Figure 2. Iterative correction of Hi-C data.
(a) Illustration of iterative correction using simulated data. (Top) two specific interactions (shown by arches) within a chromosome, (middle) its simulated Hi-C heatmap and a vector of random experimental visibility. Notice that visibility-induced noise obscures specific interactions. (bottom) Iteratively corrected map of the chromosome, where visibility is equalized, revealing two specific interactions as bright spots on the heatmap. (b) Matrix of biases computed by Yaffe and Tanay17 at 1Mb resolution (top) can be approximated by a product of bias vectors Bi × Bj (middle), yielding an essentially identical matrix of biases (r =0.99), with their algebraic difference shown at the bottom in the same colorscheme (also Supplementary Fig. 4). (c) Comparison of intra-chromosomal Hi-C maps obtained using HindIII and NcoI enzymes (200kb resolution). The correlation is computed between off-diagonal regions of the map and plotted as a function of distance from the main diagonal, that is, the genomic separation, as shown in the inset. Analysis was performed on raw data (red), single corrected (blue) and iteratively corrected (yellow). (d) Inter-chromosomal heatmaps (chr1 vs. chr2, coarse-grained to 10MB, contact frequencies shown by color for HindIII and Ncol before (top row) and after correction (bottom raw) (also see Supplementary Fig. 5). (e) (left) Cross-validation for biases inferred from 10% vs. 90% of the reads. (right) Scaling of intra-chromosomal contact probability with genomic distance, L for Hi-C HindIII8 data, at 200 kb resolution, before (red) and after correction (yellow). Black line shows 1/L scaling reported previously8.