Post-replicative pairing of sister ter regions in Escherichia coli involves multiple activities of MatP

The ter region of the bacterial chromosome, where replication terminates, is the last to be segregated before cell division in Escherichia coli. Delayed segregation is controlled by the MatP protein, which binds to specific sites (matS) within ter, and interacts with other proteins such as ZapB. Here, we investigate the role of MatP by combining short-time mobility analyses of the ter locus with biochemical approaches. We find that ter mobility is similar to that of a non ter locus, except when sister ter loci are paired after replication. This effect depends on MatP, the persistence of catenanes, and ZapB. We characterise MatP/DNA complexes and conclude that MatP binds DNA as a tetramer, but bridging matS sites in a DNA-rich environment remains infrequent. We propose that tetramerisation of MatP links matS sites with ZapB and/or with non-specific DNA to promote optimal pairing of sister ter regions until cell division.

B acterial nucleoid structuration is due to a variety of processes including DNA supercoiling, proteins and complexes working on the DNA (e.g., RNA polymerases), nucleoidassociated proteins and condensins (SMCs) 1 . These act together to shape the chromosomes in a dynamic structure while keeping DNA accessible to polymerases and repair proteins. Replication and segregation re-organise nucleoids on a large scale 2,3 . Whilst some details may vary, common to all bacteria is the bidirectional replication of the chromosome, starting at a unique origin and finishing in the opposite terminus region, which is the last to be segregated before cell division.
Macrodomains are large regions with specific cellular positioning that contain either the origin or terminus of replication 4-8 . In Escherichia coli (E. coli), the Ter macrodomain (ter) is very distinctive (Fig. 1a), spreading along 800 kb encompassing the replication terminus region 7 . It contains 23 matS sites that are recognised by the MatP protein 9 . MatP is known to play a key role in ter positioning and setting its segregation pattern: it keeps the sister ter regions paired near the divisome, at mid-cell, allowing their processing by the DNA-translocase FtsK 10 . Since FtsK activity is oriented by KOPS DNA motifs, segregation ends at the dif site, where final unlinking of sister chromosomes occurs 10,11 .
How MatP achieves its functions is currently unclear. MatP forms dimers in the absence of DNA, and tetramers upon binding to matS-containing DNA 12 . This was proposed to pair matS sites, forming large chromosome loops, though they were not detected in contact maps of the chromosome 13 . MatP was also shown to interact with the divisome-associated ZapB protein 14 and the condensin MukB 15 . A truncated variant of MatP (deletion of the last 20 residues), MatPΔ20, was reported unable to form tetramers 12 nor to interact with ZapB 14 , yet retaining interaction with MukB 15 . MukBEF was reported to promote long-range interactions between chromosome loci, probably by forming loops, in a MatP-dependent manner 13,16 . Consistent with this view, MatP and MatPΔ20 lower long-range interactions and/or promote short-range interactions inside ter 13 while excluding MukB from ter 15 . Since MukB interacts with TopoIV, its exclusion by MatP probably delays decatenation of sister ter, thus coupling their segregation with cell division 15 . Interaction of MatP with ZapB has been proposed to induce a positive control of divisome assembly around ter, (the Ter-linkage) 17,18 . Mutation of zapB, as well as matPΔ20, alters the mid-cell positioning of MatP-bound sister ter and shortens the co-localisation times of ter loci 12,14 .
Foci movements have also been recorded at different time scales, revealing important differences between chromosome regions. At long time scales, loci tracking captures their segregation dynamics [19][20][21][22][23][24] . Loci of ter localise accurately at mid-cell 19 , then separate when early divisome components have formed a complex at mid-cell. At short-time intervals, they sub-diffuse 21,[25][26][27] , reflecting constraints imposed by their environment 9,13,27 . A previous study showed that the mobility of loci varied depending on chromosomal localisation 27 , the ter loci being less mobile when located at mid-cell.
In this report, we investigate the role of MatP in constraining the mobility of a ter locus. Surprisingly, low-fluorescence foci of the ter locus are as mobile as those of an oriC-proximal locus, showing that the higher constraint of the ter locus is not an intrinsic property but depends on context. We further show that highly intense and poorly mobile foci form most often at the ter locus and depend on the presence of MatP, suggesting they contain pairs of unsegregated sister loci. This effect depends on MatP, its 20 C-terminal residues and ZapB to different levels. We characterise MatP/DNA complexes and conclude that while MatP binds DNA as a tetramer, it rarely forms specific DNA loops by bridging matS sites in a DNA-rich environment, suggesting that the tetramers play a different role.

Results
Monitoring chromosome loci mobility in vivo. To monitor the mobility of chromosome loci, we used strains carrying a parS site inserted on the chromosome and producing cognate ParB-GFP proteins 28 (Fig. 1a). We recorded the position of foci every 0.5 s during 20 s (Fig. 1b), then extracted the mean squared displacements (MSD) from these trajectories. An example of 30 MSD for Ter4 is shown in Fig. 1c.
