Efficient Computation Of Base-Pairing Probabilities In Multi-Strand Rna Folding

RNA folding algorithms, including McCaskill's partition function algorithm for computing base pairing probabilities, can be extended to N >= 2 interacting strands by considering all permutations it of the N strands. For each it, the inside dynamic programming recursion for connected structures needs to be extended by only a single extra case corresponding to a base pair connecting exactly two connected substructures. This leaves the cubic running time unchanged. A straightforward implementation of the corresponding outside recursion, however results in a quartic algorithm. We show here how cubic running time asymptotically equal to McCaskill's partition function algorithm can be achieved by introducing linear-size auxiliary arrays. The algorithm is implemented within the framework of the ViennaRNA package and conforms to the theoretical performance bounds.