DNA-loop extruding SMC complexes can traverse one another in vivo

Abstract

Chromosome organization mediated by structural maintenance of chromosomes (SMC) complexes is vital in many organisms. SMC complexes act as motors that extrude DNA loops, but it remains unclear what happens when multiple complexes encounter one another on the same DNA in living cells and how these interactions might help to organize an active genome. We therefore created a crash-course track system to study SMC complex encounters in vivo by engineering defined SMC loading sites in the Bacillus subtilis chromosome. Chromosome conformation capture (Hi-C) analyses of over 20 engineered strains show an amazing variety of chromosome folding patterns. Through 3D polymer simulations and theory, we determine that these patterns require SMC complexes to bypass each other in vivo, as recently seen in an in vitro study. We posit that the bypassing activity enables SMC complexes to spatially organize a functional genome.

Chromosomes from all kingdoms of life are actively maintained and spatially organized to ensure cell viability. SMC complexes play a key role in spatially organizing chromosomes and function in many processes like chromatin compaction, sister-chromatid cohesion, DNA break repair, and regulation of the interphase genome^1,2. While their importance has been recognized for over 25 years, evidence for a molecular mechanism of how SMC complexes function has only recently emerged. Recent single molecule experiments and chromosome conformation capture (Hi-C) studies have shown that the condensin and cohesin SMC complexes can translocate on DNA and extrude DNA loops at rates of ~1 kb/s^3–11. The process of DNA loop extrusion by SMC complexes is emerging as a universal mechanism by which these proteins organize the 3D genome in eukaryotes and prokaryotes². It remains unclear, however, what happens in a living cell when multiple SMC complexes encounter one another¹². Understanding the outcome of such encounters is fundamental to elucidating how chromosomes are spatially organized by the process of DNA loop extrusion.

Encounters between SMC complexes are expected to occur frequently in a cell. In eukaryotes, the cohesin and condensin SMC complexes are loaded at multiple chromosomal loci, at estimated densities between ~1/200 kb - 1/40 kb and extrude loops of 100’s of kilobases (reviewed in¹³). In many bacteria, SMC complexes are loaded by the protein ParB primarily at centromeric sequences called parS sites^14–18. These sites often exist in multiple copies close to one another¹⁹. In bacteria without the ParB/parS system, such as E. coli, the SMC-like MukBEF complex loads non-specifically, but creates long DNA loops^20,21. Therefore, in both eukaryotes and bacteria, SMC complexes will frequently encounter others when extruding DNA loops. Most efforts towards understanding the chromosome organizing capacity of SMC loop extruders have assumed that translocating complexes are impenetrable to each other²² (also reviewed in^2,12). A recent single-molecule study using Saccharomyces cerevisiae condensins challenged this assumption and demonstrated that condensins can traverse past each other in vitro²³. How SMC complexes interact in vivo, (i.e. traversing, blocking, or unloading each other, etc.), and the implications of these interactions for chromosome folding remain unknown. Here we show that B. subtilis SMC complexes can traverse past each other in vivo in a quantitatively predictable manner, resulting in an unexpected diversity of chromosome folding structures.

Results

Engineering an in vivo system for SMC complex encounters.

We set up an SMC complex “crash-course track” system to probe the effects of encounters between loop extruding factors (Fig. 1a). We engineered B. subtilis strains to contain one, two or three parS sites, and we varied the relative separations and positions of the SMC loading sites (Fig. 1b). This allowed us to better resolve the effects of encounters between SMCs than in the wild-type system, which has nine parS sites in proximity to one another^24–26. Moreover, to remove potential confounding effects of interactions between the replication machinery and SMCs, and to eliminate potential interactions between sister chromatids, we synchronized cells in G1 phase by expressing the protein SirA. SirA inhibits replication initiation while allowing ongoing rounds of replication to complete, leaving cells with single chromosomes²⁷. We then investigated chromosome interaction patterns using Hi-C and protein distributions by Chromatin Immunoprecipitation (ChIP-seq) assays^10,26,28.

Figure 1: Experimental system to study the effect of “collisions” between SMC complexes.

(a) Experimental setup. (b) Schematic of strains indicating the positions of single parS sites inserted on the chromosome of B. subtilis. (c) Hi-C maps of G1-arrested cells. B. subtilis strains contain a single parS site at −94° (2981 kb, left), −59° (3377 kb, middle) or at both sites (right). (d) HiC maps from a time course experiment following induction of ParB, the SMC loading protein, for the indicated times. The schematic illustrates the paths of SMC loop extruders superimposed on the chromosome for each strain at 10 min following ParB induction.

SMCs translocating towards one another slow each other down.

Consistent with our previous findings, strains containing single SMC loading sites at −94° or −59° (i.e. genome positions of 2981 kb or 3377 kb out of 4033 kb, Extended Data Fig. 1a) displayed DNA juxtaposition, or “lines” on the Hi-C map, indicative of large tracks of DNA being brought together in a hairpin-like structure (Fig. 1c, left and center panels)^10,29. In striking contrast, a strain with both of these parS sites exhibited a complex star-shaped pattern (Fig. 1c, right). This pattern has additional features that are absent from strains with single parS sites, indicating that non-trivial interactions occur between SMC complexes translocating from opposing sites. Hi-C performed for the same strains growing in asynchronous cultures revealed similar patterns, albeit less intense, showing that these patterns are not specific to G1-arrest (Extended Data Fig. 1b). To understand how a star-shaped pattern emerged, we performed a time-course Hi-C experiment in cells with an IPTG-inducible expression of the SMC loader, ParB, as the sole source of the ParB protein (Fig. 1d). We took samples in the absence of IPTG and at 5-minute intervals after its addition. By tracking the juxtaposition of DNA flanking the parS site over time, we measured the rates of DNA loop extrusion. In the strains with a single parS site, the extrusion rate was ~0.8 kb/s towards the replication terminus (ter) and ~0.6 kb/s towards the replication origin (ori), similar to previous measurements^10,29. In contrast, in the strain with both parS sites, the extrusion rate in the section between the parS sites (i.e. where SMC complexes move towards one another), was lower by a factor of ~1.2, but outside that section the rates remained unaltered (Extended Data Fig. 2a; see Methods and Supplementary Notes 1–5). This slowdown is most evident from the change in the tilt of the lines when comparing to strains with single parS sites (Extended Data Fig. 2b, 2c). These results suggest that SMCs translocating towards one another can effectively slow each other down. We thus investigated the underlying mechanism by which SMCs interact to create such complex chromosome folding patterns.

Interactions between SMCs help explain contact patterns.

