Domain calling using Directionality Index and HMM

The read normalized 10 kb binned 5C pairwise interaction files for each chromosome were saved from my5C web-tool. TAD boundaries were obtained using the Directionality Index method described in [28, 29] and available at http://doc.genomegitar.org/DI_calculation.html. This method is based on the concept that regions at the periphery of TAD are highly biased in their interaction frequencies. It is based on Chi squared test statistic where the null hypothesis is that bins do not show biased upstream and downstream interaction. Directionality Index (DI) calculation was performed using an R script, in a 100 kb × 100 kb square along the diagonal of the interaction frequency matrix for each replicate using the following formula:

where A is the sum of all interactions from a given 10 kb bin to the upstream till 100 kb, B is the sum of all interactions from a given 10 kb bin to the downstream till 100 kb, E is the expected number of interactions for each bin under the null hypothesis and it equals (A + B)/2.

To predict TADs after the estimation of DI, a Hidden Markov Model was constructed. The MATLAB script for HMM previously described in [29] was rewritten in R language using CRAN package HMM. TADs were predicted across the replicates for each chromosome except for chr3R (because of too few interactions mapped, the HMM did not pick up any signals). TAD boundary called for each replicate was pooled for a consensus boundary definition. Thus, to identify consensus TAD borders across replicates, a combined distribution plot for the distance between boundaries called for three replicates was plotted. Boundaries within 50 kb of each other among replicates were considered consistent (> 72.3% of boundaries called across chromosomes overlapped within this window). Using these parameters, consensus TADs and TAD borders were defined for each chromosome.