Connecting Chromatin Structures to Gene Regulation Using Dynamic Polymer Simulations

Reviewer #1 (Public review):

Summary:

The authors of this study use an optimization algorithm approach, based on the established Nelder-Mead method, to infer polymer models that best match input bulk Hi-C contact data. The procedure infers the best parameters of a generic polymer model that combines loop-extrusion (LE) dynamics and compartmentalisation of chromatin types driven by weak biochemical affinities. Using this and DNA FISH, the authors investigate the chromatin structure of the MYC locus in leukaemia cells, showing that loop extrusion alone cannot explain local pathogenic chromatin rearrangements. Finally, they study the locus single-cell heterogeneity and time dynamics.

In the revised manuscript the authors have adequately addressed my questions and comments. The exception concerns point #5 of my original review:

(5) Besides cumulative probability distributions, I asked the authors to show the TAD2-TAD4 (model vs. exp) distances in Fig. 3c as relative frequency histograms. This allows readers to more accurately evaluate whether model and experimental distributions have same shape and variance.

Author response:

The following is the authors’ response to the original reviews.

Public Reviews:

Reviewer #1 (Public Review):

Summary:

The authors of this study aim to use an optimization algorithm approach, based on the established NelderMead method, to infer polymer models that best match input bulk Hi-C contact data. The procedure infers the best parameters of a generic polymer model that combines loop-extrusion (LE) dynamics and compartmentalization of chromatin types driven by weak biochemical affinities. Using this and DNA FISH, the authors investigate the chromatin structure of the MYC locus in leukemia cells, showing that loop extrusion alone cannot explain local pathogenic chromatin rearrangements. Finally, they study the locus single-cell heterogeneity and time dynamics.

Strengths:

- The optimization method provides a fast computational tool that speeds up the parameter search of complex chromatin polymer models and is a good technical advancement.

- The method is not restricted to short genomic regions, as in principle it can be applied genome-wide to any input Hi-C dataset, and could be potentially useful for testing predictions on chromatin structure.

Weaknesses:

(1) The optimization is based on the iterative comparison of simulated and Hi-C contact matrices using the Spearman correlation. However, the inferred set of the best-fit simulation parameters could sensitively depend on such a specific metric choice, questioning the robustness of the output polymer models. How do results change by using different correlation coefficients?

This is an important question. We have tested several metrics in the process of building the fitting procedure. We now showcase side-by-side comparisons of the fitting results obtained using these different metrics in supplementary figure 2.

(2) The best-fit contact threshold of 420nm seems a quite large value, considering that contact probabilities of pairs of loci at the mega-base scale are defined within 150nm (see, e.g., (Bintu et al. 2018) and (Takei et al. 2021)).

This is a good point. Unfortunately, there is no established standard distance cutoff to map distances to Hi-C contact frequency data. Indeed, previous publications have used anywhere between 120 nm to 500 nm (see e.g. (Cardozo Gizzi et al. 2019), (Cattoni et al. 2017) , (Mateo et al. 2019), (Hafner et al. 2022), (Murphy and Boettiger 2022), (Takei et al. 2021), (Fudenberg and Imakaev 2017) , (Wang et al. 2016), (Su et al. 2020), (Chen et al. 2022), (Finn et al. 2019)).

We have included a supplementary table in the revised preprint (supplementary table 3) listing these values to demonstrate the lack of consensus. This large variation could reflect different chromatin compaction levels across distinct model systems, and different spatial resolutions in DNA FISH experiments performed by different labs. The variance in the threshold choice is also likely partially explained by Hi-C experimental details, e.g. the enzyme used for digestion, which biases the effective length scale of interactions detected (Akgol Oksuz et al. 2021). Among commonly used restriction enzymes, HindIII has a relatively low cutting frequency which results in a lower sensitivity to short-range interactions; on the other hand, MboI has a higher cutting frequency which results in a higher sensitivity to short-range interactions (Akgol Oksuz et al. 2021). Because the Hi-C data we used for the Myc locus in (Kloetgen et al. 2020) was generated using HindIII, we chose a distance cutoff close to the larger end of published values (420 nm).

(3) In their model, the authors consider the presence of LE anchor sites at Hi-C TAD boundaries. Do they correspond to real, experimentally found CTCF sites located at genomic positions, or they are just assumed? A track of CTCF peaks of the considered chromatin loci would be needed.

We apologize this was not clear. The LE anchor sites in the simulation model were chosen because they correspond to experimental CTCF sites and ChIP-seq peaks located at the corresponding genomic positions. Representative CTCF ChIP-seq tracks from (Kloetgen et al. 2020) have been added to figure 2A in the revised preprint version to emphasize this point.

