RF-Interaction Concept
RF-interactions are protein-ligand interactions based on the Ratio Of Frequencies (RF). When looking at a ligand inside a protein binding site, one wants to know which contacts help binding and which don't. The classic approach (e.g. PLIP) uses geometric rules to determine which atoms interact with each other. Typically, rules can tell that a contact exists, but don't really allow to quantify interaction strength. The Ratio of Frequencies (RF) approach adresses this question with statistics. It counts how often a given pair of precisely defined atom types occurrs in real crystal structures and compares that count with what pure chance would give. The concept was originally conceived by R. Taylor to study crystal packing on small molecule crystal structures: Which intermolecular interactions have a significant influence on crystal packing? R Taylor; CrystEngComm, 2014, 16, 6852; DOI: 10.1039/c4ce00452c.
Later the concept was extended and applied to binding sites: B Kuhn, E Gilberg, R Taylor, J Cole, O Korb; How Significant Are Unusual Protein-Ligand Interactions? Insights from Database Mining; J Med Chem, 62, 22, (2019), 10441-55; DOI: 10.1021/acs.jmedchem.9b01545.
The RF-concept will be explained here first for the crystal packing study. Afterward, the extention to ligand-protein interactions will be discussed. In order to build the interaction statistics for small molecule crystals, all non-covalent atom-atom contacts were studied in about 137,000 crystal structures from the Cambridge Structural Database. Simple atom types were assigned to all atoms based on atomic number and close neighbor environment.
Imagine molecules packed with random orientations. Then, the chance that a particular atom of type A touches any atom of type B would depend only on how much of the molecular surface belongs to atoms of type B. For each structure, the expected number of A⇢B contacts is E(A⇢B) = NA * SB / St. Here NA is the number of type A atoms that form a contact, SB the exposed surface area of B atoms, and St is the total exposed surface area. RF is the observed number of contacts divided by this expected number, averaged over the whole dataset:
- RF > 1: the contact occurs more often than chance predicts. Nature prefers it.
- RF ≈ 1: the contact is neutral and occurs as often as random packing would produce.
- RF < 1: the contact is avoided. Other contacts win.
When applying the concept to protein-ligand complexes, the situation gets a little more complicated, because two different kinds of molecules interact with eachother. Since ligand atom types are much more diverse than protein atoms types, ligand and protein atoms are classified by different rules. For the same reason, individual RF-values can be calculated from a ligand perspective and from the protein perspective, always considering surface fractions of the type of the opposite atom. Final RF-values for the complete interaction are then calulated as a geometric mean from both individual values.
Since the original paper described the concept, but didn't publish the final statistics with it, the RF-statistics for DataWarrior was rebuilt from scratch by processing all PDB structure entries submitted before Aug 2026. From these, we considered all non-covalent binding sites, which don't contain metal atoms, with ligands containing at least eight non-hydrogen atoms, with a resolution of at least 2.5Å, and that are not redundant regarding PDB-ID and ligand structure. This yielded about 200,000 binding sites.
Atom types were assigned to all ligand atoms applying a predefined dictionary of 265 meaningful substructures, that distinguish atoms of different interaction behavior. Likewise, 53 protein atom types were assigned to all protein cavity atoms applying a different substructure dictionary. Thus, we distinguish 14045 (265*53) potential interactions, considering that any ligand atom type can interact with any protein type. The substructure definitions and atom type names were taken J. Cole's GitHub repository (https://github.com/jasonccole/relative-interaction-frequencies/tree/main/atom_types), but were slightly adapted, because of incompatibilities of the original SMARTS based encoding with our OpenChemLib concepts, mainly regarding aromaticity.
As in the 2019 paper described, we consider ligand-protein atom contacts only, if the atoms are closer that the sum of their VDW-radii + 0.5A, and if there is an unobstructed line of sight between the atom center coordinates. Then, for every ligand and protein atom type combination we determined all bindings sites that contained at least one atom of the ligand type and one of the protein type. From these binding sites we calculated the RF-value RFL from the ligand perspective using surface fractions on the protein side. Likewise, we calculated RF-value RFP from the protein perspective using surface fractions on the ligand side. Finally, we obtained the raw RF-value for the ligand-protein type combination as SQRT(RFL * RFP).
The published RF-approach defines an atom type specific angle as one additional parameter. Then, from the angle distribution statistics an angle range is derived, beyond which a contact is not considered an interaction anymore. Different to that binary cutoff, we went a step further for DataWarrior: We assigned a geometry class to any ligand and protein atom type. Basically, the geometry class depends on the interacting atom's neighbor count and its or its neighbor's hybridization. Then, we defined two geometry class specific parameters, an angle and a torsion value.
angle and torsion definition for geometry class n1-sp2
For every geometry class we harvested the binding sites to collect a two-dimensional frequency map with angle and torsion as parameters. Since shorter and longer interactions differ somewhat regarding the angle-torsion distribution, we build separate maps for shorter and for longer interactions. Then, using a kernel density estimation, we built smoother versions of the maps. With this we are able to calculate a geometry aware RF-value by multiplying the raw RF-value with a normalized density value taken from the map with angle and torsion as input parameters.
Smooth frequency maps for geometry class n4sp3 (4 neighbors at interacting atom)