Deconvolution of Ensemble Chromatin Interaction Data Reveals the Latent Mixing Structures in Cell Subpopulations

Chromosome conformation capture (3C) experiments provide a window into the spatial packing of a genome in three dimensions within the cell. This structure has been shown to be correlated with gene regulation, cancer mutations, and other genomic functions. However, 3C provides mixed measurements on a population of typically millions of cells, each with a different genome structure due to the fluidity of the genome and differing cell states. Here, we present several algorithms to deconvolve these measured 3C matrices into estimations of the contact matrices for each subpopulation of cells and relative densities of each subpopulation. We formulate the problem as that of choosing matrices and densities that minimize the Frobenius distance between the observed 3C matrix and the weighted sum of the estimated subpopulation matrices. Results on HeLa 5C and mouse and bacteria Hi-C data demonstrate the methods' effectiveness. We also show that domain boundaries from deconvolved matrices are often more enriched or depleted for regulatory chromatin markers when compared to boundaries from convolved matrices.