Fig. 1

Study of chromatin contacts with polymer physics and key analysis phases. a Top panel: schematic representation of background chromatin interactions (blue line) for a viewpoint (blue inverted triangle) bordering a 4.3 Mb DNA deletion. Most of the interactions are expected to be surrounding the viewpoint given the smaller distance separating them. Notice how interactions further downstream of the viewpoint have a low contact probability. Lower left panel: upon deletion, two different genomic regions are joined together in physical proximity (pink and green rectangles), and the viewpoint presents a new interaction profile (black curve). Using current statistical methods, all the contacts established with the green region would be catalogued as differential, given their comparison to the original distal contact profile (dashed blue line). However, overlay of the previous WT background profile (blue dashed curve) shows that the majority of these contacts are simply following the expected WT background contact probability for the viewpoint (and are therefore physical changes in interaction), and only the peak marked with an asterisk would be considered as a genuine change in chromatin interactions (of a biological origin). b Analysis Phase 1: Result of bias-correction for a typical PE-4Cseq experiment on 12 viewpoints located on WT chromosome 4. Viewpoints index is on the x and y axis. The heatmap on the left is the relative asymmetry matrix \( \frac{\left|{F}_{IJ}-{F}_{JI}\right|}{F_{IJ}+{F}_{JI}} \) in BCP per viewpoint where only the upper triangle is shown because the matrix is symmetric. The heatmap on the right is the relative asymmetry \( \frac{\left|{P}_{IJ}-{P}_{JI}\right|}{P_{IJ}+{P}_{JI}} \) for P _IJ obtained after bias-correction. Notice the reduction in both row and column-wise biases and in the net asymmetry between viewpoints. Heatmaps are displayed in a log₁₀ scale. c Analysis Phase 2: The CPP after bias correction for a typical viewpoint in a WT chromosome. Analysis Phase 3: A typical comparison between WT and deletion viewpoint CPPs to identify DIRs. The DIRs are shown in asterisks, and represented as vertical bands with widths proportional to their sizes. Color intensity is proportional to strength of signal, with reds for increase and blues for decrease of signal in the deletion versus WT comparisons. d Analysis Phase 4. Left panel: example spline-fit to the fall-off of CP (in log-log scale) against genomic viewpoint-fragment distances in a deletion (red) and WT (blue) datasets. The slope of the fit at 100 Kb is our local measure of compaction ν _I , which may differ significantly in WT and deletion as illustrated in this panel for a typical viewpoint. Right panel: Example of a 3D DNA FISH experiment where a DIR pair was differentially-labeled using red and green probes to measure physical distances between them. The inclusion of a probe inside the deletion region (white), allows for the distinction of deletion (Df) and WT (+ ^Bl6 _D ) chromosomes within the same nuclei (blue)