Structure-conditioned amino-acid couplings: How contact geometry affects pairwise sequence preferences

Relating a protein's sequence to its conformation is a central challenge for both structure prediction and sequence design. Statistical contact potentials, as well as their more descriptive versions that account for side-chain orientation and other geometric descriptors, have served as simplistic but useful means of representing second-order contributions in sequence-structure relationships. Here we ask what happens when a pairwise potential is conditioned on the fully defined geometry of interacting backbones fragments. We show that the resulting structure-conditioned coupling energies more accurately reflect pair preferences as a function of structural contexts. These structure-conditioned energies more reliably encode native sequence information and more highly correlate with experimentally determined coupling energies. Clustering a database of interaction motifs by structure results in ensembles of similar energies and clustering them by energy results in ensembles of similar structures. By comparing many pairs of interaction motifs and showing that structural similarity and energetic similarity go hand-in-hand, we provide a tangible link between modular sequence and structure elements. This link is applicable to structural modeling, and we show that scoring CASP models with structured-conditioned energies results in substantially higher correlation with structural quality than scoring the same models with a contact potential. We conclude that structure-conditioned coupling energies are a good way to model the impact of interaction geometry on second-order sequence preferences.