Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential
Reconstructing three-dimensional (3D) chromosomal structures based on single-cell Hi-C data is a challenging scientific problem due to the extreme sparseness of the single-cell Hi-C data. In this research, we used the Lennard-Jones potential to reconstruct both 500 kb and high-resolution 50 kb chrom...
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MDPI AG
2021-05-01
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| Series: | International Journal of Molecular Sciences |
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| Online Access: | https://www.mdpi.com/1422-0067/22/11/5914 |
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| author | Mengsheng Zha Nan Wang Chaoyang Zhang Zheng Wang |
| author_facet | Mengsheng Zha Nan Wang Chaoyang Zhang Zheng Wang |
| author_sort | Mengsheng Zha |
| collection | DOAJ |
| description | Reconstructing three-dimensional (3D) chromosomal structures based on single-cell Hi-C data is a challenging scientific problem due to the extreme sparseness of the single-cell Hi-C data. In this research, we used the Lennard-Jones potential to reconstruct both 500 kb and high-resolution 50 kb chromosomal structures based on single-cell Hi-C data. A chromosome was represented by a string of 500 kb or 50 kb DNA beads and put into a 3D cubic lattice for simulations. A 2D Gaussian function was used to impute the sparse single-cell Hi-C contact matrices. We designed a novel loss function based on the Lennard-Jones potential, in which the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ε</mi></semantics></math></inline-formula> value, i.e., the well depth, was used to indicate how stable the binding of every pair of beads is. For the bead pairs that have single-cell Hi-C contacts and their neighboring bead pairs, the loss function assigns them stronger binding stability. The Metropolis–Hastings algorithm was used to try different locations for the DNA beads, and simulated annealing was used to optimize the loss function. We proved the correctness and validness of the reconstructed 3D structures by evaluating the models according to multiple criteria and comparing the models with 3D-FISH data. |
| first_indexed | 2024-03-10T10:51:02Z |
| format | Article |
| id | doaj.art-b4f4d05d6c514c53b85b53578e6eb77d |
| institution | Directory Open Access Journal |
| issn | 1661-6596 1422-0067 |
| language | English |
| last_indexed | 2024-03-10T10:51:02Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
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| series | International Journal of Molecular Sciences |
| spelling | doaj.art-b4f4d05d6c514c53b85b53578e6eb77d2023-11-21T22:15:08ZengMDPI AGInternational Journal of Molecular Sciences1661-65961422-00672021-05-012211591410.3390/ijms22115914Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones PotentialMengsheng Zha0Nan Wang1Chaoyang Zhang2Zheng Wang3School of Computing Sciences and Computer Engineering, University of Southern Mississippi, 118 College Dr, Hattiesburg, MS 39406, USADepartment of Computer Science, New Jersey City University, 2039 Kennedy Blvd, Jersey City, NJ 07305, USASchool of Computing Sciences and Computer Engineering, University of Southern Mississippi, 118 College Dr, Hattiesburg, MS 39406, USADepartment of Computer Science, University of Miami, 1364 Memorial Drive, Coral Gables, FL 33124, USAReconstructing three-dimensional (3D) chromosomal structures based on single-cell Hi-C data is a challenging scientific problem due to the extreme sparseness of the single-cell Hi-C data. In this research, we used the Lennard-Jones potential to reconstruct both 500 kb and high-resolution 50 kb chromosomal structures based on single-cell Hi-C data. A chromosome was represented by a string of 500 kb or 50 kb DNA beads and put into a 3D cubic lattice for simulations. A 2D Gaussian function was used to impute the sparse single-cell Hi-C contact matrices. We designed a novel loss function based on the Lennard-Jones potential, in which the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ε</mi></semantics></math></inline-formula> value, i.e., the well depth, was used to indicate how stable the binding of every pair of beads is. For the bead pairs that have single-cell Hi-C contacts and their neighboring bead pairs, the loss function assigns them stronger binding stability. The Metropolis–Hastings algorithm was used to try different locations for the DNA beads, and simulated annealing was used to optimize the loss function. We proved the correctness and validness of the reconstructed 3D structures by evaluating the models according to multiple criteria and comparing the models with 3D-FISH data.https://www.mdpi.com/1422-0067/22/11/59143D genomesingle-cell Hi-C3D chromosomal structureLennard-Jones potential |
| spellingShingle | Mengsheng Zha Nan Wang Chaoyang Zhang Zheng Wang Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential International Journal of Molecular Sciences 3D genome single-cell Hi-C 3D chromosomal structure Lennard-Jones potential |
| title | Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential |
| title_full | Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential |
| title_fullStr | Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential |
| title_full_unstemmed | Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential |
| title_short | Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential |
| title_sort | inferring single cell 3d chromosomal structures based on the lennard jones potential |
| topic | 3D genome single-cell Hi-C 3D chromosomal structure Lennard-Jones potential |
| url | https://www.mdpi.com/1422-0067/22/11/5914 |
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