A posterior probability approach for gene regulatory network inference in genetic perturbation data

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2016, 13(6): 1241-1251. doi: 10.3934/mbe.2016041

A posterior probability approach for gene regulatory network inference in genetic perturbation data

William Chad Young ^1, , Adrian E. Raftery ^1, and Ka Yee Yeung ^2,

1.	University of Washington, Department of Statistics, Box 354322, Seattle, WA 98195-4322, United States, United States
2.	University of Washington, Institute of Technology, Box 358426, 1900 Commerce Street, Tacoma, WA 98402-3100, United States

Received September 2015 Revised May 2016 Published August 2016

Abstract
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Inferring gene regulatory networks is an important problem in systems biology. However, these networks can be hard to infer from experimental data because of the inherent variability in biological data as well as the large number of genes involved. We propose a fast, simple method for inferring regulatory relationships between genes from knockdown experiments in the NIH LINCS dataset by calculating posterior probabilities, incorporating prior information. We show that the method is able to find previously identified edges from TRANSFAC and JASPAR and discuss the merits and limitations of this approach.

Keywords: statistics, gene regulatory network, statistical computation., Bayesian analysis.

Mathematics Subject Classification: Primary: 62P10, 92D10; Secondary: 92C4.

Citation: William Chad Young, Adrian E. Raftery, Ka Yee Yeung. A posterior probability approach for gene regulatory network inference in genetic perturbation data. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1241-1251. doi: 10.3934/mbe.2016041

References:

