Escherichia coli Chromosomal Loci Segregate from Midcell with Universal Dynamics

Abstract

The structure of the Escherichia coli chromosome is inherently dynamic over the duration of the cell cycle. Genetic loci undergo both stochastic motion around their initial positions and directed motion to opposite poles of the rod-shaped cell during segregation. We developed a quantitative method to characterize cell-cycle dynamics of the E. coli chromosome to probe the chromosomal steady-state mobility and segregation process. By tracking fluorescently labeled chromosomal loci in thousands of cells throughout the entire cell cycle, our method allows for the statistical analysis of locus position and motion, the step-size distribution for movement during segregation, and the locus drift velocity. The robust statistics of our detailed analysis of the wild-type E. coli nucleoid allow us to observe loci moving toward midcell before segregation occurs, consistent with a replication factory model. Then, as segregation initiates, we perform a detailed characterization of the average segregation velocity of loci. Contrary to origin-centric models of segregation, which predict distinct dynamics for oriC-proximal versus oriC-distal loci, we find that the dynamics of loci were universal and independent of genetic position.

Introduction

Efficient and timely segregation of the chromosome is essential to bacterial cell proliferation. Although a segregation mechanism in Bacillus subtilis and Caulobacter crescentus has been extensively characterized, Escherichia coli is of particular interest due both to its historical role as a model bacterial system and to the absence of homologs of the well-established partitioning genes parAB. The mechanisms responsible for DNA segregation in E. coli have not yet been identified.

E. coli possess a single, circular chromosome that is condensed into a nucleic acid and protein complex called the nucleoid (1). Chromosome replication is initiated near midcell at the origin of replication (oriC) and proceeds bidirectionally around the chromosome (2, 3). Before replicated sister loci can segregate, a brief “cohesion” period occurs, with intercatenation linkages holding the sister chromosomes together (4, 5, 6). These linkages are protected by a sequestering protein, SeqA, which prevents Topoisomerase IV from removing linkages (6). After cohesion, sister loci are segregated sequentially (7, 8). The underlying dynamics for the critical process of moving the replicated DNA remains poorly characterized and the mechanisms responsible are unknown (9, 10).

To understand the mechanisms for chromosome dynamics in this model organism, it is important to accurately characterize the spatial organization of its chromosome. However, there have been conflicting reports about the subcellular localization of loci in the E. coli nucleoid. Currently, one point of contention is the positioning of the left and right arms of the chromosome relative to oriC. In a “left-right filament” model of nucleoid structure, oriC begins at midcell, and each arm of the chromosome extends toward one of the cell poles (see Fig. 1 A). This model is supported by live-cell snapshot imaging using either the fluorescent repressor-operator system or the ParB-parS system (11, 12, 13). Our own live-cell quantitative characterization of the nucleoid in the model strain AB1157 showed that the left-right linear structure was maintained with a very high level of precision and that just 10% of the chromosome (the ter region) was decondensed and stretched between the left and the right poles of the nucleoid (14). On the other hand, analysis of MG1655 was consistent with a domain-based organization consisting of four structured macrodomains (ori, left, right, and ter) and two unstructured regions (15). Although these results were qualitatively consistent with the left-right filament structure, it was difficult to reconcile a ter macrodomain in MG1655 with the observation that it was decondensed in AB1157.

Figure 1.

Cellular-scale models for chromosome structure. Schematic models of the nucleoid with a left-right filament structure (A) and an ori-ter filament structure (B). The left (right) arm of the chromosome is green (orange). oriC is shown in red and ter is in purple. From top to bottom, the cells in each stack represent chromosome structure at cell birth, during chromosome replication, and before division. To see this figure in color, go online.

In another model of nucleoid arrangement, the “ori-ter filament” model, oriC is positioned either at the old pole or midcell, with the left and right arms of the chromosome folded together, forming an ori-ter filament extending toward the new-pole side of the cell (Fig. 1 B). This arrangement has been observed in a study characterizing E. coli in rapid growth (16). Further complicating our current understanding of the E. coli nucleoid arrangement, initial investigations of nucleoid structure using fluorescence in situ hybridization in fixed cells showed both the above-described arrangements successively. Early in the segregation process, oriC is positioned at the pole, with the left and right arms of the chromosome folded together, forming an ori-ter filament (17, 18, 19) (as in the first frame of Fig. 1 B, but with oriC at the old pole). Then, later in the segregation process, oriC moves to midcell, with the left and right arms on opposite sides of the origin, forming a left-right filament (17, 20) (as in the final frame of Fig. 1 A).

