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3D genome reconstruction from chromosomal contacts


A computational challenge raised by chromosome conformation capture (3C) experiments is to reconstruct spatial distances and three-dimensional genome structures from observed contacts between genomic loci. We propose a two-step algorithm, ShRec3D, and assess its accuracy using both in silico data and human genome-wide 3C (Hi-C) data. This algorithm avoids convergence issues, accommodates sparse and noisy contact maps, and is orders of magnitude faster than existing methods.

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Figure 1: Application of ShRec3D to a simulated data set.
Figure 2: Quantitative assessment of ShRec3D performance and reliability.
Figure 3: 3D multiscale visualization of human autosomal chromosomes from Hi-C data.

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The authors thank D. Arendt for the online-available implementation of the Floyd-Warshall algorithm. They acknowledge funding from UPMC (Université Pierre et Marie Curie, Sorbonne-Universités), grant CONVERGENCE2011, project CVG1110 (J.M.), from the French National Cancer Institute, grant INCa_5960 (A.L.), from the French National Research Agency (ANR), grant ANR-13-BSV5-0010-03 (A.L.) and from the French National Research Agency (ANR), grant ANR-09-PIRI-0024 (A.C.).

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Authors and Affiliations



J.M., A.L. and J.R. designed the algorithm. J.M. implemented it. J.R., P.R., A.C. and J.M. tested its validity. A.C. analyzed experimental data sets. J.M. and A.L. wrote the paper.

Corresponding author

Correspondence to Julien Mozziconacci.

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The authors declare no competing financial interests.

Integrated supplementary information

Supplementary Figure 1 Comparison of ShRec3D with the simple MDS-inverse-frequency approach.

The top panels display the spectrum (eigenvalue histogram) of the metric matrix, Eq. 3, derived from our simulated contact map (with here N = 2,600) using (a) our shortest-path distance and (b) the simple distance equal to the inverse contact frequency (both distances are dimensionless: the units on the abscissa axis depend on the chosen normalization for the contact frequencies). The three rightmost black arrows underline the first three eigenvalues and the leftmost red arrow underlines the fourth one, demonstrating the presence of a significant spectral gap in a, and the absence of spectral gap in b. The bottom panels presents a scatter plot of the original distances in our simulated benchmark (horizontal axis, simulation unit equal to 10 nm, N = 2,600) and the distances reconstructed from the corresponding contact map using as a preliminary step either (a) our shortest-path distance or (b) distances obtained as the inverse contact frequencies, followed in both cases by the MDS procedure described in Figure 1a, step 5 followed by step 4 (vertical axis, dimensionless distances). Spearman rank correlation coefficient R is indicated in inset.

Supplementary Figure 2 Polymer connectivity in ShRec3D reconstruction.

Normalized histogram of the reconstructed distances Di, i+1 between neighbors along the genome (light blue peaked curves), for (a) our simulated benchmark (here N = 2,600 points) and (b) genome-wide real Hi-C data18, compared to the normalized histogram of all distances taken as a reference (dark blue broad curves).

Supplementary Figure 3 Visualization of human autosomal chromosomes using ShRec3D.

Color labeling of the different chromosomes: 1: blue, 2: red, 3: grey, 4: orange, 5: yellow, 6: gold, 7: silver, 8: green, 9: pink, 10: cyan, 11: purple, 12: lime, 13: mauve, 14: ochre, 15: ice blue, 16: black, 17: light green,18: light cyan, 19: violet,20: magenta, 21: dark red, 22: light orange. (Hi-C data in lymphoblastoid cells)18.

Supplementary Figure 4 Annotation of human chromosome 1 structure.

(a) Overlay of human chromatin partition in two compartments2 (highlighted by the color code on the structure and boxes; yellow indicates gene rich, GC rich regions, on the left; red indicates gene poor, AT rich regions, on the right). (b) Overlay of two histone H3 modifications on lysine 9. In cyan regions harboring a high level of acetylation, in pink regions harboring a high level of tri-methylation and in purple region harboring both modifications.

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Supplementary Figures 1–4 (PDF 890 kb)

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Lesne, A., Riposo, J., Roger, P. et al. 3D genome reconstruction from chromosomal contacts. Nat Methods 11, 1141–1143 (2014).

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