Advertisement

Formal Aspects of Computing

, Volume 31, Issue 1, pp 27–46 | Cite as

GPU-accelerated steady-state computation of large probabilistic Boolean networks

  • Andrzej Mizera
  • Jun PangEmail author
  • Qixia Yuan
Original Article
  • 21 Downloads

Abstract

Computation of steady-state probabilities is an important aspect of analysing biological systems modelled as probabilistic Boolean networks (PBNs). For small PBNs, efficient numerical methods to compute steady-state probabilities of PBNs exist, based on the Markov chain state-transition matrix. However, for large PBNs, numerical methods suffer from the state-space explosion problem since the state-space size is exponential in the number of nodes in a PBN. In fact, the use of statistical methods and Monte Carlo methods remain the only feasible approach to address the problem for large PBNs. Such methods usually rely on long simulations of a PBN. Since slow simulation can impede the analysis, the efficiency of the simulation procedure becomes critical. Intuitively, parallelising the simulation process is the ideal way to accelerate the computation. Recent developments of general purpose graphics processing units (GPUs) provide possibilities to massively parallelise the simulation process. In this work, we propose a trajectory-level parallelisation framework to accelerate the computation of steady-state probabilities in large PBNs with the use of GPUs. To maximise the computation efficiency on a GPU, we develop a dynamical data arrangement mechanism for handling different size PBNs with a GPU. Specially, we propose a reorder-and-split method to handle both large and dense PBNs. Besides, we develop a specific way of storing predictor functions of a PBN and the state of the PBN in the GPU memory. Moreover, we introduce a strongly connected component (SCC)-based network reduction technique to further accelerate the computation speed. Experimental results show that our GPU-based parallelisation gains approximately a 600-fold speedup for a real-life PBN compared to the state-of-the-art sequential method.

Keywords

Probabilistic Boolean networks Biological networks Computational modelling Discrete-time Markov chains Simulation Statistical methods Graphics processing unit (GPU) 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

We would like to thank the anonymous referees who read carefully the previous versions of this paper and gave a lot of valuable comments. Those comments helped us to greatly improve the quality of our paper both in content and presentation. Qixia Yuan was supported by the National Research Fund, Luxembourg (Grant 7814267). Jun Pang was partially supported by the project SEC-PBN (funded by the University of Luxembourg) and the ANR-FNR Project AlgoReCell (INTER/ANR/15/11191283). Andrzej Mizera contributed to this work while holding a postdoctoral researcher position at the Computer Science and Communications Research Unit, University of Luxembourg.

References

  1. GR92.
    Gelman A, Rubin DB (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7(4): 457–472CrossRefzbMATHGoogle Scholar
  2. HSIO06.
    Lähdesmäki H, Hautaniemi S, Shmulevich I, Yli-Harja O (2006) Relationships between probabilistic Boolean networks and dynamic Bayesian networks as models of gene regulatory networks. Signal Process 86(4): 814–834CrossRefzbMATHGoogle Scholar
  3. Kau69.
    Kauffman SA (1969) Homeostasis and differentiation in random genetic control networks. Nature 224: 177–178CrossRefGoogle Scholar
  4. MPY15a.
    Mizera A, Pang J, Yuan J (2015) ASSA-PBN: An approximate steady-state analyser of probabilistic Boolean networks. In: Proceedings of 13th international symposium on automated technology for verification and analysis, volume 9364 of LNCS. Springer, pp 214–220Google Scholar
  5. MPY15b.
    Mizera A, Pang J, Yuan Q (2015) Reviving the two-state markov chain approach (technical report). http://arxiv.org/abs/1501.01779
  6. MPY16a.
    Mizera A, Pang J, Yuan Q (2016) ASSA-PBN 2.0: A software tool for probabilistic Boolean networks. In: Proceedings of 14th international conference on computational methods in systems biology, volume 9859 of LNCS. Springer, pp 309–315Google Scholar
  7. MPY16b.
    Mizera A, Pang J, Yuan Q (2016) Fast simulation of probabilistic Boolean networks. In: Proceedings of 14th international conference on computational methods in systems biology, volume 9859 of LNCS. Springer, pp 216–231Google Scholar
  8. MPY16c.
    Mizera A, Pang J, Yuan Q (2016) GPU-accelerated steady-state computation of large probabilistic Boolean networks. In: Proceedings of 2nd international symposium on dependable software engineering: theories, tools, and applications, volume 9984 of LNCS. Springer, pp 50–66Google Scholar
  9. MPY16d.
    Mizera A, Pang J, Yuan Q (2016) Parallel approximate steady-state analysis of large probabilistic Boolean networks. In: Proceedings of 31st ACM symposium on applied computing, pp 1–8Google Scholar
  10. MPY17.
    Mizera A, Pang J, Yuan Q (2017) Reviving the two-state Markov chain approach. In: IEEE/ACM transactions on computational biology and bioinformaticsGoogle Scholar
  11. RL92.
    Raftery AE, Lewis S (1992) How many iterations in the Gibbs sampler ?. Bayesian Stat 4: 763–773Google Scholar
  12. SD10.
    Shmulevich I, Dougherty ER (2010) Probabilistic Boolean networks: the modeling and control of gene regulatory networks. SIAM Press, AucklandCrossRefzbMATHGoogle Scholar
  13. SDKZ02.
    Shmulevich I, Dougherty ER, Kim S, Zhang W (2002) Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 18(2): 261–274CrossRefGoogle Scholar
  14. SGH+03.
    Shmulevich I, Gluhovsky I, Hashimoto RF, Dougherty ER, Zhang W (2003) Steady-state analysis of genetic regulatory networks modelled by probabilistic Boolean networks. Comp Funct Genom 4(6): 601–608CrossRefGoogle Scholar
  15. SSV+09.
    Schlatter R, Schmich K, Vizcarra IA, Scheurich P, Sauter T, Borner C, Ederer M, Merfort I, Sawodny O (2009) ON/OFF and beyond—a Boolean model of apoptosis. PLOS Comput Biol 5(12): e1000595CrossRefGoogle Scholar
  16. TMP+13.
    Trairatphisan P, Mizera A, Pang J, Tantar A-A, Schneider J, Sauter T (2013) Recent development and biomedical applications of probabilistic Boolean networks. Cell Commun Signal 11: 46CrossRefGoogle Scholar
  17. TMP+14.
    Trairatphisan P, Mizera A, Pang J, Tantar A-A, Sauter T (2014) optPBN: An optimisation toolbox for probabilistic boolean networks. PLoS ONE 9(7): e98001CrossRefGoogle Scholar

Copyright information

© British Computer Society 2018

Authors and Affiliations

  1. 1.Department of Infection and ImmunityLuxembourg Institute of HealthEsch-sur-AlzetteLuxembourg
  2. 2.Luxembourg Centre for Systems BiomedicineUniversity of LuxembourgEsch-sur-AlzetteLuxembourg
  3. 3.Faculty of Science, Technology and Communication and Interdisciplinary Centre for SecurityReliability and Trust University of LuxembourgEsch-sur-AlzetteLuxembourg
  4. 4.Faculty of Science, Technology and CommunicationUniversity of LuxembourgEsch-sur-AlzetteLuxembourg

Personalised recommendations