Single-cell 3D genome reconstruction in the haploid setting using rigidity theory
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.
Authors
- Sean Dewar (ORCID: https://orcid.org/0000-0003-2220-4576)
- Anthony Nixon (ORCID: https://orcid.org/0000-0003-0639-1295)
- Kaie Kubjas (ORCID: https://orcid.org/0000-0002-2227-2272)
- Georg Grasegger (ORCID: https://orcid.org/0000-0001-7421-8115)
- Fatemeh Mohammadi (ORCID: https://orcid.org/0000-0001-5187-0995)
Institutions
- Austrian Academy of Sciences (AT)
- University of Bristol (GB)
- VIB-KU Leuven Center for Microbiology (BE)
- Johann Radon Institute for Computational and Applied Mathematics (AT)
- Lancaster University (GB)
- Aalto University (FI)
- KU Leuven (BE)
Publication Details
- Journal
- Journal of Mathematical Biology
- Published
- 2025-03-29
- DOI
- https://doi.org/10.1007/s00285-025-02203-2
- Primary Topic
- Single-cell and spatial transcriptomics
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Academy of Finland
- Austrian Science Fund
- Aalto-Yliopisto
- Fonds Wetenschappelijk Onderzoek
- KU Leuven
- Engineering and Physical Sciences Research Council