [Rf] and the rate of transcription per gene would decrease to one half (see Fig. 3 in ref. [1]). Similarly, if all promoters would double their strength due to some regulation, it would not significantly change their activity, but again the free RNA polymerase would decrease by 50%; i.e. the reduced concentration of free RNA polymerase would generate the same promoter activities as before because of the twofold increased promoter strength (in this assumed, hypothetical example), reflecting the fact that the total rate of transcription is limited by the total concentration of (mature) RNA polymerase. During growth in rich (post-shift) media most transcription comes from the stable rRNA and tRNA genes (e.g., at the maximum growth rate of 3.0 doublings/h rs/rt ¼ 0.9; i.e. 90% of all transcription is stable RNA and only 10% is mRNA; see Table 1 with data from ref. [3]). Therefore, it follows from the considerations above that any control that increases the strength of the stable RNA promoters after a nutritional up-shift to a rich growth medium would only marginally increase the activity of stable RNA genes unless, in addition, the concentration of free RNA polymerase would also increase. The concentration of free, functional RNA polymerase in the bacteria is not exactly known. Experiments with a minicellproducing E. coli K-12 strain growing at 2.5 doublings/h in LB medium have indicated that about 17% of the b and b0 -subunits of RNA polymerase are in the cytoplasm, whereas 83% of the core enzyme is sequestered with the DNA [48]. Since the assembly and maturation of RNA polymerase may last at least 5 min ([49], see also

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Fig. 3. Fractional synthesis rate of stable RNA (rs/rt, circles) and fraction of functioning RNA polymerase engaged in the synthesis of stable RNA (Js, triangles) as a function of time after an up-shift of E. coli B/r from succinate minimal to glucose amino acids medium in three different experiments done on different days [same as in Fig. 2 above; from Fig. 6 of ref. [11]; Copyright Ó 1980 American Society for Microbiology].

discussion in ref. [48]), one can expect for a 25-min doubling time that at least 15% of the total polymerase subunits in the cell are in the form of immature precursors of the active enzyme (2(5/25) ¼ 1.15). Therefore, most of the 17% cytoplasmic b, b0 subunits found in minicells were assumed to constitute this immature enzyme fraction. This is consistent with the observation that the polymerase activity of a minicell extract was below the measurable limit, i.e. less than 2.5% of the activity measured in extracts from an equal amount (mass) of whole cells [48]. This is also consistent with the conclusion above that the fraction of free, functional RNA polymerase should be very small under cytoplasmic conditions of excess DNA. Calculations for E. coli B/r based on observed total RNA polymerase concentrations and assumed promoter properties and activities for all genes have suggested values of about 5 and 8% free, functional RNA polymerase at 1.0 and 2.5 doublings/h, respectively [26]. The latter value, 8%, should have been detectable in the minicell extracts, but since this was not found, either the free RNA polymerase has been overestimated in those calculations or, alternatively, most of the free RNA polymerase is in rapid equilibrium with polymerase non-specifically bound to DNA. In this latter case the free RNA polymerase concentration could be lower in DNA-free minicells than the free plus non-specifically bound RNA polymerase concentration in the nucleoid. Bratton et al. [50] have constructed an E. coli strain with an inframe fusion of the gene for a green fluorescent protein (GFP) with the rpoC gene of the RNA polymerase. The b0 :GFP fusion did not significantly alter the growth rate, suggesting that the altered polymerase had normal activity. By also labeling DNA with a red fluorescent dye and using two-color fluorescence, they imaged the distributions of both RNA polymerase and chromosomal DNA within a live cell. By bleaching the green fluorescence in part of the cell and then observing the redistribution of fluorescent polymerase during the following 40-ms time intervals, they obtained information about the heterogeneous diffusion of the RNA polymerase within the cell. Particularly significant for the question above about the extent of nonspecific DNA binding is a result seen after treating the cells with rifampicin, which prevents transcript initiation. In this case (after transcription run-off), one expects all RNA polymerase to become either free or non-specifically bound to DNA. The observed distribution of the RNA polymerase under these conditions (Fig. 7B of ref. [50]) mirrors the distribution of the DNA, suggesting that most of the RNA polymerase not involved in transcription is non-specifically bound to DNA, and further suggesting that, indeed, the free RNA polymerase concentration should be lower in the DNA-free cytoplasm of the minicells than the free plus non-specifically bound concentration in the vicinity of the nucleoid.

