A Tutorial to Identify Nonlinear Associations in Gene Expression Time Series Data

Protocol
First Online:
Part of the Methods in Molecular Biology book series (MIMB, volume 1164)

Abstract

The study of gene regulatory networks is the basis to understand the biological complexity of several diseases and/or cell states. It has become the core of research in the field of systems biology. Several mathematical methods have been developed in the last decade, especially in the analysis of time series gene expression data derived from microarrays and sequencing-based methods. Most of the models available in the literature assumes linear associations among genes and do not infer directionality in these connections or uses a priori biological knowledge to set the directionality. However, in several cases, a priori biological information is not available. In this context, we describe a statistical method, namely nonlinear vector autoregressive model to estimate nonlinear relationships and also to infer directionality at the edges of the network by using the temporal information of the time series gene expression data without a priori biological information.

Key words

Regulatory network Systems biology Granger causality Vector autoregressive model Nonlinear vector autoregressive model 
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Notes

Acknowledgments

This work was supported by Genome Network Project—Japan and partially by FAPESP—Brazil.

References

  1. 1.
    Shiraki T, Kondo S, Katayama S, Waki K, Kasukawa T, Kawaji H, Kodzius R, Watahiki A, Nakamura M, Arakawa T, Fukuda S, Sasaki D, Podhajska A, Harbers M, Kawai J, Carninci P, Hayashizaki Y (2003) Cap analysis gene expression for high-throughput analysis of transcriptional starting point and identification of promoter usage. PNAS 109:15776–15781CrossRefGoogle Scholar
  2. 2.
    Mukhopadhyay ND, Chatterjee S (2007) Causality and pathway search in microarray time series experiment. Bioinformatics 23:442–449PubMedCrossRefGoogle Scholar
  3. 3.
    Fujita A, Sato JR, Garay-Malpartida HM, Sogayar MC, Ferreira CE, Miyano S (2008) Modeling nonlinear gene regulatory networks from time series gene expression data. J Bioinforma Comput Biol 6:961–979CrossRefGoogle Scholar
  4. 4.
    Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37:424–438CrossRefGoogle Scholar
  5. 5.
    Chang T, Lee C-C, Chang C-H (2013) Does insurance activity promote economic growth? Further evidence based on bootstrap panel Granger causality test. Eur J Finance (in press)Google Scholar
  6. 6.
    Hsueh S-J, Hu Y-H, Tu C-H (2013) Economic growth and financial development in Asian countries: a bootstrap panel Granger causality analysis. Econ Model 32:294–301CrossRefGoogle Scholar
  7. 7.
    Faes L, Nollo G (2013) Measuring frequency domain Granger causality for multiple blocks of interacting time series. Biol Cybern 107:217–232PubMedCrossRefGoogle Scholar
  8. 8.
    Qi R, Zhang LJ, Zhong J, Zhang Z, Ni L, Jiao Q, Liao W, Zheng G, Lu G (2013) Altered effective connectivity network of the basal ganglia in low-grade hepatic encephalopathy: a resting-state fMRI study with Granger causality analysis. PLoS One 8:e53677PubMedCentralPubMedCrossRefGoogle Scholar
  9. 9.
    Shojaie A, Michailidis G (2010) Discovering graphical Granger causality using the truncating lasso penalty. Bioinformatics 26:i517–i523PubMedCentralPubMedCrossRefGoogle Scholar
  10. 10.
    Fujita A, Sato JR, Garay-Malpartida HM, Yamaguchi R, Miyano S, Sogayar MC, Ferreira CE (2007) Modeling gene expression regulatory networks with the sparse vector autoregressive model. BMC Syst Biol 1:39PubMedCentralPubMedCrossRefGoogle Scholar
  11. 11.
    Fujita A, Sato JR, Garay-Malpartida HM, Morettin PA, Sogayar MC, Ferreira CE (2007) Time-varying modeling of gene expression regulatory networks using the wavelet dynamic vector autoregressive method. Bioinformatics 23:1623–1630PubMedCrossRefGoogle Scholar
  12. 12.
    Fujita A, Patriota AG, Sato JR, Miyano S (2009) The impact of measurement error in the identification of regulatory networks. BMC Bioinforma 10:412CrossRefGoogle Scholar
  13. 13.
    Fujita A, Sato JR, Kojima K, Gomes LR, Nagasaki M, Sogayar MC, Miyano S (2010) Identification of Granger causality between gene sets. J Bioinforma Comput Biol 8:679–701CrossRefGoogle Scholar
  14. 14.
    Fujita A, Kojima K, Patriota AG, Sato JR, Severino P, Miyano S (2010) A fast and robust statistical test based on Likelihood ratio with Bartlett correction to identify Granger causality between gene sets. Bioinformatics 26:2349–2351PubMedCrossRefGoogle Scholar
  15. 15.
    Fujita A, Severino P, Kojima K, Sato JR, Patriota AG, Miyano S (2012) Functional clustering of time series gene expression data by Granger causality. BMC Syst Biol 6:137PubMedCentralPubMedCrossRefGoogle Scholar
  16. 16.
    Baccalá LA, Sameshima K (2001) Partial directed coherence: a new concept in neural structure determination. Biol Cybern 84:463–474PubMedCrossRefGoogle Scholar
  17. 17.
    Lütkepohl H (2007) New introduction to multiple time series analysis. Springer, New YorkGoogle Scholar
  18. 18.
    Graybill FA (1976) Theory and application of the linear model. Duxbury, Belmont, CAGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Computer Science, Institute of Mathematics and StatisticsUniversity of São PauloSão PauloBrazil
  2. 2.Human Genome Center, The Institute of Medical Science, The University of TokyoMinato-kuJapan

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