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[2]	K. Basso, A. A. Margolin, G. Stolovitzky, U. Klein, R. D. Favera and A. Califano, Reverse engineering of regulatory networks in human B cells,, Nature Genetics, 37 (2005), 382. doi: 10.1038/ng1532.
[3]	P. Bühlmann, M. Kalisch and L. Meier, High-dimensional statistics with a view towards applications in biology,, Annual Review of Statistics and Its Application, 1 (2014), 255.
[4]	E. Y. Chen, C. M. Tan, Y. Kou, Q. Duan, Z. Wang, G. V. Meirelles, N. R. Clark and A. Ma'ayan, Enrichr: Interactive and collaborative HTML5 gene list enrichment analysis tool,, BMC Bioinformatics, 14 (2013), 128. doi: 10.1186/1471-2105-14-128.
[5]	S. Christley, Q. Nie and X. Xie, Incorporating existing network information into gene network inference,, PLoS One, 4 (2009). doi: 10.1371/journal.pone.0006799.
[6]	M. Clyde and E. I. George, Model uncertainty,, Statistical Science, 19 (2004), 81. doi: 10.1214/088342304000000035.
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[8]	P. D'haeseleer, X. Wen, S. Fuhrman and R. Somogyi, Linear modeling of mRNA expression levels during CNS development and injury,, Pacific Symposium on Biocomputing, 4 (1999), 41. doi: 10.1142/9789814447300_0005.
[9]	C. Ding and H. Peng, Minimum redundancy feature selection from microarray gene expression data,, Bioinformatics Conference, (2003), 523. doi: 10.1109/CSB.2003.1227396.
[10]	, DREAM4 In Silico Network Challenge, website,, , ().
[11]	Q. Duan, C. Flynn, M. Niepel, M. Hafner, J. M. Muhlich, N. F. Fernandez, A. D. Rouillard, C. M. Tan, E. Y. Chen, T. R. Golub, P. K. Sorger, A. Subramanian and A. Ma'ayan, LINCS Canvas Browser: Interactive web app to query, browse and interrogate LINCS L1000 gene expression signatures,, Nucleic Acids Research, 42 (2014). doi: 10.1093/nar/gku476.
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[13]	J. J. Faith, B. Hayete, J. T. Thaden, I. Mogno, J. Wierzbowski, G. Cottarel, S. Kasif, J. J. Collins and T. S. Gardner, Large-scale mapping and validation of Escherichia coli transcriptional regulation from a compendium of expression profiles,, PLoS Biol, 5 (2007). doi: 10.1371/journal.pbio.0050008.
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[23]	S. Klamt, R. J. Flassig and K. Sundmacher, TRANSWESD: inferring cellular networks with transitive reduction,, Bioinformatics, 26 (2010), 2160. doi: 10.1093/bioinformatics/btq342.
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[28]	, Library of Integrated Network-based Cellular Signatures (LINCS), website,, , ().
[29]	K. Lo, A. E. Raftery, K. M. Dombeck, J. Zhu, E. E. Schadt, R. E. Bumgarner and K. Y. Yeung, Integrating external biological knowledge in the construction of regulatory networks from time-series expression data,, BMC Systems Biology, 6 (2012). doi: 10.1186/1752-0509-6-101.
[30]	F. M. Lopes, E. A. de Oliveira and R. M. Cesar, Inference of gene regulatory networks from time series by Tsallis entropy,, BMC Systems Biology, 5 (2011). doi: 10.1186/1752-0509-5-61.
[31]	M. J. McGeachie, H. Chang and S. T. Weiss, CGBayesNets: Conditional Gaussian Bayesian network learning and inference with mixed discrete and continuous data,, PLoS Computational Biology, 10 (2014). doi: 10.1371/journal.pcbi.1003676.
[32]	D. Marbach, T. Schaffter, C. Mattiussi and D. Floreano, Generating realistic in silico gene networks for performance assessment of reverse engineering methods,, Journal of Computational Biology, 16 (2009), 229.
[33]	D. Marbach, R. J. Prill, T. Schaffter, C. Mattiussi, D. Floreano and G. Stolovitzky, Revealing strengths and weaknesses of methods for gene network inference,, Proceedings of the National Academy of Sciences, 107 (2010), 6286. doi: 10.1073/pnas.0913357107.
[34]	A. A. Margolin, I. Nemenman, K. Basso, C. Wiggins, G. Stolovitzky, R. D. Favera and A. Califano, ARACNE: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context,, BMC Bioinformatics, 7 (2006). doi: 10.1186/1471-2105-7-S1-S7.
[35]	F. Markowetz and R. Spang, Inferring cellular networks: A review,, BMC Bioinformatics, 8 (2007). doi: 10.1186/1471-2105-8-S6-S5.
[36]	P. Menéndez, Y. Kourmpetis, C. J. ter Braak and F. A. van Eeuwijk, Gene regulatory networks from multifactorial perturbations using Graphical Lasso: Application to the DREAM4 challenge,, PLoS One, 5 (2010).
