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.
