Skip to main content

Overview and Evaluation of Recent Methods for Statistical Inference of Gene Regulatory Networks from Time Series Data

  • Protocol
  • First Online:
Gene Regulatory Networks

Part of the book series: Methods in Molecular Biology ((MIMB,volume 1883))

Abstract

A challenging problem in systems biology is the reconstruction of gene regulatory networks from postgenomic data. A variety of reverse engineering methods from machine learning and computational statistics have been proposed in the literature. However, deciding on the best method to adopt for a particular application or data set might be a confusing task. The present chapter provides a broad overview of state-of-the-art methods with an emphasis on conceptual understanding rather than a deluge of mathematical details, and the pros and cons of the various approaches are discussed. Guidance on practical applications with pointers to publicly available software implementations are included. The chapter concludes with a comprehensive comparative benchmark study on simulated data and a real-work application taken from the current plant systems biology.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ptashne M, Gann A (2001) Genes and signals. Cold Spring Harbor Laboratory Press, Cold Spring Harbor

    Google Scholar 

  2. Barenco M, Tomescu D, Brewer D, Callard R, Stark J, Hubank M (2006) Ranked prediction of p53 targets using hidden variable dynamic modeling. Genome Biol 7(3):R25

    Article  Google Scholar 

  3. Lawrence ND, Girolami M, Rattray M, Sanguinetti G (2010) Learning and inference in computational systems biology. MIT Press, Cambridge

    Google Scholar 

  4. Husmeier D (2003) Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks. Bioinformatics 19:2271–2282

    Article  CAS  Google Scholar 

  5. Zoppoli P, Morganella S, Ceccarelli M (2010) TimeDelay-ARACNE: reverse engineering of gene networks from time-course data by an information theoretic approach. BMC Bioinf 11:154

    Article  Google Scholar 

  6. Morrissey ER, Juárez MA, Denby KJ, Burroughs NJ (2011) Inferring the time-invariant topology of a nonlinear sparse gene regulatory network using fully Bayesian spline autoregression. Biostatistics 12(4):682–694

    Article  Google Scholar 

  7. Schäfer J, Strimmer K (2005) A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Stat Appl Genomics Mol Biol 4(1). https://doi.org/10.2202/1544-6115.1175

  8. Friedman J, Hastie T, Tibshirani R (2008) Sparse inverse covariance estimation with the graphical Lasso. Biostatistics 9:432–441

    Article  Google Scholar 

  9. Opgen-Rhein R, Strimmer K (2007) From correlation to causation networks: a simple approximate learning algorithm and its application to high-dimensional plant gene expression data. BMC Syst Biol 1(37). https://doi.org/10.1186/1752-0509-1-37

    Article  Google Scholar 

  10. Tibshirani R (1995) Regression shrinkage and selection via the Lasso. J R Stat Soc Ser B (Methodol) 58(1):267–288

    Google Scholar 

  11. Hastie T, Tibshirani R, Friedman JJH (2009) The elements of statistical learning. Springer, New York

    Book  Google Scholar 

  12. Zou H, Hastie T (2005) Regularization and variable selection via the Elastic Net. J R Stat Soc Ser B (Stat Methodol) 67(2):301–320

    Article  Google Scholar 

  13. Ahmed A, Xing EP (2009) Recovering time-varying networks of dependencies in social and biological studies. Proc Natl Acad Sci 106:11878–11883

    Article  CAS  Google Scholar 

  14. Grzegorczyk M, Husmeier D (2012) A non-homogeneous dynamic Bayesian network with sequentially coupled interaction parameters for applications in systems and synthetic biology. Stat Appl Genet Mol Biol 11(4). Article 7

    Google Scholar 

  15. Bishop CM (2006) Pattern recognition and machine learning. Springer, Singapore

    Google Scholar 

  16. Tipping M (2001) Spare Bayesian learning and the relevance vector machine. J Mach Learn Res 1:211–244

    Google Scholar 

  17. Rogers S, Girolami M (2005) A Bayesian regression approach to the inference of regulatory networks from gene expression data. Bioinformatics 21(14):3131–3137

    Article  CAS  Google Scholar 

  18. Murphy KP (2012) Machine learning: a probabilistic perspective. MIT Press, Cambridge

    Google Scholar 

  19. Smith M, Kohn R (1996) Nonparametric regression using Bayesian variable selection. J Econom 75:317–343

    Article  Google Scholar 

  20. Beal M, Falciani F, Ghahramani Z, Rangel C, Wild D (2005) A Bayesian approach to reconstructing genetic regulatory networks with hidden factors. Bioinformatics 21(3):349–356

    Article  CAS  Google Scholar 

  21. Beal M (2003) Variational algorithms for approximate Bayesian inference. PhD thesis, Gatsby Computational Neuroscience Unit, University College London, London

