A MODEL OF GENETIC CODE BASED ON U q->0 (sl(2)®sl(2)) *) L. FRAPPAT, P. SORBA**) Laboratoire de Physique Theorique LAPTH, URA 1436, Chemin de Bellevue, BP 110, F-74941 Annecy-le-Vieux, France A. SCIARRINO + ) Dipartimento di Scienze Fisiche, Universita di Napoli "Federico II", I.N.F.N., Sezione di Napoli, Mostra, d'Oltremare Pad. 20, 80125 Napoli, Italy Received 3 August 1999 The ratios of the codon usage in the quartets and sextets for 6 biological species be- longing to the vertebrate series, with a statistics of codons larger than 200.000, exhibit a correlated behaviour, which fits naturally in the framework of the crystal basis model of the genetic code based on U ->0 (sl(2) @ sl(2)) . The double helix-shaped DNA is formed by sequences of 4 basic bases, which we shall in the following call nucleotides: adenine (A), guanine (G), thymine (T) and cytosine (C); the first two belonging to the purines and the last two to pyrimidines. The genetic information is transmitted from the DNA trough the RNA (where T is replaced by uracyl (U)). By genetic code we mean the correspondance law which translates a nucleotides sequence in an ammo-acids (a.a.) sequence (i.e. in the biosynthesis of proteins). The. information for the biosynthesis of an a.a. is read from a triple of nucleotides: codon. It is a known fact that, in the genetic code, 64 codons code the biosynthesis of 20 a.a. plus an end signal (stop or nonsense codons), with a structure in multiplets reported, for the eukaryotic code, in the first two columns of Table 1. It is also a known fact that the frequency of usage (codon usage) of the different codons inside a multiplet is not the same. We put in evidence [1], a correlation in the codon usage, in the quartets and in the sub-quartet parts of the sextets (i.e. the 4 elements of a sextet which differ only for the last codon) for 6 biological species belonging to the vertebrates with statistics in the number of of codons larger than 200.000 [2], In Ref. 3 the same analysis has been considered for 34 biological species, representatives of vertebrates, invertebrates, plants and fungi, with statistics in the number of codons larger than about 64.000 showing the same correlated behaviour, even if some differences in the two series of data appear, which can be attributed to lower statistics. This correlation well matches with the mathematical model of the genetic code recently proposed [4]. Let us state the main hypothesis of our model [4], see [5] for more details on the mathematical definition of crystal basis. *) Presented by A. Sciarrino at the 8th Colloquium "Quantum Groups and Integrable Systems", Prague, 17-19 June 1999. **) E-mail: frappat(sorba)@lapp.in2p3.fr + ) E-mail: sciarrino@na.infn.it Czechoslovak Journal of Physics, Vol. 50 (2000), No. 1 65