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. 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 [4,5], Rosenberg et al. evaluated the effect of codon identity on a finer scale, analyzing whether the distribution of (ϕ, ψ) dihedral angles within secondary structure elements is significantly altered when synonymous codons are used. However, their statistical methodology is formally incorrect, casting doubt on the obtained results. The origin of the incorrectness is described in the following section. Then, using an appropriate methodology, we reanalyzed the data presented in [1]. Our results confirm the influence of the codon on the distribution of the dihedral angles, but differ from those of Rosenberg et al. in the strength of significance of the differences depending on the secondary structure type. Finally, we assessed whether these findings may be affected by the structural classification or the local sequence context. These additional analyses show that codon-specific effects have similar significance in different areas of Ramachandran space, although the effect may be stronger for a particular type of secondary structure, such as β-strands compared to α-helices. They also indicate that synonymous codon effects are stronger when considered in the context of the local sequence.