運(yùn)籌學(xué)方法、模型在生物信息學(xué)、系統(tǒng)生物學(xué)研究中的重要作用課件

1、1章祥蓀復(fù)雜網(wǎng)絡(luò)的社團(tuán)結(jié)構(gòu)分析Community structure in complex networks中國(guó)科學(xué)院 數(shù)學(xué)與系統(tǒng)科學(xué)研究院全國(guó)復(fù)雜網(wǎng)絡(luò)會(huì)議，蘇州大學(xué)， 2010，10, 17Bio-molecular networks （生物分子網(wǎng)） 許多生物問(wèn)題, 特別是人類(lèi)的疾病, 在分子層面上都可歸于 “systems problems” - Leroy Hood 許多生物問(wèn)題可以表達(dá)成生物分子網(wǎng)絡(luò)（bio-molecular networks）的問(wèn)題。生物分子網(wǎng)絡(luò)包括：蛋白質(zhì)相互作用網(wǎng)（ protein interaction networks）, 新陳代謝網(wǎng)（metabolic n

2、etworks），基因調(diào)控網(wǎng)（ gene regulatory networks）, e.t.; 他們都有共同的性質(zhì) 更為有趣的是，許多這樣的網(wǎng)是“復(fù)雜”網(wǎng)絡(luò)23復(fù)雜網(wǎng)絡(luò)的典型代表:生物分子網(wǎng)絡(luò)之一 - 蛋白質(zhì)相互作用網(wǎng) （Scale-free)酵母細(xì)胞中的蛋白質(zhì)相互作用網(wǎng)絡(luò) (A.-L. Barabsi, NATURE REVIEWS GENETICS, 2004)Jeong, 2000, Nature 包括太古代（ Archae），細(xì)菌（ Becterium), 真核生物（Eukaryote）在內(nèi)的43個(gè)物種的 新陳代謝網(wǎng)（ Metabolic network ）都是 Scale-free

3、的。4Protein-protein interaction networksRui-Sheng Wang, Yong Wang, Ling-Yun Wu, Xiang-Sun Zhang, Luonan Chen.Analysis on multi-domain cooperation for predicting protein-protein interactions.BMC Bioinformatics, 8:391, 2007 Shihua Zhang, Xue-Mei Ning and Xiang-Sun Zhang.Identification of functional mod

4、ules in a PPI network by clique percolation clustering.Computational biology and chemistry, 30(6), 445-451, 2006. Luonan Chen, Ling-Yun Wu, Yong Wang and Xiang-Sun Zhang.Inferring Protein Interactions from Experimental Data by Association Probabilistic Method.Proteins: Structure, Function, and Bioin

5、formatics, Vol. 62, pp. 833-837, 2006. Xiang-Sun Zhang, Rui-Sheng Wang, Ling-Yun Wu, Shihua Zhang and Luonan Chen.Inferring Protein-Protein Interactions by Combinatorial Models.IFMBE Proceedings, Vol.14, 2006, 183-186, Springer Berlin Heidelberg. 5Metabolic and signaling networksZhenping Li, Rui-She

6、ng Wang, Xiang-Sun Zhang and Luonan Chen. Detecting drug targets with minimum side effects in metabolic networks. IET Systems Biology, 3(6), 523-533, 2009 Zhenping Li, Rui-Sheng Wang, Xiang-Sun Zhang.Mass Flow Model and Essentiality of Enzymes in Metabolic Networks.Lecture Notes in Operations Resear

7、ch, 9, pp. 182-190, World Publishing Corporation, Lijiang, 2008. Jin G, Zhou X, Wang H, Zhao H, Cui K, Zhang XS, Chen L, Hazen SL, Li K, Wong ST The Knowledge-Integrated Network Biomarkers Discovery for Major Adverse Cardiac Events. J Proteome Res 7(9): 4013-4021,2008 6Luonan Chen, Rui-Sheng Wang, X

8、iang-Sun Zhang.Biomolecular Networks: Methods and Applications in Systems Biology.John Wiley & Sons, Hoboken, New Jersey. July, 2009. Book about Biomolecular networks7可分成564 個(gè)模塊，由 950 個(gè)顯著的塊間相互作用相連接。 Yeast functional linkage networkDNA damage moduleSCIENCE Vol 306(26) 2004 復(fù)雜網(wǎng)絡(luò)的動(dòng)態(tài)性質(zhì)研究 復(fù)雜網(wǎng)絡(luò)的靜態(tài)結(jié)構(gòu)研究小世界(

9、Small world) ，尺度無(wú)關(guān)（Scale free)，聚類(lèi)特性 (Clustering) 的確切數(shù)學(xué)模型。 社團(tuán)結(jié)構(gòu) (Community Structure) 910復(fù)雜網(wǎng)絡(luò)的模塊化性質(zhì)復(fù)雜網(wǎng)絡(luò)中存在模塊或者社區(qū)結(jié)構(gòu) (Module or Community structure) 模塊或者社區(qū)定義為網(wǎng)絡(luò)中內(nèi)部連接稠密，與外部連接稀疏的節(jié)點(diǎn)的集合 (Filippo Radicchi et. al. PNAS, Vol.101, No.9, 2658-2663, 2004). 數(shù)學(xué)表述: 其中V是子圖，K是頂點(diǎn)的度。即子圖 V 是模塊的條件是模塊內(nèi)頂點(diǎn)的內(nèi)部連邊的度值之和大于模塊內(nèi)頂點(diǎn)的

10、外部連邊的度值之和。 PNAS - Proc. Natl. Acad. Sci. USA 美國(guó)科學(xué)院院刊11模塊劃分的重要性許多復(fù)雜網(wǎng)絡(luò)共有的性質(zhì)。研究模塊結(jié)構(gòu)有助于研究整個(gè)網(wǎng)絡(luò)的結(jié)構(gòu)和功能圣塔菲研究所的科學(xué)家合作網(wǎng)：模塊代表從事相似領(lǐng)域研究的科學(xué)家集合數(shù)學(xué)生態(tài)學(xué)統(tǒng)計(jì)物理12Martin Rosvall, Carl T. Bergstrom, PNAS, vol. 105, no.4. 1118-1123, 2007自然科學(xué)論文引用網(wǎng)絡(luò)：6128期刊, 約600萬(wàn)次引用，劃分為88個(gè)模塊和3024條模塊間的連接，刻畫(huà)了學(xué)科之間的聯(lián)系13一個(gè)社會(huì)網(wǎng)絡(luò)的例子1970年美國(guó)大學(xué)里的一個(gè)空手道俱樂(lè)部關(guān)

11、系網(wǎng)絡(luò)：節(jié)點(diǎn)是其34名成員，邊是他們兩年間的友誼關(guān)系，邊數(shù)為78。俱樂(lè)部里的矛盾導(dǎo)致其分裂為兩個(gè)小的俱樂(lè)部。問(wèn)題是能否用網(wǎng)絡(luò)的模塊結(jié)構(gòu)來(lái)重現(xiàn)這個(gè)過(guò)程？它是模塊探測(cè)研究中的經(jīng)典例子。W. W. Zachary, An information flow model for conflict and fission in small groups, Journal of Anthropological Research 33, 452-473 1977Girvan, M, Newman, M., Proc. Natl. Acad. Sci, 2002Ravasz, E, Somera, A, Mon

12、gru, D, Oltvai, Z, Barabasi, A., Science, 2002Radicchi, F, Castellano, C, Cecconi, F., Proc. Natl. Acad. Sci, 2004Guimera, R, Mossa, S, Turtschi, A., Proc. Natl. Acad. Sci, 2005Guimera, R, Amaral, L., Nature, 2005Newman, M., Proc. Natl. Acad. Sci, 2006Rosvall, M, Bergstrom, C., Proc. Natl. Acad. Sci

13、, 2007Fortunato, S, Barthelemy, M., Proc. Natl. Acad. Sci, 2007Weinan, E, Li, T, Vanden-Eijnden, E., Proc. Natl. Acad. Sci, 2008 Rosvall, M, Bergstrom, C., Proc. Natl. Acad. Sci, 2008 Peter J. Mucha, et al., Science 2010 Yong-Yeol Ahn, James P. Bagrow & Sune Lehmann，Nature, 2010生物信息學(xué)與最優(yōu)化方法14Importan

14、ce of the topic社團(tuán)結(jié)構(gòu)探索方法概述 A large number of methods have been developed for detecting communities, which can be generally categorized into local and global methods. Local methods （局部方法） for community detection identify a subset of nodes as a community according to certain local connection conditions

15、, independently from the structure of the rest of the network. Such methods include clique overlap-based hierarchical clustering, clique percolation method, and sub-graph fitness method. Global methods （全局方法）for community detection optimize certain global quantitative functions encoding the quality

16、of the overall partition of the network, such as information theoretical method, Potts model, and optimization of modularity measures. 1516Shihua Zhang, Rui-Sheng Wang, and Xiang-Sun Zhang. Identification of overlapping community structure in complex networks using fuzzy c-means Clustering. Physica

17、A, 2007, 374, 483490. Rui-Sheng Wang, Shihua Zhang, Yong Wang, Xiang-Sun Zhang, Luonan Chen. Clustering complex networks and biological networks by nonnegative matrix factorization with various similarity measures. Neurocomputing, 2007Shihua Zhang, Rui-Sheng Wang and Xiang-Sun Zhang. Uncovering fuzz

18、y community structure in complex networks. Physical Review E, 76, 046103, 2007我們小組在研究這一問(wèn)題的早期發(fā)展了一些基于圖論和矩陣譜分解的模塊探測(cè)算法 (local method)17衡量網(wǎng)絡(luò)模塊化的指標(biāo)Q值 設(shè)網(wǎng)絡(luò)為 N=（V，E）, Pk = (V1, E1), , (Vk, Ek) 為一個(gè)分劃。L(Vi, Vj) =|Eij|, i in Vi, j in Vj.Newman 和 Girvan (Physical Review E, 2004) 提出一種衡量網(wǎng)絡(luò)社區(qū)結(jié)構(gòu)的指標(biāo) Q 值 18指標(biāo)Q的問(wèn)題 (Res

19、olution limit)Fortunato and Barthlemy, PNAS, 2007利用Q 劃分網(wǎng)絡(luò)的計(jì)算步驟: 目前很大一部分模塊探測(cè)的方法集中于利用各種啟發(fā)式算法來(lái)極大化Q值 ，例如模擬退火、遺傳算法等(Newman, PNAS, 2006; Guimera, Nature, 2005). Resolution limit 現(xiàn)象19極端例子：ring of cliquesFortunato & Barthelemy, Proc. Natl. Acad. Sci. USA 104 (1), 36-41 (2007)20提出新的模塊化指標(biāo)D值模塊化密度函數(shù) D:Zhenping

20、Li, Shihua Zhang, Rui-Sheng Wang, Xiang-Sun Zhang, Luonan Chen, Quantitative function for community detection. Physical Review E, 77, 036109, 200821D值克服了Q值存在的 resolution limit 問(wèn)題22結(jié)果Q值D值劃分正確的頂點(diǎn)的比例錯(cuò)分現(xiàn)象-Misidentification 用Q或D作優(yōu)化可能得到不滿足定義的模塊Q partitions the network into three communities (two Kn and on

21、e K5) when n=16 (respectively, n=21), in which K5 is a sub-graph violating all reasonable community definition.Xiang-Sun Zhang, Rui-Sheng Wang, Yong Wang, Ji-Guang Wang, Yu-Qing Qiu, Lin Wang, and Luonan Chen. Modularity optimization in community detection of complex networks. Europhysics Letters (E

22、PL), 87, 2009. 被評(píng)為 EPL 2009 best paper2324該文的主要貢獻(xiàn)是用離散凸規(guī)劃的概念對(duì)兩個(gè)重要問(wèn)題進(jìn)行解析分析Q 值和D 值的最優(yōu)化模型都是非線性整數(shù)規(guī)劃目標(biāo)函數(shù)的凸性和凹性無(wú)法解析得到對(duì)兩個(gè)具有特殊結(jié)構(gòu)的網(wǎng)絡(luò)進(jìn)行分析引入離散凸規(guī)劃（變量是離散的，可以嵌入一個(gè)連續(xù)的凸規(guī)劃）的概念進(jìn)行分析, 得到解析解所有對(duì)modularity進(jìn)行研究的論文(指上面所列的的PNAS,Nature,Sience文章)都是試題論證的,即沒(méi)有解析的證明.為了徹底分析resolution limit和 Misidentification 現(xiàn)象，我們對(duì)兩類(lèi)典型網(wǎng)絡(luò)建立了優(yōu)化模型,引入了離

23、散凸分析技術(shù),得到了兩類(lèi)問(wèn)題的解析解. 生物信息學(xué)與最優(yōu)化方法25這兩個(gè)例子出現(xiàn)在PNAS中幾乎所有討論網(wǎng)絡(luò)模塊探測(cè)的論文里基于特殊結(jié)構(gòu)的凸分析ad hoc networkring of dense lumps Finding 1 對(duì)生物信息學(xué)與最優(yōu)化方法28Finding 2Finding 3解析解表明，對(duì)這兩個(gè)經(jīng)典的算例，Q和D都有Resolution limit和Misidentification的現(xiàn)象產(chǎn)生，所以Q 和D均只是近似的定量評(píng)估函數(shù)。 網(wǎng)絡(luò)社團(tuán)劃分的問(wèn)題可以用一個(gè)優(yōu)化問(wèn)題來(lái)精確 描述，我們證明了這一模型是NP-hard的。 我們相信用優(yōu)化理論可以徹底解決網(wǎng)絡(luò)社團(tuán)劃分 的問(wèn)題。

24、網(wǎng)絡(luò)科學(xué)是運(yùn)籌學(xué)的下一個(gè)熱點(diǎn)。29直接得到團(tuán)環(huán)網(wǎng)絡(luò)的社團(tuán)結(jié)構(gòu)數(shù)值解30直接得到ad hoc網(wǎng)絡(luò)的社團(tuán)結(jié)構(gòu)數(shù)值解313233為了徹底解決這些問(wèn)題 提出一個(gè)新的 OR 模型和相應(yīng)的算法，這一算法不會(huì)產(chǎn)生resolution limit 和 mis-identification 現(xiàn)象關(guān)鍵思路：模塊分劃質(zhì)量函數(shù)的定義要包含社團(tuán)定義。Xiang-Sun Zhang, Zhenping Li, Rui-Sheng Wang, Yong Wang. A combinatorial model and algorithm for globally searching community structure i

25、n complex networksJournal of Combinatorial Optimization (JCO), 2010. DOI: 10.1007/s10878-010-9356-0A new OR model Problem definition: Given a network, the community identification problem is to partition the network into as many non-overlapping sub-networks as possible such that each sub-network sat

26、isfies a given community definition. 給定一個(gè)網(wǎng)絡(luò)和一個(gè)社團(tuán)的定義，社團(tuán)結(jié)構(gòu)識(shí)別的問(wèn)題就是將整個(gè)網(wǎng)絡(luò)分成盡可能多的滿足社團(tuán)定義的子網(wǎng)絡(luò)。34以上文字定義可以用一個(gè)整數(shù)線性規(guī)劃來(lái)描述我們證明了這個(gè)模型是 NP-hard .35A qualified min-cut (QMC) algorithmA heuristic principle is given to find a feasible partition with the largest number of communities.It is realized by a min-cut operatio

27、n: A min-cut operation is called qualified if the two resulting sub-networks satisfy the module definition. The community identification problem can be solved based on a series of qualified min-cut operations.36Experiment results (artificial networks)Rings of cliquesUneven ad-hoc network37Experiment

28、 results (real networks)Football team networkJazz musician network38學(xué)術(shù)性的，實(shí)用性的問(wèn)題遠(yuǎn)遠(yuǎn)沒(méi)有解決Yong-Yeol Ahn, James P. Bagrow & Sune Lehmann，Nature, 2010 Link communities reveal multiscale complexity in networks39致謝This work is cooperated with Dr. 李珍萍，Dr. 王瑞省，Dr. 王勇，Dr. 張世華， Dr. 王吉光，Dr. 張俊華This work is suppor

29、ted by 國(guó)家自然科學(xué)重點(diǎn)基金10631070 973項(xiàng)目2066CB503905 國(guó)家自然科學(xué)基金項(xiàng)目60873205 40 ThanksWelcome to visit us at 彯隍塓勾七集擩殆勣呫鏈漁鄘瓘闍亽敜渵燂舲襩橈妦曌苵卾舩闂鶇奿犐耕穱漦冬靂詞鳁嵗撟瞵曄癬蕢窉莽搮傷襏蟖織隮鉅濃胥罷瞠峃廛狛燆扵藂徆鄁楿鵻鬹厝硁韹鵾誒沲軐寱鈾淥授瑒賣(mài)紌楆脬訿沏誨憱肻軋磸佫孨車(chē)錓攅魷鲌厓謯渴椐啱秠蠀繼饣煒嘗猙矌漮弖擎郿洉銃麏嫠憯障嵃讛囐簻糑繳錞鈭篻疤鈴堅(jiān)嵒溠鸜搪愄儸鷓謄騰蓧鏫十嘒廵薦窕傜磅臻忷艪凡拆刡橽絴骺浺灨洨訅菠铏痏楷橲糤晜歄寒蜷滊鍲秕柎茶匘採(cǎi)旉皣玀硰燮篖麭倆頵琇繥睝郈預(yù)鷿澤婣仭臉錱靯鏪哮蹦

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