Cohesin distribution alone predicts chromatin organization in yeast via conserved-current loop extrusion

  1. Tianyu Yuan
  2. Hao Yan
  3. Kevin C. Li
  4. Ivan Surovtsev
  5. Megan C. King
  6. Simon G. J. Mochrie

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Abstract

Background

Inhomogeneous patterns of chromatin-chromatin contacts within 10–100-kb-sized regions of the genome are a generic feature of chromatin spatial organization. These features, termed topologically associating domains (TADs), have led to the loop extrusion factor (LEF) model. Currently, our ability to model TADs relies on the observation that in vertebrates TAD boundaries are correlated with DNA sequences that bind CTCF, which therefore is inferred to block loop extrusion. However, although TADs feature prominently in their Hi-C maps, non-vertebrate eukaryotes either do not express CTCF or show few TAD boundaries that correlate with CTCF sites. In all of these organisms, the counterparts of CTCF remain unknown, frustrating comparisons between Hi-C data and simulations.

Results

To extend the LEF model across the tree of life, here, we propose the conserved-current loop extrusion (CCLE) model that interprets loop-extruding cohesin as a nearly conserved probability current. From cohesin ChIP-seq data alone, we derive a position-dependent loop extrusion rate, allowing for a modified paradigm for loop extrusion, that goes beyond solely localized barriers to also include loop extrusion rates that vary continuously. We show that CCLE accurately predicts the TAD-scale Hi-C maps of interphase Schizosaccharomyces pombe , as well as those of meiotic and mitotic Saccharomyces cerevisiae , demonstrating its utility in organisms lacking CTCF.

Conclusions

The success of CCLE in yeasts suggests that loop extrusion by cohesin is indeed the primary mechanism underlying TADs in these systems. CCLE allows us to obtain loop extrusion parameters such as the LEF density and processivity, which compare well to independent estimates.

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  1. Version published to 10.1186/s13059-024-03432-2
  2. Version published to 10.1101/2023.10.05.560890v4 on bioRxiv
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    Reply to the reviewers

    Reply to the Reviewers

    We thank the referees for their careful reading of the manuscript and their valuable suggestions for improvements.

    General Statements:

    Existing SMC-based loop extrusion models successfully predict and characterize mesoscale genome spatial organization in vertebrate organisms, providing a valuable computational tool to the genome organization and chromatin biology fields. However, to date this approach is highly limited in its application beyond vertebrate organisms. This limitation arises because existing models require knowledge of CTCF binding sites, which act as effective boundary elements, blocking loop-extruding SMC complexes and thus defining TAD boundaries. However, CTCF is the predominant boundary element only in vertebrates. On the other hand, vertebrates only contain a small proportion of species in the tree of life, while TADs are nearly universal and SMC complexes are largely conserved. Thus, there is a pressing need for loop extrusion models capable of predicting Hi-C maps in organisms beyond vertebrates.

    The conserved-current loop extrusion (CCLE) model, introduced in this manuscript, extends the quantitative application of loop extrusion models in principle to any organism by liberating the model from the lack of knowledge regarding the identities and functions of specific boundary elements. By converting the genomic distribution of loop extruding cohesin into an ensemble of dynamic loop configurations via a physics-based approach, CCLE outputs three-dimensional (3D) chromatin spatial configurations that can be manifested in simulated Hi-C maps. We demonstrate that CCLE-generated maps well describe experimental Hi-C data at the TAD-scale. Importantly, CCLE achieves high accuracy by considering cohesin-dependent loop extrusion alone, consequently both validating the loop extrusion model in general (as opposed to diffusion-capture-like models proposed as alternatives to loop extrusion) and providing evidence that cohesin-dependent loop extrusion plays a dominant role in shaping chromatin organization beyond vertebrates.

    The success of CCLE unambiguously demonstrates that knowledge of the cohesin distribution is sufficient to reconstruct TAD-scale 3D chromatin organization. Further, CCLE signifies a shifted paradigm from the concept of localized, well-defined boundary elements, manifested in the existing CTCF-based loop extrusion models, to a concept also encompassing a continuous distribution of position-dependent loop extrusion rates. This new paradigm offers greater flexibility in recapitulating diverse features in Hi-C data than strictly localized loop extrusion barriers.

    Reviewer #1 (Evidence, reproducibility and clarity (Required)):

    This manuscript presents a mathematical model for loop extrusion called the conserved-current loop extrusion model (CCLE). The model uses cohesin ChIP-Seq data to predict the Hi-C map and shows broad agreement between experimental Hi-C maps and simulated Hi-C maps. They test the model on Hi-C data from interphase fission yeast and meiotic budding yeast. The conclusion drawn by the authors is that peaks of cohesin represent loop boundaries in these situations, which they also propose extends to other organism/situations where Ctcf is absent.

    __Response: __

    We would like to point out that the referee's interpretation of our results, namely that, "The conclusion drawn by the authors is that peaks of cohesin represent loop boundaries in these situations, ...", is an oversimplification, that we do not subscribe to. The referee's interpretation of our model is correct when there are strong, localized barriers to loop extrusion; however, the CCLE model allows for loop extrusion rates that are position-dependent and take on a range of values. The CCLE model also allows the loop extrusion model to be applied to organisms without known boundary elements. Thus, the strict interpretation of the positions of cohesin peaks to be loop boundaries overlooks a key idea to emerge from the CCLE model.

    __ Major comments:__

    1. More recent micro-C/Hi-C maps, particularly for budding yeast mitotic cells and meiotic cells show clear puncta, representative of anchored loops, which are not well recapitulated in the simulated data from this study. However, such punta are cohesin-dependent as they disappear in the absence of cohesin and are enhanced in the absence of the cohesin release factor, Wapl. For example - see the two studies below. The model is therefore missing some key elements of the loop organisation. How do the authors explain this discrepency? It would also be very useful to test whether the model can predict the increased strength of loop anchors when Wapl1 is removed and cohesin levels increase.

    Costantino L, Hsieh TS, Lamothe R, Darzacq X, Koshland D. Cohesin residency determines chromatin loop patterns. Elife. 2020 Nov 10;9:e59889. doi: 10.7554/eLife.59889. PMID: 33170773; PMCID: PMC7655110. Barton RE, Massari LF, Robertson D, Marston AL. Eco1-dependent cohesin acetylation anchors chromatin loops and cohesion to define functional meiotic chromosome domains. Elife. 2022 Feb 1;11:e74447. doi: 10.7554/eLife.74447. Epub ahead of print. PMID: 35103590; PMCID: PMC8856730.

    __Response: __

    We are perplexed by this referee comment. While we agree that puncta representing loop anchors are a feature of Hi-C maps, as noted by the referee, we would reinforce that our CCLE simulations of meiotic budding yeast (Figs. 5A and 5B of the original manuscript) demonstrate an overall excellent description of the experimental meiotic budding yeast Hi-C map, including puncta arising from loop anchors. This CCLE model-experiment agreement for meiotic budding yeast is described and discussed in detail in the original manuscript and the revised manuscript (lines 336-401).

    To further emphasize and extend this point we now also address the Hi-C of mitotic budding yeast, which was not included the original manuscript. We have now added an entire new section of the revised manuscript entitled "CCLE Describes TADs and Loop Configurations in Mitotic S. cerevisiae" including the new Figure 6, which presents a comparison between a portion of the mitotic budding yeast Hi-C map from Costantino et al. and the corresponding CCLE simulation at 500 bp-resolution. In this case too, the CCLE model well-describes the data, including the puncta, further addressing the referee's concern that the CCLE model is missing some key elements of loop organization.

    Concerning the referee's specific comment about the role of Wapl, we note that in order to apply CCLE when Wapl is removed, the corresponding cohesin ChIP-seq in the absence of Wapl should be available. To our knowledge, such data is not currently available and therefore we have not pursued this explicitly. However, we would reinforce that as Wapl is a factor that promotes cohesin unloading, its role is already effectively represented in the optimized value for LEF processivity, which encompasses LEF lifetime. In other words, if Wapl has a substantial effect it will be captured already in this model parameter.

