Physics-Based Modeling of Sparse Single-Cell Hi-C Uncovers Structural and Epigenetic Variability

Chromatin conformation capture technologies have revealed the complex 3D organization of the genome and its key regulatory role. Single-cell Hi-C (scHi-C) maps this architecture at single-cell level, but its sparse nature makes data interpretation challenging, and tools for their analysis remain limited. Here, we present a physics-based framework that combines polymer modeling with computational methods to reconstruct full 3D genome structures from sparse scHi-C data. Using both artificial and experimental data, we show that our approach imputes missing contacts and recovers accurate structures validated against independent Hi-C and established polymer models. Applied to scHi-C from a 15 Mb region of human HeLa-S3 cells as a case study, the method uncovers distinct structural classes defined by the spatial distribution of chromatin binding domains. The reconstructed models enable robust downstream analyses, including the identification of single-cell topologically associated domains (TADs), which appear highly variable across cells yet tend to accumulate around those observed in bulk. Importantly, the inferred 3D polymer models capture diverse epigenetic signatures, with active chromatin domains exhibiting greater structural variability than repressive ones across single cells. Overall, our study provides a mechanistic and interpretable framework to analyze sparse scHi-C data, highlighting how polymer physics can be leveraged to uncover genome architecture and its functional variability at single-cell resolution.