We first used the P1 parS site and ParB protein to tag loci in the ori and ter regions, and we reproduced published results for Ori2 and Ter3 27 (Fig. 1e). However, this P1-derived system has been reported to increase post-replicative cohesion of tagged loci 10,28,29 . We thus tested another set of strains, with loci tagged with parS-pMT1 and producing a ParB-pMT1-GFP 28 . The comparison revealed important differences: (1) The number of cells with a single focus decreased and those with two foci increased when using the pMT1-derived system (Fig. 1d); (2) The MSDs obtained with the pMT1 system were larger than with the P1 system (Fig. 1e); (3) The difference in MSDs between the ori and ter loci were largely reduced when using the pMT1-derived system (Fig. 1e); (4) For a same intensity, a remarkable drop of mobility was observed for Ter loci labelled with parS-P1 27 . The P1-derived system thus not only delays ter segregation, but creates aggregates of proteins that result in brighter foci (Supplementary Fig. 1) with very low mobility, biasing the results obtained. We chose to proceed with the pMT1-derived system in this work.
The mobility of a ter locus depends on foci intensity. We next analysed the fate of foci formed at Ori2 and Ter4. Foci populations were binned into categories depending on their number per cell and their localisation, for which we defined two categories: (M) mid-cell (0-1/6th cell length from the cell centre) and (R) rest of the cell (1/6th-1/2). Consistent with previous reports [29][30][31] , segregated foci of Ori2 preferentially localised at the quarter positions, and near mid-cell for single foci. Also consistent with previous reports, Ter4 foci were preferentially located at mid-cell ( Supplementary Fig. 2), unsegregated foci being closer from midcell than segregated ones.
Foci intensity varied between loci. Ori2 foci followed a sharp distribution centred around 500 AU (Fig. 2a). In contrast, Ter4 foci followed a wider distribution with more high-intensity foci. For moderately intense foci (below 1000 AU), we observed a monotonous decrease of mobility when intensity increased (Fig. 1f). Strikingly, Ori2 and Ter4 foci had equivalent MSDs at corresponding intensities. The low mobility of ter loci is thus not an intrinsic property of ter but depends on the intensity of the foci (Fig. 1f). At intensities above 1000 AU, foci mobility no longer varied in a monotonous way with increasing intensity and was clearly different between Ori2 and Ter4. From this observation, we defined two categories of foci: foci of low intensity, hereafter called FL, below 1000 AU, and foci of high intensity, hereafter called FH, above 1000 AU. FH were rare at Ori2 (2%) but rather frequent at Ter4 (30%) (Fig. 2b). Double FH of Ter4 were rare and tended to position like double FL.
Calibrating the number of GFP molecules in foci (from the increase of variance in intensity along time) gave an estimated mean of 33 GFP molecules for Ter4 and Ori2 FL, whereas the mean for Ter4 FH was 70 GFP (Supplementary Fig. 3 and "Methods").
FL and FH show different dynamics. We analysed the trajectory of foci using four parameters characterising the nature of movement ("Methods" 32 ): (1) The anomalous exponent (α) is computed from the MSD behaviour for small increments. It indicates the nature of the locus motion. α = 1 describes normal diffusion, α < 1 is sub-diffusive (constrained) and α > 1 is superdiffusive (directed) movement. (2) The length of confinement (L c ) is the standard deviation (SD) of the locus position with respect to its mean averaged over time. This estimates the apparent radius of the volume explored by a finite trajectory. (3) The diffusion coefficient (D c ) reflects the second-order statistical properties of a trajectory, and accounts for local crowding that may vary along the trajectory. (4) The effective spring coefficient (K c ) represents an external force acting on a locus. It is modelled as a spring force applied on a single monomer belonging to a polymer. This force affects the entire polymer motion and can be recovered from the first-order moment statistics of single locus trajectories.
Considering only FL (Fig. 2d), the value of each parameter was poorly dependent of their position, suggesting that loci properties do not change significantly during the cell cycle. Ori2 foci had a low value of α (0.16), whereas Ter4 showed a slightly higher α (0.2, p = 3.8 × 10 −13 ), suggesting that the local condensation is slightly higher in ori than in ter, according to the RCL model [32][33][34] . The length of confinement for both loci was small (0.084 and 0.081 μm for Ori2 and Ter4, respectively), revealing loci are confined in small regions, which size depends slightly on chromosomal or cellular location. The diffusion coefficient was higher for Ori2 than for Ter4 (3.5 × 10 3 and 2.9 × 10 3 μm 2 s −1 , respectively, p = 2.7 × 10 −22 ), showing that despite a greater condensation, Ori2 is freer to diffuse than Ter4. Finally, the spring coefficient revealed equivalent forces tethering both Ori2 and Ter4 (331 and 319 k B T μm −2 ). In cells harbouring two foci, 2FL showed the same behaviour as 1FL ( Supplementary Fig. 4a).
Ter4 FH behaved differently than FL (Fig. 2d). Ter4 FH α was close to the FL value (0.22 for FH and 0.2 for FL, p = 7 × 10 −5 ) and remained the same for both cell positions (p = 0.5), suggesting a monotonous condensation of the ter region. However, L c was lower than for FL (p = 10 −125 ) and lower at mid-cell than in the rest of the cell (p = 8 × 10 −4 ). This suggests Ter4 FH are more confined than FL and more confined when at mid-cell. D c showed the same trends as L c , showing that Ter4 FH are diffusing less than FL (p = 10 −200 ) and less when in the midcell area (p = 5 × 10 −5 ). These changes are consistent with a doubling in the force applied to Ter4 FH when at mid-cell (620 k B T μm −2 for FH and 331 k B T μm −2 for FL, p = 10 −130 ).
