Using basic properties of p-adic numbers, we consider a simple new approach to describe main aspects of DNA sequence and genetic code. Central role in our investigation plays an ultrametric p-adic information space which basic elements are nucleotides, codons and genes. We show that a 5-adic model is appropriate for DNA sequence. This 5-adic model, combined with 2-adic distance, is also suitable for genetic code and for a more advanced employment in genomics. We find that genetic code degeneracy is related to the p-adic distance between codons.

The present paper is devoted to foundations of p-adic modelling in genomics. Considering nucleotides, codons, DNA and RNA sequences, amino acids, and proteins as information systems, we have formulated the corresponding p-adic formalisms for their investigations. Each of these systems has its characteristic prime number used for construction of the related information space. Relevance of this approach is illustrated by some examples. In particular, it is shown that degeneration of the genetic code is a p-adic phenomenon. We have also put forward a hypothesis on evolution of the genetic code assuming that primitive code was based on single nucleotides and chronologically first four amino acids. This formalism of p-adic genomic information systems can be implemented in computer programs and applied to various concrete cases.

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Aegilops columnaris is a tetraploid species originated from Ae. umbellulata (2n=2x=14, UU) and a yet unknown diploid grass species. Although Ae. columnaris possesses some agronomically valuable traits, such as heat and drought tolerance and resistance to pests, it has never been used in wheat breeding because of difficulties in producing hybrids and a lack of information on the relationships between Ae. columnaris and common wheat chromosomes. In this paper, we report the development of 57 wheat - Ae. columnaris introgressive lines covering 8 of the14 chromosomes of Aegilops. Based on substitution spectra of hybrids and the results of FISH analysis of the parental Ae. columnaris line with seven DNA probes, we have developed the genetic nomenclature of the U and X chromosomes. Genetic groups and genome affinities were established for 11 of 14 chromosomes; the classification of the remaining three chromosomes remains unsolved. Each Ae. columnaris chromosome was characterized on the basis of C-banding pattern and the distribution of seven DNA sequences. Introgression processes were shown to depend on the parental wheat genotype and the level of divergence of homoeologous chromosomes. We found that lines carrying chromosome 5X are resistant to leaf rust; therefore, this chromosome could possess novel resistance genes that have never been utilized in wheat breeding.

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