Finding Common Modules in a Time-Varying Network with Application to the Drosophila Melanogaster Gene Regulation Network

ABSTRACT Finding functional modules in gene regulation networks is an important task in systems biology. Many methods have been proposed for finding communities in static networks; however, the application of such methods is limited due to the dynamic nature of gene regulation networks. In this article, we first propose a statistical framework for detecting common modules in the Drosophila melanogaster time-varying gene regulation network. We then develop both a significance test and a robustness test for the identified modular structure. We apply an enrichment analysis to our community findings, which reveals interesting results. Moreover, we investigate the consistency property of our proposed method under a time-varying stochastic block model framework with a temporal correlation structure. Although we focus on gene regulation networks in our work, our method is general and can be applied to other time-varying networks. Supplementary materials for this article are available online.

[1]  P. Newbold,et al.  Estimation and Prediction , 1985 .

[2]  P. Bickel,et al.  A nonparametric view of network models and Newman–Girvan and other modularities , 2009, Proceedings of the National Academy of Sciences.

[3]  Jean-Loup Guillaume,et al.  Fast unfolding of communities in large networks , 2008, 0803.0476.

[4]  T. Snijders,et al.  Estimation and Prediction for Stochastic Blockstructures , 2001 .

[5]  A. Raftery,et al.  Model‐based clustering for social networks , 2007 .

[6]  M. Newman,et al.  Finding community structure in networks using the eigenvectors of matrices. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Pablo Tamayo,et al.  Gene set enrichment analysis: A knowledge-based approach for interpreting genome-wide expression profiles , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Lamellocitáira Jellemz,et al.  Drosophila Melanogaster , 1944, Nature.

[9]  Mike Tyers,et al.  Systematic Identification of Pathways That Couple Cell Growth and Division in Yeast , 2002, Science.

[10]  B. S. Baker,et al.  Gene Expression During the Life Cycle of Drosophila melanogaster , 2002, Science.

[11]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[12]  Purnamrita Sarkar,et al.  Hypothesis testing for automated community detection in networks , 2013, ArXiv.

[13]  Nam P. Nguyen,et al.  Dynamic Social Community Detection and Its Applications , 2014, PloS one.

[14]  D. Pe’er,et al.  Module networks: identifying regulatory modules and their condition-specific regulators from gene expression data , 2003, Nature Genetics.

[15]  Bin Yu,et al.  Spectral clustering and the high-dimensional stochastic blockmodel , 2010, 1007.1684.

[16]  J. Reichardt,et al.  Statistical mechanics of community detection. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Le Song,et al.  KELLER: estimating time-varying interactions between genes , 2009, Bioinform..

[18]  C. Lee Giles,et al.  Efficient identification of Web communities , 2000, KDD '00.

[19]  Edward A. Bender,et al.  The Asymptotic Number of Labeled Graphs with Given Degree Sequences , 1978, J. Comb. Theory A.

[20]  Guoyan Zhao,et al.  Identification of muscle-specific regulatory modules in Caenorhabditis elegans. , 2007, Genome research.

[21]  J. Doye,et al.  Identifying communities within energy landscapes. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Edoardo M. Airoldi,et al.  Mixed Membership Stochastic Blockmodels , 2007, NIPS.

[23]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[24]  Michael Ashburner,et al.  Annotation of the Drosophila melanogaster euchromatic genome: a systematic review , 2002, Genome Biology.

[25]  C. Nichols,et al.  Human Disease Models in Drosophila melanogaster and the Role of the Fly in Therapeutic Drug Discovery , 2011, Pharmacological Reviews.

[26]  Leon Danon,et al.  Comparing community structure identification , 2005, cond-mat/0505245.

[27]  Evangelos Kranakis,et al.  Advances in Network Analysis and its Applications , 2012 .

[28]  Ulrik Brandes,et al.  On Modularity Clustering , 2008, IEEE Transactions on Knowledge and Data Engineering.

[29]  Mason A. Porter,et al.  Robust Detection of Dynamic Community Structure in Networks , 2012, Chaos.

[30]  R. Guimerà,et al.  Modularity from fluctuations in random graphs and complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Natali Gulbahce,et al.  The art of community detection , 2008, BioEssays : news and reviews in molecular, cellular and developmental biology.

[32]  Ken Wakita,et al.  Finding community structure in mega-scale social networks: [extended abstract] , 2007, WWW '07.

[33]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  M. Newman,et al.  Finding community structure in very large networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Sanjukta Bhowmick,et al.  Fast Community Detection for Dynamic Complex Networks , 2011, CompleNet.

[36]  Jiashun Jin,et al.  FAST COMMUNITY DETECTION BY SCORE , 2012, 1211.5803.

[37]  Jingfei Zhang,et al.  A hypothesis testing framework for modularity based network community detection , 2017 .

[38]  F. Chung,et al.  Connected Components in Random Graphs with Given Expected Degree Sequences , 2002 .

[39]  Ji Zhu,et al.  Consistency of community detection in networks under degree-corrected stochastic block models , 2011, 1110.3854.

[40]  Albert Y. Kim,et al.  Hypothesis Testing , 2019, Encyclopedic Dictionary of Archaeology.

[41]  Jukka-Pekka Onnela,et al.  Community Structure in Time-Dependent, Multiscale, and Multiplex Networks , 2009, Science.

[42]  Charles A Tilford,et al.  Gene set enrichment analysis. , 2009, Methods in molecular biology.

[43]  M Gribskov,et al.  A systematic analysis of human disease-associated gene sequences in Drosophila melanogaster. , 2001, Genome research.

[44]  Sui Huang,et al.  Empirical Multiscale Networks of Cellular Regulation , 2007, PLoS Comput. Biol..

[45]  Béla Bollobás,et al.  A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs , 1980, Eur. J. Comb..

[46]  Jing Wang,et al.  WEB-based GEne SeT AnaLysis Toolkit (WebGestalt): update 2013 , 2013, Nucleic Acids Res..

[47]  M. Newman.  Analysis of weighted networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.