Mutation model for nucleotide sequences based on crystal basis

Details Mutation model for nucleotide sequences based on crystal basis Mutation model for nucleotide sequences based on crystal basis

2005-06-08

arxiv.org/abs/q-bio/0506010v1

Biology

Quantitative Biology

Biomolecules

27 pages, 9 figures

Scientific paper

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.

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