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J Bacteriol. 2010 March; 192(5): 1175–1183.
Published online 2009 November 6. doi:  10.1128/JB.01245-09
PMCID: PMC2820840

P1 Plasmid Segregation: Accurate Redistribution by Dynamic Plasmid Pairing and Separation[down-pointing small open triangle]

Abstract

Low-copy-number plasmids, such as P1 and F, encode a type Ia partition system (P1par or Fsop) for active segregation of copies to daughter cells. Typical descriptions show a single central plasmid focus dividing and the products moving to the cell quarter regions, ensuring segregation. However, using improved optical and analytical tools and large cell populations, we show that P1 plasmid foci are very broadly distributed. Moreover, under most growth conditions, more than two foci are frequently present. Each focus contains either one or two plasmid copies. Replication and focus splitting occur at almost any position in the cell. The products then move rapidly apart for approximately 40% of the cell length. They then tend to maintain their relative positions. The segregating foci often pass close to or come to rest close to other foci in the cell. Foci frequently appear to fuse during these encounters. Such events occur several times in each cell and cell generation on average. We argue that foci pair with their neighbors and then actively separate again. The net result is an approximately even distribution of foci along the long cell axis on average. We show mathematically that trans-pairing and active separation could greatly increase the accuracy of segregation and would produce the distributions of foci that we observe. Plasmid pairing and separation may constitute a novel fine-tuning mechanism that takes the basic pattern created when plasmids separate after replication and converts it to a roughly even pattern that greatly improves the fidelity of plasmid segregation.

Low-copy-number plasmids encode partition systems for proper distribution of the plasmids during cell division. The par loci encode a cis-acting centromere-like sequence, parS, and two trans-acting proteins, ParA and ParB. ParB is a DNA binding protein that binds to parS, and ParA is an ATPase that is thought to power plasmid segregation. Par systems are classified as type I or type II according to whether they have Walker-type or actin-type ATPase domains in ParA. Type I partition system can be further divided into Ia and Ib by their different genetic organizations and general sequence dissimilarity (12). P1 is a bacteriophage that is maintained as a stable low-copy-number plasmid in its Escherichia coli host (28). It contains a typical type Ia partition system that is essential for proper plasmid segregation (13, 17, 27). The P1par locus is an operon producing ParA and ParB proteins followed directly by the centromere analog site, parS (9). The ParB protein binds specifically to the parS site (35). The ParA protein is an ATPase that interacts with the ParB-parS complex (3, 4, 11). P1 ParA has a nonspecific DNA binding activity (5). F partition depends on the interaction of its ParA protein (SopA) with nonspecific DNA (2). The P1parS site loads ParB in two steps, first binding a core dimer onto the site and then loading additional ParB copies that spread out on the surrounding sequences (31, 32). The latter activity causes a fluorescence-labeled ParB to form a bright focus that marks the position of the plasmid in the living cell (23).

Observations of fluorescently labeled F and P1 plasmids show that, when a single plasmid focus is present in the newborn cell, it is located approximately at the cell center.

The focus divides, and the products migrate to positions approximating the cell quarters (15, 23, 26). Cell division results in one plasmid focus in each daughter cell. This evidence has been used to suggest that specific sites exist at the cell center and quarters to tether the plasmids (15, 26). However, the limited data presented show that the distribution of focus positions is rather broad and, at least in the P1 case, that the positions to which the plasmid foci migrate are quite variable (23). This casts some doubt on the existence of fixed cell locations. The unrelated type Ib par system of pB171 distributes plasmid foci evenly along the cell length without reference to any particular cell location (7). This distribution has been linked to observations of an oscillation in the local concentration of ParA protein that appears to sweep slowly through the cell between the boundaries of the nucleoid (7). A similar oscillation has been reported for the F plasmid ParA protein, SopA (16).

