Mutation model for nucleotide sequences based on crystal basis

A nucleotide sequence is identified, using a two (four)-letter alphabet, by the the labels of a vector state of an irreducible representation of Uq→0(sl(2)) (Uq→0(sl(2)⊕sl(2))). A master equation for the distribution function is written, where the intensity of the one-spin flip is assumed to depend on the variation of the labels of the state. In the two-letter approximation, the numerically computed equilibrium distribution for short sequences is fitted nicely 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.