Distance Matrix Prediction

The core transformation converts Hi-C interaction frequencies into Euclidean distance estimates using inverse power-law relationships. Since contact probability decays approximately as 1/d^α in polymer physics, models learn to map normalized contact counts to spatial distances.

• Polymer physics constraints enforce realistic distance distributions
• Distance-dependent decay curves calibrate the frequency-to-distance mapping
• Ensemble averaging accounts for cell population heterogeneity
• Output is a symmetric N×N matrix where each entry represents the 3D distance between loci i and j

Beyond MDS, distance geometry frameworks formulate structure determination as a constrained optimization problem. The goal is to find 3D coordinates that minimize the discrepancy between predicted and target distances while satisfying physical constraints.

• Semidefinite programming relaxations provide global convergence guarantees
• Gradient descent on stress functions iteratively refines coordinates
• Bound smoothing tightens feasible distance ranges before optimization
• Excluded volume constraints prevent non-physical chain crossings

Each pairwise distance prediction carries inherent uncertainty due to population heterogeneity and experimental noise. Modern approaches output distance distributions rather than point estimates, enabling probabilistic structure reconstruction.

• Bayesian neural networks produce posterior distance distributions
• Ensemble methods capture model uncertainty across multiple predictions
• Conformal prediction provides statistically valid confidence intervals
• Uncertainty correlates with genomic regions of high structural variability

Training distance prediction models requires specialized loss functions that respect the geometric constraints of 3D space. Standard MSE is often augmented with structure-aware penalties.

• Stress functions measure preservation of distance rank order
• Triplet losses enforce triangle inequality constraints (d_ij + d_jk ≥ d_ik)
• Spectral losses match eigenvalue distributions of predicted and true distance matrices
• Stratum-adjusted losses account for genomic distance-dependent error patterns

GNN-based architectures predict distances by learning pairwise relationships directly from the chromatin interaction graph. Message passing between genomic loci nodes captures both local neighborhood structure and long-range dependencies.

• Edge prediction heads output scalar distances for each node pair
• Attention mechanisms weight the influence of neighboring loci
• Equivariant layers ensure predictions respect rotational and translational symmetry
• Graph topology reflects the Hi-C contact map adjacency structure

A genome-wide matrix quantifying the interaction frequencies between all pairs of genomic loci. This is the primary experimental input and prediction target for 3D genome folding models. Contact probability is typically normalized to account for systematic biases like GC content and mappability.

• Stored in scalable formats like Cooler for efficient out-of-core computation.
• Serves as the raw data from which a distance matrix is ultimately derived via optimization.

The computational process of converting a Hi-C contact matrix into a consensus 3D structure. This involves inferring a pairwise Euclidean distance matrix from contact frequencies, often using an inverse relationship (e.g., distance ∝ contact^(-1)).

• Constraints from polymer physics ensure physically plausible structures.
• DNA FISH serves as a gold-standard experimental validation for the predicted spatial distances.

A reproducibility metric specifically designed for Hi-C data that measures the similarity between two contact maps while accounting for the distance-dependent signal. This is the standard benchmark for evaluating distance matrix prediction accuracy.

• Unlike simple correlation, SCC controls for the expected background contact frequency decay.
• Essential for comparing predicted structures against experimental replicates.

A statistical correction applied to Hi-C contact maps to account for the expected background contact frequency decay as a function of linear genomic distance. This normalization is critical for isolating biologically significant interactions.

• Enables the detection of chromatin loops and TADs.
• The normalized matrix is the direct input for inferring the true spatial distance matrix.

A deep learning architecture that represents genomic loci as nodes and their interactions as edges. GNNs predict 3D genome structures by learning relational patterns from DNA sequence and epigenomic features.

• Directly predicts the pairwise distance matrix by message passing between loci.
• Models like Akita use convolutional architectures, but GNNs offer a natural inductive bias for relational data.

A deep learning model that integrates principles of polymer physics to generate physically plausible 3D genome structures. These networks constrain the predicted distance matrix to obey physical laws.

• Incorporates excluded volume constraints to prevent loci from occupying the same space.
• Uses contact probability decay functions derived from polymer theory to regularize predictions.