Chromatin jets deﬁne the properties of cohesin-driven in vivo loop extrusion

Complex genomes show intricate organization in three-dimensional (3D) nuclear space. Current models posit that cohesin extrudes loops to form self-interacting domains delimited by the DNA binding protein CTCF. Here, we describe and quantitatively characterize cohesin-propelled, jet-like chromatin contacts as land-marks of loop extrusion in quiescent mammalian lymphocytes. Experimental observations and polymer simulations indicate that narrow origins of loop extrusion favor jet formation. Unless constrained by CTCF, jets propagate symmetrically for 1–2 Mb, providing an estimate for the range of in vivo loop extrusion. Asymmetric CTCF binding deﬂects the angle of jet propagation as experimental evidence that cohesin-mediated loop extrusion can switch from bi- to unidirectional and is controlled independently in both directions. These data offer new insights into the physiological behavior of in vivo cohesin-mediated loop extrusion and further our understanding of the principles that underlie genome organization. minutes at room temperature and then the reaction was quenched with 125 mM glycine at room temperature for 5 minutes. Cell nuclei were isolated using a RIPA lysis buffer (10mM Tris pH7.5, 1mM EDTA, 1% Triton X-100, 0.1% Sodium deoxycholate, 0.1% SDS, 0.15M NaCl, 1X Roche protease inhibitors). Following isolation of cell nuclei, genomic DNA was sonicated in a high-salt RIPA buffer (10mM Tris pH7.5, 1mM EDTA, 1% Triton X-100, 0.1% Sodium de-oxycholate, 1% SDS, 0.8M NaCl, 1X Roche protease inhibitors) for 30 minutes on a sonicator (Bioruptor) with high power setting, and 30 seconds on and 30 seconds off per minute. Immunoprecipitation was performed in a RIPA buffer (10mM Tris pH7.5, 1mM EDTA, 1% Triton X-100, 0.1% Sodium deoxycholate, 0.1% SDS, 0.15M NaCl, 1X Roche protease inhibitors), and antibody-antigen complex was precipitated using Dynabead Protein G (Thermo Fisher). Protein was digested using Proteinase K, and then DNA-pro-tein complex was reverse crosslinked overnight at 65 (cid:4) C. RNase A was added to remove RNA after decrosslinking. ChIP-seq library


In brief
Cohesin organizes the genome in 3D nuclear space. In this issue of Molecular Cell, Guo et al. describe and characterize ''jets,'' an unusual form of cohesinmediated chromatin interactions. Jets offer insights into the physiological behavior of cohesin-mediated loop extrusion and the principles that underlie genome organization.
During DNA replication in bacteria, SMC complexes are loaded from predefined sites, providing evidence that individual SMC complexes can align entire chromosome arms comprising several million base pairs of DNA (Marbouty et al., 2015;Tran et al., 2017;Wang et al., 2017Wang et al., , 2018; reviewed by . In contrast to bacteria, loading sites for SMC complexes are not well defined in mammalian cells. Active regulatory elements are enriched for cohesin and the cohesin component and loading factor NIPBL. ATAC-seq accessibility and the acetylation of histone H3 on lysine 27 (H3K27ac) are part of the chromatin signature of active regulatory elements and therefore considered as chromatin features of potential cohesin loading sites (Vian et al., 2018). Biochemical, functional, and genetic interactions of NIPBL/cohesin with H3K27ac-associated BET proteins (Olley et al., 2018;Luna-Pelá ez et al., 2019;Linares-Saldana et al., 2021), the enhancer-associated MLL3/4 complex (Yan et al., 2018), and the components of the transcriptional machinery (Kagey et al., 2010;Liu et al., 2021b;van den Berg et al., 2017) implicate enhancers and super-enhancers as candidate loading sites for cohesin within chromatin domains and TADs (Vian et al., 2018;Kagey et al., 2010). However, in the absence of direct assays for cohesin loading in living cells, the identity of in vivo cohesin loading sites remains uncertain. Moreover, chromatin regions that give rise to domains, loops, and stripes in mammalian genomes typically contain multiple potential cohesin loading sites. Therefore, it is unclear whether cohesin-dependent contacts are established by the continuous action of individual cohesin complexes or by a succession of multiple cohesin complexes.
Here, we describe cohesin-dependent chromatin contacts that originate from small, isolated sites of accessible chromatin and traverse adjacent B compartment regions in a jet-like fashion in primary mammalian cells. Jet origins feature local chromatin accessibility, NIPBL, cohesin, and H3K27ac. Our experimental and computational modeling suggest that lone accessible sites favor focal cohesin loading and chromatin jet formation, whereas broad or multiple accessible sites drive diffuse cohesin loading and favor the formation of contact domains (Fudenberg et al., 2016;Fudenberg et al., 2017;Banigan et al., 2022). Once initiated, jets can propagate symmetrically for 1-2 Mb. Unilateral CTCF encounters can convert bi-to unidirectional extrusion, indicating that both directions of extrusion are controlled independently. These data provide new insights into the physiological behavior of in vivo cohesin-mediated loop extrusion in unperturbed mammalian cells.