    Google Scholar 

  22. Rasmussen C, Williams C (2006) Gaussian processes for machine learning, vol 1. MIT Press, Cambridge

    Google Scholar 

  23. Äijö T, Lähdesmäki H (2009) Learning gene regulatory networks from gene expression measurements using non-parametric molecular kinetics. Bioinformatics 25(22):2937–2944

    Article  Google Scholar 

  24. Ko Y, Zhai C, Rodriguez-Zas S (2007) Inference of gene pathways using Gaussian mixture models. In: International conference on bioinformatics and biomedicine, Fremont, pp 362–367

    Google Scholar 

  25. Ko Y, Zhai C, Rodriguez-Zas S (2009) Inference of gene pathways using mixture Bayesian networks. BMC Syst Biol 3:54

    Article  Google Scholar 

  26. Geiger D, Heckerman D (1994) Learning Gaussian networks. In: International conference on uncertainty in artificial intelligence. Morgan Kaufmann Publishers, San Francisco, pp 235–243

    Google Scholar 

  27. Aderhold A, Husmeier D, Grzegorczyk M (2017) Approximate Bayesian inference in semi-mechanistic models. Stat Comput 27(4):1003–1040

    Article  Google Scholar 

  28. Oates CJ, Dondelinger F, Bayani N, Korkola J, Gray JW, Mukherjee S (2014) Causal network inference using biochemical kinetics. Bioinformatics 30(17):i468–i474

    Article  CAS  Google Scholar 

  29. Pokhilko A, Hodge S, Stratford K, Knox K, Edwards K, Thomson A, Mizuno T, Millar A (2010) Data assimilation constrains new connections and components in a complex, eukaryotic circadian clock model. Mol Syst Biol 6(1):416

    PubMed  PubMed Central  Google Scholar 

  30. Pokhilko A, Fernández A, Edwards K, Southern M, Halliday K, Millar A (2012) The clock gene circuit in Arabidopsis includes a repressilator with additional feedback loops. Mol Syst Biol 8:574

    Article  Google Scholar 

  31. Marin JM, Robert CP (2007) Bayesian core: a practical approach to computational Bayesian statistics. Springer, New York

    Google Scholar 

  32. Chib S, Jeliazkov I (2001) Marginal likelihood from the Metropolis–Hastings output. J Am Stat Assoc 96(453):270–281

    Article  Google Scholar 

  33. Holsclaw T, Sansó B, Lee HK, Heitmann K, Habib S, Higdon D, Alam U (2013) Gaussian process modeling of derivative curves. Technometrics 55(1):57–67

    Article  Google Scholar 

  34. Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. MIT Press, Cambridge

    Google Scholar 

  35. Friedman J, Hastie T, Tibshirani R (2010) Regularization paths for generalized linear models via coordinate descent. J Stat Softw 33(1): 1–22

    Article  Google Scholar 

  36. Brooks S, Gelman A (1999) General methods for monitoring convergence of iterative simulations. J Comput Graph Stat 7:434–455

    Google Scholar 

  37. Gelman A, Rubin D (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7:457–472

    Article  Google Scholar 

  38. Tipping M, Faul A, et al (2003) Fast marginal likelihood maximisation for sparse Bayesian models. In: International workshop on artificial intelligence and statistics, vol 1, pp 3–6

    Google Scholar 

  39. Aderhold A, Husmeier D, Grzegorczyk M (2014) Statistical inference of regulatory networks for circadian regulation. Stat Appl Genet Mol Biol 13(3):227–273

    Article  CAS  Google Scholar 

  40. Nabney I (2002) NETLAB: algorithms for pattern recognition. Springer, Berlin

    Google Scholar 

  41. Locke JCW, Kozma-Bognár L, Gould PD, Fehér B, Kevei E, Nagy F, Turner MS, Hall A, Millar AJ (2006) Experimental validation of a predicted feedback loop in the multi-oscillator clock of Arabidopsis thaliana. Mol Syst Biol 2(59). https://doi.org/10.1038/msb4100102

  42. Pokhilko A, Mas P, Millar AJ, et al (2013) Modelling the widespread effects of TOC1 signalling on the plant circadian clock and its outputs. BMC Syst Biol 7(1):1–12

    Article  Google Scholar 

  43. Trejo-Banos D, Millar AJ, Sanguinetti G (2015) A Bayesian approach for structure learning in oscillating regulatory networks. Bioinformatics 31:3617–3624

    PubMed  PubMed Central  Google Scholar 

  44. Guerriero M, Pokhilko A, Fernández A, Halliday K, Millar A, Hillston J (2012) Stochastic properties of the plant circadian clock. J R Soc Interface 9(69):744–756

