Stochastic modeling of RNA pseudoknotted structures: a grammatical approach

Abstract

We introduce a new grammar modeling approach for RNA pseudoknotted structures based on parallel communicating grammar systems (PCGS). Our new approach can specify pseudoknotted structures, while avoiding context-sensitive rules, using a single CFG synchronized with a number of regular grammars. Technically, the stochastic version of the grammar model can be as simple as an SCFG. As with SCFG, the new approach permits automatic generation of a single-RNA structure prediction algorithm for each specified pseudoknotted structure model. This approach also makes it possible to develop full probabilistic models of pseudoknotted structures to allow the prediction of consensus structures by comparative analysis and structural homology recognition in database searches.

Predicting RNA secondary structures with pseudoknots by MCMC sampling

“…Knudsen and Hein [30]; Rivas and Eddy [48]; Cai et al [5]) we use a stochastic grammar to define a prior probability distribution on the set of possible secondary structures. Our grammar (together with a non-standard notion of derivations) allows the generation of pseudoknots in a non-context-free way.…”

“…We do not intend to put too much information into this prior and therefore use a very simple grammar. We combine a stochastic context-free grammar (used to generate a pseudoknot-free core structure) with the possibility to add arbitrary stems (in order to insert pseudoknots) in a similar way as described by Cai et al [5]. The context-free part of our grammar is similar to the grammar of Knudsen and Hein [30]; the non-terminal F generates stems, the non-terminal L generates loops, and the non-terminal S is the starting-symbol of the grammar.…”

“…Recently much attention has been paid to predicting the RNA secondary structure including pseudoknots (see e.g. Akutsu [1], Cai et al [5], Lyngsø and Pedersen [33], Rivas and Eddy [48], Uemura et al [53] and Xayaphoummine et al [61]). Again, one approach is to minimize the free energy of all possible foldings.…”

“…One step towards this direction has been taken by Cai et al [5] who use parallel communicating grammar systems to process pseudoknots leading to an algorithm with running time in O(n 6 ) and space in O(n 4 ); Uemura et al [53] changed to tree adjoining grammars yielding also a restricted class of pseudoknots.…”

Modelling DNA and RNA secondary structures using matrix insertion–deletion systems

“…In the work of Theis et al (2010), prediction of RNA secondary structure is carried out including kissing hairpins. Cai et al (2003) propose a grammatical approach for stochastic modelling of RNA pesudoknotted structures. In the work of Brown and Wilson (1995), RNA pseudoknot interactions are modelled using the intersection of stochastic context-free grammars.…”