Ter4 FH are thus, compared to FL: brighter, submitted to twice the force, more confined, less diffusive and preferentially located at mid-cell. A straightforward hypothesis is that they mostly contain sister loci held together in post-replicative cohesion. This is consistent with the extended cohesion period reported for sister ter regions 21,29,30 , even when the pMT1 system was used 10 . This also explains the higher percentage of FH for Ter4 compared to Ori2. It follows that most FL contain single copies of loci. Assuming this hypothesis, a strong constrain is applied to ter loci only when they are in post-replicative cohesion. The rest of the time, their dynamics is much more similar to the one of other chromosome regions than previously thought. NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-17606-6 ARTICLE MatP is required for FH formation and maintenance in ter. We next deleted matP from our strains and observed the fate of Ter4 foci. The strongest effect was on FH. Cells with one FH decreased drastically (from 27 to 8%; Fig. 3a), whereas cells with one FL decreased moderately (from 58 to 48%). Consistently, cells with two foci increased and mostly contained FL. This increase in two-foci cells is consistent with MatP acting to keep sister ter regions together after replication 9 . The large decrease in 1FH cells thus confirms that FH contain pairs of unsegregated loci. In the Δ(matP) strain, the remaining FH were more mobile and less confined than in the wild type. They showed increased L c and D c and decreased K c (Fig. 3b, p = 10 −8 , p = 1.9 × 10 −12 , p = 7.6 × 10 −11 , respectively). These values are close to the ones obtained for Ori2 FH (Supplementary Data 2, p = 0.75, p = 4 × 10 −3 , p = 0.56 for L c , D c and K c ). In addition, FH at mid-cell were not different anymore from the ones located in the rest of the cell (Fig. 3b, p = 0.6, p = 0.4, p = 0.5 for L c , D c and K c ). We conclude that MatP is required both for the high number of FH Ter4 and for their specific constrain at mid-cell. A slight but significant difference in mobility and confinement between FH and FL in the Δ(matP) strain persisted ( Fig. 3; p = 4 × 10 −17 , p = 2 × 10 −33 and p = 4 × 10 −14 for L c , D c and K c ). Remaining FH may be rare single loci with high fluorescence intensity, which should reduce their mobility 35 . However, a fraction of remaining FH certainly contains foci present on chromosome dimers, which may pair during FtsK/Xer resolving process, since this is MatP-independent 9 . Interestingly, deletion of matP had only a slight effect on α of Ter4 FH (p = 0.02) and none on FL (p = 0.06), suggesting that MatP only marginally influences the local condensation of ter DNA. Deleting matP also had a small but significant effect on Ter4 FL dynamics (Fig. 3c). They were less confined and more mobile in the Δ(matP) strain (higher L c (p = 3 × 10 −7 ) and D c (p = 6 × 10 −7 ), lower K c (p = 7 × 10 −10 )). This appears as a general effect, as equivalent variations were observed with Ori2 ( Supplementary Fig. 5b).
Different activities of MatP are required for FH formation. We then used two mutants: a deletion of zapB, coding for the divisome-associated protein interacting with MatP 14,36 , and matPΔ20, coding for a version of MatP deleted of the last 20 Cterminal residues, defective for both interaction with ZapB and tetramerisation 12 . In these two mutants, MatP still binds matS (ref. 12 , and below) and interacts with MukB 15 .
Both Δ(zapB) and matPΔ20 mutants showed a phenotype intermediate between the wild-type and Δ(matP) strains considering Ter4 foci (Fig. 3a). The number of cells with two FL increased, whereas those with a single FH decreased. This effect was slightly more pronounced in the Δ(zapB) than in the matPΔ20 strain. This shows that two activities of MatP are mainly required for FH formation: one not affected in MatPΔ20 and the other one depending on an interaction with ZapB.
A detailed analysis of Ter4 FH in the two mutants was fully consistent with the above conclusion ( Fig. 3b, Supplementary Data 3). FH confinement decreased and mobility increased (higher L c and D c , lower K c ) compared to the wild-type strain; these effects were more marked in the matPΔ20 strain, yet lower than in the Δ(matP) strain. In both mutant strains, FH were more confined and less mobile when located at mid-cell, as in the wildtype strain.
In the matPΔ20 strain, Ter4 FL behaved as in the Δ(matP) strain (Fig. 3c), i.e., slightly increased L c and D c and decreased K c compared to the wild-type strain, indicating a moderate decrease of confinement and increase in mobility. MatP activities other than tetramerisation and/or interaction with ZapB are thus not required to constrain FL. Surprisingly, the Δ(zapB) mutation had a larger effect than either the Δ(matP) or the matPΔ20 mutation on Ter4 FL (Fig. 3c). This was unexpected but may be explained by properties of ZapB that are independent of its interaction with MatP (see "Discussion").