[37]	P. E. Meyer, K. Kontos, F. Lafitte and G. Bontempi, Information-theoretic inference of large transcriptional regulatory networks,, EURASIP Journal on Bioinformatics and Systems Biology, 2007 (2007). doi: 10.1155/2007/79879.
[38]	P. E. Meyer, F. Lafitte and G. Bontempi, minet: A R/Bioconductor package for inferring large transcriptional networks using mutual information,, BMC Bioinformatics, 9 (2008). doi: 10.1186/1471-2105-9-461.
[39]	G. Michailidis and F. d'Alché-Buc, Autoregressive models for gene regulatory network inference: Sparsity, stability and causality issues,, Mathematical Biosciences, 246 (2013), 326. doi: 10.1016/j.mbs.2013.10.003.
[40]	K. Murphy and S. Mian, Modelling Gene Expression Data Using Dynamic Bayesian Networks,, Vol. 104. Technical report, (1999).
[41]	A. Pinna, N. Soranzo and A. De La Fuente, From knockouts to networks: Establishing direct cause-effect relationships through graph analysis,, PLoS One, 5 (2010). doi: 10.1371/journal.pone.0012912.
[42]	A. E. Raftery, D. Madigan and J. A. Hoeting, Bayesian model averaging for linear regression models,, Journal of the American Statistical Association, 92 (1997), 179. doi: 10.1080/01621459.1997.10473615.
[43]	A. E. Raftery, Bayes factors and BIC,, Sociological Methods & Research, 27 (1999), 411.
[44]	S. Rogers and M. Girolami, A Bayesian regression approach to the inference of regulatory networks from gene expression data,, Bioinformatics, 21 (2005), 3131. doi: 10.1093/bioinformatics/bti487.
[45]	F. H. M. Salleh, M. A. Arif, S. Zainudin and M. Firdaus-Raih, Reconstructing gene regulatory networks from knockout data using Gaussian Noise Model and Pearson Correlation Coefficient,, Computational Biology and Chemistry, 59 (2015), 3.
[46]	M. Sanchez-Castillo, I. Tienda-Luna, D. Blanco, M. C. Carrion-Perez and Y. Huang, Bayesian sparse factor model for transcriptional regulatory networks inference,, Signal Processing Conference (EUSIPCO), (2013), 1.
[47]	A. Sandelin, W. Alkema, P. Engström, W. W. Wasserman and B. Lenhard, JASPAR: an open-access database for eukaryotic transcription factor binding profiles,, Nucleic Acids Research, 32 (2004).
[48]	M. Scutari, Learning Bayesian Networks with the bnlearn R Package,, Journal of Statistical Software, 35 (2010), 1.
[49]	A. Shojaie and G. Michailidis, Analysis of gene sets based on the underlying regulatory network,, Journal of Computational Biology, 16 (2009), 407. doi: 10.1089/cmb.2008.0081.
[50]	A. Shojaie and G. Michailidis, Discovering graphical Granger causality using the truncating lasso penalty,, Bioinformatics, 26 (2010). doi: 10.1093/bioinformatics/btq377.
[51]	A. Shojaie, A. Jauhiainen, M. Kallitsis and G. Michailidis, Inferring regulatory networks by combining perturbation screens and steady state gene expression profiles,, PLoS One, 9 (2014). doi: 10.1371/journal.pone.0082393.
[52]	R. Tibshirani, Regression shrinkage and selection via the lasso,, Journal of the Royal Statistical Society. Series B (Methodological), 58 (1996), 267.
[53]	V. G. Tusher, R. Tibshirani and G. Chu, Significance analysis of microarrays applied to the ionizing radiation response,, Proceedings of the National Academy of Sciences, 98 (2001), 5116.
[54]	N. Verzelen, Minimax risks for sparse regressions: Ultra-high dimensional phenomenons,, Electronic Journal of Statistics, 6 (2012), 38. doi: 10.1214/12-EJS666.
[55]	M. J. Wainwright, Sharp thresholds for high-dimensional and noisy sparsity recovery using-constrained quadratic programming (Lasso),, IEEE Transactions on Information Theory, 55 (2009), 2183. doi: 10.1109/TIT.2009.2016018.
[56]	E. Wingender, X. Chen, R. Hehl, H. Karas, I. Liebich, V. Matys, T. Meinhardt, M. Prüß, I. Reuter and F. Schacherer, TRANSFAC: an integrated system for gene expression regulation,, Nucleic Acids Research, 28 (2000), 316. doi: 10.1093/nar/28.1.316.
[57]	K. Y. Yeung, K. M. Dombeck, K. Lo, J. E. Mittler, J. Zhu, E. E. Schadt, R. E. Bumgarner and A. E. Raftery, Construction of regulatory networks using expression time-series data of a genotyped population,, Proceedings of the National Academy of Sciences, 108 (2011), 19436. doi: 10.1073/pnas.1116442108.
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show all references

References:

[1]	M. Bansal, G. Della Gatta and D. Di Bernardo, Inference of gene regulatory networks and compound mode of action from time course gene expression profiles,, Bioinformatics, 22 (2006), 815. doi: 10.1093/bioinformatics/btl003.
[2]	K. Basso, A. A. Margolin, G. Stolovitzky, U. Klein, R. D. Favera and A. Califano, Reverse engineering of regulatory networks in human B cells,, Nature Genetics, 37 (2005), 382. doi: 10.1038/ng1532.
[3]	P. Bühlmann, M. Kalisch and L. Meier, High-dimensional statistics with a view towards applications in biology,, Annual Review of Statistics and Its Application, 1 (2014), 255.
[4]	E. Y. Chen, C. M. Tan, Y. Kou, Q. Duan, Z. Wang, G. V. Meirelles, N. R. Clark and A. Ma'ayan, Enrichr: Interactive and collaborative HTML5 gene list enrichment analysis tool,, BMC Bioinformatics, 14 (2013), 128. doi: 10.1186/1471-2105-14-128.
[5]	S. Christley, Q. Nie and X. Xie, Incorporating existing network information into gene network inference,, PLoS One, 4 (2009). doi: 10.1371/journal.pone.0006799.
[6]	M. Clyde and E. I. George, Model uncertainty,, Statistical Science, 19 (2004), 81. doi: 10.1214/088342304000000035.
[7]	A. P. Dempster, N. M. Laird and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm,, Journal of the Royal Statistical Society. Series B (Methodological), 39 (1977), 1.
[8]	P. D'haeseleer, X. Wen, S. Fuhrman and R. Somogyi, Linear modeling of mRNA expression levels during CNS development and injury,, Pacific Symposium on Biocomputing, 4 (1999), 41. doi: 10.1142/9789814447300_0005.
[9]	C. Ding and H. Peng, Minimum redundancy feature selection from microarray gene expression data,, Bioinformatics Conference, (2003), 523. doi: 10.1109/CSB.2003.1227396.
[10]	, DREAM4 In Silico Network Challenge, website,, , ().
[11]	Q. Duan, C. Flynn, M. Niepel, M. Hafner, J. M. Muhlich, N. F. Fernandez, A. D. Rouillard, C. M. Tan, E. Y. Chen, T. R. Golub, P. K. Sorger, A. Subramanian and A. Ma'ayan, LINCS Canvas Browser: Interactive web app to query, browse and interrogate LINCS L1000 gene expression signatures,, Nucleic Acids Research, 42 (2014). doi: 10.1093/nar/gku476.
[12]	S. A. Dunbar, Applications of Luminex® $xMAP^{TM}$ technology for rapid, high-throughput multiplexed nucleic acid detection,, Clinica Chimica Acta, 363 (2006), 71.
[13]	J. J. Faith, B. Hayete, J. T. Thaden, I. Mogno, J. Wierzbowski, G. Cottarel, S. Kasif, J. J. Collins and T. S. Gardner, Large-scale mapping and validation of Escherichia coli transcriptional regulation from a compendium of expression profiles,, PLoS Biol, 5 (2007). doi: 10.1371/journal.pbio.0050008.
[14]	N. Friedman, M. Linial, I. Nahman and D. Pe'er, Using bayesian networks to analyze expression data,, RECOMB '00 Proceedings of the fourth annual international conference on Computational molecular biology, (2000), 127. doi: 10.1145/332306.332355.
[15]	H. Fröhlich, M. Fellmann, H. Sueltmann, A. Poustka and T.Beissbarth, Large scale statistical inference of signaling pathways from RNAi and microarray data,, BMC Bioinformatics, 8 (2007).
[16]	N. Guelzim, S. Bottani, P. Bourgine and F. Kèpés, Topological and causal structure of the yeast transcriptional regulatory network,, Nature Genetics, 31 (2002), 60. doi: 10.1038/ng873.
[17]	M. Gustafsson, M. Hörnquist, J. Lundström, J. Björkegren and J. Tegnér, Reverse engineering of gene networks with LASSO and nonlinear basis functions,, Annals of the New York Academy of Sciences, 1158 (2009), 265. doi: 10.1111/j.1749-6632.2008.03764.x.
[18]	M. Hecker, S. Lambeck, S. Toepfer, E. Someren and R. Guthke, Gene regulatory network inference: Data integration in dynamic models, A review,, Biosystems, 96 (2009), 86. doi: 10.1016/j.biosystems.2008.12.004.
[19]	J. A. Hoeting, D. Madigan, A. E. Raftery and C. T. Volinsky, Bayesian model averaging: A tutorial,, Statistical Science, 14 (1999), 382. doi: 10.1214/ss/1009212519.
