Bioinformatics Research and Applications: 5th International Symposium, ISBRA 2009 Fort Lauderdale, FL, USA, May 13-16, 2009 Proceedings [1 ed.] 3642015506, 9783642015502

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Lecture Notes in Bioinformatics

5542

Edited by S. Istrail, P. Pevzner, and M. Waterman Editorial Board: A. Apostolico S. Brunak M. Gelfand T. Lengauer S. Miyano G. Myers M.-F. Sagot D. Sankoff R. Shamir T. Speed M. Vingron W. Wong

Subseries of Lecture Notes in Computer Science

Ion M˘andoiu Giri Narasimhan Yanqing Zhang (Eds.)

Bioinformatics Research and Applications 5th International Symposium, ISBRA 2009 Fort Lauderdale, FL, USA, May 13-16, 2009 Proceedings

13

Series Editors Sorin Istrail, Brown University, Providence, RI, USA Pavel Pevzner, University of California, San Diego, CA, USA Michael Waterman, University of Southern California, Los Angeles, CA, USA Volume Editors Ion M˘andoiu University of Connecticut Computer Science & Engineering Department 371 Fairfield Way, Unit 2155, Storrs, CT 06269, USA E-mail: [email protected] Giri Narasimhan Florida International University School of Computing and Information Sciences Bioinformatics Research Group (BioRG) 11200 SW 8th Street, Room ECS254, University Park, Miami, FL 33199, USA E-mail: [email protected] Yanqing Zhang Georgia State University Department of Computer Science Atlanta, GA 30302-3994, USA E-mail: [email protected]

Library of Congress Control Number: Applied for CR Subject Classification (1998): J.3, H.2.8, F.1, F.2.2, G.3 LNCS Sublibrary: SL 8 – Bioinformatics ISSN ISBN-10 ISBN-13

0302-9743 3-642-01550-6 Springer Berlin Heidelberg New York 978-3-642-01550-2 Springer Berlin Heidelberg New York

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. springer.com © Springer-Verlag Berlin Heidelberg 2009 Printed in Germany Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper SPIN: 12672264 06/3180 543210

Preface

The 5th edition of the International Symposium on Bioinformatics Research and Applications (ISBRA 2009) was held during May 13–16, 2009 at Nova Southeastern University in Ft. Lauderdale, Florida. The symposium provides a forum for the exchange of ideas and results among researchers, developers, and practitioners working on all aspects of bioinformatics and computational biology and their applications. The technical program of the symposium included 26 contributed papers, selected by the Program Committee from a number of 55 full submissions received in response to the call for papers. The technical program also included contributed papers and abstracts submitted to the Second Workshop on Computational Issues in Genetic Epidemiology (CIGE 2009), which was held in conjunction with ISBRA 2009. Additionally, the symposium included poster sessions and featured invited keynote talks by four distinguished speakers: Mikhail Gelfand from the Russian Academy of Sciences and Moscow State University spoke on evolution of regulatory systems in bacteria, Nicholas Tsinoremas from the Miller School of Medicine and the College of Arts and Sciences at the University of Miami spoke on bioinformatics challenges in translational research, Esko Ukkonen from the University of Helsinki spoke on motif construction from high-throughput SELEX data, and Shamil Sunyaev from Brigham and Women’s Hospital and Harvard Medical School spoke on interpreting population sequencing data. We would like to thank the Program Committee members and external reviewers for volunteering their time to review and discuss symposium papers. We would also like to thank the Chairs and the Program Committee of CIGE 2009 for enriching the technical program of the symposium with a workshop on an important and active area of bioinformatics research. We would like to extend special thanks to the Steering and General Chairs of the symposium for their leadership, and to the Finance, Publicity, Local Organization, Posters Chairs, and Web Master for their hard work in making ISBRA 2009 a successful event. Last but not least, we would like to thank all authors for presenting their work at the symposium. May 2009

Ion M˘ andoiu Giri Narasimhan Yanqing Zhang

Organization

5th International Symposium on Bioinformatics Research and Applications (ISBRA 2009) Steering Chairs Dan Gusfield Yi Pan Marie-France Sagot

University of California, Davis, USA Georgia State University, USA INRIA, France

General Chairs Matthew He Alexander Zelikovsky

Nova Southeastern University, USA Georgia State University, USA

Program Chairs Ion M˘ andoiu Giri Narasimhan Yanqing Zhang

University of Connecticut, USA Florida International University, USA Georgia State University, USA

Publicity Chair Raj Sunderraman

Georgia State University, USA

Finance Chair Anu Bourgeois

Georgia State University, USA

Poster Chairs Yufeng Wu Craig E. Nelson

University of Connecticut, USA University of Connecticut, USA

Local Organization Chairs Edward Keith Miguel A. Jimenez-Montano

Nova Southeastern University, USA Universidad Veracruzana, Mexico

VIII

Organization

Local Organization Committee Ahmed Albatineh Ricardo Carrera Josh Loomis Evan Haskell Saeed Rajput Reza Razeghifard Raisa Szabo

Nova Nova Nova Nova Nova Nova Nova

Southeastern Southeastern Southeastern Southeastern Southeastern Southeastern Southeastern

University, University, University, University, University, University, University,

USA USA USA USA USA USA USA

Web Master Zejin Jason Ding

Georgia State University, USA

Program Committee Srinivas Aluru Iowa State University, USA

Bhaskar Dasgupta University of Illinois at Chicago, USA

Danny Barash Ben-Gurion University, Israel

Colin Dewey University of Wisconsin-Madison, USA

Anne Bergeron Universit´e du Qu´ebec `a Montr´eal, Canada

Werner Dubitzky University of Ulster, UK

Tanya Berger-Wolf University of Illinois at Chicago, USA Daniel Berrar University of Ulster, UK Olivier Bodenreider National Library of Medicine, NIH, USA

Guillaume Fertin Universit´e de Nantes, France Liliana Florea George Washington University, USA Jean Gao University of Texas at Arlington, USA

Mikhail Gelfand Paola Bonizzoni IITP, Russia Univ. de Studi di Milano-Bicocca, Italy Michael Gribskov Daniel Brown Purdue University, USA University of Waterloo, Canada Katia Guimar˜ aes Liming Cai Universidade Federal de University of Georgia, USA Pernambuco, Brazil Luonan Chen Osaka Sangyo University, Japan

Robert Harrison Georgia State University, USA

Organization

Jieyue He Southeast University, China Vasant Honavar Iowa State University, USA Lars Kaderali University of Heidelberg, Germany Ming-Yang Kao Northwestern University, USA George Karypis University of Minnesota, USA Yury Khudyakov Centers for Disease Control and Prevention, USA Jing Li Case Western Reserve University, USA Yiming Li National Chiao Tung University, Taiwan Guohui Lin University of Alberta, Canada Stefano Lonardi University of California at Riverside, USA Jingchu Luo Peking University, China Osamu Maruyama Kyushu University, Japan Satoru Miyano University of Tokyo, Japan

Itsik Pe’er Columbia University, USA Mihai Pop University of Maryland, USA Teresa Przytycka NCBI, USA Sven Rahmann Technical University of Dortmund, Germany Sanguthevar Rajasekaran University of Connecticut, USA Shoba Ranganathan Macquarie University, Australia Isidore Rigoutsos IBM Research, USA Cenk Sahinalp Simon Fraser, Canada David Sankoff University of Ottawa, Canada Russell Schwartz Carnegie Mellon University, USA Jo˜ ao Carlos Setubal Virginia Polytechnic Institute and State University, USA Mona Singh Princeton University, USA

Bernard Moret Ecole Poly. Fed. de Lausanne, Switzerland

Steve Skiena State University of New York at Stony Brook, USA

Craig Nelson University of Connecticut, USA

Donna Slonim Tufts University, USA

Laxmi Parida IBM T.J. Watson Research Center, USA

Ramanathan Sowdhamini NCBS, India

IX

X

Organization

Jens Stoye Universit¨ at Bielefeld, Germany

Li-San Wang University of Pennsylvania, USA

Wing-Kin Sung National University of Singapore, Singapore

Lusheng Wang City University of Hong Kong, China

Sing-Hoi Sze Texas A&M University, USA

Carsten Wiuf University of Aarhus, Denmark

Haixu Tang Indiana University, USA

Hongwei Wu University of Georgia, USA

Gabriel Valiente Technical University of Catalonia, Spain

Yufeng Wu University of Connecticut, USA

Jean-Philippe Vert Ecole des Mines de Paris, France

Dong Xu University of Missouri-Columbia, USA

St´ephane Vialette Universit´e Paris-Est Marne-la-Vall´ee, France

Kaizhong Zhang University of West Ontario, Canada

Gwenn Volkert Kent State University, USA

Leming Zhou University of Pittsburgh, USA

External Reviewers Angibaud, S´ebastien Araujo, Flavia Assareh, Amin Astrovakaya, Irina Bernauer, Julie Blin, Guillaume Chen, Shihyen Comin, Matteo DeRonne, Kevin Della Vedova, Gianluca Dewal, Ninad Dondi, Riccardo Ghodsi, MohammadReza Guillemot, Sylvain Harris, Elena Husemann, Peter Jahn, Katharina Jin, Guangxu

Kauffman, Chris Kim, Dongchul Kim, Yoo-Ah Knapp, Bettina Krishnan, Yamuna Lara, James Li, Weiming Liu, Bo Liu, Zhiping Mangul, Serghei Marschall, Tobias Martin, Marcel Mazur, Johanna Monteiro, Carla Offmann, Bernard Palamara, Pierre Podolyan, Yevgeniy Pugalenthi, Ganesan

Organization

Radde, Nicole Rizzi, Raffaella Rosa, Rogerio Rusu, Irena Salari, Rahele Schoenhuth, Alex Sheikh, Saad Stoffer, Deborah

Tripathi, Lokesh Wittler, Roland Wojtowicz, Damian Wu, Lingyun Zhao, Xingming Zheng, Jie Zola, Jaroslaw

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Second Workshop on Computational Issues in Genetic Epidemiology (CIGE 2009)

Steering Committee Andrew Allen Ion M˘ andoiu Dan Nicolae Yi Pan Alex Zelikovsky

Duke University, USA University of Connecticut, USA University of Chicago, USA Georgia State University, USA Georgia State University, USA

Program Chairs Andrew Allen Itsik Pe’er

Duke University, USA Columbia University, USA

Program Committee Dave Cutler Frank Dudbridge Eleazar Eskin Eran Halperin David Heckerman Chun Li Eden Martin Shaun Purcell Hongyu Zhao

Emory University, USA Cambridge University, UK UCLA, USA UC Berkeley/Tel Aviv University, USA/Israel Microsoft Research, USA Vanderbilt University, USA Miami University, USA Harvard University, USA Yale University, USA

Table of Contents

Evolution of Regulatory Systems in Bacteria (Invited Keynote Talk) . . . Mikhail S. Gelfand, Alexei E. Kazakov, Yuri D. Korostelev, Olga N. Laikova, Andrei A. Mironov, Alexandra B. Rakhmaninova, Dmitry A. Ravcheev, Dmitry A. Rodionov, and Alexei G. Vitreschak

1

Integrating Multiple-Platform Expression Data through Gene Set Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ˇ Matˇej Holec, Filip Zelezn´ y, Jiˇr´ı Kl´ema, and Jakub Tolar

5

Practical Quality Assessment of Microarray Data by Simulation of Differential Gene Expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Brian E. Howard, Beate Sick, and Steffen Heber

18

Mean Square Residue Biclustering with Missing Data and Row Inversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stefan Gremalschi, Gulsah Altun, Irina Astrovskaya, and Alexander Zelikovsky Using Gene Expression Modeling to Determine Biological Relevance of Putative Regulatory Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Peter Larsen and Yang Dai Querying Protein-Protein Interaction Networks . . . . . . . . . . . . . . . . . . . . . . Guillaume Blin, Florian Sikora, and St´ephane Vialette Integrative Approach for Combining TNFα-NFκB Mathematical Model to a Protein Interaction Connectivity Map . . . . . . . . . . . . . . . . . . . . . . . . . . Mahesh Visvanathan, Bernhard Pfeifer, Christian Baumgartner, Bernhard Tilg, and Gerald Henry Lushington

28

40 52

63

Hierarchical Organization of Functional Modules in Weighted Protein Interaction Networks Using Clustering Coefficient . . . . . . . . . . . . . . . . . . . Min Li, Jianxin Wang, Jianer Chen, and Yi Pan

75

Bioinformatics Challenges in Translational Research (Invited Keynote Talk) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nicholas F. Tsinoremas

87

Untangling Tanglegrams: Comparing Trees by Their Drawings . . . . . . . . Balaji Venkatachalam, Jim Apple, Katherine St. John, and Dan Gusfield An Experimental Analysis of Consensus Tree Algorithms for Large-Scale Tree Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Seung-Jin Sul and Tiffani L. Williams

88

100

XVI

Table of Contents

Counting Faces in Split Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lichen Bao and Sergey Bereg

112

Relationship between Amino Acids Sequences and Protein Structures: Folding Patterns and Sequence Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alexander Kister

124

Improved Algorithms for Parsing ESLTAGs: A Grammatical Model Suitable for RNA Pseudoknots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sanguthevar Rajasekaran, Sahar Al Seesi, and Reda Ammar

135

Efficient Algorithms for Self Assembling Triangular and Other Nano Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vamsi Kundeti and Sanguthevar Rajasekaran

148

Motif Construction from High–Throughput SELEX Data (Invited Keynote Talk) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Esko Ukkonen

159

Rearrangement Phylogeny of Genomes in Contig Form . . . . . . . . . . . . . . . . Adriana Mu˜ noz and David Sankoff

160

Prediction of Contiguous Regions in the Amniote Ancestral Genome . . . A¨ıda Ouangraoua, Fr´ed´eric Boyer, Andrew McPherson, ´ Eric Tannier, and Cedric Chauve

173

Pure Parsimony Xor Haplotyping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Paola Bonizzoni, Gianluca Della Vedova, Riccardo Dondi, Yuri Pirola, and Romeo Rizzi

186

A Decomposition of the Pure Parsimony Haplotyping Problem . . . . . . . . . Allen Holder and Thomas Langley

198

Exact Computation of Coalescent Likelihood under the Infinite Sites Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yufeng Wu

209

Imputation-Based Local Ancestry Inference in Admixed Populations . . . Bogdan Pa¸saniuc, Justin Kennedy, and Ion M˘ andoiu

221

Interpreting Population Sequencing Data (Invited Keynote Talk) . . . . . . . Shamil R. Sunyaev

234

Modeling and Visualizing Heterogeneity of Spatial Patterns of Protein-DNA Interaction from High-Density Chromatin Precipitation Mapping Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Juntao Li, Fajrian Yunus, Zhu Lei, Majid Eshaghi, Jianhua Liu, and R. Krishna Murthy Karuturi

236

Table of Contents

XVII

A Linear-Time Algorithm for Analyzing Array CGH Data Using Log Ratio Triangulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matthew Hayes and Jing Li

248

Mining of cis-Regulatory Motifs Associated with Tissue-Specific Alternative Splicing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jihye Kim, Sihui Zhao, Brian E. Howard, and Steffen Heber

260

Analysis of Cis-Regulatory Motifs in Cassette Exons by Incorporating Exon Skipping Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sihui Zhao, Jihye Kim, and Steffen Heber

272

A Class of Evolution-Based Kernels for Protein Homology Analysis: A Generalization of the PAM Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Valentina Sulimova, Vadim Mottl, Boris Mirkin, Ilya Muchnik, and Casimir Kulikowski

284

Irreplaceable Amino Acids and Reduced Alphabets in Short-Term and Directed Protein Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Miguel A. Jim´enez-Monta˜ no and Matthew He

297

A One-Class Classification Approach for Protein Sequences and Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andr´ as B´ anhalmi, R´ obert Busa-Fekete, and Bal´ azs K´egl

310

Prediction and Classification of Real and Pseudo MicroRNA Precursors via Data Fuzzification and Fuzzy Decision Trees . . . . . . . . . . . . . . . . . . . . . Na’el Abu-halaweh and Robert Harrison

323

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

335

Evolution of Regulatory Systems in Bacteria (Invited Keynote Talk) Mikhail S. Gelfand1,2, Alexei E. Kazakov1, Yuri D. Korostelev2, Olga N. Laikova3, Andrei A. Mironov1,2, Alexandra B. Rakhmaninova1,2, Dmitry A. Ravcheev1, Dmitry A. Rodionov1,4, and Alexei G. Vitreschak1 1

A.A.Kharkevich Institute for Information Transmission Problems, RAS, Bolshoi Karetny pereulok 19, Moscow, 127994, Russia {gelfand,kazakov,ravcheyev,rodionov,vitreschak}@iitp.ru 2 Faculty of Bioengineering and Bioinformatics, M.V.Lomonosov Moscow State University, Vorobievy Gory 1-73, Moscow, 119992, Russia {[email protected],abr@belozersky}.msu.ru 3 Research Institute for Genetics and Selection of Industrial Microorganisms, Pervy Dorozhny proezd 1, Moscow, 127994, Russia 4 A.A. Burnham Institute for Medical Research, 10901 North Torrey Pines Road, La Jolla, CA 92037, USA

Abstract. Recent comparative studies indicate surprising flexibility of regulatory systems in bacteria. These systems can be analyzed on several levels, and I plan to consider two of them. At the level of regulon evolution, one can attempt to characterize the evolution of regulon content formed by loss, gain and duplications of regulators and regulated genes, as well as gain and loss of individual regulatory sites and horizontal gene transfer. At the level of transcription factor families, one can study co-evolution of DNA-binding proteins and the motifs they recognize. While this area is not yet ripe for fully automated analysis, the results of systematic comparative studies gradually start to coalesce into an understanding of how bacteria regulatory systems evolve. Keywords: Comparative genomics, bacteria, regulation of transcription, regulation of translation, transcription factor, binding site, T-box.

1 Introduction Sequencing of hundreds of bacterial genomes has created a situation when in many taxa we have rather dense and relatively uniform sampling of genomes at varying evolutionary distance from each other. This paves way for careful comparative genomic analysis of regulatory systems and their evolution. Identification of candidate transcription factor binding sites and regulatory RNA structures and analysis of their distribution in related genomes allows one to reconstruct the evolutionary history of regulons, whereas analysis of candidate binding sites for transcription factors forming a structural family creates an opportunity for studying co-evolution of transcription factors and their binding motifs, and hence, elucidation of family-specific proteinDNA interaction code. I. Măndoiu, G. Narasimhan, and Y. Zhang (Eds.): ISBRA 2009, LNBI 5542, pp. 1–4, 2009. © Springer-Verlag Berlin Heidelberg 2009

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2 Evolution of Regulons The list of basic events shaping the regulons includes gain (via duplication and horizontal gene transfer) and loss of regulators, changes of specificity, gain, loss and duplication of regulated genes, shuffling of genes in operons, and gain and loss of individual regulatory sites. While it is not currently possible to estimate the rate of these events, it is clear that these rates are not uniform for different regulons and their life stages. Further, it is clear that in most cases there are significant overlaps between individual regulons, and it makes more sense to speak of interacting regulatory systems. Life without FUR: Evolution of Iron Homeostasis in the Alpha-Proteobacteria [1]. One of examples where the evolutionary history could be reconstructed in sufficient detail is the regulation of iron homeostasis in the alpha-proteobacteria. In this case the starting even was change of ligand specificity that transformed the usual iron repressor FUR into manganese-responsive MUR in the common ancestor of the Rhizobiales and Rhodobacteriales. The role of iron regulator was assumed by a distant member of the FUR family, Irr, and this state is conserved in the Bradirhizobiceae. In the Rhizobiaceae, IscR, a regulator of genes involved in the synthesis of the iron-sulfur clusters also was lost. Further on, in the Rhizobiaceae the RirA regulator appeared, and the job of iron-dependent regulation is shared by Irr (mainly responsible for iron storage, Fe-S clusters, heme and iron-dependent enzymes) and RirA (main regulator of iron acquisition and also some Fe-S and iron storage genes). In the Rhodobacteriales, iron acquisition is regulated by an unknown transcription factor binding to the motif CTGActrawtyagTCAG, that is somewhat similar to the binding moitif of IscR; iron storage genes are co-regulated by this factor and Irr, Fe-S synthesis, by IscR and Irr, and iron-dependent enzymes, solely by Irr. Fatty Acid and Branched-Chain Amino Acid Utilization in the Gamma- and Beta-proteobacteria [2]. A similar reconstruction could be performed for a large system regulating the catabolism of fatty acids (FA) and branched-chain amino acids (ILV) in the gamma- and beta-proteobacteria. This system involves six transcriptional factors from the MerR, TetR, and GntR families binding to eleven distinct DNA motifs. The ILV degradation genes in the gamma- and beta-proteobacteria are regulated mainly by a newly identified regulator from the MerR family (e.g., LiuR in Pseudomonas aeruginosa) and, in some beta-proteobacteria, by a TetR-family regulator LiuQ. In addition to the core set of ILV utilization genes, the LiuR regulon in some lineages is expanded to include genes from other metabolic pathways, such as the glyoxylate shunt and glutamate synthase, as well as salt- and alkaline stress response in the Shewanella species. The FA degradation genes are controlled by four regulators including FadR in the gamma-proteobacteria, PsrA in the gamma- and betaproteobacteria, FadP in the beta-proteobacteria, whereas in the alpha-proteobacteria it is regulated by LiuR orthologs. The most parsimonious evolutionary scenario for the ILV and FA regulons seems to be that LiuR and PsrA were likely present in the common ancestor of the gamma- and beta-proteobacteria, and they have been partially or fully substituted by LiuQ and FadP in the Burkholderiales and by FadR in some groups of the gamma-proteobacteria.

Evolution of Regulatory Systems in Bacteria

3

T-boxes and Regulation of Amino Acid Metabolism in the Firmicutes [3]. T-boxes are regulatory RNA structures that bind to uncharged tRNAs and regulate aminoacyltRNA synthetase genes as well as genes encoding amino acid transporters and metabolic enzymes. T-boxes are sufficiently large to retain the phylogenetic signal, at least at short evolutionary distances, and hence it is possible to follow the history of Tbox duplications. Further, since the specificity of T-boxes is dictated by the interaction between a well-defined structural element (so-called specifier codon) and the tRNA anticodon, they are an ideal material for studying changes in specificity. One of the most interesting observations is rapid, duplication-driven, lineage-specific expansion of some specific T-box regulon following the loss of previously existing transcription factors. Regulon Expansion, or how FruR Has Become CRA and Duplicated RbsR Has Become PurR. The fructose repressor FurR, a member of the LacI family, is a standard sugar regulator in most lineages of the gamma-proteobacteria, whereas in E.coli it is a well-studied global regulator named CRA (catabolism repressor and activator). Following the fate of known binding sites in the genomes ordered by increasing phylogenetic distance from E. coli, one can see that the regulon expansion started with the glycolysis pathway and then extended to some genes of the Krebs cycle and sugar catabolic pathways. Similarly, the ribose operon regulator RbsR duplicated in the common ancestor of the Enterobacteriales and Vibrionales. The RbsR copy retained the ligand (ribose) specificity and the regulon, but its DNA motif changed somewhat (to AGCGAAACGTTTCGCT), whereas the other copy retained the DNA motif (ACGCAAACGTTTGCGT), but has become the purine repressor PurR regulating, in E. coli, more than twenty genes from the purine biosynthesis pathway and some adjacent pathways.

3 Co-evolution of Transcription Factors and DNA Motifs They Recognize As mentioned in the previous section, evolution of regulons is often accompanied by changes in the DNA motifs. To study co-evolution of transcription factors (TFs) and their binding sites systematically, we are doing large-scale comparative genomics analysis of several families of TFs. An outcome of such studies is lists of TFs, each with a set of candidate binding sites. Several recently developed programs are used to identify correlated positions in proteins and DNA. Indeed, it turns out that when this analysis was applied to the LacI family of TFs, the identified set of correlated positions was consistent with several known X-ray structures of TF-DNA complexes. Notably, however, the set of protein positions correlated with specific nucleotides was not limited to residues in immediate contact with the DNA: in several families this set also included positions situated on the other side of the DNA-binding alpha-helix and forming hydrophobic interactions with the rest of the protein. Further, these studies revealed that the familyspecific protein-DNA recognition code is not limited to known universal correlations

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(like “arginine binds to guanine”), nor to pairwise correlations. Some of predictions coming from these analyses were recently confirmed in experiment [4]. Acknowledgments. The reported studies were supported by grants from the Howard Hughes Medical Institute (55005610 to M.S.G.), the Russian Fund of Basic Research (08-04-01000 to A.E.K.), and the Russian Academy of Sciences (program «Molecular and Cellular Biology»).

References 1. Rodionov, D.A., Gelfand, M.S., Todd, J.D., Curson, A.R.J., Johnston, A.W.B.: Comparative Reconstruction of Transcriptional Network Controlling Iron and Manganese Homeostasis in Alpha-Proteobacteria. PLoS Comp. Biol. 2, e163 (2006) 2. Kazakov, A.E., Rodionov, D.A., Alm, E., Arkin, A., Dubchak, I., Gelfand, M.S.: Comparative Genomics of Regulation of Fatty Acid and Branched-Chain Amino Acid Utilization in Proteobacteria. J. Bacteriol. 191, 52–64 (2009) 3. Vitreschak, A.G., Mironov, A.A., Lyubetsky, V.A., Gelfand, M.S.: Functional and Evolutionary Analysis of the T-box Regulon in Bacteria. RNA 14, 717–735 (2008) 4. Desai, T., Rodionov, D., Gelfand, M., Alm, E., Rao, C.: Engineering Transcription Factors with Novel DNA-binding Specificity Using Comparative Genomics. Nucleic Acids Res. (in press)

Integrating Multiple-Platform Expression Data through Gene Set Features ˇ Matˇej Holec1 , Filip Zelezn´ y1 , Jiˇr´ı Kl´ema1, and Jakub Tolar2 1

Czech Technical University, Prague University of Minnesota, Minneapolis {holecm1,zelezny,klema}@fel.cvut.cz, [email protected] 2

Abstract. We demonstrate a set-level approach to the integration of multiple platform gene expression data for predictive classification and show its utility for boosting classification performance when singleplatform samples are rare. We explore three ways of defining gene sets, including a novel way based on the notion of a fully coupled flux related to metabolic pathways. In two tissue classification tasks, we empirically show that the gene set based approach is useful for combining heterogeneous expression data, while surprisingly, in experiments constrained to a single platform, biologically meaningful gene sets acting as sample features are often outperformed by random gene sets with no biological relevance.