    1. Related to the point above, the simulated data has much higher resolution than the experimental data (1kb vs 10kb in the fission yeast dataset). Given that loop size is in the 20-30kb range, a good resolution is important to see the structural features of the chromosomes. Can the model observe these details that are averaged out when the resolution is increased?

    __Response: __

    We agree with the referee that higher resolution is preferable to low resolution. In practice, however, there is a trade-off between resolution and noise. The first experimental interphase fission yeast Hi-C data of Mizuguchi et al 2014 corresponds to 10 kb resolution. To compare our CCLE simulations to these published experimental data, as described in the original manuscript, we bin our 1-kb-resolution simulations to match the 10 kb experimental measurements. Nevertheless, CCLE can readily predict the interphase fission yeast Hi-C map at higher resolution by reducing the bin size (or, if necessary, reducing the lattice site size of the simulations themselves). In the revised manuscript, we have added comparisons between CCLE's predicted Hi-C maps and newer Micro-C data for S. pombe from Hsieh et al. (Ref. [50]) in the new Supplementary Figures 5-9. We have chosen to present these comparisons at 2 kb resolution, which is the same resolution for our meiotic budding yeast comparisons. Also included in Supplementary Figures 5-9 are comparisons between the original Hi-C maps of Mizuguchi et al. and the newer maps of Hsieh et al., binned to 10 kb resolution. Inspection of these figures shows that CCLE provides a good description of Hsieh et al.'s experimental Hi-C maps and does not reveal any major new features in the interphase fission yeast Hi-C map on the 10-100 kb scale, that were not already apparent from the Hi-C maps of Mizuguchi et al 2014. Thus, the CCLE model performs well across this range of effective resolutions.

    3.* Transcription, particularly convergent has been proposed to confer boundaries to loop extrusion. Can the authors recapitulate this in their model?*

    __Response: __

    In response to the suggestion of the reviewer we have now calculated the correlation between cohesin ChIP-seq and the locations of convergent gene pairs, which is now presented in Supplementary Figures 17 and 18. Accordingly, in the revised manuscript, we have added the following text to the Discussion (lines 482-498):

    "In vertebrates, CTCF defines the locations of most TAD boundaries. It is interesting to ask what might play that role in interphase S. pombe as well as in meiotic and mitotic S. cerevisiae. A number of papers have suggested that convergent gene pairs are correlated with cohesin ChIP-seq in both S. pombe [65, 66] and S. cerevisiae [66-71]. Because CCLE ties TADs to cohesin ChIP-seq, a strong correlation between cohesin ChIP-seq and convergent gene pairs would be an important clue to the mechanism of TAD formation in yeasts. To investigate this correlation, we introduce a convergent-gene variable that has a nonzero value between convergent genes and an integrated weight of unity for each convergent gene pair. Supplementary Figure 17A shows the convergent gene variable, so-defined, alongside the corresponding cohesin ChIP-seq for meiotic and mitotic S. cerevisiae. It is apparent from this figure that a peak in the ChIP-seq data is accompanied by a non-zero value of the convergent-gene variable in about 80% of cases, suggesting that chromatin looping in meiotic and mitotic S. cerevisiae may indeed be tied to convergent genes. Conversely, about 50% of convergent genes match peaks in cohesin ChIP-seq. The cross-correlation between the convergent-gene variable and the ChIP-seq of meiotic and mitotic S. cerevisiae is quantified in Supplementary Figures 17B and C. By contrast, in interphase S. pombe, cross-correlation between convergent genes and cohesin ChIP-seq in each of five considered regions is unobservably small (Supplementary Figure 18A), suggesting that convergent genes per se do not have a role in defining TAD boundaries in interphase S. pombe."

    *Minor comments: *

    1. In the discussion, the authors cite the fact that Mis4 binding sites do not give good prediction of the HI-C maps as evidence that Mis4 is not important for loop extrusion. This can only be true if the position of Mis4 measured by ChIP is a true reflection of Mis4 position. However, Mis4 binding to cohesin/chromatin is very dynamic and it is likely that this is too short a time scale to be efficiently cross-linked for ChIP. Conversely, extensive experimental data in vivo and in vitro suggest that stimulation of cohesin's ATPase by Mis4-Ssl3 is important for loop extrusion activity.

    __Response: __

    We apologize for the confusion on this point. We actually intended to convey that the absence of Mis4-Psc3 correlations in S. pombe suggests, from the point of view of CCLE, that Mis4 is not an integral component of loop-extruding cohesin, during the loop extrusion process itself. We agree completely that Mis4/Ssl3 is surely important for cohesin loading, and (given that cohesin is required for loop extrusion) Mis4/Ssl3 is therefore important for loop extrusion. Evidently, this part of our Discussion was lacking sufficient clarity. In response to both referees' comments, we have re-written the discussion of Mis4 and Pds5 to more carefully explain our reasoning and be more circumspect in our inferences. The re-written discussion is described below in response to Referee #2's comments.

    Nevertheless, on the topic of whether Nipbl-cohesin binding is too transient to be detected in ChIP-seq, the FRAP analysis presented by Rhodes et al. eLife 6:e30000 "Scc2/Nipbl hops between chromosomal cohesin rings after loading" indicates that, in HeLa cells, Nipbl has a residence time bound to cohesin of about 50 seconds. As shown in the bottom panel of Supplementary Fig. 7 in the original manuscript (and the bottom panel of Supplementary Fig. 20 in the revised manuscript), there is a significant cross-correlation (~0.2) between the Nipbl ChIP-seq and Smc1 ChIP-seq in humans, indicating that a transient association between Nipbl and cohesin can be (and in fact is) detected by ChIP-seq.

    1. *Inclusion of a comparison of this model compared to previous models (for example bottom up models) would be extremely useful. What is the improvement of this model over existing models? *

    __Response: __

    As stated in the original manuscript, as far as we are aware, "bottom up" models, that quantitatively describe the Hi-C maps of interphase fission yeast or meiotic budding yeast or, indeed, of eukaryotes other than vertebrates, do not exist. Bottom-up models would require knowledge of the relevant boundary elements (e.g. CTCF sites), which, as stated in the submitted manuscript, are generally unknown for fission yeast, budding yeast, and other non-vertebrate eukaryotes. The absence of such models is the reason that CCLE fills an important need. Since bottom-up models for cohesin loop extrusion in yeast do not exist, we cannot compare CCLE to the results of such models.

    In the revised manuscript we now explicitly compare the CCLE model to the only bottom-up type of model describing the Hi-C maps of non-vertebrate eukaryotes by Schalbetter et al. Nat. Commun. 10:4795 2019, which we did cite extensively in our original manuscript. Schalbetter et al. use cohesin ChIP-seq peaks to define the positions of loop extrusion barriers in meiotic S. cerevisiae, for which the relevant boundary elements are unknown. In their model, specifically, when a loop-extruding cohesin anchor encounters such a boundary element, it either passes through with a certain probability, as if no boundary element is present, or stops extruding completely until the cohesin unbinds and rebinds.

    In the revised manuscript we refer to this model as the "explicit barrier" model and have applied it to interphase S. pombe, using cohesin ChIP-seq peaks to define the positions of loop extrusion barriers. The corresponding simulated Hi-C map is presented in Supplementary Fig. 19 in comparison with the experimental Hi-C. It is evident that the explicit barrier model provides a poorer description of the Hi-C data of interphase S. pombe compared to the CCLE model, as indicated by the MPR and Pearson correlation scores. While the explicit barrier model appears capable of accurately reproducing Hi-C data with punctate patterns, typically accompanied by strong peaks in the corresponding cohesin ChIP-seq, it seems less effective in several conditions including interphase S. pombe, where the Hi-C data lacks punctate patterns and sharp TAD boundaries, and the corresponding cohesin ChIP-seq shows low-contrast peaks. The success of the CCLE model in describing the Hi-C data of both S. pombe and S. cerevisiae, which exhibit very different features, suggests that the current paradigm of localized, well-defined boundary elements may not be the only approach to understanding loop extrusion. By contrast, CCLE allows for a concept of continuous distribution of position-dependent loop extrusion rates, arising from the aggregate effect of multiple interactions between loop extrusion complexes and chromatin. This paradigm offers greater flexibility in recapitulating diverse features in Hi-C data than strictly localized loop extrusion barriers.