RESULTS
To elucidate the properties of cohesin-mediated chromatin contact propagation in vivo, we performed in situ Hi-C on wild-type, Ctcf À/À , and Rad21 À/À Ctcf À/À primary DP thymocytes ( Figure S1; Table S1). The efficiency of CTCF depletion was 80.0% ± 10.1% (n = 7), and the efficiency of RAD21 depletion was 83.3% ± 4.2% (n = 7; Figure S1C). We chose small DP thymocytes because they are quiescent and therefore require cohesin and CTCF for 3D genome organization in interphase but not for cell cycle-related functions such as DNA replication or chromosome segregation (Seitan et al., 2011;Nasmyth and Haering, 2009). We examined the resulting Hi-C maps for features consistent with loop extrusion. In addition to the familiar Hi-C patterns of ubiquitous pleat-like compartments and diamond-shaped domains (see Figure 1A for a schematic and illustrative example, Figure S1 for quantification), visual inspection revealed a smaller number of jet-like projections from the Hi-C diagonal (see Figure 1B for a schematic and illustrative example, Table S2 for quantification), reminiscent of Hi-C patterns that are formed by aligned chromosome arms in bacteria (Tran et al., 2017;Wang et al., 2017Wang et al., , 2018; reviewed by . The examination of published Hi-C data  shows that similar jets are present in B cells ( Figure S2).
The majority of jets originated from small regions denoted as open chromatin, i.e., A compartment intervals based on Hi-C eigenvector. Jets projected into surrounding closed chromatin regions (B compartment intervals, Figure 1C; Table S2). We identified a set of n = 38 jets and developed a protractor tool to quantify jet strength and jet angles in individual Hi-C replicates (see method details section; Figures 1D and 1E; Table S2). Protractor scanning confirmed increased chromatin contacts around small A compartment intervals that contained visually identified jets compared with small A compartment intervals that lacked jets, including regions that contained contact domains, or neither jets nor contact domains ( Figure 1F; Table S2). The propagation of chromatin jets perpendicular to the Hi-C diagonal is consistent with bidirectional loop extrusion in vivo ( Figure 1G).

