The standard genetic code (SGC) describes how 64 trinucleotides (codons) encode 20 amino acids and the stop translation signal. Biochemical and statistical studies have shown that the standard genetic code is optimized to reduce the impact of errors caused by incorporation of wrong amino acids during translation. This is achieved by mapping codons that differ by only one nucleotide to the same amino acid or one with similar biochemical properties, so that if misincorporation occurs, the structure and function of the translated protein remain relatively unaltered. Some previous studies have extended the analysis of SGC optimality to the effect of frameshift errors on the conservation of amino acids. Here, we compare the optimality of the SGC with a set of circular codes, and in particular the X circular code identified in genes, on the basis of various biochemical properties over all possible frameshift errors. We show that the X circular code is more optimized to minimize the impact of frameshift errors than the SGC for the chosen amino acid properties. Furthermore, in the context of a problem that has been unresolved since 1996, we also demonstrate that the X circular code has a frameshift optimality in its combinatorial class of 216 maximal self-complementary C3 circular codes. To our knowledge, this is the first demonstration of the role of the X circular code in mitigation of translation errors. These results lead us to discuss the potential role of the X circular code in the evolution of the standard genetic code.
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