[20]	R. E. Kass and A. E. Raftery, Bayes factors,, Journal of the American Statistical Association, 90 (1995), 773. doi: 10.1080/01621459.1995.10476572.
[21]	S. Y. Kim, S. Imoto and S. Miyano, Inferring gene networks from time series microarray data using dynamic Bayesian networks,, Briefings in Bioinformatics, 4 (2003), 228. doi: 10.1093/bib/4.3.228.
[22]	S. Y. Kim, S. Imoto and S. Miyano, Dynamic Bayesian network and nonparametric regression for nonlinear modeling of gene networks from time series gene expression data,, Computational Methods in Systems Biology, 2602 (2003), 104. doi: 10.1007/3-540-36481-1_9.
[23]	S. Klamt, R. J. Flassig and K. Sundmacher, TRANSWESD: inferring cellular networks with transitive reduction,, Bioinformatics, 26 (2010), 2160. doi: 10.1093/bioinformatics/btq342.
[24]	S. Lèbre, J. Becq, F. Devaus, M. Stumpf and G. Lelandais, Statistical inference of the time-varying structure of gene-regulation networks,, BMC Systems Biology, 4 (2010).
[25]	W. Lee and W. Tzou, Computational methods for discovering gene networks from expression data,, Briefings in Bioinformatics, 10 (2009), 408. doi: 10.1093/bib/bbp028.
[26]	J. Li and R. Tibshirani, Finding consistent patterns: A nonparametric approach for identifying differential expression in RNA-Seq data,, Statistical Methods in Medical Research, 22 (2013), 519. doi: 10.1177/0962280211428386.
[27]	Z. Li, P. Li, A. Krishnan and J. Liu, Large-scale dynamic gene regulatory network inference combining differential equation models with local dynamic Bayesian network analysis,, Bioinformatics, 27 (2011), 2686. doi: 10.1093/bioinformatics/btr454.
[28]	, Library of Integrated Network-based Cellular Signatures (LINCS), website,, , ().
[29]	K. Lo, A. E. Raftery, K. M. Dombeck, J. Zhu, E. E. Schadt, R. E. Bumgarner and K. Y. Yeung, Integrating external biological knowledge in the construction of regulatory networks from time-series expression data,, BMC Systems Biology, 6 (2012). doi: 10.1186/1752-0509-6-101.
[30]	F. M. Lopes, E. A. de Oliveira and R. M. Cesar, Inference of gene regulatory networks from time series by Tsallis entropy,, BMC Systems Biology, 5 (2011). doi: 10.1186/1752-0509-5-61.
[31]	M. J. McGeachie, H. Chang and S. T. Weiss, CGBayesNets: Conditional Gaussian Bayesian network learning and inference with mixed discrete and continuous data,, PLoS Computational Biology, 10 (2014). doi: 10.1371/journal.pcbi.1003676.
[32]	D. Marbach, T. Schaffter, C. Mattiussi and D. Floreano, Generating realistic in silico gene networks for performance assessment of reverse engineering methods,, Journal of Computational Biology, 16 (2009), 229.
[33]	D. Marbach, R. J. Prill, T. Schaffter, C. Mattiussi, D. Floreano and G. Stolovitzky, Revealing strengths and weaknesses of methods for gene network inference,, Proceedings of the National Academy of Sciences, 107 (2010), 6286. doi: 10.1073/pnas.0913357107.
[34]	A. A. Margolin, I. Nemenman, K. Basso, C. Wiggins, G. Stolovitzky, R. D. Favera and A. Califano, ARACNE: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context,, BMC Bioinformatics, 7 (2006). doi: 10.1186/1471-2105-7-S1-S7.
[35]	F. Markowetz and R. Spang, Inferring cellular networks: A review,, BMC Bioinformatics, 8 (2007). doi: 10.1186/1471-2105-8-S6-S5.
[36]	P. Menéndez, Y. Kourmpetis, C. J. ter Braak and F. A. van Eeuwijk, Gene regulatory networks from multifactorial perturbations using Graphical Lasso: Application to the DREAM4 challenge,, PLoS One, 5 (2010).
[37]	P. E. Meyer, K. Kontos, F. Lafitte and G. Bontempi, Information-theoretic inference of large transcriptional regulatory networks,, EURASIP Journal on Bioinformatics and Systems Biology, 2007 (2007). doi: 10.1155/2007/79879.
[38]	P. E. Meyer, F. Lafitte and G. Bontempi, minet: A R/Bioconductor package for inferring large transcriptional networks using mutual information,, BMC Bioinformatics, 9 (2008). doi: 10.1186/1471-2105-9-461.
