Computational RNA secondary structure design:: empirical complexity and improved methods

Background: We investigate the empirical complexity of the RNA secondary structure design problem, that is, the scaling of the typical difficulty of the design task for various classes of RNA structures as the size of the target structure is increased. The purpose of this work is to understand better the factors that make RNA structures hard to design for existing, high-performance algorithms. Such understanding provides the basis for improving the performance of one of the best algorithms for this problem, RNA-SSD, and for characterising its limitations. Results: To gain insights into the practical complexity of the problem, we present a scaling analysis on random and biologically motivated structures using an improved version of the RNA-SSD algorithm, and also the RNAinverse algorithm from the Vienna package. Since primary structure constraints are relevant for designing RNA structures, we also investigate the correlation between the number and the location of the primary structure constraints when designing structures and the performance of the RNA-SSD algorithm. The scaling analysis on random and biologically motivated structures supports the hypothesis that the running time of both algorithms scales polynomially with the size of the structure. We also found that the algorithms are in general faster when constraints are placed only on paired bases in the structure. Furthermore, we prove that, according to the standard thermodynamic model, for some structures that the RNA-SSD algorithm was unable to design, there exists no sequence whose minimum free energy structure is the target structure. Conclusion: Our analysis helps to better understand the strengths and limitations of both the RNA-SSD and RNAinverse algorithms, and suggests ways in which the performance of these algorithms can be further improved.