Techniques and Challenges in Reconstructing 3D Genome Structures from 2D Chromosome Conformation Capture Data

Abstract

Chromosome conformation capture technologies that provide frequency information for contacts between genomic regions have been crucial for increasing our understanding of genome folding and regulation. However, such data do not provide direct evidence on the spatial 3D organization of chromatin. In this opinion article, we discuss the development and application of computational methods to reconstruct chromatin 3D structures from experimental 2D contact data, highlighting how such modeling provides biological insights and can suggest mechanisms anchored to experimental data. By applying different reconstruction methods to the same contact data, we illustrate some state-of-the-art of these techniques and discuss our gene resolution approach based on Brownian dynamics and Monte Carlo sampling.

1. Introduction

Since its introduction in 2002 [1], Chromosome Conformation Capture (3C) techniques have grown exponentially. Indeed, as we found in the Scopus database, a total of 3,558 articles containing the term “Chromosome Conformation Capture” or “Hi-C” in their title, abstract, or keywords (similar to the search we reported in our review [2]) have been published since 2002. Such 3C methods for mapping the genome 3D architecture have contributed to our knowledge of how chromosomes are positioned and folded within the cell nucleus, and how this folding and spatial organization regulates gene expression [3]. For example, early 3C experiments revealed that genomic compartments of active and inactive chromatin are organized based on epigenetic marks [4], CTCF mediates loop formation [5], and the genome is organized in topologically associated domains (TADs) [6, 7, 8].

Although 3C methods provide information on the contact frequencies associated with pairs of genomic regions, they do not describe chromosome three-dimensional spatial information directly. Thus, translating these contact frequencies into tertiary structures is a separate process.

Because many 3D structures can map onto the same contact map, the mathematical problem of deriving structures from 2D contact data is not uniquely solvable. Over the past few years, advances in both physical and statistical models have led to the development of many techniques that attempt to bridge the gap between 3C contact maps and genomic conformations [9, 10, 11, 12]. Such modeling not only allows for visualization of the experimental data; it also provides insights into genome structure-function relationships, including proposed and testable mechanisms [13, 14].

In this opinion, we discuss the different modeling approaches for reconstructing 3D genome structures from experimental 2D contact data, highlighting how modeling helps relate frequency patterns among DNA regions to the 3D organization of the genome to provide mechanistic insights. We also illustrate different aspects of reconstruction algorithms by presenting 3D structures from the same contact map using different methods. We conclude with future prospects and direction.

2. Techniques for 3D structure reconstruction

Techniques for structure reconstruction can be categorized as physics-based and knowledge-based.

Knowledge-based methods apply machine learning trained with Hi-C contact data and other bioinformatics data to predict spatial properties, such as promoter-enhancer interactions [15], loops [16], many-body chromatin interactions [17], and contact probabilities [18, 19]. However, such methods do not necessarily generate tangible 3D models. More details on their implementation and use can be found in [11].

Physics-based methods use physical assumptions about the structures which are treated as beads and spring models. In this section, we focus on physics-based models, describing the reconstruction procedure and discussing what types of methods are available in each step (Figure 1). The final combination of approaches used for each step defines the reconstruction method. Of course, various ways to categorize reconstruction methods are possible.

Figure 1:

General workflow of 3D structure reconstruction from Hi-C maps. Input Data: the input for reconstruction is an averaged or single cell Hi-C contact map. Some methods also integrate extra data like Chip-seq or FISH to increase the accuracy. Correction: Normalization can be introduced to remove technical biases. Probability-based methods use probability terms to understand the uncertainties present in the experimental Hi-C data. Conversion: Distance-based techniques use an inverse relationship between the frequencies of interactions between two genomic loci and their corresponding spatial distances in 3D space. Contact-based techniques employ Hi-C contacts as restraints for modeling, often by introducing hypothetical bonds between the restrained loci. Model: The analytical model is usually applied by the distance-based method using distance matrices. Distance or contact matrices can also be used as restraints during the simulation of 3D structures with Monte Carlo, Brownian Dynamics, or other techniques until the convergence condition is satisfied. Output Structures: Consensus methods generate a single structure from ensemble Hi-C data. Resampling methods generate an ensemble of structures that satisfy the distance matrices converted from Hi-C data. Population-based methods generate a population of individual structures from ensemble Hi-C data. Validation: The correlation between experimental frequency or distance-based contact maps and the computed contact maps from the reconstructed structures can be assessed by calculating Pearson (PCC) or Spearman (SCC) correlation coefficients. Low resolution (i.e., FISH and soft X-Ray tomography) or high resolution (i.e., STORM) microscopy structures can also be compared with the reconstructed structures.

