Abstract Motivation Most amino acids are encoded by multiple synonymous codons, some of which are used more rarely than others. Analyses of positions of such rare codons in protein sequences revealed that rare codons can impact co-translational protein folding and that positions of some rare codons are evolutionarily conserved. Analyses of their positions in protein 3-dimensional structures, which are richer in biochemical information than sequences alone, might further explain the role of rare codons in protein folding. Results We model protein structures as networks and use network centrality to measure the structural position of an amino acid. We first validate that amino acids buried within the structural core are network-central, and those on the surface are not. Then, we study potential differences between network centralities and thus structural positions of amino acids encoded by conserved rare, non-conserved rare, and commonly used codons. We find that in 84% of proteins, the three codon categories occupy significantly different structural positions. We examine protein groups showing different codon centrality trends, i.e., different relationships between structural positions of the three codon categories. We see several cases of all proteins from our data with some structural or functional property being in the same group. Also, we see a case of all proteins in some group having the same property. Conclusion Our work shows that codon usage is linked to the final protein structure and thus possibly to co-translational protein folding. Availability https://nd.edu/~cone/CodonUsage/ Supplementary information Attached.

Protein structural classification (PSC) is a supervised problem of assigning proteins into pre-defined structural (e.g., CATH or SCOPe) classes based on the proteins' sequence or 3D structural features. We recently proposed PSC approaches that model protein 3D structures as protein structure networks (PSNs) and analyze PSN-based protein features, which performed better than or comparable to state-of-the-art sequence or other 3D structure-based PSC approaches. However, existing PSN-based PSC approaches model the whole 3D structure of a protein as a static (i.e., single-layer) PSN. Because folding of a protein is a dynamic process, where some parts (i.e., substructures) of a protein fold before others, modeling the 3D structure of a protein as a PSN that captures the sub-structures might further help improve the existing PSC performance. Here, we propose to model 3D structures of proteins as multi-layer sequential PSNs that approximate 3D sub-structures of proteins, with the hypothesis that this will improve upon the current state-of-the-art PSC approaches that are based on single-layer PSNs (and thus upon the existing state-of-the-art sequence and other 3D structural approaches). Indeed, we confirm this on 72 datasets spanning ~44 000 CATH and SCOPe protein domains.

Most amino acids are encoded by multiple synonymous codons. For an amino acid, some of its synonymous codons are used much more rarely than others. Analyses of positions of such rare codons in protein sequences revealed that rare codons can impact co-translational protein folding and that positions of some rare codons are evolutionary conserved. Analyses of positions of rare codons in proteins' 3-dimensional structures, which are richer in biochemical information than sequences alone, might further explain the role of rare codons in protein folding. We analyze a protein set recently annotated with codon usage information, considering non-redundant proteins with sufficient structural information. We model the proteins' structures as networks and study potential differences between network positions of amino acids encoded by evolutionary conserved rare, evolutionary non-conserved rare, and commonly used codons. In 84% of the proteins, at least one of the three codon categories occupies significantly more or less network-central positions than the other codon categories. Different protein groups showing different codon centrality trends (i.e., different types of relationships between network positions of the three codon categories) are enriched in different biological functions, implying the existence of a link between codon usage, protein folding, and protein function.

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