Because of these and other technical difficulties, it has not been possible to measure the concentration of free RNA polymerase under in vivo conditions. Its concentration is expected to increase during a nutritional up-shift as a result of the repression of mRNA genes and due to the activation of a polymerase fraction that was inactive in the pre-shift medium (see the following section). For the up-shift from succinate minimal to glucose amino acids medium the extent of this increase is estimated to be about 5-fold, based on the observed rrn gene activities as follows. During steady-state exponential growth in the pre-shift succinate minimal medium and the post-shift glucose amino acids medium the rrn activities have been found to be respectively 6 and 60 rrn transcripts initiated per minute per rrn gene [29, reproduced in Fig. 6c of ref. 1], which corresponds to a 10-fold increased rrn (P1P2) gene activity. This ten-fold increase in the rrn activities is achieved in two distinct steps. The initial abrupt increase in rrn gene activity after the up-shift was found to be 3.2-fold and corresponds to an initial increase from 6 to 19 rrn transcripts initiated per minute per gene (6$3.2 ¼ 19). This abrupt increase is followed by a more gradual 3.2 fold increase (60/19 ¼ 3.2) to the steady-state level of about 60 transcripts/min (on average during the cell cycle) during the transition to steady-state growth in the post-shift medium. Steady-state exponential growth is achieved only after completion of this second phase. Assuming an approximate doubling of the combined strength of the two promoters of stable RNA genes immediately after the upshift from succinate minimal to glucose-amino acids medium (resulting from Fis activation and ppGpp depletion; see Section 4.5 above), we estimate that the free RNA polymerase concentration must initially increase about 1.6-fold in order to produce the observed rapid 3.2-fold initial increase in stable RNA transcription. As explained above, a small fraction of the polymerase molecules liberated from repressed mRNA genes (i.e. 43% of the total active RNA polymerase; see section 4.3 above) would suffice to produce this initial 1.6-fold increase in [Rf]. To produce the gradual 3.2-fold second-phase increase in rrn gene activity during post-shift growth (i.e. from 19 to 60 initiations/ min) requires the free RNA polymerase concentration [Rf] to increase further by the same factor of 3.2. This is because the P1 promoter strength is already maximal (due to full Fis activation and low ppGpp concentration) and because the P2 promoter is occluded due to the high level of transcription from the upstream P1 promoter. Therefore both the initial 1.6-fold abrupt increase and the following 3.2-fold gradual increase would produce a 5.1-fold (1.6$3.2 ¼ 5.1) total increase in [Rf] to drive the high level of transcription from stable RNA genes at the more rapid steady-state growth in the post-shift environment.

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Relative concentrations of free RNA polymerase during exponential growth of E. coli B/r in different media have also been estimated from the activities of the constitutive rrn P2 promoter [51]. According to those estimates, [Rf] equals about 0.08 relative units (one unit defined as the concentration at which rrn P2 promoters are 50% saturated) during growth at 0.67 doublings/h in the pre-shift succinate minimal medium, and about 0.40 relative units during steady-state growth at 2.14 doublings/h in the postshift glucose-amino acid-medium (Fig. 1A of ref. [51], reproduced in Fig. 1a of ref. [1]). This corresponds to a 5.0-fold increase in [Rf] (0.40/0.08 ¼ 5.0) after the medium shift, in agreement with the 5.1fold increase estimated above from the two-step post-shift increase in rrn promoter activities. Based on a theoretical model of the partitioning of RNA polymerases in bacteria, Klumpp and Hwa [47] have proposed a different interpretation of the changes in free RNA polymerase concentration and of the control of stable RNA synthesis during fast growth; however, experimental support for their alternative model has not been provided (see Section 6 below). 4.7. Increased RNA polymerase activity A contributing factor to the initial 1.6-fold increase in the free RNA polymerase concentration after the up-shift is an activation of RNA polymerase molecules that are transcriptionally inactive in the pre-shift medium. The active RNA polymerase fraction, bp, is defined as the fraction of total RNA polymerase in the bacteria that is engaged in RNA chain elongation at any instant. Experimentally bp is determined from the synthesis rates of mRNA and stable RNA, rm and rs, and the average chain elongation rates for mRNA and stable RNA, cm and cr. The value of bp increases from about 15% during slow growth in succinate minimal medium at 0.6 doublings/ h to about 36% during fast growth in LB medium at 3.0 doublings/h (Table 1). This means that the majority of RNA polymerase in the cell, although associated with the nucleoid, is not involved in active RNA chain elongation at any given instant. The proportion of inactive RNA polymerase is the difference (1bp) that varies between 64 and 85% of the total amount of RNA polymerase in the cell. It therefore seems that the fraction of non-transcribing RNA polymerase is remarkably high during growth in both poor and rich media. In a model of global transcription in E. coli we have previously estimated the proportions of five different kinds of inactive RNA polymerase at different growth rates: (i) newly synthesized immature enzyme; (ii) promoter-bound enzyme before initiating a transcript, especially at mRNA promoters with long promoter clearance times; (iii) polymerase temporarily idling (“pausing”) during transcription; (iv) polymerase non-specially bound to DNA; and (v) free holoenzyme, ready to bind to a promoter [26]. For the sum of (iii) and (iv) a value of 51% of total polymerase was estimated at 2.5 doublings/h (Table 4 in ref. [26]). In ppGpp-deficient bacteria growing at a similar rate bp increases about twofold from 30 to 60% of the total polymerase in comparison to ppGppproficient strains, and the rate of total mRNA synthesis is similarly increased [36]. It therefore appears that about 30% of the polymerase in ppGpp-proficient bacteria is transiently stalled at ppGpp-dependent transcriptional pause sites of mRNA genes [36,52]. This leaves about 20% of the total RNA polymerase to be either stalled at ppGpp-independent transcriptional pause sites or perhaps non-specifically bound to DNA [26]. It is not known how much RNA polymerase is non-specifically bound to DNA under in vivo conditions. In the up-shift from succinate minimal to glucose-amino acids medium considered here, bp, is estimated to increase about 1.5-fold from approximately 16% to 24% of the total RNA polymerase in the

