School of Computing Sciences and Computer Engineering, University of Southern Mississippi, 118 College Dr, Hattiesburg, MS 39406, USA.
Department of Computer Science, New Jersey City University, 2039 Kennedy Blvd, Jersey City, NJ 07305, USA.
Int J Mol Sci. 2021 May 31;22(11):5914. doi: 10.3390/ijms22115914.
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 ε 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.
基于单细胞 Hi-C 数据重建三维(3D)染色体结构是一个具有挑战性的科学问题,因为单细胞 Hi-C 数据非常稀疏。在这项研究中,我们使用 Lennard-Jones 势能,基于单细胞 Hi-C 数据重建了 500kb 和高分辨率 50kb 的染色体结构。染色体由一连串 500kb 或 50kb 的 DNA 珠子表示,并放入 3D 立方晶格中进行模拟。使用二维高斯函数来插补稀疏的单细胞 Hi-C 接触矩阵。我们设计了一种新的基于 Lennard-Jones 势能的损失函数,其中 ε 值,即势阱深度,用于表示每对珠子的结合稳定性。对于具有单细胞 Hi-C 接触的珠子对及其相邻的珠子对,损失函数赋予它们更强的结合稳定性。采用 Metropolis-Hastings 算法尝试 DNA 珠子的不同位置,并使用模拟退火优化损失函数。我们通过根据多个标准评估模型并将模型与 3D-FISH 数据进行比较,证明了重建的 3D 结构的正确性和有效性。