RNA Secondary Structure Prediction with Simple Pseudoknots

Pseudoknots are widely occurring structural motifs in RNA. Pseudoknots have been shown to be functionally important in different RNAs which play regulatory, catalytic, or structural roles in cells. Current biophysical methods to identify the presence of pseudoknots are extremely time consuming and expensive. Therefore, bioinformatics approaches to accurately predict such structures are highly desirable. Most methods for RNA folding with pseudoknots adopt different heuristics such as quasi-Monte Carlo search, genetic algorithms, stochastic context-free grammars, and the Hopfield networks, and techniques like dynamic programming (DP). These approaches, however, have limitations. The DP algorithm has worst case time and space complexities of O(n) and O(n), respectively. The algorithm is not practical for sequences longer than 100 nucleotides. In this paper, we present a dynamic programming algorithm for prediction of simple pseudoknots in optimal secondary structure of a single RNA sequence using standard thermodynamic parameters for RNA folding. Our approach is based on a pseudoknot technique for maximizing the number of base pairs proposed by Akutsu (Akutsu 2000). The algorithm has worst case time and space complexities of O(n) and O(n), respectively. We validate the accuracy of our algorithm by experimental results on the entire set of simple pseudoknot collection in the PseudoBase database. Our program folds 163 pseudoknots out of 169 total in the Pseudobase database predicting the structure of 131 pseudoknots correctly or almost correctly. The algorithm is quite efficient. For example, a sequence of 75 nucleotides takes 55 seconds (compared to 20 minutes with the existing software) and a sequence of 114 nucleotides takes 8 minutes (4 hours 30 min). To our knowledge, this is most accurate and efficient algorithm for predicting simple pseudoknots in optimal secondary structure of a single RNA sequence.