Journal of Mathematical Biology

, Volume 69, Issue 6–7, pp 1743–1772 | Cite as

Asymptotic distribution of motifs in a stochastic context-free grammar model of RNA folding

  • Svetlana PoznanovićEmail author
  • Christine E. Heitsch


We analyze the distribution of RNA secondary structures given by the Knudsen–Hein stochastic context-free grammar used in the prediction program Pfold. Our main theorem gives relations between the expected number of these motifs—independent of the grammar probabilities. These relations are a consequence of proving that the distribution of base pairs, of helices, and of different types of loops is asymptotically Gaussian in this model of RNA folding. Proof techniques use singularity analysis of probability generating functions. We also demonstrate that these asymptotic results capture well the expected number of RNA base pairs in native ribosomal structures, and certain other aspects of their predicted secondary structures. In particular, we find that the predicted structures largely satisfy the expected relations, although the native structures do not.


RNA secondary structure Stochastic context-free grammar  Central limit theorem 

Mathematics Subject Classification (2000)

92D20 05A16 60F05 



The authors would like to thank Christian Reidys for useful comments on an earlier version of these results, David Esposito for implementing the CYK parsing and running the predictions, and the reviewers for their thoughtful comments which helped improve the presentation in this article.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematical SciencesClemson UniversityClemsonUSA
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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