    We have also added the following paragraph in the Discussion section of the manuscript to elaborate this point (lines 499-521):

    "Although 'bottom-up' models which incorporate explicit boundary elements do not exist for non-vertebrate eukaryotes, one may wonder how well such LEF models, if properly modified and applied, would perform in describing Hi-C maps with diverse features. To this end, we examined the performance of the model described in Ref. [49] in describing the Hi-C map of interphase S. cerevisiae. Reference [49] uses cohesin ChIP-seq peaks in meiotic S. cerevisiae to define the positions of loop extrusion barriers which either completely stall an encountering LEF anchor with a certain probability or let it pass. We apply this 'explicit barrier' model to interphase S. pombe, using its cohesin ChIP-seq peaks to define the positions of loop extrusion barriers, and using Ref. [49]'s best-fit value of 0.05 for the pass-through probability. Supplementary Figure 19A presents the corresponding simulated Hi-C map the 0.3-1.3 kb region of Chr 2 of interphase S. pombe in comparison with the corresponding Hi-C data. It is evident that the explicit barrier model provides a poorer description of the Hi-C data of interphase S. pombe compared to the CCLE model, as indicated by the MPR and Pearson correlation scores of 1.6489 and 0.2267, respectively. While the explicit barrier model appears capable of accurately reproducing Hi-C data with punctate patterns, typically accompanied by strong peaks in the corresponding cohesin ChIP-seq, it seems less effective in cases such as in interphase S. pombe, where the Hi-C data lacks punctate patterns and sharp TAD boundaries, and the corresponding cohesin ChIP-seq shows low-contrast peaks. The success of the CCLE model in describing the Hi-C data of both S. pombe and S. cerevisiae, which exhibit very different features, suggests that the current paradigm of localized, well-defined boundary elements may not be the only approach to understanding loop extrusion. By contrast, CCLE allows for a concept of continuous distribution of position-dependent loop extrusion rates, arising from the aggregate effect of multiple interactions between loop extrusion complexes and chromatin. This paradigm offers greater flexibility in recapitulating diverse features in Hi-C data than strictly localized loop extrusion barriers."

    Reviewer #1* (Significance (Required)):*

    This simple model is useful to confirm that cohesin positions dictate the position of loops, which was predicted already and proposed in many studies. However, it should be considered a starting point as it does not faithfully predict all the features of chromatin organisation, particularly at better resolution.

    Response:

    As described in more detail above, we do not agree with the assertion of the referee that the CCLE model "does not faithfully predict all the features of chromatin organization, particularly at better resolution" and provide additional new data to support the conclusion that the CCLE model provides a much needed approach to model non-vertebrate contact maps and outperforms the single prior attempt to predict budding yeast Hi-C data using information from cohesin ChIP-seq.

    *It will mostly be of interest to those in the chromosome organisation field, working in organisms or systems that do not have ctcf. *

    __Response: __

    We agree that this work will be of special interest to researchers working on chromatin organization of non-vertebrate organisms. We would reinforce that yeast are frequently used models for the study of cohesin, condensin, and chromatin folding more generally. Indeed, in the last two months alone there are two Molecular Cell papers, one Nature Genetics paper, and one Cell Reports paper where loop extrusion in yeast models is directly relevant. We also believe, however, that the model will be of interest for the field in general as it simultaneously encompasses various scenarios that may lead to slowing down or stalling of LEFs.

    This reviewer is a cell biologist working in the chromosome organisation field, but does not have modelling experience and therefore does not have the expertise to determine if the modelling part is mathematically sound and has assumed that it is.

    Reviewer #2 (Evidence, reproducibility and clarity (Required)):

    Summary: Yuan et al. report on their development of an analytical model ("CCLE") for loop extrusion with genomic-position-dependent speed, with the idea of accounting for barriers to loop extrusion. They write down master equations for the probabilities of cohesin occupancy at each genomic site and obtain approximate steady-state solutions. Probabilities are governed by cohesin translocation, loading, and unloading. Using ChIP-seq data as an experimental measurement of these probabilities, they numerically fit the model parameters, among which are extruder density and processivity. Gillespie simulations with these parameters combined with a 3D Gaussian polymer model were integrated to generate simulated Hi-C maps and cohesin ChIP-seq tracks, which show generally good agreement with the experimental data. The authors argue that their modeling provides evidence that loop extrusion is the primary mechanism of chromatin organization on ~10-100 kb scales in S. pombe and S. cerevisiae.

    Major comments:

    1. I am unconvinced that this analysis specifically is sufficient to demonstrate that extrusion is the primary organizer of chromatin on these scales; moreover, the need to demonstrate this is questionable, as extrusion is widely accepted, even if not universally so. How is the agreement of CCLE with experiments more demonstrative of loop extrusion than previous modeling?

    __Response: __

    We agree with the referee's statement that "loop extrusion is extrusion is widely accepted, even if not universally so". We disagree with the referee that this state of affairs means that "the need to demonstrate this (i.e. loop extrusion) is questionable". On the contrary, studies that provide further compelling evidence that cohesin-based loop extrusion is the primary organizer of chromatin, such as ours, must surely be welcomed, first, in order to persuade those who remain unconvinced by the loop extrusion mechanism in general, and, secondly, because, until the present work, quantitative models of loop extrusion, capable of reproducing Hi-C maps quantitatively, in yeasts and other non-vertebrate eukaryotes have been lacking, leaving open the question of whether loop extrusion can describe Hi-C maps beyond vertebrates. CCLE has now answered that question in the affirmative. Moreover, the existence of a robust model to predict contact maps in non-vertebrate models, which are extensively used in the pursuit of research questions in chromatin biology, will be broadly enabling to the field.

    It is fundamental that if a simple, physically-plausible model/hypothesis is able to describe experimental data quantitatively, it is indeed appropriate to ascribe considerable weight to that model/hypothesis (until additional data become available to refute the model).

    How is the agreement of CCLE with experiments more demonstrative of loop extrusion than previous modeling?

    Response:

    As noted above and in the original manuscript, we are unaware of previous quantitative modeling of cohesin-based loop extrusion and the resultant Hi-C maps in organisms that lack CTCF, namely non-vertebrate eukaryotic models such as fission yeast or budding yeast, as we apply here. As noted in the original manuscript, previous quantitative modeling of Hi-C maps based on cohesin loop extrusion and CTCF boundary elements has been convincing that loop extrusion is indeed relevant in vertebrates, but the restriction to vertebrates excludes most of the tree of life.

    Below, the referee cites two examples of loop extrusion outside of vertebrates. The one that is suggested to correspond to yeast cells (Dequeker et al. Nature 606:197 2022) actually corresponds to mouse cells, which are vertebrate cells. The other one models the Hi-C map of the prokaryote, Bacillus subtilis, based on loop extrusion of the bacterial SMC complex thought to most resemble condensin (not cohesin), subject to barriers to loop extrusion that are related to genes or involving prokaryote-specific Par proteins (Brandao et al. PNAS 116:20489 2019). We have referenced this work in the revised manuscript but would reinforce that it lacks utility in predicting the contact maps for non-vertebrate eukaryotes.

    Relatedly, similar best fit values for S. pombe and S. cerevisiae might not point to a mechanistic conclusion (same "underlying mechanism" of loop extrusion), but rather to similar properties for loop-extruding cohesins in the two species.

    Response:

    In the revised manuscript, we have replaced "suggesting that the underlying mechanism that governs loop extrusion by cohesin is identical in both species" with "suggesting loop-extruding cohesins possess similar properties in both species" (lines 367-368).

    As an alternative, could a model with variable binding probability given by ChIP-seq and an exponential loop-size distribution work equally well? The stated lack of a dependence on extrusion timescale suggests that a static looping model might succeed. If not, why not?

    Response:

    A hypothetical mechanism that generates the same instantaneous loop distributions and correlations as loop extrusion would lead to the same Hi-C map as does loop extrusion. This circumstance is not confined to CCLE, but is equally applicable to previous CTCF-based loop extrusion models. It holds because Hi-C and ChIP-seq, and therefore models that seek to describe these measurements, provide a snapshot of the chromatin configuration at one instant of time.

