A dynamic programming algorithm for RNA structure prediction including pseudoknots

We describe a dynamic programming algorithm for predicting optimal RNA seco ndary structure, including pseudoknots. The algorithm has a worst case comp lexity of O(N-6) in time and O(N-4) in storage. The description of the algo rithm is complex, which led us to adopt a useful graphical representation ( Feynman diagrams) borrowed from quantum field theory. We present an impleme ntation of the algorithm that generates the optimal minimum energy structur e for a single RNA sequence, using standard RNA folding thermodynamic param eters augmented by a few parameters describing the thermodynamic stability of pseudoknots. We demonstrate the properties of the algorithm by using it to predict structures for several small pseudoknotted and non-pseudoknotted RNAs. Although the time and memory demands of the algorithm are steep, we believe this is the first algorithm to be able to fold optimal (minimum ene rgy) pseudoknotted RNAs with the accepted RNA thermodynamic model. (C) 1999 Academic Press.