At most growth rates, more than one P1 plasmid copy is present at cell birth. How are the additional copies accommodated? For the F plasmid, measurements of foci and plasmid copy numbers suggest that the center-to-quarters paradigm holds at increased copy numbers and that each migrating focus can contain more than one plasmid copy (15). In our initial studies, this appeared to hold for P1 also (23). In these studies, the fluorescent marker protein, green fluorescent protein (GFP)-ParB, was transiently induced to the highest practicable level in order to visualize the foci. We now know that this treatment has adverse effects on the plasmid. The plasmids are subject to a reduction in copy number and delayed segregation through the period of observation (data not shown). The advent of improved optics has allowed us to avoid these problems and to study foci when the fluorescent protein is expressed continuously at a low level. We quickly realized that multiple foci were present under these conditions, that the positions and behaviors of foci were more dynamic, and that the center-to-quarters paradigm did not hold for P1 in the majority of cells.

MATERIALS AND METHODS

Bacterial strains and media.

E. coli MG1655, carrying the mini-P1 plasmid λP1-5RKm and plasmid pALA2702, which expresses GFP-ParB (21), was used for the study. Cells were grown at 32°C in AB minimal medium supplemented with 0.2% glucose, 0.05% Casamino Acids (CAA), 1 μg/ml thiamine, and 1 μg/ml uracil. Kanamycin (50 μg/ml) and ampicillin (100 μg/ml) were used to maintain the plasmids. Isopropyl-β-d-thiogalactopyranoside (IPTG) (10 μM) was used to induce GFP-ParB expression continuously. For real-time quantitative PCR (qPCR), a control strain, CC4756, was used. This strain has the P1parS-kanamycin cassette inserted near the origin at 84.2 min (25). For studying localization of ParA, pALA2709 expressing a GFP-ParA fusion protein was used. A PCR product of pALA1413 (29) was made using the primers 5′ CCCCCGAGCTCATGAGGTGAATCCAGCCAGCTT and 5′ CCCCCCCCGGGTCAGTTAGATCTGATAAATTCAAT. The product was cut with SacI and SmaI, and the large fragment was inserted into the same sites in the linker region of plasmid pDSW209 (36) to give pALA2709.

General microscopy.

A 1.5-ml portion of the growing culture was harvested at an optical density at 600 nm (OD600) of 0.1. The cell pellet was resuspended in 50 μl of the growth medium. Ten microliters of the concentrated cells was placed on a polylysine-coated glass slide and covered with a coverslip. The cells were immobilized by moderate pressure on the coverslip. Microscopy was carried out on a Nikon Eclipse E-1000 microscope equipped with a Nikon C-CU Universal condenser, a Semrock GFP-3035 bright-line zero band-pass filter cube, and a Hamamatsu Orca-ER c4742-95 charge-coupled device (CCD) camera. Images were acquired using Openlab 4.2 software. A Nikon Plan Fluor 100× objective was used. The pictures were analyzed with the Image Pro Plus 6.1 program using macrodirected cell recognition and measurement of the focus number and position, as previously described (25). At least 1,000 cells were inspected for each experimental set. The automated detection system is capable of finding faint foci that the eye can miss. However, very few plasmid foci are found near the lower limit of detection, and in populations of cells averaging fewer than three copies per cell, the class containing no detectable foci is less than 2% and is only marginally higher than the class of cells that have no plasmid (ca. 1.5%) (data not shown). This suggests that the efficiency of focus detection is high.

Time-lapse microscopy.

A concentrated cell culture was placed on the slide on a 1% agarose slab containing minimal AB glucose medium with appropriate antibiotics and 10 μM IPTG. The slab was covered with a coverslip and sealed with petroleum jelly. The slide was left in a moist chamber at 32°C for an hour. During this time, the cells adapted to the low-oxygen conditions on the slide and formed microcolonies containing 2 to 4 cells. Pictures were taken at 2-min intervals for 3 h. The cells went through approximately two generations of growth under these conditions. The growth rate of the cells declined gradually until the cells were barely growing after 3 h. Thus, the cells were not always growing under well-defined conditions, and the data may not be strictly comparable to those obtained from cells in balanced growth.