    We would reinforce that there is no physical basis for a diffusion capture model with an approximately-exponential loop size distributions. Nevertheless, one can reasonably ask whether a physically-sensible diffusion capture model can simultaneously match cohesin ChIP-seq and Hi-C. Motivated by the referee's comment we have addressed this question and, accordingly, in the revised manuscript, we have added (1) an entire subsection entitled "Diffusion capture does not reproduce experimental interphase S. pombe Hi-C maps" (lines 303-335) and (2) Supplementary Figure 15. As we now demonstrate, the CCLE model vastly outperforms an equilibrium binding model in reproducing the experimental Hi-C maps and measured P(s).

    *2. I do not understand how the loop extrusion residence time drops out. As I understand it, Eq 9 converts ChIP-seq to lattice site probability (involving N_{LEF}, which is related to \rho, and \rho_c). Then, Eqs. 3-4 derive site velocities V_n and U_n if we choose rho, L, and \tau, with the latter being the residence time. This parameter is not specified anywhere and is claimed to be unimportant. It may be true that the choice of timescale is arbitrary in this procedure, but can the authors please clarify? *

    __Response: __

    As noted above, Hi-C and ChIP-seq both capture chromatin configuration at one instant in time. Therefore, such measurements cannot and do not provide any time-scale information, such as the loop extrusion residence time (LEF lifetime) or the mean loop extrusion rate. For this reason, neither our CCLE simulations, nor other researchers' previous simulations of loop extrusion in vertebrates with CTCF boundary elements, provide any time-scale information, because the experiments they seek to describe do not contain time-scale information. The Hi-C map simulations can and do provide information concerning the loop size, which is the product of the loop lifetime and the loop extrusion rate. Lines 304-305 of the revised manuscript include the text: "Because Hi-C and ChIP-seq both characterize chromatin configuration at a single instant of time, and do not provide any direct time-scale information, ..."

    In practice, we set the LEF lifetime to be some explicit value with arbitrary time-unit. We have added a sentence in the Methods that reads, "In practice, however, we set the LEF dissociation rate to 5e-4 time-unit-1 (equivalent to a lifetime of 2000 time-units), and the nominal LEF extrusion rate (aka \rho*L/\tau, see Supplementary Methods) can be determined from the given processivity" (lines 599-602), to clarify this point. We have also changed the terminology from "timesteps" to "LEF events" in the manuscript as the latter is more accurate for our purpose.

    1. The assumptions in the solution and application of the CCLE model are potentially constraining to a limited number of scenarios. In particular the authors specify that current due to binding/unbinding, A_n - D_n, is small. This assumption could be problematic near loading sites (centromeres, enhancers in higher eukaryotes, etc.) (where current might be dominated by A_n and V_n), unloading sites (D_n and V_{n-1}), or strong boundaries (D_n and V_{n-1}). The latter scenario is particularly concerning because the manuscript seems to be concerned with the presence of unidentified boundaries. This is partially mitigated by the fact that the model seems to work well in the chosen examples, but the authors should discuss the limitations due to their assumptions and/or possible methods to get around these limitations.

    *4. *Related to the above concern, low cohesin occupancy is interpreted as a fast extrusion region and high cohesin occupancy is interpreted as a slow region. But this might not be true near cohesin loading and unloading sites.

    __Response: __

    Our response to Referee 2's Comments 3. and 4. is that both in the original manuscript and in the revised manuscript we clearly delineate the assumptions underlying CCLE and we carefully assess the extent to which these assumptions are violated (lines 123-126 and 263-279 in the revised manuscript). For example, Supplementary Figure 12 shows that across the *S. pombe *genome as a whole, violations of the CCLE assumptions are small. Supplementary Figure 13 shows that violations are similarly small for meiotic S. cerevisiae. However, to explicitly address the concern of the referee, we have added the following sentences to the revised manuscript:

    Lines 277-279:

    "While loop extrusion in interphase S. pombe seems to well satisfy the assumptions underlying CCLE, this may not always be the case in other organisms."

    Lines 359-361:

    "In addition, the three quantities, given by Eqs. 6, 7, and 8, are distributed around zero with relatively small fluctuations (Supplementary Fig. 13), indicating that CCLE model is self-consistent in this case also."

    In the case of mitotic S. cerevisiae, Supplementary Figure 14 shows that these quantities are small for most of genomic locations, except near the cohesin ChIP-seq peaks. We ascribe these greater violations of CCLE's assumptions at the locations of cohesin peaks in part to the low processivity of mitotic cohesin in S. cerevisiae, compared to that of meiotic *S. cerevisiae *and interphase S. pombe, and in part to the low CCLE loop extrusion rate at the cohesin peaks. We have added a paragraph at the end of the Section "CCLE Describes TADs and Loop Configurations in Mitotic S. cerevisiae" to reflect these observations (lines 447-461).

    1. *The mechanistic insight attempted in the discussion, specifically with regard to Mis4/Scc2/NIPBL and Pds5, is problematic. First, it is not clear how the discussion of Nipbl and Pds5 is connected to the CCLE method; the justification is that CCLE shows cohesin distribution is linked to cohesin looping, which is already a questionable statement (point 1) and doesn't really explain how the model offers new insight into existing Nipbl and Pds5 data. *

    Furthermore, I believe that the conclusions drawn on this point are flawed, or at least, stated with too much confidence. The authors raise the curious point that Nipbl ChIP-seq does not correlate well with cohesin ChIP-seq, and use this as evidence that Nipbl is not a part of the loop-extruding complex in S. pombe, and it is not essential in humans. Aside from the molecular evidence in human Nipbl/cohesin (acknowledged by authors), there are other reasons to doubt this conclusion. First, depletion of Nipbl (rather than binding partner Mau2 as in ref 55) in mouse cells strongly inhibits TAD formation (Schwarzer et al. Nature 551:51 2017). Second, at least two studies have raised concerns about Nibpl ChIP-seq results: 1) Hu et al. Nucleic Acids Res 43:e132 2015, which shows that uncalibrated ChIP-seq can obscure the signal of protein localization throughout the genome due to the inability to distinguish from background * and 2) Rhodes et al. eLife 6:e30000, which uses FRAP to show that Nipbl binds and unbinds to cohesin rapidly in human cells, which could go undetected in ChIP-seq, especially when uncalibrated. It has not been shown that these dynamics are present in yeast, but there is no reason to rule it out yet.*

    Similar types of critiques could be applied to the discussion of Pds5. There is cross-correlation between Psc3 and Pds5 in S. pombe, but the authors are unable to account for whether Pds5 binding is transient and/or necessary to loop extrusion itself or, more importantly, whether Pds5 ChIP is associated with extrusive or cohesive cohesins; cross-correlation peaks at about 0.6, but note that by the authors own estimates, cohesive cohesins are approximately half of all cohesins in S. pombe (Table 3).

    *Due to the above issues, I suggest that the authors heavily revise this discussion to better reflect the current experimental understanding and the limited ability to draw such conclusions based on the current CCLE model. *

    __Response: __

    As stated above, our study demonstrates that the CCLE approach is able to take as input cohesin (Psc3) ChIP-seq data and produce as output simulated Hi-C maps that well reproduce the experimental Hi-C maps of interphase S. pombe and meiotic S. cerevisiae. This result is evident from the multiple Hi-C comparison figures in both the original and the revised manuscripts. In light of this circumstance, the referee's statement that it is "questionable", that CCLE shows that cohesin distribution (as quantified by cohesin ChIP-seq) is linked to cohesin looping (as quantified by Hi-C), is demonstrably incorrect.

    However, we did not intend to suggest that Nipbl and Pds5 are not crucial for cohesin loading, as the reviewer states. Rather, our inquiries relate to a more nuanced question of whether these factors only reside at loading sites or, instead, remain as a more long-lived constituent component of the loop extrusion complex. We regret any confusion and have endeavored to clarify this point in the revised manuscript in response to Referee 2's Comment 5. as well as Referee 1's Minor Comment 1. We have now better explained how the CCLE model may offer new insight from existing ChIP-seq data in general and from Mis4/Nipbl and Pds5 ChIP-seq, in particular. Accordingly, we have followed Referee 2's advice to heavily revise the relevant section of the Discussion.

    To this end, we have removed the following text from the original manuscript:

    "The fact that the cohesin distribution along the chromatin is strongly linked to chromatin looping, as evident by the success of the CCLE model, allows for new insights into in vivo LEF composition and function. For example, recently, two single-molecule studies [37, 38] independently found that Nipbl, which is the mammalian analogue of Mis4, is an obligate component of the loop-extruding human cohesin complex. Ref. [37] also found that cohesin complexes containing Pds5, instead of Nipbl, are unable to extrude loops. On this basis, Ref. [32] proposed that, while Nipbl-containing cohesin is responsible for loop extrusion, Pds5-containing cohesin is responsible for sister chromatid cohesion, neatly separating cohesin's two functions according to composition. However, the success of CCLE in interphase S. pombe, together with the observation that the Mis4 ChIP-seq signal is uncorrelated with the Psc3 ChIP-seq signal (Supplementary Fig. 7) allows us to infer that Mis4 cannot be a component of loop-extruding cohesin in S. pombe. On the other hand, Pds5 is correlated with Psc3 in S. pombe (Supplementary Fig. 7) suggesting that both proteins are involved in loop-extruding cohesin, contradicting a hypothesis that Pds5 is a marker for cohesive cohesin in S. pombe. In contrast to the absence of Mis4-Psc3 correlation in S. pombe, in humans, Nipbl ChIP-seq and Smc1 ChIP-seq are correlated (Supplementary Fig. 7), consistent with Ref. [32]'s hypothesis that Nipbl can be involved in loop-extruding cohesin in humans. However, Ref. [55] showed that human Hi-C contact maps in the absence of Nipbl's binding partner, Mau2 (Ssl3 in S. pombe [56]) show clear TADs, consistent with loop extrusion, albeit with reduced long-range contacts in comparison to wild-type maps, indicating that significant loop extrusion continues in live human cells in the absence of Nipbl-Mau2 complexes. These collected observations suggest the existence of two populations of loop-extruding cohesin complexes in vivo, one that involves Nipbl-Mau2 and one that does not. Both types are present in mammals, but only Mis4-Ssl3-independent loop-extruding cohesin is present in S. pombe."

    And we have replaced it by the following text in the revised manuscript (lines 533-568):

    "As noted above, the input for our CCLE simulations of chromatin organization in S. pombe, was the ChIP-seq of Psc3, which is a component of the cohesin core complex [75]. Accordingly, Psc3 ChIP-seq represents how the cohesin core complex is distributed along the genome. In S. pombe, the other components of the cohesin core complex are Psm1, Psm3, and Rad21. Because these proteins are components of the cohesin core complex, we expect that the ChIP-seq of any of these proteins would closely match the ChIP-seq of Psc3, and would equally well serve as input for CCLE simulations of S. pombe genome organization. Supplementary Figure 20C confirms significant correlations between Psc3 and Rad21. In light of this observation, we then reason that the CCLE approach offers the opportunity to investigate whether other proteins beyond the cohesin core are constitutive components of the loop extrusion complex during the extrusion process (as opposed to cohesin loading or unloading). To elaborate, if the ChIP-seq of a non-cohesin-core protein is highly correlated with the ChIP-seq of a cohesin core protein, we can infer that the protein in question is associated with the cohesin core and therefore is a likely participant in loop-extruding cohesin, alongside the cohesin core. Conversely, if the ChIP-seq of a putative component of the loop-extruding cohesin complex is uncorrelated with the ChIP-seq of a cohesin core protein, then we can infer that the protein in question is unlikely to be a component of loop-extruding cohesin, or at most is transiently associated with it.

    For example, in S. pombe, the ChIP-seq of the cohesin regulatory protein, Pds5 [74], is correlated with the ChIP-seq of Psc3 (Supplementary Fig. 20B) and with that of Rad21 (Supplementary Fig. 20D), suggesting that Pds5 can be involved in loop-extruding cohesin in S. pombe, alongside the cohesin core proteins. Interestingly, this inference concerning fission yeast cohesin subunit, Pds5, stands in contrast to the conclusion from a recent single-molecule study [38] concerning cohesin in vertebrates. Specifically, Reference [38] found that cohesin complexes containing Pds5, instead of Nipbl, are unable to extrude loops.

    Additionally, as noted above, in *S. pombe *the ChIP-seq signal of the cohesin loader, Mis4, is uncorrelated with the Psc3 ChIP-seq signal (Supplementary Fig. 20A), suggesting that Mis4 is, at most, a very transient component of loop-extruding cohesin in S. pombe, consistent with its designation as a "cohesin loader". However, both References [38] and [39] found that Nipbl (counterpart of S. pombe's Mis4) is an obligate component of the loop-extruding human cohesin complex, more than just a mere cohesin loader. Although CCLE has not yet been applied to vertebrates, from a CCLE perspective, the possibility that Nipbl may be required for the loop extrusion process in humans is bolstered by the observation that in humans Nipbl ChIP-seq and Smc1 ChIP-seq show significant correlations (Supplementary Fig. 20G), consistent with Ref. [32]'s hypothesis that Nipbl is involved in loop-extruding cohesin in vertebrates. A recent theoretical model of the molecular mechanism of loop extrusion by cohesin hypothesizes that transient binding by Mis4/Nipbl is essential for permitting directional reversals and therefore for two-sided loop extrusion [41]. Surprisingly, there are significant correlations between Mis4 and Pds5 in S. pombe (Supplementary Fig. 20E), indicating Pds5-Mis4 association, outside of the cohesin core complex."

    In response to Referee 2's specific comment that "at least two studies have raised concerns about Nibpl ChIP-seq results", we note (1) that, while Hu et al. Nucleic Acids Res 43:e132 2015 present a general method for calibrating ChIP-seq results, they do not measure Mis4/Nibpl ChIP-seq, nor do they raise any specific concerns about Mis4/Nipbl ChIP-seq, and (2) that (as noted above, in response to Referee 1's comment) while the FRAP analysis presented by Rhodes et al. eLife 6:e30000 indicates that, in HeLa cells, Nipbl has a residence time bound to cohesin of about 50 seconds, nevertheless, as shown in Supplementary Fig. 20G in the revised manuscript, there is a significant cross-correlation between the Nipbl ChIP-seq and Smc1 ChIP-seq in humans, indicating that a transient association between Nipbl and cohesin is detected by ChIP-seq, the referees' concerns notwithstanding.

    We thank the referee for pointing out Schwarzer et al. Nature 551:51 2017. However, our interpretation of these data is different than the referee's. As noted in our original manuscript, Nipbl has traditionally been considered to be a cohesin loading factor. If the role of Nipbl was solely to load cohesin, then we would expect that depleting Nipbl would have a major effect on the Hi-C map, because fewer cohesins are loaded onto the chromatin. Figure 2 of Schwarzer et al. Nature 551:51 2017, shows the effect of depleting Nibpl on a vertebrate Hi-C map. Even in this case when Nibpl is absent, this figure (Figure 2 of Schwarzer et al. Nature 551:51 2017) shows that TADs persist, albeit considerably attenuated. According to the authors' own analysis associated with Fig. 2 of their paper, these attenuated TADs correspond to a smaller number of loop-extruding cohesin complexes than in the presence of Nipbl. Since Nipbl is depleted, these loop-extruding cohesins necessarily cannot contain Nipbl. Thus, the data and analysis of Schwarzer et al. Nature 551:51 2017 actually seem consistent with the existence of a population of loop-extruding cohesin complexes that do not contain Nibpl.

    Concerning the referee's comment that we cannot be sure whether Pds5 ChIP is associated with extrusive or cohesive cohesin, we note that, as explained in the manuscript, we assume that the cohesive cohesins are uniformly distributed across the genome, and therefore that peaks in the cohesin ChIP-seq are associated with loop-extruding cohesins. The success of CCLE in describing Hi-C maps justifies this assumption a posteriori. Supplementary Figure 20B shows that the ChIP-seq of Pds5 is correlated with the ChIP-seq of Psc3 in S. pombe, that is, that peaks in the ChIP-seq of Psc3, assumed to derive from loop-extruding cohesin, are accompanied by peaks in the ChIP-seq of Pds5. This is the reasoning allowing us to associate Pds5 with loop-extruding cohesin in S. pombe.

