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Journal of Bacteriology, January 2004, p. 207-211, Vol. 186, No. 1
0021-9193/04/$08.00+0 DOI: 10.1128/JB.186.1.207-211.2004
Copyright © 2004, American Society for Microbiology. All Rights Reserved.
and Kurt Nordström*
Department of Cell and Molecular Biology, Biomedical Center, Uppsala University, S-751 24 Uppsala, Sweden
Received 31 March 2003/ Accepted 1 October 2003
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FIG. 1. Basic replicon of plasmid R1, consisting of an origin of replication (oriR1), the structural gene repA for the initiator protein RepA (many copies of which bind to oriR1 in order to initiate replication), the gene for an antisense RNA (CopA) that inhibits translation of the repA mRNA by binding to an upstream region (copT) of the repA mRNA (top left of panels), the structural gene copB for an inhibitor of expression of the prepA promoter, and the constitutively expressed prepA and pcopB promoters. (A) Under normal conditions, the prepA promoter is almost totally switched off by the CopB protein (7, 21). (B) At low copy numbers, the concentration of the tetrameric CopB is too low to repress transcription from prepA.
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Predicting distributions requires probabilistic assumptions about replication control and partitioning. Nordström and Aagaard-Hansen (11) reported simplified theoretical calculations based on the so-called +n mode of replication. Parameter n is the copy number per average newborn cell, as well as the average number of replications per cell cycle, irrespective of the copy number at birth (5, 10, 15). Assuming that the number of replications has a Poissonian spread around n leads to the copy number distributions shown in Fig. 2. Combined with binomial partitioning, when all copies segregate independently to identical daughters, stochastic theory shows that the copy distribution is approximately Poissonian (17). The width of distributions is evolutionary important because it determines the probability of plasmid loss at cell division. For instance, the basic replicon of plasmid R1 is presumably partitioned binomially (12). If replication control worked perfectly, all dividing cells would contain 2n plasmid copies and the frequency of formation of a plasmid-free daughter would be L = (1/2)2n per cell generation, where L is the rate of loss (12, 14). But if copy numbers have a Poissonian spread around 2n, the rate of loss has been shown (17) to increase to approximately (0.6)2n, which can be a much higher number. The reason for this is that the main contribution to losses comes from cells with lower-than-average copy numbers, as shown in Fig. 2. For Par+ plasmids, like wild-type R1, this argument is even stronger, and with a perfect partition function all losses come from fluctuations down to a single copy.
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FIG. 2. Histogram showing the relative copy number distribution (solid bars) and the rate of loss per cell cycle (open bars) calculated for an n value of 3. Replication was assumed to be according to the +n mode and to have a Poissonian distribution around n (11, 15). The rate of loss for each class was calculated to be (1/2)copy number (12). Partition was assumed to be according to equipartition (12).
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Nordström and Aagaard-Hansen (11) showed that the rate of loss of a Par- derivative of plasmid R1 increased from 1.5 to 2.5% per cell generation when the cells also contained a compatible plasmid expressing the copB gene constitutively. This finding somewhat supports the hypothesis that CopB evolved to lower the risk of plasmid loss, but the effect is moderate (11). However, a plasmid with a partition system that works well should be more strongly affected since only cells with one plasmid copy at the time of cell division would produce plasmid-free daughters. The frequency of such cells in a population must be fairly low, since a Par+ plasmid is lost with a very low frequency (about 10-5 to 10-4 per cell, compared to 10-2 per cell division for a Par- derivative) (3). Since wild-type R1 is Par+, it is thus possible that CopB plays a greater role in replication control than previously thought. In this paper, we describe direct studies of the effect of the CopB protein on the stability of inheritance of plasmid R1.
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TABLE 1. E. coli K-12 strains and plasmids used
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To determine the frequency of bacteria in the population that carried plasmid pOU47, the bacteria were plated on X-Gal (5-bromo-4-chloro-3-indolyl-ß-D-galactopyranoside) plates, and the ratio of the number of blue colonies to the total number of colonies was determined.
Determination of the rate of formation of plasmid-free cells.
The bacteria were pregrown in either LB medium with ampicillin (50 µg) and tetracycline (15 µg/ml) (pOU47 plus pOU18) or M9 medium with lactose and tetracycline (15 µg/ml) (pOU47 plus pOU16). At an optical density at 600 nm (OD600) of about 0.3, the cultures were diluted into 200 ml of LB medium with tetracycline when appropriate and were incubated at 30°C. The OD600 was never allowed to exceed 0.3 (corresponding to about 108 cells per ml). At an OD600 of about 0.3, the cultures were diluted 102- to 104-fold and again grown to an OD600 of
0.3. The cultures were repeatedly diluted and grown for about 100 cell generations; the 102-fold dilution was used in the first rounds of growth. At each dilution step, samples were taken for determination of plasmid-free cells.
Determination of ß-galactosidase activity. The ß-galactosidase activity was determined essentially as described by Miller (9).
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Plasmid pOU47 is a Par+ derivative of the basic replicon of plasmid R1. It also contains the wild-type lac operon. The TOP10 host strain used is lactose negative. Hence, the presence of the plasmid was visualized by plating the cultures on indicator (X-Gal) plates, which made scoring plasmid loss easy.
In order to inhibit expression from the prepA promoter, two plasmids carrying the copB gene with its promoter were used, pOU16 and pOU18; the former plasmid has a high copy number, and the latter has a moderate copy number. These plasmids were introduced into a lac mutant of E. coli that contained the reporter plasmid pJL228 with the lac operon under control of the prepA promoter. The efficiency of repression is shown in Table 2. The presence of the intermediate-copy-number plasmid pOU18 reduced transcription from the prepA promoter by 93%, whereas inhibition was 99% effective with the high-copy-number vector pOU16.