Jets can be constrained by CTCF and released by CTCF removal
In comparison with wild-type thymocytes (Figure 1), additional jets arise in Ctcf À/À thymocytes (Figures 2A, 2B, and S3; Table S2). Aggregate subtraction plots confirmed that average jet strength increased in the absence of CTCF ( Figures 2C and S4). Protractor scan quantification showed that a subset of jets became significantly stronger in CTCF-deficient (Ctcf À/À ) compared with wildtype DP thymocytes. Integration with CTCF chromatin immunoprecipitation sequencing (ChIP-seq) data showed that this increase in strength was confined to those jets that were targets of CTCF binding in wild-type DP thymocytes ( Figure 2D). The loss of CTCF led to a significant decrease in the variance of jet length distributions ( Figure 2E). This is consistent with the role of CTCF in blocking cohesin-mediated loop extrusion (Li et al., 2020) and indicates that CTCF is a major determinant of jet propagation. Polymer simulations in which CTCF stalls cohesin reproduced the experimentally observed impact of CTCF on the propagation of jets in the presence and the absence of CTCF ( Figure 2F; see method details section and Table S3 for parameters). These data indicate that jet propagation can be constrained by CTCF and released by CTCF removal ( Figure 2G).
We observed that jets were substantially weakened by the depletion of cohesin ( Figures 1A and 2A; Table S2). The jet remnants visible in Hi-C maps of cohesin-deficient thymocytes are likely due to the imperfect depletion of the RAD21 protein ( Figure S1C). The aggregate analysis and subtraction plots confirmed the weakening of jets in the absence of cohesin ( Figure 3A). The protractor scan quantification of jet strength of wild-type, CTCF-deficient (Ctcf À/À ), and cohesin-deficient (Rad21 À/À Ctcf À/À ) DP thymocytes showed that reduced jet strength after cohesin depletion was significant, whether or not CTCF was bound at jet origins ( Figure 3B). The analysis of published dilution Hi-C data from wild-type and Rad21 À/À DP thymocytes (Seitan et al., 2013) confirmed that depletion of cohesin alone was sufficient to weaken jet formation ( Figure S5).  distinctly smaller in size ( Figure 4A). Among A compartment intervals <1 Mb, jets preferentially originated from smaller A compartment intervals compared with contact domains (Figure 4B). To identify chromatin features of A compartment intervals that form jets, we integrated Hi-C with ATAC-seq, which identifies accessible chromatin, ChIP-seq for the cohesin subunit RAD21 and NIPBL, as well as H3K27ac as a mark for active regulatory elements. H3K27ac-associated BET proteins (   Example of a jet that gains in strength in Ctcf À/À DP thymocytes (center) compared with wild type (left). Rad21 À/À Ctcf À/À DP thymocytes are shown for comparison (right). Genome browser view of chr17 69.8 Mb with A/B compartment eigenvector, subcompartments, contact domains (black 5 + 10 kb, red: 5 kb), ChIP-seq tracks, and directionality of CTCF motifs associated with CTCF ChIP-seq peaks.
(B) Replicate-based protractor scan quantification of the jet shown in (A).
(C) Mean Hi-C contact subtraction of n = 38 jets in CTCF KO minus wild-type thymocytes. Jet pileups for wild-type and CTCF KO are shown in Figure S4.
(D) Comparison of jet strength in wild-type and Ctcf À/À DP thymocytes. Jets overall increased in strength in Ctcf À/À compared with wild-type DP thymocytes (CTCF KO, p = 0.006, one-sided t test, n = 38 jets). Jets with at least one CTCF ChIP-seq peak within 200 kb of the jet origin increased in strength in Ctcf À/À compared with wild-type DP thymocytes (CTCF KO, p = 0.002, one-sided t test, n = 19 jets, 13/19 gained strength), whereas jets without a CTCF ChIP-seq peak within 200 kb of the jet origin did not (p = 0.483, one-sided t test, n = 18 jets, 6/18 gained strength). The mean (red) and 95% confidence interval are shown (gray).
(E) Comparison of jet reach in wild-type and Ctcf À/À DP thymocytes. The jet length shows a narrower distribution in Ctcf À/À than in wild-type thymocytes ( Figure 4C, quantification in Figure 4D). Cohesin loading has been associated with active chromatin regions and components of the transcriptional machinery (Kagey et al., 2010;van den Berg et al., 2017;Yan et al., 2018;Olley et al., 2018;Luna-Pelá ez et al., 2019;Linares-Saldana et al., 2021), and jet origins have chromatin features consistent with these studies.

Isolated focal areas of open chromatin favor jet formation
Jets showed a more focused distribution of ATAC-seq and H3K27ac ChIP-seq signals than contact domains ( Figure 5A; quantification in Figure 5B), indicating that jets are more likely to arise from isolated focal areas of open chromatin. We used polymer simulations to model the impact of narrow versus broad cohesin loading areas on the resulting chromatin contacts. In these simulations, 100 monomers represented narrow cohesin loading 2,000 monomers represented broad areas of cohesin loading. All other parameters such as total polymer length, number of cohesins, drift, and unloading probability were kept constant (see simulations 1 and 2 in Table S3). Narrow cohesin loading resulted in jet-like features ( Figure Figure 2C) with Rad21 À/À Ctcf À/À DP thymocytes (DKO, right). The difference in mean Hi-C signal CTCF KO minus wild type (right). x and y axes are in Mb. (B) Numerical comparison of jet strength in wildtype and Ctcf À/À (as in Figure 2D) with Rad21 À/À Ctcf À/À (DKO) DP thymocytes n = 38. Jets with at least one CTCF ChIP-seq peak within 200 kb of the jet origin (CTCF bound, n = 19) and jets without a CTCF ChIP-seq peak within 200 kb of the jet origin (not CTCF bound, n = 18) were affected by the loss of cohesin (one-sided t test). The mean (red) and 95% confidence interval are shown (gray). origins, and the associated polymer simulations support the notion that jet origins have features of isolated cohesin loading sites. We propose that jets arise from isolated chromatin regions with focal accessibility and focal H3K27ac marks ( Figure 5D).