    Article  CAS  Google Scholar 

  45. Wilkinson DJ (2009) Stochastic modelling for quantitative description of heterogeneous biological systems. Nat Rev Genet 10(2): 122–133

    Article  CAS  Google Scholar 

  46. Wilkinson D (2011) Stochastic modelling for systems biology, vol 44. CRC Press, Boca Raton

    Google Scholar 

  47. Ciocchetta F, Hillston J (2009) Bio-PEPA: a framework for the modelling and analysis of biological systems. Theor Comput Sci 410(33):3065–3084

    Article  Google Scholar 

  48. Gillespie D (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25):2340–2361

    Article  CAS  Google Scholar 

  49. Flis A, Fernández AP, Zielinski T, Mengin V, Sulpice R, Stratford K, Hume A, Pokhilko A, Southern MM, Seaton DD, McWatters HG, Stitt M, Halliday KJ, Millar AJ (2015) Defining the robust behaviour of the plant clock gene circuit with absolute RNA timeseries and open infrastructure. Open Biol 5(10):150042. https://doi.org/10.1098/rsob.150042

    Article  Google Scholar 

  50. Edwards K, Akman O, Knox K, Lumsden P, Thomson A, Brown P, Pokhilko A, Kozma-Bognar L, Nagy F, Rand D, et al (2010) Quantitative analysis of regulatory flexibility under changing environmental conditions. Mol Syst Biol 6(1):424

    PubMed  PubMed Central  Google Scholar 

  51. Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143(1):29–36

    Article  CAS  Google Scholar 

  52. Davis J, Goadrich M (2006) The relationship between precision-recall and ROC curves. In: Proceedings of the 23rd international conference on machine learning (ICML). ACM, New York, pp 233–240

    Google Scholar 

  53. Marbach D, Costello JC, Küffner R, Vega NM, Prill RJ, Camacho DM, Allison KR, Kellis M, Collins JJ, Stolovitzky G, et al (2012) Wisdom of crowds for robust gene network inference. Nat Methods 9(8): 796–804

    Article  CAS  Google Scholar 

  54. Rasmussen CE (1996) Evaluation of Gaussian processes and other methods for non-linear regression. PhD thesis, Citeseer

    Google Scholar 

  55. Rasmussen CE, Neal RM, Hinton GE, van Camp D, Revow M, Ghahramani Z, Kustra R, Tibshirani R (1996) The DELVE repository was developed as part of a PhD thesis, which could be cited as an alternative to the technical report: Carl Edward Rasmussen Evaluation of Gaussian Processes and other Methods for Non-Linear Regression PhD thesis University of Toronto

    Google Scholar 

  56. Brandt S (1999) Data analysis: statistical and computational methods for scientists and engineers. Springer, New York

    Book  Google Scholar 

  57. Neuneier R, Hergert F, Finnoff W, Ormoneit D (1994) Estimation of conditional densities: a comparison of neural network approaches. In: International conference on artificial neural networks. Springer, Berlin, pp 689–692

    Google Scholar 

  58. Mockler T, Michael T, Priest H, Shen R, Sullivan C, Givan S, McEntee C, Kay S, Chory J (2007) The DIURNAL project: DIURNAL and circadian expression profiling, model-based pattern matching, and promoter analysis. In: Cold Spring Harbor symposia on quantitative biology, vol 72. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, pp 353–363

    Google Scholar 

  59. Fogelmark K, Troein C (2014) Rethinking transcriptional activation in the Arabidopsis circadian clock. PLoS Comput Biol 10(7):e1003705

    Article  Google Scholar 

  60. Grzegorczyk M, Aderhold A, Husmeier D (2015) Inferring bi-directional interactions between circadian clock genes and metabolism with model ensembles. Stat Appl Genet Mol Biol 14(2):143–167

    Article  Google Scholar 

  61. Locke JCW, Southern MM, Kozma-Bognár L, Hibberd V, Brown PE, Turner MS, Millar AJ (2005) Extension of a genetic network model by iterative experimentation and mathematical analysis. Mol Syst Biol 1(1)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dirk Husmeier .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Science+Business Media, LLC, part of Springer Nature

About this protocol

Check for updates. Verify currency and authenticity via CrossMark

Cite this protocol

Grzegorczyk, M., Aderhold, A., Husmeier, D. (2019). Overview and Evaluation of Recent Methods for Statistical Inference of Gene Regulatory Networks from Time Series Data. In: Sanguinetti, G., Huynh-Thu, V. (eds) Gene Regulatory Networks. Methods in Molecular Biology, vol 1883. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-8882-2_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4939-8882-2_3

  • Published:

  • Publisher Name: Humana Press, New York, NY

  • Print ISBN: 978-1-4939-8881-5

  • Online ISBN: 978-1-4939-8882-2

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics