Many interesting RNAs conserve a secondary structure of base-pairing interactions more than they conserve their sequence. This makes RNA sequence analysis more complicated and difficult than protein or DNA sequence analysis. RNA secondary structure problems are a natural application for probabilistic models based on the stochastic context-free grammars introduced in Chapter 9. In this chapter, we will examine two RNA analysis problems of biological interest.

The first problem is RNA secondary structure prediction for a single sequence. We will outline two well-known dynamic programming algorithms for RNA secondary structure prediction, the Nussinov and the Zuker algorithms. Then we will use RNA secondary structure prediction as an introductory example for the use of SCFGs for RNA analysis, by developing a small SCFG that implements a probabilistic version of the Nussinov algorithm.

The second is a related set of problems, having to do with the analysis of multiple alignments of families of related RNAs. Like Chapter 5, where profile HMMs were used for both multiple alignment and for database searching, we develop RNA structure profiles called ‘covariance models’ (CMs) for dealing with RNA multiple alignments with secondary structure constraints included. Covariance models are used for both RNA multiple alignment and database searches. Consensus structure prediction from RNA multiple alignments, a process called comparative RNA sequence analysis, is also somewhat automated by RNA covariance model training algorithms.

As you read this chapter, bear in mind that SCFG-based RNA analysis methods are not widely known or used.