Data input.

The input for reconstruction can be a cell-averaged or single-cell Hi-C contact map, in which each {i,j} data point represents the average frequency or the presence of a contact between regions i and j. Some methods also incorporate additional information, such as Chip, RNA, or DNase-seq data to incorporate positional constraints that describe interaction of the genome with nuclear elements, like for example, the nuclear lamin [20], or information on chromatin accessibility [21**] [22*].

Data correction.

Raw Hi-C data are subject to technical biases and noise from various sources, such as PCR amplification, DNA fragmentation, and sequencing errors. As shown in Figure 1, Correction panel, normalization is often used to remove biases introduced by experimental procedures so that the interaction frequencies can be preserved as much as possible. For example, iterative correction and eigenvector decomposition (ICE) [23] is an iterative method that normalizes matrices by assuming that all loci are equally characterizable, and the sequential component normalization (SCN) [24] method performs sequential matrix normalization in a column by column way. See [25, 26, 27, 28] for more examples of normalization techniques, and [29] for a review comparing different normalization methods. Probability-based methods like MCMC5C [30] and SIMBA3D [31] can treat the problem as a Bayesian inference or a maximum likelihood problem and weigh contact values differently depending on data reliability. Other methods infer the “missing data” using the ‘shortestpath’ equivalence [32] in which map data points are treated as weighted edges in a graph and each missing edge weight is replaced with the smallest possible sum of weights traversing the graph along the observed edges.

Data conversion.

Typically, distance-based techniques use an inverse relationship for the frequencies of interactions between two genomic loci, f_ij, and their corresponding spatial distances in 3D space, d_ij. This relationship is defined as $d_{ij}\propto 1/f_{ij}^{\alpha }$, where the parameter α accounts for the genomic distance and resolution of the Hi-C map. Through this conversion process, distance-based methods enable the reconstruction of 3D structures from Hi-C data by inferring spatial distances between genomic loci based on their frequency of interactions. However, limitations exist, for example, handling zero as non-zero denominators when dealing with sparse matrices to avoid overflow. In addition, some distance-based methods, e.g., ShNeigh [33*], calculate the eigenvalues of a matrix derived from the distance matrix, so this matrix must be non-negative (i.e., have all eigenvalues non negative eigenvalues). As a result, not all Hi-C data can be reconstructed with a distance-based conversion without further approximations.

Examples of distance-based methods include the recent 3DMax [34], EVR [35*], ShNeigh [33*], Hierarchical3DGenome [36], ParticleChromo3D [37*], MiOS [21**], TADdyn [38**], and FLAMINGO [22*]. Distance-based methods are relatively simple to implement and interpret, and are computationally efficient. However, they work poorly on single-cell Hi-C or high-resolution Hi-C data due to matrix sparsity.

Contact-based techniques, on the other hand, infer genomic loci spatial proximity and relative positioning within the chromatin structure by employing Hi-C contacts as restraints for modeling, often introduced with hypothetical bonds between the restrained loci. An advantage is that theses methods can deal with large-scale structures when optimization techniques are used for the reconstruction procedure. However, contact-based methods can be difficult to implement when combined with dynamic sampling approaches (mentioned below), which are computationally intense and dependent on system setup. Chrom3D [20], GEM [39], GEM-FISH [40], 4DHiC [41**], and Hi-BDiSCO [42**] all belong to this contact-based category.

Both distance and contact-based methods can integrate multiple types of data, which improves the accuracy of 3D reconstructions. For example, ChIP-seq can be incorporated to consider epigenetic modifications or protein binding [42**], FISH data can be introduced to include chromosomal radii of gyration [40], or DNase-seq supplemented to consider chromatin accessibility [22*].

3D Model.

The 3D reconstruction is then employed by analytical (closed-form) formulations or by simulations. The analytical model usually applies to distance-based methods. The Multidimensional Scaling method (MDS) is widely used for analytical reconstructions as it can translate pairwise distances among a set of n objects onto a configuration of n points mapped into an abstract Cartesian space.