    1. I suggest that the authors recalculate correlations for Hi-C maps using maps that are rescaled by the P(s) curves. As currently computed, most of the correlation between maps could arise from the characteristic decay of P(s) rather than smaller scale features of the contact maps. This could reduce the surprising observed correlation between distinct genomic regions in pombe (which, problematically, is higher than the observed correlation between simulation and experiment in cervisiae).

    Response:

    We thank the referee for this advice. Following this advice, throughout the revised manuscript, we have replaced our original calculation of the Pearson correlation coefficient of unscaled Hi-C maps with a calculation of the Pearson correlation coefficient of rescaled Hi-C maps. Since the MPR is formed from ratios of simulated to experimental Hi-C maps, this metric is unchanged by the proposed rescaling.

    As explained in the original manuscript, we attribute the lower experiment-simulation correlation in the meiotic budding yeast Hi-C maps to the larger statistical errors of the meiotic budding yeast dataset, which arises because of its higher genomic resolution - all else being equal we can expect 25 times the counts in a 10 kb x10 kb bin as in a 2 kb x 2 kb bin. For the same reason, we expect larger statistical errors in the mitotic budding yeast dataset as well. Lower correlations for noisier data are to be expected in general.

    *7. Please explain why the difference between right and left currents at any particular site, (R_n-L_n) / Rn+Ln, should be small. It seems easy to imagine scenarios where this might not be true, such as directional barriers like CTCF or transcribed genes. *

    __Response: __

    For simplicity, the present version of CCLE sets the site-dependent loop extrusion rates by assuming that the cohesin ChIP-seq signal has equal contributions from left and right anchors. Then, we carry out our simulations which subsequently allow us to examine the simulated left and right currents and their difference at every site. The distributions of normalized left-right difference currents are shown in Supplementary Figures 12B, 13B, and 14D, for interphase S. pombe, meiotic S. cerevisiae, and mitotic S. cerevisiae, respectively. They are all centered at zero with standard deviations of 0.12, 0.16, and 0.33. Thus, it emerges from our simulations that the difference current is indeed generally small.

    8. Optional, but I think would greatly improve the manuscript, but can the authors: a) analyze regions of high cohesin occupancy (assumed to be slow extrusion regions) to determine if there's anything special in these regions, such as more transcriptional activity

    __Response: __

    In response to Referee 1's similar comment, we have calculated the correlation between the locations of convergent genes and cohesin ChIP-seq. Supplementary Figure 18A in the revised manuscript shows that for interphase S. pombe no correlations are evident, whereas for both of meiotic and mitotic S. cerevisiae, there are significant correlations between these two quantities (Supplementary Fig. 17).

    *b) apply this methodology to vertebrate cell data *

    __Response: __

    The application of CCLE to vertebrate data is outside the scope of this paper which, as we have emphasized, has the goal of developing a model that can be robustly applied to non-vertebrate eukaryotic genomes. Nevertheless, CCLE is, in principle, applicable to all organisms in which loop extrusion by SMC complexes is the primary mechanism for chromatin spatial organization.

    1. *A Github link is provided but the code is not currently available. *

    __Response: __

    The code is now available.

    Minor Comments:

    1. Please state the simulated LEF lifetime, since the statement in the methods that 15000 timesteps are needed for equilibration of the LEF model is otherwise not meaningful. Additionally, please note that backbone length is not necessarily a good measure of steady state, since the backbone can be compacted to its steady-state value while the loop distribution continues to evolve toward its steady state.

    __Response: __

    The terminology "timesteps" used in the original manuscript in fact should mean "the number of LEF events performed" in the simulation. Therefore, we have changed the terminology from "timesteps" to "LEF events".

    The choice of 15000 LEF events is empirically determined to ensure that loop extrusion steady state is achieved, for the range of parameters considered. To address the referee's concern regarding the uncertainty of achieving steady state after 15000 LEF events, we compared two loop size distributions: each distribution encompasses 1000 data points, equally separated in time, one between LEF event 15000 and 35000, and the other between LEF event 80000 and 100000. The two distributions are within-errors identical, suggesting that the loop extrusion steady state is well achieved within 15000 LEF events.

    2. How important is the cohesive cohesin parameter in the model, e.g., how good are fits with \rho_c = 0?

    __Response: __

    As stated in the original manuscript, the errors on \rho_c on the order of 10%-20% (for S. pombe). Thus, fits with \rho_c=0 are significantly poorer than with the best-fit values of \rho_c.

    *3. A nice (but non-essential) supplemental visualization might be to show a scatter of sim cohesin occupancy vs. experiment ChIP. *

    __Response: __

    We have chosen not to do this, because we judge that the manuscript is already long enough. Figures 3A, 5D, and 6C already compare the experimental and simulated ChIP-seq, and these figures already contain more information than the figures proposed by the referee.

    1. *A similar calculation of Hi-C contacts based on simulated loop extruder positions using the Gaussian chain model was previously presented in Banigan et al. eLife 9:e53558 2020, which should be cited. *

    __Response: __

    We thank the referee for pointing out this citation. We have added it to the revised manuscript.

    1. It is stated that simulation agreement with experiments for cerevisiae is worse in part due to variability in the experiments, with MPR and Pearson numbers for cerevisiae replicates computed for reference. But these numbers are difficult to interpret without, for example, similar numbers for duplicate pombe experiments. Again, these numbers should be generated using Hi-C maps scaled by P(s), especially in case there are systematic errors in one replicate vs. another.

    __Response: __

    As noted above, throughout the revised manuscript, we now give the Pearson correlation coefficients of scaled-by-P(s) Hi-C maps.

    1. *In the model section, it is stated that LEF binding probabilities are uniformly distributed. Did the authors mean the probability is uniform across the genome or that the probability at each site is a uniformly distributed random number? Please clarify, and if the latter, explain why this unconventional assumption was made. *

    __Response: __

    It is the former. We have modified the manuscript to clarify that LEFs "initially bind to empty, adjacent chromatin lattice sites with a binding probability, that is uniformly distributed across the genome." (lines 587-588).

    *7. Supplement p4 line 86 - what is meant by "processivity of loops extruded by isolated LEFs"? "size of loops extruded by..." or "processivity of isolated LEFs"? *

    __Response: __

    Here "processivity of isolated LEFs" is defined as the processivity of one LEF without the interference (blocking) from other LEFs. We have changed "processivity of loops extruded by isolated LEFs" to "processivity of isolated LEFs" for clarity.

    1. The use of parentheticals in the caption to Table 2 is a little confusing; adding a few extra words would help.

    __Response: __

    In the revised manuscript, we have added an additional sentence, and have removed the offending parentheses.

    1. *Page 12 sentence line 315-318 is difficult to understand. The barrier parameter is apparently something from ref 47 not previously described in the manuscript. *

    __Response: __

    In the revised manuscript, we have removed mention of the "barrier parameter" from the discussion.

    1. *Statement on p14 line 393-4 is false: prior LEF models have not been limited to vertebrates, and the authors have cited some of them here. There are also non-vertebrate examples with extrusion barriers: genes as boundaries to condensin in bacteria (Brandao et al. PNAS 116:20489 2019) and MCM complexes as boundaries to cohesin in yeast (Dequeker et al. Nature 606:197 2022). *

    __Response: __

    In fact, Dequeker et al. Nature 606:197 2022 concerns the role of MCM complexes in blocking cohesin loop extrusion in mouse zygotes. Mouse is a vertebrate. The sole aspect of this paper, that is associated with yeast, is the observation of cohesin blocking by the yeast MCM bound to the ARS1 replication origin site, which is inserted on a piece of lambda phage DNA. No yeast genome is used in the experiment. Therefore, the referee is mistaken to suggest that this paper models yeast genome organization.

