Graph-theoretic formalization of hybridization in DNA sticker complexes

Abstract

Abstract. Sticker complexes are a formal graph-based data model for a restricted class of DNA complexes, motivated by potential applications to databases. This data model allows for a purely declarative definition of hybridization. We introduce the notion of terminating hybridization, and characterize this notion in purely graph-theoretic terms. Terminating hybridization can still produce results of exponential size. We indicate a class of complexes where hybridization is guaranteed to be polynomially bounded.

A comparison of graph-theoretic DNA hybridization models

“…In this paper, we show that the hybridization models of pot tiles [4] and sticker complexes [2] are equivalent. In this way, results from either of the two models may be carried over to the other model.…”

“…In this paper we do not recall the other DNA operations which form together with hybridization the full database model, as these other DNA operations are not used or considered in this paper. Hybridization in this model is studied in more detail in [2], and for notational convenience we recall now the more succinct description of this model formulated in [2].…”

“…A crucial operation within this database model is a context-free type of hybridization. This context-free type of hybridization, which we refer to as the sticker complex hybridization model, is more thoroughly studied in [2]. There it is shown, using graph-theoretical arguments, that it can be decided in polynomial time whether or not the set of DNA complexes obtainable (up to isomorphism) through hybridization is infinite for a given initial complex (appearing in a unbounded multiplicity).…”

“…In Section 2 we recall basic notions and notation regarding multisets and graphs. We recall the pot tile model of [4] in Section 3, and the sticker complex hybridization model of [3,2] in Section 4. In Section 5 we show that both models are equivalent.…”

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AbstractWe show that the graph-theoretic DNA hybridization models of pot tiles [4,5] and of sticker complexes [3,2] are equivalent. This allows one to carry over known results from one model to the other.

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