Abstract

i Abstract Secondary structures of nucleic acids are a particularly interesting class of contact structures. Many important RNA molecules,however contain pseudoknots, which are excluded explicitly by the definition of secondary structures. We propose here a generalization of secondary structures that incorporates "non-nested" pseudoknots. We also introduce a measure for the complexity of more general contact structures in terms of the chromatic number of their intersection graph. We show that RNA structures without nested pseudoknots form a special class of planar graphs, the so called "bi-secondary structures". Upper bounds on their number are derived, showing that there are fewer different structures than sequences. An energy function capable of dealing with bi-secondary structures was implemented into a generalized kinetic folding algorithm. Sterical hindrances involved in pseudoknot formation are taken into account with the help of two simplifications: stacked regions are viewed ...

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