RNA secondary structure prediction via energy density minimization

There is a resurgence of interest in RNA secondary structure prediction problem (a.k.a. the RNA folding problem) due to the discovery of many new families of non-coding RNAs with a variety of functions. The vast majority of the computational tools for RNA secondary structure prediction are based on free energy minimization. Here the goal is to compute a non-conflicting collection of structural elements such as hairpins, bulges and loops, whose total free energy is as small as possible. Perhaps the most commonly used tool for structure prediction, mf old/RNAfold, is designed to fold a single RNA sequence. More recent methods, such as RNAscf and alifold are developed to improve the prediction quality of this tool by aiming to minimize the free energy of a number of functionally similar RNA sequences simultaneously. Typically, the (stack) prediction quality of the latter approach improves as the number of sequences to be folded and/or the similarity between the sequences increase. If the number of available RNA sequences to be folded is small then the predictive power of multiple sequence folding methods can deteriorate to that of the single sequence folding methods or worse. In this paper we show that delocalizing the thermodynamic cost of forming an RNA substructure by considering the energy density of the substructure can significantly improve on secondary structure prediction via free energy minimization. We describe a new algorithm and a software tool that we call Densityfold, which aims to predict the secondary structure of an RNA sequence by minimizing the sum of energy densities of individual substructures. We show that when only one or a small number of input sequences are available, Densityfold can outperform all available alternatives. It is our hope that this approach will help to better understand the process of nucleation that leads to the formation of biologically relevant RNA substructures.