We first broke down the star-shaped Hi-C interaction pattern into different line segments and investigated how these lines may be explained by a process of DNA loop extrusion by SMC complexes (Fig. 2a). Lines 1 and 2, similar to those seen in maps for strains with one parS site, can be formed by single SMC complexes (making “singlet contacts”) as they translocate away from their respective parS loading sites and juxtapose the flanking DNA. In contrast, Lines 3, 4 and 5, are likely formed by interactions between SMC complexes, and we provide below a possible origin for these lines: Line 3 can emerge when two SMC complexes coming from different parS sites meet in between the parS sites. In addition to each of their singlet contacts (i.e. on Lines 1 and 2), they produce another contact by bridging DNA along their flanks (Fig. 2a ii). Since SMC complexes in different cells can meet at different genome positions, the location of the additional contact varies. Thus, when averaged over a population of cells, the contacts mediated by SMC collisions (i.e. “collision-doublets”) result in Line 3 (Fig. 2a ii, Supplementary Fig. 1). Line 4 can emerge if the SMC complexes’ meeting point is at the parS site. For example, if one SMC complex from parS site S2 extrudes past the site S1, and a second SMC complex loads at site S1 at that moment, then the SMC complexes enter into a “nested-doublet” configuration. As long as the two complexes maintain their contact with each other and continue to extrude DNA, they generate Line 4 over time (Fig. 2a iii). Finally, if the second SMC complex (loaded from S1) of the “nested-doublet” configuration meets a third SMC complex (loaded from S2), then different meeting points between three SMC complexes produces the contacts of Line 5 (see Fig. 2a iv) in addition to Lines 3 and 4. It is possible to envision an alternative mechanism for the formation of Line 5 (and Line 4) (Stephan Gruber, personal communication) (Supplementary Fig. 2), whereby ParB molecules form a “temporary loading site” at a mirrored parS1 location on the juxtaposed DNA; however, we can rule this out on theoretical grounds as well as experimentally (see Supplementary Fig. 2). Thus, our line-based decomposition provides a framework for interpreting complex Hi-C patterns as assemblies of SMC complexes and describes a possible series of events leading to each of the lines of the star-shaped pattern.

Figure 2: Specific interactions between SMC complexes leave unique Hi-C signatures.

(a) Decomposition of the Hi-C map into assemblies of SMC complexes. The schematic diagram (top row) and the arch-diagram representation (middle row) of the SMC assemblies are superimposed on a Hi-C map (bottom row). Locations of point-like SMC-mediated contacts are depicted either by a yellow arrow (top, middle), or by a yellow/pink dot on the Hi-C map (bottom). S1 and S2 are SMC loading sites (blue dots). SMCs loaded on S1 are orange and on S2 pink. These colors are consistent between rows to facilitate comparison. SMC complexes in different cells can meet at different genome positions; when averaged over a population of cells, the contacts mediated by SMC collisions generate ‘lines’ in the HiC map. (b) Possible interaction rules of SMC complexes (blocking, unloading, bypassing). The schematic diagram (top row) illustrates the interaction. The arch diagram (second row) captures the 1D contact along the DNA. The 2D Hi-C-like contact trace (third row) captures the spatio-temporal behaviour of a single interaction by a pair of extrusion complexes. For second and third rows, extrusion time is shown over a 15 min period, and times are indicated by arch or dot colours. A 3D polymer simulation and the resulting contact map for each interaction rule is shown on the bottom row. A broader parameter sweep can be found in Extended Data Figs. 3, 4, 5. (c) A parameter sweep over the three interaction rules accounting for different rates gives a best-match model (Supplementary Figs. 4–7 and Methods): For N=40 extrusion complexes per chromosome, we find that bypassing rates are ~1/20 s⁻¹ and unloading rates are ~1/300 s⁻¹. A comparison between the experimental data and a 3D polymer simulation of the model is shown.

Polymer simulations rule out certain mechanisms of pattern formation.

Next, we used polymer simulations to understand how the patterns observed by Hi-C emerge from the rules of engagement between SMC complexes. In our simulations, each loop extruding factor was represented by two connected motor subunits^29–31 (e.g. Fig. 2a). By translocating away from their loading site, the connected motors bring genomic loci into spatial proximity. Based on previous studies of B. subtilis SMC complexes³², we allowed loop extruders to load anywhere on the genome, but with a preferential bias (see below) such that most loaded at parS sites. Since previous studies showed that two motor activities of the same loop extruding factor are independent of each other, we allowed continued extrusion by a motor subunit even if the other subunit’s translocation was blocked^9,10,29. From the simulations of loop extrusion on a 3D polymer, we then created Hi-C-like contact maps^30,31 (see Supplementary Notes 1–5 for all simulation details).

Our attention turned to three main rules of interaction between SMC complexes: blocking, unloading, or bypassing (Fig. 2b, Supplementary Fig. 1). We also explored various other models, including 3D interactions between extruders, the effect of sticky DNA, the effect of extruder subunits reversing direction after collision, among others (Supplementary Figs. 2, 3). However, we ruled out these other models due to their inability to create Lines 4 and 5, or because they generated lines not observed experimentally (Supplementary Figs. 2, 3).

Similar to prior work, we first considered models involving only blocking^13,22,30, and extended the model to include a facilitated unloading of blocked SMC complexes. We allowed collided motor subunits to pause (in the blocked state) before unloading with a specified rate. By sweeping over a broad range of unloading rates and SMC complex numbers, we found that it was not possible to reproduce Lines 4 and 5 at intensities visible by contact maps (Extended Data Fig. 3). The failure of this class of models in reproducing Lines 4 and 5 is due to an inability to efficiently form nested configurations: For example, with few SMC complexes per chromosome, it is easy for an SMC complex loaded at parS site S2 to reach parS site S1; however, a small loading rate due to few SMC complexes, makes it unlikely that a second SMC complex will bind to S1 at the moment the S2 SMC complex extrudes past it. With high numbers of SMC complexes, the loading rate at each parS site is larger; however, traffic jams due to SMC collisions between the S1 and S2 sites prevent most SMCs from ever reaching the opposing site. Therefore, the blocking and unloading model results in low numbers of nested doublet configurations and cannot create Lines 4 and 5 at the intensities observed experimentally (see Supplementary Note 5).

A model of SMC complexes bypassing each other explains experimental data.

We extended the blocking-only model by allowing SMC complexes to bypass one another, which was also motivated by recent single molecule experiments²³. In this blocking and bypassing model, we assumed that, when two SMCs meet, the collided subunits pause but can traverse each other with some specified rate; however, we did not allow facilitated unloading. Strikingly, the blocking and bypassing model was sufficient to robustly reproduce the star-shaped Hi-C pattern (Figs. 2b, Extended Data Fig. 4a). Moreover, bypassing produced the observed “tilting” of Lines 1 and 2 away from each other for certain bypassing rate and SMC number combinations (Extended Data Fig. 4b). Nevertheless, the bypassing mechanism by itself generated Lines 4 and 5 more intensely than observed experimentally, suggesting that too many SMC complexes were entering nested configurations (Fig. 2a). Therefore, we added back the facilitated unloading assumption to the blocking and bypassing model. This allowed us to tune relative intensities of Lines 3, 4 and 5 and obtain Hi-C maps that looked strikingly similar to the experimental data (Extended Data Fig. 5). Of all the models that were tested, the combined bypassing and unloading model was the only one that produced all the Lines 1–5 at the same time, with the observed relative intensities.

The resulting integrated model included the rules for SMC encounters (i.e. bypassing and facilitated unloading), as well as the rules for basal SMC dynamics and totaled six parameters: the bypassing rate, the facilitated unloading rate, the number of SMC complexes per chromosome, the SMC loading rates at parS sites versus other sites, and the spontaneous dissociation rate of SMCs in the absence of collisions (see Supplementary Notes 1–5). Uniquely, we found that we could fix all the six model parameters experimentally using a combination of Hi-C, ChIP-seq data and theoretical constraints between parameters (see Methods), finding a unique region of parameter space which best fit all of the available data (Supplementary Figs. 4, 5, 6, 7; and Supplementary Notes 1–5).

