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A folding algorithm for extended RNA secondary structures.

Höner zu Siederdissen C, Bernhart SH, Stadler PF, Hofacker IL - Bioinformatics (2011)

Bottom Line: Successful prediction of these structural features leads to improved secondary structures with applications in tertiary structure prediction and simultaneous folding and alignment.We accompany this model with a number of programs for parameter optimization and structure prediction.All sources (optimization routines, RNA folding, RNA evaluation, extended secondary structure visualization) are published under the GPLv3 and available at www.tbi.univie.ac.at/software/rnawolf/.

View Article: PubMed Central - PubMed

Affiliation: Institute for Theoretical Chemistry, University of Vienna, A-1090 Vienna, Austria. choener@tbi.inivie.ac.at

ABSTRACT

Motivation: RNA secondary structure contains many non-canonical base pairs of different pair families. Successful prediction of these structural features leads to improved secondary structures with applications in tertiary structure prediction and simultaneous folding and alignment.

Results: We present a theoretical model capturing both RNA pair families and extended secondary structure motifs with shared nucleotides using 2-diagrams. We accompany this model with a number of programs for parameter optimization and structure prediction.

Availability: All sources (optimization routines, RNA folding, RNA evaluation, extended secondary structure visualization) are published under the GPLv3 and available at www.tbi.univie.ac.at/software/rnawolf/.

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A simple unambiguous grammar for non-crossing 2-diagrams (The symbols used here denote (non-)terminals in a context-free grammar and are not to be confused with the LW notation used in other figures). Connected parts of diagrams correspond to terminal [individual bullet with no arc (closed circle) = unpaired nucleotide; arc with circular end points (closed circle, open circle) = base pair; arc with triangular endpoints (left-faced triangle, right faced triangle, cross) = part of base triple] or non-terminal (horizontal lines and semicircle) symbols of the grammar. It is important to realize that left-faced and right-faced triangles refer to the same nucleotide when they are adjacent. In terms of a recursion, the index for both left-faced and right-faced triangles is therefore the same. One triangle ‘points’ to the outer arc and one to the inner arc incident to the same nucleotide.
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Figure 3: A simple unambiguous grammar for non-crossing 2-diagrams (The symbols used here denote (non-)terminals in a context-free grammar and are not to be confused with the LW notation used in other figures). Connected parts of diagrams correspond to terminal [individual bullet with no arc (closed circle) = unpaired nucleotide; arc with circular end points (closed circle, open circle) = base pair; arc with triangular endpoints (left-faced triangle, right faced triangle, cross) = part of base triple] or non-terminal (horizontal lines and semicircle) symbols of the grammar. It is important to realize that left-faced and right-faced triangles refer to the same nucleotide when they are adjacent. In terms of a recursion, the index for both left-faced and right-faced triangles is therefore the same. One triangle ‘points’ to the outer arc and one to the inner arc incident to the same nucleotide.

Mentions: Here, we consider only structures with at most two base pairs involving the same nucleotide, i.e. 2-diagrams. In this case, there is a convenient string representation generalizing the Vienna (dot-parentheses) notation for secondary structures by introducing three additional symbols <, >, X for positions in which two arcs meet: (( = <, )) = > and )( = X. For general b, the number of necessary symbols grows quadratically, sb=(b+1)(b+2)/2, since each must encode b1 opening and b2 closing pairs with b1,b2≥0 and b1+b2≤b. These symbols provide a direct representation of the arc nodes ‘⊳,⊲, ×’ of Figure 3 and are an optional output of the folding program described below to visualize 2-diagrams in the secondary structure.Fig. 3.


A folding algorithm for extended RNA secondary structures.

Höner zu Siederdissen C, Bernhart SH, Stadler PF, Hofacker IL - Bioinformatics (2011)

A simple unambiguous grammar for non-crossing 2-diagrams (The symbols used here denote (non-)terminals in a context-free grammar and are not to be confused with the LW notation used in other figures). Connected parts of diagrams correspond to terminal [individual bullet with no arc (closed circle) = unpaired nucleotide; arc with circular end points (closed circle, open circle) = base pair; arc with triangular endpoints (left-faced triangle, right faced triangle, cross) = part of base triple] or non-terminal (horizontal lines and semicircle) symbols of the grammar. It is important to realize that left-faced and right-faced triangles refer to the same nucleotide when they are adjacent. In terms of a recursion, the index for both left-faced and right-faced triangles is therefore the same. One triangle ‘points’ to the outer arc and one to the inner arc incident to the same nucleotide.
© Copyright Policy - creative-commons
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3117358&req=5

Figure 3: A simple unambiguous grammar for non-crossing 2-diagrams (The symbols used here denote (non-)terminals in a context-free grammar and are not to be confused with the LW notation used in other figures). Connected parts of diagrams correspond to terminal [individual bullet with no arc (closed circle) = unpaired nucleotide; arc with circular end points (closed circle, open circle) = base pair; arc with triangular endpoints (left-faced triangle, right faced triangle, cross) = part of base triple] or non-terminal (horizontal lines and semicircle) symbols of the grammar. It is important to realize that left-faced and right-faced triangles refer to the same nucleotide when they are adjacent. In terms of a recursion, the index for both left-faced and right-faced triangles is therefore the same. One triangle ‘points’ to the outer arc and one to the inner arc incident to the same nucleotide.
Mentions: Here, we consider only structures with at most two base pairs involving the same nucleotide, i.e. 2-diagrams. In this case, there is a convenient string representation generalizing the Vienna (dot-parentheses) notation for secondary structures by introducing three additional symbols <, >, X for positions in which two arcs meet: (( = <, )) = > and )( = X. For general b, the number of necessary symbols grows quadratically, sb=(b+1)(b+2)/2, since each must encode b1 opening and b2 closing pairs with b1,b2≥0 and b1+b2≤b. These symbols provide a direct representation of the arc nodes ‘⊳,⊲, ×’ of Figure 3 and are an optional output of the folding program described below to visualize 2-diagrams in the secondary structure.Fig. 3.

Bottom Line: Successful prediction of these structural features leads to improved secondary structures with applications in tertiary structure prediction and simultaneous folding and alignment.We accompany this model with a number of programs for parameter optimization and structure prediction.All sources (optimization routines, RNA folding, RNA evaluation, extended secondary structure visualization) are published under the GPLv3 and available at www.tbi.univie.ac.at/software/rnawolf/.

View Article: PubMed Central - PubMed

Affiliation: Institute for Theoretical Chemistry, University of Vienna, A-1090 Vienna, Austria. choener@tbi.inivie.ac.at

ABSTRACT

Motivation: RNA secondary structure contains many non-canonical base pairs of different pair families. Successful prediction of these structural features leads to improved secondary structures with applications in tertiary structure prediction and simultaneous folding and alignment.

Results: We present a theoretical model capturing both RNA pair families and extended secondary structure motifs with shared nucleotides using 2-diagrams. We accompany this model with a number of programs for parameter optimization and structure prediction.

Availability: All sources (optimization routines, RNA folding, RNA evaluation, extended secondary structure visualization) are published under the GPLv3 and available at www.tbi.univie.ac.at/software/rnawolf/.

Show MeSH
Related in: MedlinePlus