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Dyadic groups, dyadic trees and symmetries in long nucleotide sequences

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      Abstract

      The conception of multi-alphabetical genetics is represented. Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have revealed algebraic properties of this system. These properties are connected with well-known notions of dyadic groups and dyadic-shift matrices. Matrix genetics shows relations of the genetic alphabets with some types of hypercomplex numbers including dual numbers and bicomplex numbers together with their extensions. A possibility of new approach is mentioned to simulate genetically inherited phenomena of biological spirals and phyllotaxis laws on the base of screw theory and Fibonacci matrices. Dyadic trees for sub-sets of triplets of the whole human genome are constructed. A new notion is put forward about square matrices with internal complementarities on the base of genetic matrices. Initial results of the study of such matrices are described. Our results testify that living matter possesses a profound algebraic essence. They show new promising ways to develop algebraic biology.

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      Author and article information

      Journal
      2012-04-27
      2013-01-17
      1204.6247

      http://arxiv.org/licenses/nonexclusive-distrib/1.0/

      Custom metadata
      43 pages, 50 figures, added materials
      q-bio.OT

      Quantitative & Systems biology

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