In the best models, there were 25–45 SMC complexes present on each chromosome after 1 hour of G1-arrest. SMCs paused for ~20 s when they met each other before either bypassing or unloading from the chromosome (Fig 2c). These momentary pauses upon SMC collisions can explain the overall observed “slowdown” of SMC complexes discussed earlier. Moreover, we found that bypassing was ~10–20 times more likely to occur than unloading (i.e. the bypassing rate was ~0.03–0.1 s⁻¹ whereas unloading was ~0.002–0.005 s⁻¹). Thus, the bypassing mode of conflict resolution dominated over unloading and was essential for explaining the observed lines on the Hi-C map mediated by SMC complex dynamics. Fixing the rates for bypassing at 0.05 s⁻¹ and unloading at 0.003 s⁻¹, and with 40 extruders/chromosome, polymer simulations quantitatively reproduced the SMC-mediated Lines 1–5 seen in the experimental Hi-C data (Fig. 2c), and raised the possibility of predicting chromosome folding in other engineered strains.

A model of SMC complexes bypassing each other predicts new patterns.

Thus, we investigated whether the bypassing and unloading rules were generally applicable to SMC encounters. We generated seven other strains containing two parS sites at various locations and two strains containing three parS sites and performed Hi-C in G1-arrested cells (Fig. 3a, 3b) and exponentially growing cells (Extended Data Fig. 6). These engineered strains produced an impressive diversity of Hi-C contacts patterns, which depended on the relative spacing and positioning of SMC loading sites. Nevertheless, all the complex multi-layered interactions features could be understood via the descriptions of SMC-mediated contacts (Fig. 2a). Strikingly, using the same parameter values as above (i.e. from Fig. 2c), the model of SMC bypassing and unloading reproduced all the emergent Hi-C contact features away from the primary diagonal, showing strong agreement with all nine strains (Fig. 3a, 3b). We note that in the experimental Hi-C maps, chromosomal interaction domains (CIDs) on the primary diagonal are evident in all of our strains (Figs. 2c, 3a, 3b). These CIDs are also present in a strain without parS sites (Supplementary Fig. 5), suggesting that they are loci-specific and are not related to specific loading of SMC complexes at parS sites. We did not add these locus-specific assumptions to reproduce these CIDs in our simulations.

Figure 3: Validating and testing a model of in vivo Z-loop formation.

Data and simulations of Hi-C maps of strains containing two parS sites (a) or three parS sites (b); all models use the same parameters as identified in Fig. 2c. (c) A comparison of SMC occupancy between experimental ChIP-seq (red) and our model for different rates of bypassing (blue, green and yellow); notably, a bypassing rate of ~1/20 s⁻¹ identifies the best-fit model. This comparison is independent of the comparisons between Hi-C results and modeling.

As an independent way of investigating the consequences of SMC encounters, we determined SMC distributions by performing ChIP-seq and compared experiments to our model predictions (Fig. 3c). We found that a bypassing rate of ~1/20 s⁻¹ was necessary for quantitative agreement between experiments and simulations (Fig. 3c). With the bypassing rate too low, SMCs tended to accumulate strongly near the loading sites; with the bypassing rate too high, the occupancy profile was too flat. This rate of bypassing (~1/20 s⁻¹) obtained by modelling of ChIP-seq is in strong agreement with the value inferred from modelling of Hi-C data. We note that our models work well to capture the genome-wide trends of SMC occupancy except near the terminus region, indicating that our understanding of the SMC loading at parS sites and interaction rules is good, but future work needs to be done to elucidate how SMCs interact with the terminus. Together, the agreement of the model with both Hi-C and ChIP-seq lends strong support for the notion that SMC complexes can translocate past one another on DNA in vivo after short pauses.

SMC traffic jams explain the time-dependent change of Hi-C patterns.

Having studied the effects of changing loading site positions and spacings, we next studied the effect of time on chromosome reorganization after G1-arrest. In wild-type cells, which harbour nine parS sites, the spatial chromosome organization changes dramatically; the most prominent feature of the Hi-C map (the central diagonal) vanishes after two hours and is replaced by two smaller tilted lines²⁶. However, before examining the time-dependent changes in the wild-type system, we investigated the time course in a simplified system with one and two parS sites. Over a two-hour window, although no changes occurred to the Hi-C Lines 1 or 2 with one parS site (Extended Data Fig. 7a), we observed major changes in strains with two sites (Fig. 4a, Extended Data Fig. 7b). Specifically, the star-shape became progressively larger due to an increased tilt of Lines 1 and 2 away from each other (Fig. 4a, Extended Data Fig. 7b). This indicated that the SMC translocation between the parS sites was further slowed down over time and demonstrated that the observed changes were due to interactions of SMCs translocating from different parS sites. By simulations, we could also achieve a similar effect (Fig. 4a, Extended Data Fig. 4). By increasing the numbers of loop extruders present on the chromosome we obtained more frequent SMC collisions which led to an overall slowing down of extrusion between parS sites and the larger star-shaped pattern. The numbers of loop extruders per chromosome necessary to recapitulate the Hi-C data were 40±10, 60±15, 90±20 (Fig. 4a). Reassuringly, the numbers of extruders per chromosome that gave the best agreement with Hi-C also independently reproduced SMC ChIP-seq profiles for the specific time points (Fig. 4b). We thus hypothesized that continued protein synthesis after replication inhibition resulted in a higher number of SMC complexes per DNA molecule.

Figure 4: Numbers of SMC complexes per chromosome tunes the shape of contact maps.

A time-course of Hi-C (a) and SMC ChIP-seq (b) tracking chromosome structure changes and SMC occupancy following replication arrest by SirA; experiments are compared to simulations in which the numbers of SMC complexes per chromosome are increased, but all other simulation parameters are kept as determined in Fig. 2c. (c) Top row: fluorescence microscopy of tagged chromosome loci marking the ori (green), DAPI-stained nucleoid (blue). Bottom Row: nucleoids in a strain containing −27° −59° parS sites. Membranes are stained in red. This experiment was independently performed twice with similar results. Scale bar indicates 4 μm. Quantification of the data is provided in Extended Data Fig. 8b. (d) Western blots for the indicated proteins. (e) Quantification of the number of extrusion complexes per cell (assuming extrusion complexes as dimers of SMC complexes); numbers are calculated using the fluorescence microscopy, Western blot, and whole-genome sequencing data quantifications. For simulations, confidence intervals are estimated by qualitatively matching simulated contact maps (i.e. size of the star-shape, angles and intensities of Lines 1–5) to experimental Hi-C maps. Mean and standard deviation are shown for the experimental fold-change in SMC abundance values. The numbers of cells analyzed were n=725, 580, 702, 557 for the four time points. See also Extended Data Fig. 8. Unprocessed images for panel c and full scans of the blots in panel d are uploaded to Mendeley Data⁴⁷.

To quantify the change in SMC abundance experimentally, we measured the chromosome copy numbers per cell and SMC complex abundances over time: Marker frequency analyses³³ by whole genome sequencing and fluorescence microscopy showed that cells retained only one copy of the genome per cell for the duration of the experiment (Fig. 4c, Extended Data Fig. 8). Immunoblot analyses of cells growing in the same conditions showed that ParB and SMC complex subunit levels per unit cell mass remained constant over time (Fig. 4d). However, we found that at 90 min and 120 min after G1 arrest, the nucleated cells’ length/mass increased to 1.7-fold and 2.4-fold of the 60 min value (Fig 4c, Extended Data Fig. 8). From the increased cell lengths and constant density of SMC subunits, we inferred the relative changes in SMC complex numbers per chromosome (Fig. 4e). These fold-change values in SMC complex numbers are in good agreement with the numbers of loop extruders independently identified by Hi-C and simulations above (Fig. 4e). Thus, continued protein synthesis after replication inhibition leads to increased numbers of SMC complexes per chromosome.

Next, we directly tested the role of SMC complex abundance on chromosomal organization by perturbation. We hypothesized that overexpression of SMC complex would lead to a faster evolution of the observed Hi-C patterns in a G1 arrest time course. Consistently, we observed this trend experimentally in a strain with two parS sites (Extended Data Fig. 9): at the 60 min mark, we saw the traces typical of 90 min in the absence of SMC overexpression. This confirms the role of SMC abundance in tuning chromosome spatial organization and the changing shapes of the Hi-C interaction patterns.

Finally, we studied the most complex systems: strains with three parS sites or 9 parS sites (i.e. wild-type cells), and investigated the mystery of the vanishing “central” lines. In these strains, the disappearance of the central line in Hi-C was accompanied by the accumulation of SMCs between the parS sites as seen in ChIP-seq (Fig. 5, 6a). Despite the complexity of the changes over time, our model captured these effects (Fig. 5, 6a) and helped to understand what was happening: In normal growth conditions, with basal SMC levels, collisions between SMCs from adjacent parS sites are resolved by bypassing (i.e. in ~20 s) before the next extrusion complex arrives. However, the increased number of SMCs makes the rate of new collisions higher than the rate of bypassing. This effect is particularly strong for the central sites, where extruders are jammed in from both sides. This finally results in effective extrusion only from the out-most parS sites and gives rise to the disappearance of the central line (Fig. 5, 6a). We conclude that bypassing plays an important role in preventing traffic jams between SMC complexes in wild-type cells under normal growth conditions, by allowing productive extrusion from multiple neighboring parS sites.

Figure 5: Time-dependent change of Hi-C patterns in strains with 3 parS sites.

(a) Hi-C time-course experiments upon SirA induction (top) and corresponding 3D polymer simulations (bottom) for a strain with three parS sites at positions −91°, −59°, −27°. (b) Anti-SMC ChIP-seq performed for the same strains; experiments (red) and simulations of SMC abundance (blue). (a-b) In the simulations, the bypassing rate was 0.05 s⁻¹ and the facilitated dissociation rate was 0.003 s⁻¹ (i.e. the same as Fig. 4a).

Figure 6: Time-dependent change of Hi-C patterns in strains with wild-type parS sites.

(a) Experiments (top) and simulations (bottom) of G1-arrested wild-type B. subtilis cells. The wild-type parS sites occur at positions (−27°, −6°, −5°, −4°, −1°, +4°, +17°, +42°, +91°). In the simulation, we excluded the +91° parS site because SMC complex loading is strongly attenuated by the proximal chromosome interaction domain boundary and SMC binding at this site is substantially weaker than at the others²⁴. In both experiments and simulations, the central diagonal gradually vanishes due to traffic jams between extruders at the ori-proximal parS sites after increasing numbers of loop extruders. The bypassing rate was 0.05 s⁻¹ and the unloading rate was 0.003 s⁻¹ in the simulations. (b) Calculated average time between SMC collision events from the model shown in (a). The violin plot (top panel) shows the distribution of the average time between SMC collisions from 61 independent simulations, where each simulation contains a measurement of at least 150 collision events. Horizontal bars indicate the extrema of simulation values; even for cells with only 5 SMC complexes per chromosome, encounters are expected approximately every 10 minutes on every chromosome. For the expected number of SMC complexes in wild-type cells (black dotted line, bottom panel), the mean collision time is less than 1 min.

Discussion

Thus, a model where SMC complexes can traverse one another on the chromosome after momentary pausing is consistent with results from many strains and conditions tested here (Fig. 7). Our study demonstrates that by harnessing the SMC-ParB-parS system, we can create complex chromosome folding patterns not seen before in natural systems, which helped understand what is happening in the wild-type cells. Strikingly, these structures could be predicted by a quantitative model of SMC dynamics, which was central to identifying the bypassing mechanism as a key feature of B. subtilis SMC loop extrusion. We inferred that SMC complexes can traverse past each other within ~20 s of an encounter in vivo. This time scale is consistent with the in vitro times of ~8 s measured by single molecule experiments for yeast condensins to traverse past one another on naked DNA²³. These times are also consistent with the ~10 s in B. subtilis to traverse sites of active transcription as shown previously²⁹. Together, these results suggest that the phenomenon of SMCs traversing past one another, and other steric obstacles, may be general to many species and processes.

Figure 7: Schematic model illustrating how SMC encounters are resolved.

Upon an encounter, SMC complexes first mutually block one another and then may resolve the conflict either by bypassing (top row) or unloading from the DNA (bottom row). The bypassing mode of conflict resolution occurs at least 10 times more frequently than unloading (indicated by the thickness of the arrows).

In specific situations, we found it is possible to overwhelm the bypassing mechanism and create SMC traffic jams. The jamming, caused by elevated numbers of chromosome-bound SMC complexes, is similar to the phenomenon where high RNA polymerase traffic (that opposes the direction of SMC translocation, e.g. at rRNA genes) leads to the accumulation (and pausing) of loop extruders at transcription end sites^9,29,34. At first glance, SMC complexes bypassing each other to form structures such as z-loops appear to tangle the DNA. However, bypassing generally helps avoid traffic jams formed with SMCs loaded at adjacent sites. This is important in bacteria since parS sites often occur in multiple copies close to the ori¹⁹. A recent preprint³⁵ that proposed that SMCs do not collide frequently in B. subtilis, however, our quantitative analysis indicates that SMCs collide very often in wild-type cells: With the estimated number of 15–30 SMC complexes per chromosome, a collision event between SMCs is expected on average at least once a minute (see Fig. 6b). Thus, if bypassing were not a feature of SMC complexes in wild-type B. subtilis cells, then pervasive tethers between the ori and other genome positions would frequently occur, potentially affecting ori segregation (Extended Data Fig. 10b). To minimize such long-range tethers, B. subtilis cells would have to organize chromosomes with no more than 4 SMC complexes per chromosome (i.e. <20% of experimentally measured values³²). In such a case, however, the chromosome arm juxtaposition is poor as seen by simulations (Extended Data Fig. 10b), and much weaker than seen experimentally²⁶; moreover, even with as few as 5 SMCs per chromosome, at least one collision event is expected every 10 minutes for every chromosome (Fig. 6b). Thus, in addition to mechanisms that may help fine-tune the numbers of SMCs per chromosome³⁵, bypassing appears to be an essential property that allows multiple parS sites to function together efficiently, not only in engineered strains, but also in wild-type cells in exponential growth conditions.

In eukaryotes, bypassing can help promote chromosome compaction and sister chromatid segregation^30,36. However, we hypothesize that bypassing could have a function beyond compaction and segregation. For instance, bypassing of obstacles and other SMC complexes could potentially facilitate spreading of cis-related chromatin marks (e.g. around a DNA double-strand break^37–39), or help trafficking of various factors along the chromosome^40–42. Speculatively, if the ability to bypass obstacles is rampant, cells may have developed specific mechanisms to control this process and stop extrusion (e.g. CTCFs for cohesins⁴³).

Recent biochemical, cryo-EM and AFM studies indicate that the SMC complexes are flexible and dynamic^44–46, but the underlying molecular mechanism of loop extrusion remains elusive. A future challenge of the field is to investigate the molecular mechanism of bypassing using biochemical and structural approaches. In addition, single molecule approaches will be powerful to determine the ability and efficiency of various SMC complexes to bypass one another, as shown previously²³. However, the targeted SMC complex loading approach (as we showed here) can produce distinct signatures visible by Hi-C that can help distinguish bypassing from other mechanisms. Employing this idea in a eukaryotic system could be very powerful to investigate if bypassing occurs in vivo in eukaryotes.

In summary, we have shown that B. subtilis SMC complexes can resolve encounters by simply translocating past one another allowing them to spatially organize a functional and busy genome.

Methods

General methods.

Bacillus subtilis strains were derived from the prototrophic strain PY79⁴⁹. Cells were grown in defined rich medium (CH)⁵⁰ at 37°C with aeration. Cells were arrested at the G1 phase by expressing SirA²⁷ for indicated durations using IPTG (isopropyl β-d-1-thiogalactopyranoside) at a final concentration of 1 mM or xylose at 0.5%. A list of Next-Generation Sequencing samples can be found in Supplementary Table 1 arranged by the figure in which they appear. Lists of strains, plasmids and oligonucleotides can be found in Supplementary Tables 2–4. Unprocessed microscopy images and uncropped Western blots can be found in Mendeley Data⁴⁷.

Hi-C.

The detailed Hi-C procedure was previously described²⁶. Briefly, 5×10⁷ cells were crosslinked with 3% formaldehyde at room temperature for 30 min then quenched with 125 mM glycine. Cells were lysed using Ready-Lyse Lysozyme (Epicentre, R1802M) followed by 0.5% SDS treatment. Solubilized chromatin was digested with HindIII for 2 hrs at 37°C. The cleaved ends were filled in with Klenow and Biotin-14-dATP, dGTP, dCTP, dTTP. The products were ligated in dilute reactions with T4 DNA ligase overnight at 16°C. Crosslinks were reversed at 65°C overnight in the presence proteinase K. The DNA was then extracted twice with phenol/chloroform/isoamylalcohol (25:24:1) (PCI), precipitated with ethanol, and resuspended in 20 μl of QIAGEN EB buffer. Biotin from non-ligated ends was removed using T4 polymerase (4 hrs at 20°C) followed by extraction with PCI. The DNA was then sheared by sonication for 12 min with 20% amplitude using a Qsonica Q800R2 water bath sonicator. The sheared DNA was used for library preparation with the NEBNext UltraII kit (E7645) according to the manufacturer’s instructions for end repair, adapter ligation, and size selection. Biotinylated DNA fragments were purified using 10 μl streptavidin beads. 5 μl DNA-bound beads were used for PCR in a 50 μl reaction for 14 cycles. PCR products were purified using Ampure beads and sequenced at the Indiana University Center for Genomics and Bioinformatics using NextSeq 550. Paired-end sequencing reads were mapped to the genome of B. subtilis PY79 (NCBI Reference Sequence NC_022898.1) using the same pipeline described in Wang et al., 2015²⁶. The B. subtilis PY79 genome was first divided into 404 10-kb bins. Subsequent analysis and visualization was done using R and Python scripts. The genetic loci marked by degree (°) were calculated using the PY79 genome, which results in a slight shift from data published using B. subtilis 168 genomic coordinates.

ChIP-seq.

Chromatin immunoprecipitation (ChIP) was performed as described previously²⁶. Briefly, cells were crosslinked using 3% formaldehyde for 30 min at room temperature and then quenched, washed, and lysed. Chromosomal DNA was sheared to an average size of 250 bp by sonication using a Qsonica Q800R2 water bath sonicator. The lysate was then incubated overnight at 4°C with anti-SMC⁵¹ antibodies, and was subsequently incubated with Protein A-Sepharose (GE HealthCare) for 1h at 4°C. After washes and elution, the immunoprecipitate was incubated at 65°C overnight to reverse the crosslinks. The DNA was further treated with RNaseA, Proteinase K, extracted with PCI, resuspended in 50 μl EB and used for library preparation with the NEBNext UltraII kit (E7645) and sequenced using the Illumina MiSeq or NextSeq550 platforms. The sequencing reads were aligned to the B. subtilis PY79 genome (NCBI NC_022898.1) using CLC Genomics Workbench (CLC Bio, QIAGEN), and subsequently normalized, plotted and analyzed using R and Python scripts.

Whole Genome Sequencing for DNA replication profiling.

Cells were grown and collected at the indicated time points. Genomic DNA was extracted using the QIAgen DNeasy Blood and Tissue kit (QIAgen 69504). DNA was sonicated using Qsonica Q800R2 sonicator for 12 min at 20% amplitude, to achieve an average fragment size of 250 bp. DNA library was prepared using NEBNext UltraII kit (NEB E7645), and sequenced using Illumina NextSeq550. Sequencing reads were mapped to B. subtilis PY79 genome (NCBI Reference Sequence NC_022898.1) using CLC Genomics Workbench (QIAgen). The mapped reads were normalized to the total number of reads for that sample and plotted in R or Python using matplotlib 3.2.0.

Microscopy.

Fluorescence microscopy was performed on a Nikon Ti2E microscope equipped with Plan Apo 100x/1.4NA phase contrast oil objective and an sCMOS camera. Images were acquired using Nikon Elements software. Cells were immobilized using 2% agarose pads containing growth media. Membranes were stained with FM4–64 (Molecular Probes) at 3 μg/ ml. DNA was stained with DAPI at 2 μg/ml. Images were cropped, linearly adjusted and analyzed using MetaMorph software (Molecular Devices). Final figures were prepared in Adobe Illustrator.

Immunoblot analysis.

Cells were collected at appropriate time points and resuspended in lysis buffer (20 mM Tris pH 7.0, 1 mM EDTA, 10 mM MgCl₂, 1 mg/ml lysozyme, 10 μg/ml DNase I, 100 μg/ml RNase A, 1 mM PMSF and 1% proteinase inhibitor cocktail (Sigma P-8340) to a final OD₆₀₀ of 10 for equivalent loading. The cell resuspensions were incubated at 37°C for 10 min for lysozyme treatment, and followed by the addition of an equal volume of 2x Laemmli Sample Buffer (Bio-Rad 1610737) containing 10% β-Mercaptoethanol. Samples were heated for 5 min at 80°C prior to loading. Proteins were separated by precast 4–20% polyacrylamide gradient gels (Bio-Rad 4561096), electroblotted onto mini PVDF membranes using Bio-Rad Transblot Turbo system and reagents (Bio-Rad 1704156). The membranes were blocked in 5% nonfat milk in phosphate-buffered saline (PBS) with 0.5% Tween-20, and then probed with anti-ParB (1:5,000)⁵², anti-SMC (1:5,000)⁵¹, anti-SigA (1:10,000)⁵³, anti-ScpA (1:10,000)¹⁰, or anti-ScpB (1:10,000)¹⁰ diluted into 3% BSA in 1x PBS with 0.05% Tween 20. Primary antibodies were detected using Immun-Star horseradish peroxidase-conjugated goat anti-rabbit antibodies (Bio-Rad 1705046) and Western Lightning Plus ECL chemiluminescence reagents (Perkin Elmer NEL1034001) as described by the manufacturer. The signal was captured using ProteinSimple Fluorchem R system. The intensity of the bands was quantified using ProteinSimple AlphaView software.

