Physical model for the evolution of the genetic code

Using the shape space of codons and tRNAs we give a physical description of the genetic code evolution on the basis of the codon capture and ambiguous intermediate scenarios in a consistent manner. In the lowest dimensional version of our description, a physical quantity, codon level is introduced. In terms of the codon levels two scenarios are typically classified into two different routes of the evolutional process. In the case of the ambiguous intermediate scenario we perform an evolutional simulation implemented cost selection of amino acids and confirm a rapid transition of the code change. Such rapidness reduces uncomfortableness of the non-unique translation of the code at intermediate state that is the weakness of the scenario. In the case of the codon capture scenario the survival against mutations under the mutational pressure minimizing GC content in genomes is simulated and it is demonstrated that cells which experience only neutral mutations survive.