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J Bacteriol, January 1998, p. 265-273, Vol. 180, No. 2
0021-9193/98/$04.00+0
Copyright © 1998, American Society for Microbiology. All rights reserved.
Initiation and Velocity of Chromosome Replication
in Escherichia coli B/r and K-12
Meeshel
Bipatnath,1
Patrick P.
Dennis,2,* and
Hans
Bremer1
Molecular and Cell Biology Programs,
University of Texas at Dallas, Richardson, Texas
75083-0688,1 and
Department of
Biochemistry and Molecular Biology, University of British Columbia,
Vancouver, British Columbia V6T 1Z3, Canada2
Received 8 September 1997/Accepted 13 November 1997
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ABSTRACT |
The macromolecular composition and a number of parameters affecting
chromosome replication were examined over a range of exponential growth
rates in two common Escherichia coli strains, B/r and K-12 AB1157. Based on improved measurements of DNA after treatment of
exponential cultures with rifampin, the cell mass per chromosomal replication origin (initiation mass) and the time required to replicate
the chromosome from origin to terminus (C period) were determined. For these two strains, the initiation mass approached values of 8 × 10
10 and 10 × 1010 units of optical density (at 460 nm) of culture mass
per oriC, respectively, at growth rates above 1 doubling/h
(at 37°C). The amount of protein per oriC decreased with
increasing growth rate for AB1157 and remained nearly constant for the
B/r strain. The C period decreased for both strains in an
essentially identical manner from about 70 min at 0.6 doublings/h to
about 33 min at 3 doublings/h. From the initiation mass and
C period, relative or absolute copy numbers for genes with
known map locations can be accurately determined at different growth
rates. At growth rates above 2 doublings/h, when chromosomes are highly
branched, genes near the origin are about threefold more prevalent than genes near the terminus. At a growth rate of 0.6 doubling/h, this ratio
is only about 1.7, which reflects the lower degree of chromosome branching.
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INTRODUCTION |
During exponential growth of a
bacterium such as Escherichia coli, chromosome replication
and other aspects of macromolecular synthesis are maintained in precise
balance. At a given growth rate, the activity of a particular gene,
measured either as RNA transcripts or as protein product, depends both
on genetic control of the gene in question and on the copy number. The
average copy number of a gene per unit of cell mass depends on (i) the
location of the gene relative to the replication origin and terminus,
(ii) the velocity of replication fork movement, and (iii) the timing of
initiation of replication at the origin. The location or map position
of a gene is determined by standard genetic or molecular techniques.
The replication velocity is given by the time required to replicate the
chromosome (C period) and was first measured by Helmstetter
and Cooper (20) for E. coli B/r. The timing of replication initiation is characterized by the cell mass or by the
amount of protein per replication origin at the time of initiation (initiation mass, Mi [16]).
More conveniently, a related parameter (M0) is
used; this is the cell mass or protein in a given volume of exponential
culture, divided by the total number of oriC copies in that
volume. The two parameters are related by the simple relationship M0 = ln 2 · Mi
(10). Of the two parameters, C and
M0, the former determines the extent of
chromosome branching and thereby affects the copy number of particular
genes depending on their map location; the latter determines the
overall DNA concentration and thereby affects the transcription of all
genes by influencing the concentration of free RNA polymerase.
Few attempts have been made to measure the initiation mass,
particularly for E. coli K-12 strains. Because of this,
uncertainty exists as to whether the initiation mass is constant
(16), increases (15), or decreases
(32) with increasing growth rate. Moreover, there is also
uncertainty about whether the C period is constant at growth
rates above 1 doubling per h (20) or whether it continues to
decrease with increasing growth rate (14). In this work, we
have attempted to carefully measure the initiation mass
(M0) and replication velocity (C
period), in addition to DNA, RNA, and protein content, for E. coli B/r and the K-12 strain AB1157 at different growth rates. The
results supplement and extend our previously reported values for the
macromolecular composition of E. coli B/r (11).
In the accompanying Appendix, we have used the measurements of
M0 and C to determine the copy number
of various loci located around the bacterial chromosome. This provides
a basis for distinguishing between the contributions of gene dosage and
the effects of genetic regulation on the level of expression of a gene.
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MATERIALS AND METHODS |
Bacterial strains and growth conditions.
The E. coli K-12 strain AB1157 (2) requires arginine,
histidine, proline, leucine, threonine, and thiamine. The E. coli B/r A strain HB123 requires phenylalanine and threonine.
Cultures were grown at 37°C in a shaker water bath, with medium C
(18), supplemented with 0.2% (wt/vol) carbon source
(succinate, glycerol, or glucose) and required amino acids at 50 µg/ml and thiamine (for AB1157) at 2 µg/ml. To obtain faster
growth, 0.2% Difco Casamino Acids plus 50 µg of tryptophan per ml
and 500 µg of serine per ml or Luria-Bertani (LB) medium
(27) with 0.2% glucose were used.
For consistency, the succinate minimal medium for both strains was
supplemented with the same five amino acids (arginine, histidine,
proline, leucine, and threonine required by AB1157). In our hands,
strain AB1157 grew at almost the same rate in succinate minimal medium
as it did in glycerol minimal medium. This was surprising since
glycerol, a glycolytic intermediate, is considered to be more energy
rich than succinate, a Krebs cycle intermediate. With five required
amino acids, these media used are not typical minimal media; it is
likely that some of the amino acids were also metabolized as a carbon
source.
For both
E. coli B/r and AB1157, threonine, when present at
low concentrations, is depleted from the medium in overnight cultures.