    We thank the referee for pointing out Brandao et al. PNAS 116:20489 2019, which includes the development of a tour-de-force model of condensin-based loop extrusion in the prokaryote, Bacillus subtilis, in the presence of gene barriers to loop extrusion. To acknowledge this paper, we have changed the objectionable sentence to now read (lines 571-575):

    "... prior LEF models have been overwhelmingly limited to vertebrates, which express CTCF and where CTCF is the principal boundary element. Two exceptions, in which the LEF model was applied to non-vertebrates, are Ref. [49], discussed above, and Ref. [76] (Brandao et al.), which models the Hi-C map of the prokaryote, Bacillus subtilis, on the basis of condensin loop extrusion with gene-dependent barriers."

    *Referees cross-commenting

    I agree with the comments of Reviewer 1, which are interesting and important points that should be addressed.

    *Reviewer #2 (Significance (Required)):

    Analytically approaching extrusion by treating cohesin translocation as a conserved current is an interesting approach to modeling and analysis of extrusion-based chromatin organization. It appears to work well as a descriptive model. But I think there are major questions concerning the mechanistic value of this model, possible applications of the model, the provided interpretations of the model and experiments, and the limitations of the model under the current assumptions. I am unconvinced that this analysis specifically is sufficient to demonstrate that extrusion is the primary organizer of chromatin on these scales; moreover, the need to demonstrate this is questionable, as extrusion is widely accepted, even if not universally so. It is also unclear that the minimal approach of the CCLE necessarily offers an improved physical basis for modeling extrusion, as compared to previous efforts such as ref 47, as claimed by the authors. There are also questions about significance due to possible limitations of the model (detailed above). Applying the CCLE model to identify barriers would be interesting, but is not attempted. Overall, the work presents a reasonable analytical model and numerical method, but until the major comments above are addressed and some reasonable application or mechanistic value or interpretation is presented, the overall significance is somewhat limited.*

    __Response: __

    We agree with the referee that analytically approaching extrusion by treating cohesin translocation as a conserved current is an interesting approach to modeling and analysis of extrusion-based chromatin organization. We also agree with the referee that it works well as a descriptive model (of Hi-C maps in S. pombe and S. cerevisiae). Obviously, we disagree with the referee's other comments. For us, being able to describe the different-appearing Hi-C maps of interphase S. pombe (Fig. 1 and Supplementary Figures 1-9), meiotic S. cerevisiae (Fig. 5) and mitotic S. cerevisiae (Fig. 6), all with a common model with just a few fitting parameters that differ between these examples, is significant and novel. The reviewer prematurely ignores the fact that there are still debates about whether "diffusion-capture"-like model is the more dominant mechanism that shape chromatin spatial organization at the TAD-scale. Many works have argued that such models could describe TAD-scale chromatin organization, as cited in the revised manuscript (Refs. [11, 14, 15, 17, 20, 22-24, 55]). However, in contrast to the poor description of the Hi-C map using diffusion capture model (as demonstrated in the revised manuscript and Supplementary Fig. 15), the excellent experiment-simulation agreement achieved by CCLE provides compelling evidence that cohesin-based loop extrusion is indeed the primary organizer of TAD-scale chromatin.

    Importantly, CCLE provides a theoretical base for how loop extrusion models can be generalized and applied to organisms without known loop extrusion barriers. Our model also highlights that (and provides means to account for) distributed barriers that impede but do not strictly block LEFs could also impact chromatin configurations. This case might be of importance to organisms with CTCF motifs that infrequently coincide with TAD boundaries, for instance, in the case of Drosophila melanogaster. Moreover, CCLE promises theoretical descriptions of the Hi-C maps of other non-vertebrates in the future, extending the quantitative application of the LEF model across the tree of life. This too would be highly significant if successful.

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    Referee #2

    Evidence, reproducibility and clarity

    Summary:

    Yuan et al. report on their development of an analytical model ("CCLE") for loop extrusion with genomic-position-dependent speed, with the idea of accounting for barriers to loop extrusion. They write down master equations for the probabilities of cohesin occupancy at each genomic site and obtain approximate steady-state solutions. Probabilities are governed by cohesin translocation, loading, and unloading. Using ChIP-seq data as an experimental measurement of these probabilities, they numerically fit the model parameters, among which are extruder density and processivity. Gillespie simulations with these parameters combined with a 3D Gaussian polymer model were integrated to generate simulated Hi-C maps and cohesin ChIP-seq tracks, which show generally good agreement with the experimental data. The authors argue that their modeling provides evidence that loop extrusion is the primary mechanism of chromatin organization on ~10-100 kb scales in S. pombe and S. cerevisiae.

    Major comments:

    1. I am unconvinced that this analysis specifically is sufficient to demonstrate that extrusion is the primary organizer of chromatin on these scales; moreover, the need to demonstrate this is questionable, as extrusion is widely accepted, even if not universally so. How is the agreement of CCLE with experiments more demonstrative of loop extrusion than previous modeling? Relatedly, similar best fit values for S. pombe and S. cerevisiae might not point to a mechanistic conclusion (same "underlying mechanism" of loop extrusion), but rather to similar properties for loop-extruding cohesins in the two species. As an alternative, could a model with variable binding probability given by ChIP-seq and an exponential loop-size distribution work equally well? The stated lack of a dependence on extrusion timescale suggests that a static looping model might succeed. If not, why not?
    2. I do not understand how the loop extrusion residence time drops out. As I understand it, Eq 9 converts ChIP-seq to lattice site probability (involving N_{LEF}, which is related to \rho, and \rho_c). Then, Eqs. 3-4 derive site velocities V_n and U_n if we choose rho, L, and \tau, with the latter being the residence time. This parameter is not specified anywhere and is claimed to be unimportant. It may be true that the choice of timescale is arbitrary in this procedure, but can the authors please clarify?
    3. The assumptions in the solution and application of the CCLE model are potentially constraining to a limited number of scenarios. In particular the authors specify that current due to binding/unbinding, A_n - D_n, is small. This assumption could be problematic near loading sites (centromeres, enhancers in higher eukaryotes, etc.) (where current might be dominated by A_n and V_n), unloading sites (D_n and V_{n-1}), or strong boundaries (D_n and V_{n-1}). The latter scenario is particularly concerning because the manuscript seems to be concerned with the presence of unidentified boundaries. This is partially mitigated by the fact that the model seems to work well in the chosen examples, but the authors should discuss the limitations due to their assumptions and/or possible methods to get around these limitations.
    4. Related to the above concern, low cohesin occupancy is interpreted as a fast extrusion region and high cohesin occupancy is interpreted as a slow region. But this might not be true near cohesin loading and unloading sites.
    5. The mechanistic insight attempted in the discussion, specifically with regard to Mis4/Scc2/NIPBL and Pds5, is problematic. First, it is not clear how the discussion of Nipbl and Pds5 is connected to the CCLE method; the justification is that CCLE shows cohesin distribution is linked to cohesin looping, which is already a questionable statement (point 1) and doesn't really explain how the model offers new insight into existing Nipbl and Pds5 data.

    Furthermore, I believe that the conclusions drawn on this point are flawed, or at least, stated with too much confidence. The authors raise the curious point that Nipbl ChIP-seq does not correlate well with cohesin ChIP-seq, and use this as evidence that Nipbl is not a part of the loop-extruding complex in S. pombe, and it is not essential in humans. Aside from the molecular evidence in human Nipbl/cohesin (acknowledged by authors), there are other reasons to doubt this conclusion. First, depletion of Nipbl (rather than binding partner Mau2 as in ref 55) in mouse cells strongly inhibits TAD formation (Schwarzer et al. Nature 551:51 2017). Second, at least two studies have raised concerns about Nibpl ChIP-seq results: 1) Hu et al. Nucleic Acids Res 43:e132 2015, which shows that uncalibrated ChIP-seq can obscure the signal of protein localization throughout the genome due to the inability to distinguish from background and 2) Rhodes et al. eLife 6:e30000, which uses FRAP to show that Nipbl binds and unbinds to cohesin rapidly in human cells, which could go undetected in ChIP-seq, especially when uncalibrated. It has not been shown that these dynamics are present in yeast, but there is no reason to rule it out yet.

