Angeliki Platania

Cathie Erb

Mariano Barbieri

Bastien Molcrette

Erwan Grandgirard

Marit Ac De Kort

Karen Meaburn

Tiegh Taylor

Virlana M Shchuka

Silvia Kocanova

Marit Ac De Kort

Guilherme Monteiro Oliveira

Jennifer A Mitchell

Evi Soutoglou

Tineke L Lenstra

Nacho Molina

Argyris Papantonis

Kerstin Bystricky

Tom Sexton
email: sexton@igbmc.fr.

Competition between transcription and loop extrusion modulates promoter and enhancer dynamics

Keywords: Chromatin dynamics, enhancer, transcription, anomalous diffusion, molecular dynamics, live imaging

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INTRODUCTION

Metazoan gene expression is finely controlled by regulatory inputs from promoter sequences and distal regulatory elements, such as enhancers. How these dispersed elements are spatiotemporally coordinated to determine transcriptional output has been a topic of intense study, but key questions remain unresolved [START_REF] Sexton | The role of chromosome domains in shaping the functional genome[END_REF][START_REF] Schoenfelder | Long-range enhancer-promoter contacts in gene expression control[END_REF] . For example, most chromosome conformation capture-based experiments support a model where distal enhancers require close spatial proximity to target genes to confer activation [START_REF] Palstra | The beta-globin nuclear compartment in development and erythroid differentiation[END_REF][START_REF] Sanyal | The long-range interaction landscape of gene promoters[END_REF][START_REF] Javierre | Lineage-specific genome architecture links enhancers and non-coding disease variants to target gene promoters[END_REF] , often presumed via chromatin "looping", and engineered promoter-enhancer contacts have been shown to stimulate expression [START_REF] Deng | Controlling long-range genomic interactions at a native locus by targeted tethering of a looping factor[END_REF] . However, recent imaging experiments at different loci have shown clear physical separation of enhancers and active genes (often in the order of ~200-300 nm), with conflicting results as to whether their separation decreases [START_REF] Chen | Dynamic interplay between enhancerpromoter topology and gene activity[END_REF][START_REF] Chen | Widespread increase in enhancer-promoter interactions during developmental enhancer activation in mammals[END_REF] , stays the same [START_REF] Alexander | Live-cell imaging reveals enhancer-dependent Sox2 transcription in the absence of enhancer proximity[END_REF] or may actually increase [START_REF] Benabdallah | Decreased enhancer-promoter proximity accompanying enhancer activation[END_REF] on transcriptional activation. The identification of nuclear clusters of lineage-specific transcription factors [START_REF] Chong | Imaging dynamic and selective low-complexity domain interactions that control gene transcription[END_REF][START_REF] Li | Single-gene imaging links genome topology, promoter-enhancer communication and transcription control[END_REF] , RNA polymerase II (PolII) [START_REF] Cisse | Real-time dynamics of RNA polymerase II clustering in live human cells[END_REF][START_REF] Ghamari | In vivo live imaging of RNA polymerase II transcription factories in primary cells[END_REF] , and genes and regulatory elements themselves [START_REF] Schoenfelder | Preferential associations between co-regulated genes reveal a transcriptional interactome in erythroid cells[END_REF][START_REF] Papantonis | TNFα signals through specialized factories where responsive coding and miRNA genes are transcribed[END_REF][START_REF] Allahyar | Enhancer hubs and loop collisions identified from single-allele topologies[END_REF][START_REF] Oudelaar | Single-allele chromatin interactions identify regulatory hubs in dynamic compartmentalized domains[END_REF][START_REF] Espinola | Cis-regulatory chromatin loops arise before TADs and gene activation, and are independent of cell fate during early Drosophila development[END_REF] has led to the proposal that transcription is organized into specialized nuclear microenvironments or "hubs" [START_REF] Lim | Enhancer-promoter communication: hubs or loops?[END_REF] . In this model, high local concentrations of regulatory factors accumulate near genomic sequences that are loosely coassociated; the shared location of regulatory elements within this microenvironment is more important for transcriptional regulation than their direct physical juxtaposition. These hubs are potentially built up through specific protein-protein interactions and/or phase-separated condensate formation between intrinsically disordered domains found on many transcription factors [START_REF] Li | Single-gene imaging links genome topology, promoter-enhancer communication and transcription control[END_REF][START_REF] Sabari | Coactivator condensation at super-enhancers links phase separation and gene control[END_REF] . How genes and distal regulatory elements locate or nucleate such hubs, and how the different regulatory inputs are coordinated into a transcriptional decision within, remain open questions.

An often-overlooked aspect determining how regulatory chromatin architectures are built or maintained is the underlying mobility (and freedom of movement) of the component factors. Whereas non-histone chromatin proteins, including transcription factors, are highly mobile in the nucleoplasm [START_REF] Lionnet | Single-molecule tracking of transcription protein dynamics in living cells: seeing is believing, but what are we seeing?[END_REF] , the large polymeric chromatin fiber has more constrained movement, due to a crowded environment and elastic interactions with neighboring segments of the polymer [START_REF] Tortora | Chromosome dynamics during interphase: a biophysical perspective[END_REF] . This is often characterized as subdiffusive movement, whereby the mean squared displacement (MSD) of the genomic element follows the relationship with time, t: MSD ∝ Dt α where D is the diffusion coefficient (a proxy for diffusive speed) and α, the anomalous exponent, is smaller than the value of 1 found in classical Brownian diffusion. Initial studies of randomly inserted tags suggested that heterochromatin was inherently less mobile than euchromatin in yeast [START_REF] Heun | Chromosome dynamics in the yeast interphase nucleus[END_REF] , but we recently reported significant locus-specific differences in chromatin diffusive properties at euchromatic regions in mouse embryonic stem cells (ESCs), suggesting finer-scale modulation of chromatin dynamics, potentially linked to underlying function [START_REF] Oliveira | Precise measurements of chromatin diffusion dynamics by modeling using Gaussian processes[END_REF] . As methods for tracking specific genomic regions in vivo has recently become available, researchers have asked whether the transcriptional activity of genes affects their mobility. We previously showed that an estrogen-inducible transgene could only explore a much smaller nuclear volume on acute induction, and that this constraint was dependent on transcriptional initiation [START_REF] Germier | Real-time imaging of a single gene reveals transcription-initiated local confinement[END_REF] , consistent with a model whereby the activated gene becomes confined within a transcriptional hub. This is supported by analogous studies showing slowed movement of the pluripotency gene Nanog when transcriptionally active [START_REF] Ochiai | Simultaneous live imaging of the transcription and nuclear position of specific genes[END_REF] and global enhanced chromatin mobility on treatment with transcriptional inhibitors [START_REF] Nozaki | Dynamic organization of chromatin domains revealed by super-resolution live-cell imaging[END_REF][START_REF] Nagashima | Single nucleosome imaging reveals loose genome chromatin networks via active RNA polymerase II[END_REF] . However, mobility of the Oct4 gene was found to be insensitive to transcriptional status [START_REF] Ochiai | Simultaneous live imaging of the transcription and nuclear position of specific genes[END_REF] , and a different study of transition between ESCs and epiblastlike cells reported acceleration of both promoters and enhancer-proximal sequences specific to the cell state where the elements are active [START_REF] Gu | Transcription-coupled changes in nuclear mobility of mammalian cis-regulatory elements[END_REF] . A clear understanding of how transcriptional events modulate chromatin dynamics (or vice versa) is thus still lacking.

At a larger scale, promoter-enhancer communication takes place within the context of topologically associated domains (TADs), regions of enhanced intra-domain chromatin contacts identified in population-average Hi-C maps [START_REF] Dixon | Topological domains in mammalian genomes identified by analysis of chromatin interactions[END_REF][START_REF] Sexton | Three-dimensional folding and functional organization principles of the Drosophila genome[END_REF] , which have been proposed to prevent inappropriate promoterenhancer communication across TAD borders, and/or to reduce the effective search space for enhancers to co-associate with target genes [START_REF] Sexton | The role of chromosome domains in shaping the functional genome[END_REF][START_REF] Lupiáñez | Disruptions of topological chromatin domains cause pathogenic rewiring of gene-enhancer interactions[END_REF][START_REF] Symmons | The Shh topological domain facilitates the action of remote enhancers by reducing the effects of genomic distances[END_REF][START_REF] Zuin | Nonlinear control of transcription through enhancer-promoter interactions[END_REF] . The major mechanism believed to organize TAD architecture is loop extrusion by SMC protein complexes, particularly cohesin (reviewed in ref. 36, and references therein). Cohesin loads on chromatin, extrudes loops of the chromatin fiber (mostly bidirectionally), and is dissociated by the factor WAPL to generate metastable chromatin loops in an equilibrium. Sites where loop extrusion are stalled, particularly the juxtaposition of convergently facing sites for the factor CTCF (CCCTC-binding factor), whose N-terminus specifically interacts with the cohesin complex [START_REF] Li | The structural basis for cohesin-CTCF-anchored loops[END_REF] , form the bases of more stabilized loops at TAD borders. These are observed in Hi-C maps [START_REF] Rao | A 3D map of the human genome at kilobase resolution reveals principles of chromatin looping[END_REF] , although recent live imaging experiments have revealed these to also be relatively rare and transient interactions in individual cells [START_REF] Gabriele | Dynamics of CTCF-and cohesin-mediated chromatin looping revealed by live-cell imaging[END_REF][START_REF] Mach | Cohesin and CTCF control the dynamics of chromosome folding[END_REF] . The so-called "architectural interactions" brought about by convergent CTCF sites have been proposed to facilitate juxtaposition of adjacent promoters and enhancers [START_REF] Kubo | Promoter-proximal CTCF binding promotes distal enhancer-dependent gene activation[END_REF] , and loop extrusion has also been shown to be required for efficient activity of more distal, as opposed to proximal, enhancers [START_REF] Kane | Cohesin is required for long-range enhancer action at the Shh locus[END_REF][START_REF] Rinzema | Building regulatory landscapes reveals that an enhancer can recruit cohesin to create contact domains, engage CTCF sites and activate distant genes[END_REF] .

Further, recent simulations and experimental results show that cohesin-mediated loop extrusion generally reduces chromatin mobility [START_REF] Nozaki | Dynamic organization of chromatin domains revealed by super-resolution live-cell imaging[END_REF][START_REF] Mach | Cohesin and CTCF control the dynamics of chromosome folding[END_REF] , perhaps further "stabilizing" such genomic configurations. However, we and others have observed extensive persistence of promoter-enhancer interactions when CTCF and/or cohesin is ablated [START_REF] Taylor | Transcriptional regulation and chromatin architecture maintenance are decoupled functions at the Sox2 locus[END_REF][START_REF] Hsieh | Enhancer-promoter interactions and transcription are largely maintained upon acute loss of CTCF, cohesin, WAPL or YY1[END_REF][START_REF] Chakraborty | Enhancer-promoter interactions can bypass CTCF-mediated boundaries and contribute to phenotypic robustness[END_REF] . This latter finding is reminiscent of the apparent competition that exists between TADs and chromosome compartmentation (higher-order co-associations between domains of homotypic chromatin, such as active with active): cohesin ablation eliminates TADs, but appears to strengthen compartments [START_REF] Rao | Cohesin loss eliminates all loop domains[END_REF][START_REF] Schwarzer | Two independent modes of chromatin organization revealed by cohesin removal[END_REF] . The exact mechanisms promoting chromosome compartmentation genome-wide are unclear, but since co-association of active domains appears to depend on transcription itself [START_REF] Rowley | Evolutionarily conserved principles predict 3D chromatin organization[END_REF] and transcription co-factors like BRD2 [START_REF] Xie | BRD2 compartmentalizes the accessible genome[END_REF] , it is reasonable to hypothesize that these could be the same biochemical principles involved in clustering transcription factors and active elements at proposed transcriptional hubs, raising the curious possibility that loop extrusion may sometimes antagonize such nuclear microenvironments.

To assess more closely the interplay of enhancer activity, transcription and cohesin-mediated loop extrusion on the spatiotemporal organization of gene regulation, we tagged the promoter and major enhancer (SCR; Sox2 control region) of the pluripotency gene Sox2 in mouse ESCs, in combination with detection of nascent transcription from the same allele, for their tracking at high temporal resolution. With a battery of genetic and other experimental perturbations, we confirmed the decoupling of transcription and promoter-enhancer proximity that was previously described at this locus [START_REF] Alexander | Live-cell imaging reveals enhancer-dependent Sox2 transcription in the absence of enhancer proximity[END_REF][START_REF] Taylor | Transcriptional regulation and chromatin architecture maintenance are decoupled functions at the Sox2 locus[END_REF][START_REF] Chakraborty | Enhancer-promoter interactions can bypass CTCF-mediated boundaries and contribute to phenotypic robustness[END_REF] , and also found a hitherto unappreciated localized effect of transcription on chromatin dynamics. Promoter kinetics are disrupted on severe transcriptional inhibition, but when comparing transcriptionally bursting and "poised" Sox2 alleles, it is the enhancer which specifically becomes less mobile on gene firing. Most strikingly, we observed that deleting either CTCF or transcription factor binding sites induced opposing effects on localized chromatin mobility. In addition, molecular dynamics simulations were able to recapitulate these experimental findings only when competition between loop extrusion and transcription-linked enhancerpromoter communication was reinforced, suggesting they may be antagonistic processes on chromatin dynamics, even though from a population-average viewpoint they are assumed to mediate the same interaction. These findings unify some of the seemingly conflicting results from previous studies and highlight the pitfalls of relying solely on population-averaged experiments on fixed cells to draw conclusions about a dynamic process such as spatiotemporal gene regulation.

RESULTS

Enhancer-promoter proximity is frequently maintained at the Sox2 locus independent of transcription

To follow promoter-enhancer communication in living cells, we tagged the Sox2 promoter and SCR with orthologous parS sites (ANCHOR1 and ANCHOR3) in the musculus allele of F1 (Mus musculus 129 × Mus castaneus) hybrid ESCs (we term this line Sox2-SCR WT ), enabling their visualization on transfection with plasmids encoding fluorescently labeled ParB proteins [START_REF] Germier | Real-time imaging of a single gene reveals transcription-initiated local confinement[END_REF][START_REF] Saad | DNA dynamics during early double-strand break processing revealed by non-intrusive imaging of living cells[END_REF] . The small size (~1 kb) of the parS sequences allowed us to place the tags very close to the promoter (5.5 kb upstream of the TSS) and actually inside the SCR, in between the elements known to control Sox2 transcription [START_REF] Taylor | Transcriptional regulation and chromatin architecture maintenance are decoupled functions at the Sox2 locus[END_REF] , facilitating direct imaging of the promoter and enhancer themselves. As a control, we also generated an ESC line (Inter-Down) with parS integration sites shifted by ~60 kb, allowing visualization of non-regulatory loci with equivalent genomic separation (Fig 1a,b). Allele-specific qRT-PCR showed that neither integration of the parS sites, nor their binding by transfected ParB proteins, affected Sox2 expression in cis (Fig 1c). Cell cycle progression and expression of other pluripotency markers was similarly unaffected by the parS/ParB system (Fig S1a,b). Further, allele-specific 4C-seq showed that Sox2-SCR interaction strength was also unaltered by parS integration and ParB binding (Fig 1d), strongly suggesting that the imaging setup has negligible functional impact on the loci that are visualized in this study.

For these two ESC lines, we imaged the labeled loci at high temporal resolution (500 ms per frame) in 2D with spinning disk confocal microscopy, using a set of optimized affine transformations to correct for chromatic aberrations and control for camera misalignment. Further enhancement of spot centroid localization was performed by fitting a 2D Gaussian shape to a precision of ~30 nm [START_REF] Oliveira | Precise measurements of chromatin diffusion dynamics by modeling using Gaussian processes[END_REF] . In line with previous high-throughput DNA FISH studies [START_REF] Finn | Extensive heterogeneity and intrinsic variation in spatial genome organization[END_REF][START_REF] Huang | CTCF mediates dosage-and sequence-context-dependent transcriptional insulation by forming local chromatin domains[END_REF] , median inter-probe distances demonstrated a large cell-to-cell heterogeneity, varying from 69-286 nm (n = 72) for Sox2-SCR distances and from 71-426 nm (n = 49) for the control regions (Fig 1e; Table S1). Over the short periods over which images were acquired, separation distances were relatively stable (median absolute deviation 30-107 nm; inter-decile range 74-293 nm). As may be expected from ESC Hi-C maps, the median distance between Sox2 and the SCR (164 nm) is significantly smaller than the control regions of equivalent genomic separation (187 nm; p = 0.036; Wilcoxon rank sum test). The Sox2-SCR separation distances we measured agree very well with the 2D distances measured in the wild-type Sox2 locus in recent multiplexed DNA FISH studies [START_REF] Huang | CTCF mediates dosage-and sequence-context-dependent transcriptional insulation by forming local chromatin domains[END_REF] (median 160 nm; p = 0.78; Wilcoxon rank sum test) (Fig S2a). Although this implies that the parS/ParB system does not perturb endogenous chromosomal locus configurations within the nucleus, the ANCHOR1-tagged control region downstream of the SCR was not included in the multiplexed DNA FISH design. We therefore performed 3D DNA FISH in wild-type F1 and ANCHOR-labeled Sox2-SCR WT ESCs, using fosmid probes covering the locations of each of the parS integration sites, further confirming that average Sox2-SCR separation distances are smaller than the control regions (p < 2.2x10 -16 ; Wilcoxon rank sum test), and that ANCHOR labeling has negligible effects on underlying chromatin organization (p = 0.14; Wilcoxon rank sum test) (Fig S2b,c). We note that a previous study using Tet-and Cu-repeat operators to label regions a little further upstream of the Sox2 promoter and downstream of the SCR measured significantly larger distances (median 221 nm; p = 5.4x10 -8 ; Wilcoxon rank sum test) than obtained with either ANCHOR or DNA FISH in untagged loci [START_REF] Alexander | Live-cell imaging reveals enhancer-dependent Sox2 transcription in the absence of enhancer proximity[END_REF] (Fig S2a). This suggests that, at least for this locus, the repetitive operator system may artificially inflate physical separation of tagged loci compared to untagged counterparts.

We previously identified by 4C-seq a near-complete loss of Sox2-SCR interaction in the early stages of ESC differentiation to neuronal precursors when Sox2 expression is shut down [START_REF] Zouari | 4See: a flexible browser to explore 4C data[END_REF] . We recapitulated this finding when differentiating the labeled Sox2-SCR WT cells, observing a significant increase in average Sox2-SCR distance (median 200 nm; p = 0.02; Wilcoxon rank sum test) by the third day, in agreement with the timing of loss of interaction observed by allele-specific 4C (Fig 2a,b). This cannot be solely explained by general chromatin compaction changes accompanying loss of pluripotency, because the average distances between the control regions were not significantly increased (Fig 2c ;   median 208 nm; p = 0.15; Wilcoxon rank sum test). It has been proposed that promoter-enhancer "interactions" are somehow causal in transcriptional activation [START_REF] Palstra | The beta-globin nuclear compartment in development and erythroid differentiation[END_REF][START_REF] Deng | Controlling long-range genomic interactions at a native locus by targeted tethering of a looping factor[END_REF] , and the onset of increased promoterenhancer separation corresponds to near-complete transcriptional shutdown of Sox2 (Fig S1c). However, recent studies, including those at the murine Sox2 locus, have brought this into question [START_REF] Alexander | Live-cell imaging reveals enhancer-dependent Sox2 transcription in the absence of enhancer proximity[END_REF][START_REF] Benabdallah | Decreased enhancer-promoter proximity accompanying enhancer activation[END_REF][START_REF] Taylor | Transcriptional regulation and chromatin architecture maintenance are decoupled functions at the Sox2 locus[END_REF] . To directly test the effect of transcription on promoter-enhancer proximity, we also measured Sox2-SCR distances upon either global inhibition of transcription by treatment of the Sox2-SCR WT cells with the drug triptolide (which globally shuts down transcription by inhibiting TFIIH and inducing PolII degradation) [START_REF] Titov | XPB, a subunit of TFIIH, is a target of the natural product triptolide[END_REF] , or specific inhibition of Sox2 expression in cis by the allele-specific deletion of two critical elements of the SCR (SRR107 and SRR111) [START_REF] Taylor | Transcriptional regulation and chromatin architecture maintenance are decoupled functions at the Sox2 locus[END_REF] Overall, we thus find that the Sox2 promoter and SCR are frequently in relatively close proximity, over the sort of range traditionally called as "interactions" or "looping events" (<200 nm), and significantly closer than control regions of equivalent genomic separation. However, whereas early stages of neuronal differentiation can increase average physical separation between promoter and enhancer, their distances remain relatively close. Moreover, the promoter and enhancer remain proximal on orthogonal perturbations disrupting Sox2 transcription to the same extent, such as deletion of key SCR elements or pharmacological inhibition of transcriptional initiation. The idea that chromatin "interaction" and transcriptional activation can be decoupled is thus further reinforced.

Promoters and enhancers have more constrained chromatin motion than control sequences

We previously reported that seemingly neutral elements within the HoxA locus exhibit different and locus-specific diffusive properties of labeled chromatin [START_REF] Oliveira | Precise measurements of chromatin diffusion dynamics by modeling using Gaussian processes[END_REF] . We therefore questioned whether chromatin mobilities are further different in promoters and enhancers, and whether these properties are linked to transcriptional output. Indeed, on examination of the tracks of labeled regions around the Sox2 locus, as well as their ensemble MSD curves, it was apparent that the promoter and enhancer were more limited to explore the nuclear volume than the control regions (Fig 3a,b). To assess the local chromatin mobilities more quantitatively, we applied our previously developed GPTool to fit the track trajectories to a fractional Brownian motion (FBM) model and extract their apparent diffusion coefficients, D α_app , and anomalous exponents, α app [START_REF] Oliveira | Precise measurements of chromatin diffusion dynamics by modeling using Gaussian processes[END_REF] . As previously, we confirmed that the trajectories approximated to self- S1). We note that these measured values correspond well with the α ~ 0.2 determined from fits to radial MSD curves for lac/TetO-tagged CTCF-mediated interacting sites with a similar genomic separation of ~150 kb [START_REF] Mach | Cohesin and CTCF control the dynamics of chromosome folding[END_REF] .

Analogous radial MSD analysis for the Sox2-SCR WT and Inter-Down trajectories revealed similarly constrained motion, with the promoter and enhancer significantly more constrained than the neutral sequences (p = 5.7x10 -6 ; ANCOVA test; Fig S5b ). However, the nature of this analysis, by comparing the motion of one locus relative to the "fixed" second locus, does not allow any mobility differences between the two loci to be discerned. Using substrate-corrected GP-FBM, we further found that the promoter exhibited significantly more constrained motion than the enhancer (q = 2x10 -5 ; Wilcoxon rank sum test with Benjamini-Hochberg correction), and all four labeled regions around the Sox2 locus exhibited more constrained motion than was observed around the generally inactive HoxA locus in ESCs [START_REF] Oliveira | Precise measurements of chromatin diffusion dynamics by modeling using Gaussian processes[END_REF] (Fig S5c).

These results are in line with our previous observations in a transgenic system that genes explore a more restricted nuclear volume when they are induced [START_REF] Germier | Real-time imaging of a single gene reveals transcription-initiated local confinement[END_REF] , potentially due to their engagement in specialized nuclear microenvironments for transcription. To explore these properties further, we modeled the 800 kb of ESC chromatin around the Sox2 locus as a self-avoiding polymer chain of 1 kb beads, classed as either "neutral", binding PolII (Sox2 promoter and enhancers, determined by peaks of the active histone mark, acetylation of lysine-27 of histone H3 (H3K27ac)), transcribed genic regions (Sox2 gene body), or binding CTCF (determined by ChIP-seq peaks and with motif orientation information included). As we previously did for a theoretical locus to explain chromatin conformation changes on acute loss of PolII [START_REF] Zhang | Enhancer-promoter contact formation requires RNAPII and antagonizes loop extrusion[END_REF] , we performed molecular dynamics simulations using Langevin equations to model thermal motion of the chromatin and its binding factors, with the following additions to account for biological processes: PolII molecules have affinity for promoters and enhancers, and traverse the gene body to simulate transcription; PolII molecules also have affinity to each other to simulate condensate formation; cohesin complexes can bind anywhere on the polymer and extrude loops, but has preference to load at promoters and enhancers, and is unable to process past a CTCF-bound site when the motif is oriented towards the extruding loop (see Methods). The ensemble of chromatin conformations resulting from these simulations generated a contact map closely resembling that of the experimental Hi-C results In accordance, application of GPTool to the simulated trajectories gave significantly smaller α app measurements at the promoter and enhancer than control regions (q < 5x10 -22 ; Wilcoxon rank sum test with Benjamini-Hochberg correction) (Fig 3e). This relatively simplified depiction of the locus thus supports the experimental results, suggesting that promoter-enhancer "affinity" brought about by transcriptional regulation and/or loop extrusion processes is sufficient to explain their reduced chromatin dynamics.

Transcriptional perturbation specifically reduces Sox2 promoter mobility

We next measured the chromatin dynamics of the labeled loci on different means of transcriptional perturbation, reasoning that mobility constraints at the promoter and/or enhancer may be specifically relaxed. However, the distribution of apparent anomalous exponents of the Sox2 promoter did not change when the gene was silenced by either onset of differentiation or deletion of SRR107 [START_REF] Xiong | Oct4 differentially regulates chromatin opening and enhancer transcription in pluripotent stem cells[END_REF] . Further, general chromatin mobility, as measured in tagged histones, was found to actually be increased on pharmacological inhibition of transcription [START_REF] Nozaki | Dynamic organization of chromatin domains revealed by super-resolution live-cell imaging[END_REF] . Taken together, our results suggest a clear but complex contribution of gene activity to chromatin dynamics. On the one hand, active elements are significantly more constrained than "neutral" genomic sequences, but transcriptional inhibition does not appear to "rescue" chromatin mobility at the former sequences. Conversely, we find evidence that a highly constrained promoter becomes even less mobile at extreme perturbation of target gene expression.

