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1 Problem Description and Model Mining Cross-graph Quasi-cliques in Gene Expression and Pro

1 Problem Description and Model Mining Cross-graph Quasi-cliques in Gene Expression and Pro
1 Problem Description and Model Mining Cross-graph Quasi-cliques in Gene Expression and Pro

Mining Cross-graph Quasi-cliques in Gene Expression and Protein Interaction Data?

Jian Pei Simon Fraser University jpei@cs.sfu.ca

Daxin Jiang

State University of New York at Buffalo

djiang3@https://www.doczj.com/doc/fa5866169.html,

Aidong Zhang

State University of New York at Buffalo

azhang@https://www.doczj.com/doc/fa5866169.html,

1Problem Description and Model

A protein is the product of a gene.From the gene expres-sion data,we can?nd co-expressed genes,which are groups of genes that demonstrate coherent patterns on samples.On the other hand,from the protein interaction data,we can?nd groups of proteins that frequently interact with each other. If we can conduct a joint mining of both gene expression data and protein interaction data,then we may?nd the clus-ters of genes that are co-expressed and also their proteins interact.

Such clusters found from the joint mining are interesting and meaningful for at least two reasons.First,both the gene expression data and the protein data are very noisy.The clusters con?rmed by both data sets will strongly indicate the correlation/connection among the genes in a cluster.In other words,the clusters found from the joint mining are more reliable.We may thus have the high con?dence that the genes in a cluster found as such are regulated by the same mechanism or belong to the same biological process.

Second,although highly related,gene expression data and protein interaction data still carry different biological meaning.The coincidence of co-expressed genes and in-teracting proteins is biologically signi?cant.As indicated in[5],many pathways exhibit two properties:their genes exhibit a similar gene expression pro?le,and the protein products of the genes often interact.

1.1Model

Technically,a gene expression data set is a matrix W= {w ij}for a set G of n genes and a set S of m samples, where w i,j(1≤i≤n,1≤j≤m)is the expression level of gene g i on sample s j.

Two genes g1and g2are called coherent if they show similar expression patterns on the set of samples.There are ?This research is partly supported by the Endowed Research Fellow-ship and the President Research Grant from Simon Fraser University,NSF grants IIS-0308001,DBI-0234895,and NIH grant1P20GM067650-01A1.All opinions,?ndings,conclusions and recommendations in this paper are those of the authors and do not necessarily re?ect the views of the funding agencies.different methods to measure the similarity(or distance)be-tween gene expression patterns as required by the applica-tion domain,such as Euclidean distance,Pearson’s correla-tion coef?cient,KL-distance[2],and pattern-based similar-ity measures[1,6].Without loss of generality,in this paper, we simply assume that a similarity measure sim(·)is spec-i?ed,and the higher the similarity value,the more similar the genes.

We can de?ne a binary relation~on the set of genes. For genes g1and g2,g1~g2if sim(g1,g2)≥δ,whereδis a user-speci?ed minimum similarity threshold.

Naturally,the relation~can be represented as gene ex-pression graph geneG=(G,E):the genes are the vertices, and(g1,g2)∈E if g1~g2.

Similarly,for a set of proteins P,if we have the data about the interactions between proteins,we can de?ne a protein interaction graph proteinG=(P,I):the proteins are treated as vertices,and(p,p )∈I if proteins p and p interact with each other.

For gene expression data,a subset of genes forms a per-fect cluster if each gene in the subset is similar to all the others in the same subset.For protein interaction data,a subset of proteins forms a perfect cluster if each protein in the subset interacts with all the others in the same subset.To generalize,in gene expression/protein interaction graphs,a perfect cluster is a clique1.

However,due to the noise in the data sets,we may not be able to expect perfect clusters.Instead,a user may be interested in a subset of genes/proteins as a cluster such that each gene in the subset is similar to most of the other genes in the cluster,and each protein in the subset interacts with most of the other proteins in the cluster.

To quantify,for a user-speci?ed thresholdγ(0<γ≤1),a subset C of k genes forms aγ-quasi-cluster if each gene g∈C is similar to at leastγ·(k?1)other genes in C.Similarly,we can de?neγ-quasi-cluster for protein interaction data.Clearly,a maximalγ-quasi-cluster is aγ-quasi-clique in the corresponding gene expression/protein interaction graph.

1In this paper,we follow the terminology usage that a clique is a maxi-mal subset of mutually adjacent vertices in a graph.

Since a protein is a product of a gene,there is a mapping f from the set of proteins P to the set of genes G:f(p)=g if protein p is the product of gene g.

We are particularly interested in subsets of proteins C such that C is aγ1-quasi-cluster in the protein interaction data and{f(c)|c∈C}is aγ2-quasi-cluster in the gene expression data,whereγ1andγ2are user-speci?ed param-eters.We call C a cross-data set cluster.Moreover,C is particularly interesting if it is maximal.

1.2Why Is the Problem Challenging?

One may ask,“Can we solve the joint mining problem by a simple extension of the existing techniques?”Unfortu-nately,the answer is no.

A natural thinking may be as follows.We can integrate the multiple graphs into one based on a similarity function between data objects.The integrated similar function com-bines the similarity between data objects in different data sets in some weighted manner.Then,we can?nd quasi-cliques in the integrated graph.

However,the above na¨?ve method does not work at all. The key is that vertices of cross-graph quasi-cliques can be connected in different ways in individual graphs.Therefore, the integrated graph cannot capture the cross-graph quasi-cliques.It is easy to come up with a counter example to show that a cross-graph quasi-clique is not a quasi-clique in the integrated graph.

2Experimental Results

We use the cell-cycle gene expression data CDC28and the corresponding protein-protein interaction data from DIP as the data set.We found4,668matched gene-protein pairs between CDC28and DIP.For CDC28data set,we set the coherence thresholdρ=0.5(using Pearson’s correlation coef?cient as measure).As a result,the gene graph G E contains865,080edges whose both endpoints(genes)ap-pear in the matched gene-protein pairs.After removing the self-interacting protein pairs,the protein graph G P contains 15,115edges whose both endpoints(proteins)appear in the matched gene-protein pairs.

In our experiments,we?nd the complete set of quasi-cliques across the gene graph G E and the protein graph G P.We setγE=1for G E,γP=0.5for G P,and min s=5.That is,we are interested in a subset of at least5genes whose expression patterns are coherent with each other,and the corresponding proteins frequently inter-act with each other.

Figure1shows an example pattern Q(γE=1and γP=0.4).The induced graph of G E(the gene expres-sion graph)on Q is a perfect clique,so we only show the induced graph of G P(the protein interaction graph)on Q here.The pattern contains11vertices.We use the ORF (Open Reading Frame)names to identify the corresponding genes and proteins.

Figure1.A cluster of11proteins.

Although the exact biological meaning of this pattern is still under investigation,it is very interesting in biol-ogy since these11genes are highly coherent and the cor-responding11proteins are intensively interacting.

3Related Work

For more examples on joint mining of multiple sources, Page and Craven[3]surveyed the biological applications of mining multiple tables,such as pharmacophore discov-ery,gene regulation,information extraction from text and sequence analysis.

Recently,joint mining of multiple biological data sets has received intense interest.As a pioneer work,Segal et al.[5]proposed a uni?ed probabilistic model to learn the pathways from gene expression data and protein interaction data.However,their method requires the users to input the number of pathways that is usually unknown in advance.

4About the Full Version of This Paper

In the full version of this paper[4],we built a general model,investigated the properties of the problem and the computational complexity,and developed an effective and ef?cient algorithm to tackle the problem.A systematic per-formance study was also reported.

References

[1]Cheng,Y.and Church,G.M.Biclustering of expression data.

Proceedings of ISMB’00,8:93–103,2000.

[2]Kasturi,J.,Ramanathan,M.and Acharya,R.An information

theoretic approach for analyzing temporal patterns of gene ex-pression.Bioinformatics.

[3]Page,D.and Craven,M.Biological Applications of Multi-

relational Data Mining.SIGKDD Explorations,5(1):69–79, July2003.

[4]Pei,J.,Jiang,D.and Zhang,A.On Mining Cross-graph

Quasi-cliques.Technical Report TR2004-15,School of Com-puting Science,Simon Fraser University.

[5]Segal,E.,Wang,H.and Koller,D.Discovering molecular

pathways from protein interaction and gene expression data.

Bioinformatics,19:i264–i272,2003.

[6]Wang,H.,Wang,W.,Yang,J.et al.Clustering by Pattern

Similarity in Large Data Sets.In Proceedings of SIGMOD’02, pages394–405,2002.

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2017年6月英语四级真题 作文一: For this part,you are allowed 30 minutes to write a short essay based on the picture below. You should start your essay with a brief account of the impact of the Internet on the way people communicate and then explain whether electronic communication can replace face-to-face contact.You should write at least 120 words but no more than 180 words. “Dear Andy-How are you? Your mother and I are fine.We both miss you and hope you are doing well.We look forward to seeing you again the nest time your computer crashes and you come down-stairs for something to eat,Love,Mom and Dad.” 作文二: For this part,you are allowed 30 minutes to write a short essay based on the picture below. You should start your essay with a brief account of the impact of the Internet on learning and then explain why doesn’t simply mean learning to obtain information. You should write at least 120 words but no more than 180 words.

英语小短文(带翻译)

Whether sixty or sixteen, there is in every human being's heart the lure of wonders, the unfailing childlike appetite of what's next and the joy of the game of living. In the center of your heart and my heart there is a wireless station: so long as it receives messages of beauty, hope, cheer, courage and power from men and from the infinite, so long are you young. 无论是60岁还是16岁,你需要保持永不衰竭的好奇心、永不熄灭的孩提般求知的渴望和的欢乐与热情。在你我的心底,有一座无线电台,它能在多长里接收到人间万物传递来的、、欢乐、鼓舞和力量的信息,你就会年轻多长时间。 An individual human existence should be like a river—small at first, narrowly contained within its banks, and rushing passionately past boulders and over waterfalls. Gradually the river grows wider, the banks recede, the waters flow more quietly, and in the end, without any visible break, they become merged in the sea, and painlessly lose their individual being. 应当像河流,开始是涓涓细流,受两岸的限制而十分狭窄,尔后奔腾咆哮,翻过危岩,飞越瀑布,河面渐渐开阔,河岸也随之向两边隐去,最后水流平缓,森森无际,汇入大海之中,个人就这样地消失了。 Youth means a temperamental predominance of courage over timidity,of the appetite for adventure over the love of ease.This often exists in a man of sixty more than a boy of twenty.Nobody grows old merely by a number of years.We grow old by deserting our ideals. 意味着战胜懦弱的那股大丈夫气概和摈弃安逸的那种冒险精神。往往一个60岁的老者比一个20岁的青年更多一点这种劲头。人老不仅仅是岁月流逝所致,更主要的是不思进取的结果。 Years may wrinkle the skin,but to give up enthusiasm wrinkles the soul. Worry, fear, self-distrust bows the heart and turns the spirit back to dust. 光阴可以在颜面上留下印记,而热情之火的熄灭则在上刻下皱纹。烦恼、恐惧、会扭曲人的灵魂,并将青春化为灰烬。 爱情的世界很大也很小 The love world is big, which can hold hundreds of disappointments; the love world is small which is crowded even with three people inside. 原来的世界很大,大到可以装下上百种委屈; 原来爱情的世界很小,小到三个人就挤到窒息。 To the world you may be one person, but to one person you may be the world. 对于世界而言,你是一个人;但是对于某个人,你是他的整个世界。 Don’t waste your time on a man/woman, who isn’t willing to waste their time on you. 不要为那些不愿在你身上花费的人而浪费你的时间。

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