How optimal is the genetic code

Abstract

The genetic code is well-known to be fault tolerant, in the sense that transcription errors in the third codon position frequently do not influence the amino acid expressed, while errors in other codon positions often lead to amino acids having similar chemical properties. Several articles in the recent past ([?, ?, ?] etc.) have studied the question of optimality of the genetic code. In [?] Di Giulio estimated that the natural code has achieved 68% minimization of polarity distance, by comparing the natural code with random block respecting codes (those codes obtained by relabeling the 20 amino acids in the natural table by a permutation thereof). When considering single base changes in the codons, let Ni,j be the number of times the i-th amino acid changes into the j-th amino acid, and Xi be the polarity index [?] of the i-th amino acid. The percent minimization is defined by