Structure

A structure is a spatial arrangement of atoms, residues, or coarse-grained sites with coordinates and geometry.

A structure can be written as typed coordinates:

$$S=\{(a_i,x_i){\}}_{i=1}^N,x_i\in {\mathbb{R}}^3$$

where $a_i$ is atom, residue, or site identity and $x_i$ is its coordinate.

Why It Matters

• Structure carries the geometric information needed for docking, folding, and interaction modeling.
• Equivariance helps models treat rotated or translated structures consistently.
• Structural representations must distinguish coordinates, frames, distances, and chemical identity.
• A structure can be represented as coordinates, distances, contact maps, residue graphs, surfaces, grids, or local frames.

Structure Contract

Field	Question	Example
Unit	atom, residue, chain, pocket, complex, surface, grid?	protein backbone, ligand atoms
Source	experimental, predicted, template-derived, docked, generated?	X-ray, cryo-EM, predicted structure
Coordinate frame	global, receptor-aligned, ligand-centered, local residue frame?	arbitrary PDB frame
Resolution	all atom, backbone, C-alpha, coarse-grained, surface points?	$C_{\alpha }$ trace
Chemical state	protonation, tautomer, charge, waters, cofactors, metals?	prepared receptor
Missing data	unresolved residues, missing atoms, alternate locations?	loop gaps, side-chain completion
Allowed information	what was available at inference time?	no test ligand pose

For coordinate matrices:

$$X\in {\mathbb{R}}^{N\times 3}$$

the model should state whether atom/residue order is meaningful, arbitrary, or tied to a public indexing scheme.

Symmetry Boundary

Rigid motions should not change scalar labels:

$$f(X{R}^{\top }+1t^{\top })=f(X)$$

Coordinate outputs should transform with the input:

$$F(X{R}^{\top }+1t^{\top })=F(X)R^{\top }+1t^{\top }$$

If a paper uses absolute coordinates without explaining the frame, the structure claim is incomplete.

Source and Evidence

Structure Source	Claim Strength	Risk
experimental structure	strongest for measured geometry	resolution, missing atoms, construct differences
predicted structure	useful input or hypothesis	model bias and circular evidence
template-derived structure	prior from homolog	template leakage
docked structure	generated pose	scoring and pose quality must be separated
generated structure	model output	validity and physical plausibility required

Structure source should be recorded before comparing metrics.

Evaluation Boundary

Claim	Metric or Check
coordinate accuracy	RMSD, aligned error, distance error
contact prediction	precision/recall over contact map
pose quality	pose RMSD, clash, interaction recovery
geometry validity	bond lengths, angles, chirality, sterics
functional relevance	assay, binding, or downstream task evidence

Checks

• What coordinate frame, atom subset, and resolution are used?
• Are missing atoms, alternate conformations, and flexible regions handled?
• Does the model use distances only, coordinates, local frames, or full equivariant features?
• Is the output invariant, equivariant, or a mixture of scalar and coordinate predictions?
• Is the structure experimental, predicted, relaxed, docked, or generated?
• Does preprocessing leak a reference ligand, template, or future evaluation context?
• Are atom/residue mappings and alignment policies specified for coordinate metrics?
• Are invalid or incomplete structures counted rather than silently removed?

Related

• Protein
• Ligand
• Protein-ligand complex
• 3D structure
• Coordinate frame
• Distance geometry
• Contact map
• Sequence-structure alignment
• Equivariant GNN
• Coordinate modeling contract
• Pose quality