Efficient Analysis of Homeostasis of Gene Networks with Compositional Approach

Sohei Ito, Kenji Osari, Shigeki Hagihara, Naoki Yonezaki

2017

Abstract

Homeostasis is an important property of life. Thanks to this property, living organisms keep their cellular conditions within an acceptable range to function normally. To understand mechanisms of homeostasis and analyse it, the systems biology approach is indispensable. For this purpose, we proposed a qualitative approach to model gene regulatory networks with logical formulae and formulate the homeostasis in terms of a kind of logical property – called realisability of linear temporal logic. This concise formulation of homeostasis naturally yields the method for analysing homeostasis of gene networks using realisability checkers. However, the realisability problem is well-known for its high computational complexity – double-exponential in the size of a formula – and the applicability of this approach will be limited to small gene networks, since the size of formula increases as the network does. To overcome this limitation, we leverage a compositional method to check realisability in which a formula is divided into a few sub-formulae. The difficulty in compositional approach is that we do not know how we obtain a good division. To tackle this issue, we introduce a new clustering algorithm based on a characteristic function on formulae, which calculates the size of formulae and the variation of propositions. The experimental results show that our method gives a good division to benefit from the compositional method.

References

  1. Abadi, M., Lamport, L., and Wolper, P. (1989). Realizable and unrealizable specifications of reactive systems. In ICALP 7889: Proceedings of the 16th International Colloquium on Automata, Languages and Programming, volume 372 of LNCS, pages 1-17, London, UK. Springer-Verlag.
  2. Batt, G., Salah, R. B., and Maler, O. (2007). On timed models of gene networks. In FORMATS 2007, volume 4763 of LNCS, pages 38-52.
  3. Bernot, G., Comet, J., Richard, A., and Guespin, J. (2004). Application of formal methods to biological regulatory networks: extending Thomas' asynchronous logical approach with temporal logic. J. Theor. Biol., 229(3):339-347.
  4. Bloem, R., Cimatti, A., Greimel, K., Hofferek, G., Könighofer, R., Roveri, M., Schuppan, V., and Seeber, R. (2010). RATSY - a new requirements analysis tool with synthesis. In Proceedings of the 22nd international conference on Computer Aided Verification, volume 6174 of LNCS, pages 425-429, Berlin, Heidelberg. Springer-Verlag.
  5. Bohy, A., Bruyère, V., Filiot, E., Jin, N., and Raskin, J.-F. (2012). Acacia+, a tool for LTL synthesis. In Proceedings of the 24th International Conference on Computer Aided Verification, CAV'12, pages 652-657.
  6. Ciocchetta, F. and Hillston, J. (2009). Bio-PEPA: A framework for the modelling and analysis of biological systems. Theor. Comput. Sci., 410:3065-3084.
  7. de Jong, H., Geiselmann, J., Hernandez, G., and Page, M. (2003). Genetic network analyzer: Qualitative simulation of genetic regulatory networks. Bioinformatics, 19(3):336-344.
  8. Donzé, A., Fanchon, E., Gattepaille, L. M., Maler, O., and Tracqui, P. (2011). Robustness analysis and behavior discrimination in enzymatic reaction networks. PLOS One, 6(9):e24246.
  9. Fages, F. and Rizk, A. (2008). On temporal logic constraint solving for analyzing numerical data time series. Theor. Comput. Sci., 408(1):55-65.
  10. Fages, F., Soliman, S., and Chabrier-Rivier, N. (2004). Modelling and querying interaction networks in the biochemical abstract machine BIOCHAM. J. Biol. Phys. Chem., 4:64-73.
  11. Filiot, E., Jin, N., and Raskin, J.-F. (2009). An antichain algorithm for ltl realizability. In Proceedings of the 21st International Conference on Computer Aided Verification, volume 5126 of LNCS, pages 263-277, Berlin, Heidelberg. Springer-Verlag.
  12. Filiot, E., Jin, N., and Raskin, J.-F. (2011). Antichains and compositional algorithms for LTL synthesis. Formal Methods in System Design, 39(3):261-296.
  13. Fisher, J. and Henzinger, T. (2007). Executable cell biology. Nat. Biotechnol., 25(11):1239-1249.
  14. Funahashi, A., Tanimura, N., Morohashi, M., and Kitano, H. (2003). Celldesigner: a process diagram editor for gene-regulatory and biochemical networks. BIOSILICO, 1:159-162.
  15. Heiner, M., Gilbert, D. R., and Donaldson, R. (2008). Petri nets for systems and synthetic biology. In SFM 2008, volume 5016 of LNCS, pages 215-264.
  16. Helikar, T., Kowal, B., McClenathan, S., Bruckner, M., Rowley, T., Madrahimov, A., Wicks, B., Shrestha, M., Limbu, K., and Rogers, J. A. (2012). The cell collective: Toward an open and collaborative approach to systems biology. BMC Systems Biology, 6(1):96.
