Protein-Ligand Interaction

Protein-ligand interaction describes how a ligand and a protein binding site make contacts in 3D space. It connects docking, scoring, pose quality, binding affinity, and structure-based model interpretation.

A protein-ligand complex can be represented as:

$$C=(P,L,X_P,X_L)$$

where $P$ is the protein or pocket, $L$ is the ligand, and $X_P$, $X_L$ are their coordinates.

Pairwise protein-ligand distances are:

$$d_{ij}=\Vert x_i^{(P)}-x_j^{(L)}{\Vert }_2$$

for protein atom or residue coordinate $x_i^{(P)}$ and ligand atom coordinate $x_j^{(L)}$.

Common Interaction Types

• Steric complementarity and shape fit.
• Hydrogen bonds.
• Hydrophobic contacts.
• Salt bridges and electrostatic interactions.
• Pi-stacking or pi-cation interactions.
• Metal coordination.
• Water-mediated contacts.

Interaction Predicate

An interaction is more than a short distance. It usually combines atom types, geometry, and chemical state:

$$I_{ij}^{(r)}=1\left[d_{ij}\le {\tau }_r\wedge \mathrm{type}(i,j)=r\wedge G_r(i,j)=1\right]$$

where $r$ is an interaction rule, ${\tau }_r$ is a distance threshold, and $G_r$ encodes geometry such as angle, directionality, aromatic plane, or coordination constraints.

Distance-only contacts can be useful features, but they should not be described as chemically validated interactions without rule definitions.

Representation Contract

Representation	Captures	Risk
distance matrix	pairwise proximity	ignores atom type and direction
binary contact map	local pocket-ligand adjacency	threshold-sensitive
interaction fingerprint	rule-based interaction classes	depends on protonation and hydrogens
heterogeneous graph	atom/residue nodes and typed edges	graph construction can leak pose assumptions
3D grid or point cloud	spatial field around pocket	resolution and frame dependence
learned pair representation	model-specific interaction features	harder to interpret chemically

For a pair graph:

$$G_{PL}=(V_P\cup V_L,E_{PP}\cup E_{LL}\cup E_{PL})$$

where $E_{PL}$ defines cross protein-ligand edges. The edge rule should be stated before interpreting model attention or message passing as interaction evidence.

Modeling Views

• Contact map between pocket atoms/residues and ligand atoms.
• Interaction fingerprint over predefined interaction rules.
• Geometric graph with protein and ligand nodes.
• Grid or point-cloud representation around the binding site.
• Learned pair representation for scoring or pose refinement.

Pose vs Affinity Boundary

A plausible interaction pattern does not automatically imply strong binding affinity:

$$\text{good contacts}\nRightarrow \Delta G\text{ is accurate}$$

Pose quality asks whether the ligand geometry is plausible or close to a reference pose. Affinity asks whether the thermodynamic or assay endpoint is predicted. Scoring functions often mix these claims, so the note should separate:

Claim	Evidence
contact plausibility	interaction rules, clashes, geometry checks
pose recovery	RMSD, symmetry-aware atom mapping, PoseBusters-style checks
affinity prediction	assay endpoint, unit, split, regression/ranking metric
virtual screening	candidate pool, enrichment, false positive handling

Chemical State Sensitivity

Hydrogen bonds, salt bridges, metal coordination, and charge interactions depend on preparation:

$$I(P,L)=I(P_{\mathrm{state}},L_{\mathrm{state}},X_P,X_L)$$

Changing protonation, tautomer, hydrogens, metal treatment, water retention, or side-chain states can change the interaction fingerprint even when heavy-atom coordinates look similar.

Checks

• Are hydrogens, protonation states, waters, metals, and cofactors handled consistently?
• Is the interaction evaluated from a predicted pose or an experimental structure?
• Are contacts physically plausible, or only close in Euclidean distance?
• Is the model using interaction evidence available at deployment time?
• Are pose quality and affinity claims separated?
• Are interaction rules, thresholds, and angle constraints stated?
• Is the pocket definition independent of leaked ligand or template information?
• Are cross-edges built from predicted geometry, reference geometry, or deployment-available inputs?

Related

• Interaction prediction
• Protein-ligand complex
• Binding site
• Pocket definition contract
• Interaction fingerprint
• Pose quality
• Pose RMSD
• Scoring function
• Binding affinity
• Chemical state contract