Hierarchy of codon usage frequencies from codon-anticodon interaction in the crystal basis model

Analyzing the codon usage frequencies of a specimen of 20 plants, for which the codon-anticodon pattern is known, we have remarked that the hierarchy of the usage frequencies present an almost "universal" behavior. Searching to explain this behavior, we assume that the codon usage probability results from the sum of two contributions: the first dominant term is an almost "universal" one and it depends on the codon-anticodon interaction; the second term is a local one, i.e. depends on the biological species. The codon-anticodon interaction is written as a spin-spin plus a z-spin term in the formalism of the crystal basis model. From general considerations, in particular from the choice of the signs and some constraints on the parameters defining the interaction, we are able to explain most of the observed data.