  17. Ito, S., Hagihara, S., and Yonezaki, N. (2014a). A qualitative framework for analysing homeostasis in gene networks. In Proceedings of BIOINFORMATICS 2014, pages 5-16.
  18. Ito, S., Hagihara, S., and Yonezaki, N. (2015a). Formulation of homeostasis by realisability on linear temporal logic. In Plantier, G., Schultz, T., Fred, A., and Gamboa, H., editors, Biomedical Engineering Systems and Technologies: 7th International Joint Conference, BIOSTEC 2014, Angers, France, March 3-6, 2014, Revised Selected Papers, pages 149-164. Springer International Publishing, Cham. http://dx.doi.org/10.1007/978-3-319-26129-4 10.
  19. Ito, S., Ichinose, T., Shimakawa, M., Izumi, N., Hagihara, S., and Yonezaki, N. (2013). Modular analysis of gene networks by linear temporal logic. J. Integrative Bioinformatics, 10(2). http://dx.doi.org/10.2390/biecoll-jib-2013-216.
  20. Ito, S., Ichinose, T., Shimakawa, M., Izumi, N., Hagihara, S., and Yonezaki, N. (2015b). Qualitative analysis of gene regulatory networks by temporal logic. Theor. Comput. Sci., 594(23):151-179. http://dx.doi.org/10.1016/j.tcs.2015.06.017.
  21. Ito, S., Izumi, N., Hagihara, S., and Yonezaki, N. (2010). Qualitative analysis of gene regulatory networks by satisfiability checking of linear temporal logic. In Proceedings of BIBE 2010, pages 232-237. http://dx.doi.org/10.1109/BIBE.2010.45.
  22. Jobstmann, B., Galler, S., Weiglhofer, M., and Bloem, R. (2007). Anzu: a tool for property synthesis. In Proceedings of the 19th international conference on Computer aided verification, volume 4590 of LNCS, pages 258-262, Berlin, Heidelberg. Springer-Verlag.
  23. Mori, R. and Yonezaki, N. (1993). Several realizability concepts in reactive objects. In Information Modeling and Knowledge Bases IV, pages 407-424.
  24. Naldi, A., Berenguier, D., Fauré, A., Lopez, F., Thieffry, D., and Chaouiya, C. (2009). Logical modelling of regulatory networks with ginsim 2.3. Biosystems, 97:134- 139.
  25. Osari, K., Murooka, T., Hagiwara, K., Ando, T., Shimakawa, M., Ito, S., Hagihara, S., and Yonezaki, N. (2014). An object-oriented language for parameterised reactive system specification based on linear temporal logic. In Theory and Practice of Computation, pages 121-143. WORLD SCIENTIFIC.
  26. Palsson, B. (2000). The challenges of in silico biology. Nat. Biotechnol., 18:1147-50.
  27. Pnueli, A. and Rosner, R. (1989). On the synthesis of a reactive module. In POPL 7889: Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pages 179-190, New York, NY, USA. ACM.
  28. Rizk, A., Batt, G., Fages, F., and Soliman, S. (2009). A general computational method for robustness analysis with applications to synthetic gene networks. Bioinformatics, 25(12):i169-i178.
  29. Schaub, M. A., Henzinger, T. A., and Fisher, J. (2007). Qualitative networks: A symbolic approach to analyze biological signaling networks. BMC Systems Biology, 1:4.
  30. Thomas, R. (1991). Regulatory networks seen as asynchronous automata: A logical description. J. Theor. Biol., 153(1):1-23.
  31. Vanitha, V., Yamashita, K., Fukuzawa, K., and Yonezaki., N. (2000). A method for structuralisation of evolutional specifications of reactive systems. In ICSE 2000, The Third International Workshop on Intelligent Software Engineering (WISE3), pages 30 - 38.
  32. Wang, Q., Zuliani, P., Kong, S., Gao, S., and Clarke, E. M. (2015). SReach: A probabilistic bounded deltareachability analyzer for stochastic hybrid systems. In Roux, O. and Bourdon, J., editors, CMSB 2015, volume 9308 of LNCS, pages 15-27, Cham. Springer International Publishing.
  33. Zhang, Q. and Andersen, M. E. (2007). Dose response relationship in anti-stress gene regulatory networks. PLoS Comput. Biol., 3(3).
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Paper Citation


in Harvard Style

Ito S., Osari K., Hagihara S. and Yonezaki N. (2017). Efficient Analysis of Homeostasis of Gene Networks with Compositional Approach . In Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 3: BIOINFORMATICS, (BIOSTEC 2017) ISBN 978-989-758-214-1, pages 17-28. DOI: 10.5220/0006093600170028


in Bibtex Style

@conference{bioinformatics17,
author={Sohei Ito and Kenji Osari and Shigeki Hagihara and Naoki Yonezaki},
title={Efficient Analysis of Homeostasis of Gene Networks with Compositional Approach},
booktitle={Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 3: BIOINFORMATICS, (BIOSTEC 2017)},
year={2017},
pages={17-28},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006093600170028},
isbn={978-989-758-214-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 3: BIOINFORMATICS, (BIOSTEC 2017)
TI - Efficient Analysis of Homeostasis of Gene Networks with Compositional Approach
SN - 978-989-758-214-1
AU - Ito S.
AU - Osari K.
AU - Hagihara S.
AU - Yonezaki N.
PY - 2017
SP - 17
EP - 28
DO - 10.5220/0006093600170028