Matrix genetics, part 1: permutations of positions in triplets and symmetries of genetic matrices

Details Matrix genetics, part 1: permutations of positions in triplets and symmetries of genetic matrices Matrix genetics, part 1: permutations of positions in triplets and symmetries of genetic matrices

2008-03-06

arxiv.org/abs/0803.0888v3

Biology

Quantitative Biology

Other Quantitative Biology

17 pages; 11 figures; added materials; added references.

Scientific paper

The Kronecker family of the genetic matrices is investigated, which is based on the genetic matrix [C A; U G], where C, A, U, G are the letters of the genetic alphabet. The matrix [C A; U G] in the third Kronecker power is the (8*8)-matrix, which contains 64 triplets. It is significant that peculiarities of the degeneracy of the genetic code are reflected in the symmetrical black-and-white mosaic of this genetic (8*8)-matrix of 64 triplets. This matrix is reformed into new mosaic matrices when internal positions in all triplets are permuted simultaneously. For all six variants of positional permutations in triplets, the appropriate genetic matrices possess symmetrical mosaics of the code degeneracy. These matrices are connected with projector operators. Kronecker families of the genetic matrices are transformed into families of unitary matrices if the genetic letters are presented in a form of complex numbers taking into account their molecular peculiarities. The genetic unitary (8*8)-matrices are transformed into new unitary matrices by means of permutations of positions in triplets. The author's viewpoint and initial data about the importance of the genetic projectors and of some kinds of unitary symmetries and their cyclic groups for genetic mechanisms are presented.

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