Only one MatP activity is mediated by TopoIV control. Since MatP was proposed to control the removal of catenanes by TopoIV 15 , we assayed the effect of a moderate overproduction of both TopoIV subunits. This was previously reported to shorten the post-replicative co-localisation period of non-ter loci by premature resolution of precatenanes 37 . Overproduction of TopoIV increased the portion of cells with a single FL, suggesting it somehow modifies the cell cycle, delaying replication and/or postponing cell division (Fig. 4). As expected, the number of Ori2 FH decreased (from 1.3 to 0.5%), consistent again with most FH being paired loci. Strikingly, this effect was not observed at Ter4 in the wild-type strain but was clearly observed in both the    ). We conclude that post-replicative co-localisation between sister ter loci results from at least two different mechanisms involving MatP: one depends on the last 20 C-terminal residues of MatP and on ZapB and is not affected by increased levels of TopoIV, the second one depends on an increased level of TopoIV, suggesting a MatP-dependent catenane persistence.
MatP bridges DNA molecules in vitro. As we assume FH contain paired loci dependent on MatP, we attempted to characterise DNA bridging by MatP. We designed an assay based on DNA pull-down (Fig. 5a). A biotinylated DNA molecule containing 0-2 matS was bound to a streptavidin-covered magnetic bead (DNA b ). This complex was mixed with a free DNA (DNA f ) containing 0 or 2 matS. The mix was then incubated with MatP, washed, pulled-down with a magnet and eluted with a low concentration of SDS. The amount of DNA f recovered represents the capacity of MatP to bridge the two DNA molecules. When they both contained two matS (Fig. 5b), 18% of DNA f were recovered with the lowest concentration of MatP used (0.1 μM), increasing to 63% at the highest concentration (2 μM). When repeating the same experiment with DNA that did not contain matS, DNA f was recovered with lower efficiency (Fig. 5c). When only one DNA contained a matS, the amount of DNA f recovered was intermediate ( Fig. 5d and Supplementary Fig. 6). We conclude that MatP is able to bridge independent DNA molecules containing or devoid of matS. The presence of matS stimulates this activity and/ or stabilises the complexes formed.
MatP bridging activity involves non-specific DNA binding. To better describe MatP bridging activity, we used a high-throughput tethered particle motion (TPM) set-up 38 . This tracks beads attached at one end of a DNA molecule while the other extremity is tethered to a coverslip (Fig. 6a). The amplitude of motion at equilibrium of the bead (A eq ) directly depends on the apparent length of the DNA 39 . We used DNA containing 0, 1 or 2 matS separated by 1207 bp. The traces (example Fig. 6b) are plotted as densities of probability of their A eq and fitted to Gaussian distributions (Fig. 6c). Without protein we observed a single population centred on 250 nm (Fig. 6c, *). Adding MatP resulted in the displacement of the whole population toward shorter A eq , independently of the DNA used. This corresponds to an apparent shortening of around 30 nm (Fig. 6c, **). This moderate decrease in A eq cannot correspond to MatP-induced DNA looping between the matS sites, because it is independent on matS. Moreover, the shortening predicted from bridging two matS would be around 100 nm. An equivalent moderate decrease in A eq was previously observed using another site-specific, DNA-binding protein in the same set-up and was attributed to protein binding to a single site 40,41 . Surprisingly, this moderate decrease in A eq was not observed with MatPΔ20 (Fig. 6c). We verified that MatPΔ20 and MatP bound matS-containing DNA (Supplementary Fig. 7a). Tagged or untagged versions of MatPΔ20 bound a matScontaining DNA with equivalent efficiency as MatP. However, the mobility of the complexes was unexpected. Indeed, MatPΔ20tag formed complexes migrating faster than MatP, despite being twice bigger (Fig. 7). Assuming MatPΔ20 binds DNA as a dimer 12 , these observations suggest that MatP binds DNA as a tetramer. This explains the difference observed between MatP and MatPΔ20 in TPM experiments, suggesting the moderate decrease in A eq (Fig. 6c, **) is due to tetrameric MatP binding to a single matS, or to non-specific DNA, and changing DNA conformation. A second population with shorter A eq was obtained upon incubation of the 2-matS DNA with MatP (Fig. 6c, ***). Gaussian fitting of this population indicates that it was centred at 147 nm (±22), corresponding to the 100 nm shortening predicted for looping between two matS. Accordingly, this peak was neither observed when using DNA without matS nor when using MatPΔ20 (Fig. 6c). However, it was also detected upon incubation of the 1-matS DNA with MatP. This peak was centred on 153 nm (±23) and contained three times fewer events (13%) than with the 2-matS DNA (36%). The second peak formed with DNA containing one or two matS exhibited very similar centres, as if 1200 bp was the most favourable inter-matS distance for looping by MatP. We next repeated the experiment using a 2-matS DNA with non-specific DNA as a competitor. The moderate decrease in A eq was readily observed (Supplementary Fig. 8a; **), but the peak corresponding to a greater shortening was not, showing that pairing of distant DNA loci by MatP is sensitive to non-specific DNA competition. The analysis of the kinetics of loop formation ( Supplementary Fig. 8b, c) showed that the presence of matS enhances the formation of loops by increasing the duration of long-lived looped events. Taken together, these results show that MatP can pair distant DNA loci in TPM. This activity depends on the 20 C-terminal residues of MatP, is stimulated by the presence of matS but is highly dynamic, and strongly sensitive to the presence of non-specific DNA.
