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

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.

References in corpus (8)

• Enumerating rigid sphere packings
• From Hi-C Contact Map to Three-dimensional Organization of Interphase Human Chromosomes
• Contact numbers for congruent sphere packings in Euclidean 3-space
• A minimal G$\bar{\text{o}}$-model for rebuilding whole genome structures from haploid single-cell Hi-C data
• Apollonian Ball Packings and Stacked Polytopes
• 3D genome reconstruction from partially phased Hi-C data
• Identifying contact graphs of sphere packings with generic radii
• On the uniqueness of collections of pennies and marbles