11

cell (from interpolation of the bp data in Table 1). We suggest that this 1.5-fold increase in the fraction of total RNA polymerase that is actively engaged in transcription results from a reduction in transcriptional pausing during the synthesis of mRNA with ppGppdependent or -independent transcriptional pause sites. In addition, nonspecific binding of polymerase to DNA might also decrease after an up-shift, for example due to some topological change in the structure of the nucleoid. 5. Exponential accumulation of stable RNA during post-shift growth After clarifying the complex causes for the initial stepwise increase in the rate of stable RNA synthesis immediately after the bacteria enter a nutritionally enriched environment, we now address the second question: what maintains the continuing exponential increase in the amount of stable RNA (per unit volume of culture) at a rate whose value is set by its initial stepwise increase (Fig. 1a)? To answer this question, we begin with a theoretical relationship between ribosome and RNA polymerase synthesis that has been derived previously [14]. 5.1. Theoretical relationship between ribosome and RNA polymerase synthesis The essential elements of the connection between the rates of bacterial ribosome and RNA polymerase synthesis [14] can be summarized as follows. The rate of ribosome synthesis (dNr/dt), given as number of ribosomes synthesized per minute per unit volume of a bacterial culture, can be expressed by the equation:

dNr =dt ¼ Jr $cr $bp $Np




ðnuc=ribÞ;

(1a)

where the numerator on the right side represents the rate of rRNA synthesis in nucleotides per minute per unit volume of culture and the denominator is the number of nucleotides present in a 70S ribosome (nuc/rib ¼ 4566, Table 1 in ref. [3]. The four factors in the numerator are: Jr, the fraction of active RNA polymerase synthesizing rRNA; cr, the rRNA chain elongation rate in nucleotides polymerized per minute per average RNA polymerase engaged in rRNA synthesis; bp, the fraction of total RNA polymerase molecules that are actively engaged in RNA chain elongation at a given moment; Np, the total number of RNA polymerase molecules per unit volume of culture. Their product, i.e. the rate of rRNA synthesis, dRr/dt, is a constant fraction (¼0.86) of the rate of stable RNA synthesis dRs/dt, i.e. about 86% of the stable RNA synthesized is rRNA and 14% is tRNA (e.g. Table 1 in ref. [3]). During steady-state exponential growth, the first three factors in the numerator are constant in time, and the fourth factor, Np, increases to produce the exponential increase in the number of ribosomes, Nr (per unit volume of culture). Thus, the rate of ribosome synthesis is proportional to the number of RNA polymerases:

dNr =dt ¼ a$Np ;

(1b)

where a ¼ (Jr$cr$bp)/(nuc/rib). Values of Jr, cr, and bp for different growth rates are shown in Table 1.The rate of RNA polymerase synthesis, dNp/dt, in that culture can be expressed by a similar equation:

dNp =dt ¼ ap $cp $br $Nr


 ðaa=polÞ

(2a)

The numerator on the right side is the rate of RNA polymerase synthesis in amino acid residues going into the four subunits of the

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RNA polymerase core enzyme per minute per unit volume of culture. The denominator is the number of amino acid residues present in a bb0 a2 polymerase core enzyme (aa/pol ¼ 3707, e.g. Table 1 in ref. [3]). The four factors in the numerator are: ap, the fraction of active ribosomes engaged in the synthesis of the four RNA polymerase subunits; cp, the peptide chain elongation rate in amino acid residues polymerized per minute per average active ribosome; br, the fraction of total ribosomes that are actively engaged in peptide chain elongation at a given moment; Nr, the total number of 70S ribosomes per unit volume of culture. During exponential growth, the first three factors in the numerator are again constant in time, and only the number of ribosomes, Nr, increases to produce the exponential increase in the number of RNA polymerases, Np (per unit volume of culture). The equation can be similarly simplified:

dNp =dt ¼ b$Nr ;

(2b)

where b ¼ (ap cp br)/(aa/pol), with factor values at different growth rates shown in Table 1. Equations (1b) and (2b) express the important concepts that (i) the rate of ribosome synthesis in a growing culture is proportional (by factor a) to the increasing number of RNA polymerase molecules in that culture, and reciprocally, (ii) that the rate of RNA polymerase synthesis in a growing culture is proportional (by factor b) to the number of 70S ribosomes. By forming the second derivatives and mutually substituting the values for the first derivative from Equations (1a) and (2a), we obtain two symmetrical equations:

dðdNr =dtÞ=dt ¼ abNr d dNp =dt




dt ¼ abNp

(3) (4)

