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Grammar-based compression approach to extraction of common rules among multiple trees of glycans and RNAs.

Zhao Y, Hayashida M, Cao Y, Hwang J, Akutsu T - BMC Bioinformatics (2015)

Bottom Line: Many tree structures are found in nature and organisms.The results suggest that our method can be successfully applied to determining the minimum grammar and several common rules among glycans and RNAs.The proposed methods can provide clues for the determination of hierarchical structures contained in tree-structured biological data, beyond the extraction of frequent patterns.

View Article: PubMed Central - PubMed

Affiliation: Bioinformatics Center, Institute for Chemical Research, Kyoto University, Gokasho, Uji, Japan. tyoyo@kuicr.kyoto-u.ac.jp.

ABSTRACT

Background: Many tree structures are found in nature and organisms. Such trees are believed to be constructed on the basis of certain rules. We have previously developed grammar-based compression methods for ordered and unordered single trees, based on bisection-type tree grammars. Here, these methods find construction rules for one single tree. On the other hand, specified construction rules can be utilized to generate multiple similar trees.

Results: Therefore, in this paper, we develop novel methods to discover common rules for the construction of multiple distinct trees, by improving and extending the previous methods using integer programming. We apply our proposed methods to several sets of glycans and RNA secondary structures, which play important roles in cellular systems, and can be regarded as tree structures. The results suggest that our method can be successfully applied to determining the minimum grammar and several common rules among glycans and RNAs.

Conclusions: We propose integer programming-based methods MinSEOTGMul and MinSEUTGMul for the determination of the minimum grammars constructing multiple ordered and unordered trees, respectively. The proposed methods can provide clues for the determination of hierarchical structures contained in tree-structured biological data, beyond the extraction of frequent patterns.

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Illustration of subtree Tα,i,t,h,k in Tα. Tα,i,t,h,k denotes the subtree rooted at vertex vi having the child vertices vj(h≤j≤k) and vertex vt labeled with a tag in Tα.
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Fig8: Illustration of subtree Tα,i,t,h,k in Tα. Tα,i,t,h,k denotes the subtree rooted at vertex vi having the child vertices vj(h≤j≤k) and vertex vt labeled with a tag in Tα.

Mentions: Here, lch(α,i), rch(α,i), and ch(α,i) denote the leftmost child of the vertex vi in Tα, the rightmost child of vi in Tα, and the set of child vertices of vi in Tα, respectively. Tα,i,t,h,k denotes the subtree rooted at vertex vi, with the child vertices vj(h≤j≤k) and vt labeled with a tag in Tα, which does not have a tag when t=ε (Figure 8). I(T) denotes the set of internal vertices, except for the root and leaves of tree T. anc(α,j) denotes the set of ancestor vertices of vj, where j∉anc(j) and anc(ε)=∅.Figure 8


Grammar-based compression approach to extraction of common rules among multiple trees of glycans and RNAs.

Zhao Y, Hayashida M, Cao Y, Hwang J, Akutsu T - BMC Bioinformatics (2015)

Illustration of subtree Tα,i,t,h,k in Tα. Tα,i,t,h,k denotes the subtree rooted at vertex vi having the child vertices vj(h≤j≤k) and vertex vt labeled with a tag in Tα.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4419412&req=5

Fig8: Illustration of subtree Tα,i,t,h,k in Tα. Tα,i,t,h,k denotes the subtree rooted at vertex vi having the child vertices vj(h≤j≤k) and vertex vt labeled with a tag in Tα.
Mentions: Here, lch(α,i), rch(α,i), and ch(α,i) denote the leftmost child of the vertex vi in Tα, the rightmost child of vi in Tα, and the set of child vertices of vi in Tα, respectively. Tα,i,t,h,k denotes the subtree rooted at vertex vi, with the child vertices vj(h≤j≤k) and vt labeled with a tag in Tα, which does not have a tag when t=ε (Figure 8). I(T) denotes the set of internal vertices, except for the root and leaves of tree T. anc(α,j) denotes the set of ancestor vertices of vj, where j∉anc(j) and anc(ε)=∅.Figure 8

Bottom Line: Many tree structures are found in nature and organisms.The results suggest that our method can be successfully applied to determining the minimum grammar and several common rules among glycans and RNAs.The proposed methods can provide clues for the determination of hierarchical structures contained in tree-structured biological data, beyond the extraction of frequent patterns.

View Article: PubMed Central - PubMed

Affiliation: Bioinformatics Center, Institute for Chemical Research, Kyoto University, Gokasho, Uji, Japan. tyoyo@kuicr.kyoto-u.ac.jp.

ABSTRACT

Background: Many tree structures are found in nature and organisms. Such trees are believed to be constructed on the basis of certain rules. We have previously developed grammar-based compression methods for ordered and unordered single trees, based on bisection-type tree grammars. Here, these methods find construction rules for one single tree. On the other hand, specified construction rules can be utilized to generate multiple similar trees.

Results: Therefore, in this paper, we develop novel methods to discover common rules for the construction of multiple distinct trees, by improving and extending the previous methods using integer programming. We apply our proposed methods to several sets of glycans and RNA secondary structures, which play important roles in cellular systems, and can be regarded as tree structures. The results suggest that our method can be successfully applied to determining the minimum grammar and several common rules among glycans and RNAs.

Conclusions: We propose integer programming-based methods MinSEOTGMul and MinSEUTGMul for the determination of the minimum grammars constructing multiple ordered and unordered trees, respectively. The proposed methods can provide clues for the determination of hierarchical structures contained in tree-structured biological data, beyond the extraction of frequent patterns.

Show MeSH