Single-cell 3D genome reconstruction in the haploid setting using rigidity theory

TL;DR

This paper introduces a novel approach for reconstructing 3D genome structures in haploid cells using graph rigidity theory, leveraging multiple data sources and mathematical models to ensure unique and accurate reconstructions.

Contribution

It develops a new framework combining graph rigidity and semidefinite programming for 3D genome reconstruction from diverse biological data.

Findings

Proved conditions for uniqueness of genome reconstructions.

Demonstrated method effectiveness on synthetic and real datasets.

Achieved accurate 3D models consistent with biological data.

Abstract

This article considers the problem of 3-dimensional genome reconstruction for single-cell data, and the uniqueness of such reconstructions in the setting of haploid organisms. We consider multiple graph models as representations of this problem, and use techniques from graph rigidity theory to determine identifiability. Biologically, our models come from Hi-C data, microscopy data, and combinations thereof. Mathematically, we use unit ball and sphere packing models, as well as models consisting of distance and inequality constraints. In each setting, we describe and/or derive new results on realisability and uniqueness. We then propose a 3D reconstruction method based on semidefinite programming and apply it to synthetic and real data sets using our models.