Efficient calculation of exact probability distributions of integer features on RNA secondary structures

Background: Although the needs for analyses of secondary structures of RNAs are increasing, prediction of the secondary structures of RNAs are not always reliable. Because an RNA may have a complicated energy landscape, comprehensive representations of the whole ensemble of the secondary structures, such as the probability distributions of various features of RNA secondary structures are required. Results: A general method to efficiently compute the distribution of any integer scalar/vector function on the secondary structure is proposed. We also show two concrete algorithms, for Hamming distance from a reference structure and for 5' - 3' distance, which can be constructed by following our general method. These practical applications of this method show the effectiveness of the proposed method. Conclusions: The proposed method provides a clear and comprehensive procedure to construct algorithms for distributions of various integer features. In addition, distributions of integer vectors, that is a combination of different integer scores, can be also described by applying our 2D expanding technique.