Jets allow estimates of the range of in vivo loop extrusion
The observation that jets project from defined origins, are powered by cohesin, and are constrained by CTCF provides a unique opportunity to determine the properties of in vivo loop extrusion. We developed a stencil tool to quantify the range of jet propagation (see method details section, Figure 6A). We found that jets can propagate for $1-2 Mb in wild-type and CTCF-deficient DP thymocytes ( Figure 6B; Table S2) and for similar distances in resting B cells ( Figure S2).
Jet angles are modulated by CTCF, providing experimental evidence for one-sided loop extrusion We next analyzed the impact of CTCF on the angle of jet propagation. Jets that propagate perpendicular to the diagonal in a cohesin-dependent manner illustrate that in vivo loop extrusion by cohesin can progress bidirectionally (e.g., Figure 1A; Table S2). However, we found that a subset of jets deviates from the perpendicular (Figures 7A and S6; Table S2). The jet depicted in Figure 7A has a negative projection angle, indicating that this jet is deflected toward upstream sequences in wild-type cells. This jet is flanked by downstream CTCF sites. The jet depicted in Figure S6A has a positive projection angle in wild-type cells, indicating that it is deflected toward downstream sequences in wildtype cells. This jet is flanked by upstream CTCF sites.
In contrast to the jets shown in previous figures, these angled jets are not symmetrical in wild-type cells. Accordingly, the distance traveled by loop extrusion is greater in one direction ( Figure 7C; Table S2). Interestingly, the projection angles of these deflected jets change in CTCF-deficient cells, and jets align more closely with the perpendicular (Figures 7A, 7B, S6A, and S6B; Table S2). Consequently, the range of jet angles is broader in wild-type than in CTCF-deficient cells ( Figure 7D). We next counted the number of CTCF motifs with CTCF ChIP-seq peaks in DP thymocytes as CTCF motif scores, where positive scores indicate CTCF downstream binding and negative motif scores with CTCF upstream binding. Positive CTCF motif scores were associated with jet deflection toward upstream sequences and negative CTCF motif scores were associated with jet deflection toward downstream sequences ( Figure 7E).
The observation that CTCF can alter the projection angle of jets is informative with respect to the behavior of the loop extru-sion machinery upon encounter with CTCF. The loop extrusion model posits that extrusion is blocked by CTCF bound to sites in convergent orientation (Fudenberg et al., 2016), and recent studies provide a mechanism for how the encounter of cohesin with the N terminus of CTCF arrests loop extrusion and stabilizes cohesin at CTCF sites (Li et al., 2020;Nora et al., 2020;Pugacheva et al., 2020). If loop extrusion encounters CTCF in only one direction, extrusion may either stop completely or continue

OPEN ACCESS
Article in the direction that is not blocked by CTCF (Fudenberg et al., 2017; Figure 7F). Our observation that jets can be deflected by an encounter with CTCF indicates that loop extrusion can switch from bidirectional to unidirectional in a CTCF-dependent manner. Using polymer simulations to model how unilateral CTCF encounter affects jet angles, we find that models where a unilateral encounter with CTCF imposes a bidirectional block on cohesin-mediated loop extrusion do not reproduce the experimental observation of altered jet angles ( Figure 7G). We next modeled CTCF effects on jet angles under the assumption that unilateral encounter with CTCF imposes a unidirectional block on cohesin-mediated loop extrusion ( Figure 7H). The results of this simulation reproduce the experimental observations that (1) jet angles change in response to unilateral CTCF encounter and that (2) both arms of the jets show different lengths in response to unilateral CTCF encounter ( Figures 7C and 7F; Table S2). These findings provide experimental evidence for previous assumptions that when blocked in one direction, loop extrusion continues in the other direction (Fudenberg et al., 2017). Taken together, our experimental data and in silico simulations support a model where cohesin-driven loop extrusion in vivo is by default symmetrical and therefore bidirectional. However, CTCF can significantly deflect the projection angle of cohesin-driven chromatin contacts, indicating that extrusion can switch from bidirectional to unidirectional.
Taken together, these data provide a mechanistic dissection of in vivo loop extrusion. A model for jet formation is depicted in Figure S7, including symmetrical extrusion in the absence of CTCF ( Figure S7A) the impact of bi-( Figure S7B) and unidirectional ( Figure S7C) CTCF encounters and propagation from narrow versus broad origins ( Figures S7A and S7D).