The foci were tracked using the tracking option of the Image Pro Plus 6.1 program and plotted using Microsoft Excel. Because the behavior of foci between time points was unknown, the tracks shown in the figures are an interpretation of the actual motion of the foci. Other interpretations are possible. For example, when a cell compartment containing two foci has one of them splitting, it is not certain from which focus the splitting event occurred. One or more of the following indicators were used in the interpretations given in Fig. Fig.55 and and7.7. The split foci may form the closest pair after the split; the split may occur progressively with respect to a pair of products, or the intensity differences of the parental and the product foci may clearly indicate a split. Similar considerations affected choice when foci fused in three-focus compartments. When two foci join and separate, their individual identities are generally lost. However, size differences in the foci sometimes suggest focus identity through a split (see below).

FIG. 5.
Time-lapse analysis of representative cells. (Top) Selected time-lapse images of a microcolony. (Bottom) The plotted tracks of cells 1 and 4. The colored lines distinguish the tracks of individual foci but do not necessarily indicate the actual focus ...
FIG. 7.
Data from time-lapse images of cells 1 and 4b. The outlines of the cells were masked manually to distinguish them from the surrounding cells in the microcolony. Occasionally, a portion of a focus from an adjacent cell can still be seen at the mask boundary. ...

DAPI staining.

An exponentially growing culture (1.5 ml) was mixed with 1.5 μl of 5-mg/ml 4′-6-diamidino-2-phenylindole (DAPI) (final concentration, 5 μg/ml) and incubated on ice in darkness for 15 min. The cells were harvested and resuspended in 50 μl of fresh medium. Microscopy was done immediately as described previously, using a filter cube designed to detect DAPI fluorescence.

Determination of the P1 copy number by real-time quantitative PCR.

E. coli strain MG1655 carrying λ-P1:5RKm and control strain CC4756 carrying a kanamycin resistance gene at the origin (84 min) were grown in 20 ml minimal AB glucose medium with 0.05% CAA and 10 μg IPTG. The cultures contained kanamycin to ensure plasmid retention and were grown at 32°C. The cells were harvested at an OD600 of 0.1. One aliquot was used for microscopy, and the total DNA was isolated from the other using a DNeasy tissue kit from Qiagen (catalog no. 69504) and was measured using a Victor fluorometer and the Quant-iT dsDNA HS Assay Kit (Invitrogen). Tenfold serial dilutions were used as templates for real-time qPCR. Primer sets for the kanamycin resistance gene (kan) from pACYC177 (forward, 5′ GCGAGTGATTTTGATGACGAGC, and reverse, 5′ ACCATGAGTGACGACTGAATCC) and the d-1-deoxyxylulose 5-phosphate synthase gene (dxs) (forward, 5′ CGAGAAACTGGCGATCCTTA, and reverse, 5′ CTTCATCAAGCGGTTTCACA) were used to amplify the target (kan) and the reference (dxs) genes. The kan gene is present as a single copy in λ-P1:5R and in the chromosomal origin region of strain CC4756. The dxs sequence is a single-copy gene on the E. coli chromosome.

A calibrator plasmid was constructed by introducing the dxs and kan genes as PCR products into a pBluescript II SK vector (Stratagene). A 5-fold serial dilution series of the calibrator plasmid ranging from 3.2 × 102 to 1.0 × 106 copies/μl was used to construct the standard curves for both kan and dxs. From the slope of each standard curve, the PCR amplification efficiency (E) was determined. Real-time qPCR amplification and analysis were performed using the iCycler iQ Multicolor Real-Time Detection System with software version 3.1 (Bio-Rad). The qPCR assays were optimized with respect to the annealing temperature and primer concentration. The optimal conditions were 57°C and 400 nM for both primer sets. The real-time qPCR mixture was prepared using iQ SYBR green Supermix (Bio-Rad). Five microliters of template DNA was used for each reaction. A 2-step amplification protocol with melting curve analysis was used. The protocol was as follows: initial denaturation for 3 min at 95°C was followed by 50 cycles of 10 s at 95°C and 30 s at 57°C. The signal was measured at the end of each cycle. After amplification, a melting curve analysis with a temperature gradient of 0.5°C per cycle starting at 55°C was performed to confirm that only the specific products were amplified.