It is helpful to consider these inconsistencies in the larger context of bacterial chromosome organization by comparing the nucleoid structure of E. coli to other model bacteria. As in E. coli, reports of B. subtilis have suggested a variety of organizational patterns, including ori-ter (21, 22, 23, 24, 25, 26) or left-right arrangement (27, 28), as well as alternation between the two (29). Reports in C. crescentus and V. cholerae have been more straightforward, with both bacteria possessing ori-ter chromosome arrangement (7, 30, 31). Furthermore, the segregation mechanisms present in these bacteria have been identified and extensively characterized; both C. crescentus and V. cholerae possess the well-known active partitioning ParAB proteins (32, 33, 34, 35, 36), whereas the homologous Spo0J-Soj system acts as the segregating mechanism in B. subtilis (37, 38). With no homologous system yet discovered in E. coli, the mechanisms responsible for segregation in this model bacterium remain unknown.

It is possible that conflicting models in E. coli are a consequence of the failure to account for the cell-cycle dynamics of the nucleoid structure. In our study, we set out to address these unresolved issues by imaging cells over the entire cell cycle to capture the cell-cycle-dependent structure directly instead of relying on cell length as a proxy for cell age. Although many previous studies have made contributions to the effort of resolving nucleoid arrangement inconsistencies, they are largely focused on short timescales (e.g., (39, 40, 41, 42)) and are therefore not suited to studying the segregation processes that play out on the timescale of the cell cycle. Those studies that have captured trajectories throughout the cell cycle analyze relatively few trajectories (39, 43, 44). The capture and analysis of a large number of trajectories is of central importance. We have previously reported our detailed study of the dynamics of oriC throughout the cell cycle, in which we observed that locus segregation is achieved by loci undergoing weakly biased stochastic motion (10). To detect the weak bias in the motion, the motion must be averaged over many trajectories to average out the stochastic motion.

In this article, we use quantitative methods and robust statistics to further probe the segregation dynamics of the entire chromosome. This effort to describe the cell-cycle dynamics of individual loci is achieved through four distinct steps: 1) establishment of a detailed quantitative and dynamic model for nucleoid structure throughout the cell cycle in the wild-type strain MG1655; 2) determination, analysis, and comparison of the step-size distributions for oriC and other loci; 3) characterization of the relationship between genomic position and the motional bias (or drift velocity) just after the initialization of segregation to probe the uniqueness of oriC dynamics; and 4) analysis of these dynamics in a seqA deletion to perturb the segregation process at an early stage.

Materials and Methods

Strains and growth conditions

Single chromosomal loci were fluorescently labeled using a ParB-parS system. These strains were constructed from an MG1655 background with parS-CmR cassettes inserted at different intergenic loci (Fig. 2 A) (39). A full list of these insert locations is provided in Table S1 in the Supporting Material. The isopropyl β-D-1-thiogalactopyranoside (IPTG)-inducible ampicillin-resistant plasmid pALA2705 encoding the fusion green fluorescent protein (GFP)-ParB (8) was transformed into these strains for fluorescent imaging of loci. For full-nucleoid imaging, an IPTG-inducible ampicillin-resistant plasmid harboring a Fis-GFP fusion (45) was transformed into MG1655. For a 1 h cell cycle, cells were grown in M9 minimal media supplemented with 0.2% glycerol as the carbon source and 0.2% casamino acids, 10 μg/mL thiamine hydrochloride and 100 μg/mL ampicillin. All experiments were performed in this medium unless otherwise specified. For slow growth (2 h cell cycle), casamino acids were replaced by 100 μg/mL of arginine, histidine, leucine, threonine, and proline. For locus imaging, overnight liquid cultures were diluted into fresh medium and grown to an OD₆₀₀ of ∼0.1–0.2 at 30°C. Cells were induced for 30 min at 30°C with 0.5 mM IPTG. For nucleoid imaging, overnight liquid cultures were diluted into fresh media and cultured for at least three doubling times before cells were induced. ParB-GFP was induced with 1 mM IPTG for 30 min at 30°C, then harvested and inoculated onto agarose pads for imaging.

Figure 2.

Trajectory alignment. (A) Chromosome map of all labeled genetic loci and the sample cell to visualize normalization of positions to cell-length units, L. $X=0$ indicates midcell, and $X>0$$\left(X<0\right)$ represents the old (new)-pole sides of the cell. (B) An example kymograph. To produce kymographs, cell images were projected along the long axis of the cell and aligned sequentially at midcell. Gray regions indicate cell boundaries determined by the brightfield image. Red pixels indicate a fluorescent signal. (C) Three sample fluorescent tracks from oriC kymographs in physical coordinates display a high level of cell-to-cell variation in localization dynamics. (D) Tracks from (C) are normalized to cell length at each point in time, oriented by cell pole, synchronized by splitting times, and overlaid. This method, when repeated with thousands of tracks, can then be used to generate a 3D histogram of locus positioning throughout the cell cycle. To see this figure in color, go online.

Sample preparation and microscopy

Slides were prepared by pouring 1 mL growth medium mixed with 0.2% low-melting-point agarose (cat. no. 16520-020) into 1.5 cm square wells. Two microliters of induced cells were spotted onto the pads and then covered with a coverslip and sealed using VaLP (1:1:1 vaseline/lanolin/paraffin). To minimize drift, slides were allowed to rest for 1 h at 30°C before imaging. Imaging was completed using a Nikon Ti-E inverted wide-field fluorescence microscope with a large-format scientific complementary metal-oxide semiconductor camera (NEO, Andor Technology, Belfast, United Kingdom) and controlled by NIS-Elements. Samples were kept at 30°C throughout the imaging process using an environmental chamber. The total imaging time for each slide was 4 h, with an imaging frame rate of 1 frame/min. For each frame, both brightfield and fluorescent images were captured. Image processing and analysis was completed using custom MATLAB (Natick, MA) software (10).

Results

Complete cell-cycle imaging

To observe locus positioning within growing cells, we labeled loci with the widely used ParB-parS system (39). Seven strains were constructed in total, each with an exogenous parS inserted at a unique intergenic chromosomal locus. These insertions were found to have no measurable effects on cell growth or morphology (Fig. S1), with cells doubling every 50 min. Chromosome structure was imaged using wide-field fluorescence microscopy at 1 min intervals for 4 h, allowing us to capture the dynamics of fluorescently labeled loci throughout the entire cell cycle in thousands of cells over multiple generations. Locus dynamics are visualized in kymographs (Fig. 2 B), which display long-axis locus dynamics as a function of time. At each time point, the brightfield image of the cell is used to identify the cell boundaries, and the position of the fluorescently labeled chromosomal loci along the long axis of the cell is determined by fitting a Gaussian point-spread function. The kymograph is thus the trajectory of the chromosomal locus through time, with the long-axis position of the locus along the y axis of the kymograph and time from cell birth along the x axis.

One significant concern regarding all live-cell DNA labeling methods is the introduction of exogenous cohesion between the sister chromosomes due to the labeling system (46). Complete-cell-cycle imaging facilitates a detailed analysis of the duration of the cell cycle and the lengths of newborn and dividing cells. Analysis of these distributions reveals that the induction of the labeling system does not significantly perturb the cell cycle, as would be predicted if there were significant cohesion induced by the labeling system (see Fig. S1).

Locus trajectory alignment

Fig. 2 C demonstrates that there is significant cell-to-cell variation in the length of the cell cycle, cell morphology, and the timing of replication initiation. Therefore, to statistically analyze data from many independent cells, we required a consistent and tractable method to combine locus trajectories from thousands of cells. To achieve this goal, we first determine the long-axis displacement of each locus from the cell center, $X_i$, at each time point i as a fraction of cell length, $L_i$, to generate the relative long-axis position, $X_i\text{/}{L}_i$ (Fig. 2 A), and then temporally align each trajectory by its split time, i.e., the time in which newly replicated chromosomal loci copies become visually distinct before segregation (Fig. 2 D). As trajectories are calculated from projections along a single axis, we also have to choose a consistent coordinate system to orient the long axis of the cell. Since we observe the entire cell cycle, we can orient the cells either by the orientations of the new pole (polar orientation) or by the average position of the locus at the end of the cell cycle (genomic orientation), as described in the Supporting Material.

Locus occupancy dynamics

To visualize the typical cell-cycle dynamics of loci, we plot the locus occupancy as a function of the relative cellular position and time relative to the locus splitting time. The locus occupancy is a two-dimensional histogram of locus position, with long-axis locus position on the y axis and time on the x axis. We have generated histograms for both polar and genomic orientation. The polar-oriented occupancy for four different loci is shown in Fig. 3. The mean trajectory for each locus is shown as a solid black line.

Figure 3.

Trajectory histograms. Histograms of synchronized trajectories (see Fig. 1D) throughout the cell cycle for several chromosomal loci. Tracks are oriented with $X>0$ indicating the old-pole side of the cell and $X<0$ indicating the new-pole side. The locus label and number of cells contributing to each histogram are as follows: oriC, N = 3528; L2, N = 2254; R3, N = 1416; ter1, $N=406$. Histograms for all seven loci are included in Fig. S2.

Consistent with the canonical model of locus positioning in slow-growing cells (47), the oriC locus begins the cell cycle at midcell and moves to the quarter-cell positions over a period of ∼10 min. oriC then remains at the quarter-cell positions for the rest of the cell cycle. Also consistent with the filament model (10, 14), a majority of the chromosome appears well positioned about a mean position, with the exception of ter-proximal loci, which display a wide distribution of locus positions. For example, the ter-proximal locus ter1 shows a wide localization distribution throughout the new-pole side of the cell before splitting, as previously reported (14), although the locus appears to localize to midcell before splitting. This behavior for ter1 has been observed previously (48). However, we observe a broader pattern of this behavior; consistent with the ter1 and R3 locus occupancies, regardless of pre-split localization, all loci appear to split in close spatial proximity to midcell with high fidelity (see Fig. 4 C). In the canonical model of E. coli replication, the fork moves with the chromosome, and therefore, loci would be expected to initiate segregation from their home position. In contrast to that model, all loci move toward midcell before splitting.

Figure 4.

Mean locus position trajectories and histogram of split positions. (A and B) Mean locus trajectories aligned by split time oriented using polar (A) and genomic orientation (B). The observation that all loci lie inside oriC demonstrates the predominance of the oriC-ter nucleoid orientation. Loci are also observed to move toward midcell shortly before the initiation of segregation. The tight spacing of the mean trajectory curves demonstrates that the nucleoid configuration is much more compact than observed in AB1157. The noisiness of the mean trajectory at long and short times is due to the small number of cells with cell cycles significantly exceeding 1 h. (Error regions show the error in the mean assuming all observations are uncorrelated. Note that the mean is less meaningful for ter-proximal loci, as their positioning before and after the split is less precise, as can be seen from the locus occupancy of ter1 shown in Fig. 3.) (C) Histogram of splitting locations for all loci in all cells when trajectories are aligned by pole orientation (as in A). Regardless of genetic location or locus long-axis positioning at cell birth, all seven loci split near midcell with high fidelity. To see this figure in color, go online.

However, the ter1 locus occupancy also shows very significant quantitative differences from the quantitative map of nucleoid structure in AB1157 that we previously reported (14). In MG1655, R3 is localized at roughly the new-pole quarter-cell position early in the cell cycle. The left-right filament model predicts that this histogram should show peaks at both the new- and old-pole quarter-cell positions. Orienting the chromosome by genomic orientation is also consistent with R3 localizing to the new pole position.

The dynamics of mean locus position

To compare the dynamics of loci, it is convenient to compute the mean locus position during the cell cycle. (Note that this perspective is less meaningful for ter-proximal loci, since the mean is not representative of the typical locus position, as can be seen from the locus occupancy of ter1 shown in Fig. 3.) We compute the mean using both genomic and polar orientations, as described in the Supporting Material. These trajectories are plotted in Fig. 4 as a function of the cell-cycle age, relative to the oriC split time.

As described previously, oriC is initially positioned at midcell before splitting and then moves to the quarter-cell positions after splitting. The data have excellent sampling, and the mean can be seen to transition smoothly between midcell and the quarter-cell position with no obvious features.

However, for non-oriC-proximal loci, the polar-orientation mean trajectories reveal a structure consistent with the structure implied by the positioning of R3: The oriC-ter filament structure appears to be predominant in MG1655. Since all loci are localized closer to midcell on average than the origin after segregation initiates at $t=0$ min, the ori-ter filament structure (i.e., Fig. 1 B) is predominate over the left-right filament structure (i.e., Fig. 1 A). These observations are consistent with the structure that has been reported for rapidly proliferating cells (16).

To test whether the observed ori-ter filament structure was an artifact of the GFP-ParB labeling system conferred by sister cohesion, we repeated the experiment using the strain AB1157 under slow growth conditions. This strain has a left-right filament structure (e.g., (14)). As shown in Fig. S3, the right arm of the chromosome is not oriented with respect to the new pole in AB1157, even when labeled using the ParB-parS system under analogous imaging conditions. Therefore, ParB-parS does not appear to result in new-pole localization in complete-cell-cycle imaging experiments.

These observations are not wholly unexpected, since both Niki et al. (17) and Bates and Kleckner (20) reported similar patterns in fixed cells where the chromosome is oriented in the oriC-ter configuration for a significant fraction of the cell cycle. Furthermore, this appears to be the dominant structure in rapidly proliferating cells (16).

Dynamics of the nucleoid density

The mean locus position and the occupancy also imply that on average the loci are all much closer to midcell than observed in AB1157 (14). To confirm that this more condensed nucleoid was not an artifact of locus labeling or analysis, we directly imaged the nucleoid using a Fis-GFP fusion (45).

The Fis-GFP fusion nonspecifically coats the nucleoid without affecting cell growth, allowing us to visualize in vivo DNA localization throughout the cell cycle. As in the locus tracking experiments, this cell-cycle imaging offers us the ability to orient cells by pole age. Example snapshots of labeled nucleoids in individual cells at different points in their life cycle are shown in Fig. 5 A. These images show a clear asymmetry in DNA positioning, with a strong bias toward the single new pole at the beginning of the cell cycle and toward the cell center (which will become the two new poles) near the end of the cell cycle. To get an average nucleoid shape distribution throughout the cell cycle, we build a consensus localization pattern, as described in (49).

Figure 5.

Whole-nucleoid imaging. (A) Fis-GFP-labeled nucleoids in single cells. Arrows indicate the new pole (or future new poles) of cells. (B) Consensus localization image of labeled nucleoids from 230 complete cell cycles shows a compact nucleoid asymmetrically distributed toward the new cell pole. (C) Mean DNA density in the first frame of the cell cycle oriented by cell pole (where the right side is negative).

We observe that the consensus localization pattern is consistent with our model: the regions of highest chromosomal concentration fill no more than 50% of the cell length at all points in the cell cycle, and tend to be localized asymmetrically toward the new pole at cell birth (Fig. 5 C), and therefore, we find the overall nucleoid conformation to be significantly more compact in MG1655 than we previously observed in AB1157 (14).

Step-size distributions

Both the locus occupancy distributions and the mean locus position trajectories provide insight into the global dynamics of segregation, but the step-size distribution provides the most direct probe of how the locus motion is perturbed on a local level during the segregation process. The step size is defined by

$$x_i=X_{i+1}-X_i,$$ (1)

where $X_i$ is the locus position in frame j and the time interval between frames is 1 min.

The null hypothesis for the step-size distribution is a normal or Gaussian distribution, with probability distribution function

$$p\left(x|\mu ,\sigma \right)=\frac{1}{\sqrt{2\pi {\sigma }^2}}\text{exp}\left(-\frac{{\left(x-\mu \right)}^2}{2{\sigma }^2}\right),$$ (2)

where μ is the mean (which we will refer to as the bias) and σ is the standard deviation, which is directly related to the mobility of the locus. The Gaussian distribution emerges in quite generic circumstances, even if the underlying dynamics is not diffusive and the cell (i.e., media) in which the loci (i.e., particles) are diffusing is disordered (e.g., (50)).

A number of the existing models of chromosome structure make predictions that are most naturally quantified via analysis of the step-size distribution. For instance, Kleckner and co-workers have proposed that large displacements, which are observed during the segregation process, correspond to a large-scale structural rearrangement of the chromosome due to the unsnapping of structural elements, referred to as “chromosome snaps” (51). Our own analysis of the motion of oriC in the model strain AB1157 did identify large steps (10, 42), but we could not reject the null hypothesis that large steps were a generic feature of chromosome loci, irrespective of whether loci were undergoing segregation or stay-at-home motion (10, 52). Since AB1157 has a significant number of mutations that could inactivate some segregation mechanisms, it was therefore interesting to repeat our analysis in wild-type cells (MG1655) (53).

To compare step-size distributions between strains and phases of the cell cycle, we use the Kullback-Leibler divergence, a natural measure of the difference between two distributions p and q (54, 55):

$$K\equiv \int \text{d}xp\left(x\right)\text{log}\frac{p\left(x\right)}{q\left(x\right)}.$$ (3)

The divergence is interpreted as the information loss of modeling true distribution p with model q. (Note that the frequentist statistical test for whether two distributions are identical is the Kolmogorov-Smirnov test. This is not the question of interest. Our interest is measuring the difference between many distributions that are statistically distinct.) We will interpret the divergence as the distance between distributions. For identical distributions, K is identically zero; otherwise, $K>0$. The magnitude of K is interpreted as follows: the number of observations before information loss is significant is $N\approx K^{-1}$.

Our analysis of the step-size distributions in MG1655 was consistent with our previous observations of oriC in AB1157 (10). As previously reported, we observe that the step-size distribution has fat tails: the number of large magnitude steps is greater than predicted by diffusion (a Gaussian step-size distribution) (10, 42, 44). Two lines of evidence argue against this phenomenon playing a generic and indispensable role in the segregation process.

• 1)The existence of large steps alone does not necessarily imply that these steps are the consequence of an active and segregation-specific mechanism. Similar fat-tailed step-size distributions are generically observed for other large complexes tracked in the cell (42, 56, 57, 58). To quantitate the degree of failure of the diffusion model, we compare the divergence between the observed and diffusion-modeled distributions for both oriC and a control data set of nonfunctional MS2-GFP-mRNA complexes (58) (Fig. S5):

$$K_{oriC}=0.026\text{and}{K}_{\text{MS}2}=0.13,$$ (4)

• demonstrating that the observed oriC step-size distribution is in fact far more Gaussian than one might predict from the dynamics of a large exogenous complex, which is expected to have no specific interactions. Clearly the non-Gaussian distribution is not remarkable in itself.

• Furthermore the absolute size of the divergence is quite small. For our experimental frame rate we are able to capture 10 steps in the first 10 min of segregation during the most rapid motion. The information loss from those 10 steps cumulatively is $10\times K_{oriC}$, which is still not significant (i.e., $>1$). Therefore, the typical cell does not experience steps that are significantly different from the predictions of a Gaussian step-size distribution, but one in four cells do.

• 2)Although the snap model predicts large steps in the direction of increased locus separation, we observe large steps in both directions with nearly equal probability. To demonstrate this, we generate two step-size distributions: $p\left(x\right)$ and $q\left(\delta x\right)$ (Fig. S6). $p\left(x\right)$ is the step-size distributions during the first 10 min of locus segregation, oriented in the direction of the position of locus at the end of the cell cycle (Fig. S6, A). $q\left(\delta x\right)$ is identical to p, except that it is the distribution of mean-subtracted steps, $\delta x\equiv x-\overline{x}$ (Fig. S6, B). We then compute the divergence between $p\left(x\right)$ and $p\left(-x\right)$ and between $q\left(\delta x\right)$ and $q\left(-\delta x\right)$:

$$K_{pp}=9.7\times {10}^{-2}\text{and}{K}_{qq}=5.7\times {10}^{-3},$$ (5)

• respectively. $K_{pp}$ measures the size of the bias in the direction of motion. If the motional bias is caused by a simple shift of the distribution (a drift velocity), then $K_{qq}=0$. Since $K_{qq}$ is just 6% of $K_{pp}$, it suggests that the bias is almost entirely created by a drift velocity, since a shift removes all but 6% of the bias-induced divergence. In summary, although large steps are observed, they do not appear to be the dominant mechanism of movement of loci.

The analysis of the dependence of the step-size distributions on locus genomic position could potentially provide insight into proposed oriC-centric models of segregation if significant differences in the distributions were observed. But, in the first 10 min of segregation, we observe the step-size distribution of loci at different genomic positions to be strikingly similar. The distributions for L2 and oriC are shown in Fig. 6. The divergence between the oriC and L2 distributions is just $K=5.1\times {10}^{-3}$. We shall discuss the significance of this result under Drift Velocity.

Figure 6.

Step-size distributions. (A) The step-size distribution is the probability of observing a step size with a lag time of 1 min. The width of the distribution characterizes the stochasticity of the motion, whereas the mean step size characterizes the directedness of the motion. The initiation of segregation results in a weak bias of the stochastic motion in the direction of average motion. The motion of oriC transitions between unbiased motion (red) and weakly biased motion (green), as seen by the shift in the distribution. The oriC (green) and L2 (blue) loci show essentially identical step-size distributions during the first 10 min of motion. (Error regions show the expected counting error.) (B) Time-dependent histogram of oriC step sizes. Aside from an increased spread in step sizes at the time of locus splitting (t = 0), the distribution in step size is quite homogeneous for the times before and after the split, with a zero bias and consistent spread before the split and a similar spread but with small positive bias after the split.

Subdiffusion and the Gaussian step-size distribution

It has already been reported that loci undergo subdiffusive motion (10, 39, 40, 41, 42, 43, 59, 60, 61). It is important to note that the observation of a Gaussian step-size distribution, although consistent with diffusion, does not imply that the motion is diffusive (e.g., (50)). If the motion were described by diffusion, the step-size variance (i.e., the MSD) would scale linearly with time, ${\sigma }^2=2Dt$, but in fact, ${\sigma }^2\propto t^{\alpha }$, where the scaling exponent, α, has been reported as subdiffusive: $0<\alpha <1$ (39, 40, 41, 42, 43, 59, 60, 61), consistent with our own observations (10). However, our immediate interest is bias in the motion, the component of the motion that does not average to zero during segregation and is therefore responsible for ensuring that one locus is localized to each daughter at the end of the cell cycle (10). Since the step-size distributions are well approximated by a Gaussian distribution with a time-dependent bias, as seen for oriC in Fig. 6 B, it is convenient to focus on a discussion of the time dependence of the bias (drift velocity).

Drift velocity

The drift velocity is defined as the average bias in the locus motion:

$$\overline{v}\equiv \mu /\tau ,$$ (6)

where $\mu \equiv \overline{x}$ is the averaged (oriented) step size and τ is the inverse frame rate. The drift velocity is the property of locus motion that underlies the segregation process (10). As we described previously, at oriC in slowly growing cells, loci transition from nearly unbiased motion $\left(\overline{v}=0\right)$ to biased motion $\left(\overline{v}\ne 0\right)$ during segregation before returning to unbiased motion around the locus home position (10). A second motivation for the analysis of the drift velocity is that in models it is related to the average applied force (10, 59). It is important to note that we define the drift velocity in terms of a finite difference in Eq. 1, and therefore, the drift velocity should not be interpreted as an instantaneous velocity. (See the Supporting Material for a more detailed discussion.)

