Fig 1.
Chain organization of chr3 of mouse ES cells measured in the DNA seqFISH+ experiment [24].
(A) 3D positions of 151 imaged loci spaced about 1 Mb apart (large empty dots) and 60 consecutive loci with an equal space of 25 kb (small solid dots) in one of 446 sample cells. (B) Angular correlation of the chromatin segments at 25 kb resolution. (C) Distribution of the physical distance of four loci pairs at 1 Mb resolution (markers) with their fittings to our theory (lines, Eq 3), which are rescaled by using the fitting parameter (γij) and plotted in the inset. (D) Rescaled pairwise distance distributions of all loci pairs, which are colored by their genomic lengths. (E, F) Similar as (C, D) but at 25 kb resolution.
Fig 2.
Flow chart of HLM that is enclosed by the dashed orange box.
It takes two-body contacts from Hi-C as input, and calculates n-body (n > 2) contact probability. The stiffness matrix is updated until the algorithm finds
that minimizes the cost function
which quantifies the difference between pairwise contact probabilities of Hi-C data and those determined from
matrix.
Fig 3.
Three-body contacts predicted with HLM versus those from Tri-C.
(A) Gene notation, DNase hypersensitive sites, CTCF-binding sites [59, 60] and genomic regions of interest (sites of interest, SOI) at mouse α-globin locus on chr11. (B) log10(pij) from Capture-C (top triangle) and HLM (bottom triangle) at 2-kb resolution. (C, D) log10(pijk) from Tri-C (top) and HLM (bottom) at k = R2 and k = HS-39, whose positions are labeled with black strips. The Pearson correlations between Tri-C and HLM are 0.80 (ES) and 0.75 (erythroid) for k = R2, and 0.89 (EC) and 0.85 (erythroid) for k = HS-39. (E) Cell-line difference of the predicted three-body contacts, , among the SOIs with respect to the viewpoints R2, HS-39 and (F) Hba-a1, HS+44.
Fig 4.
Comparing many-body contact predictions with MC-4C.
(A) Comparing log10(pij) from Hi-C and HLM at 10-kb resolution of a 1.28 Mb region on chr8, where there are thirteen CTCF-binding sites labeled from A to M. The genomic position of forward- and backward-oriented CTCF sites are marked with red and blue sticks, respectively. (B, C) Comparing log10(pijk) from MC-4C and HLM at a viewpoint of site E and K, respectively. From the viewpoint of E (K), the values of PC between the model and the MC-4C experiment are 0.83 (0.81) and 0.71 (0.73) for the WT and ΔWAPL cells, respectively. (D) Cell-line difference of the predicted three-body contacts, namely , among the CTCF-binding sites from the viewpoint of A, E and (E) H, K, respectively. (F, G) Cell-line difference of four- and five-body contacts from double- and triple-anchored viewpoints, whose positions are marked with the black strips. The numbers label the maximum amplitudes of changes.
Fig 5.
Comparing triplet contact predictions with SPRITE.
(A) Genes, RNA-seq and H3K27ac ChIP-seq signals [60, 67] in a 0.45 Mb region on human chr18 with the positions of three types of SOIs (Enhancers, Promoters and Super-enhancers). (B) log10(pij) from Hi-C compared with that from HLM at 5-kb resolution. (C) The triplet contact frequency from SPRITE is compared with log10(pijk) from HLM anchored at an active promoter site. (D) SPRITE frequency of triplets which are divided into four quantiles based on ascending order of pijk. (E) For three sites, i < j < k, along a polymer chain, the minor and major sections denoted by m and t, respectively, are depicted with dashed lines. (F) The expected three-body contact probability , and (G) the specificity Z-score
. (H) The mean specificity Z-score of triplet contacts with respect to all possible combinations of annotations (E: Enhancers, P: Promoters, S: Super-enhancers, #: sites without any annotation). The error bars are the standard deviations.
Fig 6.
Many-body contacts in a Gaussian polymer chain consisting of 20 sites.
(A) Two-body contact probability log10(pij). (B) Three-body contact probability log10(pijk) anchored at the 7-th site (k = 7). (C) Four-body contact probability log10(pijkl) double anchored at the 6-th and 15-th sites (k = 6, l = 15). (D-F) Boost factor pijk/pij pjk, hub-score Hijk, and association z-score Aijk from the viewpoint of the 7-th site.