Construction of genetic code from evolutionary stability

The construction of the genetic code is investigated based on a stability principle. The concept and formulation of mutational deterioration (MD) of the genetic code is proposed. It is proved that the degeneracies of codon multiplets obey the rule to best resist MD. The MD for each ideal multiplet of codons is expressed by four parameters and it takes on a minimum value for real distributions of codons in the multiplet. Then the global mutational deterioration (GMD) of code table is calculated and the minimal code is deduced. The domain-like distribution of hydrophobic and hydrophilic amino acids on the genetic code is explained from the minimization of GMD. It is demonstrated that the standard code is approximately GMD-minimal. By introducing some constraints that are related to the initial condition of the system, we have deduced the standard genetic code from the minimization of GMD. The minimization shows the general trend of evolutionary process to some stable state while the constraints reflect a 'frozen accident.' Many deviant codon assignments are also explained through MD minimization assuming the changeable degrees of degeneracies for some multiplets. So, a possible answer to the question of "Why are synonymous codons and amino acids distributed in the code table just as they are?" is given.