DISCUSSION
Here, we describe and quantitatively characterize cohesindependent chromatin jets and provide insights into the physiological behavior of in vivo cohesin-mediated loop extrusion.

OPEN ACCESS
Article from their origins and propagate perpendicular to the Hi-C diagonal provide powerful evidence for the location of cohesin loading. Computational modeling supports the interpretation that cohesin is loaded at jet origins. In these simulations, narrow sites of cohesin loading give rise to jets. Previous simulations suggested that focal cohesin loading at promoters might generate jet-like features (Banigan et al., 2022), although these were not observed experimentally. In contrast to narrow loading sites, broad areas of cohesin loading lead to domain formation (Fudenberg et al., 2016(Fudenberg et al., , 2017. This interpretation is further strengthened by experimental observations that the likelihood of jet formation is inversely related to the size of the potential cohesin loading area. Jets echo the SMC-driven process that aligns bacterial chromosome arms, both in terms of Hi-C pattern and the requirement for defined loading sites (Gruber and Errington, 2009;Ganji et al., 2018;Marbouty et al., 2015;Golfier et al., 2020;Kong et al., 2020;Terakawa et al., 2017;Tran et al., 2017;Wang et al., 2017Wang et al., , 2018Anchimiuk et al., 2021). Akin to the alignment of bacterial chromosome arms, jets may reflect the continuous, linear activity of stacked SMC complexes ( Figure S7C). Indeed, our simulations indicate that the ''re-loading'' of additional cohesin complexes along the length of the jet would disrupt jet formation ( Figure S7D).
Recent reports describe interesting chromatin features that are similar to jets in appearance and likely related in terms of mechanism. In yeast, pericentromeric jet-like features form when centromeres are engaged by mitotic spindles (Paldi et al., 2020), and the jet-like alignment of chromatin fragments are associated with double-strand break repair (Piazza et al., 2021;Arnould et al., 2021). These features are characterized by their short range of $25 kb. Chromatin flares have been found to form in the specialized chromatin environment of zebrafish sperm (Wike et al., 2021). Flares show evidence of linear alignment of DNA sequences, but with an average length of $175 kb, they are on a smaller scale than jets. Flare formation has not been linked to specific SMC complexes (Wike et al., 2021). A recent preprint observes the transient occurrence of cohesin-dependent jet-like chromatin features in response to the co-depletion of WAPL and CTCF in mouse ES cells, referred to as plumes (Liu et al., 2021b). As described here for jets, these structures originate from small accessible regions surrounded by B compartments (Liu et al., 2021b). However, because plumes form only after the depletion of the cohesin unloading factor WAPL, they cannot serve to establish the physiological range of cohesin-mediated loop extrusion. Although WAPL depletion was required, it was not sufficient for plume formation unless CTCF was also depleted (Liu et al., 2021b), which masks unidirectional in vivo loop extrusion upon a one-sided CTCF encounter. Similar to flares and plumes, jets arise from focal origins. However, unlike flares (Wike et al., 2021), jets form in somatic cells, rather than in the specialized chromatin environment of sperm, and are unequivocally cohesin dependent. Unlike plumes (Liu et al., 2021b), jets form in unperturbed primary cells at steady state and therefore reflect in vivo loop extrusion under conditions of physiological cohesin residence time. Therefore, jets allow measurements of the genomic distances traversed by cohesin complexes loaded at specific sites, and jet length may reflect the range of individual cohesin complexes on chromatin in vivo. From their origins at isolated areas of accessible chromatin, jets propagate across neighboring closed (B compartment) chromatin to cover distances of approximately 1-2 Mb.
Our findings are consistent with the assumption that cohesinmediated loop extrusion is symmetrical in the absence of CTCF and therefore bidirectional by default . We find that unilateral CTCF encounter deflects the angle of jet propagation. This provides strong evidence that cohesin-mediated loop extrusion can switch from bi-to unidirectional in vivo (Fudenberg et al., 2017;Vian et al., 2018) and therefore is independently controlled in both directions. Jets provide new insights into the physiological behavior of in vivo cohesin-mediated loop extrusion and further our understanding of the principles that underlie genome organization.

