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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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Horizontal bisection of Tα,i,j,h,k in Tα. The nonterminal symbol corresponding to Tα,i,j,h,k is generated if the nonterminal symbols corresponding to subtrees Tα,i,j,h,l and Tα,i,j,l+1,k are generated.
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Fig9: Horizontal bisection of Tα,i,j,h,k in Tα. The nonterminal symbol corresponding to Tα,i,j,h,k is generated if the nonterminal symbols corresponding to subtrees Tα,i,j,h,l and Tα,i,j,l+1,k are generated.

Mentions: The variable yα,i,j,h,l,k takes on a value of 1 if Tα,i,j,h,k is constructed from Tα,i,j,h,l and Tα,i,j,l+1,k using an (RHB) production rule; otherwise, the value is maintained at 0 (Figure 9). The variable zα,i,j,h,k,t is denoted as 1 if Tα,i,j,h,k is constructed from Tα,i,t,h,k and Tα,t,j,lch(α,t),rch(α,t) using an (RVB) production rule; otherwise, the value is retained as 0 (Figure 10). Eqs. (4) and (7) indicate that the subtree Tα,i,j,h,k is constructed by at least one established production rule of (RHB) and (RVB) in the grammar. Eqs. (5), (6), (8), (9), and (10) indicate that a production rule of (RHB) and (RVB) becomes a candidate rule in the grammar when both of the two source subtrees are constructed.Figure 9


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)

Horizontal bisection of Tα,i,j,h,k in Tα. The nonterminal symbol corresponding to Tα,i,j,h,k is generated if the nonterminal symbols corresponding to subtrees Tα,i,j,h,l and Tα,i,j,l+1,k are generated.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Fig9: Horizontal bisection of Tα,i,j,h,k in Tα. The nonterminal symbol corresponding to Tα,i,j,h,k is generated if the nonterminal symbols corresponding to subtrees Tα,i,j,h,l and Tα,i,j,l+1,k are generated.
Mentions: The variable yα,i,j,h,l,k takes on a value of 1 if Tα,i,j,h,k is constructed from Tα,i,j,h,l and Tα,i,j,l+1,k using an (RHB) production rule; otherwise, the value is maintained at 0 (Figure 9). The variable zα,i,j,h,k,t is denoted as 1 if Tα,i,j,h,k is constructed from Tα,i,t,h,k and Tα,t,j,lch(α,t),rch(α,t) using an (RVB) production rule; otherwise, the value is retained as 0 (Figure 10). Eqs. (4) and (7) indicate that the subtree Tα,i,j,h,k is constructed by at least one established production rule of (RHB) and (RVB) in the grammar. Eqs. (5), (6), (8), (9), and (10) indicate that a production rule of (RHB) and (RVB) becomes a candidate rule in the grammar when both of the two source subtrees are constructed.Figure 9

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