Statistical curve models for inferring 3D chromatin architecture

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. Most existing algorithms that operate on Hi-C contact matrices produce reconstructed 3D configurations in the form of a polygonal chain. However, none of the methods exploit the fact that the target solution is a (smooth) curve in 3D: this contiguity attribute is either ignored or indirectly addressed by imposing spatial constraints that are challenging to formulate. In this paper we develop both B-spline and smoothing spline techniques for directly capturing this potentially complex 1D curve. We subsequently combine these techniques with a Poisson model for contact counts and compare their performance on a real data example. 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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>DBMS</mml:mi></mml:math> ) 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.