Statistical curve models for inferring 3D chromatin architecture

Abstract

Reconstructing three dimensional (3D) chromatin structure from conformation capture assays (such as Hi-C) is a critical task in computational biology, since chromatin spatial architecture plays a vital role in numerous cellular processes and direct imaging is challenging. We previously introduced Poisson metric scaling (PoisMS), a technique that models chromatin by a smooth curve, which yielded promising results. In this paper, we advance several ways for improving PoisMS. In particular, we address initialization issues by using a smoothing spline basis. The resulting SPoisMS method produces a sequence of reconstructions re-using previous solutions as warm starts. Importantly, this approach permits smoothing degree to be determined via cross-validation which was problematic using our prior B-spline basis. In addition, motivated by the sparsity of Hi-C contact data, especially when obtained from single-cell assays, we appreciably extend the class of distributions used to model contact counts. We build a general distribution-based metric scaling (DBMS) framework, from which we develop zero-inflated and Hurdle Poisson models as well as negative binomial applications. Illustrative applications make recourse to bulk Hi-C data from IMR90 cells and single-cell Hi-C data from mouse embryonic stem cells.