The SCR has reduced chromatin dynamics on transcriptional firing

The experiments performed so far have relied on perturbations, such as cell differentiation, cis-sequence [START_REF] Schoenfelder | Preferential associations between co-regulated genes reveal a transcriptional interactome in erythroid cells[END_REF] and/or condensates [START_REF] Sabari | Coactivator condensation at super-enhancers links phase separation and gene control[END_REF] , although chromatin dynamics will need to be traced over longer time periods, spanning several transcription bursts, to determine whether any volume restriction is exclusive to active states. Overall, this direct observation of chromatin dynamics relative to ongoing transcription shows an expectedly high cell-to-cell variability [START_REF] Germier | Real-time imaging of a single gene reveals transcription-initiated local confinement[END_REF] , with the recurrent trend that in wild-type ESCs, the highly expressed Sox2 gene appears to have high constraints to local mobility that are not altered by transcriptional state. On the other hand, the SCR, while maintaining relative proximity (but not necessarily complete juxtaposition) to the target gene, has greater freedom of movement when the gene is transcriptionally poised yet inactive, but becomes constrained to levels comparable with the gene itself on transcriptional firing.

deletions

Opposing effects of loop extrusion and promoter-enhancer communication on local chromatin mobility

Aside from transcription, chromatin topology itself may have an influence on local dynamics. For example, multiple distal interactions such as those defining TAD borders may be expected to "tether" different chromatin regions and thus impose greater constraints on their movement [START_REF] Shinkai | PHi-C: deciphering Hi-C data into polymer dynamics[END_REF] . Differentiation to neural precursors causes loss of the ESC-specific TAD border at the SCR, whereas the strong TAD border just upstream of the Sox2 promoter is maintained 60 (Fig S7a). This loss of "anchoring" to distal regions could thus be responsible for the previously observed reduced mobility constraints at the SCR (and into the downstream TAD; Fig 3f,g), potentially independent of transcriptional changes. We previously showed that in ESCs, the SCR TAD border is resilient to large genetic deletions, including SRR107, SRR111 and the predominant CTCF site at the enhancer, even though the latter site was able to mediate chromatin interactions in other contexts, presumably by stalling loop extrusion [START_REF] Taylor | Transcriptional regulation and chromatin architecture maintenance are decoupled functions at the Sox2 locus[END_REF] 6b-e). These findings mirror the observed increase in radial MSD on deletion of CTCF binding sites within a transgenic CTCF-mediated looping construct [START_REF] Mach | Cohesin and CTCF control the dynamics of chromosome folding[END_REF] , although the nature of this experimental setup could not distinguish whether dynamics are specifically altered locally at the CTCF anchor site, or whether they are also propagated to looping anchor partners. Our results support a more localized effect on chromatin dynamics. Previously published simulations suggest that, at short time scales consistent with our measurements, active loop extrusion increases mobility of the underlying chromatin fiber [START_REF] Nuebler | Chromatin organization by an interplay of loop extrusion and compartmental segregation[END_REF] , although cohesin loading itself generally imposes constraints on the underlying chromatin at larger scales [START_REF] Nozaki | Dynamic organization of chromatin domains revealed by super-resolution live-cell imaging[END_REF][START_REF] Mach | Cohesin and CTCF control the dynamics of chromosome folding[END_REF] . We propose that removal of CTCF from one site, by removing the barrier to loop extrusion through it, permits a localized relaxation of movement constraints, explaining the focal increase in α app . The observed relaxation does not appear to efficiently propagate to their "looping partners", presumably because actual CTCF-CTCF juxtapositions are rather rare events [START_REF] Gabriele | Dynamics of CTCF-and cohesin-mediated chromatin looping revealed by live-cell imaging[END_REF] . An alternative hypothesis is that the general binding of non-nucleosomal factors to DNA changes its biophysical properties to result in "stiffer", more constrained chromatin motion.

However, this is not supported in our experiments since the median apparent anomalous exponent at the SCR is actually significantly reduced (i.e. even greater mobility constraints are imposed) on deletion of multiple transcription factor binding sites at SRR107 and SRR111 (0.161; p = 0.0048; Wilcoxon rank sum test; Fig 6d,e). Dispersed transcription factor binding sites at the Sox2 and other loci have been shown to cluster via protein-protein interactions in ESCs [START_REF] Li | Single-gene imaging links genome topology, promoter-enhancer communication and transcription control[END_REF] , and such homotypic interactions are believed to be a basis for chromosome compartment formation [START_REF] Misteli | The self-organizing genome: principles of genome architecture and function[END_REF] . Various studies suggest that loop extrusion and chromosome compartmentation are antagonistic processes organizing population-averaged chromatin architectures [START_REF] Rao | Cohesin loss eliminates all loop domains[END_REF][START_REF] Schwarzer | Two independent modes of chromatin organization revealed by cohesin removal[END_REF][START_REF] Zhang | Enhancer-promoter contact formation requires RNAPII and antagonizes loop extrusion[END_REF][START_REF] Nuebler | Chromatin organization by an interplay of loop extrusion and compartmental segregation[END_REF][START_REF] Nora | Targeted degradation of CTCF decouples local insulation of chromosome domains from genomic compartmentalization[END_REF] . It is therefore possible that processes responsible for compartmentation are also generally antagonistic to cohesin-mediated loop extrusion.

To assess this possibility further, we ran molecular dynamics simulations of the above genetic perturbations within our framework, by either converting one or other of the CTCF-bound beads to a In particular, the model predicted that transcription factor site deletions at the SCR would increase mobility at the enhancer, instead of placing greater constraints as we had observed. Strikingly, better agreement to experimental observations was accomplished by increasing RNA polymerase stability at bound enhancers, effectively reinforcing the competition between transcription-linked compartmentation and loop extrusion (see Methods). In these simulations, removal of the local transcription factor binding sites placed greater constraints on the enhancer, and removal of CTCF had the inverse effect (Fig 7a,b).

Moreover, these simulations predicted greater cohesin occupancy at the SCR CTCF site on deletion of the flanking transcription factor binding sites. This may be predicted to allow more loop extrusion to pass through the locus, resulting in greater average local constraints as more alleles have stalled cohesin at the adjacent CTCF site. In support, we found by allele-specific ChIP-qPCR that binding of the cohesin subunit Rad21 is increased at the SCR CTCF site when adjacent transcription factor binding regions,

DISCUSSION

By combining live imaging of labeled endogenous loci with a battery of perturbation experiments and molecular dynamics simulations, we have teased apart some of the spatiotemporal complexities of enhancer-promoter communication. The ANCHOR system employs relatively small tags that can be placed extremely close to genomic loci of interest with negligible observable effects on transcription, nuclear organization and cell state, so is a valuable tool for such studies. The first question we addressed was whether promoters and enhancers need to directly juxtapose for transcriptional firing, since conventional C-method and light microscopy approaches have given rather different viewpoints [START_REF] Lim | Enhancer-promoter communication: hubs or loops?[END_REF] . We found that Sox2 and the SCR are frequently in close proximity (distances < 200 nm), and significantly closer than control regions of identical genomic separation, in agreement with Hi-C predictions. However, transcriptionally active loci can be also be found with greater physical separation between the Sox2 and SCR than non-transcribing alleles, strongly arguing against any obligation for their direct juxtaposition for expression. Moreover, promoter-enhancer distances were unchanged in all transcriptional perturbations in this study that did not affect the TAD border at the SCR, completely in line with recent C-method studies at this locus [START_REF] Taylor | Transcriptional regulation and chromatin architecture maintenance are decoupled functions at the Sox2 locus[END_REF][START_REF] Chakraborty | Enhancer-promoter interactions can bypass CTCF-mediated boundaries and contribute to phenotypic robustness[END_REF] . So if direct juxtaposition of the enhancer is not required for transcription, how close is close enough? Clusters of PolII and transcription factors have been observed to have diameters of ~100-200 nm in live nuclei [START_REF] Li | Single-gene imaging links genome topology, promoter-enhancer communication and transcription control[END_REF][START_REF] Cisse | Real-time dynamics of RNA polymerase II clustering in live human cells[END_REF] , providing a reasonable first estimate of the size of proposed transcriptional hubs, and thus the maximum separation of regulatory elements if they need to share the same microenvironment for transcriptional firing. What is unclear so far is whether the enhancer needs to be engaged in the hub during the whole transcriptional cycle, or if it is free to disengage after initiation in a "hit and run" mechanism. Since control sequences separated by only 150 kb are also frequently closer than the proposed 200 nm threshold, and these measurements are below the diffraction limit of our microscopy setup, we could not resolve these models in this study. However, since the SCR is less constrained than Sox2 in non-transcribing alleles, but has average dynamics indistinguishable from the promoter when the gene is transcribed, our results indirectly favor enhancer engagement in the transcriptional hub/environment on at least the minute scale, in line with studies in a Drosophila transgene [START_REF] Chen | Dynamic interplay between enhancerpromoter topology and gene activity[END_REF] . Studies in loci with more distal enhancers, particularly those which seem to depend on cohesin-mediated loop extrusion for gene activation (presumably as a mechanism to help the enhancer "find" its distal target) [START_REF] Kane | Cohesin is required for long-range enhancer action at the Shh locus[END_REF][START_REF] Rinzema | Building regulatory landscapes reveals that an enhancer can recruit cohesin to create contact domains, engage CTCF sites and activate distant genes[END_REF] , in combination with visualization of any hubs themselves, will be required to formally address these questions.

Whereas average inter-probe distances only demonstrated subtle differences at best in this study, MSD plots revealed more dramatic locus-and condition-specific differences in chromatin dynamics, with the most obvious being the greater relative freedom of movement of control sequences compared to the constrained promoter and enhancer. Conventional fits to ensemble log-transformed MSD curves are not precise and only robustly identify very flagrant differences in dynamics; our previously developed GP-FBM framework demonstrably gives greater precision in diffusive property measurements of single trajectories, both on simulations [START_REF] Oliveira | Precise measurements of chromatin diffusion dynamics by modeling using Gaussian processes[END_REF] and in complex and noisy experimental data (see fits in Fig S5a ). A limitation of this approach, which is also shared by radial MSD analysis, is the requirement to use crosscorrelations of co-measured trajectories to correct for global nuclear movements and rotations, which can be quite large in ESCs (trials of alternative means to measure substrate movement revealed them to be much less robust). Since the movements of monomers are more highly correlated when they are closer along the polymer, the dynamics of loci separated by 150 kb are underestimated, resulting in anomalous diffusion exponents much smaller than expected from most polymer physics models [START_REF] Mach | Cohesin and CTCF control the dynamics of chromosome folding[END_REF] , also explaining the consistently lower measured α app values, when compared to results of our simulations, which do not have nuclear movements. These underestimated α app values are nevertheless precise and comparable between experimental conditions, allowing quantitative comparisons of chromatin mobility changes. There is the possibility that a perturbation could affect the coupling of the two labeled loci more than the individual particle dynamics in themselves, which could be missed by GPTool, but this does not seem to be the case, since most perturbations were found to have localized effects on only SCR or Sox2, and not both together.

The major question we wished to address was how chromatin mobility is affected by transcription. For the Sox2 locus, we found clear links between chromatin dynamics and gene expression:

the constrained promoter, but not the SCR, was sensitive to strong transcriptional inhibition by either enhancer element deletion or triptolide treatment, becoming even less mobile. Furthermore, when directly comparing transcribing and non-transcribing alleles within minimally perturbed cells, Sox2 promoter dynamics were relatively unaltered, whereas the SCR became more constrained upon transcriptional firing of its partner gene. A model that may explain these findings are that there are (at least) two distinct processes linking transcriptional control and local chromatin mobility: entry into a transcriptional hub, and transcription itself (Fig 7e). Due to apparent confinement within a more limited volume, delimited by the hub, or perhaps just because of the even more crowded environment, presence of a locus in a transcriptional hub would be expected to reduce its underlying chromatin mobility. Conversely, as proposed previously [START_REF] Gu | Transcription-coupled changes in nuclear mobility of mammalian cis-regulatory elements[END_REF] , the ATP hydrolysis and/or PolII tracking associated with transcription may be expected to add kinetic energy to the local chromatin and thus increase its mobility. In this manner, the results can then be explained by the Sox2 gene, a key pluripotency gene with many constitutive and tissue-specific transcription factor binding sites at its promoter and proximal enhancers, as frequently nucleating its own hub in ESCs, partly explaining its consistent low mobility. The SCR, in contrast, has dynamics behavior consistent with it specifically entering the hub (and hence increasing its constraint) on transcriptional activation. Although the SCR is itself transcribed [START_REF] Xiong | Oct4 differentially regulates chromatin opening and enhancer transcription in pluripotent stem cells[END_REF] , this is at much lower levels than Sox2, so may not feature significantly in the measurements. Moreover, it is not clear if the SCR eRNA is cotranscribed with Sox2, so may not necessarily occur when the SCR is sharing a transcriptional hub with Sox2. While explaining our results, and coherent with results from different prior studies, this hypothesis requires experiments beyond current technological capabilities to formally test, simultaneously tagging hub components, nascent RNA and the promoter and enhancer over sufficiently long time periods to cover multiple transcription cycles while maintaining high temporal resolution. However, the results of our study alone are highly evocative in suggesting that some loci are able to nucleate their own transcription-competent microenvironments, whereas others need to "find" them, raising questions about how such a "hierarchy" is formed, and the mechanisms influencing the search time to access pre-existing hubs.

