Abstract
Methods for exploring genetic interactions have been developed in an attempt to move beyond single gene analyses. Because biological molecules frequently participate in different processes under various cellular conditions, investigating the changes in gene coexpression patterns under various biological conditions could reveal important regulatory mechanisms. One of the methods for capturing gene coexpression dynamics, named liquid association (LA), quantifies the relationship where the coexpression between two genes is modulated by a third “coordinator” gene. This LA measure offers a natural framework for studying gene coexpression changes and has been applied increasingly to study regulatory networks among genes. With a wealth of publicly available gene expression data, there is a need to develop a meta-analytic framework for LA analysis. In this paper, we incorporated mixed effects when modeling correlation to account for between-studies heterogeneity. For statistical inference about LA, we developed a Markov chain Monte Carlo (MCMC) estimation procedure through a Bayesian hierarchical framework. We evaluated the proposed methods in a set of simulations and illustrated their use in two collections of experimental data sets. The first data set combined 10 pancreatic ductal adenocarcinoma gene expression studies to determine the role of possible coordinator gene USP9X in the Hippo pathway. The second experimental data set consisted of 907 gene expression microarray Escherichia coli experiments from multiple studies publicly available through the Many Microbe Microarray Database website (http://m3d.bu.edu/) and examined genes that coexpress with serA in the presence of coordinator gene Lrp.
References
Barrett, T., S. E. Wilhite, P. Ledoux, C. Evangelista, I. F. Kim, M. Tomashevsky, K. A. Marshall, K. H. Phillippy, P. M. Sherman, M. Holko, A. Yefanov, H. Lee, N. Zhang, C. L. Robertson, N. Serova, S. Davis and A. Soboleva (2013): “NCBI GEO: archive for functional genomics data sets–update,” Nucleic Acids Res., 41, D991–D995.10.1093/nar/gks1193Search in Google Scholar PubMed PubMed Central
Brooks, S. P. and A. Gelman (1998): “General methods for monitoring convergence of iterative simulations,” J. Comput. Graph. Stat., 7, 434–455.Search in Google Scholar
Chan, T. E., M. P. Stumpf and A. C. Babtie (2017): “Gene regulatory network inference from single-cell data using multivariate information measures,” Cell Syst., 5, 251–267.10.1016/j.cels.2017.08.014Search in Google Scholar PubMed PubMed Central
Dawson, J. A. and C. Kendziorski (2012): “An empirical bayesian approach for identifying differential coexpression in high-throughput experiments,” Biometrics, 68, 455–465.10.1111/j.1541-0420.2011.01688.xSearch in Google Scholar PubMed PubMed Central
Edgar, R., M. Domrachev and A. Lash (2002): “Gene Expression Omnibus: NCBI gene expression and hybridization array data repository,” Nucleic Acids Res., 30, 207–10.10.1093/nar/30.1.207Search in Google Scholar PubMed PubMed Central
Faith, J. J., M. E. Driscoll, V. A. Fusaro, E. J. Cosgrove, B. Hayete, F. S. Juhn, S. J. Schneider and T. S. Gardner (2007a): “Many microbe microarrays database: uniformly normalized affymetrix compendia with structured experimental metadata,” Nucleic Acids Res., 36(suppl_1), D866–D870.10.1093/nar/gkm815Search in Google Scholar PubMed PubMed Central
Faith, J. J., B. Hayete, J. T. Thaden, I. Mogno, J. Wierzbowski, G. Cottarel, S. Kasif, J. J. Collins and T. S. Gardner (2007b): “Large-scale mapping and validation of transcriptional regulation from a compendium of expression profiles,” PLoS Biol., 5, e8.10.1371/journal.pbio.0050008Search in Google Scholar PubMed PubMed Central
Gelfand, A. E. and A. F. M. Smith (1990): “Sampling-based approaches to calculating marginal densities,” J. Am. Stat. Assoc., 85, 398–409.10.21236/ADA208388Search in Google Scholar
Gelman, A. (2006): “Prior distributions for variance parameters in hierarchical models,” Bayesian Anal., 1, 515–534.Search in Google Scholar