Limitations of the study
Although our data show that jets are cohesin dependent and can be blocked or deflected by CTCF, we do not yet fully understand the rules that govern jet formation and, in particular, why not all focal sites of accessibility give rise to jets. We do not know the residence time of cohesin in quiescent primary lymphocytes and, as a result, can only speculate on cohesin extrusion speeds during jet propagation. Estimates of cohesin residence times in interphase range between 10 and 25 min in other cell types (Gerlich et al., 2006;Tedeschi et al., 2013;Hansen et al., 2017;Wutz et al., 2020). Assuming that cohesin residence times are similar in quiescent primary lymphocytes, our data suggest that cohesin can traverse ''closed'' B compartment chromatin at speeds that are comparable with-and possibly in excess of-SMC complex extrusion speed in bacteria and cohesin-mediated extrusion in vitro (Ganji et al., 2018;Golfier et al., 2020;Kong et al., 2020;Terakawa et al., 2017;Tran et al., 2017;Wang et al., 2017Wang et al., , 2018Davidson et al., 2019;Kim et al., 2019). Our current model for the formation of jets is that individual cohesin complexes mediate continuous extrusion along the full length of the jet. It is possible that additional experiments and/or modeling approaches may provide alternative views of jet formation that may not involve continuous extrusion along the full length of the jet. Even in the absence of CTCF, not all jets are the same length, and further work will be required to understand the differences between jets with faster and slower decay rates. Similarly, it will be important to further investigate obstacles in the extrusion path that affect cohesin processivity to result in jets that remain narrowly focused versus jets that become more diffuse as they propagate. Finally, our study indicates that cohesin-mediated loop extrusion is independently controlled in both directions but does not address whether cohesin complexes work as dimers (Kim et al., 2019), monomers (Yatskevich et al., 2019;Davidson et al., 2019), or multimers (Xiang and Koshland, 2021).

STAR+METHODS
Detailed methods are provided in the online version of this paper and include the following:

RESOURCE AVAILABILITY
Lead contact Further information and requests for resources and reagents should be directed to the lead contact, Matthias Merkenschlager (matthias.merkenschlager@lms.mrc.ac.uk).

Materials availability
This study did not generate new unique reagents.

Data and code availability
In situ Hi-C data for Hi-C CD69 -DP wild-type, CD4 Cre Ctcf -/-(CTCF KO), and CD4Cre Rad21 -/-Ctcf -/-(DKO) thymocytes and ChIPseq data for RAD21, CTCF, and H3K27ac in wild-type DP thymocytes generated in this study have been deposited at the NCBI Gene Expression Omnibus (GEO) under accession number GSE199059 and are publicly available as of the date of publication. ATAC-seq data in wild-type DP thymocytes are publicly available at GEO GSE141223 (Miyazaki et al., 2020). Dilution Hi-C for wild-type and CD4 Cre Rad21 -/-DP thymocytes and ChIP-seq data for NIPBL in wild-type DP thymocytes are publicly available at GEO GSE48763 (Seitan et al., 2013). Mouse B cell Hi-C data are publicly available at GEO GSE82144 .
All original code has been deposited at Zenodo and is publicly available as of the date of publication. The DOI for code for jet simulations is https://doi.org/10.5281/zenodo.7028262. The DOI for code for jet quantification is https://doi.org/10.5281/zenodo. 7034657.
Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

EXPERIMENTAL MODEL AND SUBJECT DETAILS Animals
Mice harbouring a conditional Ctcf allele (Ctcf lox/lox , Heath et al., 2008)