To characterize the genomic-position and cell-cycle-dependent variation in segregation dynamics, we measured the drift velocity of foci as a function of both genomic position and period of the cell cycle. Again, our expectation was that oriC would be distinct, since replication initiates at this locus and loci are known to segregate sequentially beginning with oriC (8, 62). It is generally believed that whatever the mechanism driving segregation, oriC is expected to undergo different dynamics (e.g., (63)). Our null hypothesis is that all loci move with identical dynamics.

As we previously reported for the origin (59), the drift velocities for all loci follow an approximate power with time (Fig. S8). Fig. 7 shows the drift velocity for three loci (oriC, L2, and ter) as a function of time since the locus-segregation initiated. The observed drift velocity clearly rejects the null hypothesis that all loci are identical, but strikingly, this mismatch occurs late in the segregation process rather than early. Shortly after segregation initiates, all loci experience large, but nearly identical, drift velocities:

$$\overline{v}=0.33\pm 0.01\mu \text{m}/\text{min}.$$ (7)

The observation of a genomic-position-independent drift velocity is counterintuitive, since large drift velocities correspond to large forces that are experienced early in the segregation processes and that we had speculated were the consequence of an active mechanism. However, with respect to these early drift velocities, the behavior at oriC is generic: all other loci characterized had similar drift velocities to oriC.

Figure 7.

Mean drift velocities. Profiles of the relative drift velocities of sister loci are provided for ori, L2, and ter. At short time periods after the initial splitting of sister loci, all loci appear to have similar drift velocities, consistent with a model for segregation that treats all loci identically. At later time periods, sister oriC loci have larger relative drift velocities, allowing them a larger net separation along the length of the cell. (Error regions show the error in the mean.) To see this figure in color, go online.

To test whether the universal drift velocity was an artifact of the ParB-parS labeling system, we compared the dynamics of loci labeled by LacI-mCherry and GFP-ParB in the same strain. Nearly identical drift velocities were observed in this strain as well (Fig. S9).

seqA mutant

To perturb the motion immediately after the initiation of segregation, we characterized the drift velocity in a seqA mutant. SeqA is a regulator of replication initiation that acts by sequestering hemimethylated GATC sites during the replication process (64). Dam methyltransferase competes for the SeqA binding sites and methylates them, reducing SeqA binding affinity. SeqA binds newly replicated DNA specifically and binds many sites in the vicinity of oriC. It has been hypothesized that SeqA plays an important structural role in physically sequestering SeqA sites in addition to its regulatory role (6, 65, 66, 67). We therefore tested whether a seqA mutant perturbs segregation dynamics and, in particular, segregation dynamics during the initial rapid translocation period.

We capture chromosome dynamics in MG1655 $\Delta$ seqA. As expected, we observed that a significant fraction of the cells had multiple copies of oriC at the beginning of the cell cycle. To characterize changes that were not the result of increased DNA copy number, we analyzed only cells with a single copy of oriC at the beginning of the cell cycle.

To investigate whether SeqA perturbs the initial locus segregation dynamics, we computed the drift velocity as a function of time after the initiation of segregation. Although SeqA does perturb the segregation dynamics, the initial segregation velocity is nearly identical to that observed in wild-type cells, as shown in Fig. 8 A. In $\Delta$ seqA, like wild-type cells, ori-proximal loci move more rapidly later in the segregation process. However, the fastest-moving loci in the $\Delta$ seqA cells were still slower than all locus positions observed in the wild-type cells. These observations are consistent with SeqA playing either a direct or indirect role in facilitating the movement of loci to their home positions, but interestingly, it has only a weak effect on the initial locus dynamics.

Figure 8.

Segregation phenotype of the seqA mutant. To perturb DNA structure shortly after replication, we constructed a seqA deletion. (A) $\Delta$seqA has a nearly universal initial drift velocity. (B) The smaller separation for seqA loci implies that all loci segregate with a lower drift velocity. This is observed as the integrated effect of a velocity that is only slightly smaller acting throughout the segregation process.

Discussion

In this study, we have used complete-cell-cycle imaging to observe dynamic chromosome structure throughout the entire E. coli cell cycle. We aim both to map out the cell-cycle-dependent structure of the chromosome and to perform a detailed analysis of the segregation dynamics of loci.