If a and b are constant in time, then the numbers of ribosomes and RNA polymerase molecules present in a given volume of culture (before or after an arbitrarily chosen zero time) are found from the integrals of these differential equations:


Nr ðtÞ ¼ Nr 0 $ekmt ; t < 0 or t > 0

(5)

Np ðtÞ ¼ Np ð0Þ$ekmt ; t < 0 or t > 0

(6)

where m is the growth rate in doublings per hour and k ¼ ln2/ 60 min (see Section 2.1 above). Nr and Np are seen to increase exponentially with time t at the growth rate m (in doublings per hour) given by the six growth medium-dependent parameters:

m ¼ ð60=ln 2ÞOab
   ¼ ð60=ln 2ÞO Jr $cr $bp $ap $cp $br ðnuc=ribÞ$ðaa=polÞ

(7) beg

With values for the six parameters (Table 1, footnotes ) Equation (7) gives the value for m equal to the growth rate at which the parameters were obtained (Table 1, footnote o: m ¼ 0.6e3.0). Since the equation follows from the definition of its parameters, this agreement is to be expected and does not explain the control of the growth rate. In the following the effect of changing the parameters a and b by a nutritional up-shift will be examined in order to provide additional insights into this control. 5.2. Ribosome and RNA polymerase synthesis after shifts to more nutritious minimal media If the factors a and b (defined above) increase stepwise at t ¼ 0 by the same factor f, then Equations (5) and (6) predict that the

numbers of ribosomes and RNA polymerases should immediately begin to increase exponentially at an f-fold increased rate and thus produce an f-fold increased growth rate after a nutritional up-shift (see ref. [14] for details). The question is: do a and b in fact increase stepwise by the same factor after an up-shift at t ¼ 0? If so, then it would mean that ribosome and RNA polymerase synthesis are coregulated. Such a coregulation of RNA polymerase synthesis with the rate of ribosome synthesis would keep the number of ribosomes increasing exponentially at a constant rate during post-shift growth. That is, it would answer the question at the beginning of this section: what causes the exponential increase in stable RNA after the up-shift? As will be shown in the following, the answer to this question depends on the growth media involved. The calculated values of a and b for different growth rates are shown in Table 1. We now consider a pre-shift culture growing at m ¼ 0.6 doublings per hour, i.e., at the lowest growth rate in Table 1, 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 per hour, i.e., the higher growth rates shown in Table 1. For each of these five (hypothetical) shifts, the factor increases in a and b (fa and fb respectively), were calculated (Table 1, footnotes p and q) and compared with the factor increase in the final growth rate, fm (Table 1, footnote r). First we consider a shift from a medium in which the cells grow at 0.6 doublings/h (e.g. in succinate minimal medium) to a medium that gives a final growth rate of 1.0 doublings/h (e.g. in glycerol minimal medium). The factor increase in m (fm) then equals 1.7 (1.0/0.6 ¼ 1.7). The factor increases in a and b (fa and fb) are seen to be 1.6 and 1.7, respectively (Table 1), i.e. they are both about equal to the increase in the growth rate. This suggests that the increase in the product (Jr$cr$bp) of factor a is equal to the increase in the product (ap$cp$br) of factor b, and that all six parameters determining a and b (i.e. Jr, cr, bp, ap, cp and br) assume their final postshift values immediately after the medium shift. In this case Equations (5) and (6) predict that ribosomes and RNA polymerases molecules should begin to increase exponentially at the new, 1.7fold higher rate immediately after the shift (at t ¼ 0), as observed. The agreement between the observations and the theoretical expectations suggests that in this up-shift (e.g. from succinate to glycerol minimal medium), RNA polymerase and ribosome synthesis are coregulated. The fractions of total protein that are RNA polymerase (ap) or ribosomal protein (ar), respectively, change, indeed, by the same factor, so that their ratio (ap/ar ¼ 0.12; Table 1, footnotel) is not affected by the shift. Similarly the ratio of the number of RNA polymerase molecules to the number of ribosomes remains constant during the shift (Np/Nr ¼ 0.24; Table 1, footnote k), corresponding to about one RNA polymerase made per every four ribosomes. As was seen above, the initial increase in the synthesis rate of rRNA (and thus of ribosomes) reflects a shift of RNA polymerase molecules from the transcription of mRNA genes to stable RNA (mainly rRNA) genes which, together with the higher chain elongation rate of rRNA in comparison to mRNA, produces the immediate (here 1.7-fold) increase in the product Jr$cr. Similarly the initial (1.7-fold) increase in RNA polymerase synthesis reflects the immediate increases in the peptide chain elongation rate (cp) and in the fraction of active ribosomes translating mRNA for RNA polymerase subunits (ap). Thus, the two simultaneous and equal (1.7fold) increases in the products (Jr$bp) and (cp$ap) produce the stepwise increase followed by continuing exponential increase in the numbers of ribosomes and of RNA polymerase molecules during post-shift growth, which results in the 1.7-fold increased final growth rate for the shift from succinate to glycerol minimal medium. This co-regulation of ribosomes and RNA polymerase can be understood as follows. The initially increased rate of rRNA synthesis