The relative quantification method was used to quantify plasmid copy numbers using a modification of the ΔΔCT method (24). The ratio of kan to dxs was determined for both the P1-carrying strain and the control strain with kan at the origin. The number of plasmids per origin was determined by dividing the former by the latter. The number of origins per cell was determined by Helmstetter's equation (19). The product of P1 per origin and the number of origins per cell gave the number of P1 plasmids per cell for a particular growth condition.

Null mutants of λ-P1:5RKm.

A plasmid containing a deletion of the parA and parB genes is very unstable in the host strain. Even under selection, most of the cells have no plasmid foci, and those that do have a single focus located randomly (22, 23). We found that the partition-defective phenotype was even more deleterious than previously indicated. Cells containing the partition-defective plasmids lost the plasmid at high frequency, and the resulting cured cells were prone to λ reinfection. Most of the P1 plasmid foci present in a partition-defective culture under selection are formed by plasmids recently reintroduced (data not shown). λ lysis-defective variants of the plasmid (λD15-P1:5RKm and λD15-P1:5R ΔparA-parB Km) which could not propagate as phages in a nonsuppressing host were constructed. On introduction into our standard host, λD15-P1:5RKm efficiently formed plasmids that behaved in the same way as those formed by its D+ (wild-type) parent (data not shown). However, very few cells containing λD15-P1:5R ΔparA-parB Km could be recovered. The plasmids were extremely unstable and integrated into the chromosome on extended selection (data not shown). Thus, null mutations in the P1 par system are lost at a higher frequency than previously thought, and study of foci formed by them in a steady state appears to be impractical.

Mathematical simulation of P1 plasmid partition.

The simulation of P1 plasmid partition was programmed in Microsoft VBA as a Microsoft Excel macro. Details of the program are given in Document S1 in the supplemental material. The user-variable parameters were as follows, with typical values given in parentheses. (i) Lnr = the range of possible positions of the nucleoid ends centered on a point 0.2 newborn-cell lengths (nbl) from the cell pole (0.1 nbl). (ii) Lsep = the distance apart that will ensure that two foci form a pair (0.15 nbl). (iii) N3 = the maximum number of cycles of focus separation and pairing in three focus cells considered in each cell cycle (6). (iv) N4 = the maximum number of cycles of focus separation and pairing in four focus cells considered in each cell cycle (6). (v) Lran = the limit of random movement to left or right of its resting position achieved by each nonseparating focus in each movement operation cycle (0.1 nbl). (vi) Lmax = the maximum travel of a focus after separation (0.4 nbl). (vii) Lmin = the minimum travel of a focus after separation (0.2 nbl). (viii) eop = the efficiency with which foci that pass each other pair at the closest point of interception (60%).

The typical values given in parentheses were used in a simulation (see Fig. Fig.8A).8A). The effects of changes in the above parameters are also shown (see Fig. Fig.8B,8B, as well as Fig. S2 in Document S1 in the supplemental material). The simulation is relatively insensitive to modest changes in any given parameter. Interestingly, random variations in the distance traveled by separating foci are important for optimum stability of plasmid maintenance.

FIG. 8.
Loss rates for a mathematical simulation of P1 plasmid partition. The program was run for 30 generations using the standard parameters listed in Materials and Methods. The result varied slightly for each time that the simulation was run, but the results ...

RESULTS

Multiple plasmid foci with only one or two plasmid copies each.

