Lecture 21, Phylogeny & RNA: Pfold (cont.)
12/6; 

No note taker today.  In a nutshell, Pfold uses a stochastic context free grammar (SCFG) to model (pseudoknot-free) RNA 2ary structure.  E.g. the rule F -> dFd | X generates a nested set of base pairs (the d's), with whatever X generates at the end of that helix.  Probabilities on the rules provide a prior on structures; e.g. average length of helices, etc.  In Pfold, the terminal symbols (d above) are not individual letters, but columns in an alignment, and the probabilities of those columns come from the given phylogenetic tree and Felsenstein's algorithm.  All this gives a generative framework for RNA 2ary structure alignments.  As usual, we turn this into algorithms for scoring an alignment and predicting its structure by a Viterbi-like approach: among all parses consistent with the given input alignment (tree, evolutionary rate matrix, etc.) find  the the one of maximum posterior probability.  This can be done by a generalization of the Cocke-Kasami-Younger context-free grammar recognition algorithm.  Validation presented in the papers is a bit thin, but empirically the method works well.