Crystalizing the genetic code.

New developments are presented in the framework of the model introduced bythe authors in References [1, 2] and in which nucleotides as well ascodons are classified in crystal bases of the quantum group U(q)(sl(2) ⊕ sl (2)) in the limit q → 0. An operator whichgives the correspondence between the amino-acids and the codons isobtained for any known genetic code. The free energy released by basepairing of dinucleotides as well as the relative hydrophilicity andhydrophobicity of the dinucleosides are also computed. For the vertebrateseries, a universal behaviour in the ratios of codon usage frequencies isput in evidence and is shown to fit nicely in our model. Then a firstattempt to represent the mutations relative to the deletion of apyrimidine by action of a suitable crystal spinor operator is proposed.Finally recent theoretial descriptions are reviewed and compared with ourmodel.PACS number: 87.10.+e, 02.10.-v.