  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.