As Sox2 and the SCR are strong TAD borders in ESCs, and cohesin-mediated loop extrusion has recently been shown to affect chromatin mobility [START_REF] Mach | Cohesin and CTCF control the dynamics of chromosome folding[END_REF] , much of their local constraints could perhaps be explained by mechanisms independent of transcription. Indeed, abrogation of CTCF binding caused localized increases in chromatin mobility, which was particularly noteworthy at the SCR, considering that deletion of this site had negligible changes on global chromatin conformation (as determined by population-average 4C-seq) or Sox2 expression. We also note that identifying the localized changes in chromatin dynamics is only possible by the analytical framework that we have developed. Even more striking was the finding that deletion of transcription factor binding sites had opposing effects on local dynamics to CTCF site deletion. Assuming that transcription factor clustering is one aspect of chromosome compartmentation [START_REF] Xie | BRD2 compartmentalizes the accessible genome[END_REF] , this is reminiscent of the known antagonism between loop extrusion and compartments in defining chromosome conformations (Fig 7d). Indeed, our molecular dynamics simulations required direct competition between the loop extrusion and transcription-linked interaction processes to recapitulate the experimental findings. Since transcription hubs are assumed to place greater movement constraints on the chromatin within, this model implies a) that stalled cohesin is quantitatively more constraining than residing within a hub; b) that transcription factor clusters impede loop extrusion without causing stalled cohesin. This latter point is supported by the recent finding that transcription start sites form cohesin-independent TAD borders [START_REF] Valton | A cohesin traffic pattern genetically linked to gene regulation[END_REF] , although the exact mechanisms are unclear, particularly as SMC complexes are able to bypass RNA polymerase and other large chromatin complexes in vitro [START_REF] Pradhan | SMC complexes can traverse physical roadblocks bigger than their ring size[END_REF] .

Whatever the exact mechanisms, the implications for transcriptional regulation are very important: loop extrusion is believed necessary to allow the more distal enhancers to search effectively for their targets, but may actually be a barrier itself to forming the transcriptionally competent microenvironment. More detailed studies on the interplay of these two processes in living cells will be highly challenging but fascinating.

The Sox2 locus, containing an ESC-dedicated (super)enhancer ~150 kb from the promoter, comprising clusters of binding sites for tissue-specific transcription factors oriented around one major CTCF site facing the gene, and with no other confounding genes within the locus, was a convenient model for the studies presented here. Although many of the organizational principles uncovered here likely apply to many genes, more systematic studies will be required to formally test this. For example, the limited deletion studies performed so far have already shown large differences in robustness of TAD structures to loss of specific CTCF sites [START_REF] Sikorska | Defining functionally relevant spatial chromatin domains: it is a TAD complicated[END_REF] , which could also play out in their dynamics. Transcribing alleles show a more distinctive plateau on the MSD curve, suggesting that there is a stricter limit on the area that is explored. S3). Two days after transfection, the cells were cultured for 24 h with 3 µg/mL, then 48 S3).

Sox2-SCR ΔCTCF_Sox2 and Sox2-SCR ΔCTCF_SCR cells were derived from the Sox2-SCR WT line, essentially as in ref 61. 1 million cells were co-transfected with 2 µg plasmid containing Cas9-GFP, a puromycin resistance marker and a scaffold to encode a gRNA targeting the relevant CTCF site (generated by the IGBMC molecular biology platform; sequences given in Table S3) and 1 µg Alt-R homology-directed repair single-stranded DNA oligonucleotide (IDT; sequences given in Table S4) with Lipofectamine-2000. The repair oligonucleotides are designed to replace the CTCF motif with an EcoRI site to help screening knock-outs. Two days after transfection, the cells were cultured for 24 h with 3 µg/mL, then 48 Imaging was performed on an inverted Nikon Eclipse Ti microscope equipped with a PFS (perfect focus system), a Yokogawa CSU-X1 confocal spinning disk unit, two sCMOS Photometrics Prime 95B cameras for simultaneous dual acquisition to provide 95% quantum efficiency at 11 µm x 11 µm pixels and a Leica Objective HC PL APO 100x/1.4 oil. A Tokai Hit Stage incubator allowed for maintenance at 37ºC and 5% CO 2 throughout the experiment. The system was controlled using Metamorph 7.10 software.

h
For double-label experiments, EGFP and IRFP were excited by 491-nm and 635-nm lasers. Green and far-red fluorescence were detected with an emission filter using a 525/50 nm and 708/75 nm detection window, respectively. Time-lapse was performed in 2D, acquiring 241 time points at 0.5 s interval. For triple-label experiments, EGFP and IRFP were first imaged as for the double-label, then mScarletI was excited at an identical z-position with a 561-nm laser, and red fluorescence was detected with an emission filter using a 609/54 nm detection window. Time-lapse was performed in 2D, acquiring 301 time points at 1 s interval. For assessment of transcriptional bursting of Sox2-SCR MS2 cells, mScarletI was excited with a 561-nm laser, and red fluorescence was detected with an emission filter using a 609/54 nm detection window. Ten positions were taken per acquisition session, obtaining 20 z-stacks of 0.5 µm interval for each position every 2 min, for a total of 2 hr. All time lapse was performed with Perfect focus system (PFS) of the microscope to avoid any focus drift.

ESC differentiation

ESCs were passaged onto laminin-511-coated 35 mm glass bottom petri dishes, transfected with OR vectors as previously, and switched to DMEM (4.5 g/L glucose) supplemented with 2 mM GlutaMAX, 10% FBS, 0.1 mM MEM non-essential amino acids, 0.1 mM 2-mercaptoethanol without LIF or 2i inhibitors. After 24 h, the medium was changed daily and supplemented with 5 µM retinoic acid.

Triptolide treatment

Two days after transfection with OR vectors, as previously, cell medium was changed for fresh medium, supplemented with either 500 nM triptolide or 1:2000 dilution of DMSO and incubated for 4 h prior to image acquisition.

qRT-PCR

Total RNA was extracted using the Nucleospin RNA extraction kit (Macherey-Nagel) and reversetranscribed using random hexamer primers and SuperScript IV (Invitrogen). qRT-PCR was performed on 10 ng cDNA aliquots in technical triplicates per biological replicate (three minimum) using QuantitTect SYBR Green PCR kit (Qiagen). Amplification was normalized to SDHA (succinate dehydrogenase complex flavoprotein subunit A). SNPs allowed primer design to distinguish musculus and castaneus Sox2 expression [START_REF] Taylor | Transcriptional regulation and chromatin architecture maintenance are decoupled functions at the Sox2 locus[END_REF] . Primer sequences are given in Table S5. Statistical comparisons were made by twotailed t-tests.

Cell cycle analysis

1 million cells were fixed in 66% ethanol on ice for 2 h, washed with PBS, then resuspended in 750 µL 50 µg/mL propidium iodide and 2 µg/mL RNase A in PBS, before incubation at 37ºC for 30 min. Analysis of propidium iodide staining with a FACS Fortesa (BD Biosciences) allowed cells to be gated to G1 (2n DNA content), S (2n < DNA content < 4n) and G2/M (4n DNA content) phases. Statistical comparisons were made by two-tailed t-tests. S6). PCR reactions were pooled, primers removed by washing with 1.8× AMPure XP beads, then quantified on a Bioanalyzer (Agilent) before sequencing with a HiSeq 4000 (Illumina). Sequencing read fastq files were demultiplexed with sabre (https://github.com/najoshi/sabre) and aligned to the mm10 genome with Bowtie 72 , and intrachromosomal reads were assigned to DpnII fragments by utility tools coming with the 4See package [START_REF] Zouari | 4See: a flexible browser to explore 4C data[END_REF] . 4See was also used to visualize the 4C profiles. Interactions were called for each replicate with peakC [START_REF] Geeven | peakC: a flexible, non-parametric peak calling package for 4C and Capture-C data[END_REF] with window size set to 21 fragments, and were then filtered to only include the regions called as interacting across all wild-type replicates. For statistical comparison of specific interactions, the 4C read counts within 1 Mb of the bait for all replicates and conditions (from the same bait) were quantile normalized using the limma package [START_REF] Ritchie | limma powers differential expression analyses for RNA-sequencing and microarray studies[END_REF] . The means of summed normalized 4C scores over tested interacting regions were taken as "interaction scores", and were compared across conditions by two-tailed t-tests.

Allele

3D DNA FISH

FISH probes were generated by nick translation from fosmids centered on the ANCHOR insertion sites (WI1-2125O9 for Sox2, WI1-788C1 for Inter, WI1-111C20 for SCR, WI1-156F5 for Down), labeling the DNA with dUTP conjugated to biotin (SCR and Down probes) or digoxigenin (Sox2 and Inter probes).

For each hybridization experiment, 300 ng each probe was combined with 3 µg mouse C 0 t DNA and 20 µg yeast tRNA and resuspended in 5 µL hybridization mix (10% (w/v) dextran sulphate, 50% formamide, 1% Tween-20 in 2x SSC). Probe was denatured at 95ºC for 5 min just before application to cells. FISH was performed as in ref 75. Briefly, cells were plated on 0.1% gelatin-coated coverslips in ES medium and fixed after 5 h (before colony formation) for 10 min with 4% paraformaldehyde in PBS, then permeabilized for 20 min in 0.5% (w/v) saponin, and incubated for 15 min with 0.1 N HCl, with washes in PBS between each incubation. Cells were then washed in 2x SSC and equilibrated in 50% formamide/2x SSC, before co-denaturing nuclei and probes at 85ºC for 5 min, then hybridizing overnight at 37ºC in a humidified chamber. Cells were washed three times with 50% formamide/2x SSC at 45ºC for 5 min each, then three times with 1x SSC at 60ºC for 5 min each, before cooling to room temperature in 0.05% Tween-20/4x SSC and blocking for 20 min in 3% BSA in 0.05% Tween-20/4x SSC. Antidigoxigenin-rhodamine and fluorescein-avidin DN were diluted 1:100 in the same blocking solution and incubated with the cells for 1 h. Cells were washed three times for 5 min in 0.05% Tween-20/4x SSC, then coverslips were mounted in DAPI-containing Vectashield mounting medium. Interphase nuclei were imaged on a LSM 880 AxioObserver (Olympus) microscope, using a x63/1.4 objective lens (C plan-Aprochromat 63x/1.4 Oil DIC UV-VIS-IT M27), under 2x zoom and line-averaging 4 settings. The interval between z-slices was 0.37 µm and the x-and y-pixel size was 132 nm. Nuclei were segmented and inter-probe 3D distances were measured by custom scripts in ImageJ [START_REF] Kocanova | 3D FISH to analyse gene domain-specific chromatin re-modeling in human cancer cell lines[END_REF] . Distance distribution differences were assessed by Wilcoxon rank sum tests.

Single-molecule RNA FISH

MS2v6 and Sox2 probes were designed with Stellaris Probe Designer and labeled with Cy3 and Cy5, respectively, on the 3' ends. Glass coverslips were placed into a 12-well plate and coated overnight with Poly-D-lysine. 400,000 cells were seeded per well and allowed to attach for 3 h to 70-80% confluency at 37ºC, 5% CO 2 . Cells were washed three times with pre-warmed HBSS buffer (Hanks' Balanced Salt Solution; no calcium, magnesium or phenol red; Thermo Fisher), before aspiration of buffer and cell fixation in 4% paraformaldehyde in PBS for 10 min at 23ºC, then two washes in PBS for 10 min at 23ºC.

Cells were permeabilized overnight in 70% ethanol at 4ºC, then washed for 5 min at 37ºC with prewarmed wash buffer (10% (v/v) formamide in 2x SSC). Coverslips were aspirated and dried for 5 min, before applying hybridization mix (50 nM each probe in 10% (w/v) dextran sulphate sodium salt, 10%

(v/v) formamide, 2x SSC) and incubating overnight at 37ºC in a humidified chamber. Coverslips were washed three times in wash buffer for 30 min at 37ºC, then rinsed in 2x SSC and washed in PBS for 5 min at 23ºC. Samples were mounted in Prolong Gold with DAPI (Invitrogen) on glass slides, and left to dry in the dark for 24 h before imaging on a Zeiss AxioObserver 7 inverted wide-field fluorescence microscope with LED illumination (SpectrX, Lumencor) and sCMOS ORCA Flash 4.0 V3 717 (Hamamatsu). A 40x oil objective lens (NA 1.4) with 1.6x Optovar was used. 27 z-stacks with 300 nm slices and 1x1 binning were taken with an exposure time of 500 ms for Cy3, 750 ms for Cy5 (100% LED power for both), and 25 ms for DAPI (10% LED power). Micromanager 1.4 software was used. A custom Python script was used to detect, localize and classify the spots (https://github.com/Lenstralab/smFISH).

Cells and nuclei were segmented using Otsu thresholding and watershedding. Spots were localized by fitting a 3D Gaussian mask after local background subtraction [START_REF] Coulon | Kinetic competition during the transcription cycle results in stochastic RNA processing[END_REF] and counted per cell. Chromatin was sonicated in a probe sonicator at 20 A (15 s on/30 s off) for 2.5 min at 4°C. Triton X-100 was added to the sonicated lysate to precipitate any remaining debris, and the cleared lysate was incubated overnight with 5 µg anti-Rad21 antibody (Abcam ab217678) at 4°C with rotation. 80 µL protein A/G Dynabeads (Invitrogen) was added to the antibody-bound chromatin and incubated overnight at 4°C with rotation. The immunoprecipitates were washed six times at 23°C with RIPA buffer followed by a TBS buffer wash, then bound chromatin was eluted by incubation for 30 min at 65°C with elution buffer (50 mM Tris-HCl pH 8, 10 mM EDTA, 1% SDS), before addition of 4 µL 20 mg/mL proteinase K and reversal of crosslinks by incubating at 65°C overnight. DNA was purified with phenol/chloroform extraction and ethanol precipitation before qPCR quantification (primer sequences given in Table S7), using serial dilutions of pre-immunoprecipitated input material to generate the quantification standard curve. Quantification at the musculus and castaneus SRR109 (SCR CTCF site) was expressed as foldenrichment over the amplification at a non-genic, negative control sequence, not bound by Rad21, CTCF or known pluripotency transcription factors.

Western blot

~

Localizing and tracking chromatin loci

Live imaging experiments were treated essentially as in ref 25. First, spot detection and tracking was performed with ICY [START_REF] De Chaumont | Icy: an open bioimage informatics platform for extended reproducible research[END_REF] , before localization precision enhancement in GPTool [START_REF] Oliveira | Precise measurements of chromatin diffusion dynamics by modeling using Gaussian processes[END_REF] . This assumes that the spots have the shape of a 2D Gaussian function, as follows,

𝑆𝑆 𝑥𝑥,𝑦𝑦 = 𝐼𝐼 𝑜𝑜 𝑒𝑒𝑒𝑒𝑒𝑒 �- 1 2 � 𝑒𝑒 -𝜇𝜇 𝑥𝑥 𝑦𝑦 -𝜇𝜇 𝑦𝑦 � 𝑇𝑇 � 𝐿𝐿 𝑥𝑥 2 𝜃𝜃𝐿𝐿 𝑥𝑥 𝐿𝐿 𝑦𝑦 𝜃𝜃𝐿𝐿 𝑥𝑥 𝐿𝐿 𝑦𝑦 𝐿𝐿 𝑦𝑦 2 � -1 � 𝑒𝑒 -𝜇𝜇 𝑥𝑥 𝑦𝑦 -𝜇𝜇 𝑦𝑦 �� + 𝐵𝐵 𝐺𝐺
with µ i representing the center of mass of the spot, L i its size in directions x and y, -1 < θ < 1 a possible rotation, while B G and I o are background and spot signal, respectively. The localization is optimized using the NM-Simplex method, and localization error is estimated using the Metropolis-Hastings algorithm.

Any outlier detection events, defined as having any of the signal intensity, spot size or localization error deviating from the median value within the experiment by more than twice the inter-quartile range, were removed from subsequent analysis. For the Sox2-SCR MS2 line, ICY was additionally used for spot detection and tracking of MCP (mScarletI). The majority of experiments had MCP detection for virtually all or none of the frames, and were categorized as "transcribing" and "non-transcribing" cells, respectively. The other experiments were only included in the analysis if they contained at least 75 contiguous frames with MCP signal ("transcribing") and/or absence ("non-transcribing"). For these, the largest contiguous stretch of frames above this threshold was maintained for subsequent analysis.

Inter-probe distance analysis

For inter-spot distance measurements, effects of camera misalignments and chromatic aberrations were corrected with a set of generic affine transformations, including translation, rotation and scaling, defined as,

Ω = � 𝑠𝑠 𝑥𝑥 0 (1 -𝑠𝑠 𝑥𝑥 )𝑊𝑊/2 0 𝑠𝑠 𝑦𝑦 �1 -𝑠𝑠 𝑦𝑦 �𝐻𝐻/2 0 0 1 � � 1 0 𝑑𝑑 𝑥𝑥 + 𝑐𝑐 𝑥𝑥 0 1 𝑑𝑑 𝑦𝑦 + 𝑐𝑐 𝑦𝑦 0 0 1 � � cos(𝜃𝜃) sin(𝜃𝜃) 0 -sin(𝜃𝜃) cos(𝜃𝜃) 0 0 0 1 � � 1 0 -𝑐𝑐 𝑥𝑥 0 1 -𝑐𝑐 𝑦𝑦 0 0 1 �
where s i accounts for scaling in directions x and y, d i accounts for translation in both directions and θ is the angle of rotation between both channels in relation to point c i . To infer optimal parameters for correction, five frames from each of the movies recorded in the session were used and the likelihood was maximized using the Nelder-Mead simplex method,

log 𝑃𝑃 ∝ - 𝑊𝑊𝐻𝐻 2 log ��[𝐼𝐼 2 (𝑘𝑘, 𝑙𝑙|Ω) -𝐼𝐼 1 (𝑘𝑘, 𝑙𝑙|𝟙𝟙)] 2 𝑘𝑘,𝑙𝑙 �
where W and H correspond to width and height of images, and I r (k,l|A) is the value of pixel (k,l) in channel r given transformation A. Here, 𝟙𝟙 represents the identity matrix. Visual inspection of acquired images before and after correction, and comparison with direct subtractions from optical beads, found the affine transformations to work better than the optical beads. After applying these transformations to the final localized spots, the 2D distances between two spots is then computed in a Pythagorean framework.

The median distances were taken for each imaging experiment, and distributions of these distances were compared between cell lines and experimental conditions (or 2D distances determined by analogous methods such as FISH) by Wilcoxon rank sum tests.

Transcriptional bursting measurements

Using the LiveCell pipeline (github.com/Lenstralab/livecell) [START_REF] Gowthaman | The Hda1 histone deacetylase limits divergent non-coding transcription and restricts transcription initiation frequency[END_REF] , maximal intensity projections were made of the 3D movies, followed by background subtraction and cell segmentation using Otsu thresholding and watershedding. Transcription bursts were detected and tracked using a 2D Gaussian fit followed by hysteresis filtering using 5 and 8 standard deviations of the background as low/high thresholds, respectively. Output data were manually checked to reject erroneous tracking or dividing cells.

GP-FBM measurement of diffusive parameters

Diffusive parameters for individual trajectories were estimated using GPTool [START_REF] Oliveira | Precise measurements of chromatin diffusion dynamics by modeling using Gaussian processes[END_REF] , which assumes that the stochastic diffusion trajectory of a chromatin locus can be modeled as a Gaussian process with the following fractional Brownian kernel:

� (𝑡𝑡, 𝑡𝑡 ′ ) = 𝐷𝐷 𝛼𝛼 (|𝑡𝑡| 𝛼𝛼 + |𝑡𝑡 ′ | 𝛼𝛼 -|𝑡𝑡 -𝑡𝑡 ′ | 𝛼𝛼 𝐷𝐷 𝛼𝛼 ,𝛼𝛼
producing generalized Brownian motion with mean squared displacement,

〈𝑟𝑟 2 〉 = 2𝑛𝑛𝐷𝐷 𝑎𝑎 𝑡𝑡 𝛼𝛼
𝐶𝐶 𝑣𝑣 (𝜀𝜀) (𝜏𝜏) 𝐶𝐶 𝑣𝑣 (𝜀𝜀) (0) = (𝜏𝜏 + 𝜀𝜀) 𝛼𝛼 -2𝜏𝜏 𝛼𝛼 + |𝜏𝜏 -𝜀𝜀| 𝛼𝛼 2𝜀𝜀 𝛼𝛼
To measure and correct for substrate movement, GPTool builds a covariance model to handle the crosscorrelation that substrate motion introduces into the two measured particles' trajectories, generating the probability distribution:

𝜌𝜌(𝑟𝑟 1 , 𝑟𝑟 2 |𝛼𝛼, 𝐷𝐷 𝛼𝛼 ) ∝ 𝑒𝑒𝑒𝑒𝑒𝑒 �- 1 2 � 𝑟𝑟 1 𝑟𝑟 2 � 𝑇𝑇 � Σ 1 + Σ 𝑅𝑅 Σ 𝑅𝑅 Σ 𝑅𝑅 Σ 2 + Σ 𝑅𝑅 � -1 � 𝑟𝑟 1 𝑟𝑟 2 ��
where Σ 1 , Σ 2 and Σ R are FBM covariance matrices for the two particles and substrate, respectively, with estimations of diffusive parameters D α and α for each particle, with and without substrate correction;

diffusion parameters D α = {D α1 , D α2 , D αR } and α = {α 1 , α 2 , α R }.
estimations of the trajectory of the substrate, as well as its diffusive parameters, D αR and α R .

Trajectory plots

To generate the individual trajectory plots (e.g. Fig 3a), the inferred substrate motion at each time interval was subtracted from the x and y coordinates of the GPTool-refined tracked particles, then multiplied by the scaling factor (110 nm per pixel) to obtain corrected coordinates in nm for the particle at each time point. The deviation of these values from the median x-or y-value, respectively, of the trajectory were plotted, maintaining their temporal order, to generate comparable trajectory plots across experiments centered on the origin.

MSD analysis

MSD analysis was performed using the msdanalyzer utility in Matlab [START_REF] Tarantino | TNF and IL-1 exhibit distinct ubiquitin requirements for inducing NEMO-IKK supramolecular structures[END_REF] . For each individual trajectory, the time-averaged MSD was computed (time steps of 0.5-120 s for most experiments; 1-300 s for experiments with the Sox2-SCR MS2 line), using either the trajectories uncorrected or corrected by GPTool for substrate movement, as stated. Because some trajectories exhibited large deviations from the average, especially at long time, we chose to calculate the ensemble median of all individual MSD and the median absolute deviation as a measure of the variability. For testing the fit of GPTool-measured parameters to experimental data, theoretical 2D MSD curves were made from these measured parameters for each individual trajectory, giving either

𝑀𝑀𝑆𝑆𝐷𝐷 = 4𝐷𝐷 𝛼𝛼,𝑢𝑢𝑢𝑢𝑢𝑢𝑜𝑜𝑟𝑟𝑟𝑟 𝑡𝑡 𝛼𝛼,𝑢𝑢𝑢𝑢𝑢𝑢𝑜𝑜𝑟𝑟𝑟𝑟
for parameters called without substrate correction, or

𝑀𝑀𝑆𝑆𝐷𝐷 = 4𝐷𝐷 𝛼𝛼,𝑢𝑢𝑜𝑜𝑟𝑟𝑟𝑟 𝑡𝑡 𝛼𝛼,𝑢𝑢𝑜𝑜𝑟𝑟𝑟𝑟 + 4𝐷𝐷 𝛼𝛼,𝑠𝑠𝑢𝑢𝑠𝑠𝑠𝑠𝑠𝑠𝑟𝑟𝑎𝑎𝑠𝑠𝑠𝑠 𝑡𝑡 𝛼𝛼,𝑠𝑠𝑢𝑢𝑠𝑠𝑠𝑠𝑠𝑠𝑟𝑟𝑎𝑎𝑠𝑠𝑠𝑠
for the particle and substrate parameters called when substrate motion correction is applied. The ensemble medians of these MSD curves were plotted with the experimental MSD curves. Radial MSD was computed in exactly the same way as single-particle MSD, but using the evolution of Euclidean distance between two particles instead of the displacement of a single particle. The diffusive parameters were fit to the first 60 s of the log-log plots of radial MSD using linear least squares with bisquare weights, implemented in Matlab. 95% confidence intervals were estimated as two standard deviations of the point estimates. Diffusive parameter differences between Sox2-SCR and Inter-Down radial MSD were assessed by ANCOVA.

Statistical comparison of inferred diffusive parameter distributions

The distributions of inferred apparent anomalous diffusion coefficients from different genomic loci or experimental conditions were compared by Wilcoxon rank sum test, with Benjamini-Hochberg multiple testing correction in cases where four or more statistical tests were combined. Since Dα_app values cannot be fairly compared across trajectories with different inferred values of α app , the inferred values of D α_app and α app for each particle trajectory were fed into the generalized Brownian motion equation to compute, for each individual trajectory, the expected radius of exploration, r, in a given time, t:

𝑟𝑟 = �4𝐷𝐷 𝛼𝛼 𝑡𝑡 𝛼𝛼
These were computed for all trajectories for different time-lags (1, 10, 30 and 60 s), and their distributions were statistically compared with Wilcoxon rank sum tests. Note that these use the substrate-corrected inferred diffusive parameters, so the resultant "expected" explored area is smaller than experimental observations.

Molecular dynamics simulations

Molecular dynamics simulations were performed via the multipurpose EspressoMD package [START_REF] Reynwar | Aggregation and vesiculation of membrane proteins by curvature-mediated interactions[END_REF] , as in ref 56. Individual proteins are represented by "beads" interacting via phenomenological force fields and move according to the Langevin equation, and the chromatin fiber is represented as a chain of beads connected by bonds. The position of every bead in the system evolves according to the Langevin differential equation that encodes Newton's laws in the case of thermal bath with the friction γ due to an implied solvent in the presence of forces between beads encoded by energy potential functions U [START_REF] Chiariello | Polymer physics of chromosome large-scale 3D organisation[END_REF][START_REF] Buckle | Polymer simulations of heteromorphic chromatin predict the 3D folding of complex genomic loci[END_REF] .