The mini-P1 plasmid, λ-P1:5RKm, relies on its P1par locus for segregation (34, 37). Null mutations in par cause the plasmid to be extremely unstable (see Materials and Methods). Our previous study of this plasmid involved following fluorescent foci formed when GFP-ParB was transiently induced to high levels in the cells (23). However, we have since found that this transient induction leads to a temporary block to segregation so that the number of foci falls considerably over several generations before recovering. If the induction is continuous or is limited to a low level, this problem is avoided. Improvements in optics now allow us to follow the plasmid foci accurately under such conditions, where both the foci and the background fluorescence are relatively weak. Figure Figure1A1A shows cells containing the plasmid grown in minimal-glucose Casamino Acid medium at 32°C with a generation time of 55 min. The fluorescent GFP-ParB protein was continuously induced by a low level of IPTG (10 μM). The plasmid was stably maintained under these conditions, with plasmid loss rates of about 0.2% per generation (data not shown). There were from one to six foci per cell, and no obvious bias as to location at the center or cell quarters was evident. Greater than 98% of the cells contained at least one visible focus; 80% of the cells had focus numbers in the range of 2 to 6. The same result was obtained with no induction at all, although the efficiency of focus detection was somewhat lower unless manual inspection of the images was used. The population average was 2.8 foci per cell. This is in distinct contrast to the results using transient induction, where the majority of cells have only one focus. Given this significant improvement in conditions and change in the overall pattern, we felt that it was important to reexamine P1 plasmid segregation, with particular emphasis on the fate of plasmids in cells with multiple foci. Using real-time qPCR, we determined the copy numbers of the plasmids and of the origin region of the chromosome in cells grown under the improved conditions (20). From this, the mean number of plasmids per cell was found to be 4.5 ± 0.6. There are therefore approximately 1.6 plasmid copies per focus. Thus, many foci contain only a single plasmid copy.

FIG. 1.
Distribution of plasmid foci. MG1655 cells containing the mini-P1 plasmid λP1:5RKm and expressing GFP-ParB were grown in minimal AB glucose Casamino Acid medium at 32°C, giving a 55-min generation time. (A) Typical field of cells. (B) ...

The distribution of plasmid foci in individual cells.

Figure Figure1B1B shows the distribution of all foci. The multiple foci were not clustered at the center or quarter positions but were very broadly distributed. The average number of foci per cell increased with cell size. The broad distribution of foci did not extend to the cell poles (Fig. (Fig.1B).1B). This reflects containment of the plasmid foci within the nucleoid region of the cells. The focus-free regions at the cell poles approximate the regions that are free of chromosomal DNA, as seen by DAPI staining of the DNA (Fig. (Fig.1B).1B). This is also true of the F plasmid (26). Foci also tend to be sparse at the cell centers, which are also free of nucleoid as the cells prepare to divide.

Nonrandom distribution with respect to the cell center.

Though very broad, the focus distributions were not random. Ninety-eight percent of those cells containing two or more foci had at least one focus on either side of the cell center (Fig. (Fig.2).2). Thus, most of the cells would retain at least one plasmid copy on cell division. This even distribution of plasmids with respect to the cell center was not limited to cells about to divide (Fig. 2A and B). It was a feature of the entire population and therefore constitutes a trend throughout the cell division cycle.

FIG. 2.
The distribution of foci with respect to the cell center. (A) The percentages of all cells and of all dividing cells that have P1 foci disposed around the cell center are shown. The stippled cells would give rise to a plasmid-free cell if the cell divided ...

In cells with more than one focus, we hypothesized that one focus might divide and be properly segregated and that additional copies might be randomly distributed. In order to test this, we identified all cells that were dividing and contained four foci. Of these, 67% had two foci on either side of the cell center (Fig. (Fig.2B).2B). Moreover, the majority (58%) had an even distribution with one focus in each of the cell quarters. Thus, the hypothesis is incorrect. All plasmid foci appear to be involved in the nonrandom segregation pattern.

The distribution of individual foci in the population.

Figure Figure33 shows the individual focus distributions in cells with one to six foci. The distributions are broad, and no fixed positions for foci within the cell are evident. However, there is a distinct pattern present. The mean positions of the foci are always evenly spaced from each other and from the ends of the cells. This pattern resembles that of the unrelated type 1b plasmid pB171 (7).

FIG. 3.
Distributions of mini-P1 plasmid foci. The distributions of foci along the long cell axis are shown relative to cell length. In each case, the mean points for the peaks are equally spaced from each other and the ends of the cells. (Left column) The relative ...

The dynamic distribution of the P1 ParA protein in individual cells.

