Imputation-free reconstructions of three-dimensional chromosome architectures in human diploid single-cells using allele-specified contacts

The sparseness of chromosomal contact information and the presence of homologous chromosomes with very similar nucleotide sequences make Hi-C analysis difficult. We propose a new algorithm using allele-specific single-nucleotide variations (SNVs) to reconstruct the three-dimensional (3D) chromosomal architectures from the Hi-C dataset of single diploid cells. Our algorithm has a function to discriminate SNVs specifically found between homologous chromosomes to our "recurrence plot"-based algorithm to estimate the 3D chromosome structure, which does not require imputation for ambiguous segment information. The new algorithm can efficiently reconstruct 3D chromosomal structures in single human diploid cells by employing only Hi-C segment pairs containing allele-specific SNVs. The datasets of the remaining pairs of segments without allele-specific SNVs are used to validate the estimated chromosome structure. This approach was used to reconstruct the 3D structures of human chromosomes in single diploid cells at a 1-Mb resolution. Introducing a subsequent mathematical measure further improved the resolution to 40-kb or 100-kb. The reconstruction data reveals that human chromosomes form chromosomal territories and take fractal structures where the mean dimension is a non-integer value. We also validate our approach by estimating 3D protein/polymer structures.