Single-Cell Hi-C Imputation

Single-cell Hi-C contact maps are fundamentally sparse, often capturing less than 5% of possible pairwise interactions. This sparsity arises from the limited number of unique ligation events per chromosome in a single cell. Imputation models must distinguish biological zeros (true absence of contact) from technical zeros (contacts missed due to sampling depth). Deep learning approaches learn the underlying manifold of chromatin folding to infer the most probable contact values for unobserved locus pairs.

Modern imputation methods employ several neural architectures:

• Autoencoders: Compress sparse contact maps into a latent representation and reconstruct dense outputs, denoising in the process.
• Graph Convolutional Networks (GCNs): Model chromosomes as graphs where nodes are genomic bins and edges represent contacts, propagating information across the structure.
• Generative Adversarial Networks (GANs): Train a generator to produce realistic dense contact maps that a discriminator cannot distinguish from high-coverage experimental data.
• Diffusion Models: Iteratively denoise random matrices into structured contact maps by learning the reverse process of adding noise to real data.

Imputation models often incorporate bulk Hi-C data or ensemble contact maps as a structural prior. This population-level signal provides a scaffold of expected interaction frequencies, such as topologically associating domains (TADs) and chromatin loops. The model then learns cell-specific deviations from this prior, enabling the recovery of cell-type-specific folding patterns and rare structural variants that distinguish individual cells from the population average.

Validating imputed contact maps requires metrics that account for the distance-dependent nature of chromatin interactions:

• Stratum-Adjusted Correlation Coefficient (SCC): Measures similarity between imputed and ground-truth maps while controlling for genomic distance.
• Pearson Correlation by Distance: Evaluates accuracy at short-range (<100 kb), medium-range, and long-range (>1 Mb) interactions separately.
• TAD Boundary Recall: Assesses whether imputed maps preserve domain boundaries identified in high-depth data.
• Loop Detection Accuracy: Quantifies recovery of known chromatin loops from deeply sequenced controls.

Imputed contact maps serve as input for 3D genome reconstruction algorithms that convert interaction frequencies into spatial coordinates. Methods like ShRec3D and miniMDS apply multidimensional scaling or distance geometry optimization to generate consensus 3D structures. The quality of imputation directly impacts the accuracy of recovered chromosome territories, compartmentalization, and enhancer-promoter proximity measurements, making imputation a critical preprocessing step for single-cell structural biology.

Single-cell Hi-C imputation must scale to thousands of cells per experiment. Key optimization strategies include:

• Matrix factorization to reduce dimensionality before imputation
• Sparse tensor operations that avoid materializing dense matrices
• Transfer learning from models pre-trained on bulk Hi-C data
• GPU-accelerated graph convolutions for rapid inference These techniques enable genome-wide imputation at 1 kb resolution across entire single-cell atlases without prohibitive memory requirements.

A genome-wide matrix quantifying interaction frequencies between all pairs of genomic loci. In single-cell Hi-C, these maps are extremely sparse, with often less than 1-5% of possible contacts observed, making imputation essential for downstream analysis. The matrix serves as both the input for imputation models and the ground truth for evaluating reconstruction accuracy.

A deep learning architecture representing genomic loci as nodes and their interactions as edges in a graph. GNNs are particularly suited for single-cell Hi-C imputation because they can:

• Model sparse, irregular interaction patterns
• Propagate information across local neighborhoods
• Learn relational patterns from DNA sequence and epigenomic features
• Recover missing edges through message passing between observed contacts

The inference of a pairwise Euclidean distance matrix representing the 3D spatial proximity of all genomic loci. Many imputation methods first predict distances from observed contacts, then convert these back to contact probabilities. This physics-informed approach constrains imputed values to satisfy triangle inequality and other geometric constraints, producing more realistic 3D structures than direct contact imputation alone.

A reproducibility metric specifically designed for Hi-C data that measures similarity between two contact maps while accounting for distance-dependent signal decay. SCC is the standard benchmark for evaluating single-cell Hi-C imputation quality because it:

• Controls for the expected background contact frequency
• Penalizes imputation errors at short and long ranges differently
• Provides a single, interpretable score for model comparison

The computational process of converting an imputed Hi-C contact matrix into a three-dimensional consensus structure of individual chromosomes. After imputation fills missing contacts, optimization algorithms constrained by polymer physics generate spatial coordinates for each locus. This enables visualization of single-cell chromatin architecture and identification of structural features like TADs and loops that were obscured by sparsity.