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causes an equally increased rate of ribosomal protein synthesis which, by necessity, is matched to the rate of rRNA synthesis: the nascent mRNAs of r-protein operons contain internal structural elements to which their cognate free r-proteins can bind to control the elongation, translation, and life times of their mRNAs. In this manner the amounts of the individual r-proteins are exactly adjusted to the amount of available rRNA, so that any excess of free r-proteins is kept at a minimum [20,53]. The mRNAs of the b-and b0 subunits of the RNA polymerase (from the rpoB and rpoC genes) are cotranscribed with the L11-L10 r-protein operons and are further controlled at the level of termination-antitermination at an attenuator in front of the rpoB gene [54e57]. During growth in minimal media, this attenuator stops about 75% of the transcripts coming from the upstream L11 and L10 r-protein operon promoters, so that only about one quarter of the transcripts continue through rpoBC. Accordingly, the number of RNA polymerases generated equals about one quarter of the number of ribosomes made. Next we consider a shift from succinate minimal medium, in which the cells grow at 0.6 doublings/h, to a more nutritious minimal medium that produces the higher growth rate of 1.5 doublings/h, corresponding to a 2.5-fold increase in m (1.5/0.6 ¼ 2.5), approximated by post-shift growth in glucose minimal medium, in which E. coli B/r grows at 1.42 doublings/h. In this case a and b increase 2.6- and 2.4-fold, respectively (Table 1); i.e. again about the same as the 2.5-fold increase in m. This indicates again a coregulation of RNA polymerase and ribosomes (and r-protein). Thus, during nutritional up-shifts involving only minimal media from a poor to a more nutritious carbon source, RNA polymerase and ribosomes are coregulated, such that their ratio remains constant: the number of RNA polymerase molecules synthesized corresponds to about 24% of the number of ribosomes (Table 1: Np/Nr ¼ 0.22 to 0.24 between m ¼ 0.6 and 1.5 doublings/h). Presumably this coregulation reflects at least in part the constant (about 76%) probability of termination of transcription at the b-attenuator in front of the rpoB gene that allows only about one quarter of the transcripts to continue from the r-protein to the RNA polymerase genes. This coregulation of RNA polymerase with ribosomes during growth in minimal media would explain the observed post-shift exponential increase in the amount of stable RNA and the observed post-shift accumulation kinetics of other cellular components as well. But, as shown in the following, the situation changes when the post-shift media are supplemented with amino acids. 5.3. Ribosome and RNA polymerase synthesis after shifts to amino acid-supplemented media For shifts to increasingly more nutritious, amino acidsupplemented growth media that produce growth rates between 2.0 and 3.0 doublings per hour, the increase in the factor a (fa) is found to be increasingly greater than fm, and the increase in b (fb) is correspondingly smaller than fm (Table 1; note that fm ¼ Ofa$Ofb according to Equation (7)). This implies that the ratio of RNA polymerase molecules to ribosomes (Np/Nr) gradually decreases during post-shift growth, from 0.24 to 0.14 at m (post-shift) ¼ 3.0 (Table 1) and indicates that RNA polymerase and ribosomes are no longer strictly coregulated. 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 fa must become greater than fm to compensate for the lower value of fb, reflecting the lesser accumulation of RNA polymerase. These relationships raise two new questions: (i) What causes the loss of the strict coregulation of ribosomes and RNA polymerase when amino acids are added to the post shift medium? (ii) What causes the gradual post-shift increase in the factor a that