[39]	G. Michailidis and F. d'Alché-Buc, Autoregressive models for gene regulatory network inference: Sparsity, stability and causality issues,, Mathematical Biosciences, 246 (2013), 326. doi: 10.1016/j.mbs.2013.10.003.
[40]	K. Murphy and S. Mian, Modelling Gene Expression Data Using Dynamic Bayesian Networks,, Vol. 104. Technical report, (1999).
[41]	A. Pinna, N. Soranzo and A. De La Fuente, From knockouts to networks: Establishing direct cause-effect relationships through graph analysis,, PLoS One, 5 (2010). doi: 10.1371/journal.pone.0012912.
[42]	A. E. Raftery, D. Madigan and J. A. Hoeting, Bayesian model averaging for linear regression models,, Journal of the American Statistical Association, 92 (1997), 179. doi: 10.1080/01621459.1997.10473615.
[43]	A. E. Raftery, Bayes factors and BIC,, Sociological Methods & Research, 27 (1999), 411.
[44]	S. Rogers and M. Girolami, A Bayesian regression approach to the inference of regulatory networks from gene expression data,, Bioinformatics, 21 (2005), 3131. doi: 10.1093/bioinformatics/bti487.
[45]	F. H. M. Salleh, M. A. Arif, S. Zainudin and M. Firdaus-Raih, Reconstructing gene regulatory networks from knockout data using Gaussian Noise Model and Pearson Correlation Coefficient,, Computational Biology and Chemistry, 59 (2015), 3.
[46]	M. Sanchez-Castillo, I. Tienda-Luna, D. Blanco, M. C. Carrion-Perez and Y. Huang, Bayesian sparse factor model for transcriptional regulatory networks inference,, Signal Processing Conference (EUSIPCO), (2013), 1.
[47]	A. Sandelin, W. Alkema, P. Engström, W. W. Wasserman and B. Lenhard, JASPAR: an open-access database for eukaryotic transcription factor binding profiles,, Nucleic Acids Research, 32 (2004).
[48]	M. Scutari, Learning Bayesian Networks with the bnlearn R Package,, Journal of Statistical Software, 35 (2010), 1.
[49]	A. Shojaie and G. Michailidis, Analysis of gene sets based on the underlying regulatory network,, Journal of Computational Biology, 16 (2009), 407. doi: 10.1089/cmb.2008.0081.
[50]	A. Shojaie and G. Michailidis, Discovering graphical Granger causality using the truncating lasso penalty,, Bioinformatics, 26 (2010). doi: 10.1093/bioinformatics/btq377.
[51]	A. Shojaie, A. Jauhiainen, M. Kallitsis and G. Michailidis, Inferring regulatory networks by combining perturbation screens and steady state gene expression profiles,, PLoS One, 9 (2014). doi: 10.1371/journal.pone.0082393.
[52]	R. Tibshirani, Regression shrinkage and selection via the lasso,, Journal of the Royal Statistical Society. Series B (Methodological), 58 (1996), 267.
[53]	V. G. Tusher, R. Tibshirani and G. Chu, Significance analysis of microarrays applied to the ionizing radiation response,, Proceedings of the National Academy of Sciences, 98 (2001), 5116.
[54]	N. Verzelen, Minimax risks for sparse regressions: Ultra-high dimensional phenomenons,, Electronic Journal of Statistics, 6 (2012), 38. doi: 10.1214/12-EJS666.
[55]	M. J. Wainwright, Sharp thresholds for high-dimensional and noisy sparsity recovery using-constrained quadratic programming (Lasso),, IEEE Transactions on Information Theory, 55 (2009), 2183. doi: 10.1109/TIT.2009.2016018.
[56]	E. Wingender, X. Chen, R. Hehl, H. Karas, I. Liebich, V. Matys, T. Meinhardt, M. Prüß, I. Reuter and F. Schacherer, TRANSFAC: an integrated system for gene expression regulation,, Nucleic Acids Research, 28 (2000), 316. doi: 10.1093/nar/28.1.316.
[57]	K. Y. Yeung, K. M. Dombeck, K. Lo, J. E. Mittler, J. Zhu, E. E. Schadt, R. E. Bumgarner and A. E. Raftery, Construction of regulatory networks using expression time-series data of a genotyped population,, Proceedings of the National Academy of Sciences, 108 (2011), 19436. doi: 10.1073/pnas.1116442108.
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