Plasmid construction

pWX512 [amyE::Phyperspank-(optRBS)-smc (spec)was generated by inserting smc with an optimal ribosome binding site (optRBS) (amplified using oWX516 and oWX517 from B. subtilis PY79 genome and digested with NheI and SphI) into pdr111 [amyE::Phyperspan (spec)] (D. Z. Rudner, unpublished) between NheI and SphI. The construct was sequenced using oWX486, oWX524, oWX848, oWX1194, oWX1195 and oWX1196.

pWX777 [yhdG::Pxyl-(optRBS)-sirA (phleo)] was generated by inserting sirA with an optimal ribosome binding site (optRBS) (amplified using oWX1892 and oWX1893 from B. subtilis PY79 genome and digested with HindIII and NheI) into pMS25 [yhdG::Pxyl (phleo)] (D. Z. Rudner, unpublished) between HindIII and NheI. The construct was sequenced using oML87 and oWX1894.

pWX778 [yhdG::Phyperspank-(optRBS)-scpAB (phleo)] was generated by inserting scpAB with an optimal ribosome binding site (optRBS) (amplified using oWX1897 and oWX1898 from B. subtilis PY79 genome and digested with HindIII and NheI) into pMS28 [yhdG::Phyperspank (phleo)] (D. Z. Rudner, unpublished) between HindIII and NheI. The construct was sequenced using oWX428, oWX486 and oWX487.

pWX788 [yhdG::Phyperspank-(optRBS)-sirA (erm)] was generated by inserting sirA with an optimal ribosome binding site (optRBS) (amplified using oWX1892 and oWX1893 from B. subtilis PY79 genome and digested with HindIII and NheI) into pMS24 [yhdG::Phyperspank (erm)] (D. Z. Rudner, unpublished) between HindIII and NheI. The construct was sequenced using oWX486 and oWX524.

Strain construction

−91°parS loxP-kan-loxP (BWX3379).

The +4° parS sequence (TGTTACACGTGAAACA) was inserted at −91° (in the intergenic region between ktrB and yubF). An isothermal assembly product was directly transformed to parSΔ9 (BWX3212)²⁶, which has all the 9 parS sites deleted from the B. subtilis genome. The isothermal assembly reaction contained 3 PCR products: 1) a region containing ktrB (amplified from PY79 genomic DNA using oWX1279 and oWX1280); 2) loxP-kan-loxP cassette flanked by the +4° parS sequence (amplified from pWX470 using universal primers oWX1241 and oWX438) and 3) a region containing yubF (amplified from PY79 genomic DNA using primers oWX1281 and oWX1282). The transformants were amplified and sequenced using oWX1283 and oWX1284.

Multiple parS sites were combined by standard transformation protocols. loxP-kan-loxP cassette was removed using a cre expressing plasmid pDR244⁵⁴, resulting in an unmarked parS site indicated as “no a.b.”.

Calculation of SMC number and error estimation

The number of SMC complex was calculated from marker frequency analysis, fluorescence microscopy and immunoblotting experiments. The calculation and error estimation are included in the Supplementary Data 1.

Comparison of simulated and experimental Hi-C contact maps

To compare the simulated maps to the experimental maps, we quantified both the interaction frequencies that give the intensities of pixels, and the angle/tilt of the lines. For interaction frequencies/intensities, we use contact probability decay P_c(s) as a function of genomic distance, s, as seen in Supplementary Figs. 5, 6, 7. P_c(s) has been a gold-standard method for comparison between Hi-C and simulations^28,55,56. We also used the same colour scales for the simulations and experiments to visually compare the intensities of the various Lines. To quantify the angle/tilt of the Lines, we drew lines on the plots (e.g. Extended Data Fig. 2) and matched the angles between simulations and experiments – these were used as input into our mathematical models (see also Supplementary Notes 1–5). For the contact probability decay curves, the best fit values were identified as follows:

$$\text{Goodness\hspace{0.17em}of\hspace{0.17em}fit\hspace{0.17em}for\hspace{0.17em}P}\left(\text{s}\right)=\frac{1}{M}\sum _{\text{s}}^{\text{M}}|\mathit{\text{log}}\left(P{\left(s\right)}_{\mathit{\text{experiment}}}\right)-\mathit{\text{log}}\left(P{\left(s\right)}_{\mathit{\text{simulation}}}\right)|$$

where M was the number of points used plot the P(s) curves, and s was the specified genomic distance. For the intensity of Line 1 compared to background levels, we quantified the Line 1 and background intensities by computing the mean contact frequency within a “box” centered on Line 1 or away from Line 1 (Supplementary Fig. 6c). The contact frequency within the boxes were computed (using Python notation) as:

$$\begin{gathered} \text{Background\hspace{0.17em}box\hspace{0.17em}value}=\text{numpy.mean}\left(\text{A}\left[250:300,300:350\right]\right) \\ \text{Line1\hspace{0.17em}box\hspace{0.17em}value}=\text{numpy.mean}\left(\text{A}\left[286:337,337:387\right]\right) \end{gathered}$$

where A is the 404 by 404 ter-centered Hi-C contact frequency matrix. The ratio of Line 1 box value to Background box values was computed for each simulation, and compared to the experimental value of 2.66. To obtain the parS loading strength, we minimized:

$$\text{Goodness\hspace{0.17em}of\hspace{0.17em}fit\hspace{0.17em}for\hspace{0.17em}Line\hspace{0.17em}1}=|\left(\text{Line\hspace{0.17em}1\hspace{0.17em}box\hspace{0.17em}value}\right)/\left(\text{Background\hspace{0.17em}box\hspace{0.17em}value}\right)-2.66|$$

Simulations and model generation

All details on simulations and polymer modelling are included in the Supplementary Notes 1–5.

Finding the optimal model parameters that match experimental data

To obtain the best parameters for our model to match the experimental data, we used both ChIP-seq and Hi-C results. We employed a combination of quantitative measurements and semi-qualitative measurements. For quantitative measurements, we (i) compared simulated to experimental Hi-C contact maps by calculating the absolute difference between the simulated and experimental contact probability decay curves; (ii) calculated the contact frequency of Line 1 relative to its background contact frequency (iii) measured the angles of the Hi-C Lines 1 and 2 from experiments (Fig. 2a). These quantitative measures helped us choose the best-fit values for both metrics (Supplementary Figs. 5, 6), and were used as quantitative constraints into a mathematical model, which related several model parameters to one another. For semi-qualitative measurement, we did visual inspection to match the numerical values and the overall shapes of ChIP-seq profiles between simulations and experiments (Supplementary Fig. 4).