Langevin equations for all beads are simultaneously solved in EspressoMD using a standard Velocity-Verlet numerical algorithm. The potential connecting i and i+1 beads of the fiber is a finitely extensible non-linear elastic (FENE) spring that adds up to a steric repulsion potential between non-adjacent sites of the polymer, the Weeks-Chandler-Andersen (WCA) potential:

𝑈𝑈 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 = - 𝐾𝐾 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑅𝑅 0 2 2 𝑙𝑙𝑛𝑛 �1 -� 𝑟𝑟 𝑖𝑖,𝑖𝑖+1 -𝑟𝑟 0 𝑅𝑅 0 �� 𝑈𝑈 𝑊𝑊𝑊𝑊𝑊𝑊 = � 4𝜖𝜖 �� 𝜎𝜎 𝑟𝑟 � 12 -� 𝜎𝜎 𝑟𝑟 � 6 + 1 4 � 𝑖𝑖𝑖𝑖 𝑟𝑟 < 𝜎𝜎2 1 6 � 𝑖𝑖𝑖𝑖 𝑟𝑟 < 𝜎𝜎2 1 6 � 0 𝑜𝑜𝑡𝑡ℎ𝑒𝑒𝑟𝑟𝑒𝑒𝑖𝑖𝑠𝑠𝑒𝑒
where r i,i+1 is the distance between consecutive beads, and σ is where the interaction from repulsive becomes attractive and can be interpreted as the diameter of the particles. This value is a natural length scale of the system. In FENE the parameters are fixed to have an equilibrium distance of 1.6 σ with maximum extension of 0.8 σ, and a bond energy of K FENE = 30 k B T. Since the fiber is resolved at 1 kb, chromatin rigidity cannot be neglected (i.e. below the persistence length). Bending rigidity of the polymer is introduced via the Kratky-Porod potential for every three adjacent chromatin beads, where θ is the angle between three consecutive beads as given by:

𝑈𝑈 𝐾𝐾𝐾𝐾 (𝜃𝜃) = 𝐾𝐾 𝐵𝐵𝐹𝐹𝐹𝐹𝐷𝐷 (1 -cos(𝜃𝜃))
and K BEND is the bending energy. The persistence length in units of σ is given by L p = K BEND /k B T. The model includes: (i) full 3D loop extrusion by interplay of cohesin dimers and CTCF, and (ii) transcription by PolII particles. To simulate association of cohesin and PolII with chromatin, a harmonic potential was employed, mimicking formation of a stable bond between two particles that fluctuate around an equilibrium distance d 0 :

𝑈𝑈 𝐻𝐻 = 1 2 𝐾𝐾 𝐻𝐻 (𝑟𝑟 -𝑑𝑑 0 ) 2
From now on, any description of the formation of a bond means the introduction of the aforementioned harmonic bond between the particles involved. To regulate the lifetime of these harmonic interactions, mechanisms of bond formation and removal were introduced according to cutoff distance c d below which a bond is formed, with a certain probability rate of detachment in units of time τ b = 2τ (τ being the fundamental unit of time in molecular dynamics; see below). These are then set to approximate the experimentally-observed range of PolII transcription and cohesin loop extrusion speeds and chromatin residence time. Introduction of the above mechanics is added on top of the strings-binders-switch model (SBS [START_REF] Barbieri | Active and poised promoter states drive folding of the extended HoxB locus in mouse embryonic stem cells[END_REF] ), which encodes the association tendency of PolII with the Sox2 promoter (defined as the 1 kb bead containing the transcription start site within the modeled region) by means of the shifted, truncated Lennard-Jones (LJ) potential, allowing spontaneous co-localization of beads around a distance σ with lifetime and stability properties depending on the depth of the energy well 𝜖𝜖:

𝑈𝑈 𝐿𝐿𝐿𝐿 = � 4𝜖𝜖 �� 𝜎𝜎 𝑟𝑟 � 12 -� 𝜎𝜎 𝑟𝑟 � 6 + 𝑐𝑐 𝑠𝑠ℎ𝑖𝑖𝑖𝑖𝑠𝑠 � 𝑖𝑖𝑖𝑖 𝑟𝑟 < 𝑟𝑟 𝑢𝑢𝑢𝑢𝑠𝑠 0 𝑜𝑜𝑡𝑡ℎ𝑒𝑒𝑟𝑟𝑒𝑒𝑖𝑖𝑠𝑠𝑒𝑒
where r cut is a cutoff distance, r is the separation of any two beads, and r cut = 2.5σ for all LJ potentials in the simulations. This is a standard commonly used in the field to simulate phenomenological coarsegrained affinities [START_REF] Chiariello | Polymer physics of chromosome large-scale 3D organisation[END_REF][START_REF] Buckle | Polymer simulations of heteromorphic chromatin predict the 3D folding of complex genomic loci[END_REF] .

For PolII interactions and transcription, the polymerase is presented as a bead with LJ interaction with specific beads of the chromatin fiber representing the promoter, enhancers (defined as beads containing H3K27ac peaks) or gene body (beads containing Sox2 coding sequence) with energy 𝜖𝜖 = 2k B T.

Such mild affinity helps to identify promoters as the correct sites where transcription initiation will take place (i.e. PolII forming stable bonds with the promoter bead) before the elongation process starts along the gene body. LJ interactions were also introduced among PolII beads (𝜖𝜖 = 2.5k B T), to simulate their tendency to form condensates acting as transcription hubs, and between PolII and cohesin (𝜖𝜖 = 2k B T) to simulate preferential loading of cohesin at promoter/enhancer beads. PolII transcription dynamics are simulated as a four-step process: attachment to the promoter in an exclusive manner, elongation starts, elongation proceeds through the gene body, detachment at the transcription termination site (the end of the gene body). A bond forms if the beads are less distant in space than a certain cutoff (2.7σ). To simulate the tendency of RNAPII to reel in gene body beads, a secondary bond is formed with the next bead on the chromatin fiber in the direction of transcription (i+1 bead, where i is the promoter coordinate on the fiber, and if transcription occurs in the sense direction; i-1 in the antisense direction). In the next step, RNAPII moves on the next site by forming new bonds with i+1 site and dissolving the old ones with i. This happens at a given rate (0. The bond dissolves at the rate 2x10 -5 τb -1 and CTCF is again free to diffuse and search for other binding sites. Cohesin is represented as a pair of beads connected by one bond (r 0 = 1.6σ and K = 8k B T).

Extrusion has three steps: attachment, active extrusion, and detachment. For attachment, each cohesin monomer forms a bond with the chromatin fiber. Bonds form when a cohesin monomer and a chromatin site come within a given cutoff distance (1.6σ) and at a certain rate (0.1 τ b -1 ). Only the case where both monomers simultaneously form bonds on adjacent chromatin beads is considered a successful attachment and the dimer is retained for the next step; otherwise bonds dissolve. If a promoter is already engaged in a bond with RNAPII, cohesin is forbidden to bind that promoter. Also, to favor cohesin loading in correspondence of active transcribing promoters, a 90% chance of binding has been introduced when a cohesin molecule is close to a promoter/enhancer and at the same time one RNAPII is close by as well (cutoff distance 1.5 σ), otherwise cohesin binding chance drops to 10%. The active extrusion and detachment steps follow the same mechanics as for RNAPII, with the difference that RNAPII can reel through cohesin bound sites while the inverse is not allowed. New bonds are formed if the distance is below 1.1σ. Such parameters produce ranges of cohesin extruding speed of 15-30 kb/min, which is within the range of experimentally observed values [START_REF] Rao | Cohesin loss eliminates all loop domains[END_REF] . This allows cohesin to be affected by the surroundings during extrusion (e.g. presence of PolII close by or bound to adjacent sites). Cohesin detachment can occur independently at any step at a given rate (10 -4 τ b -1 ) to fit its known chromatin residence time of 20 min. CTCF "loop anchors" are modeled so that cohesin cannot form new bonds with the next i±1 site if the latter is already bound by CTCF, provided it has the binding motif in convergent orientation. This renders extrusion dependent on CTCF dynamics. Finally, cohesin has LJ affinity for PolII both in the bound (𝜖𝜖 = 2.5k B T) and unbound state (𝜖𝜖 = 2k B T, higher affinity for bound RNAPII mimicking its suggested role in cohesin loading on chromatin [START_REF] Zhang | RNA polymerase II is required for spatial chromatin reorganization following exit from mitosis[END_REF] ). PolII and loop extrusion dynamics are performed using a python script driving the EspressoMD library. The polymer initializes as a random walk and its dynamics first evolves in the absence of extrusion and transcription to generate an equilibrium coil formation. Extrusion and transcription processes are then switched on, and the evolution of the bead positions are tracked. Across all simulations, standard values for the friction coefficient (γ = 0.5) and the time step (t = 0.01) are used. To connect in silico space-time units with real distances and times, it is assumed that the concentration of DNA in the 3D simulation space is the same as that in a mammalian nucleus, giving a rough estimation of σ = 52 nm. For time units, the standard molecular dynamics relation τ = η(6πσ 3 /𝜖𝜖) is used. Assuming a viscosity ~0.5P, the fundamental time unit is τ = 0.017 s.

Concentrations of CTCF and PolII are taken from the physiological values and range from 30 to 60 nM.

The energy scale of the system is given by the Boltzmann factor k B multiplied by the temperature of the system T = 310 K.

The region modeled (mm10; chr3:34.

Sox2

Inter SCR Down q = 0.22 q = 0.023 1.2x10 -8 q = 2.0x10 -5 q = 1.7x10 -8 0.0012 Anomalous di usion coe cient, α app C 0.4 0.3 0.5 q = 1x10 -5 q = 0.6 q = 6x10 -23 q = 5x10 -22 q = 7x10 -23

Simulation

Log-density

Steps: 1 5 10 15

Steps: 1 5 10 15

Steps: 1 5 10 15

Steps: 1 5 10 15

Steps: 1 5 10 15

Steps: 1 5 10 15

Steps: 1 5 10 15

Steps:

  to create the line Sox2-SCR ΔSRR107+111 . In both cases, despite efficient loss of total or musculus-specific Sox2 expression, respectively, observed with qRT-PCR and single-molecule RNA FISH (Fig S1d-f), average Sox2-SCR (and control region) distances remained small and were nonsignificantly altered (median distances 142-172 nm; p > 0.05; Wilcoxon rank sum test; Fig 2d; Fig S2d).

  Gaussian-distributed displacements and an FBM velocity autocorrelation function over the time scale in which measurements are taken (Figs S3 and S4), affirming the suitability of the model used. The experimental MSD profiles were non-linear when plotted on double-logarithmic scales, suggesting that their properties cannot be explained by one regime, likely due in the main part to the confounding effects of nuclear and cellular movement and rotation. When analyzing cross-correlations of co-measured trajectories to estimate global movements of the cell/nuclear substrate

(

  Fig S5d). Collecting the trajectories of the beads corresponding to the parS-tagged loci, we derived simulation MSD curves indicating a clear reduced mobility of Sox2 and SCR compared to control sequences (Fig 3d).

"

  neutral" one to mimic specific loss of the binding motif, or recapitulating the Sox2-SCR ΔSRR107,111 line by deleting the corresponding beads, and abolishing PolII binding at the inactivated Sox2 promoter. The original model did not recapitulate the chromatin dynamics changes observed in the experiments (Fig S8).

  SRR107 and SRR111, are deleted in cis (p = 0.001; two-tailed t-test; Fig 7c), suggesting that these elements are indeed antagonistic to cohesin recruitment and/or loop extrusion. Overall, these results extend on recent studies into the effects of loop extrusion and its stalling by CTCF on chromatin dynamics, showing a surprising localized effect. Furthermore, two different mechanisms believed to contribute in building the same promoter-enhancer topology, CTCF-mediated architectures and enhancerpromoter "contacts", presumably via specific transcription factors and potential compartmentation, may actually have opposing effects on local chromatin dynamics (Fig 7d).

Figure 1 .

 1 Figure 1. parS/ParB labeling of specific sites at the Sox2 locus. a) Overview of the Sox2 locus used in

Figure 2 .

 2 Figure 2. Sox2-SCR distance is frequently uncoupled from transcriptional status. a) Violin plot

Figure 3 .

 3 Figure 3. The Sox2 promoter and SCR are more constrained than control sequences. a) Sample

Figure 4 .

 4 Figure 4. Severe transcriptional inhibition specifically reduces Sox2 promoter mobility. a,b) MSD

Figure 5 .

 5 Figure 5. The SCR specifically becomes more constrained on transcriptional firing in wild-type loci.

Figure 6 .

 6 Figure 6. Loop extrusion and enhancer activity have opposing effects on chromatin dynamics. a)

Figure 7 .

 7 Figure 7. Competition between loop extrusion and transcriptional compartmentation can explain

  h with 1 µg/mL puromycin to enrich for transfected cells, before sorting individual GFP-positive cells into 96-well plates and amplification of individual clones. Heterozygous clones with the correct sequences inserted in the musculus allele were screened by PCR and sequencing. Sox2-SCRΔSRR107+111 cells were derived from the Sox2-SCR WT line, essentially as in ref 44. Briefly, musculus-specific deletion of SRR111 was first achieved by co-transfection with plasmids containing four allele-specific gRNAs and Cas9D10A-GFP using Lipofectamine-2000, then PCR screening as in ref 70. Heterozygous deletion clones were subsequently co-transfected with vectors containing two allelespecific gRNAs and Cas9-GFP to delete SRR107 (sequences given in Table

  with 1 µg/mL puromycin to enrich for transfected cells, before sorting individual GFP-positive cells into 96-well plates and amplification of individual clones. Deletions were evaluated on agarose gel after PCR amplification of the region around the deletion and EcoRI digestion. Homozygous deletions were confirmed by sequencing. Sox2-SCRMS2 cells were derived from the Sox2-SCR WT line by co-transfecting 1 million cells with 2 µg plasmid containing Cas9 and the scaffold encoding a gRNA at the Sox2 3'UTR, and 2 µg targeting vector containing the MS2 cassette, comprising 24 copies of the v6 MS2 repeat 58 , a hygromycin resistance cassette flanked by loxP sites, and primer binding sites to facilitate screening for inserted clones, following the strategy of ref 71 (Fig S9), with Lipofectamine-2000. Three days after transfection, cells with integrated vector were selected with nine days of treatment with 200 µg/mL hygromycin. Individual cells were sorted into 96-well plates for clonal amplification, which were screened for heterozygous (musculus-specific) incorporation of full length 24xMS2 repeats by PCR and sequencing. To remove the selection marker, which may perturb Sox2 mRNA function, 1 million cells were transfected with 4 µg Cre-GFP vector with Lipofectamine-2000, and after three days were subjected to selection with 6 µM ganciclovir for ten days. Marker excision and maintenance of full-length MS2 construct were verified by PCR and sequencing in surviving colonies. Finally, 1 million cells were co-transfected with 1 µg ePiggyBac transposase expression plasmid (System Biosciences) and 1 µg each epB-MCP-mScarletI, epB-OR1-EGFP and epB-OR3-IRFP vectors (the OR vectors are derived from those used in ref 25 by adding flanking inverted terminal repeats for recognition by ePiggyBac transposase; original vectors available from NeoVirTech) with Lipofectamine-2000. Nine days after transfection, fluorescent cells were sorted in bins (low, medium and high) based on expression of the different fluorescent proteins, and tested by microscopy. Cells with Scarlet high /GFP low /IRFP low fluorescence were found to be optimal for imaging experiments, and this population was maintained for subsequent experiments. Live imaging Cells were transiently transfected with OR vectors (except for the stably expressing Sox2-SCR MS2 line) and imaged essentially as in ref 25. 150,000 cells were plated two days prior to imaging onto laminin-511-coated 35 mm glass bottom petri dishes and transfected with 2 µg each OR1-EFGP and OR3-IRFP plasmids with Lipofectamine-2000. Medium was changed just before imaging to remove dead cells.