    Similar types of critiques could be applied to the discussion of Pds5. There is cross-correlation between Psc3 and Pds5 in S. pombe, but the authors are unable to account for whether Pds5 binding is transient and/or necessary to loop extrusion itself or, more importantly, whether Pds5 ChIP is associated with extrusive or cohesive cohesins; cross-correlation peaks at about 0.6, but note that by the authors own estimates, cohesive cohesins are approximately half of all cohesins in S. pombe (Table 3).

    Due to the above issues, I suggest that the authors heavily revise this discussion to better reflect the current experimental understanding and the limited ability to draw such conclusions based on the current CCLE model.

    1. I suggest that the authors recalculate correlations for Hi-C maps using maps that are rescaled by the P(s) curves. As currently computed, most of the correlation between maps could arise from the characteristic decay of P(s) rather than smaller scale features of the contact maps. This could reduce the surprising observed correlation between distinct genomic regions in pombe (which, problematically, is higher than the observed correlation between simulation and experiment in cervisiae).
    2. Please explain why the difference between right and left currents at any particular site, (R_n-L_n) / Rn+Ln, should be small. It seems easy to imagine scenarios where this might not be true, such as directional barriers like CTCF or transcribed genes.
    3. Optional, but I think would greatly improve the manuscript, but can the authors: a) analyze regions of high cohesin occupancy (assumed to be slow extrusion regions) to determine if there's anything special in these regions, such as more transcriptional activity

    b) apply this methodology to vertebrate cell data

    1. A Github link is provided but the code is not currently available.

    Minor Comments:

    1. Please state the simulated LEF lifetime, since the statement in the methods that 15000 timesteps are needed for equilibration of the LEF model is otherwise not meaningful. Additionally, please note that backbone length is not necessarily a good measure of steady state, since the backbone can be compacted to its steady-state value while the loop distribution continues to evolve toward its steady state.
    2. How important is the cohesive cohesin parameter in the model, e.g., how good are fits with \rho_c = 0?
    3. A nice (but non-essential) supplemental visualization might be to show a scatter of sim cohesin occupancy vs. experiment ChIP.
    4. A similar calculation of Hi-C contacts based on simulated loop extruder positions using the Gaussian chain model was previously presented in Banigan et al. eLife 9:e53558 2020, which should be cited.
    5. It is stated that simulation agreement with experiments for cerevisiae is worse in part due to variability in the experiments, with MPR and Pearson numbers for cerevisiae replicates computed for reference. But these numbers are difficult to interpret without, for example, similar numbers for duplicate pombe experiments. Again, these numbers should be generated using Hi-C maps scaled by P(s), especially in case there are systematic errors in one replicate vs. another.
    6. In the model section, it is stated that LEF binding probabilities are uniformly distributed. Did the authors mean the probability is uniform across the genome or that the probability at each site is a uniformly distributed random number? Please clarify, and if the latter, explain why this unconventional assumption was made.
    7. Supplement p4 line 86 - what is meant by "processivity of loops extruded by isolated LEFs"? "size of loops extruded by..." or "processivity of isolated LEFs"?
    8. The use of parentheticals in the caption to Table 2 is a little confusing; adding a few extra words would help.
    9. Page 12 sentence line 315-318 is difficult to understand. The barrier parameter is apparently something from ref 47 not previously described in the manuscript.
    10. Statement on p14 line 393-4 is false: prior LEF models have not been limited to vertebrates, and the authors have cited some of them here. There are also non-vertebrate examples with extrusion barriers: genes as boundaries to condensin in bacteria (Brandao et al. PNAS 116:20489 2019) and MCM complexes as boundaries to cohesin in yeast (Dequeker et al. Nature 606:197 2022).

    Referees cross-commenting

    I agree with the comments of Reviewer 1, which are interesting and important points that should be addressed.

    Significance

    Analytically approaching extrusion by treating cohesin translocation as a conserved current is an interesting approach to modeling and analysis of extrusion-based chromatin organization. It appears to work well as a descriptive model. But I think there are major questions concerning the mechanistic value of this model, possible applications of the model, the provided interpretations of the model and experiments, and the limitations of the model under the current assumptions. I am unconvinced that this analysis specifically is sufficient to demonstrate that extrusion is the primary organizer of chromatin on these scales; moreover, the need to demonstrate this is questionable, as extrusion is widely accepted, even if not universally so. It is also unclear that the minimal approach of the CCLE necessarily offers an improved physical basis for modeling extrusion, as compared to previous efforts such as ref 47, as claimed by the authors. There are also questions about significance due to possible limitations of the model (detailed above). Applying the CCLE model to identify barriers would be interesting, but is not attempted. Overall, the work presents a reasonable analytical model and numerical method, but until the major comments above are addressed and some reasonable application or mechanistic value or interpretation is presented, the overall significance is somewhat limited.

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    Referee #1

    Evidence, reproducibility and clarity

    This manuscript presents a mathematical model for loop extrusion called the conserved-current loop extrusion model (CCLE). The model uses cohesin ChIP-Seq data to predict the Hi-C map and shows broad agreement between experimental Hi-C maps and simulated Hi-C maps. They test the model on Hi-C data from interphase fission yeast and meiotic budding yeast. The conclusion drawn by the authors is that peaks of cohesin represent loop boundaries in these situations, which they also propose extends to other organism/situations where Ctcf is absent.

    Major comments

    1. More recent micro-C/Hi-C maps, particularly for budding yeast mitotic cells and meiotic cells show clear puncta, representative of anchored loops, which are not well recapitulated in the simulated data from this study. However, such punta are cohesin-dependent as they disappear in the absence of cohesin and are enhanced in the absence of the cohesin release factor, Wapl. For example - see the two studies below. The model is therefore missing some key elements of the loop organisation. How do the authors explain this discrepency? It would also be very useful to test whether the model can predict the increased strength of loop anchors when Wapl1 is removed and cohesin levels increase.

    Costantino L, Hsieh TS, Lamothe R, Darzacq X, Koshland D. Cohesin residency determines chromatin loop patterns. Elife. 2020 Nov 10;9:e59889. doi: 10.7554/eLife.59889. PMID: 33170773; PMCID: PMC7655110. Barton RE, Massari LF, Robertson D, Marston AL. Eco1-dependent cohesin acetylation anchors chromatin loops and cohesion to define functional meiotic chromosome domains. Elife. 2022 Feb 1;11:e74447. doi: 10.7554/eLife.74447. Epub ahead of print. PMID: 35103590; PMCID: PMC8856730.

    1. Related to the point above, the simulated data has much higher resolution than the experimental data (1kb vs 10kb in the fission yeast dataset). Given that loop size is in the 20-30kb range, a good resolution is important to see the structural features of the chromosomes. Can the model observe these details that are averaged out when the resolution is increased?
    2. Transcription, particularly convergent has been proposed to confer boundaries to loop extrusion. Can the authors recapitulate this in their model?

    Minor comments

    1. In the discussion, the authors cite the fact that Mis4 binding sites do not give good prediction of the HI-C maps as evidence that Mis4 is not important for loop extrusion. This can only be true if the position of Mis4 measured by ChIP is a true reflection of Mis4 position. However, Mis4 binding to cohesin/chromatin is very dynamic and it is likely that this is too short a time scale to be efficiently cross-linked for ChIP. Conversely, extensive experimental data in vivo and in vitro suggest that stimulation of cohesin's ATPase by Mis4-Ssl3 is important for loop extrusion activity.
    2. Inclusion of a comparison of this model compared to previous models (for example bottom up models) would be extremely useful. What is the improvement of this model over existing models?

    Significance

    This simple model is useful to confirm that cohesin positions dictate the position of loops, which was predicted already and proposed in many studies. However, it should be considered a starting point as it does not faithfully predict all the features of chromatin organisation, particularly at better resolution. It will mostly be of interest to those in the chromosome organisation field, working in organisms or systems that do not have ctcf.

    This reviewer is a cell biologist working in the chromosome organisation field, but does not have modelling experience and therefore does not have the expertise to determine if the modelling part is mathematically sound and has assumed that it is.

  6. Version published to 10.1101/2023.10.05.560890v3 on bioRxiv
  7. Version published to 10.1101/2023.10.05.560890v2 on bioRxiv
  8. Version published to 10.1101/2023.10.05.560890v1 on bioRxiv