This prompted us to analyse in more details the MatP/matS complexes. Using two DNA probes carrying a single matS and labelled with different fluorophores, we performed an EMSA ( Supplementary Fig. 7c). We failed to detect complexes containing both fluorophores, showing that the MatP/DNA complexes contain a single DNA molecule. This suggests that when MatP  Fig. 6 MatP can loop DNA. a Scheme of the TPM set-up. A glass coverslip is coated with PEG and neutravidin. A DNA molecule is attached to that surface by a biotin bound to one of its 5′ end. A latex bead coated with antidigoxigenin is bound to the other extremity of the DNA molecule by the presence of digoxigenin on this 5′ end. The amplitude of the Brownian motion of the bead (A eq ) depends on the size of the DNA molecule that tethers the bead to the glass surface (for details see text and "Methods"). Right: if MatP joins the 2 matS sites together, the A eq decreases. b Example of a track following a bead tethered to a 2-matS DNA as a function of time. The dotted lines indicate the expected A eq for a naked DNA (top) or looped DNA (bottom). MatP is added after 2 min (arrow) and the bead tracked for another 13 min. Time scale is 1 min (bar). c Probability distributions of A eq , before protein injection (light grey histogram), or during the 5 min following the injection (dark grey histograms). The type of DNA (0-2 matS), the type of MatP (wt or Δ20) and the number of tracks obtained for each condition are indicated on the graphs. MatP: *population centred on (mean ± SD, in nm): 248 ± 19; 250 ± 21 and 257 ± 21 for the DNA containing 2, 1 and no matS site, respectively. **population centred on (mean ± SD, in nm): 211 ± 25, 224 ± 26 and 229 ± 28 for the DNA containing 2, 1 and no matS site, respectively. ***population centred on (mean ± SD, in nm): 147 ± 22 and 153 ± 23 for the DNA containing 2 and 1 matS site, respectively. MatPΔ20: *population centred on (mean ± SD): 252 ± 20 nm. Source data are provided as a Source Data file. tetramers are bound to matS, one DNA-binding domain is involved in the specific interaction with matS, while the second is free. This matS-free dimer could then interact with non-specific DNA and/or with other proteins, including ZapB. We directly assayed this last hypothesis by adding purified ZapB in our in vitro assays, but failed to detect significant effects. ZapB did not change the pattern obtained in EMSA ( Supplementary Fig. 9), nor the quantity of DNA f retrieved in pull-down ( Supplementary  Fig. 10). Thus, if the matS-bound MatP tetramer interacts with ZapB, this interaction is too weak, transient or unstable to be detected in our experiments.

Discussion
We combined different approaches to investigate the organisation of the ter region and the role of MatP. These results yield several new observations and unexpected conclusions: (1) ter loci are not intrinsically less mobile than ori loci; (2) a significant proportion of ter foci show a high fluorescence, preferentially when they are located at mid-cell, and are much less mobile; (3) the proportion of these foci and their low mobility depend on all described activities of MatP, specifying two separable processes, of which one depends on the persistence of catenanes, while the other one depends on interaction with ZapB; (4) MatP binds matS as a tetramer but this complex contains only one DNA fragment; (5) the bridging of matS sites can be observed in vitro but is efficiently competed by non-specific DNA. From these observations, we conclude that MatP constrains ter mobility only at a specific stage of the cell cycle, when replication has terminated and sister chromosomes are paired by their ter regions (D period of the cell cycle). MatP does so via at least two activities, only one depending on its C-terminal domain. This last activity certainly depends on tetramerisation, but not on bridging remote matS. Indeed, the pairing of matS can be observed in vitro but is readily challenged by non-specific DNA and is thus likely irrelevant in vivo. Loci of the ter region have been reported to be less mobile than other regions 9,12,14,21 . However, these comparisons did not consider the context of the foci, particularly their intensity. Tracking foci over short-time intervals, focusing on local DNA constraints, has revealed that mobility depends on foci intensity and on their sub-cellular positioning 27 . Our data extend this observation and further show the importance of the labelling system. Indeed, using the less invasive pMT1-derived system, significant differences in mobility between an ori-proximal and a ter-proximal locus are observed only for the most intense foci (FH). Indeed, less intense foci (FL) of the ter and ori loci show the same decrease in mobility when intensity increases (Fig. 1). The trajectories of FL revealed slight but significant differences between ori and ter, including a decreased α anomalous coefficient, suggesting ori is more condensed than ter (Fig. 2). This may be consistent with recent images of the E. coli nucleoid showing a donut shape in round cells, in which the ter region appears less condensed than the rest of the chromosome in a MatP-dependent way 42 . Higher α coefficient may be linked to the MatP-mediated exclusion of MukBEF from ter 13,15,16 . However, the difference in α we measured is not MatP-dependent (compare Figs. 2 and 3), arguing against this hypothesis. Despite its higher condensation, the ori locus appears freer to diffuse than the ter locus, as shown by its higher diffusion coefficient (Fig. 2). This difference is only partly suppressed by a mutation of matP and better suppressed by a mutation of zapB (compare FL foci in Figs. 2 and 3). Since ZapB self-assembles into large structures and clusters around ter (in a MatP-dependent manner) and the divisome (in a MatPindependent manner) 17,36,43,44 , we suspect these clusters limit the diffusion of ter loci via an interaction with matS-bound MatP but also by a MatP-independent mechanism, yet to be described.