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TABLE 2. Efficiency of repression of the prepA promoter by CopB
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In this type of study, there might be problems with bottlenecks; i.e., at low rates of loss, statistical variations might affect the results. To overcome this, we used 102-fold dilutions in the first rounds of the experiment.
The results are shown in Fig. 3. The number of independent experiments is evident in Fig. 3, since the color of the symbols for each experiment is distinct. There was a continuous exponential reduction in the relative frequency of the plasmid-carrying cells; the parallel experiments gave very similar results in each case. The frequency of loss of plasmid pOU47 was calculated from the slopes of the curves in Fig. 3 and was found to be 1 x 10-4 per cell generation for plasmid pOU47 alone, whereas it was 3 x 10-4 and 7 x 10-4 per cell generation in the presence of plasmids pOU18 and pOU16, respectively. The presence of the vector pBR322 did not increase the rate of loss of pOU47 (Fig. 3B). The rate of loss of plasmid pOU47 was higher in the pOU16 experiment than in the pOU18 experiment, in line with the data shown in Table 2. Hence, the prediction that extra CopB protein should increase the frequency of loss turned out to be correct.
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FIG. 3. Rate of loss of plasmid pOU47 during exponential growth. The fraction of the cells that carry plasmid pOU47 during exponential growth is plotted as a function of time. (A) TOP10 cells carrying only pOU47. (B) TPO10 cells carrying pOU47 and pBR322. (C) TOP10 cells carrying pOU47 and pOU18. (D) TOP10 cells carrying pOU47 and pOU16. Note that the scale of the vertical axis is logarithmic. In each panel the results of each independent experiment are indicated by a distinct symbol and color.
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5% of the total RepA synthesis rate (3), which in turn should produce a
5% change in the plasmid copy number (13). The use of standard numerical methods suggests that a 5% increase from n = 3.8 to n = 4 (an average of eight copies at cell division) results in a 1.9-fold decrease in the average rate of loss, while a change from n = 2.85 to n = 3 results in only a 1.5-fold decrease. However, it should be stressed that tails of distributions are notoriously difficult to predict. In this case we expect that the simple model provides a high estimate. For instance, consider a Poissonian distribution with average
so that the probability of zero is P(0) = e-
. If
= 5, a 10% increase to
= 5.5 results in a 1.6-fold decrease in P(0). If one half of the population instead is described by a Poissonian distribution with
= 2 and the other half is described by a Poissonian distribution with
= 8, the total average is still 5 and P(0) = 1/2(e-2 + e-8). However, a 10% increase in
:s now only decreases P(0) 1.2-fold. For plasmids, these types of fluctuations are often overlooked but are not unlikely if the kinetic parameters of replication control vary from cell to cell. Similarly, if partitioning is not perfect, the rate of loss additionally depends on the probabilities of having, e.g., two or three plasmid copies at the time of cell division, and these probabilities also respond less sensitively to changes in the average. We therefore concluded that the observed reduction in rates of loss was probably not caused by the simple increase in average copy number, but we also stress that such small differences would be difficult to measure reliably. It may seem that CopB could respond to changes in plasmid concentration only if it was actively degraded. However, even if CopB were completely stable, dilution in growing cells would ensure that a change in plasmid concentration would produce some change in the CopB concentration, although the two concentrations would not remain proportional. For instance, if the plasmid concentration changed by 10%, there could be a 2% change in the CopB concentration one-quarter of a cell cycle later. If the CopB system works with high sensitivity, the 2% change could be amplified to a large relative change in the repression of prepA. Because CopB acts as a tetramer, it is possible that prepA transcription responds strongly to changes in plasmid concentration even if CopB monomers are slowly degraded.
The rate of change (the slopes of the curves in Fig. 3) is dependent on the rate of loss and on differences in the growth rate between the P+ and P- populations. The latter component is increasingly important as the ratio of P- cells to (P+ + P-) cells increases, and even very small differences in the growth rates cause the curves to accelerate downwards. Since there was no sign of this even after 100 generations, we concluded that there were no measurable differences in growth rates and that, hence, the slopes of the curves give correct estimates of the rate of loss.
Plasmids are maintained with a very high degree of stability in bacterial populations, although basic replicons of low-copy-number plasmids are lost with frequencies on the order of 10-2 per cell division. This is because natural plasmids possess different types of stability functions, partition functions, killer functions, and systems for resolution of plasmid dimers (11). None of these systems is 100% efficient, but in concert the systems mediate a very high degree of stability; the native plasmid R1 is lost with a frequency that is
10-7 per cell division (11). As discussed by Nordström and Austin (12) and further developed by Paulsson and Ehrenberg (17), the copy number distribution is very important for stable inheritance of plasmids; not even a totally efficient partition system can ensure that each daughter receives a copy of the plasmid if the dividing cell contains only one plasmid copy. This is (indirectly) shown by the results described in the present paper.
The fairly moderate effect of loss of derepression of the prepA promoter raises questions about the importance of the CopB system for the plasmid. There are at least two situations in which the CopB system might make a difference: (i) in cells with a very low copy number due to statistical variations in replication and partition, and (ii) during establishment of the plasmid directly after transfer to a plasmid-free cell. The rate of replication is sixfold higher during the first 25% of the generation time after conjugal transfer of plasmid R1 compared to the steady-state rate (P. Gustafsson and K. Nordström, unpublished data). Since the CopB system has been kept by the plasmid, it appears that even its fairly moderate effect has survival value for the plasmid.
Present address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom. ![]()
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