How informative are structural alphabets for representing protein folds?

Abstract

Amino acid sequences are the primary basis for protein comparison, but sequence similarity is often difficult to detect between distantly related proteins, even when their folds remain conserved. Therefore, comparing three-dimensional (3D) protein structures can reveal relationships that are not apparent from sequence alone. Full structural alignment uses 3D coordinates, whereas structural alphabets represent protein structures as sequences of discrete states. These alphabets differ in granularity: Q3 represents helices, strands, and loops using three states; Q8 uses the eight secondary-structure states defined by DSSP; and the 20-state 3Di alphabet, developed for Foldseek, describes tertiary residue-residue interactions. Here, we quantified the fold-level information retained by Q3, Q8, and 3Di across three CATH and SCOPe fold-recognition benchmarks, using TM-scores as the reference measure of full-structure similarity. The results reveal a Pareto-like trade-off: despite reducing protein structure to a linear pattern of helices, strands, and loops and discarding explicit information about spatial distances, residue orientations, and tertiary contacts, Q3 preserves approximately 90-96\% of the global fold-recognition signal available from full-structure comparison and is on par with the richer 20-state 3Di alphabet. Although Q3 lacks the fine-grained structural details needed to capture the remaining signal, it provides a simple, interpretable, and information-rich representation of protein-fold similarity. The central purpose of this study is therefore to quantify the fold-level information retained by a three-state secondary-structure representation, rather than to introduce Q3 as an alternative to full structural comparison or optimized search methods.