Highly fluorescent foci of the ter locus (Ter4 FH) show very distinctive properties. They are less mobile than expected from their intensity compared to the ori locus (Fig.1). They are preferentially localised at mid-cell and depend on MatP, TopoIV and ZapB (Figs. 2-4). They are in majority single foci and, in mutant strains, their decrease correlates with an increase in two-foci cells (Fig. 3). From these observations, we conclude that most FH contain pairs of sister loci. An estimation of cell cycle periods duration agrees with this view. In our strain and growth conditions, about two-third of the cells have completed replication 45 . Assuming ter segregates at the onset of cell constriction 10 and that about 25% of the cells are constricting in a growing population, the 27% FH we observed can be restricted to cells having completed replication and not initiated constriction. Detailed analysis shows that the α coefficients of FH and FL are close for Ter4, suggesting paired sister ter regions are not more condensed than single ones. Ter4 FH also show lower L c and D c and higher K c than FL, consistent with their very low mobility and high constraint. Surprisingly, this is only partly suppressed by a mutation of matP (compare Figs. 2 and 3) and even less by matPΔ20 or a mutation of zapB (Fig. 3). These results agree with the low mobility of Ter4 FH being primarily due to the postreplicative pairing of sister ter regions. The role of MatP would therefore be to delay the separation of sister ter regions, hence its drastic effect on the frequency of FH, but only marginally to constrain their mobility per se.
At least two activities of MatP are involved in post-replicative pairing; one, requiring the 20 C-terminal residues of MatP, depends on ZapB but not on catenanes and the other one, independent on the last 20 residues, depends on catenanes but not on ZapB-assuming that over-expressing TopoIV leads to catenanes removal. The pairing activity unaffected in matPΔ20 involves the control of sister chromosome decatenation since it is suppressed by overproduction of TopoIV (Fig. 4). Consistently, inhibition of decatenation by depleting active TopoIV hinders sister chromosome separation 37,[46][47][48][49] . MatP may control the activity of TopoIV by several mechanisms. First, MatP could exclude TopoIV from ter by excluding MukB 13,15,16 through direct interactions 15,50,51 . Second, catalysis by TopoIV at the dif site decreases in a Δ(matP) strain 11 . Third, FtsK, which also activates TopoIV 52,53 , segregates sister ter regions in a MatPdependent manner 10 . Besides, the functions of MatP depending on its last 20 residues may involve the formation of tetramers and depends on the interaction MatP-ZapB. Indeed, most of the effect of the matPΔ20 mutation on pairing depends on zapB (Fig. 3). The ter-linkage, via ZapB and ZapA, thus appears required for the maintenance of a normal pairing of the ter regions, which suggests that it is partly independent of their catenation. Lastly, a small but significant part of MatP activity dependent on its C-terminus is independent on ZapB (Fig. 3). Thus, either the last 20 residues participate in an undescribed activity of MatP or MatP tetramerisation plays some role in pairing ter independently of either MukB or ZapB.
We further characterised the interaction of MatP with DNA and its tetramerisation. Our data are fully consistent with MatP forming tetramers when it interacts with matS (Fig. 7), as previously reported 12 . However, despite dedicated experiments, we detected only one DNA fragment per tetramer (Supplementary Fig. 7), but could see pairing of DNA molecules in vitro in two assays. This pairing activity only poorly depended on the presence of matS and was readily challenged by non-specific DNA (Figs. 5 and 6). We conclude that matS-matS looping or bridging by MatP is unlikely to occur frequently or stably in vivo, consistent with their absence in contact maps 13 . MatP tetramers may instead pair matS with non-specific DNA, ensuring a part of ter pairing this way. This should lead to compaction of the ter region, which is argued against by the absence of anomalous component modification in Δ(matP) (Fig. 3). In addition, chromatin immunoprecipitation of MatP did not reveal non-specific binding of MatP around matS sites 13 . An attractive model would thus be that MatP tetramers specifically serve to bridge matS-containing DNA with ZapB, excluding other binding activity, so that the DNA-bridging activity of MatP would be observed only when ZapB is absent. While multiple findings point to the existence of a Ter/MatP/ZapB/ZapA/FtsZ complex in vivo 14,17,43,44,54 , our attempts to detect such an interaction in vitro (Supplementary Figs. 9 and 10) were unsuccessful. These negative results do not rule out the model and could be explained by the complexes being only transients or requiring other actors like ZapA and/ or FtsZ.
Taken together, our data support the view that MatP mainly acts to pair sister ter regions until the onset of cell division but has little effect on their dynamics when unpaired. To do so, tetramers of MatP bind matS sites and act in at least two ways, which can be genetically separated. This globally results in delaying decatenation by TopoIV until FtsK gets activated [55][56][57][58] and segregate the ter regions by promoting both decatenation and dimer resolution at the dif site 10,11 .
Imaging was done as previously described 27 . Briefly, movies were taken on a Nikon Eclipse TiE with a 60× oil-immersion objective; the images were further magnified with a 2.5× TV adaptor before detection on an Andor iXon EM-CCD camera. Imaging was done at 2 fps with a 0.1 s exposure, for 20 s to avoid photobleaching.
