MCFGs for Genus-1 RNA Pseudoknots

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GPL-3 licensed by Christian Hoener zu Siederdissen, 2015

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GenussFold: RNA Pseudoknot Folding

generalized Algebraic Dynamic Programming Homepage

The implementation makes use of the gADP technique and provides a larger example on how to implement algorithms that require interleaved, split syntactic variables.

Formal background can be found in this paper:

Maik Riechert, Christian Höner zu Siederdissen, and Peter F. Stadler
Algebraic dynamic programming for multiple context-free languages
2015, submitted

As an example, consider palindromic brackets ((())). Given two types of brackets, these can be interleaved: ((( [[[ ))) ]]]. Such interleaved, long-range dependencies have been observed in human languages and, in particular, in RNA bioinformatics.

RNA structures may form so-called pseudoknots, where the RNA structure does not yield a planar structure (the canonical secondary structure) anymore, but rather forms graphs with crossing edges. Using the idea of interleaved brackets and given an input sequence AAA CCC UUU GGG (with artificial white space to make this more clear), a pseudoknotted structure may be formed:

[[[ ((( ]]] )))

A formal grammar that parses such a structure requires the ability to denote that a sub-structure has a "hole". We can write such a grammar as follows:

S     -> U V U V  
<U,U> -> [ε,ε]  
<U,U> -> [S,-] [a,-] <U,U> [-,S] [-,u]  
<V,V> -> [ε,ε]  
<V,V> -> [S,-] [c,-] <V,V> [-,S] [-,g]

The PKN grammar in GenussFold (for genus-1 structures, but much more pleasurable to write) offers the required features:

  1. state that a syntactic variable is split between two regions <U,U>
  2. state that this split system is linearized and different symbols can be interleaved: U V U V
  3. in addition, we allow syntactic variables of lower dimension (like S) to be used in dimensional stacks of symbols ([S,-]).

This system allows writing monotone multiple context-free grammars with good performance -- we are reasonably close to C in running time performance. Reasonable means around a factor of 2 slower.

Performance comparison

C-code for running time performance comparison is available in the GenussFold github repository. The direct URL is:


Christian Hoener zu Siederdissen
Leipzig University, Leipzig, Germany


  • quickcheck tests for GenussFold

  • initial checkin
  • preparing travis.yml
  • Pseudoknot-enabled Nussinov style RNA folding with basepair maximization.
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