RNA, SCFGs and Classifiers

We developed, implemented and tested a stochastic context-free grammar (SCFG)-based method to classify RNA molecules into structural classes, by training grammars to simultaneously recognize certain types of RNAs and disrecognize other types. We tested our program using datasets obtained from thermodynamic (RNAfold) predictions of structures for 6000 tRNA and 6000 miRNA sequences, and we believe our program serves as a "proof of principle" of the structural classification of RNAs. We expect that incorporating evolutionary information from sequence alignments would significantly improve structure prediction. Furthermore, our method can naturally be extended to involve a higher number of grammars. Introduction In recent years, considerable interest has developed to elucidate the relationships between RNA sequence, structure and function, especially with regards to newly discovered roles of RNAs in cells and viruses. The computational prediction of RNA structures plays a vital role in bridging the gap between sequencing and experimental structure determination, and also facilitates the interpretation of experimental data. In 1994, stochastic context free grammars (SCFGs) were introduced in two papers (Durbin and Eddy, 1994 and Sakikabara et al., 1994) to describe and analyze RNA structures. Knudsen and Hein (1999, 2003) coupled a SCFG to molecular evolution and thus created a comparative predictor. Most RNA gene predictors try to classify a sequence into two classes: "RNA gene" and "background functionless DNA". However, it is often of interest to classify an RNA gene/structure into functional classes. Typically, this is either done by homology (if two sequences are similar, they probably have the same function) or by some additional classifier algorithm (Batuwita and Palade, 2009 & Klingelhoefer, Moutsianas and Holmes, 2009). In this project, we attempted to classify RNA molecules into structural classes, by training SCFGs to recognize some types of RNAs at the same time as disrecognizing others. Our stochastic context-free grammar RNA sequences are long chains of 4 nucleotides, and can be represented as a string consisting of 4 different letters: A (adenine), C (cytosine), G (guanine) and U (uracil). RNA secondary structure (ie. the two-dimensional folding of RNA molecules) can also be described as a string of symbols: the single-nucleotide symbol ".", and the base-pairing symbols " ( ) " , where the brackets indicate that the nucleotide in position of the first one base-pairs with the nucleotide in the position of the second one. (Figure 1a) This description makes it possible to produce RNA structures using context-free grammars. A formal grammar in language theory consists of: • a set of nonterminal symbols • a set of terminal symbols (disjoint from the set of nonterminals) • a set of production rules that map one string of symbols to another. A distinguished nonterminal symbol is the start symbol. A context-free grammar is a grammar in which every production rule maps a single nonterminal symbol into a string of terminal and nonterminal symbols. In this project we used a context-free grammar designed by Bjarne Knudsen that can generate strings to describe all RNA structures that contain no pseudoknots and have a minimum of 2 nucleotides in between any base-pairs. By assigning a probability to the different rules that generate strings from the same nonterminal symbol, we obtain the stochastic context-free grammar: S -> LS prob. p1 L -> . prob. 1 p2 S -> L prob. 1 -p1 F -> (F) prob. p3 L -> (F) prob. p2 F -> LS prob. 1 p3