Image analysis and loci tracking. We achieved high precision localisation of foci on each frame by two-dimensional fitting of a Gaussian function to the diffraction limited intensity distributions of individual loci 27 . This has a higher precision than typical displacements between successive frames. Particle tracks can then be obtained by matching the nearest objects in successive frames. The centre of mass motion of all the common loci in the image pair is subtracted to remove collective motion related to microscope vibration. Loci have a distribution of initial intensity, and undergo photobleaching. Tracks were analysed using a custom written Matlab R2018a script, as previously described 27 . This was further adapted for the shorter trajectories of 40 images in our experiments. Briefly, the tracking consists of three main steps: (1) localisation of candidate particles. The aim of this step is to obtain an estimate of the particle localisation; (2) subpixel resolution detection of the position. Using the original unprocessed images, the regions around the candidate particles are fitted to a 2D Gaussian; (3) linking of the trajectories. In this step, the positions detected along the different time frames are assembled to reconstruct the particles trajectories.
Analysis of trajectories to extract the mobility parameters. The parameters have been described by Amitai et al. 32 , and they were extracted using the same algorithm. These parameters provide independent, complementary information on first and second moment statistics: (1) The length of constraint L c is defined as the SD of the locus position with respect to its mean averaged over time. This parameter provides estimation for the apparent radius of the volume explored by a finite trajectory. For a trajectory containing N p points, where is the position of a locus at a time t, L c is obtained from the empirical estimation: It characterises the confinement of a locus, which in other studies has been reported as the radius of confinement (R conf -not to be confused with R c ). The R conf is computed from the asymptotic plateau of a mean square displacement (MSD) curve, and is therefore limited to trajectories that plateau. This is strongly influenced by the length of image acquisition. The advantage of computing L C is that it gives a robust estimate of the volume: occupied by the trajectory and can be used on any kind of trajectory, as it does not require a plateau. (2) The anomalous exponent α is computed from the MSD behaviour for small increments: α was estimated by fitting the first six points of the MSD of an SPT by a power law t ɑ . (3) The effective spring coefficient K c . The spring force acting at position x a and measured at position x m is represented by: The spring constant K c allows us to estimate the effect of local tethering interactions around the locus of interest 60 . This tethering can arise from interactions of the locus with other chromosomes or cellular substructures, such as the membrane. These interactions cannot be measured directly but they can be inferred from SPTs. (4) The effective diffusion coefficient D c reflects the second-order statistical properties of a trajectory. This diffusion coefficient accounts for local crowding that may vary along the trajectory.
Calibration of the foci. In order to estimate the copy number of fluorophores, we implemented a custom intensity calibration method in MATLAB (R2018a), based on the principle described in ref. 61 . The calibration method aims at estimating the ratio between the intensity of foci and the number of GFP molecules by exploiting the intrinsic fluctuations of intensity generated by the random photobleaching process. The key idea is that the variance of the intensity drop depends on the number of emitting GFP molecules contained in the focus at the beginning of acquisition, i.e., a higher number of emitting GFP molecules corresponds to a smaller variance in the relative intensity loss (see below). We estimate the intensity/ copy number ratio (calibration ratio) by binning the foci by initial intensity, and evaluating the dependence of the variance of the intensity drop on the bin.
Detailed calculation. Given a focus with n emitting molecules, the observed intensity will be: Here we aim at estimating the calibration ratio ν from the fluctuations in the intensity drop due to photobleaching.
At any given time t, the number of emitting GFP molecules in a focus with n 0 initial emitting molecules, is described by a binomial distribution with n = n 0, and p ¼ e Àt τ where τ is the bleaching time constant. The variance of the binomial distribution is given by: where Δn represents the number of bleached molecules, and p the probability of bleaching until time t. Then the contribution of bleaching to the variance of the intensity drop is: where ΔI represents the total intensity loss for a given focus and the subscript b indicates that the term is relative to the component of variance coming from fluctuations in the bleaching process. This establishes a linear relationship between the variance of the intensity drop and the calibration ratio that can be estimated as the slope of Var(ΔI) b as a function NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-17606-6 ARTICLE NATURE COMMUNICATIONS | (2020) 11:3796 | https://doi.org/10.1038/s41467-020-17606-6 | www.nature.com/naturecommunications of I 0 p(1 − p) on a linear fit (with intercept constrained at 0) on several initial intensity bins (Supplementary Fig. 3c). P is estimated from the data through a fit on ΔI as a function of I 0 (Supplementary Fig. 3a). This also allows to estimate the bleaching time constant τ that will be used in the following steps.
In order to estimate the contribution of bleaching to the total intensity variance, we model it as follows: where γI groups non-bleaching variance contributions such as shot noise, and is expected to be proportional to intensity. Since we expect p t ð Þ ¼ e Àt τ and I t ð Þ ¼ I 0 e Àt τ we can substitute it in Eq. (9) and fit the following expression to the observed variance as a function of time ( Supplementary Fig. 3b): The bleaching dependent part of variance (the second term of the expression) has a different functional dependence on time, and therefore can be disentangled from other sources of variance and used to estimate the calibration parameter through the above described linear fitting. This process also allowed to verify that the bleaching contribution is indeed the dominant contribution in the empirical variance. As an additional pre-processing step, we estimate and subtract background intensity by extrapolating the intensity at which no bleaching is observed (Supplementary Fig. 3a).
