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

Year: 2025
Type: article
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.
DOI: 10.1007/s00285-025-02203-2
Institutions: University of Bristol, Austrian Academy of Sciences, Johann Radon Institute for Computational and Applied Mathematics, Aalto University, KU Leuven, Lancaster University
Language: English
Open Access status: hybrid
Estimated APC paid: $3,090
Funders: Academy of Finland, Austrian Science Fund, Aalto-Yliopisto, Fonds Wetenschappelijk Onderzoek, KU Leuven, Engineering and Physical Sciences Research Council, Heilbronn Institute for Mathematical Research
Awards: Exploiting combinatorial structures for algebraic and geometric decompositions, Realizations of Rigid Graphs, Abstract rigidity for natural stability problems, G4120167447, G4869584417, G4872507874, G562246749, Matroids in Applied and Combinatorial Commutative Algebra, G7618753153, G8590477180
OpenAlex ID: W4409039117
FWCI:
Cites: 64
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Related to: 10