Symmetric group of the genetic-code cubes. Effect of the genetic-code architecture on the evolutionary process

The current evidence supports that the genetic code architecture is optimized to minimize the transcriptional and translational errors and to preserve amino-acid hydrophobicity during mutational events. The genetic code is mathematically equivalent to a cube inserted in the ordinary three-dimensional (3D) space, which leads to consistent phylogenetic analyses of DNA protein-coding regions. Herein, the symmetric group (GC,°) of the genetic-code cubes is formally developed. Next, it is shown that principal component (PC) scales of amino-acid derived from subsets of the genetic-code cubes are highly correlated with hydrophobicity and other physicochemical amino-acid properties. The effect of this architecture on the evolutionary process was modelled by a Weibull probability distribution to fit the evolutionary mutational cost estimated using amino acid PC-scales optimized on a set of homologous proteins. The application of Weibull model permits the identification of mutational events with high and low probabilities of fixation in gene populations. It is illustrated how this approach conveys a valuable information for de novo vaccine design.