Statistics and reproducibility. Each strain was tested at least three times independently, and the data were pooled in the same data file after checking that the results obtained with each replicate were comparable. The final numbers of foci used for data analysis are indicated in Supplementary Data 1 and in the legends of the figures. Supplementary Data 2 shows the median for each dataset.
To compare distributions, a two-sample Kolmogorov-Smirnov test was used and p values are indicated in the text and Supplementary Data 3. Unless stated, the distributions of foci at mid-cell (M) were used to compare two strains or type of foci (FH or FL).
Multiplexed tethered particle motion (TPM). The overall TPM procedure, including data analysis, has been described previously 38,62 . DNAs were obtained as follows: PCR with F2060 and R2016 on pBR328 for 0matS-DNA (2588 bp); PCR with F2060 and R2016 on pTOC7 for 1matS-DNA (2506 bp); PCR with F1201 and R1201 on pTOC6 for 2matS-DNA (2443 bp). Fifty picomolar DNA were incubated with 50 pM anti-digoxigenin-covered beads (antibody: Roche, #11093274910 and carboxylate-modified beads F1-XC030, Merck-Estapor) in Buffer A (PBS 1X, 1 mg mL −1 Pluronic F-127, 0.1 mg mL −1 BSA, 0.1% Tween 20 and 0.05% Triton 100X) for 20 min at RT. The complexed beads-DNA were incubated O/N in the chambers at 4°C in RB3 (PBS 1X, 5 mg mL −1 Pluronic F-127, 0.1 mg mL −1 BSA, 0.1% SDS and 0.05% Triton 100X) and the free beads were washed with RB3. Chambers were then washed with RB4 (20 mM Tris pH 7.5, 1 mM MgCl 2 , 150 mM NaCl, 0.1 mg ml −1 BSA, 5 mg mL −1 Pluronic F-127), and imaged for 2 min before injection of 600 nM MatP or MatPΔ20. Traces were examined one by one as described in ref. 40 . Only those with an appropriate amplitude of motion measured in the absence of proteins, regarding the calibration curve, were conserved for further analysis. We analysed the kinetics of the amplitude of motion after 5 min after injection of proteins and used for that detection methods based on thresholds defined as midways between the peak positions found in the histograms of amplitude of motion. We thus defined two states: state 1, intact DNA, and state 2, apparently looped DNA and detected them on each trace. The histograms of the state duration were fitted with two exponential decays leading to τ fast and τ slow .
Electromobility shift assays (EMSA). The matS41 DNA (41 bp) was obtained by hybridising oligonucleotides matS41F and matS41R. The matS237 DNA (237 bp) was obtained by PCR amplification using pEL3, a pLN135 derivative containing the matS sequence (our lab collection matS site: GTGACAGTGTCAC), as a matrix and matSF and matSR as oligonucleotides. Binding reactions were done in buffer containing 10 mM Tris (pH 7.5), 125 mM NaCl, 2.5 mM MgCl2, 0.5 mM DTT, and 5% glycerol, in the presence of 1 µM of each DNA probe, 0.25 µg of poly(dI-dC) and different concentrations of indicated proteins (3 µM of proteins in Fig. 7 and Supplementary Fig. 9, and 3 µM and 6 µM in Supplementary Fig. 7) The reactions were incubated at 30°C for 30 min and analysed on 5% native TGE-PAGE.
ZapB purification. A pET32 containing zapB was transformed into BL21DE3 cells. After 2 h induction with 1 mM IPTG, cells were centrifuged and pellets were resuspended in Buffer A (20 mM Tris pH 7.5, 300 mM NaCl, 5 mM MgCl 2 ). Cells were lysed by sonication, centrifuged and resuspended in RB1 for a step of ultracentrifugation (27,000 g for 90 min at 4°C). The supernatant was loaded onto a 1 mL HisTrap FF column (GE Healthcare Life Sciences) and ZapB was eluted with an imidazole gradient (0-0.5 M). ZapB fractions were pooled, dialysed (20 mM Tris pH 7.5, 150 mM NaCl, 5 mM MgCl 2 ) and loaded on a Superdex 200 (GE Healthcare Life Sciences). ZapB fractions were pooled and frozen.
Pull-down experiments with ZapB. This experiment is performed like other pulldown experiments but with different MatP concentrations (from 1 to 6 μM) with or without ZapB (from 2 to 20 μM). Each reaction was done in double in order to be analysed by classical agarose gel electrophoresis or SDS-PAGE. For western-blot analysis, reactions were analysed by SDS-PAGE and transferred to polyvinylidene difluoride membranes (Bio-Rad) using the Trans-Blot ® Turbo TM transfer system (Bio-Rad). Membranes were blocked 1 h at RT or overnight at 4°C in 5% non-fat powder milk in PBS containing 0.05% Tween 20. Antibodies were anti-His (1:1000) (Tanaka, #631210). Blots were developed by chemiluminescence using Clarity western ECL substrate (Bio-Rad), visualised with the Chemidoc TM Touch imaging system (Bio-Rad) and analysed with Image Lab software (Bio-Rad).
Reporting summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.