13

compensates for the loss of strict coregulation and the accompanying reduced RNA polymerase synthesis? The reduced synthesis of RNA polymerase in rich growth media could reflect (i) a control at the transcriptional level (i.e. an increased probability of transcript termination at the b-attenuator), (ii) a lower frequency of translation of rpoB and rpoC mRNA compared to the mRNA of the up-stream r-protein genes, or both. There is evidence to suggest that both mechanisms could be operational. The termination at the b-attenuator is known to be responsive to the global RNA polymerase initiation capacity and the amount of total active RNA polymerase [54,55,58,59] and autogenous control of translation is known to keep the production of the b and b0 subunits in balance [60]. The molecular mechanisms that modulate transcriptional attenuation and autogenous translational control are not known. If the accumulation of RNA polymerase after a shift to rich growth media does not keep up with the accumulation of ribosomes, then the equations above predict a gradual reduction in the exponential rate of stable RNA and of ribosome synthesis (Fig. 1 in ref. [14]). Since this is not observed, the rate of ribosome synthesis must be increasingly stimulated, i.e. the factor a must further increase during post-shift growth to compensate for the lower RNA polymerase synthesis. The major component factor defining a is the fraction of active polymerase engaged in stable RNA synthesis, Js, describing the distribution of transcribing RNA polymerase between stable RNA and mRNA genes. In shifts from succinate to glucose-amino acids medium, Js (and with it Jr) does, indeed, approach its final higher value only gradually after the shift (Fig. 3, from Fig. 6 in ref. [11]), so that, as time passes, a growing fraction of RNA polymerase molecules transcribe stable RNA genes and a correspondingly decreasing fraction transcribe mRNA genes. This gradual redistribution of RNA polymerase from mRNA to stable RNA genes would keep (dRs/dt)/Rs constant during post-shift growth when fa > fb. This raises the new question: what causes the rise in Js during post-shift growth under these conditions? At the low levels of ppGpp during post-shift growth in rich media, the stable RNA promoters have their maximum strength (see Fig. 8d of ref. [1]); this means that the activity of stable RNA promoters can further increase only as a result of an increased concentration of free RNA polymerase. As was explained above (Section 4.6), in a shift from succinate minimal to glucose-amino acids medium, the rrn promoter activity increases at first 3.2-fold during the initial step, which sets the 3.2-fold increased growth rate, and then continues to increase gradually by another factor of 3.2 as a result of a further 3.2-fold gradual increase in the free RNA polymerase concentration (the total increase in free RNA polymerase concentration, including the initial 1.6-fold increase immediately after the up-shift, is about 5-fold; see Section 4.6 above). If all promoters were far from saturation, then this further post-shift increase in the free RNA polymerase concentration would equally increase stable RNA and mRNA promoter activities, so that Js (and also Jr) would remain constant after the initial step-wise increase in Js. However, as we have suggested previously, in rich media, mRNA promoters with their long promoter clearance times become saturated [51] when [Rf] increases. Therefore the further increase in [Rf] selectively elevates the relative transcription from the unsaturated stable RNA promoters [45] and thus could account for the delayed gradual second stage increase in Js to its final level during post-shift growth in rich media (Fig. 3). In other words, our model implies that the adjustment in the rate of stable RNA synthesis that keeps it exponential during post-shift growth in rich media (when the number of RNA polymerase molecules per ribosome, Np/Nr, gradually decreases), is a result of the gradual saturation of mRNA promoters at increasing free RNA polymerase concentrations.

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As an example of this we consider the hypothetical up-shift from m ¼ 0.6 to m ¼ 2.0, corresponding to fm ¼ 2.0/0.6 ¼ 3.3 (approximated by a shift from succinate minimal to glucose-amino acids medium). For this shift fa and fb are equal to 4.0 and 2.8, respectively (Table 1). This means that fa must have two components: initially a increases stepwise 3.3-fold, which sets the new growth rate, and then it gradually increases a further 1.21-fold until it reaches the value of 4.0 during final post-shift growth (3.3 $1.21 ¼ 4.0). This additional increase in a is the result of a gradual 21% increase in Js (and Jr), presumably due to a gradual saturation of mRNA promoters, which compensates for the decreasing number of RNA polymerases relative to ribosomes and keeps stable RNA increasing at a constant exponential rate during post-shift growth in rich media. 6. Alternative interpretations of rrn promoter control 6.1. Free RNA polymerase Klumpp and Hwa [47] have developed a theoretical model that predicts the growth rate-dependent partitioning of RNA polymerases in E. coli bacteria into three classes: (i) free polymerase, (ii) transcribing polymerase, and (iii) inactive polymerase, nonspecifically bound to DNA. According to their model, the largest fraction of RNA polymerase in the bacteria is nonspecifically bound to DNA and inactive rather than pausing during transcript elongation [26]. Their model predicts that the free RNA polymerase concentration increases with increasing growth rate to a constant level that is reached at growth rates greater than 2 doublings/h, i.e. in amino acid-supplemented media. The constant level of free RNA polymerase at growth rates above 2 doublings/h explains the observed constancy of mRNA promoter activities at these high growth rates [51]. In addition, it implies that the increasing rrn promoter activities during growth in rich media [at growth rates above 2 doublings/h; ref. [45] result from an as yet undefined control mechanism that stimulates transcription from rrn P1 and P2 promoters. This model is in contrast to our interpretation above (Section 4.7) that the constant activity of mRNA promoters at high growth rates reflects a saturation with RNA polymerase because of their longer promoter clearance times in comparison to stable RNA promoters and that the increasing rRNA promoter activities at high growth rates reflect an increasing concentration of free RNA polymerase [51]. To find out whether or not mRNA promoters are saturated at high growth rates Grummesson et al. [61] observed the effects of RNA polymerase overexpression and found that overproduction of functional RNA polymerase holoenzyme in rich, defined medium increases expression from rrn but not from mRNA promoters. This is consistent with the interpretation of Liang et al. [51] that mRNA promoters are saturated during growth in rich media and supports our interpretations in Sections 4.7 and 5.3 above, i.e., that the increasing rrn promoter activities after an up-shift into rich media result from increasing concentrations of free RNA polymerase, rather than from unknown rrn-specific regulatory factors. If most inactive RNA polymerase in the bacteria were nonspecifically bound to DNA, then one would expect inactive polymerase to be reduced in a replication control mutant with decreased DNA concentration. This, however, was not observed [24], again supporting the idea that most inactive polymerase is likely to be temporarily pausing during transcription [26]. 6.2. Ribosome synthesis in ppGpp-deficient bacteria Recently it was found that the RNA/protein ratio (R/P, a measure for the ribosome concentration Nr/P) and the RNA/DNA ratio (R/D),