In total, we needed to obtain 6 core parameters: a) parS-specific loading rates (i.e. parS strength), b) number of LEFs per chromosome, c) spontaneous dissociation rate, d) terminus-specific dissociation rate, e) facilitated dissociation rate (i.e. the unloading rate) and f) bypassing rate. We performed simulations to systematically vary several parameters (i.e. we performed parameter sweeps). We did not sweep all 6 parameters independently as we found that their values could be mathematically constrained relative to one another. We narrowed down the space of parameter values to 4 independent values (a-d above). As we swept those values, we compared various characteristics of our resulting model to Hi-C and ChIP-seq data for various strains. The process is detailed below.

1) We first sought to determine the spontaneous dissociation rate. We performed simulations of LEF distributions (Supplementary Fig. 4) and varied 3 parameters: the number of LEFs per chromosome, the spontaneous dissociation rate of LEFs, and the bypassing rate. At this step we assumed specific values for other parameters (including parS-specific loading rate and facilitated dissociation rate) that are varied later. We compared the simulated LEF profiles to SMC ChIP-seq for a strain containing a single parS site near the ori. We found that spontaneous dissociation rates below a certain value (<1/1260 s⁻¹) were necessary to reproduce the steady decay of SMC occupancy from the ori to ter that is observed experimentally (Supplementary Fig. 4). Within the range of dissociation rate values of ~ 1/2560 s⁻¹ to 1/1260 s⁻¹, the simulated LEF distribution profiles were in good visual agreement with the ChIP-seq curves for a broad range of bypassing rates and the numbers of LEFs. Thus after these simulations, we fixed the spontaneous dissociation rate to 1/2560 s⁻¹ (that is 0.0004 s⁻¹, or 1/43 min⁻¹) as a default value. This reciprocal of this rate (43 min) is also approximately the time for an SMC complex to travel from the ori to ter. As a comparison, in our growth condition, it takes ~40 min for a LEF to travel from ori to ter as measured previously¹⁰.

2) The terminus-specific dissociation rate was chosen qualitatively in order to give a “smooth decay” of LEF occupancy near the ter, and a smooth decay of Lines 1 and 2 at the terminus region as seen in Hi-C maps. This parameter did not affect the results above, but shaped the qualitative agreement between the simulated and experimental Hi-C maps and the ChIP-seq curves. Specifically, the 1-kb monomers at the terminus region (1950–2050) are given a dissociation rate of ~5-fold of the spontaneous dissociation rate, at 0.0025 s⁻¹. Future extensions to better simulate the ter region may incorporate the recently discovered site-specific unloading of SMCs by XDSs sites⁵⁷.

3) We next developed a theoretical framework to understand the relationship between the bypassing rate, the facilitated dissociation rate, the parS-specific loading rate, and the numbers of LEFs per chromosome. The parS-specific loading rate and the number of LEFs per chromosome dramatically affect the frequency of LEF collisions. We found that the bypassing rate and the frequency of LEFs collisions are constrained relative to each other by a constant (see in Supplementary Note 5, “Relationship between the bypassing rate, number of LEFs and the tilt of Line 1” and “Estimating the bypassing rate from the number of SMC complexes” for calculations). On the Hi-C map, these parameters are responsible for modulating the relative tilts observed for Lines 1 and 2. Thus, by measuring the angles subtended by Lines 1 and 2, we constrained the bypassing rate relative to the number of LEFs and the parS-specific loading rate. Moreover, we found that the facilitated dissociation rate could also be constrained relative to the bypassing rate and the frequency of collisions of LEFs; these parameters are also related to one another by a constant, and are estimated by the relative intensities of Lines 3 and 4 (see Supplementary Note 5, “The frequency of nested doublet interactions is controlled by the ratio of bypassing rates to unloading rates”). We provide examples in Extended Data Figs. 4, 5 to show the trade-off between the facilitated dissociation rate and bypassing rate in modulating the Line 3 and 4 intensities. In summary, from our analytical considerations, we found that instead of having to independently sweep and fit four parameters (bypassing rate, the facilitated dissociation rate, the parS-specific loading rate, and the numbers of LEFs per chromosome), we only needed to determine two of them to get all four.

4) We next found the number of LEFs per chromosome and the parS-specific loading rate using Hi-C maps. We fit the contact probability decay curve from experiments to those generated by our model (Supplementary Figs. 5, 6), and also compared the relative intensity of Line 1, measured as the contact frequency of a box centered on Line 1 compared to a background level of contacts (Supplementary Fig. 6). From these comparisons (detailed below), we were able to constrain both the number of LEFs and the parS-specific loading rate (Supplementary Figs. 5–7): Briefly, we simultaneously varied the number of LEFs per chromosome and the parS-specific loading rate, and used the analytical constraints for the bypassing rate and facilitated dissociation rate. We matched the shapes and values of the Hi-C contact probability decay curves (Pc(s)) by comparing simulations to experiments (Supplementary Figs. 5–7). For a strain with no parS sites, we identified that approximately 30–40 LEFs were needed to best match the shapes and numerical values of the Pc(s) curves (Supplementary Fig. 5) as judged by minimizing the goodness of fit metric (see calculations in the section “Comparison of simulated and experimental Hi-C contact maps”). We also simulated strains with single parS sites: We found that it was the number of “off-target” (non-parS loaded) SMC complexes which largely governed the overall shape and numerical values of the Pc(s). In contrast, the number of “on-target” (i.e. parS-loaded) LEFs largely influenced the intensity of Line 1 and not the Pc(s) curve (Supplementary Fig. 6a). The overall best matching Pc(s) curves (as judged by the goodness of fit metric) had approximately 20 “off-target” LEFs (Supplementary Fig. 6b). Moreover, the visually and quantitatively best matching Line 1 intensities corresponded to approximately 20 “on-target” LEFs (Supplementary Fig. 6c). Together, these results suggested ~40 LEFs per chromosome, which is similar to the value identified in Supplementary Fig. 5. In addition, these data indicated that the relative probability of a LEF loading at a parS lattice site is 4000 times stronger than at non-parS sites, i.e. a parS-specific loading strength of ~4000. As a self-consistency check for these two parameters (i.e. the number of LEFs ~40 and the strength of parS sites of ~4000) we compared the Pc(s) curve and line intensities for a strain with two parS sites. We found a good visual agreement between experiment and simulation for the Pc(s) curves, as well as the relative intensities of Lines 1, 2, 3 (Supplementary Fig. 7).

5) With the finding that there are approximately 30–40 LEFs/chromosome and a parS-specific loading rate of 4000, using our quantitative constraints discussed in 3), we automatically obtained the bypassing rate (in the range of 0.03–0.05 s⁻¹, i.e pausing for 20–30 sec before bypassing) and the facilitated unloading rate (in the range ~0.001–0.005 s⁻¹).

Extended Data

Extended Data Figure 1:

Exponential growth does not strongly affect the Hi-C contact patterns. (a) The B. subtilis genome is displayed in genomic coordinates (kilobases) and the angular coordinates used to designate the locations of the parS sites. (b) Hi-C maps for cells in exponential growth for the strains with parS sites at −94°, −59°, and both −94° and −59°. For details on strain names refer to Supplementary Table 1 and 2.

Extended Data Figure 2: SMC complexes can slow each other down.