Hi-C and analysis
In situ Hi-C was performed as described  with the following modifications. Cells were cross-linked in 1% formaldehyde for 10 min at room temperature. Chromatin was digested with 100 units of MboI overnight at 37 C while shaking at 900 rpm. After overnight incubation, 100 units of MboI were added for the second-round digestion for 2-4 hours. The DNA polymerase I, large (Klenow) fragment, was used to fill in MboI-digested fragment overhangs in the presence of biotin-labelled dATP. Fragment ends were then ligated with 4000 units of T4 DNA ligase by incubating at room temperature for 4-6 h with rotation at 12 rpm. After ligation, cell nuclei were collected by centrifugation, and chromatin was reverse crosslinked overnight at 65 C. RNase A was used to remove RNA after decrosslinking. Genomic DNA was isolated and precipitated by sodium acetate-ethanol precipitation, and then purified DNA was sheared for 8 min using a sonicator (Bioruptor) with high power setting, and 30 seconds on and 30 seconds off per minute. DNA fragments in the range of 300-500 bp were then selected using the AMPure XP beads (Beckmann Coulter). After biotin-labelled DNA fragments were captured on Dynabeads MyOne Streptavidin T1 (Thermo Fisher), fragment ends were repaired in a mixture of enzymes containing T4 polynucleotide kinase, T4 DNA polymerase I and DNA polymerase I, large (Klenow) fragment, and then NEBNext adaptors for Illumina sequencing were ligated to the dA-tailed fragment ends. After the USER enzyme digestion, NEBNext oligos for Illumina sequencing were used for PCR for library preparation. A PCR titration was carried out to determine the lowest number of PCR cycles (8-10 cycles in this work). Final Hi-C sequencing libraries were quantified and checked for size

Centrality score
The centrality score is the sum of ATAC-seq or ChIP-seq signal at the 50kb centred on the feature divided by the sum of the signal from the 50-75kb upstream and downstream of the feature.

In silico modelling
We use simulations to investigate the effect of cohesin loop extrusion and CTCF binding on Hi-C maps. The simulations work in two stages. One-dimensional movement of cohesin subunits across chromatin is followed by three-dimensional polymer folding simulations to produce simulated Hi-C maps. To model chromatin folding we use the publicly available software polychrom (Version v0.1.0, 10.5281/zenodo.3579473, Imakaev et al., 2019) and manually add pairs of cohesin cuffs as extra bonds that define the structure, as described in the following. Cohesin is modelled as a pair of two random walkers that move along a straight line representing chromatin, modelled as a chain of monomers. Each monomer is a possible position for a walker. We initialise the simulation by placing with uniform probability both walkers of a fixed number of cohesin molecules within a certain loading area. We may further place CTCF molecules along the polymer. After this initial setup, the one dimensional simulation follows the process described in Algorithm 1 ( Table S4). All of the actions in the algorithm have predefined probabilities. This is explicitly shown for the unloading action, and for the rest it is abbreviated.We model the movement of the two cuffs of each cohesin as a random walk with drift. The left cuff has a drift towards the left and the other towards the right. The cuffs cannot switch places or bypass each other and may therefore stall others. They can further be stopped and captured by CTCF molecules.
Two CTCF capture mechanisms and their impact on the formation of jets are investigated. In the first case, a suitably oriented CTCF captures only the cuff that it encounters while the other cuff of the same cohesin is free to move and further extrude chromatin. In the second case, when a CTCF captures one cuff of a cohesin, both cuffs are considered immobilized and cohesin stops extruding. The drift is the difference between the jump probabilities of the cuffs. Cohesin is unloaded with different probabilities. Cohesin captured by CTCF has a longer residence time on the polymer, which is reflected by the smaller unloading probability compared to free cohesin. We allow for 0, 1 or 2 CTCF sites, at the positions indicated. At each of these sites, we place 5 CTCFs equidistantly, every 50 monomers. Each CTCF may capture a cohesin cuff once it steps on the site with the probability stated and each may release them again with the much smaller release probability indicated.
not defined otherwise; ( Equation 8) (Equation 9) where D i is the set of points in the Hi-C map that are contained in each piece i along thestencil, i˛{0,.,mÀ1}. We subtract the background given by Rad21 -/-Ctcf -/from the stencil g i and find the piece i where the subtracted stencil falls below a threshold of 5. We then calculate the up-and downstream distances d 1 and d 2 ( Figure 7C).
All statistical analysis and software used is listed in the Software and algorithms section of the STAR Methods table, and all statistical details of experiments can be found in the figure legends, figures, results, and method details sections, including the statistical tests used, the number of replicate experiments, definition of center, dispersion, and precision measures, and the definition of significance. Experimental and control groups were defined by genotypes, no randomization was performed, and no data were excluded from the analysis.