were constant and maximal at different growth rates in ppGppdeficient (DrelA DspoT) bacteria [6]. From this finding the authors concluded that ppGpp is the sole determinant of R/P and R/D. They further suggested that the previously observed varying R/P and Nr/P ratios in ppGpp-deficient bacteria growing at different rates [36,45] were the anomalous result of spontaneous RNA polymerase mutations that occur frequently in this bacterial strain, where they suppress the effects of the total absence of ppGpp. With regard to this latter suggestion, we note that in our earlier experiments the cytoplasmic concentration of ppGpp in ppGpp-proficient bacteria was found to control the rrn P1 promoter strength directly as well as indirectly through the ppGpp-dependent control of Fis synthesis; in the absence of ppGpp the rrn P1 promoter behaves as a constitutive, uncontrolled promoter whose activity only depends on the concentration of free RNA polymease, Rf ([45], see Section 4.5 above]). This promoter strength was maximized when the bacteria were grown in rich media where the basal level of ppGpp is very low, as well as in the total absence of ppGpp in ppGppdeficient bacteria grown in the presence of 20 amino acids and different carbon sources [45]. Thus, the effect of the absence of ppGpp cannot have been suppressed by RNA polymerase or other mutations in our previous experiments using ppGpp-deficient strains. However, the rate of stable RNA synthesis that affects R/P depends not only on the ppGpp-dependent rrn P1 promoter strength, but also on the concentration of free RNA polymerase, Rf, which depends on several factors, including the control of RNA polymerase synthesis. From this, we suggest that the different experimental conditions used to vary the growth rate systematically led to higher Rf concentrations at low growth rates in the experiments of Potrykus et al. than in our earlier experiments. In this context, it is important to note that different strategies were employed to vary the growth rate of the ppGpp-deficient bacterial strain in the experiments of Hernandez and Bremer [36] and Zhang et al. [45] versus those of Potrykus et al. [6]. In the former case, the ppGpp-deficient bacteria were grown in media supplemented with all 20 amino acids, which were assumed to be required, based on reports from earlier studies of ppGpp-deficient bacteria [62], and the growth rate was varied by supplying different carbon sources. In contrast, Potrykus et al. grew their ppGpp-deficient bacteria in a basal glucose medium supplemented with only the 8 amino acids whose biosynthesis requires ppGpp; the remaining 12 amino acids apparently do not require ppGpp and are dispensable. They were then able to vary the growth rate by adding to the basal medium some or all of these remaining 12 of amino acids. The presence of all amino acids in the growth medium results in a maximum and constant ribosome efficiency (er) in both ppGpp-proficient (relAþ spoTþ) and ppGpp-deficient (DrelA DspoT) bacteria [36,45]. As a consequence, any changes in the growth rate (m) by supplying carbon sources of different nutritional quality are expected to be associated with varying ribosome concentrations (Nr/P), as implied in the equation that defines the exponential growth rate, me ¼ (Nr/P)$er (Section 2.3 above); this expectation was experimentally confirmed. (It might be thought that the ribosome efficiency also depends on energy supply, which might become rate-limiting at high ribosome concentrations in media with poor carbon sources, despite the presence of all amino acids in the medium; however, this was not found.) In contrast, increasing the number of amino acids in the growth medium is expected to increase the ribosome efficiency, er. At a constant ribosome concentration (Nr/P), as observed by Potrykus et al., the growth rate is then expected to be proportional to er; that is, at constant (Nr/P), the increase in er caused by the inclusion of additional amino acids in the growth medium results in a corresponding increase in the growth rate.

