Hi-C Contact Maps and TAD Triangles
A Hi-C map turns an ensemble of ligation events into a binned view of how often genomic regions were near one another.
Dense biological and visual signals resolved into structure, geometry, and interpretable layers.
Interactive model
Contact intensity around a movable boundary
Shift the boundary and watch contact intensity reorganize into two domains. Treat the display as a teaching model, not a reconstruction of one cell.
Live HTML simulation · adjust the controls and watch the computed output respond.
Interactive
TAD boundaries appear where contact intensity changes
This is a simplified teaching model. Its displayed values are computed from the controls; the article explains where the model stops.
Site connection
Read Hi-C matrices as resolution- and normalization-dependent measurements, recognize why self-interacting domains form triangles, and distinguish structural hypotheses from experimental conclusions.
Definition: What a Contact Matrix Measures
Hi-C measures pairs of DNA fragments that were cross-linked, cut, ligated, and sequenced together. After mapping and binning, entry C(i,j) is a contact count or processed contact value for genomic bins i and j. The map is symmetric for an undirected assay, and its strong diagonal largely reflects the greater contact frequency of loci close along the chromosome.
A pixel is therefore an ensemble measurement over many molecules and usually many cells. It is not a photograph, a permanent bond, or proof that every contact occurred simultaneously. Bin size sets the map's nominal resolution: a 5 kb pixel combines a much smaller genomic interval than a 100 kb pixel but generally needs more reads to be stable.
Mental model: the matrix is a weighted adjacency table for observed proximity events. The heatmap is its visual encoding—not a literal 3D chromosome.
Why Domains Become Triangles
A topologically associating domain (TAD) is a contiguous interval whose loci tend to contact other loci inside the interval more frequently than loci across its boundaries. In a square matrix, that enrichment is a square block centered on the diagonal. Showing only the upper or lower half rotates or clips the same block into a triangle; the triangle is a plotting consequence, while the enriched contacts are the biological signal.
Boundaries matter because they mark transitions between interaction neighborhoods and can constrain some enhancer–promoter communication. They are usually graded, context-dependent regions rather than impenetrable walls, and different callers may place or score them differently.
| Visual feature | Careful interpretation |
|---|---|
| Bright diagonal | Short genomic separation usually produces frequent contacts |
| Bright diagonal block or triangle | Candidate region of enriched internal contact |
| Local loss of cross-boundary signal | Possible insulation at that position |
| Off-diagonal dot or stripe | Candidate focal or extended interaction requiring statistical support |
| Difference-map color | Change under the chosen preprocessing and color scale, not automatically a biological effect |
Mechanics: From Counts to a Comparable Map
A defensible comparison fixes the genome assembly, locus, bin edges, resolution, balancing method, distance correction, masking, smoothing, and color scale. Matrix balancing reduces systematic row and column biases; observed-over-expected transforms compare contacts with the distance-dependent background. These answer different questions and should not be silently mixed.
Inspection should move from coarse structure to local detail: verify coverage and valid bins, inspect the diagonal and compartment-scale pattern, examine candidate domain enrichment, then compare boundary tracks or perturbations. Biological replicates and a quantitative summary—such as insulation, directionality, or a predefined region-of-interest statistic—are stronger evidence than visual contrast alone.
Never compare brightness across panels until normalization and the color range are known. Auto-scaled panels can make equal matrices look different or unequal matrices look similar.
Worked Example
Consider four consecutive 10 kb bins with a candidate boundary between bins 2 and 3. Within the left pair C(1,2)=80 and within the right pair C(3,4)=72. The four cross-boundary cells C(1,3), C(1,4), C(2,3), and C(2,4) contain 12, 8, 15, and 5 contacts, so their mean is (12+8+15+5)/4=10. The mean within-pair contact is (80+72)/2=76. In this simplified example, internal contacts are 7.6 times the cross-boundary mean, consistent with two locally insulated blocks.
That ratio is descriptive, not a boundary p-value. Genomic separation differs among the cells, raw counts may contain coverage biases, and four bins are too few for a robust call. A real analysis would use normalized matrices, distance-aware expectations, replicate-aware uncertainty, and a boundary statistic computed over many bins and window sizes.
| Check | Result | Interpretation |
|---|---|---|
| Internal mean | 76 contacts | Strong signal inside the two toy blocks |
| Cross-boundary mean | 10 contacts | Lower signal across the proposed split |
| Internal/cross ratio | 7.6 | Candidate insulation, conditional on preprocessing |
| Next evidence | Normalize, replicate, score | Required before treating the pattern as robust |
Perturbations, Predictions, and Limits
The portfolio project compares wild-type and deletion outputs, including AlphaGenome-predicted contact maps. A delta map can nominate regions where a deletion may alter folding, but an AlphaGenome output is a model prediction learned from experimental data—not new experimental truth. It can prioritize a CRISPR perturbation, not replace matched wet-lab measurement.
Apparent changes can arise from resolution, normalization, sequencing depth, cell mixture, batch effects, or the chosen display range. Even a reproducible contact change does not alone establish a gene-expression mechanism; orthogonal assays, appropriate controls, and a prespecified causal question are needed.
Analogy limit: a neighborhood map suggests which addresses interact often, but it does not show who visited whom in one particular household or why the visit occurred.
Common Pitfalls
- Reading every bright cell as a fixed direct contact in every cell.
- Comparing 5 kb and 100 kb maps as though bin size did not change the question and signal-to-noise ratio.
- Comparing raw, balanced, and observed-over-expected maps without labeling the transformation.
- Letting per-panel auto-scaling create an apparent perturbation effect.
- Treating TAD boundaries as perfectly sharp walls or a model-predicted delta as experimental validation.