From quantum groups to genetic mutations

In the framework of the crystal basis model of the genetic code, where each codon is assigned to an irreducible representation of $U_{q \to 0}(sl(2) \oplus sl(2))$, single base mutation matrices are introduced. The strength of the mutation is assumed to depend on the "distance" between the codons. Preliminary general predictions of the model are compared with experimental data, with a satisfactory agreement.Comment: 11 pages, Talk at Int.Conf."Symmetries in Science XIII", Bregenz July 20-24 200

A q-Analogue of the embedding chain U(6)⊃G⊃SO(3)U(6) \supset G \supset SO(3)

A q-analogue of the embedding chains of the Arima-Iachello model is proposed. The generators of the deformed U(6)-subalgebras are written in terms of the generators of gl_{q}(6), using q-bosons.Comment: 14 pages, no figur

Fermion realization of exceptional Lie algebras from maximal unitary subalgebras

From the decomposition of the exceptional Lie algebras (ELA's) under a maximal unitary subalgebra a realization of the ELA's is obtained in terms of fermionic oscillators

Mutation model for nucleotide sequences based on crystal basis

A nucleotides sequence is identified, in the two (four) letters alphabet, by the the labels of a vector state of an irreducible representation of U_q(sl(2)) (U_q(sl(2) + sl(2))), in the limit q -> 0. A master equation for the distribution function is written, where the intensity of the one-spin flip is assumed to depend from the variation of the labels of the state. In the two letters approximation, the numerically computed equilibrium distribution for short sequences is nicely fitted by a Yule distribution, which is the observed distribution of the ranked short oligonucleotides frequency in DNA. The four letter alphabet description, applied to the codons, is able to reproduce the form of the fitted rank ordered usage frequencies distribution.Comment: 27 pages, 9 figure

Symmetry and Minimum Principle at the Basis of the Genetic Code

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.Comment: To appear in BIOMAT 2016, 326 - 362, 201