Gelman, A. and D. Rubin (1992): “Inference from iterative simulation using multiple sequences,” Stat. Sci., 7, 457–472.10.1214/ss/1177011136Search in Google Scholar
Gunderson, T. and Y.-Y. Ho (2014): “An efficient algorithm to explore liquid association on a genome-wide scale,” BMC Bioinf., 15, 371.10.1186/s12859-014-0371-5Search in Google Scholar PubMed PubMed Central
Ho, Y.-Y., G. Parmigiani, T. Louis and L. Cope (2011): “Modeling Liquid Association,” Biometrics, 67, 133–141.10.1111/j.1541-0420.2010.01440.xSearch in Google Scholar PubMed
Ho, Y.-Y., L. Cope, M. Dettling and G. Parmigiani (2007): “Statistical methods for identifying differentially expressed gene combinations.” In: Ochs, Michael F. (eds), Gene Function Analysis, Springer Science + Business Media. pp. 171–191.10.1007/978-1-59745-547-3_10Search in Google Scholar PubMed
Ho, Y.-Y., L. M. Cope and G. Parmigiani (2014): “Modular network construction using eqtl data: an analysis of computational costs and benefits,” Front. Genet., 5, 40.10.3389/fgene.2014.00040Search in Google Scholar PubMed PubMed Central
Irizarry, R. A. (2003): “Exploration, normalization, and summaries of high density oligonucleotide array probe level data,” Biostatistics, 4, 249–264.10.1093/biostatistics/4.2.249Search in Google Scholar PubMed
Huynh-Thu, V. A., A. Irrthum, L. Wehenkel and P. Geurts (2010): “Inferring regulatory networks from expression data using tree-based methods,” PloS One, 5, e12776.10.1371/journal.pone.0012776Search in Google Scholar PubMed PubMed Central
Kanehisa, M. and S. Goto (2000): “Kyoto Encyclopedia of Genes and Genomes,” Nucleic Acids Res., 28, 27–30.10.1093/nar/28.1.27Search in Google Scholar PubMed PubMed Central
Kauffman, S., C. Peterson, B. Samuelsson and C. Troein (2003): “Random boolean network models and the yeast transcriptional network,” Proc. Natl. Acad. Sci., 100, 14796–14799.10.1073/pnas.2036429100Search in Google Scholar PubMed PubMed Central
Kayano, M., I. Takigawa, M. Shiga and K. T. H. Mamitsuka (2009): “Efficiently finding genome-wide three-way gene interactions from transcript- and genotype-data,” Bioinformatics, 25, 2735–2743.10.1093/bioinformatics/btp531Search in Google Scholar PubMed PubMed Central
Lai, Y., B. Wu, L. Chen and H. Zhao (2004): “A statistical method for identifying differential gene-gene co-expression patterns,” Bioinformatics, 20, 3146–3155.10.1093/bioinformatics/bth379Search in Google Scholar PubMed
Lambert, P. C. (2006): “Comment on article by Browne and Draper,” Bayesian Anal., 1, 543–546.10.1214/06-BA117CSearch in Google Scholar
Lappalainen, I., J. Almeida-King, V. Kumanduri, A. Senf, J. D. Spalding, S. ur Rehman, G. Saunders, J. Kandasamy, M. Caccamo, R. Leinonen, B. Vaughan, T. Laurent, F. Rowland, P. Marin-Garcia, J. Barker, P. Jokinen, A. C. Torres, J. R. de Argila, O. M. Llobet, I. Medina, M. S. Puy, M. Alberich, S. de la Torre, A. Navarro, J. Paschall and P. Flicek (2015): “The European Genome-phenome Archive of human data consented for biomedical research,” Nat. Genet., 47, 692–695.10.1038/ng.3312Search in Google Scholar PubMed PubMed Central
Li, K.-C. (2002): “Genome-wide coexpression dynamics: theory and application,” Proc. Natl. Acad. Sci. U.S.A., 99, 16875–16880.10.1073/pnas.252466999Search in Google Scholar PubMed PubMed Central
Li, K.-C. and S. Yuan (2004): “A functional genomic study on NCI’s anticancer drug screen,” Pharmacogenomics J., 4, 127–135.10.1038/sj.tpj.6500235Search in Google Scholar PubMed
Li, K.-C., C.-T. Liu, W. Sun, S. Yuan and T. Yu (2004): “A system for enhancing genome-wide coexpression dynamics study,” Proc. Natl. Acad. Sci., 101, 15561–15566.10.1073/pnas.0402962101Search in Google Scholar PubMed PubMed Central
Li, T. W.-H., J.-H. T. Ting, N. N. Yokoyama, A. Bernstein, M. van de Wetering and M. L. Waterman (2006): “Wnt activation and alternative promoter repression of LEF1 in colon cancer,” Mol. Cell. Biol., 26, 5284–5299.10.1128/MCB.00105-06Search in Google Scholar PubMed PubMed Central
Li, K.-C., A. Palotie, S. Yuan, D. Bronnikov, D. Chen, X. Wei, O.-W. Choi, J. Saarela and L. Peltonen (2007): “Finding disease candidate genes by liquid association,” Genome Biol., 8, R205.10.1186/gb-2007-8-10-r205Search in Google Scholar PubMed PubMed Central
Li, J., X. Chen, X. Ding, Y. Cheng, B. Zhao, Z.-C. Lai, K. A. Hezaimi, R. Hakem, K.-L. Guan and C. Y. Wang (2013): “LATS2 Suppresses oncogenic wnt signaling by disrupting β-catenin/BCL9 interaction,” Cell Rep., 5, 1650–1663.10.1016/j.celrep.2013.11.037Search in Google Scholar PubMed PubMed Central
Luo, J., G. D’Angelo, F. Gao, J. Ding and C. Xiong (2015): “Bivariate correlation coefficients in family-type clustered studies,” Biom. J., 57, 1084–1109.10.1002/bimj.201400131Search in Google Scholar PubMed PubMed Central
Ma, S., Q. Gong and H. J. Bohnert (2007): “An arabidopsis gene network based on the graphical gaussian model,” Genome Res., 17, 1614–1625.10.1101/gr.6911207Search in Google Scholar PubMed PubMed Central
Modi, S. R., D. M. Camacho, M. A. Kohanski, G. C. Walker and J. J. Collins (2011): “Functional characterization of bacterial srnas using a network biology approach,” Proc. Natl. Acad. Sci., 108, 15522–15527.10.1073/pnas.1104318108Search in Google Scholar PubMed PubMed Central
Nguyen, H. T., D. Andrejeva, R. Gupta, C. Choudhary, X. Hong, P. J. A. Eichhorn, A. C. Loya and S. M. Cohen (2016): “Deubiquitylating enzyme USP9x regulates hippo pathway activity by controlling angiomotin protein turnover,” Cell Discovery, 2, 16001.10.1038/celldisc.2016.1Search in Google Scholar PubMed PubMed Central
Pal, A., M. Young and N. J. Donato (2014): “Emerging potential of therapeutic targeting of ubiquitin-specific proteases in the treatment of cancer,” Cancer Res., 74, 4955–4966.10.1158/0008-5472.CAN-14-1211Search in Google Scholar PubMed
Parkinson, H., U. Sarkans, M. Shojatalab, N. Abeygunawardena, R. Coulson, S. Contrino, A. Farne, G. G. Lara, E. Holloway, M. Kapushesky, P. Lilja, G. Mukherjee, A. Oezcimen, T. Rayner, P. Rocca-Serra, A. Sharma, S. Sansone and A. Brazma (2005): “ArrayExpress–a public repository for microarray gene expression data at the EBI,” Nucleic Acids Res., 33, D553–D555.10.1093/nar/gki056Search in Google Scholar PubMed PubMed Central
Pérez-Mancera, P. A., A. G. Rust, L. van der Weyden, G. Kristiansen, A. Li, A. L. Sarver, K. Silverstein, R. Grützmann, D. Aust, P. Rümmele, T. Knösel, C. Herd, D. L. Stemple, R. Kettleborough, J. A. Brosnan and A. Li (2012): “The deubiquitinase USP9x suppresses pancreatic ductal adenocarcinoma,” Nature, 486, 266–270.10.1038/nature11114Search in Google Scholar PubMed PubMed Central
Plummer, M. (2003): “JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling.” In: Proceedings of the 3rd International Workshop on Distributed Statistical Computing.Search in Google Scholar
Qiu, P. and L. Zhang (2012): “Identification of markers associated with global changes in DNA methylation regulation in cancers,” BMC Bioinf., 13, S7.10.1186/1471-2105-13-S13-S7Search in Google Scholar PubMed PubMed Central
R Core Team (2016): R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria.Search in Google Scholar
Sippl, W., V. Collura and F. Colland (2011): “Ubiquitin-specific proteases as cancer drug targets,” Future Oncol., 7, 619–632.10.2217/fon.11.39Search in Google Scholar PubMed
Sun, W., S. Yuan and K.-C. Li (2008): “Trait-trait dynamic interaction: 2D-trait eQTL mapping for genetic variation study,” BMC Genomics, 9, 242.10.1186/1471-2164-9-242Search in Google Scholar PubMed PubMed Central
Wang, L., W. Zheng, H. Zhao and M. Deng (2013): “Statistical analysis reveals co-expression patterns of many pairs of genes in yeast are jointly regulated by interacting loci,” PLoS Genetics, 9, e1003414.10.1371/journal.pgen.1003414Search in Google Scholar PubMed PubMed Central
Zhang, J., Y. Ji and L. Zhang (2007): “Extracting three-way gene interactions from microarray data,” Bioinformatics, 23, 2903–2909.10.1093/bioinformatics/btm482Search in Google Scholar PubMed
Supplementary Material
The online version of this article offers supplementary material (DOI: https://doi.org/10.1515/sagmb-2017-0052).
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