## Abstract

In the vector space of DNA sequences over the Galois field of the 64 codons (GF (64)), recently published, deletions and insertions (indel) could not be analyzed. Now, in order to include these kinds of mutations, we have defined a new Galois field over the set of extended triplets X_{1}X _{2}X_{3} (C_{125}), where X_{i} ∈ {O, A, C, G, U}. Taking the polynomial coefficients a_{0}, a_{1}, a_{2} ∈ GF (5) and the bijective function ∫: GF(5) → {O, A, C, G, U}, where ∫ (0) = O, ∫ (1) = A, ∫ (2) = C, ∫ (3) = G, ∫ (4) = U, bijection Ψ is induced such that Ψ (a_{0} + a_{1}x + a_{2}x^{2}) = (f (a_{1}), ∫ (a _{2}), ∫ (a_{0})) = (X_{1}X_{2}X _{3}). The field (C_{125}, +, •) allows the definition of a novel N-dimensional vector space (S) over the field GF (5^{3}) on the set of all 125^{V} sequences of extended triplets in which all possible DNA sequence alignments of length N are included. Here the "classical gap" produced by alignment algorithm corresponds to the neutral element "O". In the vector space S, all mutational events that take place in the molecular evolution process can be described by means of endomorphisms, automorphisms and translations. In particular, the homologous (generalized) recombination between two homologous DNA duplexes involving a reciprocal exchange of DNA sequences -e.g. between two chromosomes that carry the same genetic loci- algebraically corresponds to the action of two automorphism pairs over two paired DNA duplexes.

Original language | English (US) |
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Pages (from-to) | 5-20 |

Number of pages | 16 |

Journal | Match |

Volume | 56 |

Issue number | 1 |

State | Published - Dec 14 2006 |

## All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics