A graph-theoretic modeling on GO space for biological interpretation of gene

clusters

Bioinformatics Unit, ISTECH Inc.Cancer Metastasis Research Center, Yonsei University College of

Medicine Sung Geun Lee,Jung Uk Hur andYang Seok Kim

報告人 :張家榮

Introduction

Gene Ontology (GO)– Controlled vocabulary of various genomic databases about

diverse species

Clusters of microarray data– Each cluster has some genes

Extracts GO terms for a gene cluster– Each gene has several corresponding GO terms

Purpose– To discover the meaning of each cluster

Metric structure of GO tree

Lowest common ancestor

Given a non-empty subset U, v is a common ancestor of U if every node in U is on a subtree having v as the root and v0 is an LCA of U if v0 is greater than or equal to the level of w for any common ancestor w of U.

Lowest common ancestor

Principal distance

Each level has its own weight– W: IH -> R+

– W(i) > W(i+1)– For example: W(k)=150-10(k-1)

Where w0 is LCA of v1 and v2

Principal distance

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Multiset

Mathematically, the following three sets {1}, {1, 1}, {1, 1, 1} are equal in the set notation.

Yet, we want to take the number of occurrences of elements into account.

Such set is called as a multiset.

MaxPd and AverPd

given a multiset G ={v1, v2, . . . , vn}

MaxPd and AverPd

MaxPd– give the comprehensive biological meanings of a

gene cluster– Not flexible but informs us of the existence of

some functional outliers

AverPd– Signifies the most frequent GO codes– More than one

Algorithmic approach (1)

c[i,j] is j’st GO code of i’st gene We consider ordered GO codes g[m] where 1

≤m≤α α is a constant related to the input data α≤Ω , Ω is the total number of GO code

Algorithmic approach (2)

MaxPd is used to find LCA of C Complexity : 3αn

min

MaxPd

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Algorithmic approach (3)

AverPd is used to find an optimal GO code g[m0] such that the average distance between g[m0] and each gene in C is smaller than that of any g[m]

Complexity : 3αn

AverPd

Discussion

Other algorithms consider GO term frequencies or compare specific GO term-related gene groups

In our modeling, the topological property of GO hierarchy is used.

Utility

Biological assessment of the clustering results of DNA microarray data

Coupled with any clustering technique to predict the functional category of the unknown genes

Not only DNA microarray data, but also any kinds of group analysis with any ontology having an identical structure with GO

Another approach

The length of GO code is about logα Take one number of GO code each timepseudo-code:for 1≤k≤ logα

cluster C by the kth numberbreak if no cluster above ndelete clusters under n

end

MaxPd

Complexity

Worst case : O( nlogα) Best case : O (n) Alternate

– Change the break time to cluster it in detail

disadvantage

Cannot obtain information not contained in GO such as disease-related genes

GO terms on the same level have different level information

GO hierarchy is dynamic and flexible