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CHESS enables quantitative comparison of chromatin contact data and automatic feature extraction


Dynamic changes in the three-dimensional (3D) organization of chromatin are associated with central biological processes, such as transcription, replication and development. Therefore, the comprehensive identification and quantification of these changes is fundamental to understanding of evolutionary and regulatory mechanisms. Here, we present Comparison of Hi-C Experiments using Structural Similarity (CHESS), an algorithm for the comparison of chromatin contact maps and automatic differential feature extraction. We demonstrate the robustness of CHESS to experimental variability and showcase its biological applications on (1) interspecies comparisons of syntenic regions in human and mouse models; (2) intraspecies identification of conformational changes in Zelda-depleted Drosophila embryos; (3) patient-specific aberrant chromatin conformation in a diffuse large B-cell lymphoma sample; and (4) the systematic identification of chromatin contact differences in high-resolution Capture-C data. In summary, CHESS is a computationally efficient method for the comparison and classification of changes in chromatin contact data.

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Fig. 1: CHESS overview and examples.
Fig. 2: CHESS evaluation on synthetic Hi-C matrices.
Fig. 3: Global comparison of syntenic region similarity between human and mouse using CHESS.
Fig. 4: Identification of chromatin conformational changes in fly embryos after Zelda (zld) knockdown.
Fig. 5: Identification of structural changes in a DLBCL.
Fig. 6: Feature extraction from Capture-C data.

Data availability

The datasets analyzed in this study have been obtained from the Gene Expression Omnibus (Rao et al.10, GSE63525; Bonev et al.12, GSE96107; Despang et al.50, GSE125294) and ArrayExpress (Hug et al.9, E-MTAB-4918; Díaz et al.48, E-MTAB-5875).

Code availability

The CHESS source code and the code for generating the synthetic Hi-C matrices and running tests on them is available on GitHub: ( The intervaltree and tqdm packages used internally in CHESS can be found at and, respectively. In addition, CHESS uses internally the following published packages: FAN-C71 (; Cython72; SciPy69; scikit-image59; NumPy73,74; Pandas75; Pathos76; Pybedtools77; Kneed78.


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Work in the Vaquerizas laboratory is funded by the Max Planck Society, the Deutsche Forschungsgemeinschaft (DFG) Priority Programme SPP 2202 ‘Spatial Genome Architecture in Development and Disease’ (project no. 422857230 to J.M.V.), the DFG Clinical Research Unit CRU326 ‘Male Germ Cells: from Genes to Function’ (project no. 329621271 to J.M.V.), the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 643062—ZENCODE-ITN to J.M.V.) and the Medical Research Council in the UK. This research was partially funded by the European Union’s H2020 Framework Programme through the European Research Council (grant no. 609989 to M.A.M.-R.). We thank the support of the Spanish Ministerio de Ciencia, Innovación y Universidades through grant no. BFU2017-85926-P to M.A.M.-R. The Centre for Genomic Regulation thanks the support of the Ministerio de Ciencia, Innovación y Universidades to the European Molecular Biology Laboratory partnership, the ‘Centro de Excelencia Severo Ochoa 2013–2017’, agreement no. SEV-2012-0208, the CERCA Programme/Generalitat de Catalunya, Spanish Ministerio de Ciencia, Innovación y Universidades through the Instituto de Salud Carlos III, the Generalitat de Catalunya through the Departament de Salut and Departament d’Empresa i Coneixement and cofinancing by the Spanish Ministerio de Ciencia, Innovación y Universidades with funds from the European Regional Development Fund corresponding to the 2014–2020 Smart Growth Operating Program. S.G. thanks the support from the Company of Biologists (grant no. JCSTF181158) and the European Molecular Biology Organization Short-Term Fellowship programme.

Author information




N.M. and J.M.V. conceptualized the study. S.G., N.M. and K.K. devised the methodology. N.M. and J.M.V. carried out the investigation. S.G., K.K. and N.D. obtained the resources. S.G., N.M., K.K., M.A.M.-R. and J.M.V. prepared and wrote the original draft of the manuscript. S.G., N.M., K.K., N.D., M.A.M.-R. and J.M.V. wrote, reviewed and edited the draft. J.M.V. supervised the study. M.A.M.-R. and J.M.V. acquired the funding.

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Correspondence to Juan M. Vaquerizas.

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Extended data

Extended Data Fig. 1 Performance analysis of the CHESS algorithm.

a, CHESS P values in dependence of the relative noise level in synthetic matrices. Shown are the cases of equal amounts of noise in reference R and query Q (top) and different amounts of noise (bottom, noise only added to Q). Each case is examined for normalised and observed/expected (obs/exp) matrices, and different window sizes in the SSIM algorithm. b, Empirically determined CHESS P values in dependence of the size factor between R and Q for normalised (left) and observed/expected (obs/exp) matrices (right) (details in Methods). a, b, Solid lines indicate the mean, shaded areas the standard deviation over 100 simulations per parameter combination.