(4) In the model, each TAD is assigned a specific energy affinity value. Do the different domain types (i.e., different colors) have a mutually attractive energy? If so, what is its value and how is it determined? The simulated contact maps (e.g., Figure 2C) seem to allow attractions between different blocks, yet this is unclear.

Sorry this was not explicit. The attraction energy between a pair of monomers in the simulation is determined using the geometric mean of the affinities of the two monomers. This applies to both monomers within the same domain and in different domains. This detail has been clarified in the Methods section: “To optimize the simulation duration to streamline the parameter search (Supp. Fig. 1 B), we computed the autocorrelation function of the TAD2-TAD4 inter-TAD distance using the initial guess simulation parameters of the MYC locus in CUTLL. The simulation was saved every 5 simulation blocks.”

(5) To substantiate the claim that the simulations can predict heterogeneity across single cells, the authors should perform additional analyses. For instance, they could plot the histograms (models vs. experiments) of the TAD2-TAD4 distance distributions and check whether the models can recapitulate the FISH-observed variance or standard deviation. They could also add other testable predictions, e.g., on gyration radius distributions, kurtosis, all-against-all comparison of single-molecule distance matrices, etc,.

We agree that heterogeneity prediction is a key advantage of the simulations. We do note that the histograms (models vs. experiments) of the TAD2-TAD4 distance distributions measured by FISH were plotted in Fig. 3C as empirical cumulative probability distributions (as is standard in the field), side by side with the simulation predictions. Simulations indeed recapitulate the variance observed by FISH. We also had emphasized this important point in the main text: “Importantly, not just the average distances, but the shape of the distance distribution across individual cells closely matches the predictions of the simulations in both cell types, further confirming that the simulations can predict heterogeneity across cells.”

(6) The authors state that loop extrusion is crucial for enhancer function only at large distances. How does that reconcile, e.g., with Mach et al. Nature Gen. (2022) where LE is found to constrain the dynamics of genomically close (150kb) chromatin loci?

This is an interesting question. In (Mach et al. 2022), the authors tracked the physical distance between two fluorescent labels positioned next to either anchor of a ~150 kb engineered topological domain using live-cell imaging. They found that abrogation of the loop anchors by ablation of the CTCF binding motifs, or knock-down of the cohesin subunit Rad21 resulted in increased physical distance between the loci. HMM Modeling of the distance over time traces suggests that the increased distance resulted from rarer and shorter contacts between the anchors. While this might seem at odds with the results of Fig. 4L, we note a key difference between the loci. While (Mach et al. 2022) observed the dynamics of the distance separating two CTCF loop anchors, in our model only the MYC promoter is proximal to a loop anchor, while the position of the second locus is varied, but remains far from the other anchor. The deletion of the CTCF sites at both anchors in (Mach et al. 2022) indeed results in a lowered sensitivity of the physical distance to Rad21 knock-down, reminiscent of the results of Fig. 4L in our work. This result demonstrates that loop extrusion disruption disproportionately impacts distances between loci close to loop anchors, consistent with Hi-C results (Rao et al. 2017; Nora et al. 2017). We therefore believe that the models in our work and (Mach et al. 2022) are not at odds, but simply reflect that loop extrusion perturbations impact distances between loop anchors the most. Enhancer-Promoter loops are generally distinct from CTCF-mediated loops (Hsieh et al. 2020, 2022). While (Mach et al. 2022) represents a landmark study in our understanding of the dynamics of genomic folding by loop extrusion, we therefore believe that the locus we chose here - which matches the endogenous MYC architecture - may more accurately represent Enhancer-Promoter dynamics than a synthetic CTCF loop. To better articulate the similarities between model predictions and differences between the two loci, we have simulated a synthetic locus matching that of (Mach et al. 2022) in the revised preprint. Our simulation recapitulates the results obtained by Mach et al, including the sensitivity of contact frequency and duration to in silico cohesin knock-down (supplementary figure 6). We have updated the Results section accordingly: “The dependence of contact dynamics on loop extrusion in our simulations of MYC differs from that previously observed for two TAD boundaries (45). To check whether the different results are the product of different simulation models, we simulated contact dynamics across two TAD boundaries matching the locus of (45). Our simulations recapitulate the distance distribution and loop extrusion dependence previously observed (Supp. Fig. 6), establishing that the differences between the two systems are biological. While loop extrusion controls both the frequency and duration of contacts at TAD boundaries, it exerts a more nuanced effect on the frequency of contacts in loci pairs like the MYC locus that might better reflect typical enhancer-promoter pairs.”

