Statistical tests to detect differences between codon-specific Ramachandran plots
In their recent work, Rosenberg et al. [1] studied the dependence between the identity of synonymous codons and the distribution of the backbone dihedral angles of the translated amino acids. In the past, it has been shown that the use of synonymous codons is highly relevant in multiple biological processes including, among others, mRNA splicing, translational rates and protein folding [2, 3]. While the correlation between synonymous codons and secondary structure in translated proteins has been widely studied [4-6], Rosenberg et al. evaluated the effect of codon identity on a finer scale, analyzing whether the distribution of ({phi}, {psi}) dihedral angles within secondary structure elements is significantly altered when synonymous codons are used. Their conclusion, showing significant differences, particularly for amino acid residues involved in {beta}-strands, would represent a new paradigm for the role played by synonymous codons in defining protein structure. However, the statistical methodology used in that study was formally incorrect, casting doubt on the obtained results. Besides, it is based on density estimates that might be imprecise for small sample sizes, yielding misleading comparisons. These methodological errors are described in the following section. Then, using an appropriate methodology, we reanalyzed the data presented in [1]. Our results show that the influence of the codon on the distribution of the dihedral angles is statistically non-significant for all types of secondary structures, contradicting the conclusion by Rosenberg et al.. These results were corroborated by repeating the analysis on structures extracted from the AlphaFold Database [7, 8] for the same set of proteins, and shown to be robust with respect to the definition secondary structural classes and also when considering the nature of the neighbor residues. Overall, our observations demonstrate that the influence of the synonymous codons on the backbone dihedral angles can not be inferred with current data.