Single-cell 3D genome reconstruction in the haploid setting using rigidity theory
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909972769538048 |
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| author | Dewar, Sean Grasegger, Georg Kubjas, Kaie Mohammadi, Fatemeh Nixon, Anthony |
| author_facet | Dewar, Sean Grasegger, Georg Kubjas, Kaie Mohammadi, Fatemeh Nixon, Anthony |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10700 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Single-cell 3D genome reconstruction in the haploid setting using rigidity theory Dewar, Sean Grasegger, Georg Kubjas, Kaie Mohammadi, Fatemeh Nixon, Anthony Genomics Combinatorics Metric Geometry Optimization and Control 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. |
| title | Single-cell 3D genome reconstruction in the haploid setting using rigidity theory |
| topic | Genomics Combinatorics Metric Geometry Optimization and Control |
| url | https://arxiv.org/abs/2407.10700 |