Conflicting ori-ter (i.e., Fig. 1 B) and left-right (i.e., Fig. 1 A) filament organizations have been reported for the E. coli nucleoid. Under slow-growth conditions, with a 2 h cell cycle, we had previously performed a detailed quantitative analysis of the strain AB1157 and reported a precisely structured left-right filament organization (14), consistent with other recent live-cell measurements of the chromosome structure in E. coli (11, 12). In this study, we characterized the wild-type strain MG1655 with a 1 h cell cycle. Here, we report that the dominant structure under these conditions is the ori-ter filament organization, consistent with some previous reports using fluorescence in situ hybridization (17, 18, 19, 20) and recent measurements characterizing the chromosome structure during multifork replication (16). We have supported this report using histograms of locus positions (Fig. 3), mean locus positions (Fig. 4), and nucleoid imaging (Fig. 5). Although each of these methods has limitations, we feel that the consistency between these results provides strong support for an ori-ter filament, with loci splitting at midcell. Consistent with rapid growth, we also see a segregation pattern of locus movement more reminiscent of a replication factory model (27): Loci were observed to localize to midcell before segregation initiated, then to split and move rapidly outward to their home positions. This pattern is most striking for loci on the left and right arms of the chromosome far from oriC. These observations suggest that although the replication forks in E. coli have been observed to separate (e.g, (48)), conflicting with a literal interpretation of the replication factory model, they are likely in close proximity for most of the cell cycle, consistent with the spirit of the replication factory model (27).

We analyzed the locus trajectories to determine whether the translocation during segregation was better modeled by the slow accretion of many small biased steps or by a small number of large steps, corresponding to large-scale structural transitions in the chromosome (i.e., snaps), which have been reported previously (44, 51). We observe that all loci segregate rapidly over the first minute, but we have been unable to detect an unambiguous statistical signature of large steps in segregation after this time. As we described previously (10), although large steps can happen, they occur 1) throughout the cell cycle, 2) with roughly equal probability in and against the direction of bias, and 3) in only a fraction of cells during rapid translocation. Our observations and analysis of motion of different locus positions in MG1655 are consistent with our previous report: most loci appear to move by the slow accumulation of biased motion rather than by large steps. We emphasize that the absence of an enrichment of large steps during segregation does not invalidate the snap model.

A second unexpected feature of the chromosome dynamics was the universality of the dynamics of all loci at the start of the segregation process. Our previous detailed characterization of the dynamics of oriC revealed that loci feel a directional bias immediately upon the initiation of segregation, an observation that is most consistent with an active mechanism (e.g., (63)). If an active mechanism exists that drives the segregation of the origin, it is natural to expect other loci that are segregated later by a condensation-driven mechanism to exhibit different dynamics. Furthermore, one might naïvely expect the forces to be most distinct early in the segregation process when the drift velocities and the forces themselves are strongest (10, 59). Even if the loci were segregated by an entropic mechanism (16), simulations suggest that the initial segregation of oriC should be slower than that of later loci (63). Therefore, whatever the mechanism, it was our expectation that the initial segregation dynamics of oriC-proximal loci should be qualitatively distinct from those of other loci.

Given these general arguments in favor of qualitatively distinct dynamics after segregation for different regions of the chromosome, we were therefore quite surprised to observe that both the drift velocity and the step-size distribution were nearly identical for all loci characterized. Of course, this may be a coincidence: Despite the distinct ParA-dependent mechanism that segregates the origin in C. crescentus (68), the average speed only varies by a factor of 2 (7). Still, the similarity between loci dynamics in E. coli is much greater than observed in C. crescentus, consistent with the hypothesis that there may be some universal mechanism at work in the segregation of all loci in E. coli (e.g., (69)). (The mechanism is universal in the sense that its action on the loci leads to nearly identical dynamics during the initial steps of segregation.) Kleckner and co-workers have long speculated that there is an accumulation of stress in the chromosome (70) that is released in an unsnapping event (44, 51). Since this process could be driven by MukBEF, super-coiling (71, 72), and other processes that lead to longitudinal condensation (73), these mechanisms could explain the universality in the initial segregation dynamics.

Since the greatest mismatch in the drift velocity occurs 5 or more min after segregation initiates, it is interesting to speculate about the possible mechanism for this increased drift velocity for loci proximal to oriC. The deletion of seqA was observed to have the strongest effect on the bias 5 min after the initiation of segregation, consistent with a model where late-stage segregation is facilitated by cellular machinery. There is precedence for additional mechanisms that act late in the segregation process in C. crescentus (36). On the other hand, it is important to realize that due to the overall chromosome topography in E. coli under the experimental conditions, oriC moves the furthest of all loci, and therefore, it must have a higher drift velocity to reflect this greater travel distance. The mechanism for higher drift velocity long after the initiation of segregation might be induced by nucleoid structure and quite prosaic from a mechanistic perspective (16).

Author Contributions

J.A.C., N.J.K., and P.A.W. designed research, performed research, contributed analytic tools, analyzed data, and wrote the manuscript. B.T. designed research and wrote the manuscript.

Editor: Zemer Gitai.