Inference of 3D genome architecture by modeling overdispersion of Hi-C data

Motivation: We address the challenge of inferring a consensus 3D model of genome architecture from Hi-C data. Existing approaches most often rely on a two-step algorithm: first, convert the contact counts into distances, then optimize an objective function akin to multidimensional scaling (MDS) to infer a 3D model. Other approaches use a maximum likelihood approach, modeling the contact counts between two loci as a Poisson random variable whose intensity is a decreasing function of the distance between them. However, a Poisson model of contact counts implies that the variance of the data is equal to the mean, a relationship that is often too restrictive to properly model count data.Results: We first confirm the presence of overdispersion in several real Hi-C datasets, and we show that the overdispersion arises even in simulated datasets. We then propose a new model, called Pastis-NB, where we replace the Poisson model of contact counts by a negative binomial one, which is parametrized by a mean and a separate dispersion parameter. The dispersion parameter allows the variance to be adjusted independently from the mean, thus better modeling overdispersed data. We compare the results of Pastis-NB to those of several previously published algorithms, both MDS-based and statistical methods. We show that the negative binomial inference yields more accurate structures on simulated data, and more robust structures than other models across real Hi-C replicates and across different resolutions.