DNA Codes for Non-additive Stem Similarity

Joint work with A. Dyachkov.
DNA sequences are sequences with elements from alphabet $\{A, C, G, T\}.$ Their essential feature is the ability to form duplexes in the process of hybridization - coalescence of 2 DNA sequences. Biological applications, utilizing this feature, require ensembles of DNA sequences (DNA codes) , consisting of so-called pairs of mutually reverse complementary sequences, such that hybridization energy - the measure of stability of potential DNA duplex - for any two DNA sequences, which are not reverse complementary, is bounded by some number, defined by the conditions of the specific experiment. It is straightforward to view this problem as one of the coding theory.
Continuing our previous research, in this report we introduce new non-additive similarity function, which provides the most adequate to date model of hybridization energy of DNA sequences. We will obtain the lower bound on the size of DNA codes for indicated similarity - the so-called random coding bound. In addition, we will touch upon several open probability-theoretical problems arising in research of non-additive similarity functions.