When simulations are used instead, they usually start with random structures, incorporate distance or contact matrices as restraints, and use sampling by Monte Carlo, Brownian Dynamics, Langevin Dynamics, or optimization until a converged state or termination criterion is reached.

Output Structures.

Depending on the final number of structures obtained from the reconstruction and how these structures are generated, techniques for 3D structure reconstruction can be categorized into consensus methods, resampling methods, and population-based methods [43].

Consensus methods apply a scoring scheme to identify common features among different 3D models and produce a consensus structure that maximizes the agreement among them [44, 45]. These popular methods can improve the accuracy and robustness of 3D reconstructions from Hi-C data. However, they require careful application of weighting and integration schemes to ensure that the final structure is not biased.

Resampling methods generate a set of diverse 3D models that represent different conformations of the genome structure [46]. These methods recognize the inherent heterogeneity and variability of the Hi-C data and aim to sample the conformational space more comprehensively to improve the coverage of the true structure. In this way, they produce an ensemble of structures that reflects different possible states of chromatin. Ensemble methods can capture the dynamic and heterogeneous nature of the chromatin structure. However, they pose challenges in terms of the interpretation of the large ensemble of structures; they also require some validation to ensure realistic results.

Population-based methods infer the distribution of chromatin conformations in a cell population while reflecting the contact data of individual cells [47]. These methods recognize that the chromatin structure can be highly variable and dynamic among individual cells, and aim to capture the heterogeneity of the chromatin conformational landscape across the population. They typically produce a population of structures that reflects the average or dominant chromatin conformations across the population, which can be further analyzed to identify the common features and variability in the chromatin structure. They also require careful consideration of the variability and noise in the Hi-C data and the underlying assumptions and limitations of the population model.

Validation.

The Hi-C reconstruction is a conversion problem in which 2D information is converted into 3D structures. However, a computationally-generated Hi-C map can be formulated from the resolved structures, and this matrix can be used for quantitative comparison to the experimental Hi-C map. For example, the Pearson (PCC) [48] and Spearman (SCC) [49] correlation coefficients are two measurements used for this purpose. Population-based methods can compare the contact map directly with the original Hi-C map [42], as interaction frequencies are obtained. Other methods that convert the original data into distance matrices use distance Pearson (dPCC) and distance Spearman (dSCC) correlation coefficients for validation. The 3D genome structures obtained from experiments usually have lower resolution than the reconstructed structures, but data from microscopy images obtained with the FISH technique can be used to validate the properties of the reconstructed structures (i.e., the distance between loci) [40, 22]. Other low resolution imaging techniques like cryo soft X-Ray tomography (X-ray microscopy on cryogenically preserved cells) can also been used to obtain coarse information on the location of chromosome elements, such as the centromere [47]. High-resolution structures with details on nucleosome localizations obtained with the OligoSTORM microscopy technique also provide detailed 3D spatial information [21]. For small systems, simple models [50] can be used as original structures that are then reconstructed. The accuracy of the reconstruction can be evaluated by comparing the reconstructed structures with the original structures. The distance root mean square deviation (dRMSD) or distance root mean square error (dRMSE) are often used to assess the similarity between structures.

3. Hi-BDiSCO workflow

To illustrate the overall workflow for 3D reconstruction from Hi-C data, we demonstrate the protocol for our Hi-BDiSCO [42**] method (Figure 2), a 3D reconstruction algorithm that uses Monte Carlo (MC) and Brownian Dynamics (BD) simulations to reconstruct chromatin fibers on the kb level treated with our nucleosome-resolution mesoscale chromatin model [2, 51].

Figure 2:

Hi-BDiSCO workflow. A. Data preparation: Raw Hi-C contact map without correction or conversion is used to obtain the interaction frequencies, f_ij, between genomic regions. Information from MNase and Chip-seq data are used to design the fiber system of interest with experimentally-derived nucleosome positions (bottom plots of linker length vs. nucleosome index, acetylation islands (red regions), and LH positions (turquoise regions) and schematic fiber model). B. Initial 3D structures and restraints distribution: Three representative structures out of N_copy copies obtained by MC simulations are shown. Restraints defined as R_ij = h_m(d_ij − d₀) are assigned into fiber copies by determining how many among the fibers will receive the {i,j} associated restraint: N_Rij = f_ij × N_copy. Thus, the copies are assigned these restraints to reproduce the frequencies in the given contact map. C. BD Simulations: Simplified mesoscale BD simulations with restraints are performed. The structures are folded according to the distributed restraints. D. MC Simulations: MC simulations (with tail/LH interactions) are then performed for 10 million steps without restraints and with tail/LH interaction incorporated.

Hi-BDiSCO uses as input data Micro-C maps, MNase-seq, and linker histone and H3K27ac Chip-seq data. As shown in Figure 2 for the HOXA gene loci, we use MNase-seq data to determine the nucleosome positions, H3K27ac Chip-seq to obtain the tail acetylation regions, and linker histone Chip-seq to assign linker histones to specific nucleosomes. These data are used to set up an initial structure of the gene region of interest and then to sample that system with MC simulations to generate an ensemble of initial structures.

Hi-BDiSCO does not correct for Micro-C data since the selected region is small (≈ 100 kbp), and the noise is neglegible. Hi-BDiSCO uses a contact-based approach in which the data from the raw Micro-C map are incorporated as restraints in the BD simulation. The frequency of each data point in the Micro-C map is used to assign the restraints to the replicas to reproduce the distribution of contacts. BD simulations are then performed so that regions annotated by restraints are pulled together. In these reconstruction simulations, histone tails and linker histones are neglected to accelerate the sampling time. Following BD, we perform MC simulations without restraints and with histone tails and linker histones fully considered to complete the reconstruction.

As a population-based method, Hi-BDiSCO generates an ensemble of structures representing the genome fold over the cells examined. The nucleosome-resolution fiber structures can then be used to study biological mechanisms, such as the interaction of enhancers and promoters, CTCF binding, and nucleosome clutches.

4. Illustration of performance for representative reconstruction techniques

To demonstrate resulting conformations obtained with different reconstruction methods, we invited the Li, Ma, Oluwadare, and Wang groups to generate reconstructed 3D structures using their methods for two different input data: fiber-generated Hi-C map we produced from our MC-simulated fiber; and an experimental Hi-C map of the HOXA gene loci. The general workflow of each method is shown in Table 1.

Table 1:

Workflow for demonstrated methods

	Data	Correction	Conversion	Model	Output Structures
Hi-BDiSCO (Schlick group)	Hi-C, Chip-seq, MNase-seq	Raw data	Contact-based	Simulation-driven	Population-based
ShNeigh (Li group)	Hi-C	Raw data	Distance-based	Analytical	Consensus-based
EVR(C) (Ma group)	Hi-C	Normalization	Distance-based	Simulation-driven	Consensus-based
FLAMINGO (Wang group)	Hi-C, DNase-seq	Normalization	Distance-based	Analytical	Consensus-based
HiC-GNN (Oluwadare group)	Hi-C	Normalization	Knowledge-based	Machine-learning	Consensus-based
particleChromo3D (Oluwadare group)	Hi-C	Normalization	Distance-based	Simulation-driven	Consensus-based

As shown in Figure 4, the 3D structures generated by each method differ markedly. This is because the translation of a 2D contact map into a 3D structure is not uniquely solved, as already emphasized. Each method also converts the raw Hi-C data into a different representation before the reconstruction, which may result in loss of information.

4.1. Input Hi-C Data

The first data set is a computed Hi-C map generated by our MC ensembled 100 replicas of 50-nucleosome life-like fibers simulated with our chromatin mesoscale model and Monte Carlo sampling [2, 51]. This Hi-C map is a 1047×1047 matrix with a 9-bp resolution. The second data set is a Micro-C map with 100-bp resolution [52] from which we have selected the HOXA gene region (chr6:52155590–52260802) that corresponds to a 1054×1054 matrix.

Biologically, these two maps represent different regions with different scales, while mathematically, they are matrices of similar size. Since each method is tailored to a range of Hi-C data resolutions, they can treat these data at any resolution suitable. Our analysis here focuses on the overall topology of the systems and not on quantitative validation.