Plasmid pALA2709 produces a P1 ParA protein that has a C-terminal fusion to GFP. The plasmid fully complements the partition defect of a mini-P1 plasmid with a point mutation in ParA and can be supplied in trans to a wild-type mini-P1 plasmid without affecting plasmid stability (data not shown). Thus, the localization of ParA-GFP in cells containing pALA2709 and the mini-P1 plasmid should reflect its dynamic behavior during normal plasmid partition. We saw no obvious oscillations in P1 ParA distribution with time. P1 ParA-GFP always formed a patchy field of fluorescence in an area roughly corresponding to that of the cell nucleoid (Fig. (Fig.4).4). The positions of the brighter areas in these fields were quite dynamic, but no convincing long-range oscillation of ParA concentration was ever indicated. We looked for such oscillations using a series of frame intervals between 2 min and 40 min. The maximum amount of dynamic change was small and was seen with 4-min frame intervals. Figure Figure44 represents a case in which the changes were greater than in the average cell. Thus, the behavior of P1 ParA may differ from its F relative F SopA, which appears to oscillate slowly with time (16).

FIG. 4.
Variations in ParA-GFP distribution. Time lapse microscopy of cells carrying a mini-P1 plasmid and expressing ParA-GFP was carried out. Various time windows were used. The maximum variability occurred using intervals of 4 min between frames. Only small ...

P1 plasmid foci divide, separate rapidly, and then tend to maintain their relative positions.

Time-lapse photomicroscopy of mini-P1 plasmid GFP-ParB foci was carried out in cells growing as microcolonies on a slide. Images were gathered every 2 min over a 3-h period (Fig. (Fig.5).5). We plotted the focus tracks in 23 cells and 66 of their first- and second-generation progeny. Two examples are given in Fig. Fig.5.5. Newborn cells contained one or, more often, two foci that divided to form two to four foci before cell division.

Resting foci appeared to undergo relatively small local movements continuously, possibly due to thermally driven motions. However, initial focus division was always followed by a dramatic separation of the foci. In each case, a wide, roughly symmetrical separation of the foci to new positions occurred (Fig. (Fig.6).6). This separation was usually complete within the first one or two 2-min time windows. In those cases where no further interaction occurred, the foci then remained at roughly the same relative positions indefinitely (Fig. (Fig.6).6). The initial division of a given focus did not occur at any particular point in the cell cycle or at any particular position in the cell.

FIG. 6.
Superimposed tracks of focus separation events. The time-lapse tracks are oriented so that the foci nearest to a cell pole are at the top of the graph. The tracks of foci in 7 different cells are shown in different colors. The tracks represent all the ...

Multiple foci often appear to join and separate again.

Occasionally, a cell initially contained a single focus, which split. The products separated widely and were simply segregated by cell division (5% of the cells [Fig. [Fig.5,5, cell 1, top]). However, most cells were born with two or more foci, and more complex patterns were evident (Fig. (Fig.5,5, cell 1, bottom, and cell 4). In these cases, foci often came together and separated again shortly afterward. This joining of foci occurred both between sister foci that had recently separated and with other foci in the cell that were not direct sisters (Fig. (Fig.5).5). In several cases, the center plasmid in a group of three seemed to shuttle between the outside members in multiple events. An example of this dynamic behavior is shown in detail (Fig. (Fig.77).

Cell compartments containing three or more foci almost always showed complex focus-joining and separation behavior (Fig. (Fig.7),7), with an average of three rounds of joining and splitting per focus per generation. Of these complex events, the majority (62%) involved interactions both with sisters and with other foci in the cell compartment within a single cell cycle. The net effect was always to distribute foci so that each cell received at least one focus after cell division (100% of cells were observed). However, the behavior was highly dynamic, and no tendency of foci to reside at any particular location in the cell was indicated. The 276 focus separation events recorded appeared to be randomly oriented with respect to the cell axes (data not shown).

The nature of separation and joining events.

P1 plasmid foci contain either one or two plasmid copies. Thus, the initial separation events observed must represent the separation of a pair of sister plasmids that was originally created by replication. Elongations of the focus or short-range abortive separations suggest that the replicated copies may remain associated for some time before the definitive separation event occurs (Fig. (Fig.7,7, cell 1, 18 min to 26 min). This may indicate a topological linkage of the sister copies that must be resolved before an energetic process can fully separate them.

