Contact Map

A contact map records which residue pairs are close in 3D space. It is a compact structural representation used for folding, structure comparison, and graph construction.

Given residue coordinates $x_i$, a binary contact map is:

$$C_{ij}=1\left[\Vert x_i-x_j{\Vert }_2\le \tau \right]$$

where $\tau$ is a distance cutoff.

A soft distance map keeps the continuous geometry:

$$D_{ij}=\Vert x_i-x_j{\Vert }_2$$

Contact maps are invariant to global rigid motion:

$$D_{ij}(RX+t)=D_{ij}(X)$$

for rotation $R$ and translation $t$. They discard global orientation and much of local frame information.

Contact Definition

The definition of $x_i$ changes the map:

• $C_{\alpha }$: simple backbone-based distance.
• $C_{\beta }$: common for residue contact maps, with glycine handled specially.
• Minimum heavy-atom distance: side-chain-aware but sensitive to atom completeness.
• Residue center: coarse but stable for graph construction.

Contacts can also exclude local sequence neighbors:

$$|i-j|>k$$

so that long-range structural contacts are not dominated by adjacent residues.

Map Types

Map	Formula / Value	Use
binary contact	$1[D_{ij}\le \tau ]$	graph edge, classification target
distance map	$D_{ij}$	geometry supervision and comparison
binned distance	class over distance intervals	structure prediction target
orientation-aware map	distance plus angles/frames	richer fold constraints
inter-chain contact	residue pairs across chains	complex/interface modeling
pocket-ligand contact	residue/atom vs ligand atom	SBDD interaction features

The map type should match the downstream claim. A binary contact map cannot fully recover chirality, side-chain orientation, or atom-level clashes.

Loss and Metrics

For binary contact prediction, a common loss is cross-entropy over residue pairs:

$$\mathcal{L}=-\sum _{i<j}\left[C_{ij}\log {\hat{p}}_{ij}+(1-C_{ij})\log (1-{\hat{p}}_{ij})\right]$$

Because contacts are sparse, evaluation often uses top-$L$, top-$L/2$, precision, or long-range contact precision rather than plain accuracy.

For distance maps, regression or binned classification can be used:

$${\mathcal{L}}_D=\sum _{i<j}\rho ({\hat{D}}_{ij},D_{ij})$$

where $\rho$ should respect missing residues and unresolved regions.

Use in Models

Contact maps can be:

• prediction targets
• graph edges
• structure comparison summaries
• constraints for folding or refinement
• diagnostic views for sequence-structure models

Before building a contact map from coordinates, verify Residue indexing and Protein structure cleaning.

Leakage and Preprocessing

Contact maps derived from experimental or predicted structures can leak template information:

Source	Risk
experimental structure	may overlap with benchmark template or homolog
predicted structure	teacher-model leakage if used as label or input
MSA-derived contacts	family-level information can cross splits
ligand-defined pocket contacts	unavailable in blind deployment
missing residues treated as non-contact	false negatives from unresolved structure

Checks

• Which atom represents a residue: $C_{\alpha }$, $C_{\beta }$, backbone center, or all-atom minimum?
• What cutoff defines contact?
• Are sequence-neighbor contacts separated from long-range contacts?
• Does the map ignore chirality, orientation, or side-chain geometry needed by the task?
• Are missing residues masked rather than treated as far-away residues?
• Is the contact definition identical across train, validation, test, and inference?
• Is the contact map an input, target, metric, graph edge rule, or diagnostic?
• Are local, medium-range, long-range, and inter-chain contacts separated when needed?
• Does the split prevent homolog/template leakage?

Related

• Structure
• Residue indexing
• Protein structure cleaning
• Multiple sequence alignment
• Template leakage
• Graph construction
• Protein structure prediction
• Invariance
• Geometric architecture