The resulting amino acid starvation produced a growth lag and
perturbed
the physiology of experimental cultures started from
such overnight
cultures. To avoid such starvation effects, the
threonine concentration
in overnight cultures was increased to
200 µg/ml. Experimental
cultures of bacteria were started by 1:500
(poor media) to 1:2,000
(rich media) dilution of an overnight
culture in a medium equal to or
poorer than the medium to be used,
in order to avoid a nutritional
shift-down associated with a long
growth lag (
24). Except
for cultures in LB medium, growth was
monitored by measuring the
turbidity, or optical density (OD)
at a 460-nm wavelength
(OD
460), with a 1-cm light path. In the
case of LB medium,
the OD
600 was measured. By monitoring both
the
OD
460 and the OD
600 of cultures growing in
different media,
parallel growth curves were obtained, differing by a
factor of
1.60 ± 0.03 (OD
460/OD
600),
which was used to convert OD
600 units
into
OD
460 units for cultures in LB medium. Rifampin at 300 µg/ml
(final concentration) was added at an OD
460 of
about 0.7 for minimal
medium or at an OD
600 of about 0.43 for LB medium.
Collection of bacteria on glass fiber filters.
Bacteria in
culture samples (2.5 ml for DNA; 4.0 ml for RNA and protein) were
collected on 24-mm glass fiber filters. Whatman GF/F filters with
0.7-µm maximum pore size retained 99% of the bacterial mass under
all conditions. For samples used for DNA determinations, collection
filters were presoaked in 1 mM perchloric acid (PCA) to reduce the
background in the diphenylamine assay. To remove small metabolites, the
bacteria were treated with 0.45 M PCA at 0°C before filtration. The
bacteria were washed on the filters with 1 mM PCA, and the filters were
placed into vials (scintillation vials) for further processing (see
below). Since LB medium contains significant amounts of
acid-precipitable oligonucleotides and polypeptides, bacteria in LB
medium were immediately collected on glass fiber filters without acid
precipitation and washed with 1 mM MgSO4 at 0°C. After
this washing, about 3 ml of 0.5 M PCA was slowly filtered through the
same filter with reduced vacuum. When samples contained rifampin,
filters were further washed with acetone to remove all visible
rifampin.
Determination of DNA in samples of bacterial culture.
DNA
was determined by the diphenylamine assay (13) as follows.
To each vial with a dry filter, 0.5 ml of 1.6 M PCA was added, and the
closed vials were incubated at 70°C for 30 min before the addition of
1 ml of diphenylamine reagent (1 g of diphenylamine, reagent grade
[Kodak], and 125 µl of aqueous solution of 32-mg/ml acetaldehyde
per 50 ml of glacial acetic acid). After incubation at 30°C for 14 to
16 h overnight, reaction mixtures were clarified by filtration
through glass fiber filters before the A600 was read. For filtration, a special apparatus designed to facilitate the
collection of small volumes of filtrate was used. Samples obtained with
medium without bacteria and processed in an identical manner served as
medium blanks. Assays of known amounts of deoxyadenosine (AdR) or calf
thymus DNA (CT-DNA) for calibration were incubated at the same time;
for these assays, acid precipitation and filtration steps were omitted
(see Appendix for further details).
Concentrations of DNA or AdR used for calibration were measured by
their UV absorbance at pH 12 (0.01 M NaOH), with molar
extinction
coefficients (
260 =
A260 of 1 mM
solution at pH 12)
of 15.4 for AdR and 10.61 for CT-DNA (calculated
from GC content
= 43% [
23]). Assay values
increased linearly with the amount
of DNA up to
A600 values of at least 1.0. The
E. coli genome was
assumed to be 4.7 Mbp (
3).
RNA and protein determinations.
Four to five 4-ml samples
were taken from exponential cultures over a period of one to two
generations and added to 0.16 ml of concentrated PCA at 0°C. Bacteria
were collected on glass fiber filters as described above. For cultures
in LB medium, the medium was again first removed by filtration and
washed out before acid treatment of the filter as described above. In
addition, three samples of medium without bacteria were taken as medium
blanks. The dried filters were placed in scintillation vials, and 2.0 ml of freshly prepared 0.2 M NaOH was added to dissolve proteins and
hydrolyze RNA. After overnight incubation at 30°C, 0.5 ml of the
alkaline solution was removed for protein determination, by the Lowry
assay (26) as described elsewhere (12). To the remaining 1.5 ml of hydrolysate, an equal volume of 0.5 M PCA was added
to precipitate protein and DNA at 0°C. The precipitate and debris
were removed from the samples by filtration through glass fiber
filters. The UV absorption of the clear filtrates (RNA hydrolysates)
was measured at 260 nm. The absorption spectrum suggests that the
samples were not contaminated to a significant extent by UV-absorbing
nonnucleotide materials. The A260 values were
converted into RNA nucleotides by assuming that one
A260 unit (at acid pH) corresponds to 93 nmol of
RNA nucleotides, calculated from the base composition of E. coli RNA (28).
For calibration of the Lowry assay, a concentrated stock solution of
bovine serum albumine (BSA) was first diluted into 0.2
M NaOH to a
final concentration of approximately 1 mg/ml. From
this solution, a
series of further dilutions into 0.2 M NaOH were
made to obtain
concentrations between 0 and 1 mg/ml in steps of
0.2 mg/ml; duplicate
0.5-ml aliquots from each dilution were assayed
by the addition to 2.5 ml of alkaline copper reagent (0.02% [wt/vol]
sodium tartrate,
0.01% [wt/vol] CuSO
4, 0.2 M
Na
2CO
3, 0.1 M NaOH)
and 0.5 ml of 1 N
Folin-Ciocalteu's phenol reagent (Sigma Chemical).