4.2. The effect of data correction

As mentioned above, one common technique is normalizing the raw Hi-C data to eliminate the biases generated from the experimental procedure. The Ma group normalized the raw Hi-C data we provided by 100 iterations of the ICE (iterative correction and eigenvector decomposition [23]) method, followed by one iteration of the SCN (sequential component normalization [24]) method. Then, they reconstructed the structures with EVR [43] and EVRC [53] for both raw and normalized data. As shown in Figure 4, the structures obtained from raw and normalized HOXA maps using EVR are similar (RMSD=0.001898), but not those obtained using EVRC (RMSD=1.63605). For the MC-fiber generated system, both EVR (RMSD=0.16298) and EVRC (RMSD=0.90972) produce different structures for normalized and raw data. Thus, in most cases, normalizing the data yields structures significantly different from the raw data.

4.3. Structure resolution

The ParticleChromo3D [37*] and HiC-GNN [54*] methods from the Oluwadare group were developed to work with resolutions equal or lower than 500 and 250 kb, respectively. Yet, the resulting structures and corresponding distance matrices can still capture the patterns from the original, higher-resolution Hi-C maps (Figure 4). The Wang group used FLAMINGO [22*] and the KR (Knight-Ruiz) normalization method [55] to reconstruct the HOXA and the artificial system using different resolutions (7 resolutions for HOXA and 2 for the artificial system) (Figure 4 for the 6- and 20-point resolutions). We see that the performance is good for the low-resolution (15 and 20-point) structures of the HOXA gene system but the correlation (measured by the Spearman correlation [49]) is low for the artificial system. This highlights how reconstruction techniques must incorporate some biological properties, such as system size and identity (loci, locus, chromosome, or whole genome), including correspondence between bead size and distance between beads and the experimental Hi-C map resolution. Since we only provided the raw Hi-C map, it is reasonable to obtain method-dependant structures. Additionally, results show how different methods perform better as the Hi-C map resolution approaches the designed resolution (1 to 5kb-resolution [22*]).

4.4. Matrix sparsity

As mentioned earlier, the performance of distance-based methods depends on the sparsity of the matrices. The high-resolution HOXA Hi-C map and the MC-fiber generated map have different sparsity levels, as the former is dense and the latter is more sparse (many zeros at sub-diagonal entries). As a result, not all the methods work adequately on these maps. For example, when using ShNeigh [33*], the Li group obtained pure imaginary numbers on the x-axis for the artificial gene system due to the matrix being not positive definite. This produces a 2D structure instead of 3D (Figure 4). However, for the HOXA system, a reasonable 3D structure is produced within a few seconds from an analytical model (Figure 1). Some methods try to solve this problem through different approaches. For example, when applying FLAMINGO [22*], the Wang group rescaled the Hi-C map and obtained lower resolution maps to avoid the high missing rates of data.

4.5. Output structures

Most of the methods explored here are consensus-based methods that provide as output a single structure that represents the frequencies observed on the Hi-C map. Our Hi-BDiSCO [42**] produces an ensemble of representative structures. Thus, obtaining output structures with a population-based strategy can provide information on cell to cell variability that cannot be obtained from consensus-based methods. Additionally, when analyzing the results, a population-based methods provide the opportunity to study events in a more statistical way.

5. Applications for 3D Hi-C reconstruction

From the Hi-C generated 3D structures, aspects of the 3D organization of the genome architecture can be suggested, such as chromatin loops, TADs, and compartments. In addition, mechanistic insights can be inferred on the relationship between chromatin structure and gene expression.

Di Stefano et al. developed a distance-based reconstruction method that uses time-resolved Hi–C maps and dynamic restraints to model gene activation during cell reprogramming [38**]. Their reconstructed structures revealed that the transcription start site of active genes co-localize with super enhancers during cell reprogramming, forming a 3D contact hub that facilitates transcription.

Wang et. al. recently observed with reconstructed high-resolution structures that TADs bring together enhancers and promoters, connecting them by smooth chromatin loops [22*]. Additionally, this method revealed multi-way chromatin interactions (e.g. 3, 4, or 5-way interactions). Such interactions cannot be provided by 2D Hi-C data and play crucial roles in coupled transcriptional and epigenetic activities. TAD boundaries reconstructed from Hi-C data were used recently to represent 3D chromosome structures as sequences of shape letters from a finite shape alphabet, which provides a compact and efficient way to analyze the complex and variable shapes of chromosomes [56].

Insights into compartments have also been obtained by Lappala et. al., whose reconstructed X chromosome is divided into hemispehere-like structures due to the presence of A/B and S1/S2 compartments that drive spatial phase-separation [41**]. Such architectures were also observed in the reconstructed human chromosome 1 [22*] and in multiplex FISH experiments for a single chromosome [57]. Reconstruction of chromosome structures for time-dependent Hi-C maps reveals how A/B compartments emerge during the cell cycle, namely absent in metaphase and fully formed in interphase [58].