  -specific 4C-seq 4C-seq was essentially carried out as in ref44. Cells were fixed with 2% paraformaldehyde in 10% FBS in PBS for 10 min at 23°C. The fixation was quenched with cold glycine at a final concentration of 125 mM, then cells were washed with PBS and permeabilized on ice for 1 h with 10 mM Tris-HCl, pH 8, 100 mM NaCl, 0.1% NP-40, and protease inhibitors. Nuclei were resuspended in DpnII restriction buffer at 10 million nuclei/mL concentration, and 5 million nuclei aliquots were further permeabilized by treatment for 1 h with 0.4% SDS at 37°C, then incubating for a further 1 h with 3.33% Triton X-100 at 37°C. Nuclei were digested overnight with 1500 U DpnII at 37°C, then washed twice by centrifuging and resuspending in T4 DNA ligase buffer. In situ ligation was performed in 400 μL T4 DNA ligase buffer with 20,000 U T4 DNA ligase overnight at 23°C. DNA was purified by reverse cross-linking with an overnight incubation at 65°C with proteinase K, followed by RNase A digestion, phenol/chloroform extraction, and isopropanol precipitation. The DNA was digested with 5 U/μg Csp6I at 37°C overnight, then re-purified by phenol/chloroform extraction and isopropanol precipitation. The DNA was then circularized by ligation with 200 U/μg T4 DNA ligase under dilute conditions (3 ng/μL DNA), and purified by phenol/chloroform extraction and isopropanol precipitation. For musculus-specific 4C profiles, samples of the DNA were digested with AvaII, cutting specifically at the region between the Csp6I site and the nonreading primer annealing site on the castaneus allele. 100 ng aliquots of treated DNA were then used as template for PCR with bait-specific primers containing Illumina adapter termini (primer sequences in Table

where n corresponds to

  the number of degrees of freedom. Formal derivation of the model and details of the methods used to optimize the model fit are found in ref 25 and references within. Experimental trajectories were verified as being reasonably fit by a fractional Brownian regime by checking that displacements are self-similar Gaussian distributed with the modeled covariance matrix (Fig S3) and that the velocity autocorrelation function from experimental trajectories, 𝐶𝐶 𝑣𝑣 (𝜀𝜀) (𝜏𝜏) = 1 𝜀𝜀 2 〈(𝑒𝑒(𝜏𝜏 + 𝜀𝜀) -𝑒𝑒(𝜏𝜏))(𝑒𝑒(𝜀𝜀) -𝑒𝑒(0))〉 with velocity defined as v(τ) = ε -1 [x(τ+ε)-x(τ)], fits the theoretical velocity autocorrelation function for FBM (Fig S4):

  Formal derivation of the model and details of the methods used to optimize the model fit are found in ref 25 and references within. Overall, GPTool outputs, for each individual imaging experiment: more precise trajectories for the two particles;

  3-35.1 Mb) encompasses the Sox2 gene, 16 enhancer beads from the peaks of H3K27ac, and 6 CTCF binding regions with directionality determined by orientation of binding motifs. CTCF binding regions can be composed of up to 3 beads where CTCF occupancy signal is the highest (i.e. two regions upstream of Sox2), so giving a stronger anchoring function to such regions.Polymer models for Sox2-SCR ΔCTCF_Sox2 and Sox2-SCR ΔCTCF_SCR have the relevant CTCF sites converted into non-CTCF binding beads, so to remove the cohesin anchoring effect. The model for Sox2-SCR ΔSRR107,111 has the two enhancer beads immediately flanking the SCR CTCF region completely removed from the polymer, and reduced RNAPII stability to the promoter (from 0.02 bonds lost per second to 0.2 bonds lost per second), to mimic inactivation of the gene.The positions of the beads corresponding to the positions of ANCHOR labels were tracked across 40 simulations of 1000 timepoints, and these trajectories were subsequently fed into MSD fits and GPTool diffusive parameter estimations, as for the experimental trajectories. the mean. Comparisons are made by two-tailed t-tests (* p < 0.05; ** p < 0.01; *** p < 0.001; **** p < 0.0001). d) qRT-PCR quantification of Oct4, Myc and Sox2 expression in Sox2-SCR WT and Inter-Down ESCs after acute treatment with DMSO carrier or triptolide, normalized to SDHA expression in DMSOtreated cells. Error bars show standard deviations of the mean. Paired comparisons between DMSO and triptolide treatments are made by two-tailed t-tests, with p-values given. Oct4 mRNA has a longer halflife than the triptolide treatment time, unlike short-lived Myc and Sox2 mRNA 89 . e) Histograms of singlemolecule RNA FISH results for Sox2 expression in Sox2-SCR WT cells treated with either DMSO or triptolide (>= 976 cells analyzed), showing numbers of mRNA molecules detected per cell. f) Allelespecific qRT-PCR quantification of Sox2 expression, normalized to SDHA, for F1, Sox2-SCR WT and Sox2-SCR ΔSRR107+111 cells, showing specific perturbation of Sox2 transcription on the musculus allele where SRR107 and SRR111 are deleted. Error bars show standard deviations of the mean. Comparisons are made by two-tailed t-tests, with p-values given.

Figure S2 .

 S2 Figure S2. The ANCHOR system does not affect nuclear organization. a) Violin plots showing

Figure S3 .

 S3 Figure S3. Gaussianity and self-similarity test on experimental trajectories. Displacements (left: x;

Figure S4 .

 S4 Figure S4. Experimental trajectories present FBM velocity autocorrelation. Velocity autocorrelation

Figure S5 .

 S5 Figure S5. Substrate-corrected GP-FBM-measured diffusive parameters fit well to experimental

Figure S6 .

 S6 Figure S6. The MS2 system mildly perturbs Sox2 expression. a) Allele-specific qRT-PCR

Figure S7 .

 S7 Figure S7. CTCF site deletions at the Sox2 locus. a) Differential Hi-C map, comparing chromatin

Figure S8 .

 S8 Figure S8. The original physical model poorly predicts effects of genetic perturbations on

Figure S9 .

 S9 Figure S9. Schematic for insertion of MS2 repeats in generation of Sox2-SCR MS2 line. Construct

3 ' 3 ' 58 SCR

 3358 Sox2 reverse (musculus/129-specific) 5'-CGCCTAACGTACCACTAGAACTTT-3'Sox2 reverse (castaneus-specific) 5'-CGCCTAACGTACCACTAGAACTTA-3' Table S6. 4C-seq primer sequences. Blue denotes Illumina adapter sequence for high-throughput sequencing. Red denotes position of 6-nucleotide barcodes, used to multiplex 4C samples for sequencing. ChIP-qPCR primer sequences. Red denotes allele-specific nucleotides.Name SequenceHoxA CBS5 forward (CTCF ChIP) 5'-GCTCGCTTCAAGTCGACATT-3'HoxACBS5 reverse (CTCF ChIP) 5'-GAAGTTCACGCGGGCCAG-3' Sox2 CTCF forward (CTCF ChIP) 5'-CACACCTTCTTTTAAAGGTAAAAGCACTCTAG-3' Sox2 CTCF reverse (CTCF ChIP) 5'-ACTTTTCAGCGCGCCTAG-3' SCR CTCF forward (CTCF ChIP) 5'-TGTGGATCTGGCTTACTGAGG-3' -Castillo M, Ruau D, Wilkinson AG, Ng FS, Hannah R, Diamanti E, Lombard P, Wilson NK, Gottgens B. (2015) CODEX: a next-generation sequencing experiment database for the haematopoietic and embryonic stem cell communities. Nucleic Acids Res

  WT S o x 2 -S C R ∆ S R R 1 0 7 + 1

1 S o x 2 - 2 p

 122 S C R W T S o x 2 -S C R ∆ C T C F _ S C R S o x 2 -S C R ∆ C T C F _ S o x 2 -S C R ∆ S R R 1 0 7 + 1 1 1 S o x 2 -S C R W T S o x 2 -S C R ∆ C T C F _ S C R S o x 2 -S C R ∆ C T C F _ S o x 2

  α = 0.09; D = 1.3x10 -3 µm 2 /s α α = 0.15; D = 1.3x10-3 µm 2 /s α -NC-ND 4.0 International license available under a was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which this version posted April 26, 2023. ; https://doi.org/10.1101/2023.04.25.WT Sox2-SCR ∆CTCF_SCR Sox2-SCR ∆CTCF_Sox2

/SRR111 (Fig 3f,g, 6b), and αapp

	reduced when transcription is blocked by either triptolide treatment or deletion of SRR107/SRR111 (Fig
	4a,b). The other parameter commonly used to quantify diffusive motion is the diffusion coefficient, D α ,
	but since this is expressed in units of µm 2 /s α (i.e. scaling according to α), its measurement can only be
	fairly compared between sets of trajectories containing exactly the same anomalous exponent. To quantify
	Sox2 promoter dynamics while accounting for the clear variability in measured α app between individual
	trajectories within a population (Fig 3c), we used the D α_app and α app values measured for each trajectory
	and computed r, the expected radius that the locus can explore in a given time interval, after accounting
	for substrate movement (see Methods). For all timescales appropriate for our imaging conditions (0.5-60
	s), the Sox2 promoter explored significantly less area when transcription was perturbed than during
	control conditions (q < 0.05; Wilcoxon rank sum test with Benjamini-Hochberg multiple testing
	correction; Fig 4c). It was previously proposed that "ongoing transcription may provide a source of
	nonthermal molecular agitation that can "stir" the chromatin within the local chromosomal domain" 30 .
	Our results partially support this hypothesis, although triptolide treatment had negligible effects on SCR
	dynamics (Fig 4d), despite this enhancer producing transcripts in ESCs
	of both the enhancer and promoter was only weakly and non-significantly increased on
	treatment with triptolide (p > 0.05; Wilcoxon rank sum test; Fig S5e). On the other hand, the SCR became
	significantly less constrained at the onset of ESC differentiation (median α app 0.263; p = 0.002; Wilcoxon
	rank sum test), but so did the downstream control region (median α app 0.337; p = 0.006), raising questions
	as to whether this change is directly linked to transcriptional changes (Fig 3f,g). Previous imaging
	studies, including our own, suggest that the dynamics of other gene loci are altered on their
	induction 26,27,30 , prompting us to look closer at the Sox2 locus trajectories. Indeed, inspection of the
	substrate movement-corrected ensemble MSD curves revealed that promoter mobility is generally

  (CTCF SCR site in

	Fig 6a). To assess the potential effect of loop extrusion processes on local chromatin dynamics, we
	generated derivative lines of Sox2-SCR WT cells, harboring homozygous deletions of 16-24 nt at the core
	CTCF binding motifs located either just upstream of the Sox2 promoter (Sox2-SCR ΔCTCF_Sox2 ) or within the
	SCR (Sox2-SCR ΔCTCF_SCR ) (Figs 6a and S7b). As expected, ChIP-qPCR confirmed that these deletions
	eliminated local CTCF binding (Fig S7c). Both lines maintained high expression of pluripotency marker
	genes (Fig S1b), and Sox2 expression was only mildly (and non-significantly) reduced in the Sox2-
	SCR ΔCTCF_SCR line, in agreement with previous findings for homozygous deletions of this element 61 ,
	although expression was reduced to ~60% of wild-type levels in the Sox2-SCR ΔCTCF_Sox2 line (Fig S7d). In
	agreement with previous studies of the respective roles of these CTCF sites on Sox2-SCR
	interaction 44,46,61 , allele-specific 4C-seq and ANCHOR inter-probe distance measurements showed
	negligible topological changes when the SCR CTCF site is deleted and a mild reduced interaction on
	homozygous deletion of the Sox2 CTCF site (Fig S7e,f). Despite these somewhat limited phenotypic
	effects, both lines demonstrated a significantly reduced local constraint on chromatin mobility when
	CTCF binding was abrogated: the median apparent anomalous exponent was increased at the Sox2
	promoter in Sox2-SCR ΔCTCF_Sox2 cells (0.156; p = 0.018; Wilcoxon rank sum test) and at the SCR in Sox2-
	SCR ΔCTCF_SCR cells (0.235; p = 0.036; Wilcoxon rank sum test), with negligible, insignificant changes to
	α app at the regulatory element which maintains CTCF binding (Fig

  The ANCHOR system and its derivatives, coupled to orthogonal systems to track nuclear hubs and loop extrusion processes, will open new avenues to understanding the spatiotemporal regulation of transcription.NM performed most GPTool analyses. MACdK and TLL performed single-molecule RNA FISH and analysis, generated the core constructs for the Sox2-SCR MS2 line and set up bursting analysis for AnP. KM and ES performed 3D DNA FISH, with analysis by SK. TT, VMS and JAM provided core constructs for the Sox2-SCR ΔSRR107,111 line and performed allele-specific ChIP experiments. All authors contributed to writing of the manuscript.

