Algebraic Theory of DNA Recombination

In this paper we investigate the structure and representation of n-ary algebras arising from DNA recombination, where n is a number of DNA segments participating in recombination. Our methods involve a generalization of the Jordan formalization of observables in quantum mechanics in n-ary splicing algebras. We show that the splicing algebras are an n-ary envelope for algebras of DNA recombination. We have constructed the basis for free algebra of the variety of the n-ary splicing algebras and found the defining identities for n-ary splicing operations. Using the relationship between algebras and its enveloping algebras, we have constructed the basis of the free algebra of the variety of nary algebras of DNA recombination. It is proved that every polynomial identity satisfied by n-ary DNA recombination, with no restriction on the degree, is consequence of n-ary commutativity and the special n-ary identity of the degree 3n-2. We obtain a criterion, analogous to the Specht-Wever Lie crite...

• Type: Conference
• Year: 2010
• Where: BICOB
• Authors: Sergei R. Sverchkov
• Keywords: Algebra, BICOB 2010, Computational Biology, N-ary, Splicing Algebras