The
A750 of the assay was read after 3 to 4 h.
BSA concentrations were determined from their
A280. After a sample of BSA was dried for
24 h at 50°C under vacuum in a tube
of known weight, the BSA was
weighed with an analytical balance
and dissolved in a given volume of
water. The
280 of the aqueous
solution was found to be
0.621/mg. In previous work, this value
was determined to be 0.695 (
30). The difference presumably reflects
differences in the
particular commercial BSA preparation.
The
A750 of the protein assay increases
nonlinearly with the protein concentration; the calibration curve could
be approximated
by a parabola, similar to that described below for the
mass density
(equation 9 [
Appendix]). The parameters defining this
parabola were
obtained by a best-fit method (see Fig.
A1 [
Appendix]
and Table
1)
and used to convert the observed
A750 values into protein concentrations.
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RESULTS |
Principle of the method.
Figure
1 illustrates an idealized plot of the
accumulation of DNA (measured in genome equivalents) in an exponential
culture with a doubling time of 45 min. Since most chromosomes in the culture are in the process of replication, they will have multiple origins (in this case, two) and a single terminus and will contain more
than one genome equivalent of DNA. The numbers of replication origins,
termini, and DNA genome equivalents (NoriC,
NterC, and G, respectively) increase
exponentially in a parallel fashion with the same doubling time (
),
such that, in a semilog plot of these parameters versus growth time,
the horizontal distance between the origin and terminus curve
represents the time required to replicate the chromosome from origin to
terminus (C period) and the vertical distance between the
origin and DNA curve represents the number of origins per genome
equivalent of DNA (NoriC/G, or 
G;
Fig. 1).
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FIG. 1.
Theoretical accumulation of DNA in an exponential
culture of E. coli treated with rifampin. The method used to
find the number of replication origins and the C period from
the accumulation of DNA after stopping initiations with rifampin (Rif)
is illustrated. Solid line, DNA in genome equivalents (Geq) in a given
volume of culture, normalized to 1.0 at t = 0 when
rifampin is added to the culture; stippled line, number of replication
origins (Ori); dotted line, number of replication termini (Ter). The
horizontal distance between the origin and terminus curve corresponds
to C, and the vertical distance between the origin and DNA
curve (G) represents the number of origins per genome equivalent of
DNA. Relat., relative.
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Rifampin inhibits initiation of transcription, and its action
indirectly blocks initiation of new rounds of replication without
affecting elongation and completion of replications already in
progress
(
31). As a consequence, the number of origins in a
culture
remains constant at a value equal to the number of origins
present at
the time of rifampin addition. At the same time, the
rate of
accumulation of DNA begins to diminish because there are
no new
replication forks generated by initiation and existing
forks gradually
reach the replication terminus and cease to function.
The number of
termini continues to increase at an exponential
rate until all forks
have reached the terminus. At this point,
the numbers of origins,
genome equivalents of DNA, and termini
are all equal; that is, the
chromosomes are fully replicated,
contain a single genome equivalent of
DNA, and possess a single
origin and a single terminus.
The experiments to be described below measure the accumulation of DNA
after the addition of rifampin to exponential cultures.
The factor
increase in DNA after rifampin addition (
G) is a measure
of the number of origins per genome at time zero (Fig.
1). Similarly,
the time required for the DNA accumulation curve to reach the
plateau
is a measure of the
C period.
Determination of chromosomal replication origins and replication
velocity.
The number of replication origins, oriC, and
the replication velocity (C period; the time to replicate
the chromosome from origin to terminus) were determined for the
E. coli B/r A strain HB123 and the K-12 strain AB1157 by
monitoring the accumulation of DNA after the addition of rifampin (see
above and Appendix, first section). The nonradioactive method used here
gives absolute values for DNA genome equivalents and origins. Figure
2 shows an example for strain B/r grown
in LB medium. During exponential growth before the addition of
rifampin, both mass density and DNA increased with the same 21-min
doubling time. From the data in Fig. 2a and b, the DNA/mass ratio
(G/M) was determined to be 7.3 × 108
genome equivalents of DNA per OD460 unit of culture mass.
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FIG. 2.
Accumulation of DNA in E. coli B/r grown in
LB medium after treatment with rifampin (Rif) to inhibit initiation of
rounds of replication. (a) Growth curve (OD600); (b) DNA
accumulation (A600 of diphenylamine assay); (c)
replot of the DNA curve in panel b after normalization to 1.0 at
t = 0, the time of rifampin addition. The parameter  is defined as the difference of the exponential curve (dashed) minus
observed values. The solid curve was generated as a best fit by
equation 3 (Appendix). (d) The  curve extrapolates to
d = 2.5 min on the abscissa. This value is an estimate
of the delay in the action of rifampin on initiation of replication
(see text and Appendix). Relat., relative; Theor., theoretical.
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To find the number of replication origins and the
C period
from the DNA curve, the observed DNA values
(
A600 in Fig.
2b) were
normalized to 1.0 at the
time of rifampin addition (
t = 0; Fig.
2c), and these
normalized DNA values were subtracted from the
exponential term
2
t/
(dashed curve in Fig.
2b and c). The
square root of this difference
was plotted as a function of the
sampling time (
in Fig.
2d). Extrapolation of the
curve
to the time axis gives a value that corresponds to
the delay (
d)
in the action of rifampin on initiation of
chromosome replication
(
8). In the experiment whose results
are shown in Fig.
