Random generation of RNA secondary structures according to native distributions.

Background: Random biological sequences are a topic of great interest in genome analysis since, according to a powerful paradigm, they represent the background noise from which the actual biological information must differentiate. Accordingly, the generation of random sequences has been investigated for a long time. Similarly, random object of a more complicated structure like RNA molecules or proteins are of interest.

Results: In this article, we present a new general framework for deriving algorithms for the non-uniform random generation of combinatorial objects according to the encoding and probability distribution implied by a stochastic context-free grammar. Briefly, the framework extends on the well-known recursive method for (uniform) random generation and uses the popular framework of admissible specifications of combinatorial classes, introducing weighted combinatorial classes to allow for the non-uniform generation by means of unranking. This framework is used to derive an algorithm for the generation of RNA secondary structures of a given fixed size. We address the random generation of these structures according to a realistic distribution obtained from real-life data by using a very detailed context-free grammar (that models the class of RNA secondary structures by distinguishing between all known motifs in RNA structure). Compared to well-known sampling approaches used in several structure prediction tools (such as SFold) ours has two major advantages: Firstly, after a preprocessing step in time O(n2) for the computation of all weighted class sizes needed, with our approach a set of m random secondary structures of a given structure size n can be computed in worst-case time complexity Om⋅n⋅ log(n) while other algorithms typically have a runtime in O(m⋅n2). Secondly, our approach works with integer arithmetic only which is faster and saves us from all the discomforting details of using floating point arithmetic with logarithmized probabilities.

Conclusion: A number of experimental results shows that our random generation method produces realistic output, at least with respect to the appearance of the different structural motifs. The algorithm is available as a webservice at http://wwwagak.cs.uni-kl.de/NonUniRandGen and can be used for generating random secondary structures of any specified RNA type. A link to download an implementation of our method (in Wolfram Mathematica) can be found there, too.