Extended Data Fig. 2 Technical details of the SSIM algorithm applied to Hi-C matrices.

a, Schematic overview of the structural similarity algorithm (SSIM). SSIM scores are calculated on all submatrices of R /Q at a given window size (WS). The final SSIM score is the mean of all SSIM submatrix scores. b, SSIM submatrix formula. Different components are coloured: illuminance (green), structure * contrast (red). x, y refer to submatrices (at the same positions) of the two full matrices for which the SSIM average is computed (see panel a). μ indicates the mean, σ the standard deviation, c1 and c2 are small constants that are introduced only for numerical reasons. c and d, SSIM comparisons of a matrix to itself (red dots) and 1,000 random matrices of the same size (blue dots). c, SSIM component values in dependence of SSIM score for different SSIM window sizes. d, Scatterplots of ranked SSIM scores at window size 100 vs. ranked scores at smaller window sizes.

Extended Data Fig. 3 Additional analysis of the CHESS algorithm.

a, Uniform distribution of empirically determined CHESS P values for comparisons of matrices with 100 % noise added. b, Distribution of structural similarity scores (SSIM) for background and truth comparisons at 25 k/Mb and 1.5 M/Mb simulated sequencing depth. Above each: Fractional change (value at x % noise/value at 0 % noise) of the standard deviation (std) of background scores and mean of truth scores over 100 simulations per parameter combination.

Extended Data Fig. 4 CHESS is robust to changes in noise due to random ligations and sequencing depth in real Hi-C data.

a, Examples of 5 Mb matrices used in this analysis including a 5, 80 and 95 % of added noise (random ligations between pairs of loci). We tested to what extent CHESS is able to identify two matrices as being identical, after noise and sequencing depth were adjusted independently in them. Matrices are based on chromosome 19 data from Bonev et al.12. a, examples of the data with different amounts of noise. b, empirically determined P values and z-scores of CHESS runs with different window sizes, noise levels and simulated sequencing depths (details in Methods). Step size and matrix resolution were both 25 kb. Lines for 2 x 105 and 1 x 106 overlap for runs with window sizes > 1 Mb. c, As in panel a, but comparing CHESS runs with 2.5 Mb window size on matrices binned at 25 kb and 10 kb. b and c, solid lines indicate the mean, shaded areas the standard deviation over 1976, 2066, 2156, 2246, 2300 matrix pairs for window sizes 10 Mb, 7.5 Mb, 5 Mb, 2.5 Mb, 1 Mb, respectively.

Extended Data Fig. 5 Reproducibility of CHESS using different window (WS) and step sizes (SS), sequencing depths and resolutions.

For this analysis were tested the WS (250 kb - 3 Mb), SS (25 kb - 1 Mb), sequencing depths (percentage of reads between 20 and 80) and resolutions (10 kb and 25 kb) (details in Methods). X-axis labels: varied parameters in parentheses, fixed parameters before. The first two boxplots with red dots represent the Jaccard indices (JI) between CHESS results in Bonev et al.12 using different WS, SS and sequencing depths. The boxplots with blue dots correspond to the Díaz et al.48 dataset; in this case using different WS, SS, and then between different WS, SS and resolutions. mESC mouse embryonic stem cells, NPC neural progenitor cells. Boxplot elements: centre line: median, whiskers: 1.5x interquartile range, box limits: upper-lower quartile.

Extended Data Fig. 6 CHESS benchmark against HOMER, diffHiC and ACCOST.

a, Upset plot representing the intersection size between differential interactions of CHESS, HOMER, diffHiC and ACCOST. Below, an example is shown for each intersected group. b, Computational requirements of CHESS, HOMER, diffHiC and ACCOST. The first line plot shows the CPU usage, the second the memory consumption. The vertical dashed line represents the end of the run.

Extended Data Fig. 7 CHESS performance on differently sized simulated matrices with realistic noise and sequencing depth.

Shown are empirically determined CHESS p- and z-scores (details in Methods) for comparisons of R with a read depth of 100 read pairs / 100 bins and a resized copy Q. Scaling factor is indicated on the x-axis. A noise level of 25 % was added to both matrices independently. Sequencing depth was adjusted to 100 k/Mb. Solid lines indicate the mean, shaded areas the standard deviation over 100 simulations per parameter combination. Colours correspond to the different sizes of R.

Extended Data Fig. 8 Feature extraction from Capture-C data.

Examples of differential feature extraction with CHESS between the wt (top contact map) and different mutants (middle contact map) in the Despang et al.50 dataset. Lost and gained structures in the mutants are highlighted in blue and red squares, respectively. Log2 fold-change maps are depicted below (bottom contact map) with identified features coloured according to the directionality of the change. Below each comparison, the genomic annotation is represented, highlighting the modification of each mutant. The vertical lines define the CTCF binding motifs, dashed when deleted. Red hexagons demarcate TAD boundaries. Feature extraction between wt and a, ∆Bor, in which the border was deleted. b, ∆BorC1, in which the border and the first CTCF binding motif were deleted. c, ∆BorC1-2, in which the border and the two first CTCF binding motifs were deleted. d, ∆BorC1-4, in which the border and four CTCF binding motifs were deleted. e, ∆CTCF, in which the border and all the CTCF binding motifs were removed. f, Bor-KnockIn, in which the border was moved to a new location within the Sox9 locus. g, InvC∆Bor, in which the Sox9 sequence was inverted and the border was removed.

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Galan, S., Machnik, N., Kruse, K. et al. CHESS enables quantitative comparison of chromatin contact data and automatic feature extraction. Nat Genet 52, 1247–1255 (2020).

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