1

Introduction

The problem addressed in this paper is set-level analysis of gene expression data, as opposed to the more traditional gene-level analysis approaches. In the latter, one typically seeks single statistically significant genes or constructs classification models with gene expressions acting as sample features. In set-level analysis, genes are first grouped into sets apriori determined by a chosen relevant kind of background knowledge. For example, a gene set may correspond to a group of proteins acting as enzymes in a biochemical pathway or be a set of genes sharing a gene-ontology [3] term. Naturally, gene sets considered for an analysis may on one hand overlap while on the other hand their union may not exhaust the entire gene set screened in the expression data. Any gene set may then be assigned descriptive values (such as expression, fold change, significance) by statistical aggregation of the analogical values pertaining to its members. Gene sets thus may act as derived sample features replacing the original gene expressions. The potential for set-level analysis of genomic data has been advocated recently [12,1] on the grounds of improved interpretation power and statistical significance of analysis results. The basic idea of set-level analysis is not new. Indeed, state-of-the-art tools such as DAVID [9] have supported the established protocol of enrichment analysis detecting ontology terms or pathways related to a large subset of a user-supplied gene list, thus obviously following a simple form of set-level analysis. The biological utility of set-level analysis was demonstrated by the study [11] where a significantly downregulated pathway-based I. M˘ andoiu, G. Narasimhan, and Y. Zhang (Eds.): ISBRA 2009, LNBI 5542, pp. 5–17, 2009. c Springer-Verlag Berlin Heidelberg 2009 

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gene set in a class of type 2 diabetes was discovered despite no significant expression change being detected for an individual gene. In another study [18], a method based on singular value decomposition was proposed to determine the ‘level of activity’ of a pathway based on the sampled expression values of its gene-members. The paper [5] reviews some common statistical pitfalls in the calculation of such statistics ascribed to gene sets. The recent work [15] suggests a more sophisticated method to estimate the activity level of a pathway, considering the pathway structure in addition to the expressions of the genes involved therein. Another innovative aspect of [15] is that the authors employ such pathway activities as derived features of samples and use these for sample classification by a machine learning algorithm. The main contribution of the present work is showing that the gene set based approach naturally enables to analyze in an integrated manner gene expression data collected from heterogeneous platforms, which may even encompass different organism species. The significance of this contribution is at least twofold. First, microarray experiments are costly, often resulting in numbers of samples insufficient for reliable modeling. The possibility of systematically integrating the experimenter’s data with numerous public expression samples coming from heterogeneous platforms, would obviously help the experimenter. Second, such integrated analysis provides the principal means to discover biological markers shared by different-genome species. We consider three types of gene sets. The first type groups genes that share a common gene ontology [3] term. The second type groups genes acting in biological pathways formalized by the KEGG [10] database. The third gene set type represents a further novel contribution of our work and is based on the notion of a fully coupled flux, which is a pattern prescribing pathway partitions hypothesized by [13] to involve strongly co-expressed genes. These synergize in single gradually amplified biological functions such as enzymatic catalysis or translocation among different cellular compartments. Research papers concerned with gene set based analysis, including the aforementioned studies, usually point out the statistical advantages of results based on gene sets in comparison with those based on single genes. We conjecture, however, that to assess the utility of the gene set approach, the relevant question that must be asked is how data models based on biologically meaningful gene sets compare to those based on gene sets constructed randomly, with no biological relevance. This question is important as we indeed show that even random grouping of genes into sets may lead to improved predictive accuracies. By addressing this question way we can determine whether the inclusion of background knowledge through gene sets has a positive effect on the analysis results. We are not aware of previous work considering this question1 and it is our third contribution to address it experimentally.

1

The suggested gene set randomization should not be confused with the standard class-permutation technique used for validation, also in the set-level analysis context [1].

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The paper is organized as follows. In Section 2 we describe the methodological ingredients of our approach, consisting of normalization, gene set extraction, data integration and predictive classification. Section 3 describes the expression analysis case studies and the collected relevant data used for experimental validation. In Section 4 we show and discuss the experimental results. Section 5 lays out prospects for future work and concludes the paper.

2

Methods

The input of our workflow is a set of gene expression samples (real vectors) possibly measured by different microarray platforms. Each sample is assigned two labels. The first identifies the microarray platform from which the sample originates, the second identifies a sample class (e.g. tissue type). The output is a classification model, that is, a model that estimates the sample class given an expression sample and its platform label. The model is obviously applicable to any sample not present in the input (‘training’) data, as long as its platform label is also present in the input data. The remarkable property of the output model is that it is not a combination of separate models each pertaining to a single platform. Rather, it is a single classifier trained from the entire heterogeneous sample set and represented in terms of ‘activity levels’ of units that apply to all platforms, albeit the computation of these activity levels may be different across platforms. More specifically, the activity of a unit (such as a pathway) is calculated using a different gene set in each platform. We now describe the individual steps of the method in more detail. Normalization. The first normalization step is conducted separately for each platform to consolidate same-platform samples. Quantile normalization [2] ensures that the distribution of expression values across such samples is identical. As a second step, scaling provides means to consolidate the measurements across multi-platform samples. We subtract the sample mean from all sample components, and divide them by the standard deviation within the sample. As a result, all samples independently of the platform exhibit zero mean and unit variance. We conduct these steps using the Bioconductor [4] software. Set Construction. Here we consider three types of background knowledge in order to define apriori gene sets. Each such set will be extracted from the initial pool of all genes measured by at least one of the involved platforms. The first type groups genes that share a common gene ontology [3] term. The second type groups genes acting in biological pathways formalized by the KEGG [10] database. A gene falls in a set corresponding to a pathway if it is mapped to a KEGG node of some organism ortholog of that pathway. The third gene set type is based on the notion of a fully coupled flux (FCF), motivated as follows. Many notable biological conditions are characterized by the activation of only certain parts of pathways; for example, see references [16,19,21]. The notion of ‘pathway activation’ implied by the previous gene set may thus often violate intuition and hinder interpretation. Therefore we extracted all pathway partitions which

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Fig. 1. Fully coupled fluxes in a simplified network with nodes representing chemical compounds and arrows as symbols for chemical reactions among them. Each arrow can be labeled by a protein. R3, R4 and R5 are fully coupled as a flux in any of these reactions implies a flux in the rest of them. Note that R1 and R3 do not constitute a FCF as a flux in R3 does not imply a flux in R1.

comply with the graph-theoretic notion of FCF [13]. It is known that the genes coupled by their enzymatic fluxes not only show similar expression patterns, but also share transcriptional regulators and frequently reside in the same operon in prokaryotes or similar eukaryotic multi-gene units such as the hematopoietic globin gene cluster. FCF is a special kind of network flux that corresponds to a pathway partition in which non-zero flux for one reaction implies a non-zero flux for the other reactions and vice versa. It is the strongest qualitative connectivity that can be identified in a network. The notion of an FCF is explained through an example in Fig. 1; for a detailed definition, see reference [13]. Pathway partitions forming FCF’s constitute the third gene set type. Again, a gene falls in a set corresponding to a FCF if it is mapped to a KEGG node in some organismortholog of that FCF. The extraction of fully coupled fluxes from KEGG pathways graphs was conducted in Prolog. The source code as well as the Prolog representation [8] of the pathways are available on request to the first author. The bold numbers in Table 2 display the total numbers of gene sets extracted for the respective types. In what follows, gene sets act as features acquiring a real value for each sample. Formally, let π be the set of genes interrogated by a given platform, and Σ a set of gene sets of a particular type. We define a mapping Aπ : R|π| × Σ → R For an expression sample s = [e1 , . . . , e|π| ] ∈ R|π| , Aπ (s, σ) should collectively quantify the ‘activity level’ of genes in set σ ∈ Σ, in the biological situation (e.g. a tissue type) sampled by s. Typically, not all members of σ will be measured by platform π, and the computation of Aπ (s, σ) will be based on the expressions ei of genes in σ ∩ π. For transparency, in this study we define Aπ (s, σ) as the average of expressions measured in s for all genes in σ ∩ π. We only note here that more sophisticated methods have been proposed to instantiate Aπ (s, σ), either linear, based e.g. on a weighted sum of expression values of the involved genes as in [18], or non-linear, based on additional structure information as in [15] but then constrained to pathway-type gene sets.

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Fig. 2. Integrating expression data collected from heterogeneous platforms into a unified tabular representation of pathway activations. If these platforms pertain to different organisms, we assume that (an ortholog of) each pathway pi exists in each of the organisms.

Our reasoning above assumes the aggregation of gene expression measurements. Precisely speaking, genes themselves aggregate one or more measurements since multiple probesets can represent the same gene. Here, the expression of a gene is simply defined as the average of the corresponding normalized probeset measurements, despite certain caveats of this approach.2 Data Integration. The goal of this methodological step is to integrate heterogeneous expression samples into a single-tabular representation (that is, into a set of samples sharing a common feature set) that predictive classification algorithms can process. Formally, we have a set of expression samples S= {s1 ,s2 , . . .} in which for all i si ∈ ∪j R|πj | , πj ∈ Π where Π is the set of the considered platforms. We wish to obtain a new repre¯ i ∈ Rn , n ∈ N . sentation S¯ = {¯ s1 , s¯2 , . . .} where each s This aim is achieved using the above introduced ‘gene set activation’ concepts. Formally, using gene set type Σ = {σ1 , σ2 , . . . , σm }, for each sample si labeled with platform π we stipulate s¯i = [Aπ (si , σ1 ), . . . , Aπ (si , σm )] Naturally, sample s¯i then inherits the class label from si . The integration principle is exemplified in Fig. 2 with pathways pi playing the role of gene sets σi . The described representation conversion is part of the functionality of the aforementioned Prolog code. Classification and Validation. The final step of the workflow is to employ machine learning algorithms to induce predictive classification models of the integrated samples. As the achieved unified representation S¯ can be processed by virtually any machine learning algorithm, the choice appears rather arbitrary. Since one of the usual arguments in favor of gene set based analysis is the ease 2

For example, Affymetrix chips contain probesets representing the same gene that cannot be consolidated into unique measures of transcription due to alternative splicing, use of alternative poly(A) signals, or incorrect annotations [17].

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of interpretation, we decided to test decision-tree classifiers enabling direct human inspection. Specifically, we experimented with the J48 decision tree learner included the machine learning environment Weka [20]. The design of the experiments and the validation protocol is dictated by the following questions we wish to address empirically. – (Q1) How do classifiers based on original single gene expressions compare in terms of predictive accuracy to those based on activations of biologically meaningful gene sets? – (Q2) How do classifiers based on biologically meaningful gene sets compare in terms of predictive accuracy to those based on gene sets constructed randomly, with no biological relevance? – (Q3) How do classifiers learned from single-platform data compare in terms of predictive accuracy to those learned from data integrated from heterogeneous platforms? In the case of (Q2), we constructed three families of random gene sets corresponding to the three respective kinds of genuine gene sets, for each of the involved platforms. The correspondence is in that a particular type of random gene sets contains exactly the same number of set-elements and exactly the same set-cardinality distribution as its genuine counterpart. For each platform, the members of each random gene set were drawn randomly without replacement from a uniform probability distribution cast on the genes measured by the platform. We are interested in the insights Q1-Q3 for both the ‘data-rich’ and ‘datapoor’ situation, i.e. for both small and large sets of expression samples. Therefore the preferred means of assessment is through learning curves which are diagrams plotting an unbiased estimate of the classifier’s predictive accuracy against the proportion pof the available data set used for its training. The accuracy estimate for each measured pwas obtained by inducing a classifier 20 times with a randomly chosen subset (of proportional size p ) of the entire data set and testing its accuracy on the remaining data not used for training. In each such step, the 20 empirical accuracy results were averaged into the reported value. We let p range from 0.2 to 0.8 to prevent statistical artifacts arising from overly small sets used for training or testing, respectively.

3

Classification Tasks and Data

Here we validate our methodology in biological classification tasks. In order to avoid domain bias, we chose not to tackle overly special classification cases such as those addressing particular diseases. We therefore address two general tasks of tissue type classification. The first experiment focuses on distinct features of blood-forming (hematopoietic; ‘heme’ in figure legends) and supportive (stromal; ‘stroma’) cellular compartments in the bone marrow. The second assesses differences in brain, liver and muscle tissues. Both experiments are of biological significance as they tackle novel challenges in understanding of cellular behavior: the former in the complex functional unit termed hematopoietic stem cell

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Table 1. Sample size statistics. Platforms are identified by NCBI’s GPL keys. Organism keys stand for mus musculus (mmu), homo sapiens (hsa) and rattus norvegicus (rno). Platform 1261 339 341 570 81 91 96 97 Organism mmu mmu rno hsa mmu hsa hsa hsa Heme 46 7 4 19 6 18 18 Stroma 19 8 47 26 33

Platform 1261 91 96 Organism mmu hsa hsa Brain 6 15 20 Liver 11 2 6 Muscle 11 22 41

Table 2. Gene sets statistics. Numbers in bold are independent of the specific platforms measuring the expression data, being only determined by the respective types of background knowledge. The ‘Probesets contained’ columns capture statistics over all involved platforms. The first three rows correspond to the apriori defined sets. For accuracy, we list their sizes in terms of probesets, rather than genes. The statistical relation between genes and probes are in turn shown in the last row. Set type Total Probesets contained Min Max Avg Median FCF 901 0 83 5.47 2 Pathway 251 0 457 52.09 33 GO term 5164 1 7605 25.75 3 Gene 12808∗ 1 49 1.58 1 ∗

average across platforms

niche, where inter-dependent hematopoietic and stromal cell functions synergize in the blood-forming function of the bone marrow; the latter in comparison of cell fate determined by the tissue origin from the separate layers of the embryo: ectoderm (brain), endoderm (liver) and mesoderm (muscle). While of general character, the chosen classification tasks are not just random biological exercises as these studies may illuminate cellular functions determined by gene expression signatures in complex cell system seeded by cell-type-heterogeneous undifferentiated populations (hematopoietic and stromal stem cells in the cell niche), and in the cell-type-homogeneous differentiated tissues (brain, liver and muscle), respectively. For both the first (2-class) and the second (3-class) classification problems, samples were downloaded from the Gene Expression Omnibus database [14]. We only downloaded control (non-treated, non-pathological) samples of each tissue in question. For ease of gene functional annotation, we only downloaded samples measured with platforms provided by Affymetrix. Table 1 provides the statistics on sample distribution among classes and platforms. Table 2 then shows statistics derived from the application of apriori constructed gene sets onto the collected expression samples.

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4

Results

Here we show the empirical results obtained by processing the data described in Section 3 by the method explained in Section 2 and comment on their relevance to questions Q1-Q3 formulated in the latter section. Results are of two types: single-platform (experiments conducted on a single type of microarray) and cross-platform (experiments on the integrated heterogeneous expression data). Single-platform experiments are shown in both classification tasks for the sample-richest platform pertaining to the homo sapiens organism (GPL97 and GPL96 respectively). The principal trends observed are as follows. Q1 is addressed by the top two panels of Fig. 3. While they do not provide a conclusive performance ranking of the four types of sample representation, they clearly demonstrate that predictive

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accuracy is not sacrificed by converting the representation from genes to gene sets. On the contrary, the gene set representation based on GO terms quite systematically outperforms the original gene based representation. The lower two panels of Fig. 3 compare the three gene set based approaches in the crossplatform experiments where the gene based representation is not applicable. In the Heme-Stroma task, a clear ranking is observable with fully coupled fluxes performing best, followed by GO terms and lastly pathways. Ranking induced by the Brain-Liver-Muscle task is much less crisp. Figures 4 and 5 relate to Q2. Fig. 4 provides the surprising finding that none of the three genuine gene set representations strictly outperforms its randomized counterpart in both tasks performed in the single-platform setting; with the pathway based gene set representation being strikingly outperformed in the Brain-Liver-Muscle task. To make sure that these results were not a statistical artifact we regenerated all the randomized gene sets and arrived at principally same results. Combining these results with the top row of Fig 3, we deduce another observation that the random gene set approach often improves classification accuracy upon the basic classification based on gene expressions. This latter observation can however be explained rather naturally by viewing the random gene set approach as a form of stochastic feature extraction [7] reducing the dimensionality of the data and thus suppressing the variance component [6] of the classification error. The trends are significantly different in the crossplatform setting (Fig. 5) where all genuine gene set types strictly outperform their random counterparts in both tasks. Here the value of biologically meaningful gene sets manifests itself clearly in that the sets act as links connecting diverse genes distributed across platforms. Such a link is obviously broken when the gene sets are randomized. Finally, to answer Q3 we compare the upper panels of Fig. 3 against its lower panels. With large training data sizes, accuracy differences between singleplatform (upper panels) and cross-platform (lower panels) learning are insignificant, letting us conclude that the assembling of multiple-platform data did not have a detrimental effect on classification performance. More importantly still, in the cross-platform setting, high accuracies are achieved much earlier along the xaxis than in the single-platform setting. While the reason is obvious (the same sample set proportion corresponds to a higher absolute number of samples in the cross-platform case), this observation is reassuring. An experimenter possessing a sample set too small for reliable model induction may benefit from employing the gene set based approach to include further relevant public expression samples, however coming from diverse microarray platforms.

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Conclusions and Future Work

We have demonstrated a set-level approach to the integration of multipleplatform gene expression data for predictive classification and argued its utility for boosting classification performance when single-platform samples are rare. We explored three ways of defining gene sets, including a novel way based on

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the notion of a fully coupled flux related to metabolic pathways. In two tissue classification tasks, we showed that the gene set based representation is unquestionably useful for combining heterogeneous expression data. This may be for sakes of assembling a larger sample set or to obtain general biological insights not limited to a particular organism. On the other hand, in experiments constrained to a single platform, biologically meaningful gene sets were often outperformed by random gene sets with no biological relevance. Further studies are obviously needed to conclusively compare the performance of biologically relevant gene sets with their randomized counterparts; such studies would especially be interesting in problems where the genuine gene set approach was shown successful, such as in [11,18]. Another natural extension of this work would be in the adoption of a less elementary approach to determine the pathway activation levels, e.g. along the lines of the study [15]. Acknowledgements. The authors are supported by the Czech Grant Agency through project 201/09/1665 (MH), the Czech Ministry of Education through projects ME910 (FZ) and MSM6840770012 (JK), and by the Children’s Cancer Research Fund of the University of Minnesota (JT).

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Practical Quality Assessment of Microarray Data by Simulation of Differential Gene Expression Brian E. Howard1, Beate Sick2, and Steffen Heber1,3 1

Bioinformatics Research Center, North Carolina State University, Raleigh, North Carolina, United States 2 Institute of Data Analysis and Process Design, Zurich University of Applied Science, Winterthur, Switzerland 3 Department of Computer Science, North Carolina State University, Raleigh, North Carolina, United States [email protected], [email protected], [email protected]

Abstract. There are many methods for assessing the quality of microarray data, but little guidance regarding what to do when defective data is identified. Depending on the scientific question asked, discarding flawed data from a small experiment may be detrimental. Here we describe a novel quality assessment method that is designed to identify chips that should be discarded from an experiment. This technique simulates a set of differentially expressed genes and then assesses whether discarding each chip enhances or obscures the recovery of this known set. We compare our method to expert annotations derived using popular quality diagnostics and show, with examples, that the decision to discard a chip depends on the details of the particular experiment. Keywords: Microarray, quality assessment, simulation.

1 Introduction Considerable attention has been paid to methods and metrics that can be used to measure the quality of microarray data (for recent reviews, see [1, 2]). For example, a common approach employs a routine set of diagnostic plots and statistics to identify arrays having low quality relative to the other chips in an experiment [3-8]. In the majority of cases, these methods are used as a filtering step, with the assumption that discarding low quality arrays should increase both the sensitivity and specificity of tests for differentially expressed genes [2]; however, in reality, many of these chips still contain valuable signal, even if that signal is obscured by extensive statistical noise. For a given FDR level, increasing sample size can increase the power to identify differentially expressed genes with decreased probability of declaring false positives [9]. Hence, as demonstrated in [10], discarding moderately noisy chips can actually be detrimental in many cases. Unfortunately, no clear guidelines currently exist for differentiating scenarios in which it is advantageous to discard low quality data from situations where that data should be retained. Here we present a simple procedure that can be used to assess the quality of microarray data. In contrast to other methods, however, this procedure also provides I. Măndoiu, G. Narasimhan, and Y. Zhang (Eds.): ISBRA 2009, LNBI 5542, pp. 18–27, 2009. © Springer-Verlag Berlin Heidelberg 2009

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practical advice about what to do when low quality chips are identified. The method works by first simulating a set of differentially expressed genes, using gene expression distributions estimated from the dataset. Then, the procedure identifies arrays whose inclusion impairs the recovery of this known set of genes. This method is intended not to merely categorize arrays into binary “high quality” and “low quality” categories, but to identify arrays that should actually be excluded from a particular analysis. Because this approach to quality assessment depends on the details of the particular microarray experiment considered, the assessment framework we describe is easily adaptable to a variety of analysis protocols and experimental frameworks. In the first section, we will describe the dataset used in this paper, and explain the simulation algorithm. Then, we will compare the results obtained from this approach with previous expert annotations created with the aid of a set of popular quality diagnostics. We will illustrate the observation that any decision about whether to include a given array should be dependent not only on the noise profile of the array itself, but also on the details of the specific experiment being performed, including the number of replicates in each sample and the analysis method used to interpret the results.

2 Methods 2.1 Datasets The dataset for this research consists of a set of 531 Affymetrix raw intensity (.CEL) files obtained from the NCBI GEO database [11]. These data are a subset of the dataset described in [8] and consist of all the experiments having at least three samples per treatment. Several of the most commonly used Affymetrix GeneChip 3’ expression array types are represented and were chosen to include a variety of frequently investigated tissue types, experimental treatments and species, including Arabidopsis (ath1121501 array), mouse (mgu74a, mgu74av2, mo3430a, and mouse4302 arrays), rat (rae230a and rgu34a arrays), and human (hgu133a, hgu95av2, hgu95d, and hgu95e arrays). 2.2 Expert Annotations Quality scores were assigned to each chip by a domain expert, according to a procedure previously established and applied in the Lausanne DNA Array Facility (DAFL) [7]. Briefly, this procedure involves the systematic analysis of a variety of common predictive quality assessment metrics including: chip scan images, distributions of the log scale raw and normalized PM probe intensities, plots of the 5’ to 3’ probe intensity gradients, pseudo-images of the PLM weights and residuals, and boxplots of the Normalized Unscaled Standard Error (NUSE) and Relative Log Expression (RLE) scores for each chip. After consideration of each of these quality features, the expert identified arrays that appeared to be outliers with respect to other chips in the same experiment, and each array was assigned a quality score of 0, 1, or 2, with 0 being “acceptable quality” (462 chips), 1 being “suspicious quality” (45 chips) and 2 being “unacceptable quality” (24 chips). These scores were then used as a basis of comparison to quality assessments made using the empirical quality approach described in this paper.

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2.3 Quality Assessment Algorithm Our approach takes a very practical definition of microarray data “quality”: a low quality microarray is an array that diminishes the chances of accurately detecting differentially expressed genes, given a particular experimental design, dataset, and analysis methodology. To make this determination, our algorithm uses simulated data to find out if excluding a particular chip is likely to improve the ability to detect differentially expressed genes in an experiment similar to the one intended by the investigator. The simulated dataset is constructed using the observed gene expression distributions from the original experiment. Within this simulated dataset, which includes both a “treatment” group and a “control” group, some of the genes are differentially expressed. The quality assessment procedure operates by performing a statistical test for differential expression under two different scenarios: (1) using only the simulated data, and (2) using the simulated data plus the actual expression measurements for one of the chips. If excluding the actual expression measurements for this chip enhances the recovery of the known set of simulated differentially expressed genes, then that chip is flagged as “low quality”. Note that this definition of quality depends on the details of the experiment examined, and, accordingly, our quality assessment framework is adaptable to a variety of microarray platforms and statistical procedures. For concreteness, we will describe the algorithm as it might be applied to a set of one-color microarray data of the sort that comprises our previously described test dataset. However, the details of this approach, including the normalization procedure, gene expression parameters, and choice of statistical test, are flexible. These can, and should, be adapted to match the analysis approach used for the actual experimental data. Goal • To determine whether or not a particular microarray chip should be excluded from an experiment designed to test for differential expression between two treatment groups. Input • A set of microarray expression values from treatment Group 1, which contains N1 (≥2) replicate chips. • A set of microarray expression values from treatment Group 2, which contains N2 replicate chips. • A suspected low quality chip, c, from Group 1. Output • A decision whether or not to exclude chip c from the test for differential expression between Group 1 and Group 2. Procedure 1. Normalize the complete dataset using whatever procedure would normally be used in the final analysis (e.g. quantile/RMA [12], etc.).

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2. Exclude the suspect chip, c, and use the N1-1 remaining chips from Group 1 to estimate the mean, µˆ g , and sample variance, sg2 , for every probeset, g, on the chip. Repeat 30 times:

3. Simulate a set of G1 consistently expressed genes (CEGs) as follows: • Randomly select G1 probesets from the set of all probesets on the chip. • For each selected probeset, sample N1+N2-1 values from a Normal( µˆ g , sg2)

distribution. • Append the actual expression values from chip c to the simulated data for Group 1. The result is a G1 × (N1+N2) expression matrix, where the first N1 columns correspond to “treatment 1” and the second N2 columns are “treatment 2”. 4. Use the same procedure to simulate a set of G2 differentially expressed genes (DEGs), with the following additional step: • Add a small multiple of the probeset-specific standard deviations, sg, to the N2 “treatment 2” expression values, shifting the mean of the second treatment group relative to the first.

5. Perform a test for differential expression between the two treatments (e.g. using LIMMA [13]) in each of the G1+G2 rows. 6. Evaluate the performance of this test by computing an ROC curve, which can be constructed from the sorted p-values from the tests in step 5. Using this ROC curve, compute the corresponding area under the curve (AUC). (A detailed guide to ROC curves can be found in [14]). 7. Discard the expression values from the suspect chip, and re-compute the ROC curve and AUC (i.e. repeat steps 5 and 6). 8. Record the difference between the AUC scores computed in steps 6 and 7. 9. Discard chip c if the AUC without chip c is significantly higher than with chip c.

3 Results 3.1 Comparison with Expert Annotations

After normalizing all arrays from each experiment using RMA [12], we applied the previously described simulation-based quality assessment procedure to each of the chips in our dataset. For each chip, we simulated 30 N × N experiments, where N is the number of replicates for that chip’s treatment in the original dataset. Each experiment contained 500 consistently expressed genes (CEGs) and 500 differentially expressed genes (DEGs). Differential expression was simulated by adding ± 1 standard deviation to the second treatment group (odd probesets were given positive deltas, and even probesets were given negative deltas). The R LIMMA [13] package was then

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Fig. 1. Low-quality calls by expert quality group. Expert quality score is shown on the x-axis. Light blue indicates frequency of this category among expert annotations. Dark blue shows proportion of this category flagged for exclusion using the simulation approach.

Fig. 2. Comparison of expert and simulation determined quality scores. Chips with expert quality scores of 1 or 2 are included in the “Flagged by Expert” set. Chips with simulation pvalues < .001 are included in the “Flagged by Algorithm” set.

used to identify differentially expressed genes, both with and without the suspect chip, and the resulting ROC curves were computed in each case. Chips whose inclusion significantly lowered the AUC according to a paired t-test (p-value < .001) were

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identified as having low quality. The entire analysis was performed using the R statistical programming language (code available from the author by request.) We then compared the chips identified using this procedure with those identified previously by the domain expert. Figure 1 shows that, for the 24 chips identified by the expert as having the lowest quality (i.e. scored as 2’s), the simulation identified 8 chips as being candidates for exclusion (33.3%). Among the 45 chips flagged by the expert as suspicious (1’s), 11 were identified by the simulation procedure as candidates for exclusion (24.4%). For the 462 chips regarded by the expert as having acceptable quality, only 2 were identified by the algorithm as candidates for exclusion (0.43%). Figure 2 summarizes the chips flagged as low quality by the two methods. 3.2 Practical Quality Judgment Depends on the Details of the Experiment

Quality assessment procedures based on predictive quality metrics sometimes have difficulty determining the utility of excluding suspicious chips because this decision is inextricably tied to the details of the particular experiment and the analysis method used. Unfortunately, the values for most quality metrics do not explicitly incorporate the sample size, target effect magnitude or analysis method employed. However, these experimental details are critical for making a rational decision regarding the inclusion or exclusion of low quality data. This scenario is illustrated in the following examples. Example 1. GEO dataset GSE1873 [15] contains gene expression measurements taken from liver tissue of obese mice. The experiment used 5 Affymetrix microarrays to measure gene expression of obese mice exposed to intermittent hypoxic conditions and 5 microarrays to measure gene expression of obese mice used as controls. Using the protocol described in section 2.2, our domain expert examined this dataset and identified 3 chips as having low or suspicious quality (GSM32860, GSM32861 and GSM32866). However, in a simulation using 5 chips in each treatment group, only GSM32860 and GSM32866 were found to be worthy of exclusion (when considered individually). On the other hand, in simulated 3x3 and 4x4 experiments, exclusion of chip GSM32866 is no longer recommended by our procedure. Conversely, as simulated experiment size increases, the p-value for chip GSM32861 approaches the threshold for exclusion, with a p-value of less than 0.01 for experiments of size 9x9 or greater. Example 2. Recent research has demonstrated that many of the common quality problems observed in a typical microarray experiment can be mitigated with the use of robust analysis methods. For example, many typical quality problems can be captured with a heteroscedastic variance model which allows each chip to have different levels of random noise [10]. Smyth showed in simulation that, in many cases, procedures that simply down-weight noisier chips perform better than methods that attempt to identify and exclude these low quality chips. Again, consider experiment GSE1873. Figure 3 shows the expression values for a few representative probesets (expert-identified low quality probesets are shown in colored dots). The diagram illustrates the fact that there is greater variance between probesets than among chips within each probeset. On the other hand, the expression values for the low quality chips appear to more often have extreme values than the

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Fig. 3. Normalized expression levels for 4 probesets from experiment GSE1873. Green circles correspond to ‘treatment 1’ and blue circles to ‘treatment 2.’ The colored circles represent chips flagged by the expert as low quality. The dashed lines indicate the median expression level for each treatment, while the dotted lines correspond to treatment median ± 1 MAD (median absolute deviation). X-axis is chip name; y-axis is normalized expression.

Fig. 4. Log Expression for experiment GSE1873. Height of box corresponds to interquartile range of the RLE, and midline indicates RLE median.

other chips, although not consistently in one direction. The RLE boxplot also reflects this observation (figure 4); the interquartile ranges for the low quality chips are larger than for the high quality chips. These observations suggest that the heteroscedastic

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variance model may indeed be useful in the analysis of this data set. To test this hypothesis, we repeated the quality simulation with one modification: we used the “arrayWeights” functionality of the LIMMA package to identify and downweight noisy chips. Under this analysis framework, the quality simulation showed that excluding these chips is no longer recommended. On the other hand, even robust methods can not be expected to correct the most extreme types of errors. For example, we simulated mislabeled samples by interchanging data from different GEO datasets and observed that in these cases it was often still better to remove the foreign arrays than to apply the downweighting procedure (data not shown).

4 Discussion The quality assessment method described here addresses an important question not often considered by other procedures: what to do with the low-quality chips that are identified. In many real-world scenarios, better results can be obtained by retaining slightly flawed data, instead of discarding it completely. Unfortunately, there is currently little guidance available with regard to this decision. Our method takes an empirical approach to this problem by simulating a set of differentially expressed genes and then evaluating the contribution of each suspected chip with regard to identifying these genes. For the datasets examined in our research, the chips identified by the simulation algorithm as “excludable” were roughly a subset of the chips identified by the domain expert as having low quality (figure 2). This may imply that although the expert is correctly identifying the chips with higher noise levels, many of those chips still retain useful signal, especially within the context of the small experiments considered. This approach is easily adapted to other analysis settings, and, in general, it is recommended that the analysis method and parameter settings chosen for the simulation should match the protocol intended for the real data set. For example, here we have used the LIMMA library for statistical analysis, but other methods, such as SAM [16] or Cyber-T [17] could just as easily be applied instead. Alternatively, if the researcher is interested in controlling false discoveries at a specific rate, then one could apply an FDR control procedure and compare the number of true discoveries made instead of the area under ROC curves. In future work we intend to explore more thoroughly the influence of these parameters on the resulting quality decisions. It would also be interesting to enhance our simulation approach to emulate more complex gene expression models, possibly allowing for correlated genes, non-normal distributions and variable effect sizes. It should be noted that when applying the procedure as described here, it is important to look not only at the resulting p-value, but also the magnitude of the observed difference in AUC obtained with and without each chip. Very small differences can sometimes accompany significant p-values, especially if enough replications are performed; in these cases it is probably prudent to retain the chip anyway. Like other quality assessment procedures that attempt to identify outliers among a particular set of microarrays, our method is susceptible to scenarios where the dataset is corrupted by a majority of chips with systematic error. For example, in a dataset where one of the arrays is mislabeled with regard to the experimental treatment

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applied, our method would likely identify the mislabeled array as an outlier; however, if all of the arrays except one particular array were mislabeled, our algorithm may erroneously identify the correctly labeled array as the outlier. Robust analysis methods such as the approach described in [10] can potentially mitigate many of the common problems observed in microarray datasets. On the other hand, there are still scenarios where even the most robust methods cannot recover useful signal from a particular low quality array. Arrays showing evidence of large spatial artifacts, contamination or other gross errors such as mislabeled samples can rarely be salvaged. Our method can be used to identify these scenarios. In addition, while the method we have described can be used on its own for quality assessment, this technique can also be used in conjunction with other traditional quality diagnostics, which may provide additional clues as to what sorts of errors are present in a batch of arrays and thereby assist in avoiding these problems in the future.

References 1. Larsson, O., Wennmalm, K., Sandberg, R.: Comparative microarray analysis. OMICS: A Journal of Integrative Biology 10(3), 381–397 (2006) 2. Wilkes, T., Laux, H., Foy, C.A.: Microarray data quality – review of current developments. OMICS: A Journal of Integrative Biology 11(1), 1–13 (2007) 3. Archer, K.J., Dumur, C.I., Joel, S.E., Ramakrishnan, V.: Assessing quality of hybridized RNA in Affymetrix GeneChip experiments using mixed-effects models. Biostatistics 7(2), 198–212 (2006) 4. Reimer, M., Weinstein, J.N.: Quality assessment of microarrays: visualization of spatial artifacts and quantitation of regional biases. BMC Bioinformatics 6, 166 (2005) 5. Stokes, T.H., Moffitt, R.A., Phan, J.H., Wang, M.D.: chip artifact CORRECTion (caCORRECT): a bioinformatics system for quality assurance of genomics and proteomics array data. Annals of Biomedical Engineering 35(6), 1068–1080 (2007) 6. Gentleman, R., Carey, V., Huber, W., Irizarry, R., Dudoit, S.: Bioinformatics and computational biology solutions using R and Bioconductor. Springer, New York (2005) 7. Heber, S., Sick, B.: Quality assessment of Affymetrix GeneChip data. OMICS: A Journal of Integrative Biology 10(3), 358–368 (2006) 8. Howard, B.E., Sick, B., Heber, S.: Unsupervised assessment of microarray data qQuality using a Gaussian mixture model (2009) (manuscript) (submitted) 9. Pawitan, Y., et al.: False discovery rate, sensitivity and sample size for microarray studies. Bioinformatics 21, 3017–3024 (2005) 10. Ritchie, M.E., Diyagama, D., Neilson, J., van Laar, R., Dobrovic, A., Holloway, A., Smyth, G.: Empirical array quality weights in the analysis of microarray data. BMC Bioinformatics 7, 261 (2006) 11. Edgar, R., Domrachev, M., Lash, A.E.: Gene Expression Omnibus: NCBI gene expression and hybridization array data repository. Nucleic Acids Research 30(1), 207–210 (2002) 12. Irizarry, R.A., Bolstad, B.M., Collin, F., Cope, L.M., Hobbs, B., Speed, T.P.: Summaries of Affymetrix GeneChip probe level data. Nucleic Acids Research 31(4), e15 (2003) 13. Smyth, G.K.: Linear models and empirical Bayes methods for assessing differential expression in microarray experiments. Statistical Applications in Genetics and Molecular Biology 3(1) (2004)

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14. Fawcett, T.: An introduction to ROC analysis. Pattern Recognition Letters 27, 861–874 (2006) 15. Li, J., Grigoryev, D.N., Ye, S.Q., Thorne, L., et al.: Chronic intermittent hypoxia upregulates genes of lipid biosynthesis in obese mice. Journal of Applied Physiology 99(5), 1643–1648 (2005) 16. Tusher, V.G., Tibshirani, R., Chu, G.: Significance analysis of microarrays applied to the ionizing radiation response. PNAS 98(9), 5116–5121 (2001) 17. Baldi, P., Long, A.D.: A Bayesian framework for the analysis of microarray expression data: regularized t-test and statistical inferences of gene changes. Bioinformatics 17, 509–519 (2001)

Mean Square Residue Biclustering with Missing Data and Row Inversions Stefan Gremalschi1,⋆ , Gulsah Altun2 , Irina Astrovskaya1,⋆, and Alexander Zelikovsky1 1

Department of Computer Science, Georgia State University, Atlanta, GA 30303 {stefan,iraa,alexz}@cs.gsu.edu 2 Department of Reproductive Medicine, University of California, San Diego, CA 92093 [email protected]

Abstract. Cheng and Church proposed a greedy deletion-addition algorithm to find a given number of k biclusters, whose mean squared residues (MSRs) are below certain thresholds and the missing values in the matrix are replaced with random numbers. In our previous paper we introduced the dual biclustering method with quadratic optimization to missing data and row inversions. In this paper, we modified the dual biclustering method with quadratic optimization and added three new features. First, we introduce ”row status” for each row in a bicluster where we add and also delete rows from biclusters based on their status in order to find min MSR. We compare our results with Cheng and Church’s approach where they inverse rows while adding them to the biclusters. We select the row or the negated row not only at addition, but also at deletion and show improvement. Second, we give a prove for the theorem introduced by Cheng and Church in [4]. Since, missing data often occur in the given data matrices for biclustering, usually, missing data are filled by random numbers. However, we show that ignoring the missing data is a better approach and avoids additional noise caused by randomness. Since, an ideal bicluster is a bicluster with an H value of zero, our results show a significant decrease of H value of the biclusters with lesser noise compared to original dual biclustering and Cheng and Church method. Keywords: Biclustering, Mean Square Residue.

1 Introduction The gene expression data are given in matrices. In these matrices rows represent genes and columns represent experimental conditions. Each cell in the matrix represents the expression level of a gene under a specific experimental condition. It is well known that, genes can be relevant for a subset of conditions. On the other hand, groups of conditions can be clustered by using different groups of genes. In this case, it is important to do clustering in these two dimensions simultaneously. This led to the discovery of ⋆

Partially supported by GSU Molecular Basis of Disease Fellowship.

I. M˘andoiu, G. Narasimhan, and Y. Zhang (Eds.): ISBRA 2009, LNBI 5542, pp. 28–39, 2009. c Springer-Verlag Berlin Heidelberg 2009 

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biclusters corresponding to a subset of genes and a subset of conditions with a high similarity score by Cheng and Church [4]. Biclustering algorithms perform simultaneous row-column clustering. The goal in these algorithms is to find homogeneous submatrices. Biclustering has been widely used to find appropriate subsets of experimental conditions in microarray data [1, 5, 7, 9, 11–13, 15, 18, 19]. Cheng and Church’s algorithm is based on a natural uniformity model which is the mean squared residue. They proposed a greedy deletion-addition algorithm to find a given number of k biclusters, whose mean squared residues (MSRs) are below certain thresholds. However, in their method, missing values in the matrix is replaced with random numbers. It is possible that these random numbers can interfere the discovery of future biclusters, especially those ones that have overlap with the discovered ones. Yang et al. [15, 16] referred to this as random interference. They generalize the model of bicluster to incorporate missing values and propose a probabilistic algorithm. They defined a probabilistic move-based algorithm FLOC (FLexible Overlapped biclustering) that generalizes the concept of mean squared residue and based on the concept of action and gain. However, FLOC model is still not suitable for non-disjoint clusters and there are more user parameters, including the number of biclusters. These additional features can have negative impacts to the clustering process. In this paper, we propose a similar method to handle the missing data. We have first mathematically characterized general “ideal” biclusters, i.e., biclusters with zero mean square residue. We have shown that new way of handling missing data is significantly more tolerant to noise. We have also introduced status for each row – status -1 means that the corresponding row is inverted (negated), status +1 means that the original row is not inverted. We consider the problem of finding min MSR overall possible row inversions. A limited use of row inversion (without introducing row status) has been applied in [4] when rows are added to biclusters. Based on our findings in [14], we developed a new dual biclustering algorithm and quadratic program that treats missing data accordingly and use the best status assignment. The matrix entries with missing data are not taken in account when computing averages. When comparing our method with Cheng and Church [4], we show that it is better to ignore missing data when adjusting the mean squared residue (MSR) value for finding optimal biclusters. We use a set of methods which includes a dual biclustering algorithm, quadratic program (QP) and combination of dual biclustering with QP which finds (k× l)-bicluster with MSR using a greedy approach proposed in paper [14]. We use a set of methods which includes a dual biclustering algorithm, quadratic program and combination of dual biclustering with QP which finds (k × l)-bicluster with MSR using a greedy approach proposed in paper [14]. Finally, we apply the best row status assignments and get even better average and median MSR overall set of all biclusters. The reminder of this paper is organized as follows. Section 2 gives the formal definition of mean squared residue. In section 3, we give a new definition for adjusting MSR and prove a necessary and sufficient criteria for a matrix to have a perfect correlation. Section 4 defines the inversion based MSR and shows how to compute it. In section 5, we introduce the dual problem formulation described in [14] and we illustrate the comparison between the new adjusted MSR with Cheng and Church’s method. The search

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of biclusters using the new MSR is given in section 6. The analysis and validation of experimental study is given in Section 7. Finally, we draw conclusions in Section 8.

2 Mean Squared Residue Mean squared residue problem has been defined before by Cheng and Church [4] and Zhou and Khokhar [13]. In this paper, we use the same terminology as in [13]. In this section, we give a brief introduction to the terminology as given in [14]. Our input is an (N × M)-data matrix A, with R rows and C columns, where a cell aij is a real value that represents the expression level of gene i(row i), under condition j(column j). Matrix A is defined by its set of rows, R = {r1 , r2 , ..., rN } and its set of columns C = {c1 , c2 , ..., cM }. Given a matrix, biclustering finds sub-matrices, that are subgroups of rows (genes) and subgroups of columns, where the genes exhibit highly correlated behavior for every condition. Given a data matrix A, the goal is to find a set of biclusters such that each bicluster exhibits some similar characteristic. Let AIJ = (I, J) represent a submatrix of A (I ⊆ R and J ⊆ C). AIJ contains only the elements aij belonging to the submatrix with set of rows I and set of columns J. A bicluster AIJ = (I, J) can be defined as a k by l sub-matrix of the data matrix where k and l are the number of rows and the number of columns in the submatrix AIJ . The concept of bicluster was introduced by [4] to find correlated subsets of genes and a subset of conditions. Let aiJ denote the mean of the i-th row of the bicluster (I, J), aIj the mean of the j-th column of (I, J), and aIJ the mean of all the elements in the bicluster. As given in [4], more formally, aiJ =

1  aij , i ∈ I, |J|

(1)

1  aij , j ∈ J, |I|

(2)

j∈J

aIj =

i∈I

aIJ =

1 |I||J|



aij .

(3)

i∈I,j∈J

According to [4], the residue of an element aij in a submatrix AI J equals rij = aij − aiJ − aI j + aI J

(4)

The difference between the actual value of aij and its expected value predicted from its row, column, and bicluster mean is given by the residue of an element. It also reveals its degree of coherence with the other entries of the bicluster it belongs to. The quality of a bicluster can be evaluated by computing the mean squared residue H, i.e. the sum of all the squared residues of its elements[4]: H(I, J) =

1 |I||J|

 i∈I,j∈J

(aij − aiJ − aI j + aI J )2

(5)

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31

A submatrix AI J is called a δ − bicluster if H(I, J) ≤ δ for some given threshold δ ≥ 0. In general, we can formulate biclustering problem bilaterally – maximize the size (area) of the biclusters and minimize MSR. But, these two objectives above contradict each other because smaller biclusters have smaller MSR and vice versa. Therefore, there are two optimization problem formulations. Cheng and church considered the following formulation: Maximize the bicluster size (area) subject to an upper bound on MSR.

3 Adjusting MSR for Missing Data Missing data often occur in biological data. Common practice to deal with them is to fill gaps by random numbers. However, it adds noise and may result in biclusters of lower quality. Alternative approach is to ignore missing data, keeping only originally available information. Let A be a bicluster (I, J). We denote via Ji ∈ J bicluster’s columns without missing data in i-th row and via Ij ∈ I rows without missing data in j-th column. Then the mean of the i-th row of the bicluster, the mean of the j-th column, and the mean of all the elements in the bicluster are reformulated as follows in equations 6, 7 and 8. 1  aij , i ∈ I, (6) aiJ = |Ji | j∈Ji

aIj =

1  aij , j ∈ J, |Ij |

(7)

i∈Ij

aIJ = 

1

j∈J

Ij



aij .

(8)

i∈Ij ,j∈J

In order to compare the approach with the Cheng-Church’s approach for handling missing data, a bicluster with zero H-value were used. A bicluster with H=0 is called ideal bicluster. Theorem. Let n × m matrix A be a bicluster (I, J). Then, A has a zero H-value if and only if A can be represented as a sum of n-vector X and m-vector Y in the following way aij = xi + yj , i ∈ I, j ∈ J. Proof. First, we assume that A is a n × m bicluster (I, J) with zero H value and try to prove that A can be represented as above-mentioned sum. Zero H value means zero residues rij , i ∈ I, j ∈ J. Then each element of A can be calculated as follows aij = aiJ + aI j − aI J . Denoting X = {xi = aiJ − aI2J }i∈I and Y = {yj = aI j − aI2J }j∈J results in A = X + Y where vector addition is defined as aij = xi + yj . Q.E.D. In the other direction, we assume that bicluster A can be represented as a sum of n-vector X and m-vector Y and try to show that A has zero H-value. Since aij =  xi + yj , i ∈ I, j ∈ J, the mean of the i-th row is aiJ = 

the j-th column is aIj =  

is aIJ =

m

i∈I

xi +n nm

i∈I

j∈J

yj

xi +nyj , n

mxi + j∈J yj , m

the mean of

and the mean of all the elements in the bicluster

. Obviously, the residues are equalled to zero. Indeed,

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yj

rij = xi + yj − xi − j∈J m bicluster A has zero H-value.

−



i∈I

n

xi

− yj +



i∈I

n

xi

+



j∈J

m

yj

= 0. Thus, the

Note. Theorem also covers biclusters that are product of two vectors. Indeed, applying logarithm to them produces biclusters that are represented as a sum.

4 MSR with Row Inversions In the original definition of biclusters, it is possible to invert (negate) certain rows. The row inversion corresponds to negative correlation rather than usual positive correlation of the inverted rows with other rows in the bicluster. The row inversion may result in the significant reduction of the bicluster MSR. In contrast to algorithmically handling inversions when adding rows (see [4]), we suggest to embed row inversion in the MSR definition as follows. We associate with each row its status which is equal -1 if the row is inverted and +1, otherwise. Definition. The Mean Square Residue with row inversions is minimum MSR over all possible row statuses. Finding the optimal row status assignment is not a trivial problem. Since MSR of a matrix does not change when positive linear transformations is applied, we can show that there is a single global minimum of MSR among all possible status assignments. A greedy iterative method changing status of row if the resulted MSR of the entire matrix decreases will find such minimum. Unfortunately, this greedy method is too slow to apply even once while it is better to apply it after each node deletion. Therefore, we suggest the following simple heuristic – iteratively over each row find which total row square residue is lower: the original or the one with all values inverted (negated). The better choice is used as the row status. In our experiments, this heuristic always finds the optimal inversion status assignment.

5 Dual Biclustering In this section, we give a brief overview of the dual biclustering problem and our algorithm that we described in [14]. We formulate the dual biclustering problem as follows: given expression matrix A, find k × l bicluster with the smallest mean squared residue H. For a set of biclusters, we have: Given: matrix An×m , set of bicluster sizes S, total overlapping V . Find:|S| biclusters with total overlapping at most V and total minimum sum of scores H. This algorithm implements the new computation of MSR which ignores missing data. The algorithm uses only the present data that is available. The greedy algorithm for finding a bicluster may start with the entire matrix and at each step try all single rows (columns) addition (deletion), applying the best operation if it improves the score and terminating when it reaches the bicluster size k × l. The output bicluster will have the smaller MSR for the given size. Like in [4], the algorithm uses the structure of the mean

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residue score to enable faster greedy steps: for a given threshold α, at each deletion iteration all rows (columns) for which d(i) > αH(I, J) are removed. Also, the algorithm implements the addition of inverse rows to the matrix, allowing the identification of the biclusters which contains co-regulation and inverse co-regulation. Single node deletion and addition algorithms are shown in Figure 1 and Figure 2, respectively.

Input: Expression matrix A on genes n, conditions m and bicluster size (k, l). Output: Bicluster AI,J with the smallest adjusted MSR. Initialize: I =n, J =m, ∀ w(i, j) =0, i ∈ n, j ∈ m. Iteration: 1. Calculate aiJ , aIj and H(I, J) based on adjusted MSR. If | I| = k, | J| = l output I, J.  ′ (i, j) 2. For each row calculate d(i) = |J1i | j∈Ji RSIJ  ′ 1 3. For each column calculate e(j) = |Ij | i∈Ij RSIJ (i, j) 4. Take the best row or column and remove it from I or J. Fig. 1. Single node deletion algorithm

Input: Expression matrix A and bicluster size (k, l). Output: Bicluster AI ′ ,J ′ with I ′ ⊆ I and J ′ ⊆ J. Iteration: 1. Calculate aiJ , aIj and H(I, J) based ′on the adjusted MSR. (i, j) ≤ H(I, J) 2. Add the columns with |I1j | i∈Ij RSIJ 3. Calculate aiJ , aIj and H(I, J) based on the adjusted MSR.  ′ (i, j) ≤ H(I, J) 4. Add the rows with |J1i | j∈Ji RSIJ 5. If nothing was added or | I ′ | = k, | J ′ | = l, halt. Fig. 2. Single node addition algorithm

This algorithm is used as a subroutine and repeatedly applied to the matrix. We are using bicluster overlapping control (BOC) to avoid finding the same bicluster over and over again. The penalty is applied for using the cells present in biclusters found before. By using BOC, we can preserve the original data from losing information it carries because we do not mask biclusters with random numbers. The general biclustering scheme is outlined in Figure 3, where wij is an element of weights matrix W , A′ is the resulting data matrix after node deletion on original matrix A; and A” is the resulting matrix after node addition on A′ . We used the measure of bicluster overlapping, V , introduced in [14], which is the complement to ratio of number of distinct cells used in all found biclusters and the area of all biclusters.

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Input: Expression matrix A, parameter α and a set S of bicluster sizes. Output: |S| biclusters in matrix A. Iteration: 1. ∀w( i, j) = 0, i ∈ n, j ∈ m. 2. while S not empty do 3. (k, l) = get f irst element f rom S 4. S = S − {(k, l)} 5. Apply multiple node deletion on A giving (k, l). 6. Apply node addition on A′ giving (k, l). 7. Store A” and update W . 8. end. Fig. 3. Dual biclustering algorithm

6 MSR Minimization via Quadratic Program We have defined the Dual Biclustering as an optimization problem [6], [3] in [14]. We have also defined a quadratic program for biclustering in [14]. In this paper, we have modified our QP in [14] where we reformulated the objective and constraints in order to handle missing data. We define the dual biclustering formulation as an optimization problem [14]: for a given matrix An×m , find the bicluster with bounded size (area) k×l with minimal mean squared residue. It can be easily seen that if MSR has to be defined as QP objective, it will be of a cubic form. Since QP’s objective can be contain only squared variables, the following constraint needs to be satisfied: define QP objective in such a way that only quadratic variables are present. To meet this requirement, we simulated variable multiplication by addition as described in [14]. 6.1 Integer Quadratic Program For a given normalized matrix An×m and bicluster size k × l, the Integer Quadratic Program is defined as follows: Objective M inimize :

1 |I||J|



2 i∈n,j∈m (residueij )

Subject to I=k J =l residueij  = aij xij − aiJ xij −  aI j xij + aI J xij 1 1 aiJ = |J| j∈m aij , aI j = |I| i∈n aij and aI J = xij ≥ rowi + columnj − 1 xij ≤ rowi

1 |I||J|



i∈n, j∈m

aij

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xij ≤ columnj  i∈n rowi = k j∈m columnj = l xij , rowi , columnj ∈ {0, 1} End The QP is used as a subroutine and repeatedly applied to the matrix. For each bicluster size, we generate a separate QP. In order to avoid finding the same bicluster over and over again, the discovered bicluster is masked by replacing the values of its submatrix with random values. Row inversion is simulated by adding to the input matrix A its inversed rows. The resulting matrix will have twice more rows. Missing data is handled in the following way: if an element of the matrix contains a missing value, then it does not participate in computation of mean squared residue H. In this case, the row mean AiJ will be equal to the sum of all cells in row i that are not marked as missing values and divided by their number. Similar for column mean AI j and bicluster average AI J . Since the integer QP is too slow and its not scalable enough, we used the greedy rounding and random interval rounding methods proposed in [14]. 6.2 Combining Dual Biclustering with Rounded QP In this section, we combined the adjusted dual biclustering with modified rounded QP algorithm. Here, our goal is to reduce the instance size to speed up the QP. First, we apply adjusted dual biclustering algorithm to input matrix A to reduce the instance size where the new size is specified by two parameters: ratiok and ratiol . Then, we run rounded QP on the output obtained from Dual Biclustering algorithm. This combination improves the running time of the QP and increases the quality of the final bicluster since an optimization method is applied. The general algorithm scheme is outlined in Figure 4, where W is the weights matrix, A′ is the resulting matrix after node deletion and A” is the resulting matrix after node addition.

Input: Expression matrix A, parameters α, ratiok , ratiol and a set of bicluster sizes S. Output: |S| biclusters in matrix A. 1. while S not empty do 2. (k, l) = get f irst element f rom S 3. S = S − {(k, l)} 4. k′ = k · ratiok 5. l′ = l · ratiol 6. Apply multiple node deletion on A giving (k′ , l′ ). 7. Apply node addition on A′ giving (k′ , l′ ). 8. Update W . 9. Run QP on A” giving (k′ , l′ ). 10. Round Fractional Relaxation and store A” . 11. end. Fig. 4. Combined Adjusted Dual Biclustering with Rounded QP algorithm

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7 Experimental Results In this section, we analyze results obtained from Dual Biclustering with adjusted MSR for missing data. We describe comparison criteria, define the swap rule model and analyze the p value of the biclusters. We tested our biclustering algorithms on data from [10] and compared our results with Cheng and Church [4]. For a fair comparison, we used bicluster sizes published by [4]. A systematic comparison and evaluation of biclustering methods for gene expression data is given in [17]. However, their model uses biologically relevant information, whereas our model is more generic and based on statistical approach. Therefore, we haven’t used their comparison results in this paper. 7.1 Evaluation of the Adjusted MSR To measure robustness of the proposed MSR to noise and evaluate quality of the obtained biclusters, the experiments were run on the imputed data. Let A be a (I, J) bicluster with zero H-value and variation of real data σ 2 . Corresponding imputed bicluster Ap is defined as follows in the following equation. apij = aij + εij where p is a percentage of added noise, {εij }i∈I,j∈J ∼ N (0,

(9) p 2 100 σ ).

7.2 The Goal of Our Experiments The goal of our experiments is to find percentage of noise data such that algorithm is still able to distinguish bicluster of size k from non-biclusters in the imputed data. Although, one can determine such percentage in respect to submatrices of the bicluster, the probability of having distinguishable submatrix when bicluster can not be already distinguished from non-bicluster tends which becomes zero due to uniformly distributed imputation of error. 7.3 Experimental Results Figure 5 compares Cheng and Church, dual biclustering, dual biclustering coupled with QP, adjusted dual biclustering, adjusted dual biclustering coupled with QP and adjusted dual biclustering with row inversion. Average MSR for adjusted dual and QP represents 68 percent (average) and 48 percent (median) of the data published in [4]. These results show that ignoring missing data for the dual algorithm gives much smaller MSR. The effect of noise on the MSR computation using synthesized data can be seen in Figure 6. Figure 7 shows the noise effect on adjusted MSR computation vs. random filled missing data. It is easy to see that adjusted MSR is less affected by noise than random filled missing data. Figure 8 shows how noise affects adjusted MSR random filled missing data for different levels of noise.

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Algorithms Cheng and Church*

Cheng and Church**

Dual

Dual and QP

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OC parameter

n/a

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Covering

39945

39945

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204.29

228.56

205.77

171.5

161.23

154.66

195.9

(%)

100

112

100.72

75.02

70.54

68

95

Median MSR

196.3095

204.96

123.27

104.47

104.66

95.46

77.96

(%)

100

105

62.79

47.91

51.1

47

39.71

Fig. 5. Comparison of biclustering methods

Noise vs. MSR 1000000 900000 800000 700000 0% Missing Data

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600000

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300000 200000 100000 0 0%

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Fig. 6. MSR computation for synthesized data

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Fig. 7. Adjusted MSR vs. random filled missing data

We measure the statistical significance of biclusters obtained by our algorithms using p value. P value is computed by running Dual Problem algorithm on 100 random generated input data sets. The random data is obtained from matrix A by randomly

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Missing Data vs. Random Missing Data

0% Missing Data 10% Missing Data

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Fig. 8. MSR random filled missing data for different levels of noise

selecting two cells in the matrix (aij , dkl ) and taking their diagonal elements (bkj , cil ). If aij > bkj and cil < dkl , algorithm swaps aij with cil and bkj with dkl , it is called a hit. If not, two elements aij and dkl are randomly chosen again. The matrix is considered randomized if there are nm 2 hits. In our case, p value is smaller than 0.001, which indicates that the results are not random and are statistically significant.

8 Conclusions Random numbers can interfere with the discovery of future biclusters, especially those ones that have overlap with the discovered ones. In this paper, we introduce a new approach to handle the missing data which does not take in account entries with missing data. We have characterized ideal biclusters, i.e., biclusters with zero mean square residue and shown that this approach is significantly more stable with respect to increasing noise. Several biclustering methods have been modified accordingly. Our experimental results show a significant decrease of H value of the biclusters when comparing with counterparts with noise reduction (e.g., the original Cheng and Church [4] method). Average MSR for adjusted dual and QP represents 68 percent (average) and 48 percent (median) of the data published in [4]. These results showed that ignoring missing data for the dual algorithm gives much smaller MSR. We also define MSR based on the best row inversion status. We give an efficient heuristic for finding such assignment. This new definition allow to further reduced MSR for a found set of biclusters.

References 1. Angiulli, F., Pizzuti, C.: Gene Expression Biclustering using Random Walk Strategies. In: Tjoa, A.M., Trujillo, J. (eds.) DaWaK 2005. LNCS, vol. 3589, pp. 509–519. Springer, Heidelberg (2005) 2. Baldi, P., Hatfield, G.W.: DNA Microarrays and Gene Expression. In: From Experiments to Data Analysis and Modelling. Cambridge Univ. Press, Cambridge (2002)

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3. Bertsimas, D., Tsitsiklis, J.: Introduction to Linear Optimization. Athena Scientific 4. Cheng, Y., Church, G.: Biclustering of Expression Data. In: Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology (ISMB), pp. 93–103. AAAI Press, Menlo Park (2000) 5. Madeira, S.C., Oliveira, A.L.: Biclustering Algorithms for Biological Data Analysis: A Survey. IEEE Transactions on Computational Biology and Bioinformatics 1(1), 24–45 (2004) 6. Papadimitriou, C.H., Steiglitz, K.: Combinatorial optimization: algorithms and complexity, p. 2982. Prentice-Hall, Inc., Upper Saddle River 7. Prelic, A., Bleuler, S., Zimmermann, P., Wille, A., Bhlmann, P., Gruissem, W., Hennig, L., Thiele, L., Zitzle, E.: A systematic comparison and evaluation of biclustering methods for gene expression data. Bioinformatics 22(9), 1122–1129 (2006) 8. Shamir, R., Lecture notes, http://www.cs.tau.ac.il/ rshamir/ge/05/scribes/ lec04.pdf 9. Tanay, A., Sharan, R., Shamir, R.: Discovering Statistically Significant Biclusters in Gene Expression Data. Bioinformatics 18, 136–144 (2002) 10. Tavazoie, S., Hughes, J.D., Campbell, M.J., Cho, R.J., Church, G.M.: Systematic determination of genetic network architecture. Nature Genetics 22, 281–285 (1999) 11. Yang, J., Wang, H., Wang, W., Yu, P.: Enhanced biclustering on gene expression data. In: Proceedings of the 3rd IEEE Conference on Bioinformatics and Bioengineering (BIBE), pp. 321–327 (2003) 12. Zhang, Y., Zha, H., Chu, C.H.: A time-series biclustering algorithm for revealing coregulated genes. In: Proc. Int. Symp. Information and Technology: Coding and Computing (ITCC 2005), Las Vegas, USA, pp. 32–37 (2005) 13. Zhou, J., Khokhar, A.A.: ParRescue: Scalable Parallel Algorithm and Implementation for Biclustering over Large Distributed Datasets. In: 26th IEEE International Conference on Distributed Computing Systems, ICDCS 2006 (2006) 14. Gremalschi, S., Altun, G.: Mean Squared Residue Based Biclustering Algorithms. In: M˘andoiu, I., Sunderraman, R., Zelikovsky, A. (eds.) ISBRA 2008. LNCS (LNBI), vol. 4983, pp. 232–243. Springer, Heidelberg (2008) 15. Divina, F., Aguilar, J.: Ruiz Biclustering of Expression Data with Evolutionary Computation. IEEE Transactions on Knowledge and Data Engineering 18(5), 590–602 (2006) 16. Yang, J., Wang, W., Wang, H., Yu, P.S.: Enhanced biclustering on expression data. In: Proceedings of the 3rd IEEE Conference on Bioinformatics and Bioengineering (BIBE 2003), pp. 321–327 (2003) 17. Prelic, A., Bleuler, S., Zimmermann, P., Wille, A., Bhlmann, P., Gruissem, W., Hennig, L., Thiele, L., Zitzler, E.: A Systematic Comparison and Evaluation of Biclustering Methods for Gene Expression Data. Bioinformatics 22(9), 1122–1129 (2006) 18. Xiao, J., Wang, L., Liu, X., Jiang, T.: An Efficient Voting Algorithm for Finding Additive Biclusters with Random Background. Journal of Computational Biology 15(10), 1275–1293 (2008) 19. Liu, X., Wang, L.: Computing the maximum similarity bi-clusters of gene expression data. Bioinformatics 23(1), 50–56 (2007)

Using Gene Expression Modeling to Determine Biological Relevance of Putative Regulatory Networks Peter Larsen1 and Yang Dai2 1

Core Genomics Laboratory (MC063), University of Illinois at Chicago, 835 South Wolcott Avenue, Chicago, IL 60612, USA [email protected] 2 Department of Bioengineering (MC063), University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607, USA [email protected]

Abstract. Identifying gene regulatory networks from high-throughput gene expression data is one of the most important goals of bioinformatics, but it remains difficult to define what makes a ‘good’ network. Here we introduce Expression Modeling Networks (EMN), in which we propose that a ‘good’ regulatory network must be a functioning tool that predicts biological behavior. Interaction strengths between a regulator and target gene are calculated by fitting observed expression data to the EMN. ‘Better’ EMNs should have superior ability to model previously observed expression data. In this study, we generate regulatory networks by three methods using Bayesian network approach from an oxidative stress gene expression time course experiments. We show that better networks, identified by percentage of interactions between genes sharing at least one GO-Slim Biological Process terms, do indeed generate more predictive EMN’s. Keywords: Gene expression, linear model, least-squares, expression modeling network, regulatory network.

1 Introduction Gene Regulatory networks represent genetic control mechanisms as directed graphs, in which genes are the nodes and the connecting edges signify regulatory interactions [1]. Determination of gene regulatory networks from high-throughput gene expression data is an important goal of bioinformatics analysis. There are many proposed computational methods for inferring potential gene regulatory networks from microarray data, such as relevance networks [2], clustering coefficient threshold method [3], nearest neighbor networks [4], and ARACNE [5, 6], Asymmetric-N [7], and Bayesian network (BN) [8]. Except the BN approach, most of the methods use correlation or information theoretical measurement (e.g. entropy) between gene expression profiles to determine whether two genes are related to each other. The predicted networks are essentially determined by binary interactions. There remains no universally accepted standard for identifying a ‘good’ network or to determine the ‘best’ network from a I. Măndoiu, G. Narasimhan, and Y. Zhang (Eds.): ISBRA 2009, LNBI 5542, pp. 40–51, 2009. © Springer-Verlag Berlin Heidelberg 2009

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collection of potential networks. Some methods that have been used are to assign a predicted interaction confidence determined by (1) previously observed interactions, (2) functional association derived from other ‘omic’ data such as protein-protein interactions, or (3) evolution conservation observed in other organisms. Here we propose that the best predicted gene regulatory network is the one that can be used to most accurately predict experimentally observed expression data. By considering gene expression as a linear function of the expression of its regulators, a proposed gene regulatory network can be modeled as a set of algebraic equations with constant terms for the relative strength of a regulator’s expression effect on the expression of its target. Using a set of experimentally observed data, these equations can be solved using the least-squares method. With these results, the gene regulation network becomes a predictive tool, capable of estimating the gene expression for all genes in the network from a value for the top-most node. For the equations in the EMN to be solvable, it is required that the predicted gene regulatory networks are in the form of a Directed Acyclic Graph (DAG). How well the EMN-calculated gene expression levels coincide with the experimentally observed gene expression levels can be used as a measure of the biological relevance of the proposed gene regulatory network. For validation of the proposed framework of the EMN, we have selected a subset of time course microarray data investigating yeast’s gene expression response to oxidative stress. To generate the appropriate DAG for regulatory networks, we have selected the BN to infer putative interaction networks from the time course data. As it has been previously reported that addition of biological knowledge to BN methods can improve quality of networks [9-12], we generated three BNs: BN-Unrestricted imposes no restriction of possible edges, BN-Published restricts possible edges to those interactions previously reported in the published literature, and BN-LOI, which restricts edges to those interactions calculated to be biologically likely by their similarity to known interactions. Additionally, 10 random networks were generated to serve as a baseline control. To determine whether better networks generate more predictive EMNs, a metric to rank the inferred networks is required. For this study, we selected percent of interactions in the networks that share a common biological process annotation for this metric. To measure how well EMN-calculated expression values match experimentally observed values, we have selected two metrics. The first is a Pearson Correlation Coefficient (PCC) and the second is the percent of genes that are differentially expressed in the same direction, positive or negative, in the EMNcalculated values and experimental data.

2 Methods This section introduces the concept of Expression Modeling Network (EMN), a method for using a directed acyclic graph representing a gene regulatory interaction set and estimating values representing the strength of the effect of change in expression of a regulator gene on the expression of a target gene. A previously collected time course microarray experiment studying the gene expression response of yeast to oxidative stress was used to demonstrate EMN here. Putative gene regulatory networks were inferred from data using the BN approach under three conditions: no restrictions on possible interactions, restricting interactions to those previously

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published and restricting interactions to those with high Likelihood of Interactions (LOI) scores. Additionally, 10 interaction networks were generated at random. ‘Best’ interaction network was identified as a function of percent of interactions in which regulator and target share a Gene Ontology Biological Process annotation. 2.1 Microarray Data The data used is a subset of microarray gene expression profiles that were from an experiment in yeast response to various environmental stresses by Gash et al. [15]. The subset is taken from those measured genes that indicated at least a two-fold change in expression in at least one time point when cultured under conditions of oxidative stress with 0.32mM hydrogen peroxide (H2O2) and missing expression values for no more than 25% of observations. The dataset consists of 189 genes at 11 time points. Gene expression patterns are characterized by a rapid change in expression levels of most genes, returning to initial expression levels over time. 2.2 Expression Modeling Networks EMN is an extension of Toxicological Prediction Networks (TPN) [13], which associates small, heterogeneous networks of toxic ligands and proteins with broad biological process descriptions. For EMN, a DAG representing an expression regulatory network for which nodes are genes with measured relative expressions or quantified environmental cues, and directed edges between nodes indicating that the expression of the parent node has a regulating effect on the expression of the child node. Also, a set of observed expression data and quantified environmental stimulus for multiple observations is needed. The regulatory network is represented as a set of equations in which the expression of every gene is a linear function of the expression of its regulators.

∑

Ei (t ) =

E j (t ) * v j ,i + c j ,i

(1)

j regulates i

where Ei(t) is the measure of expression of gene i at time point t, and vj,i and cj,i are constants describing the strength of the regulatory influence of the expression of gene j on gene i. The optimal EMN is determined by minimizing the sum of squared differences between the modeled and observed gene expression, i.e., minimizing

∑∑ ( E (t ) − E T

n

i

obs i

(t )) 2

(2)

t =1 i =1

where,

Eiobs (t ) is the observed gene expression of gene i at time point t, and T is the

overall number of time points in the experiment. Using the set of experimental observations of expression of all genes at different time points, the optimization problem can be solved for all constants vj,i and cj,i by using the least-squares method. The ‘v’ terms model for the strength of the effect of a change in expression in a regulator on its target. The ‘c’ terms model the influence that a regulator has on the expression of its target to maintain equilibrium at a control state. This procedure for EMN is summarized in Figure 1.

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For this study, expression data was considered as a log ratio relative to a control. ‘Expression’ values for H2O2 was set to an arbitrary 160, the total number of minutes in the time course experiment, at time 1, and then reduced by half for every subsequent time point as this was empirically observed to best model the similar drop in number of significantly expressed genes over time. The least squares fitting procedure as implemented by ‘lsfit’ function in statistical computing language R (ver.2.8.1) [14] was used to solve the optimal problem. (A)

Gene Regulatory Network as DAG Node 0

v, c 0,2

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t1 -0.41 -0.61 0.25 -0.87 0.06 -0.01

t2 -0.67 0.31 0.72 0.39 0.70 0.13

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Gene Regulation Network at set of Equations E1 t = v0,1 * E0 t + c 0 ,1 E2 t = v0,2 * E0 t + c 0 ,1 E3 t = v0,3 * E0 t + c 0,3 + v2 ,3 * E2 t + c 2 ,3 E4 t = v1,4 * E1 t + c 1 ,4 E5 t = v1,5 * E1 t + c 1,5 + v3,2 * E3 t + c 3,2

Fig. 1. Using a small example regulatory network, the process for EMN is summarized. (A) Given a putative interaction network in which every directed interaction between a regulator j and target i is characterized by two constants vj,i, and cj,i and (B) set of gene expression observations over multiple time points, the network can be described as a set of equations (C) in which the expression of a target gene is a linear function of the expression of the expression of its regulators, where En(t) is the expression of node n at time t, vj,i and cj,i are the constants describing the interaction strength between regulator i and target j. Using the values in (B), the equations in (C) can be solved for the all values vj,i and cj,i.

2.3 Previously Published Interactions In order to obtain interactions involving the genes in the subset mentioned above from literature, we used ‘PathwayStudio’ (Ariadne Genomics, Inc., Rockville, MD) to automatically extract from PubMed references. Given an input set of query genes or

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gene products, PathwayStudio searches the database of published abstracts, seeking instances in which genes are identified as interacting according to the information found in available PubMed abstracts. The nature of interactions (‘expression’, ‘regulation’, ‘genetic interaction’, ‘binding’, ‘protein modification’, and ‘chemical modification’ as defined in that software package) can be used to screen for specific types of interactions. Interaction types ‘direct regulation’, ‘regulation’ and ‘expression’ were used for this study. 2.4 Likelihood of Interaction (LOI) This study utilizes the concept of Likelihood of Interaction (LOI) scores for gene interaction pairs developed in our previous study [16] for assigning confidence for interaction for a pair of genes. The LOI-score is a measure of the likelihood that a gene or a gene product with a particular molecular function annotation influences the expression of another gene or a gene product. More specifically, if two genes closely resemble by their specific molecular function annotation from previously observed interaction pairs, then they will be considered likely to interact. The specific details of deriving the LOIscore can be found in [16]. But in general, a negative LOI-score indicates that a particular GO Molecular Function (MF) annotation pair occurs less frequently than expected by random chance. A positive LOI-score indicates an interaction between GO MF annotations occurs more frequently than expected at random. A score near zero indicates that the frequency occurs at a level near that expected by random. For the derivation of LOI-scores in this study, a set of 6150 yeast genes was selected from the Saccharomyces cerevisiae database of PathwayStudio 3.0 and used to identify 576 directed gene interaction pairs. The 25 GO MF annotations specified by the Saccharomyces Genome Database SGD GO Slim Mapper [17] were considered for the annotation of the regulator and the target genes. 2.5 Bayesian Network (BN) BN is a probabilistic framework for robust inference of interactions in the presence of noise. For using BNs in gene regulatory networks, nodes are genes or gene products. Directed edge is a regulatory interaction between nodes in which a change in expression in the regulator leads to a change in expression of the target. This edge does not necessarily imply the physical nature of the regulatory interaction and it can be assumed that regulation may occur through the physical interaction of proteins not in the set of differentially expressed genes. The input data set are measures of gene expression under multiple observations and output is a DAG. For determining networks for analysis in this study, BANJO (Bayesian Network Inference with Java Objects) was employed [18] using the following conditions. Nodes in the network represent genes with measured expressions, plus one node representing the presence of H2O2. Data were discretized into five values for more than two standard deviations below, one standard deviation below, within one standard deviation, more than one standard deviation above, and more than two standard deviations above the average expression value of all genes in the microarray study. Simulated annealing, BDe Scoring Metric [19], and Random Local Moves were selected as parameters in BANJO. A maximum of 5 parents was considered as this was in the range of observed number of parents in this set of published interactions (average number of parents is 3, with standard deviation of 3). For this study, three separate networks were generated.

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In ‘Unrestricted’, no restriction was placed on possible interactions, except that no gene was allowed to regulate node for H2O2. The H2O2 node indicates the presence of H2O2 in the media and no gene’s expression can regulate the state of environmental H2O2. In ‘Published’, possible interactions were restricted to those identified and previously observed using the tool ‘Pathway Studio’. ‘LOI’ restricted possible interaction to those that had an LOI-score in the top 25% off all LOI-scores calculated between all possible gene interaction pairs. Additionally, 10 random DAG networks were generated to serve as a baseline. All random networks have 729 interactions. 2.6 Ranking Putative Gene Regulatory Networks from Best to Worst To determine biological relevance of the identified gene networks, GO annotation descriptions [20] were used. There are three ontologies: molecular function, biological process, and cellular component. Molecular function (MF) annotation describes what gene product does at the molecular level, without specifying where or when the activity takes place in the broader context. Biological process refers to a biological objective to which a gene product contributes, though GO biological process (BP) annotations are not the equivalent of a biological pathway. Cellular component (CC) annotation refers to the place in the cell where a gene product is found. GO annotations, at their finest level do not describe specific gene products and a given gene product may have multiple GO annotations from each ontology. The specific GO ontologies considered in this study are GO-Slim BP annotations as provided by the Saccharomyces Genome Database (SGD) [17], a curator selected set of characteristic, most biologically relevant terms. For this study, the percent of proposed interactions in a regulatory network where the regulator and the target share at least on GO-Slim BP annotation is considered to be a measure of quality for the network. The higher the percentage in interaction that share an annotation, the better the proposed network is considered. 2.7 Evaluating the Fit of EMN-generated Expression Values to Experimental Observations Since the networks obtained from the BN method by using different levels of prior knowledge are of different sizes, the corresponding least squares are not comparable. Two metrics are considered to determine how well EMN-generated expression data fits with the experimentally observed data. The first is a Pearson Correlation Coefficient (PCC) between EMN and experimentally observed data. A PCC close to one is a good fit between calculated and observed data. A PCC near zero indicates no similarity between calculated and observed data. Values close to negative one indicate an inverse correlation. The second metric used here is the percent of genes in which the direction of expression change, positive or negative, is in agreement between the EMN-calculated and the observed data. A high percentage indicates that the EMN-calculated data frequently agrees with observed data as to the direction of gene expression change. 2.8 Assigning Significance to Results The significance of a calculated network was determined using the cumulative binomial distribution, where the probability that x successes out of n trials with a probability of success p.

46

P. Larsen and Y. Dai x ⎛n⎞ B( x; n, p ) = ∑ ⎜ ⎟ p i (1 − p ) n −i . i =0 ⎝ i ⎠

(3)

A p-value for each network is reported as 1-B(x,n,p). This was used to determine the significance of percent of interactions sharing GO-Slim BP terms used as a metric of network quality, and the percent of EMNcalculated gene expressions that are same direction of expression change as experimentally observed data. For the significance of a particular percent of shared GO-Slim BP annotations between calculated interactions in a given network, n is equal to the total number of interactions in the predicted network, x is the number of interactions that share a GO-Slim BP term, and p is equal to the frequency of interactions in the complete graph of 198 genes that share a GO-Slim BP annotation. For percent of calculated gene expression in same direction as observed, n is equal to the number of genes, x is equal to the number of genes in calculated expression that are changes in the same direction as observed, and p is equal to:

(

) (

)

Pos Pos Pos Pos f Obs ∗ f Calc + 1 − f Obs * 1 − f Calc ,

where

(4)

Pos f Obs is equal to the frequency of positive expression changes in the experi-

mentally observed data and

Pos f Calc is the frequency of positive expression changes in

the EMN-calculated expression data.

3 Results Here, the generated putative oxidative stress regulatory networks are compared to one another, insuring that networks are distinct from one another and that the networks can be ranked from ‘best’ to ‘worst’ with regard to percent of interactions that share a GO-Slim BP annotation. EMN was used as described in Methods section to estimate the interaction strengths between all regulator and target pairs in each network. Those interaction strengths were then used to attempt to model gene expression in the network in response to oxidative stress. 3.1 Evaluation of Generated Networks First, the generated putative regulatory networks: BN-Unrestricted, BN-Published, BN-LOI, and the 10 randomly generated networks, have to be compared to one another. As it is the goal of this study to determine that a regulatory network that can better model gene expression using EMN, it needs to be determined that the generated networks are sufficiently distinct from one another and that the networks can be ranked from ‘best’ to ‘worst’. To determine if the networks are distinct, the percent of interactions shared between the networks were considered (Table 1). In general, the overlap between networks is about 15% for the various BN-generated networks. BN-LOI and BN-Published have the most similarity with 16% overlap. BN-Unrestricted and BN-LOI have the least overlap with 13%. The 10 randomly generated networks have about a 3% overlap with each of the BN-generated networks and with one another. The number of interactions

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Table 1. The percent of interactions in common between multiple potential gene regulation networks among 198 genes is summarized here. For the ’10 Random’ networks, results are presented as average (standard deviation) for all ten randomly generated networks.

BNUnrestricted BN-Published BN-LOI 10 Random

BNUnrestricted

BNPublished

BNLOI

10 Random

-14% 13% 3% (0.007)

--16% 3% (0.007)

---3% (0.003)

---3% (0.006)

for each BN-generated interaction network is also distinct. BN-Unrestricted has 729, BN-Published has 739, and BN-LOI has 731 interactions. From this it can be judged that the different restrictions of BN estimation did in fact yield distinctly different networks that share only a minority of proposed regulator-target interactions. In order to estimate the relative quality of interaction network, percent of interactions whose regulator and target share at least one GO-Slim BP annotation was chosen as a metric. A significance of this measure was assigned using a Binomial distribution derived p-value, calculating the probability that a network of a given size would have the same of greater number of interactions that share a GO-Slim BP annotation by chance (Table 2.) BN-Unrestricted have the greatest percent of shared terms at 32% with a highly significant p-value of 3.93E-09. BN-Published is next with 30% at a significance of 2.49E-06. BN-LOI is the worst, with a 27% and relatively poor pvalue of 0.317. The random networks averaged 22% shared GO-Slim BP annotations with a p-value indicating results no better than random chance, 0.671. From this we can determine that we can rank BN-derived networks with BN-Unrestricted as best and BN-LOI as worst. All BN-generated interaction networks perform substantially better than the 10 randomly generated networks. Table 2. The relative quality of several proposed gene interaction networks is defined here as the proportion of identified interactions in which the regulator and target gene share a GO-Slim BP annotation. For the ’10 Random’ networks, results are presented as average (standard deviation) for all ten randomly generated networks. ‘#Edges’ is the total number of interactions between the 189 genes identified as involved in response to H2O2. ‘%Shared GO-BP’ is the fraction of the interactions that share a GO-Slim BP term between regulator and target. ‘Binom.pVal’ is the binonimal distribution derived significance of the ‘%Shared GO-BP’ in the identified interaction network relative to the percent shared GO-BP annotations in the complete graph of all 189 genes.

BN-Unrestricted BN-Published BN-LOI 10 Random

# Edges 729

% Shared GO-BP 32%

Binom.pVal 3.93E-09

739 731 729

30% 27% 22% (0.017)

2.49E-06 3.17E-03 6.71E-01

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3.2 Using EMN to Model Gene Expression in Response to Oxidative Stress Using the procedure described for EMN, the values for all vj,i and cj,i interaction strengths between all pairs of regulator j and target gene i were determined for the three BN-derived networks and 10 randomly generated networks. Using these values, gene expressions for all genes were estimated using EMN for the first three time points in the time course. The first three time points, at which most genes are differentially expressed, were selected to validate EMN. At later time points, where differential gene expression tapers off the correlation of EMN to data is inflated, unfairly suggesting a very good fit of the model to the data. Table 3. ‘A’ is the BN-Unrestricted network, ‘B’ is the BN-Published network, ‘C’ is the BNLOI network, and ‘D’ is the average (standard deviation) from 10 randomly generated networks. Data for the first three time points from the experimental data and the average of the results are presented here. ‘Correl with Obs.’ is the correlation of EMN-generated expression data with observed expression data. ‘%Same Dir. As Obs.’ is the percentage of genes whose direction of expression change, positive or negative, is the same as the direction of expression change in the experimental data. ‘Binom.pVal’ is the binomial distribution derived significance of the ‘%Same Dir as Obs.’ relative to the distribution of positive and negative fold changes in the EMN-derived and experimentally observed data.

Network

Time 1

Time 2

Time 3

Average

Correl with Obs. %Same Dir as Obs. Binom.pVal Correl with Obs. %Same Dir as Obs. Binom.pVal Correl with Obs. %Same Dir as Obs. Binom.pVal Correl with Obs. %Same Dir as Obs. Binom.pVal

A 0.290 70% 1.05E-08 0.381 68% 1.42E-07 0.414 68% 2.50E-07 0.362 69% 1.34E-07

B 0.429 71% 1.63E-09 0.360 65% 1.30E-05 0.249 65% 5.17E-05 0.346 67% 2.16E-05

C 0.023 54% 1.21E-01 -0.032 51% 3.30E-01 0.029 58% 1.29E-02 0.006 54% 1.55E-01

D -0.002 (0.083) 51% (0.036) 5.00E-01 -0.021 (0.090) 49% (0.029) 5.00E-01 -0.041 (0.093) 49% (0.035) 4.47E-01 -0.021 50% 4.82E-01

Results of fitting EMN-generated expression values and observed expression values are summarized in Table 3. Using EMN-calculated expression values, on average across the first three time points in the time course experiment, data for BNUnrestricted was the best PCC with experimental data at 0.362 and the highest percent agreement in direction of expression change of 69% and a significance of 1.34E-07. BN-Published performed next best on average with a PCC of 0.346 and a 67% agreement in direction of expression change at a significance level of 2.16E-05. BN-LOI preformed the worst on average of all the BN-generated interaction networks with a PCC of 0.006 and a weakly significant percent same direction of 54% and

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p-value 0.155. The 10 randomly generated networks average a PCC of -0.021 indicating no correlation with observed data and a percent same direction of 50% and significance of 0.482 indicating a result attributable to random chance. The best result at an individual time point was for the BN-Published network at the first time point with a PCC of 0.429 and highly significant 71% agreement with expression change direction and a p-Value of 1.63E-09.

4 Conclusions Here we have proposed Expression Modeling Networks (EMN), a method that (1) uses an interaction network and observed microarray gene expression data to estimate the strength of an interaction between a regulator and a target and (2) uses those estimated interaction strength to model gene expression. Using a microarray dataset studying the gene expression of yeast in response to oxidative stress, we have demonstrated that EMNs can be used to calculate gene expression in response to environmental stimulus. Better, more biologically relevant networks, as judged using a metric of percent of interactions in the network in which the regulator and the target share at least one GO-Slim Biological Process annotation, generate EMNs that more accurately model gene expression data. This positive correlation between rank of the networks and the quality of the EMNs indicates that it is the biological relevance of the proposed networks that is responsible for the fit of EMN-calculated expression values with experimentally observed data. Given this result, EMNs could be used to evaluate among multiple proposed gene interaction networks to identify those proposed networks that best model experimentally observed data, and therefore have a greater likelihood of being biologically relevant. This ability to quantifiably measure how well a proposed gene regulatory interaction network fits experimentally observed, expression data represents a potentially significant advancement, taking regulatory networks derived from high throughput data from simple hypothesis to being predictive, analytical tools. In the complimentary approach, TPN [13] was able to model the effects of several toxic ligands on rats from gene expression in liver, suggesting that linear modeling of complex system in EMN can be extended to more complex systems than yeast. It should also be noted that the framework proposed here is generally applicable to more complex models, such as S-system, for nonlinear representation of expression. Additional work remains to be done with EMN. Only a single environmental condition, response to oxidative stress, was considered here. Ultimately, to determine whether EMN not only mimics the observed experimental data but also predicts relevant biology, one must perform a biological experiment to confirm the model. Fortunately, EMN is well suited to such hypothesis driven experimentation. The effects of the deletion or amplification of a gene node expression or modifying the strength of an interaction edge on the expression of other genes in the proposed network can be simulated in EMN. Then biological experimentation can confirm or reject the model based prediction. A more complex EMN might incorporate several possible conditions and model the yeast’s more complete environmental stress response regulatory network, able to model not only single stressed but specific combination of stresses. A well designed EMN might have the ability to predict gene expression, not just model

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previously observed conditions. With a predictive EMN tool, certain gene expression studies could be performed in silico before advancing to actual biological experiments, refining biological hypotheses, allowing researchers to better design proposed experiments, and perhaps reduce the number of biological experiments that need to be performed. Acknowledgements. We thank Eyad Almasri for useful discussion.

References 1. Weaver, D., Workman, C., Stormo, G.: Modeling regulatory networks with weight matrices. In: Pacific Symp. Biocomp., vol. 99(4), pp. 112–123 (1999) 2. Butte, A.J., Tamayo, P., Slonim, D., Golub, T.R., Kohane, I.S.: Discovering functional relationships between RNA expression and chemotherapeutic susceptibility using relevance networks. Proceedings of the National Academy of Sciences of the United States of America 97(22), 12182–12186 (2000) 3. Elo, L.L., Jarvenpaa, H., Oresic, M., Lahesmaa, R., Aittokallio, T.: Systematic construction of gene coexpression networks with applications to human T helper cell differentiation process. Bioinformatics 23(16), 2096–2103 (2007) 4. Huttenhower, C., Flamholz, A., Landis, J., Sahi, S., Myers, C., Olszewski, K., Hibbs, M., Siemers, N., Troyanskaya, O., Coller, H.: Nearest Neighbor Networks: clustering expression data based on gene neighborhoods. BMC Bioinformatics 8(1), 250 (2007) 5. Margolin, A., Nemenman, I., Basso, K., Wiggins, C., Stolovitzky, G., Favera, R., Califano, A.: ARACNE: An Algorithm for the Reconstruction of Gene Regulatory Networks in a Mammalian Cellular Context. BMC Bioinformatics 7(suppl. 1), S7 (2006) 6. Basso, K., Margolin, A.A., Stolovitzky, G., Klein, U., Dalla-Favera, R., Califano, A.: Reverse engineering of regulatory networks in human B cells. Nat. Genet. 37(4), 382 (2005) 7. Chen, G., Larsen, P., Almasri, E., Dai, Y.: Rank-based edge reconstruction for scale-free genetic regulatory networks. BMC Bioinformatics 9(1), 75 (2008) 8. Friedman, N., Linial, M., Nachman, I., Pe’er, D.: Using Bayesian networks to analyze expression data. J. Comput. Biol. 7, 601 (2000) 9. Almasri, E., Larsen, P., Chen, G., Dai, Y.: Incorporating literature knowledge in Bayesian network for inferring gene networks with gene expression data. In: Măndoiu, I., Sunderraman, R., Zelikovsky, A. (eds.) ISBRA 2008. LNCS (LNBI), vol. 4983, pp. 184–195. Springer, Heidelberg (2008) 10. Hartemink, A.J., Gifford, D.K., Jaakkola, T.S., Young, R.A.: Combining location and expression data for principled discovery of genetic regulatory network models. In: Pac. Symp. Biocomput., pp. 437–449 (2002) 11. Imoto, S., Higuchi, T., Goto, T., Tashiro, K., Kuhara, S., Miyano, S.: Combining Microarrays and Biological Knowledge for Estimating Gene Networks via Bayesian Networks. In: Proceedings of the IEEE Computer Society Conference on Bioinformatics. IEEE Computer Society, Los Alamitos (2003) 12. Le Phillip, P., Bahl, A., Unga, L.H.: Using prior knowledge to improve genetic network reconstruction from microarray data. Silico Biology 4, 335–353 (2004) 13. Kulkarnia, K., Larsen, P., Linninger, A.A.: Assessing chronic liver toxicity based on relative gene expression data. Journal of Theoretical Biology 254(2), 308–318 (2008) 14. R Development Core Team: R: A Language and Environment for Statistical Computing, http://www.R-project.org

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15. Gasch, A.P., Spellman, P.T., Kao, C.M., Carmel-Harel, O., Eisen, M.B., Storz, G., Botstein, D., Brown, P.O.: Genomic expression programs in the response of yeast cells to environmental changes. Mol. Biol. Cell. 11, 4241–4257 (2000) 16. Larsen, P., Almasri, E., Chen, G., Dai, Y.: A statistical method to incorporate biological knowledge for generating testable novel gene regulatory interactions from microarray experiments. BMC Bioinformatics 8, 317 (2007) 17. GO Slim Mapper, http://db.yeastgenome.org/cgi-in/GO/goTermMapper 18. BANJO, http://www.cs.duke.edu/~amink/software/banjo/ 19. Herskovits, E., Cooper, G.: Algorithms for Bayesian belief-network precomputation. Methods Inf. Med. 30(2), 81–89 (1991) 20. Ashburner, M., Ball, C.A., Blake, J.A., Botstein, D., Butler, H., Cherry, J.M., Davis, A.P., Dolinski, K., Dwight, S.S., Eppig, J.T., et al.: Gene ontology: tool for the unification of biology. The Gene Ontology Consortium. Nat. Genet. 25, 25–29 (2000)

Querying Protein-Protein Interaction Networks G u i l l au m eBl i n ,F l o ri a nS i k o ra,a n dS t ´e p h an eV i al e t t e U n i v e r s i t ´e P a r i s - E s t , L I G M - U M R C N R S 8049, France {gblin,sikora,vialette}@univ-mlv.fr

Abstract. Recent techniques increase the amount of our knowledge of interactions between proteins. To filter, interpret and organize this data, many authors have provided tools for querying patterns in the shape of paths or trees in Protein-Protein Interaction networks. In this paper, we propose an exact algorithm for querying graphs pattern based on dynamic programming and color-coding. We provide an implementation which has been validated on real data.

1

Introduction

Con t raryt o wh a tw a sp red i ct edy earsa g o ,t h eh u m a ng en om ep ro j ecth a sh i gh l i gh t edt h a th u m a ncom p l exi t ym ayn o to n l yrel yo ni t sg en es(only 2 5 000 f or human compared to the 30 000 and 45 000 for the mouse and the poplar respectively). This observation has yield to an increase in the interest of proteins (e.g. their numbers, functions, complexity and interactions). Among others protein properties, the set of all their interactions for an organism, called Protein-Protein Interactions (PPI) networks, have recently attracted lot of interest. Knowledge on them increases in an exponential manner due to the use of various genome-scale screening techniques [10,12,23]. Unfortunately, acquiring such valuable resources is prone to high noise rate [10,19]. Comparative analysis of PPI tries to determine the extent to which protein networks are conserved among species. Indeed, numerous evidences suggest that proteins functioning together in a pathway (i.e., a path in the interaction graph) or a structural complex (i.e., an assembling of strongly connected proteins) are likely to evolve in a correlated fashion, and during evolution, all such functionally linked proteins tend to be either preserved or eliminated in a new species [17]. In this article, we focus on the following related problem called Graph Query (formaly defined later). Given a PPI network and a pattern in the shape of graph, query the pattern in the network consist of find a subnetwork of the PPI network which is most similar as possible to the pattern. Similarity is measured both in terms of sequence similarity and graph topology conservation. Unfortunately, this problem is clearly equivalent to the NP-complete subgraph homeomorphism problem [9]. Recently, several techniques have been proposed to overcome the diffi c ult y of this problem. By restricting the query to a path, Kelley et al. [16] were able to define a Fixed-Parameter Tractable (FPT) algorithm parameterized by the size of the query. Recall that a parameterized problem is FPT if it can be determined in f(k)nO (1) time where f is a function only I. M˘ andoiu, G. Narasimhan, and Y. Zhang (Eds.): ISBRA 2009, LNBI 5542, pp. 52–62, 2009. c Springer-Verlag Berlin Heidelberg 2009 

Querying Protein-Protein Interaction Networks

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depending on the parameter k, and n is the size of the input [8]. Pinter et al. [18] proposed an algorithm dealing with tree shape query that is restricted to forest PPI networks (i.e., collection of trees). Later on, Shlomi et al. [21] proposed an alternative, called QPath [16], for querying paths in a PPI network which is based on the color-coding technique introduced by Alon, Yuster and Zwick [1]. In addiction of being faster, QPath allows more flexibility by considering non-exact matches. Finally, Dost et al. [7] developed QNet, an algorithm to handle tree query in the general context of PPI networks. The authors also gave some theoretical approaches for querying graphs by using the tree decomposition of the query. Since QNet is the major reference in this field and is quite related to the work presented in this article, let us present it briefly. QNet is an exact FPT algorithm for querying trees in a PPI network. The complexity is 2O (k ) m , where k is the number of proteins in the query and m the number of edges of the PPI network. As QPath, QNet uses dynamic programming and color-coding. For querying graphs in a network, QNet uses, as a subroutine, an exact algorithm to query trees. To do so, they perform a tree decomposition. A formal definition of a tree decomposition can be found in [4]. Roughly speaking, it is a transformation of a graph into a tree. A tree node (or a bag) can contain several graph nodes. There are several ways to perform such a transformation. The treewidth of a graph is the minimum (among all decompositions) of the cardinality of the largest bag minus one. Computing this treewidth is NP-Hard [3]. From this tree decomposition, the time complexity of QNet is O(2O (k ) nt +1 ) time, where k is the size of the query, n is the size of the PPI network, and t is the treewidth of the query. QNet is an exact algorithm for querying trees in a PPI network. A logical extension would be to query graphs. The authors of [7] provides a theoretical solution, without implementation and which depends on the query treewidth. We propose in this article an exact alternative solution, using color-coding (Section 2). We provide in Section 3 some experimental results.

2

PADA1 as an Alternative to QNet

In this section, we propose an alternative to QNet called PADA1 (Protein Alignment Dealing with grAphs). At the broadest level, QNet and PADA1 use the very same approach: transform the query into a tree and find an occurrence of that tree in the PPI network by dynamic programming. However, whereas QNet uses tree decompositions, PADA1 combines feedback vertex sets together with nodes duplications (Algorithm Graph2Tree). It is worth mentioning that, following QPath and QNet, we will consider non-exact matches (i.e., allowing indels). Since we allow queries to be graphs, PADA1 is clearly an extension of QPath and an alternative to QNet. 2.1 Transformingthe Queryinto a Tree We begin by presenting Algorithm Graph2Tree to transform a graph G = (V, E) into a tree, without loss of information (i.e., one can reconstruct the graph

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G. Blin, F. Sikora, and S. Vialette

starting from the tree). Informally, the main idea of Algorithm Graph2Tree is to transform the graph into a tree by iteratively finding a cycle C, duplicating a node of C, and finally breaking cycle C by one edge deletion. Central is our approach is thus the node duplication procedure (Algorithm Duplicate), see Figure 1 for an illustration to break a cycle at vertex v1 . For each u ∈ V , write d(u) for the set of all copies of vertex u including itself.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Function Graph2Tree(G ) begin d(u ) ← u for all u of V ; for (i = 0 ; i < |V | ; i + +) do foreach subgraph G′ = (V ′ , E ′ ) of G such that |V ′ | = |V | − i do if G′ is acyclic then foreach node u of V \V ′ do foreach (u, v) ∈ E do tmp ← G; Duplicate(v, u, d); if G is not connected anymore then G ← tmp; end end end return G; end end end end

Algorithm 1. “Brute-force” transformation algorithm

1 2 3 4 5 6 7 8

Function Duplicate(G = (V, E), va , vb , d) begin Let i ← |d(vb )|; V ← V ∪ {vb i }; d(vb ) ← d(vb ) ∪ {vb i } ; E ← E − {(va , vb )}; E ← E ∪ {(va , vb i )}; end

Algorithm 2. Algorithm to duplicate a node when a cycle is detected Let F denote the set of all nodes of Gthat have been duplicated at the end of Algorithm Graph2Tree, i.e., F = {v∈ V : |d(v)| >1}. The cardinality of Fturns out to be an important parameter since, as we will prove soon, the overall time complexity of PADA1 mostly depends on |F| and not on the

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Fig. 1. Steps when Duplicate(G, v3 , v1 , d) is called on graph a). b) A node v1 1 from v1 is created. c) The edge (v3 ,v1 ) is deleted: the cycle is then broken. d) The edge (v3 ,v1 1 ) is added. Finally, the resulting graph is acyclic, and d(v1 ) = {v1 , v1 1 }.

overall number of duplications. Minimizing the cardinality of F is the well-known NP-complete Feedback Vertex Set problem [15]: Given a graph G, find a minimum cardinality subset of vertices with the property that removal of these vertices from the graph eliminates all cycles. We only have implemented an algorithm using a “brute-force” solution for the Feedback Vertex Set problem. Since there are 2|V | potential subgraphs, its complexity is O(2|V | × |E|), but it is still running in seconds. Indeed, the overall complexity of PADA1 considerably limits the size of our graph query. However, one may also consider an efficient FPT algorithm such as the one of Guo et al. [11], using iterative compression, or a cubic [5] or quadratic kernalization [22]. 2.2

Tree Matching

We now assume that the query has been transformed into a tree (with duplicated nodes) by Algorithm Graph2Tree, and hence we only consider tree queries from this point. We show that an occurrence of such a tree can be found in a PPI network by dynamic programming. Let us fix notations. PPI networks are represented by undirected weighted graphs GN = (VN , EN , w) ; each node of VN represents a protein and each weighted edge (vi , vj ) ∈ EN represents an interaction between two proteins. A query is given by a tree TQ = (VQ , EQ ) (output of Algorithm Graph2Tree on the graph query). The set VQ represents proteins while EQ represents interactions between these proteins. There is no weight for these later. Let h(p1 , p2 ) be a function that returns a similarity score between two proteins p1 and p2 . The similarity considered here will be computed according to amino-acid sequences similarity (using BLAST [2]). In the following, given two nodes v1 and v2 of VQ (or VN ), we write h(v1 , v2 ) for the similarity between the two proteins corresponding to v1 and v2 . A node v1 is considered to be homologous to a node v2 if the corresponding similarity score h(v1 , v2 ) is above a given threshold. Biologically, one can assume that two homologous proteins have probably common functions. Clearly, for every node v of F , all nodes in d(v) are homologous with the same protein. An alignment of the query TQ and GN is defined as: (i) a subgraph GA = (VA , EA , w) ⊆ GN = (VN , EN , w), such that VA ⊆ VN and EA ⊆ EN , and (ii) a

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G. Blin, F. Sikora, and S. Vialette

Fig. 2. a) The graph query with a cycle, before calling Graph2Tree algorithm. c) The query after calling Graph2Tree where q 1 has been duplicated. Thus, q 1 and q 1 1 have to be aligned with the same node of the network. b) and d) denote the resulting graph alignment GA , subgraph of the network GN . The horizontal dashed lines denote a match between two proteins.

mapping σ : VQ → VA ∪{del}. More precisely, the function σ is defined such that for all q of VQ , σ(q) = v if and only if q and v are homologous, and σ(q) = del otherwise. For a given alignment of TQ and GN , a node q of VQ is said to be deleted if σ(q) = del and matched otherwise. Moreover, any node va of VA such that σ −1 (va ) is undefined is said to be inserted. Note that, similarly to QNet, only nodes of degree two can be deleted. For practical applications, the number of insertions (resp. deletions) is limited to be at most Ni n s (resp. Nd e l ), each involving a penalty score δi (resp. δd ). The Graph Query problem can be thus defined as follow: Given a query TQ , a PPI network GN , a similarity function h, penalty scores δi and δd for each insertion and deletion, find an alignment (GA , σ) between TQ and GN of maximal score. The score of an alignment is defined as the sum of (i) similar ity scores of aligned nodes (i.e., v∈VA h(v, σ −1 (v))), (ii) the sum of all −1 (v) defined σ  edges involved in GA (i.e., e ∈E A w(e)), (iii) a penalty score δd for each node deletion (i.e., q∈VQ δd ), and (iv) a penalty score δi for each node insertion σ(q)=del  δi ). (i.e., v∈VA σ(v)−1 undefined

The general problem is NP-complete. However, it is Fixed Parameter Tractable in case the query is a tree by a combination of the color-coding technique [1] and dynamic programming. This randomized technique allows to find simple paths of length k in a network in O(2k ) time (instead of the brute-force O(nk ) time algorithm), where n is the number of proteins in the network [20]. In [7], the authors

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of QNet adapted this technique for their query algorithm. Since one is looking for an alignment, each node of the query has to be considered once (and only once) in an incremental build of the alignment by dynamic programming. Thus, one has to maintain a list of the nodes already considered in the query. Therefore, on the whole, one has to consider all O(nk ) potential alignments, with n = |VN | and k = |VQ |. Using color-coding, one may decrease this complexity to O(2k ). First, nodes of the network are colored randomly using k colors, where k = |VQ |. Then, looking for a colorful alignment (i.e., an alignment that contains each color once) leads to a potential solution (i.e., not necessarily optimal). Therefore, one only needs to maintain a list of the colors already used in the alignment, storable in a table of size in O(2k ). In order to get an optimal solution, this process is repeated. More precisely, according to QNet [7], since a colorful alignment happens with k −k times to obtain , the coloration step has to be done log( 1ǫ )e probability kk!k ≃ e an optimal alignment with high probability (1 − ǫ , for any ǫ ). The QNet dynamic programming algorithm can be summarized as follows. By an incremental construction, for each (q i , qj ) of EQ when one considers qi of VQ aligned with a node vi of VN , check whether the score of the alignment is improved through: (i) a match of qj and any vj of VN such that qj and vj are homologous and (vi , vj ) ∈ EN , (ii) an insertion of a node vj of VN in the alignment graph GA , (iii) a deletion of qj . This is made for a given coloration of the network, and repeated for each coloration. Hereafter, we define an algorithm, inspired from QNet, which consider a query tree TQ , a PPI network GN and seeks for an alignment (GA , σ). To deal with duplicated nodes (cf. Graph2Tree algorithm), we pre-compute all possible assignment of the duplicated nodes VQ of TQ . More precisely, for each q of F and for all q ′ of d(q) one assign σ(q ′ ) with each v of VN . We then compute for each assignment A an alignment with respect to A. We denote BestConstraintAlignment this step (details omitted due to space constraints). The difficulty is to construct the best alignment by dynamic programming, with respect to A. As done in QNet, we use a set SC of k + Nins colors (as needed by the colorcoding) which will be used when a node is matched or inserted. Moreover, in order to deal with potential duplicated nodes in TQ , we have to use another multi-set of colors (i.e., the colors in this set can appear more than once), rather than a classical set as in QNet. Indeed, every node in d(q) such that q ∈ F , must use the same color. Algorithm 3 may be summarized as follow. Perform log( 1ǫ )ek random colorations of the PPI network GN to ensure optimality with a probability of at least 1 − ǫ. A coloration consists in affecting a random color of SC to each node of VN . Then, for each coloration, we build all possible valid assignments A of the duplicated nodes. An assignment A is valid if no two non homologous nodes are matched in A. For each such assignment A, we compute the best alignment according to A with Algorithm BestConstraintAlignment. We keep the best score of these trials, and, get the corresponding alignment by classic backtracking technique.

