Fig. 2: Different propensities for secondary structures of synonymous codons are manifested in the dihedral angle distribution.

Out of the two codons GTA and GTT translating valine, GTA has 8% lower propensity for the β mode and 9.4% higher propensity for the α mode. Propensities are manifested through the relative weights of the corresponding modes in the Ramachandran plot, which is visible in the marginal distributions of the dihedral angle φ plotted here. When conditioned by secondary structure (i.e., restricted to a specific mode), the distributions of the two synonymous codons become indistinguishable. By conditioning on secondary structure, our analysis is made robust to distribution differences arising from propensities differences. Kernel density estimates are shown with the shaded regions denoting 10–90% confidence intervals calculated on 1000 random bootstraps.