Skip to main content
SpringerLink
Log in

Inferring Probabilistic Boolean Networks from Steady-State Gene Data Samples

  • Conference paper
  • First Online:
Complex Networks and Their Applications XI (COMPLEX NETWORKS 2016 2022)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1077))

Included in the following conference series:

Abstract

Probabilistic Boolean Networks have been proposed for estimating the behaviour of dynamical systems as they combine rule-based modelling with uncertainty principles. Inferring PBNs directly from gene data is challenging however, especially when data is costly to collect and/or noisy, e.g., in the case of gene expression profile data. In this paper, we present a reproducible method for inferring PBNs directly from real gene expression data measurements taken when the system was at a steady state. The steady-state dynamics of PBNs is of special interest in the analysis of biological machinery. The proposed approach does not rely on reconstructing the state evolution of the network, which is computationally intractable for larger networks. We demonstrate the method on samples of real gene expression profiling data from a well-known study on metastatic melanoma. The pipeline is implemented using Python and we make it publicly available.

Vytenis Sliogeris and Sotiris Moschoyiannis were funded by UKRI grant 77032. Thanks are due to Evangelos Chatzaroulas for his help with optimising the codebase.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 349.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 449.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 449.99
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

Notes

  1. 1.

    https://dreamchallenges.org/project/dream-3-in-silico-network-challenge/.

References

  1. Akutsu, T., et al.: Control of Boolean networks: hardness results and algorithms for tree structured networks. J. Theor. Biol. 244(4), 670–679 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Albert, R., Othmer, H.G.: The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. J. Theor. Biol. 223(1), 1–18 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Apostolopoulou, I., Marculescu, D.: Tractable learning and inference for large-scale probabilistic Boolean networks. IEEE Trans. Neur. Netw. Learn. Syst. 30(9) (2019)

    Google Scholar 

  4. Bar-Joseph, Z.: Analyzing time series gene expression data. Bioinformatics 20(16), 2493–2503 (2004)

    Article  Google Scholar 

  5. Bittner, M., et al.: Molecular classification of cutaneous malignant melanoma by gene expression profiling. Nature 406, 536–40 (2000)

    Google Scholar 

  6. Chatzaroulas, E., Sliogeris, V., Victori, P., Buffa, F.M., Moschoyiannis, S., Bauer, R.: A structural characterisation of the mitogen-activated protein kinase network in cancer. Symmetry 14(5) (2022)

    Google Scholar 

  7. Chen, Y.: Ratio-based decisions and the quantitative analysis of cDNA microarray images. J. Biomed. Opt. 2(4), 364 (1997)

    Article  Google Scholar 

  8. Ching, W.K., Zhang, M.K.N., Akutsu, T.: An approximation method for solving the steady-state probability distribution of probabilistic Boolean networks. Bioinformatics 23(12), 1511–1518 (2007)

    Article  Google Scholar 

  9. Datta, A., Choudhary, A., Bittner, M.L., Dougherty, E.: External control in markovian genetic regulatory networks. Mach. Learn. 4, 52, 3614 – 3619 (2003)

    Google Scholar 

  10. Davidich, M., Bornholdt, S.: The transition from differential equations to Boolean networks: a case study in simplifying a regulatory network model. J. Theor. Biol. 255(3), 269–77 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Fumia, H.F., Martins, M.L.: Boolean network model for cancer pathways: Predicting carcinogenesis and targeted therapy outcomes. PLoS ONE 8(7), e69008 (2013)

    Article  Google Scholar 

  12. Gawad, C., Koh, W., Quake, S.: Single-cell genome sequencing: current state of the science. Nat. Rev. Genet. 17, 175–188 (2016)

    Article  Google Scholar 

  13. Glymour, C., Zhang, K., Spirtes, P.: Review of causal discovery methods based on graphical models. Front. Gene. 10(524) (2019)

    Google Scholar 

  14. Karlsen, M.R., Moschoyiannis, S.: Evolution of control with learning classifier systems. Appl. Netw. Sci. 3(1), 1–30 (2018)

    Article  Google Scholar 

  15. Kauffman, S.A.: Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22(3), 437–467 (1969)

    Article  MathSciNet  Google Scholar 

  16. Kim, S., Dougherty, E., Bittner, M., Chen, Y., Sivakumar, K., Meltzer, P., Trent, J.: General nonlinear framework for the analysis of gene interaction via multivariate expression arrays. J. Biomed. Opt. 5, 411–24 (2000)

    Google Scholar 

  17. Kim, S., Dougherty, E.R., Chen, Y., Bittner, M., Suh, E.: Can markov chain models mimic biological regulation? J. Biol. Syst. 10 (2003)

    Google Scholar 

  18. Kobayashi, K., Hiraishi, K.: Design of probabilistic Boolean networks based on network structure and steady-state probabilities. IEEE Trans. Neur. Netw. Learn. Syst. 28(8), 1966–1971 (2017)

    Article  MathSciNet  Google Scholar 

  19. Liu, Y.Y., Slotine, J.J., Barabási, A.L.: Controllability of complex networks. Nature 473(7346), 167 (2011)

    Article  Google Scholar 

  20. Marbach, D., Prill, R.J., Schaffter, T., Mattiussi, C., Floreano, D., Stolovitzky, G.: Revealing strengths and weaknesses of methods for gene network inference. Proc. Nat. Acad. Sci. 107(14), 6286–6291 (2010)

    Article  Google Scholar 

  21. Matsumoto, H., et al.: SCODE: an efficient regulatory network inference algorithm from single-cell RNA-Seq during differentiation. Bioinformatics 33(15), 2314–2321 (2017)