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Function PADA1 (T Q ,GN , h, threshold) begin BestGA ← ∅; BestScore ← −∞; for (i = 0; i < log( 1ǫ )ek ; i + +) do randomly colorize GN with k + Nins colors; foreach valid assignment A do GA ← BestConstraintAlignment(GN , TQ , A, h, threshold); if score(GA ) > BestScore then BestGA ← GA ; BestScore ← score(GA ); end end end return BestGA ; end

Algorithm 3. Sketch of the PADA1 algorithm to align a query graph to a network

Let us analyze the complexity of PADA1. The whole complexity depends essentially on lines 5 to 12. Let us consider the complexity of one iteration (we have log( 1ǫ )ek iterations). The random coloration can be done in O(n), where n = |VN |. There are n|F | possible assignments. The complexity of BestConstraintAlignment is 2O(k+Nins ) m as in QNet, where k is the size of the graph query and m = |EN |, since our modifications are essentially additional tests which are done in constant time. Let us note that the complexity of Graph2Tree is negligible compared to the overall complexity of Algorithm PADA1. Indeed, the complexity of Algorithm Graph2Tree only depends on the query size k, with k ≪ n. Therefore, on the whole, the complexity of PADA1 is O(n|F | .2O(k+Nins ) m) time. Observe that the time complexity does not depends on the total number of duplicated nodes but on the size of F .

3

Experimental Results

According to the authors of QNet, one may query a PPI network by running a O(2O(k) nt+1 ) time algorithm log( 1ǫ )ek times, where t is the treewidth of the query. Thus, the difference between the two algorithms is mainly related to t + 1 versus |F | question (i.e., the size of the set of families of duplicated nodes computed by Algorithm Graph2Tree). These two parameters are not easily comparable, except for trivial cases. However, we have computed some experimental tests to compare these two parameters on random graphs. Figure 3 suggests that parameter |F | is usually smaller for moderate size graphs (i.e., those graphs for which PADA1 is still practicable). Observe however that there are graphs with treewidth smaller than |F |, and hence no definitive conclusion can be drawn.

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Algorithms Comparison QNet (Treewidth+1) PADA1 (|F|)

4.5

Value

4 3.5 3 2.5 2 1.5

4

6

8

10 Graph size

12

14

16

Fig. 3. Comparison between QNet (i.e., the treewidth+1 value) and PADA1 (i.e., the size of F computed after running the Graph2Tree algorithm). The method is as follows: for each different size of graph, we get the average treewidth and F values over 30 000 connected graphs, randomly constructed with the NetworkX library (http://networkx.lanl.gov/). Treewidth is computed with the exact algorithm provided by http://www.treewidth.com/, while the size of F is computed with our Graph2Tree algorithm.

In practice, our upper-bound is largely over estimated. Indeed, each element of F must be assigned to a different node of the network. So, there are not n possibilities for each element of F . The number of executions of BestConn! straintAlignment is (n−|F |)! , the number of combinations. Moreover, we only consider valid assignments and there are only few such assignments. Indeed, a protein is, on average, homologous to dozens of proteins, which is quite less than the number of proteins in a classical PPI network (e.g. n ≃ 5.000 for the yeast). For example, if |F | = 3 and if the protein represented by this unique element of F is homologous to ten proteins in the PPI network, then, the number of assignment will not be n3 but only 103 . Here, the running time is largely less than the worst case time complexity. Therefore, and not surprisingly, the BLAST threshold used to determine if a protein is homologous to another have a huge impact on the running time of the algorithm. Finally, observe that in QNet, for a given treewidth, the query graph can be very different. For example, in the resulting tree decomposition of the graph, there is no limit on the number of bags of size t. Furthermore, in a given bag, the topology is arbitrary (e.g., a clique), potentially requiring an exhaustive enumeration upper-bounded by nt+1 . Therefore, the treewidth value does not indicate how many times an exhaustive enumeration has to be done. We would have liked to compare in practice our algorithm to QNet, but, unfortunately, their version querying graphs is not yet implemented. Comparing

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Fig. 4. A result sample of our algorithm. a) A MAPK human query, get from [14], with three cycles. b) The alignment graph given by our algorithm in the fly PPI network. Dashed lines denotes the BLAST homology scores between the two proteins. Our algorithm retrieves a query graph in an other network. As in QNet [7], it seems to be that there is some conservation between these two species.

our algorithm for simple trees queries with QNet would not make sense since PADA1 is not optimized for this special cases. In order to validate our algorithm, we perform the experimental tests on real data, proposed by QNet [7]. In our experiments, the data for the PPI network of the fly and the yeast have been obtained from the DIP database1 [24]. The yeast network contains 4 738 proteins and 15 147 interactions, whereas the fly network contains 7 481 proteins and 26 201 interactions. The first experiment consists in retrieving trees. To do so, the authors of QNet extract randomly trees queries of size 5 to 9 from the yeast network and try to retrieve them in this network. Each query is modified with at most two insertions or deletions. We also have successfully retrieved these queries. The second experiment was performed across species. The Mitogen-Activated Protein Kinase (MAPK) are a collection of signal transduction queries. According to [6], they have a critical function in the cellular response to extracellular stimuli. They are known to be conserved through different species. We obtained the human MAPK from the KEGG database [14] and tried to retrieve them in the fly network as done in QNet. While QNet uses only trees, we were able to query graphs. The results were satisfying since we retrieved them, with few or without modifications. The Figure 4 shows a sample of our results on real data. This suggests a potential conservation of patterns across species. The BLAST threshold have deep impact on the running time. |F |. Moreover, we probably could certainly speed-up the running time by using the H¨ uffner et al. technique [13], which basically consists in increasing the number of colors used during the coloration step.

4

Conclusion

In this paper, we have tried to improve our understanding in PPI networks by developing a tool called PADA1 (available uppon request), to query graphs in 1

http://dip.doe-mbi.ucla.edu/

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PPI networks. The time complexity of this algorithm is n|F | 2O(k) , where n is the size of the PPI network, k is the size of the query, and |F | is the minimum number of nodes which have to be duplicated to transform the query graph into a tree (solving the Feedback Vertex Set problem). This is the main difference with QNet of Dost et al. [7], which uses the treewidth of the query (unimplemented algorithm). We have performed some tests on real data and have retrieved known paths in the yeast PPI network. Moreover, we have retrieved known human paths in the fly PPI network. The time complexity of our algorithm depends on the number of nodes which have to be duplicated in the graph query, depends on the initial topology of the query graph. Obtaining more information about the topology of the queries is of particular interest in this context. Future works includes using this information to predict average time complexity.

References 1. Alon, N., Yuster, R., Zwick, U.: Color coding. Journal of the ACM 42(4), 844–856 (1995) 2. Altschul, S.F., Gish, W., Miller, W., Myers, E.W., Lipman, D.J.: Basic local alignment search tool. Journal of Molecular Biology 215(3), 403–410 (1990) 3. Arnborg, S., Corneil, D.G., Proskurowski, A.: Complexity of finding embeddings in a k-tree. Journal on Algebraic and Discrete Methods 8(2), 277–284 (1987) 4. Bodlaender, H.L.: A tourist guide through treewidth. Acta Cybernetica 11, 1–23 (1993) 5. Bodlaender, H.L.: A cubic kernel for feedback vertex set. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 320–331. Springer, Heidelberg (2007) 6. Dent, P., Yacoub, A., Fisher, P.B., Hagan, M.P., Grant, S.: MAPK pathways in radiation responses. Oncogene 22, 5885–5896 (2003) 7. Dost, B., Shlomi, T., Gupta, N., Ruppin, E., Bafna, V., Sharan, R.: QNet: A Tool for Querying Protein Interaction Networks. In: Speed, T., Huang, H. (eds.) RECOMB 2007. LNCS (LNBI), vol. 4453, pp. 1–15. Springer, Heidelberg (2007) 8. Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999) 9. Garey, M.R., Johnson, D.S.: Computers and Intractability: a guide to the theory of NP-completeness. W.H. Freeman, San Franciso (1979) 10. Gavin, A.C., Boshe, M., et al.: Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature 414(6868), 141–147 (2002) 11. Guo, J., Gramm, J., H¨ uffner, F., Niedermeier, R., Wernicke, S.: Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization. Journal of Computer and System Sciences 72(8), 1386–1396 (2006) 12. Ho, Y., Gruhler, A., et al.: Systematic identification of protein complexes in Saccharomyces cerevisae by mass spectrometry. Nature 415(6868), 180–183 (2002) 13. Huffner, F., Wernicke, S., Zichner, T.: Algorithm Engineering For Color-Coding To Facilitate Signaling Pathway Detection. In: Proceedings of the 5th Asia-Pacific Bioinformatics Conference. Imperial College Press (2007) 14. Kanehisa, M., Goto, S., Kawashima, S., Okuno, Y., Hattori, M.: The KEGG resource for deciphering the genome. Nucleic acids research 32, 277–280 (2004) 15. Karp, R.M.: Reducibility among combinatorial problems. In: Thatcher, J.W., Miller, R.E. (eds.) Complexity of computer computations, pp. 85–103. Plenum Press, New York (1972)

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16. Kelley, B.P., Sharan, R., Karp, R.M., Sittler, T., Root, D.E., Stockwell, B.R., Ideker, T.: Conserved pathways within bacteria and yeast as revealed by global protein network alignment. Proceedings of the National Academy of Sciences 100(20), 11394–11399 (2003) 17. Pellegrini, M., Marcotte, E.M., Thompson, M.J., Eisenberg, D., Yeates, T.O.: Assigning protein functions by comparative genome analysis: protein phylogenetic profiles. PNAS 96(8), 4285–4288 (1999) 18. Pinter, R.Y., Rokhlenko, O., Yeger-Lotem, E., Ziv-Ukelson, M.: Alignment of metabolic pathways. Bioinformatics 21(16), 3401–3408 (2005) 19. Reguly, T., Breitkreutz, A., Boucher, L., Breitkreutz, B.J., Hon, G.C., Myers, C.L., Parsons, A., Friesen, H., Oughtred, R., Tong, A., et al.: Comprehensive curation and analysis of global interaction networks in saccharomyces cerevisiae. Journal of Biology (2006) 20. Scott, J., Ideker, T., Karp, R.M., Sharan, R.: Efficient algorithms for detecting signaling pathways in protein interaction networks. Journal of Computational Biology 13, 133–144 (2006) 21. Shlomi, T., Segal, D., Ruppin, E., Sharan, R.: QPath: a method for querying pathways in a protein-protein interaction network. BMC Bioinformatics 7, 199 (2006) 22. Thomasse, S.: A quadratic kernel for feedback vertex set. In: Proceedings SODA (2009) (to appear) (unpublished manuscript) 23. Uetz, P., Giot, L., et al.: A comprehensive analysis of protein-protein interactions in Saccharomyces cerevisae. Nature 403(6770), 623–627 (2000) 24. Xenarios, I., Salwinski, L., Duan, X.J., Higney, P., Kim, S.M., Eisenberg, D.: DIP, the Database of Interacting Proteins: a research tool for studying cellular networks of protein interactions. Nucleic Acids Research 30(1), 303 (2002)

Integrative Approach for Combining TNFα-NFκB Mathematical Model to a Protein Interaction Connectivity Map Mahesh Visvanathan1, Bernhard Pfeifer2, Christian Baumgartner2, Bernhard Tilg2, and Gerald Henry Lushington1 1

Bioinformatics Core Facility, University of Kansas, Lawrence, KS 66047 [email protected] 2 University for Health Sciences, Medical Informatics and Technology (UMIT) Hall in Tyrol, Austria

Abstract. We have investigated different mathematical models for signaling pathways and built a new pathway model for TNFα-NFκB signaling using an integrative analytical approach. This integrative approach consists of a knowledgebase, model designing/visualization and simulation environments. In particular, our new TNFα-NFκB signaling pathway model was developed based on literature studies and the use of ordinary differential equations and a detailed protein-protein interaction connectivity map within this approach. Using the most detailed mathematical model as a base model, three new relevant proteins -TRAF1, FLIP, and MEKK3 -- were identified and included in our new model. Our results show that this integrative approach offers the most detailed and consistent mathematical description for TNFα-NFκB signaling and further increases the understanding of TNFα-NFκB signaling pathway. Keywords: TNFα mediated NF-kB signaling pathway, protein-protein interaction and mathematical model.

1 Introduction Interactions of molecules are essential for almost all cellular functions. Genes and proteins seldom carry out their functions in isolation. They operate through a number of interactions with other biomolecules. Molecular interactions in biological pathways and networks are highly dynamic and may be controlled by feedback loops and forward regulation mechanisms as well as dependence on other cellular hierarchies. They make experimental elucidation and computational analysis of pathways extremely challenging. Mathematical modeling is becoming increasingly important as a tool to capture molecular interactions and dynamics from high-throughput experiments. Biological pathways and networks are often represented graphically. Ordinary differential equations (ODEs) have been commonly used to help explain the kinetic process of association and disassociation among molecules in chemical or biochemical reactions. I. Măndoiu, G. Narasimhan, and Y. Zhang (Eds.): ISBRA 2009, LNBI 5542, pp. 63–74, 2009. © Springer-Verlag Berlin Heidelberg 2009

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Tumor necrosis factor-alpha (TNFα) is a cytokine involved in systematic inflammation and is a member of a group of cytokines that all stimulate the acute phase reaction. Dysregulation and over-production of TNFα have been implicated in the pathogenesis of a wide spectrum of human diseases, e.g. sepsis, diabetes, cancer, osteoporosis, multiple sclerosis and Crohn's disease. Eliminating TNFα by a specific monoclonal antibody, e.g. infliximab, caused dramatic effects on the phenotype of the diseases, with severe side effects. To find specific ways with least side effects to block or partially block TNFα actions, we need to learn more about the signaling pathways of TNFα. Some research efforts have been shifted from intercellular to intracellular signaling in order to increase the knowledge about the involved cell proteins and to get a better understanding of the molecular dynamics of the TNFαrelated pathways, especially the TNFα-NFκB signaling pathway. Biological cartoons and analytical pathway models have been constructed for the TNFα-NFκB signaling pathway respectively. These models can be used for computer simulation studies in order to get insights on setting various experimental scenarios. The better understanding of diseases makes the drug development more appropriate with minimal side effects [1, 31]. Reliable information about proteins and molecular interactions of the signaling pathway is needed to improve the structure of a pathway model. It has known that several protein purification methods are not capable of detecting protein activities in natural concentration. Because of protein over-expression, non-natural protein complex building can occur [20, 25] which could cause faults in modeling. Although a significant amount of biological and biochemical literature is now available in this research field, some of which examine only small parts of the pathway and sometimes with methods relying on over-expression situations. In this paper, we introduce an integrative approach to analyze an experimental TNFα-NFκB signaling pathway model. We built an integrative database that includes mathematical modeling data, literature information as well as biological data. In particular, the modeling data consists of kinetic constants, rate equations and initial concentrations for building mathematical ODE models. The biological data includes descriptions of proteins, protein-protein interactions and other information about signaling pathways. All information can be retrieved and visualized within our integrative computational framework. The paper is organized as follows: Section 2 provides our methodology and delimitates the modeling of the TNFα-NFκB signaling pathway based on ODE models and the literature information. Section 3 describes the results obtained from our extended TNFα-NFκB signaling pathway model. Section 4 gives our discussion and conclusion of this work.

2 Methodology 2.1 Integrating Heterogeneous Information for Modeling The immunosuppression associated with neutralization of TNFα through infliximab results in serious adverse effects e.g. systemic tuberculosis, allergic granulomatosis of the lung, or mild leucopenia in patients with active ankylosing spondylitis [19].

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Because of these clinical adverse effects, additional information on the mechanisms of the action of infliximab is needed. In order to increase understanding of the mechanism of TNFα, to find more specific drug targets, to minimize adverse effects and to maintain the duration of the treatment, the focus of research has been shifting from intercellular signals such as TNFα, to intracellular signals, such as the signal transduction pathway from the membrane receptors of TNFα to the transcription factors AP1 and NFκB and to apoptosis. The exact description of the TNFα pathway is no easy task. Various publications on this topic exist, but none of them provides a comprehensive assessment of the interactions of all the proteins believed to participate in the pathway. Evidence for the uncertainty about the pathway structure is provided by numerous different biological cartoons dealing with TNFα and NFκB [5 8, 10,11,, 21, 22, 25, 30]. Some of these cartoons use quite different proteins. A recently developed method, the TAP (tandem affinity purification) tag strategy [6, 18], seems to overcome some of the problems and opens a new door in large scale in vitro experiments. Further problems have arisen from the fact that a lot of experiments were based on protein over-expression situations, which can produce unphysiological complex building. This problem is also solved by the TAP tag strategy [4]. The development of a precise mathematical model is a very difficult task. As the biological knowledge and the experimental data used are insufficient, various assumptions have to be made concerning kinetic parameters and concentrations of proteins involved. The first step to produce a mathematical model is to develop a detailed qualitative model or a cartoon outlining participating proteins after collecting biological and experimental data. This qualitative model/cartoon has to be translated into a quantitative mathematical model [10]. There are two principle ways to construct mathematical models to model the kinetics of biochemical reactions: a deterministic formulation based on nonlinear ordinary differential equations (ODEs) for large numbers of molecules and a stochastic formulation rooted in exponential distribution law. Deterministic models have been commonly used as they can be easily applied with existing off-the-shelf computer software programs, while stochastic models are currently getting more attention and being further developed to capture certain randomness nature of molecular interactions [26, 27]. A pathway cartoon comprises only qualitative information of the biochemical pathway of interest (e.g. the TNFα-NFκB signaling pathway in our work). The proteins in the cartoon are placed in the region where they are situated in the cell, e.g. the receptor is at the cell membrane, the interacting proteins, which may be located in the cell nucleus, are far away. Information about protein interactions and complex building is hidden in the biological cartoons. Such cartoons do not explain molecular dynamics quantitatively, but they provide a schematic visual overview of the overall dynamics and information processing in cellular systems. Mathematical models of a biochemical pathway can show the chronology of protein complex association and dissociation. This is done with respect to the initial concentrations of the proteins and the kinetic parameters that controls the simulation and analysis of theses models [11, 12, 14, 13, 19]. Protein-protein interaction connectivity maps also provide important information on which proteins are co-purified with distinct target proteins.

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To compare and integrate the pathway mathematical model with the protein-protein interaction connectivity maps is a challenge. Based on various cartoons of the TNFα-NFκB signaling pathway, we identified the graphical dynamics of protein complex building. A graphic presentation of a qualitative pathway model of the TNFα-NFκB signaling pathway is shown in Figure 1. 2.2 Architecture of the Integrative Framework Our integrative framework was designed as a 3-tier architecture shown in Figure 2. It consists of a Java-based pathway designing-visualization environment and a simulation environment in the upper application tier, a Java Database Connectivity-Open Database Connectivity (JDBC-ODBC) in the middle tier, and a relational data management system in the back-end database tier. Within this framework we first designed the TNFα-NFκB pathway model in the designing-visualization environment that allows inclusion of mathematical modeling data, simulation data and biological data from our integrated knowledgebase in the database tier. Then, the designed TNFα-NFκB pathway model was exported in an XML format from the designing environment to the simulation environment. The organizational structure of the database tier was designed to represent different levels of data. The entities of the knowledgebase contain information grouped into three categories: molecular components, reactions and pathways. These entities inherit both the biological and modeling information concerning specified pathways.

Fig. 1. The TNFαpathway model that was developed by our framework, it

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Fig. 2. The framework was designed in the form of a 3-tier architecture system that includes a Java-based pathway designing, simulation and visualization environments as the upper application tier, JDBC-ODBC middle tier, and an integrative database as the backend tier.

Specifically, the knowledgebase incorporates biological knowledge about components, reactions and pathways from three different online external protein databases: Biomolecular Interaction Network Database (BIND) [16, 14] Database of Interacting Proteins (DIP) [17], and Munich Information Center for Protein Sequences (MIPS) protein-protein interaction database [19] as well as internal experimental verifications and literature studies. The mathematical modeling knowledge includes kinetic constants, rate equations and initial concentrations and is related to the components and reactions of the pathway under investigation (e.g. TNFα-NFκB signaling pathway in our work). In general deterministic formulation, mathematical models of pathways use differential equations relying on fundamental assumptions. For example, a signal transduction system behaves as a slowly varying non-linear system (as a function of time) during a reaction period based on biological observations. Further, it is assumed that a cell keeps the concentration of each signaling protein constant before and after each signaling event; that is the concentration of these proteins return to steady state after the reaction. With these molecular kinetics assumptions, the ordinary differential equations for the mathematical models are derived and stored for simulation of the signaling pathway of interest. We have derived a new ODE model by also incorporating protein-protein interaction connectivity map information for the TNFα-NFκB signaling pathway with our integrative analysis. Simulations and analyses were done using a graphical user interface that was designed and developed using MATLAB®. More details are provided in the results section.

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3 Results For signaling pathway modeling, the following problems occur: • • •

It is not always clear which proteins should be used to set up a stable model basis which can easily be extended. What is the chronology of protein interactions and which proteins collectively constitute a complex? How fast and long do the proteins interact (i.e., what are the kinetic parameters)?

These problems are major considerations when modeling the TNFα-NFκB signaling pathway within our framework. The mathematical models described in [CH03, SC01, IH04] related to TNFα pathway demonstrate that these models contain similar proteins and the general dynamics of complex building was almost identical. Among these models we identified the model based on Cho (we referred it as Model A) as the best available model for possible further improvement in order to address the pathway modeling problems mentioned previously. Several other possible extensions/improvements for the pathway Model A were also identified depending on research foci and we concluded that three additional proteins – TRAF1, FLIP, and MEKK3 – should be introduced into Model A to improve correspondence with experimental observations. The main focus of our work was to model the TNFα- NFκB signaling pathway starting from TNFα receptor to the transcription factor AP1, rather than going into other levels. By including these three new proteins, we derived an initial extended pathway model using our integrated analytical framework. Table 1 shows a quantified summary to justify the inclusion of TRAF1, FLIP, MEKK3 which was idenfied in all the existing models but not in the interaction map. Hence we incorporated these components in to our new mathematical model. It is worth mentioning that TRAF1 and FLIP were also considered in the mathematical models by Schöberl, Ihekwaba and MEKK3 has been intensively discussed [SC01, IH05]. All proteins contained in the cell proliferation module of the extended pathway model were identified and compared among others via the TAP tagged strategy and the protein-protein interaction connectivity map [4]. We noted that some basic interactions, which were modeled, could not be found in the protein-protein interaction connectivity map (i.e. TNFR1-TRADD, TRADD-FADD, TRADD-RIP, RIP-Caspase8 and RIP-IKK). Since cIAP has not been further examined, the interaction with effector Caspases was not modeled. The analysis resulted in a final ODE pathway model that we refer to as the final ODE pathway model, Model B. In Model B, several single proteins like TNFR1, TRADD, RIP1, TRAF2, IKK, IκB and NFκB were identified in the protein-protein interaction connectivity map (Figure 4). The connectivity map comprises no complexes, only individual proteins. IKK is presented by its subunits IKKα, IKK and IKK , colored lilac, and Ι•Β is presented by its subunits IkBα, IkB and IkBε, colored orange. NFκB’s family members (monomers) are colored red and their precursors are mentioned in the connectivity map, i.e. NFκB1 (p50; precursor: p105), NFκB2 (p52; precursor: p100), p65 (RelA), c-Rel

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Fig. 3. The new TNFα-NFκB pathway model (Model B) includes three new proteins MEKK3 (m32), FLIP (m33) and TRAF1 (m35). Circles (with m and a number) represent various states for protein concentration (i.e. kinetic constants), and directed arrows represent dynamic relations (i.e. rate equations). The protein complex TNF/TNFR1/ TRADD/RIP1/ TRAF2/ MEKK3/IKK connects to NFκB is colored red. The new protein complexes are colored magenta, e.g. Caspase8/FLIP (m34), RAF1/Caspase8* (m36) and TRAF2/TRAF1c (m38).

(Rel), and RelB. All these seven proteins are present in both the Model B and the connectivity map. With limited experimental data, further modeling improvements are very difficult. The incorporated biological and modeling knowledge can be retrieved from the knowledgebase and integrated into the extended TNFα-NFκB signaling pathway model within our framework. We performed a systematic examination of the TNFα-NFκB signaling pathway by simulating different scenarios to analyze the sensitivity of the Model B with respect to possible changes of the kinetic parameters. The extended TNFα-NFκB signaling pathway model B now including all three new components namely the proteins: MEKK3, FLIP and TRAF1 is indeed quite a stable model. TRAF1 and Caspase8* are

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reversible from the complex proteins and TRAF1 is irreversibly cleaved and TRAF1c and Caspase8* were yielded. The comparison of the protein concentrations was also performed by plotting the concentrations of the components of other existing mathematical models including model by Cho [9], i.e. Model A, modles by Schöberl [23] and Ihekwaba [13] and the new Model B side-by-side. Components, which show extraordinary differences, were examined via further literature investigations. As a result, our extended TNFα-NFκB signaling pathway model B appears to be the most detailed and consistent mathematical model with protein-protein interaction connectivity information incorporated in it.

Fig. 4. The protein-protein interaction connectivity map (Bouwmeester et al. 2004). The proteins that are colored are modeled in our new TNFα-NFκB signaling pathway model B.

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Table 1. Quantifiable summary of mathematical models validated related to TNF

Existing Mathematical Models Schöberl EGF Model Ihekwaba MAPK Model Cho TNF Model Bonizzi NFkB Model Chung TGF Model TNF New Model (Model B)

Total Components Mapping to TNF Interaction Map

Total Number of Components

Common Components between the Models

94

2 (TRAF1, FLIP) 3 (TRAF1, FLIP, MEKK3)

3

14

46

2 (TRAF1, FLIP) 4 (TRAF1, FLIP, MEKK3,NFkB)

6

39

2 (MEKK3, FLIP)

3

35

4 (TRAF1, FLIP, MEKK3,NFkB)

16

81 31

3

4 Discussion Complex time-dependent interactions of intracellular proteins as a function of protein concentrations as well as other kinetic factors cause a high degree of variability in biological functions. To bring light to complex intracellular interaction systems, we first have to identify the proteins involved and then model their interactions in an appropriate manner. TNFα is a cytokine, which is implicated in the pathogenesis of various human diseases and therefore it has been a subject of intense investigations aimed at better understanding of the exact signal flow. The objective of this work was to build a new TNFα- NFκB signaling pathway model that allows integration of a protein-protein interaction connectivity map. The mathematical models relating to the TNFα-NFκB signaling pathway contained similar proteins and an identical concept underlying the complex building. Bouwmeester et al. [4] published a connectivity map giving a detailed view of protein-protein interactions of the TNFα-NFκB signaling pathway on a physiological protein concentration level and this map was used as a preliminary guide for our extended mathematical model, and employed as a point of comparison. Mathematical models based on Cho [8], Schöberl [13] and Ihekwaba [IH04] are available in relation to TNFα- NFκB signaling pathway. Improvements upon the existing pathway models are very difficult and challenging. The decision to use the mathematical model by Cho (i.e. Model A) as our base model and extending it was based on our impression that it is the most detailed mathematical model available today for TNFα- NFκB signaling starting from TNFα receptor up to the transcription factor AP1. The Schöberl [23]. and Ihekwaba. [13] models describe signaling from IKK and NFκB level onwards. The Ihekwaba’s model concentrates more on details of modeling IKK interactions rather than the TNFα-NFκB signaling.

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Having selected Model A for extension, we found out that this model contained several inconsistencies, regarding the “recycling” of particular proteins after protein complex dissociation for TNFα- NFκB signaling pathway as a whole. Cho et al. did not clearly justify all of the choices underlying their model construction. We identified some inconsistencies and correspondingly revised the model so that it corresponded more directly with information evident from the protein-protein interaction connectivity map. The resulting extended Model B can serve as a more consistent mathematical description to reflect TNFα- NFκB signaling pathway. Our overall integrative analytical approach should serve as a reasonable point of comparison with other future models as further modeling improvements arise courtesy of new or more accurate experimental data become available. In essence, the knowledgebase of our integrative framework will grow accordingly. Three new proteins – TRAF1, FLIP, and MEKK3 – were included into the extended model B. TRAF1 and FLIP were already considered in the Schöberl model and MEKK3 has also been intensively discussed in the TNFα- NFκB signaling pathway literature. The importance of this protein has also been pointed out by Bouwmeester etal. [5]. The exact localization of MEKK3 in the signaling pathway and the protein interaction network are not fully clear at the moment. That is why the actual position in the extended pathway model has to be regarded as a first approximation.

5 Conclusion One of the main goals of this work was to use the information of the protein-protein interaction connectivity map to build an improved pathway model. In practice, we found that several protein interactions mentioned in literature could not be found in the connectivity map provided by Bouwmeester et al. [5], especially those interactions situated in close proximity to the cell membrane. In this regard, the Bouwmeester connectivity map just outlines which proteins are parts of the TNFα- NFκB signaling pathway, but does not exactly specify all the occurring interactions between them. To construct a valid mathematical model, it is necessary to have a complete view on the interactions in the signaling pathway. If all of the important interactions are revealed, this might require changing the general model structure, as the connectivity map suggests several alternative inhibiting and activating signal flow paths, which have not been modeled yet. Such limitations of experimental data also make it more challenging to develop a pathway model focusing specifically on the TNFα-NFκB signaling pathway. Information from several sources has to be combined and adapted to fit into one pathway model. Hence, this task makes the possibility of combining models more challenging and interesting. Stochastic mathematical modeling approach is also one of our research interests, and we are currently working on extending a Bayesian probabilistic graphical model framework [29] for TNFα-NFκB signaling pathway and have ongoing efforts to validate the structure of TNFα-NFκB signaling pathway by incorporating information from new experimental analysis and simulation studies. Specifically, the iterative interplay between experimental analysis and modeling strategies in which new experimental data is incorporated data into the knowledgebase, yielding more informed pathway analysis models, will hopefully yield an increasingly physiologically realistic

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model, and simulation studies performed on such improved signaling pathways should enable increasingly sophisticated and accurate interpretations of the biological system from a global systemic view.

References [1] Kitano, H.: Computational systems biology. Nature 420, 206–210 (2002) [2] Alfarano, C., Andrade, C.E., Anthony, K., et al.: The Biomolecular Interaction Network Database and related tools 2005 update. Nucleic Acids Res. 33(Database issue), D418–D424 (2005) [3] Barken, D., Wang, C.J., Kearns, J., et al.: Comment on Oscillations in NF-kappaB signaling control the dynamics of gene expression. Science 308(5718), 52 (2005) [4] Bonizzi, G., Karin, M.: The two NF-kappaB activation pathways and their role in innate and adaptive immunity. Trends Immunol. 25(6), 280–288 (2004) [5] Bouwmeester, T., Bauch, A., Ruffner, H., et al.: A physical and functional map of the human TNF-alpha/NF-kappa B signal transduction pathway. Nat. Cell. Biol. 6(2), 97–105 (2004) [6] Cho, H., Shin, Y., Kolch, W., et al.: Experimental Design in systems biology based on parameter sensitivity analysis with monte carlo simulation: A case study for the TNFα Mediated NF-κB- signal transduction pathway. Simulation 12, 726–739 (2003a) [7] Cho, K.H., Shin, S.Y., Lee, H.W., et al.: Investigations into the analysis and modeling of the TNF alpha-mediated NF-kappa B-signaling pathway. Genome Res. 13(11), 2413–2422 (2003b) [8] Chung, J.Y., Lu, M., Yin, Q., et al.: Structural revelations of TRAF2 function in TNF receptor signaling pathway. Adv. Exp. Med. Biol. 597, 93–113 (2007) [9] Cox, D.M., Du, M., Guo, X., et al.: Tandem affinity purification of protein complexes from mammalian cells. Biotechniques 33(2), 267–268 (2002) [10] Dempsey, P.W., Doyle, S.E., He, J.Q., et al.: The signaling adaptors and pathways activated by TNF superfamily. Cytokine Growth Factor Rev. 14(3-4), 193–209 (2003) [11] Dixit, V., Mak, T.W.: NF-kappaB signaling. Many roads lead to madrid. Cell 111(5), 615–619 (2002) [12] Gilbert, D.: Biomolecular interaction network database. Brief Bioinform 6(2), 194–198 (2005) [13] Gregan, J., Riedel, C.G., Petronczki, M., et al.: Tandem affinity purification of functional TAP-tagged proteins from human cells. Nat. Protoc. 2(5), 1145–1151 (2007) [14] Ihekwaba, A.E., Broomhead, D.S., Grimley, R.L., et al.: Sensitivity analysis of parameters controlling oscillatory signalling in the NF-kappaB pathway: the roles of IKK and IkappaBalpha. Syst. Biol. (Stevenage) 1(1), 93–103 (2004) [15] Kitano, H.: Computational systems biology. Nature 420(6912), 206–210 (2002); Micheau, O., Tschopp, J.: Induction of TNF receptor I-mediated apoptosis via two sequential signaling complexes. Cell 114(2), 181–190 (2003) [16] Min, J.K., Kim, Y.M., Kim, S.W., et al.: TNF-related activation-induced cytokine enhances leukocyte adhesiveness: induction of ICAM-1 and VCAM-1 via TNF receptorassociated factor and protein kinase C-dependent NF-kappaB activation in endothelial cells. J. Immunol. 175(1), 531–540 (2005) [17] Nelson, D.E., Ihekwaba, A.E., Elliott, M., et al.: Oscillations in NF-kappaB signaling control the dynamics of gene expression. Science 306(5696), 704–708 (2004)

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[18] Pagel, P., Kovac, S., Oesterheld, M., et al.: The MIPS mammalian protein-protein interaction database. Bioinformatics 21(6), 832–834 (2005) [19] Phair, R.D.: Development of kinetic models in the nonlinear world of molecular cell biology. Metabolism 46(12), 1489–1495 (1997) [20] Pomerantz, J.L., Baltimore, D.: Two pathways to NF-kappaB. Mol. Cell. 10(4), 693–695 (2002) [21] Rivkin, E., Cullinan, E.B., Tres, L.L., et al.: A protein associated with the manchette during rat spermiogenesis is encoded by a gene of the TBP-1-like subfamily with highly conserved ATPase and protease domains. Mol. Reprod. Dev. 48(1), 77–89 (1997) [22] Salwinski, L., Miller, C.S., Smith, A.J., Pettit, F.K., Bowie, J.U., Eisenberg, D.: The Database of Interacting Proteins: 2004 update. NAR 32 Database issue, D449–D451 (2004) [23] Schlosser, P.M.: Experimental design for parameter estimation through sensitivity analysis. J. Toxicol. Environ. Health 43(4), 495–530 (1994) [24] Schoeberl, B., Gilles, E.D., Scheurich, P.: A Mathematical Vision of TNF Receptor Interaction. In: Proceedings of the International Congress of Systems Biology, pp. 158–167 (2001) [25] Su, C.G., Lichtenstein, G.R.: Influence of immunogenicity on the long-term efficacy of infliximab in Crohn’s disease. Gastroenterology 125(5), 1544–1546 (2003) [26] Swaffield, J.C., Melcher, K., Johnston, S.A.: A highly conserved ATPase protein as a mediator between acidic activation domains and the TATA-binding protein. Nature 374(6517), 88–91 (1995) [27] Vilimas, T., Mascarenhas, J., Palomero, T., et al.: Targeting the NF-kappaB signaling pathway in Notch1-induced T-cell leukemia. Nat. Med. 13(1), 70–77 (2007) [28] Wang, C.Y., Mayo, M.W., Korneluk, R.G., et al.: NF-kappaB antiapoptosis: induction of TRAF1 and TRAF2 and c-IAP1 and c-IAP2 to suppress caspase-8 activation. Science 281(5383), 1680–1683 (1998) [29] Wolkenhauer, O., Cho, K.H.: Analysis and Modeling of Signal Transduction Pathways in Systems Biology. Biochem. Soc. Trans., Pt6:1503-1509 (2003) [30] Wang, J., Cheung, L.W., Delabie, J.: New probabilistic graphical models for genetic regulatory networks studies. J. Biomed. Inform. 38(6), 443–455 (2005) [31] Yao, J., Duan, L., Fan, M., et al.: NF-kappaB signaling pathway is involved in growth inhibition, G2/M arrest and apoptosis induced by Trichostatin A in human tongue carcinoma cells. Pharmacol. Res. 54(6), 406–413 (2006) [32] You, L.: Toward computational systems biology. Cell Biochem. Biophys. 40(2), 167–184 (2004)

Hierarchical Organization of Functional Modules in Weighted Protein Interaction Networks Using Clustering Coefficient⋆ ⋆⋆

Min Li1 , Jianxin Wang1, , Jianer Chen1,2 , and Yi Pan1,3 1

School of Information Science and Engineering, Central South University, Changsha 410083, P. R. China 2 Department of Computer Science, Texas A&M University, College Station, TX 77843, USA 3 Department of Computer Science, Georgia State University, Atlanta, GA 30302-4110, USA

Abstract. As advances in the technologies of predicting protein interactions, huge data sets portrayed as networks have been available. Several graph clustering approaches have been proposed to detect functional modules from such networks. However, all methods of predicting protein interactions are known to yield a nonnegligible amount of false positives. Most of the graph clustering algorithms are challenging to be used in the network with high false positives. We extend the protein interaction network from unweighted graph to weighted graph and propose an algorithm for hierarchically clustering in the weighted graph. The proposed algorithm HC-Wpin is applied to the protein interaction network of S.cerevisiae and the identified modules are validated by GO annotations. Many significant functional modules are detected, most of which are corresponding to the known complexes. Moreover, our algorithm HCWpin is faster and more accurate compared to other previous algorithms. The program is available at http://bioinfo.csu.edu.cn/limin/HC-Wpin. Keywords: Protein interaction network, clustering, functional module.

1

Introduction

High-throughput methods, such as yeast-two-hybrid and mass spectrometry, have led to the emergence of large protein-protein interaction datasets [1–6]. These protein-protein interactions can be naturally represented in the form of networks and provide useful insights into functional associations between proteins[7, 8]. A wide range of graph clustering algorithms have been developed for identifying functional modules from such protein interaction networks. ⋆

⋆⋆

This research was supported in part by the National Basic Research 973 Program of China No. 2008CB317107, the National Natural Science Foundation of China under Grant No. 60773111, the Program for New Century Excellent Talents in University No. NCET-05-0683, the Program for Changjiang Scholars and Innovative Research Team in University No. IRT0661. Corresponding author.

I. M˘ andoiu, G. Narasimhan, and Y. Zhang (Eds.): ISBRA 2009, LNBI 5542, pp. 75–86, 2009. c Springer-Verlag Berlin Heidelberg 2009 

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Recently, hierarchical model of modular network has been introduced and several hierarchical clustering approaches have been applied to identify functional modules[9–12]. In general, the hierarchical clustering approaches can represent the protein interaction networks in hierarchy by tree. According to the differences of constructing the tree, hierarchical clustering approaches can be classed into two groups: the top-down approach and the bottom-up approach. The topdown approaches start from one cluster with all vertices and recursively dividing it into several dissimilar sub-clusters. A typical example is the betweenness centrality-based algorithm proposed by Girvan and Newman [9]. In contrast, the bottom-up approaches start at single vertex clusters and iteratively merge similar clusters. MoNet algorithm [12] is an example of the bottom-up approaches. However, the hierarchical clustering approaches are known to be sensitive to noisy data [8]. Up to now, all methods of predicting protein-protein interactions can not avoid yielding a non-negligible amount of noisy data (false positives)[13]. Thus, the conventional hierarchial clustering approaches are challenging to be used directly in the networks with false positives. A series of density-based clustering approaches have been proposed to identify densely connected regions from protein interaction networks which are somewhat robust to noisy data. An extreme example is the maximum clique algorithm [14] which detects fully connected subnetworks. However, only mining fully connected subnetworks is too strict to be used in real biological networks. A variety of alternative density functions have been proposed to detect dense subnetworks [15–19]. However, the density-based approaches neglect many peripheral proteins that connect to the core protein clusters with few links, even though these peripheral proteins may represent true interactions that have been experimentally verified [12]. As Barab´ asi and Oltvai have pointed out that the density-based clustering approaches are not able to partition the biological networks whose degree distributions are typically power-law [20]. In addition, biologically meaningful functional modules that do not have highly connected topologies are ignored by these approaches [12]. In this paper, we extend the protein interaction network to a weighted graph and develop an algorithm, named HC-Wpin, for hierarchical clustering in the weighted graph. Algorithm HC-Wpin is applied to the weighted protein interaction network of S.cerevisiae and the identified modules are validated by GO annotations (including Biological Process, Molecular Function, and Cellular Component ). The experimental results show that the identified modules are statistically significant in terms of three types of GO annotations. Compared to other previous competing algorithms, our algorithm HC-Wpin is faster and more accurate, which can be used in even larger protein interaction networks.

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Methods

Ed ge Clustering Coefficient In Weighted Protein Interaction Network A weighted protein interaction network can be represented as a weighted undirected graph G = (V, E), where V is a set of vertices and E is a set of edges

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between the vertices. Each edge (u, v) is assigned with a weight w(u, v), which represents the probability of this interaction being a true positive. Clustering coefficient is first proposed to describe the property of a vertex in a network. Clustering coefficient of a vertex is the ratio of the number of connections in the neighborhood of the vertex and the number of connections if the neighborhood is fully connected [21]. Roughly speaking, clustering coefficient tells how well connected the neighborhood of the vertex is. Recently, Radicchi et al. [22] generalized the clustering coefficient of a vertex to an edge, and defined it as the number of triangles to which a given edge belonged, divided by the number of triangles that might potentially include it. The definition is not feasible when the network has few triangles. In our previous studies, we have redefined the clustering coefficient of an edge by calculating the common neighbors instead of the triangles [23]. However, all the definitions of clustering coefficient in the unweighted protein interaction networks do not consider the edge reliability. Here, we redefine the clustering coefficient of an edge in the weighted graph. Let Nu be the set of neighbors of vertex u and Nv be the set of neighbors of vertex v, respectively. Then the clustering coefficient of an edge (u, v) in a weighted graph G is defined as: CCu,v

 w(u, k) · k∈Iu,v w(v, k)  =  s∈Nu w(u, s) · t∈Nv w(v, t) 

k∈Iu,v

(1)

where Iu,v denotes the set of common vertices in Nu and Nv (i.e. Iu,v = Nu ∩Nv ). Two vertices of an edge with larger clustering coefficient are more likely to lie in the same module. Quantitative Definition of Modules In Weighted Protein Interaction Network Generally, functional modules in protein interaction networks are loosely referred to as highly connected subgraphs, which have more internal edges than external edges. Several module definitions have been proposed, such as strong module and weak module [22]. For an unweighted protein interaction network with high false positive, false prediction may be generated by using these definitions. To avoid the effect of false positive interactions in protein interaction networks, we define a functional module in the weighted graph. For a weighted graph G = (V, E), the degree of a vertex v is denoted as dw (v) which is the sum of weights of the edges connecting v: dw (v) =



w(u, v).

(2)

u∈Nv ;(u,v)∈E

For a vertex v in a subgraph H ⊆ G, its in-degree, denoted as din w (H, v), is the sum of weights of edges connecting vertex v to other vertices belonging to H, and its out-degree, denoted as dout w (H, v), is the sum of weights of edges connecting

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out vertex v to other vertices in the rest of the graph G. din w (H, v) and dw (H, v) can be formed as formula (3) and formula (4), respectively.

din w (H, v) =



w(u, v).

(3)

u,v∈H;(u,v)∈E

dout w (H, v) =



w(u, v).

(4)

v∈H;u∈H;(u,v)∈E /

It is clearly that the degree dw (v) of a vertex v is equaled to the sum of din w (H, v) and dout (H, v). w Definition 1. Given a weighted undirected graph G = (V, E, W ) and a threshold λ, a subgraph H ⊆ G is a λ-module if  v∈H

din w (H, v) > λ



dout w (H, v)

(5)

v∈H

where λ is a parameter determined by user. By changing the values of parameter λ , we can get different modules in the weighted protein interaction network. Hierarchical Clustering Based on the definitions of edge clustering coefficient and λ-module in weighted protein interaction networks, we propose a novel hierarchical clustering algorithm HC-Wpin. The whole description of algorithm HC-Wpin is shown in Figure 1. In Figure 1, Ci denotes a cluster, V (Ci ) and E(Ci ) denote the set of vertices and edges in the cluster Ci , respectively. Let Din (Ci ) be the sum of the in-degree of the vertices in Ci , and Dout (Ci ) be the sum of the out-degree of the vertices in Ci . For a vertex v, L(v) indicates which cluster it is in. The input to algorithm HC-Wpin is a weighted undirected graph G(V, E). Firstly, all vertices in the graph G are initialized as singleton clusters. Then, the clustering coefficient of each edge in the graph G is calculated. We enqueue all the edges into a queue Sq in non-increasing order in terms of their clustering coefficients. The higher clustering coefficient the edge has, the more likely its two vertices are inside a module. By gradually adding edges in the queue Sq to clusters, algorithm HC-Wpin finally assembles all the singleton clusters into λ-modules. In the end, the λ-modules which consist of s or more than s proteins are outputted. Parameter s is used to control the minimum size of the output functional modules. Let n and m denote the number of vertices and edges in a weighted protein interaction network respectively and k be the average number of neighbors of all  the vertices, i.e. k = n1 v∈V |Nv |. Then, the complexity of calculating all the edge clustering coefficients is O(k 2 m), the complexity of the iterative merging is O(m). Thus, the total computational complexity of algorithm HC-Wpin is O(k 2 m). In general, k is very small and can be considered as a constant.

