  The importance of the notion of symmetry in physics is well established:
could it also be the case for the genetic code? In this spirit, a model for the
Genetic Code based on continuous symmetries and entitled the "Crystal Basis
Model" has been proposed a few years ago. The present paper is a review of the
model, of some of its first applications as well as of its recent developments.
Indeed, after a motivated presentation of our mathematical model, we illustrate
its pertinence by applying it for the elaboration and verification of sum rules
for codon usage probabilities, as well as for establishing relations and some
predictions between physical-chemical properties of amino-acids. Then, defining
in this context a "bio-spin" structure for the nucleotides and codons, the
interaction between a couple of codon-anticodon can simply be represented by a
(bio) spin-spin potential. This approach will constitute the second part of the
paper where, imposing the minimum energy principle, an analysis of the
evolution of the genetic code can be performed with good agreement with the
generally accepted scheme. A more precise study of this interaction model
provides informations on codon bias, consistent with data.