Reviewer #2 (Public Review):

Summary:

The authors Fu et al., developed polymer models that combine loop extrusion with attractive interactions to best describe Hi-C population average data. They analyzed Hi-C data of the MYC locus as an example and developed an optimization strategy to extract the parameters that best fit this average Hi-C data.

Strengths:

The model has an intuitive nature and the authors masterfully fitted the model to predict relevant biology/Hi-C methodology parameters. This includes loop extrusion parameters, the need for self-interaction with specific energies, and the time and distance parameters expected for Hi-C capture.

Weaknesses:

(1) We are no longer in the age in which the community only has access to population average Hi-C. Why was only the population average Hi-C used in this study?

Can single-cell data: i.e. single-cell Hi-C/Dip-C data or chromatin tracing data (i.e. see Tan et al Science 2018 - for Dip-C, Bintu et al Science 2018, Su et al Cell 2020 for chromatin tracing, etc.) or even 2 color DNA FISH data (used here only as validation) better constrain these models? At the very least the simulations themselves could be used to answer this essential question.

I am expecting that the single-cell variance and overall distributions of distances between loci might better constrain the models, and the authors should at least comment on it.

We agree that it is possible to recapitulate single-cell Hi-C or chromatin tracing data with simulations, and that these data modalities have a superior potential to constrain polymer models because they provide an ensemble of single allele structures rather than population-averaged contact frequencies. However, these data remain out of reach for most labs compared to Hi-C. Our goal with this work was to provide an approachable method that anyone interested could deploy on their locus of choice, and reasoned that Hi-C currently remains the data modality available to most. We envision this strategy will help reach labs beyond the small number of groups expert in single cell chromatin architecture, and thus hopefully broaden the impact of polymer simulations in the chromatin organization field.

Nevertheless, we do agree that the comparison of single-cell chromatin architectures to simulations is a fertile ground for future studies, and have modified the preprint accordingly (Discussion):

“Future work extending this framework to single cell readouts out chromatin architecture (e.g. single-cell Hi-C or chromatin tracing) holds promise to further constrain chromatin models.”

(2) The authors claimed "Our parameter optimization can be adapted to build biophysical models of any locus of interest. Despite the model's simplicity, the best-fit simulations are sufficient to predict the contribution of loop extrusion and domain interactions, as well as single-cell variability from Hi-C data. Modeling dynamics enables testing mechanistic relationships between chromatin dynamics and transcription regulation. As more experimental results emerge to define simulation parameters, updates to the model should further increase its power." The focus on the Myc locus in this study is too narrow for this claim. I am expecting at least one more locus for testing the generality of this model.

We note that we used two distinct loci in the initial version of our study, the MYC locus in leukemia vs T cells (Figs. 2-3) and a representative locus in experiments comparing WT CTCF with a mutant that leads to loss of a subset of CTCF binding sites (Fig. 1L). To further demonstrate generality, we have added to the revised preprint a demonstration of the simulation fitting to other loci acquired in different cell types (supplementary figure 3).

Recommendations for the authors:.

Reviewer #1 (Recommendations For The Authors):

(1) The Methods part of the imaging analysis lacks some quantitative details that could be useful for the readers: what is the frequency of double detections? How "small" is the 3D region around the centroid? How many cells with no spots or more than four spots are excluded?

We have clarified these important analysis parameters in the revised version of the preprint (Methods), including supplementary Table 2, listing the statistics of excluded cells:

“We then cropped out a small 3D region (20x20x10 pixels) around each approximate centroid, and subtracted the surrounding background intensity.”

“Cells with no spots or more than four spots were excluded from the cell cycle analysis (statistics in Supp. Table 2).”

(2) How is the autocorrelation function of chromatin structures computed?

We computed the autocorrelation function of the TAD2-TAD4 inter-TAD distance using the initial guess simulation parameters (Eattr, boundary permeabilities) of the MYC locus in CUTLL. All other simulation parameters are the same as other simulations in the preprint. The structure of the locus was saved every 5 simulation blocks. These structures were used to compute the TAD2-TAD4 inter-TAD distance as a function of time, which was used to calculate the autocorrelation function. This has been clarified in the revised version of the preprint (Methods):

“To optimize the simulation duration to streamline the parameter search (Supp. Fig. 1 B), we computed the autocorrelation function of the TAD2-TAD4 inter-TAD distance using the initial guess simulation parameters of the MYC locus in CUTLL. The simulation was saved every 5 simulation blocks.”