Given the low number of copies of the plasmid in each focus, the multiple joining events that we observed must have involved single copies forming a pair. That the foci concerned do indeed constitute a joint structure is often indicated by their brightness and/or elongated shape relative to their single-copy progenitors (Fig. (Fig.7,7, cell 4b, 128 min). What is the nature of this joining? Coupled joining and separation events might simply represent two plasmid copies moving independently and passing each other too closely to be resolved. Alternatively, the plasmids could pair when they encounter each other, forming a joint structure and triggering an energetic separation that is equivalent to that seen in the initial separation of sister foci. We favor the second explanation, at least for the majority of cases. First, the joint foci often appeared to stay together through several frames and to move in concert before separating again (Fig. (Fig.5,5, cell 1b, 146 min to 152 min). Second, the apparent conservation of the characteristic sizes of individual foci suggest that foci often join and then separate, reversing their directions of movement (see the legend to Fig. Fig.7).7). Third, there is considerable independent evidence for the ability of separate, partition-proficient P1 plasmids to form specific plasmid pairs both in vivo and in vitro (8, 18, 33).

Can plasmid pairing and separation improve focus distribution?

A high frequency of focus pairing seems superficially counter to efficient segregation. However, we reasoned that it might constitute a useful rescue feature that could lead to the wide separation of plasmids that, due to inadequate segregation, lie relatively close to each other. We decided to test the validity of this hypothesis mathematically.

We set the following simple rules for P1 plasmid behavior based on the experimental observations and the likelihood that closely apposed foci pair. First, plasmids that replicate constitute a pair and are separated by an active process that rapidly moves them away from each other some variable distance. Second, any plasmids that lie or pass close to each other form pairs that are separated by the same process. No particular cell position for foci or direction for segregation is assumed, except that foci are limited to the nucleoid space.

A mathematical simulation of P1 plasmid partition.

We have constructed a mathematical simulation of the behavior of the plasmids governed by the simple rules stated above. The simulation first creates a population of cells with two randomly placed foci. These are replicated as the cell cycle progresses and the foci separate. The cells are then divided, and half of the cells are returned to the start of the program to simulate subsequent cell generations. In each cell and cell generation, multiple rounds of pairing of close foci and subsequent separation events are considered. The distances traveled by separating foci are randomly chosen between user-defined limits, and an outer limit for travel is imposed within a range of positions simulating probable nucleoid end positions. The variables used are described in Materials and Methods, and details of the simulation are given in Document S1 in the supplemental material.

Figure Figure8A8A shows the projected plasmid loss frequencies for a simulation run under typical conditions for 30 generations. Without intervention, half of the initial population of cells would lose the plasmid at cell division. During the first generation, the randomly placed foci are already repositioned so that only 2.5% of the cells lose the plasmid when they divide. In subsequent generations, maintenance of the plasmid is highly stable, and plasmid loss occurs in 0.1% to 0.3% of the cells in all subsequent generations. This compares favorably with the actual rate of loss of the plasmid without selection in vivo, which approximates 0.2% per generation under optimum conditions (22). Figure Figure8B8B shows the same simulation, but without any pairing of plasmids that lie or pass close to each other. Here, the plasmid loss is some 10-fold more severe. Thus, pairing and subsequent separation of plasmids that lie or pass close to each other can be very effective in improving the overall efficiency of segregation.

The distributions of individual foci generated by the mathematical model.

Figure Figure33 (right) shows the distributions of foci in cells with 1 to 6 foci as generated by the simulation in its pseudo-steady state with pairing allowed. The theoretical distributions are remarkably similar to their experimentally generated counterparts (Fig. (Fig.3,3, left). Note that all outputs from the program vary each time the program is run. However, such variations are always small and rapidly achieve a pseudo-steady state. This indicates that the system is self-correcting, as it must also be in vivo. We conclude that the simple rules based on experimental observation are sufficient to explain both the stability of maintenance of the plasmid and the dynamic but even distributions of the foci observed in vivo.

How the proposed system would work.

