The chromatin conformation capture-related methods such as Hi-C have improved our understanding of nuclear architecture and organization in recent years. However, reconstruction of nuclear architecture of individual cells from single cell Hi-C (scHi-C) data has been challenging due to limited information of DNA contacts owing to the low efficiency of DNA recovery from a single cell. We have previously developed an algorithm named as “recurrence plot- based reconstruction (RPR) method” for reconstructing three dimensional (3D) genomic structure from Hi-C data of single haploid cells and diploid cells. This mathematical method is based on a recurrence plot, a tool of nonlinear time series analysis for visualizing temporal patterns within a time series and enables the reconstruction of a unique 3D chromosome architecture even from sparse (low-coverage) DNA contact information. Here we applied the RPR method to analyzing published scHi-C data of diploid cells derived from early-stage F1 hybrid embryos. We found that paternal and maternal chromosomes become gradually intermingled from 1 cell to 64 cell stage and that discrete chromosome territories (CTs) are largely established between 8 cell and 64 cell stages. We also observed Rabl-like polarized distribution of chromosomes from 2 cell to 8 cell stage but this polarization becomes mostly dissolved by 64 cell stage. The formation of Rabl-like configuration precedes rod-like extension of the chromosomal shape and their parallel alignment, implicating a role of Rabl-like configuration in avoiding entanglement and promoting effective mixing of chromosomes before establishment of CTs. We also found a cell-to-cell variability in chromatin configuration. Combination of scHi-C and RPR analyses thus can characterize distinct 3D chromatin architecture of individual cells at different developmental stages during early embryogenesis.

We propose an algorithm to refine the reconstruction of an original time series given a recurrence plot, which is also referred to as a contact map. The refinement process calculates the local distances based on the Jaccard coefficients with the neighbors in the previous resolution for each point and takes their weighted average using local distances. We demonstrate the utility of our method using two examples.