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A reduced value of er at low growth rates could be due to either a reduced rate of peptide chain elongation (cp) or a reduced fraction of active ribosomes (br, see Section 2.3), or both. Since earlier reports suggested that ppGpp-less bacteria need all 20 amino acids (see above) it is conceivable that the rate of transcription of the genes for the enzymes synthesizing those 12 amino acids now found to be not requiring ppGpp might still be abnormally low in the absence of ppGpp. This could lead to temporary amino acid limitations and thereby decrease the fraction of active ribosomes (br). During amino acid limitation, ribosomes beginning to translate new mRNA molecules will soon pause at a codon for the limiting amino acid, which leads to an accumulation of monosomes. Such accumulation of 70S monosomes at low growth rates has, indeed, been observed by Potrykus et al. [6]. When Nr/P remains constant at different growth rates, as in the experiments of Potrykus et al., then the rate of ribosome synthesis [(dNr/dt)/P] must be proportional to the growth rate (a mathematical property of the exponential growth function). At approximately constant rrn gene concentrations (rrn genes/P, due to the clustering of rrn genes near oriC; see Section 3.4) the rrn gene activities, and therefore (at constant rrn promoter strength in the absence of ppGpp), Rf must also be about proportional to the growth rate to produce the increased rRNA synthesis rate. In contrast, when Nr/P increases in proportion to the growth rate, as in our previous experiments, then the rrn gene activity, and thus Rf, must increase approximately with the square of the growth rate (again a mathematical consequence of the exponential growth function). In both our previous experiments and those of Potrykus et al., the highest growth rate was observed under identical conditions in glucose medium with 20 amino acids, and with identical results and thus presumably with identical Rf values. The differences were only observed at growth rates below the maximum, where Rf must have been lower in our previous experiments (increasing approximately with m2) than in the recent Potrykus experiments (i.e., increasing approximately with m). These differences in Rf are likely to reflect expected differences in the control of RNA polymerase synthesis (ap, the fraction of total protein that is RNA polymerase protein, see Table 1). In the Potrykus experiments the medium used to achieve a low growth rate resembles a minimal medium, where ribosomes and RNA polymerase are coregulated (see Section 5 above). This might explain why in their experiments both the free RNA polymease concentration and the rate of ribosome synthesis increase in proportion to m. In our previous experiments with all 20 amino acids always present, RNA polymerase and ribosome synthesis (ap and ar; Table 1) are no longer coregulated; i.e. the RNA polymerase synthesis is reduced (Section 5 above), which might explain the lower concentration of free RNA polymerase and thus the reduced rrn gene activities at low growth rates in our previous experiments in comparison to the experiments of Potrykus et al. An exact analysis of these differences requires additional measurements of RNA polymerase synthesis and activities in ppGpp-deficient bacteria grown under different conditions. However, the present analysis clearly shows that, in the absence of ppGpp, the R/P ratio may either vary or remain approximately constant, depending on the conditions used to vary the growth rate. 7. Summary To elucidate the mechanisms by which nutritional components in the environment of bacteria determine their rate of growth, we have evaluated the effects of a nutritional up-shift from succinate minimal medium to a medium containing glucose plus all 20 amino acids. This medium shift produces a 3.2-fold increased growth rate of wild-type E. coli B/r bacteria, from 0.67 to 2.14 doublings/h. The

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adaptation to the new environment begins with an immediate 3.2fold increase in the rate stable RNA (rRNA and tRNA) synthesis, which “sets” the new growth rate. This initial effect on the rate of stable RNA synthesis involves a multitude of regulatory events, starting with an increase in the cytoplasmic pools of amino acids and glucolytic intermediates. This causes a repression in the total rate of mRNA synthesis by 40% and an 8% activation of previously inactive RNA polymerase. Together this produces a 1.6-fold increase in the concentration of free RNA polymerase that becomes available for the transcription of stable RNA operons. The higher amino acid pools also cause increased tRNA charging, resulting in an increased rate of ribosome function, which, in turn, inhibits the SpoT ppGpp synthetase activity. The reduced level of ppGpp then increases the stable RNA promoter strength twofold, which, together with the 1.6-fold increase in free RNA polymerase causes the initial 3.2-fold increase in the rate of stable RNA synthesis. The next events that establish the final exponential growth rate occur gradually over several hours of post-shift growth and allow the bacteria to maintain the rate of stable RNA synthesis at the 3.2fold increased exponential rate. At the same time, this rate gradually becomes the exponential rate of accumulation of all cellular components. An essential component in this second adaptive process involves the regulation of RNA polymerase synthesis either at the transcriptional attenuator in front of the genes for the b-and b0 -subunits of the RNA polymerase and/or through autogenous translational control of rpoB and rpoC mRNA. During growth in minimal media, the b-attenuator stops about 75% of the transcripts coming from the upstream L11 and L10 r-protein operon promoter, so that about 25% of the transcripts continue through rpoBC. As a result, 1 RNA polymerase is generated for every 4 ribosomes made. In that case the theory predicts that in an up-shift from one minimal medium to another minimal medium of higher nutritional quality (e.g. from succinate to glucose minimal medium) the synthesis rates of ribosomes and of RNA polymerase will increase immediately at the time of the shift with the final postshift exponential rate, as observed. However, in rich post-shift media containing all amino acids the RNA polymerase synthesis lags behind the ribosome synthesis, possibly due to increased transcript termination at the b-attenuator. Without further control, this would gradually reduce the exponential rate of ribosome synthesis during post-shift growth. However, the lower synthesis of RNA polymerase is compensated by an increasing concentration of free RNA polymerase, presumably resulting from an increasing saturation of mRNA genes during post-shift growth in rich media. This keeps the rate of ribosome synthesis exponential at the initially established value that becomes the post-shift steady-state growth rate. The above considerations provide some insights into the factors controlling the adaptive processes that occur when E. coli transition from a poor to a rich nutritional environment. Nonetheless our understanding remains incomplete particularly with respect to the dissociation of RNA polymerase and ribosome synthesis in upshifts that involve the addition of amino acids and as a consequence an increase in the ribosome peptide chain elongation rate. Author contributions H.B. developed main theory and wrote the manuscript, P. D. wrote the manuscript and M.E. developed auxiliary theoretical concepts and wrote the manuscript. Acknowledgments We wish to thank Dr. Michael Pavlov for very valuable discussions on the manuscript. This work was supported by the Swedish

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