Reconstruction methods can also be applied to disease-related research. For example, the reorganization of TADs in laminopathies, clinical disorders produced by the mutation of the gene LMNA, which encodes A-type lamins, can be studied from reconstructions that use as additional input lamin ChIP-seq data to include TADs radial position information [20]. Such reconstructions showed that when A-type lamins are mutated, TADs re localize from the nuclear periphery to the nuclear interior, and these are gene richer than in wild type A-type lamins.

6. Future Directions

The reconstruction of 3D structures from Hi-C data is a complex and challenging computational task that requires the integration of experimental and computational methods. As discussed above, Hi-C data provide information about the frequency of interactions between different regions of the genome, but inferring the 3D structure from these data cannot be uniquely solved and requires sophisticated computational models and algorithms.

Experimentally, new techniques are generating higher-quality Hi-C data. For example, single-cell Hi-C [59] can provide more detailed information about the chromatin interactions within individual cells. Additionally, the development of new sequencing technologies that can generate longer reads could improve the accuracy of Hi-C data by increasing the number of informative reads [60].

Computationally, developing new methods that can better integrate Hi-C data with other types of genomic data is important. Integrating these different data types can be challenging, but it is necessary for a comprehensive understanding of genome organization and function. This has been proven for chromatin accessibility data, like RNA polymerase II Chip-seq data, which can improve the accuracy of 3D structure reconstruction [21**]. In addition, more machine learning (ML) algorithms could be used to better model the complex relationships between different genomic features and the 3D structure of the genome. ML algorithms can find multiple nonlinear dependencies between genetic features like epigenetic modifications identify transcription factors or structural protein binding and chromatin interactions that cannot be defined analytically [61]. This approach has been proven successful for the prediction of enhancer-promoter interactions where more than 30 ML methods have been developed to integrate chromatin contacts with data like histone marks, MNase, ATAC, DNase, and RNA-seq, DNA methylation, and transcription factor and CTCF binding [62].

While the reconstruction of 3D structures from Hi-C data is a powerful tool for studying genome organization and function, there are several limitations and challenges that must be addressed. One limitation is the inherent noise and biases present in Hi-C data [63]. Hi-C experiments are subject to various technical and biological sources of noise, such as sequencing errors, PCR bias, and variability in chromatin accessibility. These sources of noise can affect the accuracy and resolution of 3D structure reconstruction, and may lead to false positives or false negatives in the analysis. A second challenge is the computational complexity of 3D structure reconstruction from Hi-C data when physics-based simulations are used to predict the 3D structures. Such simulations are computationally intensive as they involved the modeling of systems with thousands or hundred of thousands of beads.

Third, interpreting 3D structures from Hi-C data can be challenging due to the complex nature of chromatin interactions. The interpretation of these interactions requires a deep understanding of the biology of the genome, and the functional consequences of different chromatin structures are not always clear. This problem becomes more important when we consider that there is no “true” structure to validate the modeling.

Perhaps an interesting future direction in the application on 3D reconstructions from Hi-C data is to improve our understanding of genome evolution. By comparing the 3D structure of genomes across different species, researchers are identifying conserved regions of genomes that are important for gene regulation and function, and deciphering how these regions have evolved over time. Undoubtedly, many developments in 3D reconstruction methods and genome structure analyses can be expected in the coming decade.

Figure 3:

Reconstruction of 3D structures using different methods. Left: Reconstructions from a theoretical contact map generated from MC fiber simulations of a life-like chromatin fiber using our mesoscale chromatin model [51, 2]. Right: Reconstructions using an experimental Micro-C contact map [52] of the HOXA region. First row shows the original contact map and converted distance matrix using the formula $d_{ij}\propto 1/f_{ij}^{\alpha }$. The artificial system also shows associated sampled structures (3 of the 100 replicas). The reconstructed structures and their distance matrices as calculated with EVR [35], EVRC [53], HiC-GNN [54], particleChromo3D [37], FLAMINGO [22], and ShNeigh [33] are shown below, row by row. The last row shows structures and associated contact map (contact averaging among 100 replicas) as calculated with Hi-BDiSCO [42].