Inference of 3D structure of diploid chromosomes

Abstract

The spatial organization of DNA in the cell nucleus plays an important role for gene regulation, DNA replication, and genomic integrity. Through the development of chromosome capture experiments (such as 3C, 4C, Hi-C) it is now possible to obtain the contact frequencies of the DNA at the whole-genome level. In this thesis, we study the problem of reconstructing the 3D organization of the genome from whole-genome contact frequencies. A standard approach is to transform the contact frequencies into noisy distance measurements and then apply semidefinite programming (SDP) formulations to obtain the 3D configurations. However, neglected in such reconstructions is the fact that most eukaryotes including humans are diploid and therefore contain two (from the available data) indistinguishable copies of each genomic locus. Due to this, the standard approach performs very poorly on diploid organisms. We prove that the 3D organization of the DNA is not identifiable from exclusively chromosome capture data for diploid organisms. In fact, there are infinitely many solutions even in the noise-free setting. We then discuss various additional biologically relevant constraints (including distances between neighboring genomic loci and to the nucleus center or higher-order interactions). Under these conditions we prove there are finitely many solutions and conjecture we in fact have identifiability. Finally, we provide SDP formulations for computing the 3D embedding of the DNA with these additional constraints and show that we can recover the true 3D embedding with high accuracy even under noise.