Extended shapes for the combinatorial design of RNA sequences

It is known that for two given secondary structures (defined by position of base pairings) an RNA string can easily be found that can fold into both structures. For more than two secondary structures this is not necessarily possible. In this paper, we introduce pseudo edges that are used to forbid that certain base pairs can bind and therefore can be used to define the properties of possible RNA secondary structures. We study the complexity of the problem to design an RNA sequence that can fold into different secondary structures each of them is described by a set of required and forbidden base pairs. We refine the NP-completeness results of Clote et al. (2005) and show an analogous NP-completeness result for the realisation problem concerning the removal of (pseudo) edges. We also present a polynomial time method for checking the realisability of extended shape graphs. Furthermore, we empirically analyse the influence of pseudo edges on the realisability for sets of random RNA sequences and for sets of aptamers.

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