Directionality Index

The DI quantifies the net bias of chromatin interactions. For a given genomic bin, it calculates the difference between the sum of interactions with downstream loci and the sum of interactions with upstream loci, normalized by the total interactions.

• Formula: DI = [(B - A) / |B - A|] * ((A - E)^2 / E + (B - E)^2 / E) where A is downstream signal, B is upstream signal, and E is the expected value.
• Simplified Logic: A positive DI indicates a strong downstream bias, while a negative DI indicates an upstream bias.
• Hidden Markov Model (HMM) Input: The DI vector is the primary input for HMMs that segment the genome into discrete domain states.

The primary application of the DI is to pinpoint the precise locations of Topologically Associating Domain (TAD) boundaries. These boundaries act as insulators that restrict the loop extrusion process.

• Zero-Crossing Points: TAD boundaries are identified as genomic coordinates where the DI value flips its sign, transitioning from a positive (downstream) to a negative (upstream) bias.
• Insulation Correlation: A sharp change in the DI directly correlates with a high Insulation Score, another metric for boundary detection.
• CTCF Convergence: These boundaries are typically enriched with convergent CTCF binding sites, the molecular anchors that halt the cohesin complex.

The DI provides a direct readout of the loop extrusion process. A consistent downstream bias within a domain suggests the active, unidirectional movement of a cohesin complex.

• Upstream Bias: A negative DI value indicates a region where interactions are predominantly oriented toward the left boundary, often marking the end of an extrusion track.
• Downstream Bias: A positive DI value suggests the cohesin complex is actively reeling DNA toward the right boundary.
• Stalled Extrusion: A flat DI profile near zero can indicate a region where extrusion is stalled or where symmetric interactions dominate.

Calculating the DI from raw sequencing data involves a standardized preprocessing workflow to ensure signal accuracy.

• Input Data: A binned, normalized Hi-C contact map stored in a format like Cooler.
• Distance Normalization: The contact matrix must first be corrected for the expected background decay using Genomic Distance Normalization to prevent linear proximity from dominating the signal.
• Sliding Window: The DI is calculated over a fixed-size sliding window (e.g., 40kb to 100kb) along the chromosome to smooth local noise and capture domain-scale trends.

The accuracy of DI-based predictions is validated against experimental data using specialized metrics. The Stratum-Adjusted Correlation Coefficient (SCC) is the gold standard for comparing Hi-C maps.

• Distance-Aware Metric: Unlike generic correlation, the SCC accounts for the distance-dependent signal in Hi-C data, preventing trivial agreement from dominating the score.
• Boundary Validation: Predicted DI zero-crossings are validated against orthogonal methods like DNA FISH, which physically measures the spatial distance between loci.
• Resolution Impact: The precision of DI-based boundary calls is directly limited by the resolution of the underlying Hi-C map, which can be enhanced using models like DeepHiC.

The DI is not just an analytical metric; it serves as a powerful prediction target for sequence-to-structure models like Akita.

• Training Target: Deep neural networks are trained to predict the DI vector directly from raw DNA sequence and epigenomic features.
• Feature Engineering: The predicted DI can be used as an intermediate feature to reconstruct full Hi-C contact maps or to classify A/B compartments.
• Variant Impact: By predicting the DI for a mutated sequence, models can assess how structural variants disrupt domain boundaries and cause ectopic enhancer-promoter interactions.

A quantitative metric that measures the degree to which a genomic locus is insulated from interactions with neighboring regions. Calculated by sliding a square window along the Hi-C contact map and summing interaction frequencies within the window, the insulation score produces a valley at TAD boundaries where insulation is strongest. The Directionality Index and insulation score are complementary: the DI identifies the upstream/downstream bias of interactions, while the insulation score quantifies the absolute strength of the boundary separating domains.

A self-interacting genomic region where DNA sequences physically interact with each other more frequently than with sequences outside the domain. TADs are the fundamental structural units of chromosome folding, typically spanning 100 kb to 1 Mb in mammals. The Directionality Index is a primary computational tool for identifying TAD boundaries: a sign change in the DI (from positive to negative) indicates a transition from upstream-biased to downstream-biased interactions, marking the boundary between adjacent TADs.

A reproducibility metric specifically designed for Hi-C data that measures the similarity between two contact maps while accounting for the distance-dependent signal decay. Unlike standard Pearson correlation, the SCC stratifies contacts by genomic distance before computing correlation, preventing the dominant distance-decay trend from inflating similarity scores. Used as a benchmarking standard for evaluating the accuracy of predicted 3D genome structures against experimental Hi-C data.

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. Contact probability follows a power-law relationship with distance: loci that are closer together interact more frequently regardless of 3D structure. Normalization removes this distance-dependent bias, enabling the Directionality Index and other metrics to detect genuine structural features rather than artifacts of linear proximity.

A mechanistic model wherein cohesin complexes actively reel DNA to form progressively larger loops until blocked by CTCF boundary elements. The Directionality Index provides computational evidence for loop extrusion: at a convergent CTCF site acting as an extrusion barrier, the DI shows a sharp transition reflecting the directional bias of extruding cohesin complexes. This links the DI directly to the underlying molecular mechanism of 3D genome organization.

The classification of genomic regions into open, transcriptionally active 'A' compartments or closed, inactive 'B' compartments based on long-range interaction patterns. While the Directionality Index operates at the TAD scale (100 kb–1 Mb), compartment analysis captures higher-order organization at the multi-megabase scale. The two analyses are hierarchical: TADs nest within compartments, and the DI helps delineate the fine-scale boundaries within the broader compartment landscape.