(3) How is the monomer length (35nm) chosen to best compare FISH data?

Because monomer length is difficult to derive from first principles, the standard in the field is to convert the size of a simulated monomer into a physical distance using a reference measurement in the system of choice. Similar to the Hi-C distance threshold, values for monomer size vary throughout the literature, e.g. 53 nm per 3 kbp monomer (Giorgetti et al. 2014), 50 nm per 2.5 kbp monomer (Nuebler et al. 2018), or from 36 to 60 nm per 3 kbp monomer, depending on the cell line or model details (Conte et al. 2022; Conte et al. 2020).

Here we used the mean of the median TAD2-TAD4 distances in T Cells and CUTLL as our length reference, and converted simulation distances into nm by matching this value. We obtained 35 nm per 2.5 kbp monomer, a value well within the range of the literature values (see above).

Using this simple conversion, the simulated distance distributions recapitulate two independent metrics accessible by DNA FISH: the shift in median distances between T cell and CUTLL, and the width of each distribution. This agreement indicates that simulations recapitulate both the differences between the two cell types, and the single cell heterogeneity within each cell type.

(4) The main text does not make clear the "known" biophysical parameters that establish the model ground truth.

In the initial validation of the fitting procedure, by “known biophysical parameters”, we meant that we generated simulated Hi-C maps in which we set the left/right permeabilities at each boundary, and Eattr values within each TAD to known values. We then assessed how well the fitting could recover these known ground truth values by trying to match the simulated representative Hi-C map. The specific values chosen are plotted for each set of simulations in Fig.1 F, H, J. The main text has been made more explicit in the revised preprint version (Results):

“We first validated the optimization method using ground truth maps built from simulation runs with known values of StallL, StallR, Eattr for each boundary/domainbiophysical parameters.”

(5) What are the correlation coefficients between experimental and model contact maps in Figure 1L?

We apologize for the oversight. The missing coefficient values have been added in the revised version of the manuscript (Results):

“As expected, the simulation predicted a significant drop of 0.13 in boundary permeability in CTCFmut compared to WT (Fig. 1 L; Spearman Correlation: 0.85±0.02 for CTCFmut, 0.82±0.01 for WT).”

(6) Figure 2A, B: Contact matrices look oversaturated. Next, why do model contact maps have negative values?

We apologize this was not clear. Figure 2 A,B plotted the log value of the contact matrices, thus the negative values. This has been made explicit in the revised version of the preprint (Fig. 2 Legend).

(7) For model reproducibility, the authors could report the coordinates of the Hi-C TAD boundaries employed for the model.

We have included in the revised version of the preprint an explicit mention of all genomic coordinates of the loci simulated in the Methods section:

“The model used to fit into MYC Hi-C data consists of 1920 monomers representing chr8:126,720,000131,680,000, with the TAD boundaries located at monomer 456 (chr8: 127,840,000 - 127,880,001), monomer

808 (chr8: 128,720,000 - 128,760,001), monomer 1178 (chr8: 130,160,000 - 130,200,001) and monomer 1592 (chr8: 130,680,000 - 130,720,001).”

(8) What is the shaded area in Figure 3C?

The shaded area in Figure 3C is the standard deviation calculated from three independent DNA FISH or simulation replicates for each bin of the histogram. This detail has been clarified in the revised preprint (Figure 3 legend).

(9) In the Discussion, I suggest changing as follows: "the time- and distance-gated model proposed here recapitulates several observations" -> "the time- and distance-gated model proposed here could recapitulate several observations", as they are speculations.

The sentence has been changed accordingly in the revised preprint (Discussion). Thank you for the suggestion.

Reviewer #2 (Recommendations For The Authors):

Suggest analyzing the ability of single-cell data to better constrain dynamical models.

While we agree that modeling single-cell distributions is a worthwhile endeavor to be explored in future work, we believe that the tool presented here serves a slightly different purpose: enabling labs that only have access to the most widespread technique at present to perform simulations to interrogate the forces that shape the organization of an arbitrary locus in their model of choice. Analyzing single-cell data is in principle very powerful, but would by necessity be limited to the small number of systems where these cutting-edge techniques have been deployed.

Suggest selecting another locus other than MYC to demonstrate generality.

We note that we used two distinct loci in the study, the MYC locus in leukemia vs. T cells (Figs. 2-3) and a representative locus in experiments comparing WT CTCF with a mutant that leads to loss of a subset of CTCF binding sites (Fig. 1L). To further demonstrate generality, we have added to the revised preprint a demonstration of the simulation fitting to other loci acquired in different cell types (supplementary figure 3).

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