(a) Time-course (similar to Fig. 1d) comparing the extrusion rates away from (but not between) the S1 and S2 parS sites. The green dashed line tracks the leading edge of the hairpin trace as it emerges from the −94° parS (S1) site and moves towards the ter; the red dashed line tracks the leading edge of the hairpin trace as it emerges from the −59° parS (S2) site and moves towards the ori. (b) Demonstration that when two parS sites are in one strain, the angle of the hairpin traces changes compared to single parS sites. The yellow and blue dashed lines are superimposed on the Hi-C map to help visualize the angle change. (c) The relationship between the tilt of the hairpin trace and the loop extrusion speeds (v₁, v₂ and v₃) is captured by a simple geometric relation. The equation shows that for equal v₁ across strains with one or two parS sites (as indicated in panel (a)), it follows that v₂ > v₃.

Extended Data Figure 3: The blocking and unloading model of loop extruder interactions does not produce all the features seen in the Hi-C map.

The parameter sweep was conducted for varying numbers of extruders and facilitated dissociation rates. The experimental data (for the strain with parS sites at both −94° and −59°) is shown on the top left of the figure. These contact maps were generated with the semi-analytical approach without making the shortest path approximation as described in Appendix 3 of Banigan et al, 2020³⁰ (also see Supplementary Notes 1–5). Notably, Lines 4 and 5 are missing in all of the plots with the blocking and unloading model - this is due to either traffic jams forming between extruders (for high numbers of extruders), or an insufficient loading rate (for low numbers of extruders) preventing the efficient formation of nested doublets and triplets.

Extended Data Figure 4: The number of extrusion complexes tunes the relative frequency of singlet- to adjoining-doublet interactions.

(a) In the experimental Hi-C map for the −59°−94° strain after 60 min of SirA expression, the frequency of singlet contacts to adjoining doublet contacts is close to 1:1. This is only achieved when the number of extrusion complexes is >40 and for sufficiently high bypassing rates. (b) A parameter sweep over the number of extruders and the bypassing rate. The best matched parameter combination is shown boxed in red. For a description of how we obtained the overall best parameters, see Methods and Supplementary Figs. 4–7.

Extended Data Figure 5: Parameter sweep of the bypassing and unloading rates for N=40 extruders/chromosome.

The experimental data (for the −59°−94° strain) is shown on the top left of the figure, and the model parameter sweep is below. The model with the most similar pattern in both angles of the Hi-C traces and the relative intensities of the different lines corresponds to a bypassing rate of 0.05 s⁻¹ and an unloading rate between 0.001 s⁻¹ and 0.005 s⁻¹. From the sweep, we find that the bypassing rate can control the angle between Hi-C map hairpin structures, while the ratio of the bypassing to unloading rates tunes the relative frequency of nested-doublet and nested-triplet interactions. These contact maps were generated with the semi-analytical approach³⁰ (see Supplementary Notes 1–5).

Extended Data Figure 6: Hi-C maps for exponentially growing cells.

Hi-C maps for strains with (a) two parS sites, and (b) three parS sites. Cells were growing exponentially.

Extended Data Figure 7: Hi-C time course of cells under G1 arrest.

The experimental time course of G1 arrest for a strain with (a) a single parS site at the −59° (top) and −91° (bottom), and (b) with two parS sites at −59° −91° (top) and −91° −117° (bottom). The experiments show that almost no change occurs to the angle of the hairpin traces when only a single parS site is present. However, when two parS sites are present, the hairpins increasingly tilt away from each other. (c) A 3D polymer simulation with the blocking, bypassing and unloading model of loop extrusion showing that when a single parS site is present, increasing the numbers of loop extruders, N, on the chromosome also does not change the observed hairpin angle for the same strains as in (a). Loop extrusion parameters use a bypassing rate of 0.05 s⁻¹ and a facilitated dissociation rate of 0.003 s⁻¹ (i.e. same as Fig. 4a); the number of extrusion complexes is denoted by N.

Extended Data Figure 8: Quantification of chromosome copy numbers and cell lengths per nucleoid.

(a) Whole genome sequencing plots for cells after the indicated minutes of replication inhibition by SirA. The computed ori:ter ratio indicates that by 60 min of SirA expression, cells have finished chromosome replication. (b) The quantification of microscopy images reveals the numbers of origins per nucleoid, and cell lengths per nucleoid. The numbers of cells analyzed were n=725, 580, 702, 557 for the four time points (exponential, 60 min, 90 min, 120 min), respectively. Means and standard deviations are shown. These values are used to calculate the numbers of SMC complexes per chromosome at different time points. To estimate the absolute numbers of SMC complexes/chromosome (independently of the Hi-C data and polymer simulations), we use the reference value of 30 SMC complexes/ori as measured in (Wilhelm et al, 2015)³², which converts to 34 SMC complexes/chromosome (indicated by *). We infer that these calculated values agree well with the numbers of loop extrusion complexes (as found by Hi-C and polymer modeling), if there are two SMC complexes per loop extrusion complex; this inference assumes that the error on the reference value of 30 SMC complexes/ori is sufficiently small. For calculations, see the attached Supplementary Data.

Extended Data Figure 9: Overexpression of SMC complexes speeds up the change of Hi-C patterns with time.

(a) Replication inhibition Hi-C time course following induction of SirA for a strain with parS sites at −27° and −59°. (b) The SMC complex (SMC, ScpA and ScpB) was overexpressed in the same background as the strain in panel A. We found that prolonged over-expression of SMC complexes at 90 min and 120 min did not recapitulate the experiments seen in G1 arrested cells in (a) but caused the interaction lines to become shorter. These patterns are likely due to non-specific loading of SMC complexes outside of parS, creating traffic jams along the DNA. In simulations, when we increase the numbers of off-parS loaded extruders, while keeping the numbers of on-parS loaded extruders consistent, we can observe similar changes in the Hi-C maps. Numbers of on-parS versus off-parS loading are average values for the simulation. (c) With SMC overexpression, the 60 min time point (following SirA induction) more closely resembles the 90 min point than the 60m time point with no SMC overexpression. This indicates that increasing the numbers of SMC complexes on the chromosome leads to an increase in the tilts of the hairpin diagonals away from each other.

Extended Data Figure 10: Simulations of blocking and unloading (without bypassing) do not reproduce the wild-type Hi-C map.

(a) Analytical results demonstrating there is a high likelihood of collisions between SMC complexes near the ori due to the high density of parS sites. Calculations were performed for a facilitated unloading rate of 0.0006 s⁻¹ and an extrusion rate of 0.8 kb/s. (b) 3D polymer simulations showing that even a few loop extruders (e.g. 5 extruders) results in a missing central diagonal and long-range tethers between the ori and other genome positions. With more extruders per chromosome, the traffic jams between SMC complexes near the origin becomes more likely, preventing juxtaposition of the arms. For very low numbers of extruders (e.g. 2 extruders), the central diagonal is present, but it is much fainter than observed experimentally.

Data availability statement

Hi-C and ChIP-seq data that support the findings of this study have been deposited in the Gene Expression Omnibus with accession no. GSE155279 (https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE155279). All Next-Generation Sequencing data used in this study are listed and itemized in Supplementary Table 1 with the corresponding accession numbers. Unprocessed microscopy images, uncropped blot images and their associated molecular weight/size markers can be accessed in Mendeley Data under the following DOI: 10.17632/vgw8sjxsyv.1⁴⁷.