SHAMAN: bin-free randomization, normalization and screening of Hi-C matrices

Genome wide chromosome conformation capture (Hi-C) is used to interrogate contact frequencies among genomic elements at multiple scales and intensities, ranging from high frequency interactions among proximal regulatory elements, through specific long-range loops between insulator binding sites and up to rare and transient cis- and trans-chromosomal contacts. Visualization and statistical analysis of Hi-C data is made difficult by the extreme variation in the background frequencies of chromosomal contacts between elements at short and long genomic distances. Here we introduce SHAMAN for performing Hi-C analysis at dynamic scales, without predefined resolution, and while minimizing biases over very large datasets. Algorithmically, we devise a Markov Chain Monte Carlo-like procedure for randomizing contact matrices such that coverage and contact distance distributions are preserved. We combine this strategy with bin-free assessment of contact enrichment using a K-nearest neighbor approach. We show how to use the new method for visualizing contact hotspots and for quantifying differential contacts in matching Hi-C maps. We demonstrate how contact preferences among regulatory elements, including promoters, enhancers and insulators can be assessed with minimal bias by comparing pooled empirical and randomized matrices. Full support for our methods is available in a new software package that is freely available.