Connecting Chromatin Structures to Gene Regulation Using Dynamic Polymer Simulations
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eLife assessment
This paper presents a valuable optimization algorithm for determining the spatio-temporal organization of chromatin. The algorithm identifies the polymer model that best fits population averaged Hi-C data and makes predictions about the spatio-temoral organization of specific genomic loci such as the oncogenic Myc locus. While the algorithm will be of value to biologists and physicists working in the field of genome organization, the provided methodological details and evidence are incomplete to fully substantiate the conclusions. In particular, the following would be beneficial: analysis of single-cell data, the inclusion of loci beyond Myc, testing the dependence of results on the chosen parameters, providing more details on CTCF occupancy at loop anchors, and better substantiating the claim about predictions of single-cell heterogeneity.
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Abstract
The transfer of regulatory information between distal loci on chromatin is thought to involve physical proximity, but key biophysical features of these contacts remain unclear. For instance, it is unknown how close and for how long two loci need to be in order to productively interact. The main challenge is that it is currently impossible to measure chromatin dynamics with high spatiotemporal resolution at scale. Polymer simulations provide an accessible and rigorous way to test biophysical models of chromatin regulation, yet there is a lack of simple and general methods for extracting the values of model parameters. Here we adapt the Nelder-Mead simplex optimization algorithm to select the best polymer model matching a given Hi-C dataset, using the MYC locus as an example. The model’s biophysical parameters predict a compartmental rearrangement of the MYC locus in leukemia, which we validate with single-cell measurements. Leveraging trajectories predicted by the model, we find that loci with similar Hi-C contact frequencies can exhibit widely different contact dynamics. Interestingly, the frequency of productive interactions between loci exhibits a non-linear relationship with their Hi-C contact frequency when we enforce a specific capture radius and contact duration. These observations are consistent with recent experimental observations and suggest that the dynamic ensemble of chromatin configurations, rather than average contact matrices, is required to fully predict long-range chromatin interactions.
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Author response:
eLife assessment
This paper presents a valuable optimization algorithm for determining the spatio-temporal organization of chromatin. The algorithm identifies the polymer model that best fits population averaged Hi-C data and makes predictions about the spatio-temoral organization of specific genomic loci such as the oncogenic Myc locus. While the algorithm will be of value to biologists and physicists working in the field of genome organization, the provided methodological details and evidence are incomplete to fully substantiate the conclusions. In particular, the following would be beneficial: analysis of single-cell data, the inclusion of loci beyond Myc, testing the dependence of results on the chosen parameters, providing more details on CTCF occupancy at loop anchors, and better substantiating the claim about …
Author response:
eLife assessment
This paper presents a valuable optimization algorithm for determining the spatio-temporal organization of chromatin. The algorithm identifies the polymer model that best fits population averaged Hi-C data and makes predictions about the spatio-temoral organization of specific genomic loci such as the oncogenic Myc locus. While the algorithm will be of value to biologists and physicists working in the field of genome organization, the provided methodological details and evidence are incomplete to fully substantiate the conclusions. In particular, the following would be beneficial: analysis of single-cell data, the inclusion of loci beyond Myc, testing the dependence of results on the chosen parameters, providing more details on CTCF occupancy at loop anchors, and better substantiating the claim about predictions of single-cell heterogeneity.
Public Reviews:
Reviewer #1 (Public Review):
Summary:
The authors of this study aim to 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 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 will showcase side-by-side comparisons of the fitting results obtained using these different metrics in an upcoming version of the preprint.
(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 will include a supplementary table in the upcoming revised preprint 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) will be added to figure 2 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 will be clarified in the upcoming revised preprint.
(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 will simulate a locus matching that of (Mach et al. 2022) in the upcoming revised preprint, and test the sensitivity of contact frequency and duration to in silico cohesin knock-down. This will also serve to extend the generality of our conclusions to different categories of genomic architectures, and the text will be clarified accordingly.
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. We will include a brief discussion of the potential of single-cell architectures in an upcoming version of the manuscript.
(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 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 will add to the upcoming revised preprint a demonstration of the simulation fitting to other loci acquired in different cell types.
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eLife assessment
This paper presents a valuable optimization algorithm for determining the spatio-temporal organization of chromatin. The algorithm identifies the polymer model that best fits population averaged Hi-C data and makes predictions about the spatio-temoral organization of specific genomic loci such as the oncogenic Myc locus. While the algorithm will be of value to biologists and physicists working in the field of genome organization, the provided methodological details and evidence are incomplete to fully substantiate the conclusions. In particular, the following would be beneficial: analysis of single-cell data, the inclusion of loci beyond Myc, testing the dependence of results on the chosen parameters, providing more details on CTCF occupancy at loop anchors, and better substantiating the claim about predictions of …
eLife assessment
This paper presents a valuable optimization algorithm for determining the spatio-temporal organization of chromatin. The algorithm identifies the polymer model that best fits population averaged Hi-C data and makes predictions about the spatio-temoral organization of specific genomic loci such as the oncogenic Myc locus. While the algorithm will be of value to biologists and physicists working in the field of genome organization, the provided methodological details and evidence are incomplete to fully substantiate the conclusions. In particular, the following would be beneficial: analysis of single-cell data, the inclusion of loci beyond Myc, testing the dependence of results on the chosen parameters, providing more details on CTCF occupancy at loop anchors, and better substantiating the claim about predictions of single-cell heterogeneity.
-
Reviewer #1 (Public Review):
Summary:
The authors of this study aim to 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 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 …
Reviewer #1 (Public Review):
Summary:
The authors of this study aim to 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 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?
(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. Science (2018) and Takei et al. Science (2021)).
(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.
(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.
(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,.
(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?
-
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: …
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.
(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.
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