  3 million cells were collected by trypsinization, washed with PBS and lysed in 100 µL RIPA buffer (50 HCl pH 8, 1.2 mM EDTA, 167 mM NaCl, 1% Triton X-100, 0.01% SDS, 1x complete EDTA-free protease inhibitors), then finally resuspending in an equivalent volume of ChIP dilution buffer. 100 µg chromatin aliquots were diluted eight-fold in ChIP dilution buffer and pre-cleared for 90 min with 30 µL

	mM Tris-HCl pH 8, 150 mM NaCl, 1% (v/v) NP-40, 0.5% (w/v) sodium deoxycholate, 0.1% (w/v) SDS,
	1 mM EDTA) for 30 min at 4ºC. Cell lysate was sonicated with a Covaris E220 Bioruptor in AFA prepared protein A/protein G-Dynabeads at 4ºC on a rotating wheel. The pre-cleared chromatin was then
	microtubes to shear genomic DNA (peak incident power 175 W, duty factor 10%, 200 cycles per burst, incubated overnight at 4ºC with 10 µL of either rabbit IgG (1 mg/mL, IGBMC facility) or rabbit anti-
	150 s), before addition of 100 U benzonase (Sigma) in 100 µL RIPA buffer and incubation for 30 min at CTCF (07-729, Millipore). Immunoprecipitated chromatin was then adsorbed to 100 µL prepared protein
	30ºC. Lysate was cleared by centrifugation at 22,000 g for 20 min at 4ºC and protein concentration was A/protein G-Dynabeads for 3.5 h at 4ºC on a rotating wheel. The beads were then washed twice for 5 min
	measured with a Bio-Rad protein assay. 30 µg protein extract was loaded onto a 15% Bis-Tris at 4ºC with low salt wash buffer (20 mM Tris-HCl pH 8, 150 mM NaCl, 2 mM EDTA, 1% Triton X-100,
	polyacrylamide gel for electrophoresis then transfer to a PVDF membrane using a Mini Trans Blot Cell 0.01% SDS), twice for 5 min at 4ºC with high salt wash buffer (20 mM Tris-HCl pH 8, 500 mM NaCl, 2
	mM EDTA, 1% Triton X-100, 0.01% SDS), twice for 5 min at 4ºC with LiCl wash buffer (10 mM Tris-
	ChIP-qPCR
	For Rad21 ChIP, 40 million ESCs were fixed for 45 min with 2 mM succinimidyl glurarate, then for 10
	For CTCF ChIP, 40 million ESCs were harvested with TrypLE (Invitrogen) and fixed for 10 min with 1% min with 1% formaldehyde at 23°C, before quenching with 125 mM glycine for 15 min at 23°C. Cell
	formaldehyde, then quenched with 125 mM glycine for 5 min at 23ºC then 15 min at 4ºC. Cells were pellets were washed twice with ice-cold PBS, then resuspension and incubation in lysis buffer 1 (50 mM
	washed with 10% FBS/125 mM glycine in 1x PBS, then lysed in 275 µL lysis buffer (50 mM Tris-HCl HEPES-KOH pH 7.5, 140 mM NaCl, 1 mM EDTA, 10% glycerol, 0.5% NP-40, 0.25% Triton X-100) for
	pH 8, 10 mM EDTA, 1% SDS, 1x complete EDTA-free protease inhibitors) on ice for 20 min. 320 µL 10 min at 4°C. Lysates were centrifuged for 5 min at 2000 g, 4°C, before incubation for 10 min at 4°C in
	lysate was transferred to a microtube 500 AFA and sonicated with a Covaris E220 (175 V peak incidence lysis buffer 2 (10 mM Tris-HCl pH 8, 200 mM NaCl, 1 mM EDTA, 0.5 mM EGTA). Lysates were again
	power, 20% duty factor, 200 cycles per burst) for 25 min to shear chromatin to a 200-700 bp range. Cell

(Bio-Rad). Membranes were blocked for 1 h at 23ºC in 4% milk/PBST (0.1% Tween-20 in PBS), then incubated with primary antibody (anti-SOX2, Santa Cruz #sc-365823; anti-histone H3, H31HH.3EI-IGBMC) at 1:1000 dilution in 4% milk/PBST overnight at 4ºC. Membranes were washed four times for 5 min each at 23ºC in PBST, then incubated with 1:10,000 goat anti-mouse-alkaline phosphatase (IGBMC) in 4% milk/PBST for 1 h at 23ºC, before washing four times for 5 min each at 23ºC in PBST and developing with Pierce ECL Western blotting substrate (Thermo Fisher). Image acquisition was performed on ImageQuant 800 (Amersham). debris was removed by centrifugation for 15 min at 20,000 g, 4ºC. Equal volumes of protein A-and protein G-Dynabeads (Invitrogen) were mixed and prepared by washing in ChIP dilution buffer (16.7 mM Tris-HCl pH 8, 250 mM LiCl, 1 mM EDTA, 1% NP-40, 1% sodium deoxycholate), then twice for 5 min at 4ºC with TE buffer (10 mM Tris-HCl pH 8, 1 mM EDTA). The immunoprecipitated chromatin was eluted by two incubations with 250 µL elution buffer (100 mM NaHCO 3 , 1% SDS) for 15 min at 23ºC. Eluate and input samples were decrosslinked by treatment overnight at 65ºC, then DNA purified by RNase A digestion, proteinase K digestion, phenol/chloroform extraction and ethanol precipitation. qPCR was performed with QuantitTect SYBR Green PCR kit (Qiagen), using dilutions of the input material to generate the standard curve. Primer sequences are given in Table

S7

. centrifuged for 5 min at 2000 g, 4°C, before resuspending in ice-cold lysis buffer 3 (10 mM Tris-HCl pH 8, 100 mM NaCl, 1 mM EDTA, 0.5 mM EGTA, 0.1% sodium deoxycholate, 0.5% N-laurylsarcosine).

  Upon binding with promoters RNAPII loses its LJ interaction with promoters, since this is substituted by the bond itself. PolII is also allowed to form bonds with enhancers, although in this case no transcription procedure is initiated. As for PolII-promoter case, such bond dissolves at a given rate. Since cohesin and PolII, in their chromatin bound state, interfere with one another, we explored different rates of PolII-enhancer bond dissociation to study the effect of loop extrusion-transcription competition on the

	4 τ b 1.05σ). These values are selected to obtain a RNAPII transcription speed approximately in the range of 1--1 ) and only if the beads are found closer than a cutoff distance (c d = 10 kbp/min observed experimentally. Upon reaching the TES, RNAPII stops and becomes unbound with bonds lost per second (revised model, with reinforced competition). Cohesin concentration was maintained at 20 nM in the models. For CTCF binding, a single bead interacts via LJ potential (𝜖𝜖 = 2k B T) with specific beads of the chromatin fiber (CTCF ChIP-seq peaks containing oriented cognate binding motifs). Once a bond is rate 0.2 τb. locus dynamics, ranging from 2 bonds lost per second (initial model, with limited competition) to 0.5 formed (with rate 0.8 τb-1) it is pair-exclusive (i.e., other CTCF molecules cannot bind that same site).

Table S4 . Sequences of repair cassettes used to delete CTCF motifs.

 S4

	Sox2-SCR MS2	Sox2-	AGCACAA GCCAGCC	chr3:34,762,661-chr3:34,651,363-	CRISPR/Cas9 mediated
		SCR WT	AATAAAA CTCACAT	34,762,680 34,651,382	knock-in of MS2 repeat
			TTTAAG GTGCGAC	chr3:34,762,618-	CRISPR/Cas9 mediated cassette; Cre excision of
				34,644,639 34,762,637	homologous selectable marker;
			CTATGCA	chr3:34,759,434-	recombination of ANCH1 PiggyBac transposition of
			CATGCTG	34,759,453	and ANCH3 sequences OR1-GFP, OR3-IRFP and
			GGACCA		into musculus allele MCP-ScarletI
			ACTAGAG
	Inter-Down	F1	GTTCAAA CTCAACC	chr3:34,705,417-	CRISPR/Cas9 mediated
			AACTAGA TTGGCC	34,705,436	homologous
			AACA	chr3:34,820,313-	recombination of ANCH1
			GGTTAGT	34,820,332	and ANCH3 sequences
			CCTTGCA TCTCTTC		into musculus allele
			AGCACAA AGCAAG
	Sox2-	Sox2-	GGACGC GTAAAAG	chr3:34,647,872-	CRISPR/Cas9 mediated
	Sox2-SCR ΔCTCF_Sox2	Sox2-SCR WT	TAGCATC CAAGTCC	chr3:34,759,085-34,647,891	CRISPR/Cas9 mediated homozygous knock-in of
	SCR ΔSRR107+111	SCR WT	TGGCCAA ACCAGC	34,759,104	musculus-specific deletion EcoRI site to delete CTCF
			GGAATG	chr3:34,757,618-	of SRR107 and SRR111 motif
	Sox2-	Sox2-	GTCAACT	34,757,637 chr3:34,760,108-	sequences 44 CRISPR/Cas9 mediated
	SCR ΔCTCF_SCR	SCR WT	CCCAACG AGCCGCC	chr3:34,760,897-34,760,127	homozygous knock-in of
			TACATGT AGCAGG	34,760,916	EcoRI site to delete CTCF
			TTTTGT	chr3:34,760,804-	motif 61
				34,760,823
					55 56

Platania et al. Fig 1 A B

  43, D1117-1123. 10.1093/nar/gku895. 89. Sharova LV, Sharov AA, Nedorezov T, Piao Y, Shaik N and Ko MSH. (2009). Database for mRNA half-life of 19 977 genes obtained by DNA microarray analysis of pluripotent and differentiating mouse embryonic stem cells.

		DNA Res 16, 45-58. 10.1093/dnares/dsn030.
	0
	12
				CTCF
	0
	chr3	34,600,000	34,700,000	34,800,000	34,900,000
				8000
				Normalized 4C signal
				0
				34,600,000	34,700,000	34,800,000	34,900,000
					Sox2	SCR
				E

ACKNOWLEDGEMENTS

ANCHOR constructs were provided by NeoVirTech. The MS2v6 constructs were built by Biljana Atanasovska. Sequencing was performed by the Institute of Genetics and Molecular and Cellular Biology (IGBMC) GenomEast platform, a member of the France Génomique consortium (ANR-10-INBS-0009). This study was made possible because of the IGBMC Imaging Center (ici.igbmc.fr), flow cytometry and molecular biology platforms. BioRender was used for generating Figs 7d and e. This study was funded from grants by LabEx INRT (ANR-10-LABX-0030-INRT, a French State fund managed by the Agence Nationale de la Recherche under the frame program Investissements d'Avenir ANR-10-IDEX-0002-02), ERC (Starting Grant 678624 -CHROMTOPOLOGY) and Agence Nationale de Recherche (HUBDYN). AgP was supported by a fellowship from La Ligue Nationale Contre le Cancer. Work in the Mitchell laboratory was supported by the Canadian Institutes of Health Research (FRN PJT153186 and PJT180312), the National Institutes of Health (R01-HG010045-01), the Canada Foundation for Innovation, and the Ontario Ministry of Research and Innovation. Work in the Soutoglou laboratory was supported by the Academy of Medical Sciences (AMA). Work in the Lenstra lab was supported by an institutional grant of the Dutch Cancer Society and of the Dutch Ministry of Health, Welfare and Sport, and, Oncode Institute, which is partly financed by the Dutch Cancer Society. Work in the Papantonis lab was supported by the Deutsche Forschungsgemeinschaft via the SPP2191 and SPP2202 Priority Programs (Project Nos.: PA 2456/17-1 and PA 2456/11-2). Work in the Bystricky lab was supported by the Agence Nationale de Recherche and the Fondation ARC.

Data sources

ESC and NPC Hi-C data were taken from ref 60, and re-analyzed and visualized using FAN-C [START_REF] Kruse | FAN-C: a feature-rich framework for the analysis and visualisation of chromosome conformation capture data[END_REF] . The differential Hi-C map was derived as in ref 87. The normalized scores of the ESC Hi-C submatrix were subtracted from those of the NPC Hi-C submatrix, and the difference was expressed as a z-score: (diffmean(diff))/standard deviation(diff)). Insulation was computed using FAN-C with a binsize of 7 bins (28 kb). ESC ChIP-seq datasets for H3K27ac and CTCF were obtained from the CODEX database 88 . For comparison of 2D Sox2-SCR distance distributions with analogous methods, results from oligoFISH were taken from ref 53, and results from CuO/TetO experiments were taken from ref 9.

AUTHOR CONTRIBUTIONS

AnP, AgP, KB and TS conceived and designed experiments. AnP and CE generated ANCHOR lines and performed nearly all experiments and particle tracking, with microscopy optimization assisted by EG. MB performed molecular dynamics simulations, with posterior analysis performed by BM. BM, GMO and

DECLARATION OF INTERESTS

The authors declare no competing interests. Table S3. Cell lines generated in this study. Descriptions of the parental lines and gRNA sequences used to make the cell lines used in this study.

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