3D genome reconstruction from partially phased Hi-C data

TL;DR

This paper introduces a novel method for reconstructing 3D genome structures from partially phased Hi-C data, leveraging algebraic geometry and semidefinite programming, with successful tests on simulated and real datasets.

Contribution

It provides the first theoretical guarantees for 3D genome reconstruction from partial phased data and proposes a new computational approach combining algebraic geometry and optimization.

Findings

The method accurately reconstructs 3D structures from noisy data.

Partial phased data is sufficient for unique genome structure identification.

Application to real mouse data recovers known structural features.

Abstract

The 3-dimensional (3D) structure of the genome is of significant importance for many cellular processes. In this paper, we study the problem of reconstructing the 3D structure of chromosomes from Hi-C data of diploid organisms, which poses additional challenges compared to the better-studied haploid setting. With the help of techniques from algebraic geometry, we prove that a small amount of phased data is sufficient to ensure finite identifiability, both for noiseless and noisy data. In the light of these results, we propose a new 3D reconstruction method based on semidefinite programming, paired with numerical algebraic geometry and local optimization. The performance of this method is tested on several simulated datasets under different noise levels and with different amounts of phased data. We also apply it to a real dataset from mouse X chromosomes, and we are then able to recover previously known structural features.