An interpretation of the data is summarized in Fig. Fig.9.9. The resting mini-P1 plasmid is present as a single copy. As single partition sites are not substrates for active segregation, only random, thermally driven motions occur (a). On replication, the sister plasmids are together and therefore form pairs (b). They are now substrates for partition. However, complete separation may be considerably delayed while topological linkages of the sisters are resolved, and abortive attempts at separation may be evident (c goes to b). A delay in segregation after replication largely accounts for the finding that the average copy number per focus exceeds 1 (1.6). Once free, the plasmids are rapidly moved apart by the partition system on a randomly oriented axis. The partition apparatus then dissociates from the plasmids, leaving the single copies in the resting state. In the absence of other events, the plasmids will roughly maintain their relative positions, undergoing short, random motions but otherwise moving apart only very slowly in concert with cell growth. When a plasmid comes to rest close to its sister (d), as would happen in the case of short axis separations, random motions ensure re-pairing (b), and an additional attempt at wide separation occurs (c, e). This behavior is seen both in vivo and in the simulation. Replication frequently produces three or more plasmids in the cell (f). When a plasmid rests near to or passes close to a nonsister, a new pairing and separation event occurs (h). This may result in several cycles of “shuttling” of the central copy between the outside ones (f through j). However, variability in the distance traveled and growth of the cell length eventually causes the cycles to end when the central plasmid fails to reach a position where pairing can readily occur (k). This phenomenon is seen both in vivo and in the simulation.

FIG. 9.
An interpretation of the behavior of P1 plasmids during partition. The green dots represent the partition site and its associated ParB protein. The red arrows represent ParA filaments involved in plasmid separation. A single resting plasmid is not a substrate ...

DISCUSSION

It has previously been supposed that plasmids with type Ia partition systems are located as clusters at fixed positions in the cell and that segregation translocates them from a central cluster to the cell quarters (14, 26). This concept can now be ruled out for the P1 case, as it is segregated as single units by a highly dynamic process involving no fixed cellular location. Moreover, our observations show that foci, once separated, often come together again and repeat the separation process. This becomes an overriding activity in cells where multiple plasmids are present and, we argue, constitutes an important new mechanism that improves segregation and distributes all plasmid copies into a dynamic but roughly evenly spaced pattern along the cell.

The molecular mechanism by which the copies separate is unknown. This process has been linked to the formation of ParA filaments and to the oscillation of a ParA concentration field in the type 1b plasmid pB171 and the type 1a plasmid F (1, 6). Although we have been unable to see oscillation of the active P1 ParA protein during plasmid partition, we cannot rule out the possibility that a similar activity is involved but does not give rise to sufficiently large concentration differences to be visible. It is not clear how such oscillations might pull plasmid copies apart, but the involvement of ParA fields is an attractive idea that fits with the concept that partition is a plasmid-autonomous activity that is not governed by specific host sites or functions. On the other hand, it is possible that P1 ParA behaves differently from that of plasmids like F or that ParA oscillation is a nonessential consequence of plasmid movement rather than the cause of it in the type Ia partition systems.

Ebersbach et al. (7) have proposed a model by which the spacing between type 1b plasmid copies is created by the oscillating ParA field. In a subsequent work, they suggested that plasmid pairing may be an intermediate in the separation step (30). Thus, our P1 results are consistent with these proposals. However, it was also proposed that ParA oscillation acts to actively maintain the distance between pB171 foci to give an even distribution of plasmid copies along the cell length (7). Our P1 observations show that this is not the case with P1. Rather, P1 foci are highly dynamic and regularly pass or join with each other rather than maintaining their separations. They give an even pattern only when averaged over time.

Our observations suggest a new role for plasmid pairing in creating a dynamic flux that can greatly improve proper segregation when several copies are present. ParB binding is known to pair isolated P1 plasmids in vivo and in vitro (8, 10), and the spreading out of bound P1 ParB from the partition site to occupy much of the plasmid DNA occurs (31). The spreading may aid efficient trans-pairing by bringing together plasmid copies whenever any part of one plasmid touches the other.

Supplementary Material

[Supplemental material]

Acknowledgments

This research was supported by the Intramural Research Program of the Center for Cancer Research, National Cancer Institute, NIH.

Footnotes

[down-pointing small open triangle]Published ahead of print on 6 November 2009.

Supplemental material for this article may be found at http://jb.asm.org/.

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