2,
d was estimated to be 2.5 min (Fig.
2d). In other experiments, the
extent of the delay varied both as a
function of the growth medium
and from culture to culture in a given
medium. In minimal media,
delays of up to 12 min have been observed
(see Discussion). From
the delay (
d) and the culture
doubling time (
), an expectation
for the DNA accumulation after
rifampin addition was calculated
(with equation 3 [
Appendix]) with an
assumed value for
C. By reiterative
calculations in which
the value of
C was varied, the best fit
(solid curve in Fig.
2c) with observed data points was obtained;
this happened when
C was set at 33 min (Fig.
2c). Thus, a
C period
of 33 min most closely approximates the kinetics of DNA accumulation
after rifampin treatment of the culture. In these curves, points
taken
between 10 and 30 min after rifampin addition often fell
slightly below
the theoretical best-fit curve. This suggests that
the replication
velocity may be somewhat reduced in the presence
of rifampin.
Similar experiments were carried out with
E. coli B/r and
the K-12 strain AB1157 growing in a variety of media that gave
exponential
growth rates of between 0.6 and 3.0 doublings/h. For both
strains,
the estimate for the length of
C in these
experiments was not
constant; instead,
C decreased from
about 70 min in duration at
a growth rate of 0.6 doublings/h to about
33 min at a growth rate
of 3.0 doublings/h (Fig.
3a). The estimates of
C for
B/r and K-12
strains appear to fall on the same decreasing curve that
extrapolates
to
C = 80 min for µ
0 (µ is the
bacterial growth rate in doublings
per hour, equal to 60/
).
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FIG. 3.
Growth rate variation in the velocity of chromosome
replication. (a and b) C period (in minutes in panel a;
period as a fraction of culture doubling time, , in panel b) and (c)
number of origins per genome equivalent of DNA are plotted as functions
of growth rate for E. coli B/r (circles) and the K-12 strain
AB1157 (triangles). The media used were (in the order of increasing
growth rate) succinate minimal (open symbols), glycerol minimal,
glucose minimal, glucose-amino acids, and LB (solid symbols). Genome
equ., genome equivalents.
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The velocity of the replication forks relative to the culture growth
rate (i.e., the ratio of the
C period and doubling time,
C/
) determines the extent of chromosome branching (see
Appendix).
For example, when
C is less than
(i.e.,
C/ < 1) there are either
zero or two forks per
chromosome, and when
C is greater than
(
C/ > 1), there are either two or six forks per chromosome. As
the ratio
C/
increases, the proportion of chromosomes with the
higher number of forks increases. From the
C-period data in
Fig.
3a, the curve describing
C/
as a function of growth
rate has
been calculated (Fig.
3b). At high growth rates above 1.5 doublings/h,
C/
was found to approach a constant value
(1.6 [Fig.
3b]), which
means that the replication velocity changes to
about the same
extent as the exponential growth rate. At growth rates
below 1.5
doublings/h,
C/
appears to extrapolate to a
value of zero or
near zero for very slowly growing cultures. If this
extrapolation
is valid, it implies that in poor medium, exponential
mass doubling
times increase more rapidly than the
C period.
Consequently, in
very slowly growing cultures, only a small proportion
of cells
will be in the process of replicating their chromosomes, so
that
most cells will have either a single unreplicated chromosome or
two fully replicated chromosomes.
The number of
oriC copies per genome equivalent of DNA is
equal to the value of
G after rifampin addition (Fig.
1).
G depends
on
C/
and was calculated from the
data in Fig.
3b (with equation
1 [
Appendix]). In our experiments,
G had a maximum value of about
1.65 at the highest growth
rates (Fig.
3c). Values of
G > 1.0
indicate
branched chromosome structures, i.e., structures with
a higher
proportion of origins. The apparent plateau in the
G curve at growth rates above 2.0 doublings/h indicates that the
extent
of chromosome branching does not further increase during
fast growth
and is reflected in a constant
C/
value (Fig.
3b).
During
slow growth, the
G curve extrapolates to 1.0, i.e., one
origin per genome equivalent, corresponding to unreplicated (or
fully
replicated) chromosomes. This would be expected if the culture
doubling
time became much longer than the chromosome replication
time
(
C/
0 for µ
0 [Fig.
3b]).
Protein and RNA determinations.
In addition to DNA, protein
and RNA were measured in exponential cultures of E. coli B/r
and AB1157 (Fig. 4). The two strains were
similar in their macromolecular composition, and their compositions changed nearly in parallel as the exponential growth rate was changed.
The values for the B/r strain are similar to, and, because of the
refined methodologies employed here, presumably more accurate than, our
previously reported values (11). For E. coli K-12 strains, no systematic studies of this kind have been reported.
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FIG. 4.
Protein (a), RNA (b), and DNA (c) per mass unit of
culture (OD460) were measured as functions of growth rate
for E. coli B/r and the K-12 strain AB1157. The media and
symbols used are as described in the legend to Fig. 3. aa, amino acids;
nuc, nucleotides; Geq, genome equivalents.
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Initiation mass for B/r and K-12 strains.
The cell mass per
origin (initiation mass, M0) was obtained from
the number of origins per genome equivalent of DNA (G
[Fig. 3b]) and the number of genome equivalents of DNA per
OD460 unit of cell mass (Fig. 4c). For E. coli
B/r, the initiation mass reached a nearly constant value at growth
rates above 1.3 doublings/h, equal to 8 × 1010
OD460 units per oriC (Fig.
