Tertiary alphabet for the observable protein structural universe

Abstract

Here, we systematically decompose the known protein structural universe into its basic elements, which we dub tertiary structural motifs (TERMs). A TERM is a compact backbone fragment that captures the secondary, tertiary, and quaternary environments around a given residue, comprising one or more disjoint segments (three on average). We seek the set of universal TERMs that capture all structure in the Protein Data Bank (PDB), finding remarkable degeneracy. Only ∼600 TERMs are sufficient to describe 50% of the PDB at sub-Angstrom resolution. However, more rare geometries also exist, and the overall structural coverage grows logarithmically with the number of TERMs. We go on to show that universal TERMs provide an effective mapping between sequence and structure. We demonstrate that TERM-based statistics alone are sufficient to recapitulate close-to-native sequences given either NMR or X-ray backbones. Furthermore, sequence variability predicted from TERM data agrees closely with evolutionary variation. Finally, locations of TERMs in protein chains can be predicted from sequence alone based on sequence signatures emergent from TERM instances in the PDB. For multisegment motifs, this method identifies spatially adjacent fragments that are not contiguous in sequence-a major bottleneck in structure prediction. Although all TERMs recur in diverse proteins, some appear specialized for certain functions, such as interface formation, metal coordination, or even water binding. Structural biology has benefited greatly from previously observed degeneracies in structure. The decomposition of the known structural universe into a finite set of compact TERMs offers exciting opportunities toward better understanding, design, and prediction of protein structure.tertiary motif | structural degeneracy | protein structural universe | sequence-structure relationships | structural modularity I n this work, we aim to decompose the protein structure space into its basic elements as a way of understanding its design principles and describing its limits. Reductionist representations of protein structure have been of long-standing interest (1), with many studies having shown degeneracy at various structural levels (2-5). Features ranging from backbone or side-chain dihedral angles (6, 7) to domains and folds (8, 9) have been classified, and structural basins of attraction have been found in select motifs (10-17), offering a glimpse of a modular space with frequently repeating elements. The reason behind this modularity appears to be a combination of evolutionary history and the fundamental physics of structure. In particular, degeneracy at the level of domains, folds, and functional modules is likely strongly influenced by evolution, whereby such elements recur in different proteins often because of a common ancestor (18,19). On the other hand, statistics of more detailed structural features are better explained from the thermodynamic perspective. For example, observed Ramachandran backbone dihedral angle preferences are largely determined...

Sequence statistics of tertiary structural motifs reflect protein stability

“…The search was performed by full-backbone RMSD, with the cutoff chosen automatically, as reported previously [20], based on the complexity of the query motif (see S1 Text). …”

Protein structural motifs in prediction and design

“…On the other hand, universal structural degeneracies could apply equally well to evolutionarily ancient, relatively novel, or even engineered proteins. In our own work, we have shown that the presence and location of multi-segment TERMs can be identified within proteins based purely on sequence information [34]. We built sequence models for each multi-segment TERM, from corresponding structural matches, and scored all alignments in previously unseen sequences to identify likely TERM positions.…”

“…We have developed efficient structure search algorithms, MaDCaT and MASTER, that find all matches to a given query, composed of one or more disjoint segments, within a user-specified similarity cutoff [31,32]. We have used MASTER, which searches by backbone RMSD, to describe and take advantage of higher-order degeneracies [33,34]. Towards this, we adopted a common definition of a motif that captures the secondary, tertiary, and quaternary structural environments around a given central residue.…”

“…The resulting score showed a strong correlation with model quality, evaluated as its distance from the native structure, and was further able to identify poorly predicted regions. We have also described a minimal set of TERMs that captures the observable structural universe (Figure 1) [34]. This has revealed considerable degeneracy beyond the secondary-structural level, such that only ∼600 TERMs are sufficient to describe over 50% of the known protein structural universe at sub-Angstrom resolution.…”

“…Further, we have shown that TERMs, along with their structural matches from unrelated proteins, provide an effective mapping between sequence and structure. For example, TERM-based statistics alone recapitulate close-to-native sequences given either NMR or X-ray backbones, with corresponding predicted sequence variations in close agreement with evolutionary ones [34]. …”