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Algorithm HC-Wpin input: a weighted graph G = (V, E), parameters λ and s; output: identified modules; 1. for each vertex vi ∈ V do V (Ci ) = {vi }; E(Ci ) = ∅ 2. for each edge (u, v) ∈ E do compute its clustering coefficient; 3. sort all edges to queue Sq in non-increasing order in terms of clustering coefficients; 4. while Sq = ∅ do { e(u, v) ← Sq ; if L(u) = L(v) then i = L(u); E(Ci ) = E(Ci ) ∪ {e(u, v)}; else i = L(u); j = L(v); Din (Cj ) in (Ci ) if DDout ≤ λ or Dout ≤ λ then (Ci ) (Cj ) V (Ci ) = V (Ci ) ∪ V (Cj ); E(Ci ) = E(Ci ) ∪ E(Cj ); Cj = {∅, ∅}; Sq = Sq − {e(u, v)};} 5. for i=1 to |V | do if |V (Ci )| ≥ s then output Ci ;

Fig. 1. The description of algorithm HC-Wpin

3

Experiments and Results

Identification of λ Modules In The Network of S.cerevisiae The original unweighted protein interaction network of S.cerevisiae, consisting of 4,726 proteins and 15,166 interactions, was downloaded from the DIP database[24]. To construct weighted protein interaction network, we assign confidence scores to these interactions using the logisticregression-based scheme employed in [25, 26]. Roughly speaking, the confidence score is computed based on the experimental evidences which include the type of experiments in which the interaction is observed, and the number of observations in each experimental type. We apply algorithm HC-Wpin to the weighted protein interaction network and achieve five output sets of modules by changing the values of parameter λ from 1.0 to 3.0 with 0.5 increment. Table 1 illustrates the effect of parameter λ on clustering. In Table 1, Max.Size represents the size of the largest module, and Avg.Size represents the average size of all the identified modules. As shown in Table 1, Table 1. The effect of λon clustering Parameter Modules Max.size Avg.size

λ= 1.0 145 79 9.24

λ= 1.5 132 125 10.54

λ= 2.0 117 263 12.25

λ= 2.5 91 982 16.89

λ= 3.0 77 1192 20.82

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#3 (982)

Ȝ=2.5

Ȝ=2.0 #11 (8)

#11 (5)

#14 (72)

#3 #16 (4) (125)

#3 (263)

#15 (7)

#19 (19)

#27 (3)

#18 (73)

#35 (9)

#22 (4)

#26 (5)

#30 #33 (22) (8)

#36 (3)

#37 #38 (18) (7)

#44 (73)

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#43 (4)

#51 (72)

#54 #55 #56 (8) (255) (3)

#63 (5)

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#52(73) #36 #38 (4) (50)

#46 (15)

#55 (3)

#64 (17)

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#126 (3)

Ȝ=1.0 #4 #69 #51 (79) (33) (8)

Y L R 4 1 8 C

Y B R 2 7 9 W

Y O L 1 4 5 C

Y G L 2 4 4 W

#20 #64 (45) (12)

Y O R 1 2 3 C

Y M L 0 1 0 W

Y G L 2 0 7 W

#0 (26)

Y M L 0 6 9 W

Y M R 1 9 7 C

Y K L 1 9 6 C

#35 (4)

Y B L 0 5 0 W

#19 (11)

#46 #61 #94 (9) (17) (9)

Y L R 0 9 3 C

Y O R 1 0 6 W

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Y O L 0 1 8 C

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#41 #54 #76 (27) (29) (32)

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#58 (7)

Y N L 3 3 0 C

Y D L 0 7 6 C

Y P L 1 3 9 C

Y M R 2 6 3 W

Y I L 0 8 4 C

Y P L 1 8 1 W

The identified module consisting of 982 proteins which is generated by HC-Wpin with Ȝ=2.5 The identified modules generated by HC-Wpin with Ȝ=2.0 which are included in a larger module generated by HC-Wpin with Ȝ=2.5 The identified modules generated by HC-Wpin with Ȝ=1.5 which are included in larger modules generated by HC-Wpin with Ȝ=2.0 The identified modules generated by HC-Wpin with Ȝ=1.0 which are included in larger modules generated by HC-Wpin with Ȝ=1.5 Proteins

Fig. 2. An example of hierarchical modules generated by algorithm HC-Wpin with different values of parameter λ. All the identified modules listed in this figure are available from Additional file 1.

the number of the identified modules is decreasing with the increase of λ. The average size of all the identified modules and the size of the biggest module are increasing as λ increases. Bigger modules are generated by HC-Wpin when larger value of λ is used. This is because the larger value of λ may lead to the merging of clusters in the agglomerative process. Figure 2 illustrates an example that small modules are iteratively merged with the increase of λ. As shown in Figure 2, the modules #19, #41, #54, #58 and #76 generated by HC-Wpin with λ=1.0 are merged into a larger module #65 which is generated by HC-Wpin with λ=1.5. When λ=2.0, the module #65 and the other nine green modules generated with λ=1.5 are merged into a larger module #55 which consists of 255 proteins. When λ=2.5, all the 24 modules generated with λ=2.0 are merged into a more larger module which consists of 982 proteins. By changing the values of parameter λ, we can obtain the hierarchial organization of functional modules in the protein interaction network. In the following subsection we will evaluate the significance of the identified modules by using the SGD GO Term Finder (http://www.yeastgenome.org/). The evaluation results show that the hierarchical organization of modules are approximatively corresponding to the hierarchical structure of GO annotations. Statistical Assessment of the Identified Modules To test whether the identified modules are significant, we validate them using all the three types of GO terms: Biological Process, Molecular Function, and Cellular

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Component. For each identified module, the P-value from the hypergeometric distribution is calculated based on the three types of GO annotations. A cutoff parameter is used to differentiate significant groups from insignificant ones. If an identified module is associated with a P-value larger than cutoff, it is considered insignificant. We use the recommended cutoff of 0.05 for all our validations. Firstly, we evaluate the significance of the hierarchical modules shown in Figure 2. As pointed out by Gavin et al. and Krogan et al., the larger complexes are composed, sometimes transiently, from smaller subcomplexes [3, 6]. We obtain the similar results that the smaller functional modules are hierarchically organized into the larger functional modules which is approximatively corresponding to the hierarchical structure of GO annotations. For example, the five green modules (#38, #64, #65, #69 and #72) generated with λ=1.5 are merged into a larger module #55 generated with λ=2.0. Correspondingly, the Biological Process annotation for the module #55 is the common ancestor of that for the five smaller modules #38, #64, #65, #69 and #72 in the hierarchical structure of GO annotations, as shown in Additional file 2. Similar corresponding relation between the hierarchical modules and the hierarchical structure of GO annotations is obtained both for Molecular Function and for Cellular Component annotations. Next, we evaluate all the identified modules generated by HC-Wpin. Take the modules with λ=1.0 for example, 130 out of 145 identified modules are validated to be significant with Biological Process annotations. The lowest P-values of the 130 significant modules range from 4.93E-02 to 5.82E-73. For Molecular Function annotations, 115 identified modules are validated to be significant, whose lowest P-values range from 4.70E-02 to 2.50E-52. The module with the lowest P-value of 2.50E-52 is composed of 33 members. Of all the 33 proteins, more than 75% have the function of “RNA polymerase activity”. For Cellular Component annotations, the lowest P-value of all the identified modules is 1.51E-68. The module with the lowest P-value is composed of 45 proteins, in which 37 proteins belong to the known complex “small nuclear ribonucleoprotein complex”. There are a series of small identified modules matching the known complexes perfectly in the network of S.cerevisiae. For example, the module #10 consisting of 3 proteins (EFB1, TEF4, TEF1) is exactly the “eukaryotic translation elongation factor 1 complex”, the module #136 consisting of 3 proteins (POL3, POL31, POL32) is exactly the “delta DNA polymerase complex”, the module #33 consisting of 4 proteins (APL3, APL1, APS2, APM4) is exactly the “AP-2 adaptor complex”, the module #90 consisting of 4 proteins (SEC66, SEC72, SEC63, SEC62) is exactly the “endoplasmic reticulum Sec complex”, and the module #131 consisting of 5 proteins (VPS29, PEP8, VPS35, VPS5, VPS17) is exactly the “retromer complex”. There are some identified modules which have the similar P-values validated by different types of GO annotations. For the example of module #134, all the 4 proteins (SEN34, SEN2, SEN15, SEN54) in it are exactly the entire members in the network of S.cerevisiae which have the same molecular function of “endoribonuclease activity, producing 3’-phosphomonoesters”, participate in the same biological process of “RNA splicing, via endonucleolytic cleavage and ligation” and are in the same cellular component “tRNA-intron endonuclease complex”.

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There are also a number of identified modules whose lowest P-values are very different with different validation of GO terms. For example, the module #60 is composed of 4 proteins (APM3, APL6, APS3, APL5). For Biological Process annotations, it has a lowest P-value of 4.55E-09. The 4 proteins combining with other 18 proteins participate in the process of “Golgi to vacuole transport”. For Molecular Function annotations, 3 proteins (APM3, APL6, APS3) out of the 4 proteins are directly annotated to the root term “molecular function unknown”. It has no P-value result. However, it is exactly the known complex “AP-3 adaptor complex” for Cellular Component annotation with the lowest P-value of 6.70E13. The detailed annotations of one type of GO terms may give clues to study another type of GO terms. The above analyses show that our algorithm HC-Wpin not only can identify significant functional modules but also can detect significant functional modules in hierarchy. Comp arison with Other Methods To evaluate the effectiveness of our algorithm HC-Wpin, we compare it with several previous state-of-the-art algorithms: the MoNet algorithm [12] and FAG-EC algorithm [23] as hierarchial clustering approaches, the MCODE algorithm and DPClus algorithm as density-based methods, and the STM algorithm [27]. The values of the parameters in each algorithm are selected from those recommended by the author. The accuracy of each algorithm is calculated and shown in Table 2. The accuracy of an algorithm indicates the average f -measure of the significant modules generated by it. f -measure of an identified module is defined as a harmonic mean of its recall and precision. f -measure =

2 ∗ recall ∗ precision recall + precision

recall =

|M ∩ Fi | |Fi |

precision =

|M ∩ Fi | |M |

(6) (7) (8)

where Fi is a functional category mapped to module M . The proteins in functional category Fi are considered as true predictions, the proteins in module M are considered as positive predictions, and the common proteins of Fi and M are considered as true positive predictions. Recall is the fraction of the true-positive predictions out of all the true predictions, and precision is the fraction of the true-positive predictions out of all the positive predictions[8]. As shown in Table 2, the accuracy of our algorithm HC-Wpin is much higher than that of the other four algorithms: FAG-EC, MCODE, DPClus and STM with all the validations of Biological Process (abbreviated as B.P.), Molecular Function (abbreviated as M.F.), and Cellular Component (abbreviated as C.C.). MoNet produces a giant module consisting of 3336 proteins and three small

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Table 2. Comparison of the accuracy of algorithm HC-Wpin and other previous algorithms Algorithms Modules Average of Maximum Accuracy size ≥ 3 Size Size B.P. M.F. C.C. HC-Wpin 145 9.24 79 0.34 0.29 0.50 MoNet 4 837.50 3336 FAG-EC 326 8.52 237 0.27 0.20 0.40 MCODE 59 74.78 555 0.29 0.24 0.39 DPClus 236 4.02 13 0.26 0.19 0.35 STM 10 467.80 4647 0.21 0.10 0.01

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modules. Only one module is validated to be significant for all the three type of GO annotations. Thus, we does not list the accuracy of MoNet. The false clustering of MoNet is mostly caused by the miscalculation of betweenness. The false positive interactions can yield the incorrect shortest paths in a network and the incorrect shortest paths cause miscalculation of betweenness. Figure 3 (a), (b), and (c) illustrate the P-value distributions of the significant modules generated by all these algorithms. Since the network has a lower probability to produce the module by chance, the module is more significant with lower P-value. As observed from Figure 3, the 30 best significant modules identified by our algorithm HC-Wpin are consistently more significant than those generated by other algorithms. The comparison results in Table 2 and Figure 3 show that our algorithm HC-Wpin outperforms the other previous algorithms. Efficiency Analysis All experiments in this paper are implemented on a Linux server with 4 Intel Xeon 3.6GHz CPU and 4GByte RAM. Table 3 illustrates a comparison of the running time of our algorithm HC-Wpin and the other five algorithms for identifying functional modules. The network of S.cerevisiae (4726 proteins and 15166 interactions) and the other four networks with different confidence level obtained from [28] are used as the test data. We call the network of S.cerevisiae

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Table 3. Comparison of the running time of algorithm HC-Wpin and other algorithms

Algorithms HC-Wpin FAG-EC MCODE DPClus MoNet STM

The running time (second) Y2k Y11k Y45k Y78k NSc (988, 2455) (2401, 11000) (4687, 45000) (5321, 78390) (4726, 15166) 0.1 0.6 5.6 9.8 0.7 0.1 0.6 5.6 9.8 0.7 0.2 7.2 1037.2 4129.8 480.2 0.3 32.6 1116.4 5638.6 1194.7 2.0 88.2 6593.8 9516.2 2852.4 1.0 7944.3 62360.2 140174.8 27073.2

NSc and name the other four networks Y2k, Y11k, Y45k and Y78k, respectively, according to the number of edges included in them. From Table 3, we can see the running time of MoNet, STM, MCODE and DPClus increase sharply with the size of network. It takes more than 4,000 seconds for MCODE and DPClus, about 10,000 seconds for MoNet, and more than 100,000 seconds for STM to identify modules from the network consisting of 5,321 proteins and 78,390 interactions. However, the running time of HC-Wpin and FAG-EC detecting functional modules from the same network is still small and less than 10 seconds. As one can see, algorithm HC-Wpin is extremely fast, which is hundreds of times faster than MCODE, DPClus, MoNet and STM. As the protein-protein interactions accumulating, algorithm HC-Wpin can be used in even larger protein interaction networks.

4

Conclusions

In previous studies, the protein interaction networks are generally represented as unweighted graphs. As is well known, the protein interaction networks can not avoid of false positives. Thus, directly clustering from the unweighted graphs with high false positives, most of the previous graph clustering approaches may generate a number of false predictions. In this paper, we extend the protein interaction network from unweighted graph to weighted graph and develop a fast hierarchical clustering algorithm HC-Wpin to identify functional modules from the weighted graph. The reliability of interactions is measured by the logisticregression-based scheme [25, 26]. By changing the values of parameter λ, we can identify the functional modules in a hierarchy. We use all the three types of GO Terms to validate the identified modules of S.cerevisiae. Many significant functional modules are detected, most of which are exactly corresponding to the known complexes. For most cases, the value of λ is recommended to be between 1.0 and 3.0. When you want to get small modules, you should select a small value for λ. On the contrary, you should select a relative large value for λ to obtain modules consisting of more proteins. We also compare the performances of our algorithm HC-Wpin and the other five algorithms: MoNet, FAG-EC, MCODE, DPClus, and STM. Unexpected

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giant modules are generated by MoNet and STM which are caused by their weakness to the false positives. Although MCODE and DPClus are somewhat robust to the false positives, they are not adept at identifying hierarchically distributed functional modules. The quantitative comparison of accuracy reveal that algorithm HC-Wpin outperforms the other five algorithms. Another strength of our algorithm HC-Wpin is efficiency. It is very fast and can be applied to even larger protein interaction networks of other higher-level organisms. Acknowledgments. The authors would like to thank F. Luo and his colleagues for sharing their program of MoNet, to W. Hwang and his colleagues for sharing the source code of STM. The authors are also thankful to M. Altaf-UI-Amin and his colleagues for sharing the tool of DPClus, to G.D. Bader and C.W. Hogue for their publicity of MCODE. The authors also thank T. Shlomi for providing and discussing about the data.

Additional Files Additional file 1 — Example for hierarchical organization of functional modules. This file contains the hierarchical modules shown in Figure 2 which is available at http://bioinfo.csu.edu.cn/limin/HC-Wpin/Additional file 1.txt. Additional file 2 —Supplemental Figure 1. This file contains a supplemental Figure 1 which shows the reduction of hierarchical structure of biological process annotations for the hierarchical modules shown in Figure 2. This file is available at http://bioinfo.csu.edu.cn/limin/HC-Wpin/Additional file 2.pdf.

References 1. Uetz, P., et al.: A comprehensive analysis of protein-protein interactions in Saccharomyces cerevisiae. Nature 403, 623–627 (2000) 2. Gavin, A.C., et al.: Functional organization of the yeast proteome by systematic analysis of protein complexes. Nature 415(6868), 141–147 (2002) 3. Gavin, A.C., et al.: Proteome survey reveals modularity of the yeast cell machinery. Nature 440(7084), 631–636 (2006) 4. Ho, Y., et al.: Systematic identification of protein complexes in saccharomyces cerevisiae by mass spectrometry. Nature 415(6868), 180–183 (2002) 5. Krogan, N.J., et al.: High-definition macromolecular. composition of yeast RNAprocessing complexes. Molecular Cell 13, 225–239 (2004) 6. Krogan, N.J., et al.: Global landscape of protein complexes in the yeast Saccharomyces cerevisiae. Nature 440(7084), 637–643 (2006) 7. Harwell, L.H., Hopfield, J.J., Leibler, S., Murray, A.W.: From molecular to modular cell biology. Nature 402, c47–c52 (1999) 8. Cho, Y.R., Hwang, W., Ramanmathan, M., Zhang, A.D.: Semantic integration to identify overlapping functional modules in protein interaction networks. BMC Bioinformatics 8, 265 (2007) 9. Girvan, M., Newman, M.E.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99, 7821–7826 (2002)

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10. Rives, A.W., Galitski, T.: Modular organization of cellular networks. Proc. Natl. Acad. Sci 100, 1128–1133 (2003) 11. Ravasz, E., et al.: Hierarchical organization of modularity in metaboli networks. Science 297, 1551–1555 (2002) 12. Luo, F., Yang, Y.F., Chen, C.F., Chang, R., Zhou, J.Z.: Modular organization of protein interaction networks. Bioinformatics 23(2), 207–214 (2007) 13. Brohee, S., van Helden, J.: Evaluation of clustering algorithms for protein-protein interaction networks. BMC Bioinformatics, 7–488 (2006) 14. Spirin, V., Mirny, L.A.: Protein complexes and functional modules in molecular networks. Proc. Natl. Acad. Sci., 12123–12128 (2003) 15. Bu, D., et al.: Topological structure analysis of the protein-protein interaction networks in budding yeast. Nucleic Acid Research 31(9), 2443–2450 (2003) 16. Brun, C., et al.: Clustering proteins from interaction networks for the prediction of cellular functions. BMC Bioinformatics 7, 488 (2004) 17. Bader, G.D., Hogue, C.W.: An Automated Method for Finding Molecular Complexes in Large Protein Interaction Networks. BMC Bioinformatics 4, 2 (2003) 18. Altaf-Ul-Amin, M., Shinbo, Y., Mihara, K., Kurokawa, K., Kanaya, S.: Development and implementation of an algorithm for detection of protein complexes in large interaction networks. BMC Bioinformatics, 7–207 (2006) 19. Palla, G., Derenyi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814–818 (2005) 20. Barab´ asi, A.L., Oltvai, Z.N.: Network biology: understanding the cell’s functional organization. Nature Reviews: Genetics 5, 101–114 (2004) 21. Friedel, C., Zimmer, R.: Inferring topology from clustering coefficients in proteinprotein interaction networks. BMC Bioinformatics, 7–519 (2006) 22. Radicchi, F., et al.: Defining and identifying communities in networks. Proc. Natl. Acad. Sci. 101, 2658–2663 (2004) 23. Li, M., Wang, J.X., Chen, J.E.: A fast agglomerate algorithm for mining functional modules in protein interaction networks. In: Peng, Y., Zhang, Y. (eds.) Proceedings of the First International Conference on BioMedical Engineering and Informatics: Hainan, China, May 27-30, pp. 3–7 (2008) 24. Xenarios, I., et al.: DIP: the Database of Interaction Proteins: a research tool for studying cellular networks of protien interactions. Nucleic Acids Res. 30, 303–305 (2002) 25. Sharan, R., et al.: Conserved patterns of protein interaction in multiple species. Proc. Natl. Acad. Sci. 102(6), 1974–1979 (2005) 26. Shlomi, T., Segal, D., Ruppin, E., Sharan, R.: Qpath: a method for querying pathways in a protein-protein interaction network. BMC Bioinformatics, 7–199 (2006) 27. Hwang, W., Cho, Y.R., Zhang, A., Ramanathan, M.: A novel functional module detection algorithm for protein-protein interaction networks. Algorithms for Molecular Biology 12, 1–24 (2006) 28. von Mering, C., et al.: Comparative assessment of large-scale data sets of proteinprotein interactions. Nature 417(6887), 399–403 (2002)

Bioinformatics Challenges in Translational Research (Invited Keynote Talk) Nicholas F. Tsinoremas University of Miami Center for Computational Science University of Miami, Miami, FL 33143 [email protected]

The basic goal of translational research, from a boinformatics perspective, is to relate data acquired from basic research to an outcome in a patient. The relation of data may be following the drug discovery process, where biochemical and protein structure data is linked all the way through to data collected during the clinical trial process and onward. The relation of data can also be associate with better patient care, through techniques like data mining, where data from the research environment is combined with data from the clinical environment and used for hypothesis generation, testing and potential outcomes are implemented. Translation research also requires collaboration between various clinical investigators, physicians, scientists and teams, creating a need for secure data sharing. Inherent to the nature of translational research is the integration of data from multiple systems. Data used for research resides in EMRs, LIMSs, CTMS, and other source systems. For example at the University of Miami, The Miller school and its affiliate Institutes (e.g., Jackson Hospital), have established a number of information systems to support various operational needs. These current systems include Velos (for clinical trials management) Cerner (the Jackson EMR), MetaDatach, (UMH) and IDX. The Miller School is also in the process of implementing a EPIC EMR system. We are developing a system to address the above outlined needs and challenges. It is an integration infrastructure to support translational research, but may also be applied to other data sharing and integration needs throughout UM. The system is currently referred to as UTRIX (UM Translational Research Information eXchange). More specifically, UTRIX features a utility data storage environment (FUSE), a service oriented architecture (SOA), an organization currently referred to as the ”honest broker” (HB) to control access to data, and standard tools and educational programs to support data analysis. FUSE (Flexible Utility Storage Environment) is intended to meet the data storage needs described above. The SOA and HB together address the challenges posed by data access and authorization. FUSE, the SOA and HB together provide a context in which to make available tools and educational programs to enable the data analysis and advance data mining of research data.

I. M˘ andoiu, G. Narasimhan, and Y. Zhang (Eds.): ISBRA 2009, LNBI 5542, p. 87, 2009. c Springer-Verlag Berlin Heidelberg 2009 

Untangling Tanglegrams: Comparing Trees by Their Drawings⋆ Balaji Venkatachalam1, Jim Apple1 , Katherine St. John2 , and Dan Gusfield1 1

2

Department of Computer Science, UC Davis {balaji,apple,gusfield}@cs.ucdavis.edu Department of Mathematics and Computer Science, Lehman College, and the Graduate Center, City University of New York [email protected]

Abstract. A tanglegram is a pair of trees on the same set of leaves with matching leaves in the two trees joined by an edge. Tanglegrams are widely used in biology – to compare evolutionary histories of host and parasite species and to analyze genes of species in the same geographical area. We consider optimizations problems in tanglegram drawings. We show a linear time algorithm to decide if a tanglegram admits a planar embedding by a reduction to the planar graph drawing problem. This problem was considered by Fernau, Kauffman and Poths. (FSTTCS 2005). Our reduction method provides a simpler proof and helps to solve a conjecture they posed, showing a fixed-parameter tractable algorithm for minimizing the number of crossings over all d -ary trees. For the case where one tree is fixed, we show an O (n log n ) algorithm to determine the drawing of the second tree that minimizes the number of crossings. This improves the bound from earlier methods. We introduce a new optimization criterion using Spearman’s footrule optimization and give an O (n 2 ) algorithm. We also show integer programming formulations to quickly obtain tanglegram drawings that minimize the two optimization measures discussed. We prove lower bounds on the maximum gap between the optimal solution and the heuristic of Dwyer and Schreiber (Austral. Symp. on Info. Vis. 2004) to minimize crossings.

1 Introduction Determining the evolutionary history, or the phylogeny, of a set of species is an important problem in biology. Often represented as trees, phylogenies are used for determining ancestral species, designing vaccines, and drug discovery. [27]. The popular criteria to reconstruct an optimal tree – maximum parsimony and maximum likelihood – are NP-hard [13, 24], so heuristic methods (i.e. [17, 26]) are used that can yield many possible trees. Comparing these trees, as well as those generated on multiple genes, or for co-evolving species, is a necessary task for data analysis [22]. A visual way to compare two trees is via a tanglegram which shows the spatial relationship among the leaves. Roughly, a tanglegram consists of two trees with additional edges linking pairs of corresponding leaves (see Fig. 1 and Sect. 2). Tanglegrams are ⋆

This research was partially supported by NSF grants SEI-BIO 0513910, SEI-SBE 0513660, CCF-0515378, and IIS-0803564.

I. M˘andoiu, G. Narasimhan, and Y. Zhang (Eds.): ISBRA 2009, LNBI 5542, pp. 88–99, 2009. c Springer-Verlag Berlin Heidelberg 2009 

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Fig. 1. A tanglegram from Charleston and Perkins [6]: phylogenetic trees for lizards in the Caribbean tropics and strains of malaria found there ([6], p 86), joined by dashed lines that represent the parasite-host relationship. The crossing number is 7, and the footrule distance is 10. This is not optimal; an alternative layout which interchanges the children of nodes c and d improves these to 4 and 6, respectively. The optimal drawings have crossing number 1 and distance 2, respectively.

widely used in biology, including, to compare evolutionary histories of host and parasite species and to analyze genes of species in the same geographical area [10, 29]. The number of edge crossings in tanglegrams serves as a good measure to the extent of horizontal gene transfer, which has been inferred by viewing single layouts of tanglegrams [5, pg. 204-206]. Drawings with fewer crossings or with matching leaves close together are more useful in biological analysis. We focus on two natural measures of complexity that are used for comparing permutations: the crossing number (or Kendallτ ) and Spearman’s footrule distance [7]. The former measures the number of times edges between the leaves cross, and the latter, the sum of the distances between leaf pairs. These are widely used, including, in ranking search results on the web and in voting systems [11, 8]. We focus on the complexity of these ranking problems and give efficient algorithms for drawing tanglegrams. Crossing minimization in tanglegrams has parallels to crossing minimization in graphs [14, 19]. Computing the minimum number of crossings in a graph is NPcomplete [14]. However it can be verified in linear time that a graph has a planar drawing (with zero crossings) [16, 25]. Analogously, crossing minimization in tanglegrams is NP-complete, while the special case of planarity can be decided in linear time. Fernau et al. [12] showed this by a reduction to the upward flow problem [2]. Independently, Lozano et al. [21] showed a simple dynamic programming based solution that gives a planar drawing in O(n2 ) time. In recent work, Buchin et al. [4] showed approximation results and a fixed parameter tractable algorithm for complete tanglegrams (where every leaf has the same depth). We do not use this restriction and the results in this paper hold for arbitrary trees. N¨ollenburg et al. show some experimental results [4] and discuss an integer quadratic program for the crossing problem [23]. Bansal et al. [1] define a generalized tanglegram to allow multiple edges between leaves in the two trees.

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Our results: The case where only one tree is mutable is called the one-tree crossing minimization (OTCM) problem and has been studied for balanced trees in [9]. For arbitrary trees Fernau et al. [12] showed an O(n log2 n) solution, while Bansal et al. [1] show an O(n log2 n/ log log n) solution. We provide an algorithm that improves the time bound to O(n log n) (Sect. 3.1). Previous work on tanglegrams is limited to crossing minimization. We borrow Spearman’s footrule distance function to use as an optimization criterion here. We show an O(n2 ) solution for the one-tree fixed case (Sect. 3.2). We provide a method that has a simple intuition and allows us to use well studied solutions of graph drawing problems. Further, it leads to a simple fixed parameter tractable (FPT) algorithm. We show a linear time algorithm for planarity testing by a reduction to the planar graph drawing problem (Sect. 4.1). We can also use the fixed parameter algorithm for minimizing crossing numbers in graphs [19] to improve the running time of the FPT algorithm of Fernau et al. [12] for crossing minimization in binary trees and answer their conjecture for d-ary trees for d > 2 (Sect. 4.2). For the praxis of tanglegram drawing, we show integer programming formulations to obtain tanglegram drawings that minimize the two optimization measures discussed (Sect. 5). We also show a lower bound on the worst case behavior of the heuristic of [9].

2 Preliminaries We define tanglegrams and their drawings following [10, 12]: Let L(T ) denote the leaves of a tree T . A linear order < on L(T ) is called suitable if T can be embedded into the plane such that L(T ) is mapped onto a straight line in the order given by