5a). This is in good agreement with a
previous report (15), in which the same plateau was reached at 1.6 doublings/h. The initiation mass for the K-12 strain was about
25% higher than the B/r initiation mass and was equal to 1.0 × 109 OD460 units per oriC.
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FIG. 5.
Relationship between initiation mass and exponential
growth rate. Initiation mass expressed as OD460 units of
culture mass per oriC (a) and as total protein in amino acid
residues per oriC (b) as a function of the growth rate is
illustrated. The media and symbols used are as described in the legend
to Fig. 3. Open symbols, succinate medium; solid symbols, other media.
aa, amino acids; Prot., protein.
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The initiation of chromosome replication has often been linked to
protein accumulation (reviewed in reference
9). The
amount
of protein per origin was therefore calculated by multiplying
the average mass-per-origin values shown in Fig.
5a by the average
protein-per-mass values shown in Fig.
4a. The calculation indicates
that for strain B/r, protein per origin was nearly constant, ranging
between 3 × 10
8 and 4 × 10
8 amino
acid residues per
oriC, in agreement with previous reports
(
11). In LB medium, the amount of protein per origin may be
slightly lower. For the K-12 strain, the amount of protein per
oriC decreased from about 6 × 10
8 to
4 × 10
8 amino acid residues in the range from 0.75 to
2.5 doublings/h.
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DISCUSSION |
Deviations of observed parameters from apparent growth rate
functions.
Schaechter et al. (29) found that the
composition of bacteria grown in different media is uniquely correlated
with the growth rate. Since then, physiological parameters have often
been plotted as functions of growth rate. However, the growth rate is
not an independent variable; like all other parameters, it depends on the composition of the growth medium, which does not vary in a continuous manner. Therefore, data points obtained with different growth media may not represent a defined function of growth rate, and a
curve connecting different observed points should not necessarily imply
that actual points exist on this curve between and beyond observed
points.
For AB1157 grown in glucose-amino acids medium, the values for the
C period, and thus also the values for
C/
and
oriC per
genome (Fig.
3, triangles at 2 doublings/h),
representing four
repeats of the same experiment done on different
days, are on
the average significantly above the curves drawn. Because
every
observed point shown in Fig.
3 was obtained as an average from
many samples taken from a single exponential culture (as in Fig.
2),
the fluctuations of the points in the plot of Fig.
3 are assumed
to
represent mainly variations from culture to culture, rather
than
inaccuracies of the measuring data. The exponentially decreasing
curve
in Fig.
3a and the monotonously increasing curves in Fig.
3b and c
appear to be reasonable interpretations of the trend.
If the curves had
been drawn through the averages of the measuring
points, the
C/
and
oriC-per-genome curves for AB1157 would
show
a maximum, and the
C-period curve would show a bump, at
2 doublings/h.
Growth rate dependence of the initiation mass.
For both
E. coli strains studied here, the cell mass per replication
origin (M0) approached nearly constant levels
with increasing growth rate; the values for the K-12 strain were about
25% higher than the values for E. coli B/r (Fig. 5a).
Observations obtained with a flow cytometer have suggested that the
initiation mass for E. coli K-12 decreases with increasing
growth rate (32). The discrepancy might be due to
differences in measurement of cell mass. The flow cytometer measures
the light scattering of individual cells, whereas we have used culture
turbidity as a measure for mass density. When the initiation mass was
expressed in terms of protein per oriC, it decreased with
increasing growth rate for AB1157 (Fig. 5b). This result agrees with
the work of Wold et al. (32), who used a fluorescent protein
dye in connection with the flow cytometer to estimate protein per
oriC. For the control of replication, as well as for the
calculation of gene dosages and absolute gene activities, protein
rather than culture turbidity per origin is assumed to be the more
relevant parameter.
The constancy or nonconstancy of the initiation mass has been
frequently discussed in the literature (e.g., see references
9,
16, and
22). In consecutive
cell cycles within a given
culture, replication is not initiated at the
same exact time (cell
age) during the cell cycle. Instead, replication
is initiated
when the cell has reached a particular mass, or amount of
protein.
The cell age at which this happens varies from one division
cycle
to the next because the timing of the division event is
imprecise.
For this reason, the mass of newborn daughter cells shows a
stochastic
variation. This has been shown elsewhere for synchronous
cultures
(
6) and more recently for exponential cultures
growing very
slowly with nonoverlapping rounds of replication
(
5). This
indicates that replication is linked to the
accumulation of cell
mass or, more likely, to the accumulation of some
protein. The
values for the cell mass or protein at the time of
initiation
vary discontinuously with the growth rate, showing twofold
steps,
but the number of replication origins per cell in which
initiation
occurs also varies with twofold steps, so that the cell mass
or
protein per replication origin becomes a smooth function of the
growth rate (
16). This suggests that a certain structural
protein
which is made as a constant proportion of total protein is
required
in stoichiometric amounts per
oriC to trigger
initiation of replication;
this protein is assumed to accumulate during
the cell cycle either
at
oriC (
17) or at a
structure that also doubles at the time
of replication initiation
(
9). However, the constancy of the
initiation mass from
initiation to initiation within a given culture
must be distinguished
from potential changes in the initiation
mass at different growth
rates. At different growth rates, the
protein (or mass) per origin
would be constant only if the initiation
protein were synthesized as a
constant fraction of total protein
(or mass), independent of the growth
rate. There is no compelling
reason to believe that this is or should
be the case.
Growth rate dependence of the replication velocity.
Available
literature values for the C period have been compiled and
plotted as a function of growth rate by Helmstetter (19). Those data suggest a decreasing C period when the growth
rate increases from about 0.1 to 1.0 doublings/h and a nearly constant C period of about 43 min at growth rates between 1.0 and 2.5 doublings/h. Our data (Fig. 3a) showed a gradual decrease in the
C period with increasing growth rate, in agreement with
previously determined values of C from this laboratory (Fig.
4 in reference 14). By inclusion of cultures grown
in LB medium, the lowest values observed for C were 33 to 34 min at 3.0 doublings/h (Fig. 3b). The discrepancies between our new
values and some of the previously reported values might result from the
more precise determination in this work of the delay in the cessation
of replication initiation after the addition of rifampin (as in Fig.
2d).
Our method for determination of
C depends on the assumption
that rounds of replication go essentially to completion in the
presence
of rifampin. That this is probably the case has been
shown elsewhere by
flow cytometry (
31), which shows the accumulation
of
discrete bands of DNA during rifampin treatment. These bands
represent
integer multiples of genome equivalents; i.e., the cells
have one, two,
four, or eight fully replicated chromosomes, depending
on the
exponential growth rate before the drug treatment. This
observation
does not rule out the possibility that some last sequences
near the
replication terminus are not replicated in the presence
of rifampin.
However, this would not significantly affect our
calculation of
C.
Delay in the action of rifampin on initiation of replication.
The analysis of DNA accumulation curves after rifampin addition
indicated a few minutes' delay in the action of rifampin on initiation. This delay was 1 to 3 min in rich media and 5 to 12 min in
minimal media (Fig. 2d and other data not shown). During this delay,
DNA continues to accumulate exponentially. An alternative interpretation of this apparent delay would be that rifampin stops initiation immediately but that replication forks pause for a few
minutes at a second control site shortly after initiation. Such
temporary stalling of replication forks close to oriC has been shown elsewhere for Bacillus subtilis (25).
If that were also true for E. coli, then the C
periods estimated here (Fig. 2b) would represent the times for
replication of the chromosome from this putative pause site, rather
than from oriC, to the terminus. For estimating gene
dosages, it does not matter how the delay is interpreted as long as the
pause site is close to oriC. For the mechanism of
replication control, the distinction would be important, however, since
a pause site would suggest that the timing of replication is controlled
at two levels, at oriC and at a downstream site.
Use of replication data to determine gene dosages.
As was
pointed out above (in the introduction), to evaluate the
transcriptional control of bacterial genes, especially when experiments
involve different growth rates, it is necessary to relate the observed
gene expression to the number of gene copies present. For genes with
known map locations on the bacterial chromosome, accurate gene dosages
can be found from the values of the initiation mass and the
C period presented above (Fig. 5 and 3, respectively), by
using the mathematical relationships provided below (Appendix). As an
example, Table 1 shows how the activity
of the first gene in the r-protein spc operon,
rplN (r-protein L14), may be found from observed data in
Fig. 3, 4, and 5 above and from genetic data on the map locations of
rplN and oriC. In this case, the gene activity
was calculated as number of L14 molecules produced per minute per gene.
The increase in the synthesis rate per rplN gene with
increasing growth rate reflects the genetic (transcriptional and
translational) control of this locus.
| |
APPENDIX |
This Appendix has four parts. In the first part, the principle of
the method to determine the oriC copy numbers and the
C period is explained in detail. The relationships and
equations in this part have been derived previously in different
contexts (e.g., see references 7, 8, 10, and
21). The second part describes how the initiation
mass and C period can be used to find exact copy numbers of
genes with known map locations on the bacterial chromosome. The third
part describes the relationship between culture turbidity and cell mass
density. This relationship has been used for accurate determinations of
culture mass and generation time. The last part describes controls for
the colorimetric DNA assay and for the conversion of assay values into
absolute units in E. coli genome equivalents.
(i) Principle of method to determine the initiation mass and
C period. After the addition of the antibiotic
rifampin to a bacterial culture, initiation of new rounds of
replication stops, but ongoing rounds of replication are completed.
This has been most directly shown with the aid of a flow cytometer that measures the amount of DNA in individual cells: 90 min after the addition of rifampin, all cells have only fully replicated chromosomes (31). When initiation of replication stops, the number of
replication origins becomes constant, and at essentially undiminished
speed of the replication forks, the numbers of replication termini and of DNA genome equivalents (G) become equal to this number of
origins after C minutes (Fig. 1). Thus, the number of
oriC copies (NoriC) present at the
time of rifampin addition equals the number of DNA genome equivalents
reached at the plateau. Figure 1 also shows that the increase factor in
DNA (G) is equal to NoriC/G. Since NoriC/G is a function of the replication
velocity relative to the bacterial growth rate (ratio
C/), G can be used to find C, by
using the relationship (8)
![&Dgr;G = N<SUB>oriC</SUB>/G = <UP>ln</UP> 2 · (C/&tgr;)/[1 − 2<SUP>−C/&tgr;</SUP>]](/content/vol180/issue2/fulltext/265/img002.gif)
|
(1)
|
Together with the amount of DNA per mass present during
exponential growth (
G/M),
G is then used to
determine the number
of copies of
oriC per culture mass
(1/
M0), i.e., the reciprocal
of the initiation
mass:
|
(2)
|
The curve describing the residual accumulation of DNA after
stopping initiation (solid curve in Fig.
1) is given by the
relationship
(
8)
![G<SUB>t</SUB>/G<SUB>0</SUB> = 1 + t · <UP>ln</UP> 2/[&tgr;(1 − 2<SUP>C/&tgr;</SUP>)] − (2<SUP>t/&tgr;</SUP> − 1)/(2<SUP>C/&tgr;</SUP> − 1)](/content/vol180/issue2/fulltext/265/img004.gif)
|
(3)
|
Gt and
G0 are the
amounts of DNA present at the times
t and 0, respectively.
Equation
3 is based on the two assumptions that
rifampin immediately
stops initiation and that it does not affect
the velocity of the
replication forks. A comparison of the observed
DNA curve with this
theoretical expectation allows one to determine
a potential delay
(
d) in the action of rifampin on initiation
of replication,
which must be taken into account for determination
of
M0 and
C. Mathematically, this is
done by replacing
t in equation
3 with the difference
(
t 
d) and the first term on the right
side, i.e., 1, with 2
d/, which
represents the exponential growth during the delay. Equation
3 then
describes the accumulation of DNA in the time range between
d and
C +
d. Before
t =
d, DNA accumulation is described by the
exponential growth function, 2
t/, and after
t = (
C +
d), the amount of
DNA remains constant, equal
to the plateau value given by equation 3 for
t = (
C +
d).
(ii) Determination of gene copy numbers from initiation mass and
C period. The average copy number of a gene per cell is to be distinguished from its copy number per cell mass. Only the
latter is relevant for studies on gene control. The copy number per
cell mass depends on the control of replication characterized by the
initiation mass, whereas the copy number per cell depends on the
control of cell division and not on the control of chromosome replication.
The copy number (NX) of any gene X
per cell mass (M) can be found if the map location
(m) of that gene on the E. coli chromosome relative to the replication origin is known. The ratio of copy numbers,
NX/NoriC, is given by the
relationship (7)
|
(4)
|
Combining equations 2 and 4, we find the copy number of gene
X per unit of culture mass:
|
(5)
|
For example, for
m = 0 (
oriC),
equation 5 gives
NoriC/M = 1/
M0, and for
m = 1, i.e., for a
gene near the replication terminus
(
terC), we find
NterC/M = 2
C//
M0. This
shows that genes near the replication origin have the
highest copy
number and genes near the replication terminus have
the lowest copy
number; the maximum difference in an exponential
culture is given by
the factor 2
C/, corresponding to the ratio of
origins over termini. Moreover,
the faster a culture grows (small
),
the lower the relative frequency
of genes at some distance from
oriC is. During growth in rich
medium (assuming
= 20 min
and
C = 33 min [Fig.
3a]), the greatest
differential
is expected to be 2
33/20 = 3.1. Thus, during growth in rich
medium, a gene located near
oriC has a 3.1-fold higher copy
number than a gene located near
terC.
The location of a gene on the circular chromosome map is given in map
units (MU) between 0 and 100 min (representing the chromosome transfer
time in a particular type of mating experiment). With oriC
located at 84 min on the E. coli chromosome map
(1) and bidirectional chromosome replication (4),
the location in MU can be converted into the location relative to
oriC (m) by using one of the following
relationships (11):
|
(6a)
|
|
(6b)
|
|
(6c)
|
(iii) Determination of cell mass density and growth.
The turbidity (OD) of a culture does not increase exactly in
proportion
to the mass density (
M), as can be seen by making a
number
of dilutions from a concentrated culture and plotting the
observed OD
against the relative concentration (Fig.
A1). Rather
than diluting every sample
of culture before reading the OD, it
is more accurate to read the OD
directly and correct for the nonlinearity.
The observed OD curve in
Fig.
A1 can be approximated by the parabola
|
(7)
|
where
O is the observed OD,
b is an
empirically determined factor (see below), and
M is the
(wanted) true mass density, defined
by the initial slope (
a)
of the curve and the relative concentration
(
C) in the
diluted sample (setting the concentration of the undiluted
culture
equal to 1.0 [Fig.
A1]) as follows:
|
(8)
|
The quadratic term in equation 7 can be understood as the
probability that two bacteria are in one line of sight between
the
light source and detector of the spectrophotometer, so that
the second
bacterium is in the shade of another one and does not
contribute to the
light scattering observed. The parameters
a and
b
in equations 7 and 8 have been determined by a best-fit
method from the
observed data in Fig.
A1 (Table
A1). To
find the
true mass density from the observed OD, only
b is
needed (resolving
equation 7 for
M):
![M = [1 − <RAD><RCD> (1 − 4bO)</RCD></RAD>]/2b](/content/vol180/issue2/fulltext/265/img013.gif)
|
(9)
|
For
E. coli B/r and K-12 strains, we found that
b = 0.15 if the OD
460 is measured (example
in Table
A1) and
b = 0.17 if the
OD
600 is
measured. Different growth media did not seem to make
a significant
difference.
View larger version (22K):
[in this window]
[in a new window]
|
FIG. A1.
Relationship between culture mass density and OD. A
culture with an OD460 = 0.812 was diluted to 0.2, 0.4, etc.
(relative concentrations on abscissa), and the OD460 of
these dilutions was determined (points on the curve). The curve shown
is a parabola that has been calculated (equation 7, with
b = 0.15). The parabolic relationship can be used to
find exact mass densities (triangles, curve labeled M) of cultures from
the observed OD (see text for details). obs., observed; calc.,
calculated; Relat., relative.
|
|
The OD of the medium without bacteria (medium blank) is not exactly
zero, especially for LB medium. The observed medium blank value
(B) was subtracted in the calculation of the culture mass density (M) by substituting the difference
(O B) for O in equation 9.
Equation 9 is valid for OD readings up to about 1.3. For mass
densities > 1.3, as in stationary cultures, dilutions have to be
made. Generally, the observed mass densities, after correction by
equation 9, deviated by less than 1% from the best-fit exponential curve.
(iv) Determination of DNA by the diphenylamine assay. The
diphenylamine assay is specific for deoxyribose. In the case of DNA,
nucleotide bases have to be removed to make deoxyribose residues in the
DNA accessible to the diphenylamine reagent. This is done by a 30-min
treatment of the DNA with PCA at 70°C, which generates apurinic acid
through efficient depurination. The diphenylamine reaction is enhanced
about threefold by acetaldehyde and produces a blue compound measured
by its light absorption at 600 nm (A600). The
exact chemistry of the reaction is not known (13).
Acetaldehyde was also found to give a deoxyribose-independent
diphenylamine reaction (Fig. A2a;
blanks) in addition to enhancing the deoxyribose-dependent reaction
(Fig. A2b). The deoxyribose-dependent reaction was complete after about
10 h and was independent of the acetaldehyde concentration above
0.08 mg/ml (Fig. A2b), whereas the deoxyribose-independent reaction
continued for longer periods and increased with the acetaldehyde
concentration (Fig. A2a). Acetaldehyde concentrations producing the
lowest blank value without significantly reducing the
deoxyribose-dependent reaction give the highest signal-to-noise ratio
and therefore the greatest accuracy. Since stock solutions of
acetaldehyde have a tendency to decompose during storage at 4°C, the
optimal acetaldehyde concentration was determined (as illustrated in
Fig. A2) before determining DNA in bacterial cultures.
View larger version (30K):
[in this window]
[in a new window]
|
FIG. A2.
Effect of different acetaldehyde concentrations on the
colorimetric diphenylamine assay for DNA. (a) Assays with DNA (filled
symbols) and without DNA (open symbols; blanks). (b) Differences of
assay values, with DNA minus blank. The graph shows that acetaldehyde
alone reacts with the diphenylamine without reaching a plateau, whereas
the reaction with DNA is complete in 5 to 10 h and independent of
the acetaldehyde concentration in the range tested. Blk., blank;
nucleot., nucleotides; acetald., acetaldehyde.
|
|
Glass fiber filters used to collect bacteria for DNA determinations,
but without any bacteria or DNA, were found to react weakly in the
diphenylamine assay. The reaction was proportional to the number of
filters in the assay. This increased the blank values in the DNA assays
and led to extra scatter in the data. Repeated washes of the filters
with salt (1 M NaCl) or alkali (1 M NaOH) did not remove the substrate
for the reaction but rather increased the readings obtained with
filters only, suggesting that sodium or other metal ions bound to the
glass surface might be involved. Acid washes, however, decreased the
reaction (although not to zero) and reduced the scatter. Thus, for
improved accuracy, filters for measuring DNA in bacteria were soaked
overnight in 1 mM PCA before use.
The DNA assay may be calibrated with known amounts of deoxyribose,
deoxyribonucleosides, or DNA. For this purpose, we have routinely used
either AdR or CT-DNA. Per mole of purine nucleotides, CT-DNA gave 23%
higher assay values than did AdR (Fig.
A3b). Since the 23% difference was
found to be independent of the source of DNA (calf thymus, salmon
sperm, and phage 
, all highly purified) or of the nucleoside (AdR
and deoxyguanosine, different lot numbers and brands), we have assumed
that the calibration with known amounts of DNA gives correct values for
assaying unknown DNA. For convenience, however, DNA assays were
generally calibrated with AdR, in which case an empirical factor
(1.23 ± 0.03, as in Fig. A3b) was applied. The 23% difference in
the final plateau and the observation that the reaction kinetics differ
for DNA and nucleosides (Fig. A3b; ratio of assay values, CT-DNA to
AdR, decreases with reaction time) suggest that the deoxyribose
residues in apurinic acid, i.e., with two phosphate ester bonds, react
differently with diphenylamine than does the deoxyribose in nucleosides
like AdR or deoxyguanosine, i.e., without phosphate bonds.
View larger version (24K):
[in this window]
[in a new window]
|
FIG. A3.
Calibration of diphenylamine assay for DNA, with either
CT-DNA or AdR. (a) Reaction kinetics observed with equal amounts of
CT-DNA or AdR. In DNA, only deoxyribose residues of purine nucleotides
are assumed to react. (b) Ratio of the two curves in panel a,
CT-DNA/AdR, after division by 0.5 (50% purines in DNA). The curve
shows that the reaction with DNA (apurinic acid) is faster than the
reaction with AdR and reaches a 23% higher value than expected from
the assumption that the contribution of purine nucleotides in DNA to
the diphenylamine reaction is equivalent to that of AdR. Blk., blank;
nucleot., nucleotides.
|
|
| |
ACKNOWLEDGMENTS |
This work was supported by grants from NIH and MRC.
We thank E. Boye for advice in the preparation of the manuscript.
| |
FOOTNOTES |
*
Corresponding author. Mailing address: Department of
Biochemistry and Molecular Biology, University of British Columbia,
2146 Health Sciences Mall, Vancouver, British Columbia V6T 1Z3, Canada. Phone: (604) 822-5975. Fax: (604) 822-5227. E-mail:
pdp1{at}unixg.ubc.ca.
| |
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J Bacteriol, January 1998, p. 265-273, Vol. 180, No. 2
0021-9193/98/$04.00+0
Copyright © 1998, American Society for Microbiology. All rights reserved.
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Abstract
Introduction