    Article  Google Scholar 

  22. Melkman, A.A., Cheng, X., Ching, W.K., Akutsu, T.: Identifying a probabilistic Boolean threshold network from samples. IEEE Trans. Neur. Netw. Learn. Syst. 29(4), 869–881 (2018)

    Article  Google Scholar 

  23. Mizera, A., Pang, J., Yuan, Q.: Assa-pbn: An approximate steady-state analyser of probabilistic boolean networks. In: Automated Technology for Verification and Analysis. Springer International Publishing, Cham, pp. 214–220 (2015)

    Google Scholar 

  24. Moschoyiannis, S., Shields, M.: A set-theoretic framework for component composition. Fundamenta Informaticae 59(4), 373–396 (2004)

    MathSciNet  MATH  Google Scholar 

  25. Pal, R., Datta, A., Dougherty, E.R.: Optimal infinite-horizon control for probabilistic Boolean networks. IEEE Trans. Sign. Process. 54(6), 2375–2387 (2006)

    Article  MATH  Google Scholar 

  26. Papagiannis, G., Moschoyiannis, S.: Learning to control random Boolean networks: A deep reinforcement learning approach. In: Complex Networks 2019, Vol. 881. Springer, Cham, pp. 721–734 (2019)

    Google Scholar 

  27. Papagiannis, G., Moschoyiannis, S.: Deep reinforcement learning for control of probabilistic Boolean networks. In: Complex Networks 2020, Vol. 944. Springer, pp. 361–371 (2020)

    Google Scholar 

  28. Savvopoulos, S., Moschoyiannis, S.: Impact of removing nodes on the controllability of complex networks. In: Complex Networks (2017)

    Google Scholar 

  29. Shmulevich, I., Dougherty, E.R.: Probabilistic Boolean Networks: The Modeling and Control of Gene Regulatory Networks. SIAM (2010)

    Google Scholar 

  30. Shmulevich, I., Dougherty, E.R., Kim, S., Zhang, W.: Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 18(2), 261–74 (2002)

    Article  Google Scholar 

  31. Shmulevich, I., et al.: Steady-state analysis of genetic regulatory networks modelled by probabilistic Boolean networks. Comp. Funct. Genom. 4(6), 601–608 (2003)

    Article  Google Scholar 

  32. Silescu, A., Honavar, V.: Temporal Boolean network models of genetic networks and their inference from gene expression time series. Compl. Syst. 13(2001), 61–78 (2001)

    MathSciNet  MATH  Google Scholar 

  33. Sirin, U., Polat, F., Alhajj, R.: Employing Batch Reinforcement Learning to Control Gene Regulation Without Explicitly Constructing Gene Regulatory Networks, pp. 2042–2048 (2013)

    Google Scholar 

  34. Velarde, C., Rubio-Escudero, C., Romero-Zaliz, R.: Boolean networks: a study on microarray data discretization. In: ESTYLF08, Cuencas Mineras (Mieres-Langreo), pp. 17–19 (2008)

    Google Scholar 

  35. Voukantsis, D., Kahn, K., Hadley, M., Wilson, R., Buffa, F.M.: Modeling genotypes in their microenvironment to predict single- and multi-cellular behavior. GigaScience 8(3) (2019). https://doi.org/10.1093/gigascience/giz010

  36. Wu, Y., Shen, T.: Policy iteration algorithm for optimal control of stochastic logical dynamical systems. IEEE Trans. Neur. Netw. Learn. Syst. 29(5), 2031–2036 (2019)

    Article  MathSciNet  Google Scholar 

  37. Zhang, K., Johansson, K.H.: Efficient verification of observability and reconstructibility for large boolean control networks with special structures. IEEE Trans. Autom. Contr. 65(12), 5144–5158 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  38. Zhu, Q., Liu, Y., Lu, J., Cao, J.: Controllability and observability of Boolean control networks via sampled-data control. IEEE Trans. Control. Netw. Syst. 6(4), 1291–1301 (2019)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, University of Surrey, Guildford, UK

    Vytenis Šliogeris & Sotiris Moschoyiannis

  2. School of Computer Science and Informatics, De Montfort University, Leicester, UK

    Leandros Maglaras

Authors
  1. Vytenis Šliogeris
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leandros Maglaras
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sotiris Moschoyiannis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sotiris Moschoyiannis .

Editor information

Editors and Affiliations

  1. University of Burgundy, Dijon, France

    Hocine Cherifi

  2. Dipartimento di Fisica e Chimica Emilio Segrè, Università degli Studi Palermo, Palermo, Italy

    Rosario Nunzio Mantegna

  3. Thomas J. Watson College of Engineering and Applied Science, Binghamton University, Binghamton, NY, USA

    Luis M. Rocha

  4. IUT Lumière - Université Lyon 2, University of Lyon, Bron, France

    Chantal Cherifi

  5. Dipartimento di Fisica e Chimica Emilio Segrè, Università degli Studi Palermo, Palermo, Italy

    Salvatore Miccichè

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Šliogeris, V., Maglaras, L., Moschoyiannis, S. (2023). Inferring Probabilistic Boolean Networks from Steady-State Gene Data Samples. In: Cherifi, H., Mantegna, R.N., Rocha, L.M., Cherifi, C., Miccichè, S. (eds) Complex Networks and Their Applications XI. COMPLEX NETWORKS 2016 2022. Studies in Computational Intelligence, vol 1077. Springer, Cham. https://doi.org/10.1007/978-3-031-21127-0_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-21127-0_24

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-21126-3

  • Online ISBN: 978-3-031-21127-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation