Abstract
Toward the system level understanding of the mechanisms contributing homeostasis in organisms, a computational framework to model a system and analyse its properties is indispensable. We propose a novel formalism to model and analyse homeostasis on gene networks. Since gene networks can be considered as reactive systems which respond to environmental input, we reduce the problem of analysing gene networks to that of verifying reactive system specifications. Based on this reduction, we formulate homeostasis as realisability of reactive system specifications. An advantage of this formulation is that we can consider any input sequence over time and any number of inputs, which are difficult to be captured by quantitative models. We demonstrate the usefulness and flexibility of our framework in analysing a number of small but tricky networks.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Although the same symbols (i.e. \(x_y\) and \(y_x\)) are used to represent both thresholds and propositions, we can clearly distinguish them from the context.
- 2.
- 3.
We have ‘\( on \)’ propositions for each node and threshold propositions for each edge.
References
Abadi, M., Lamport, L., Wolper, P.: Realizable and unrealizable specifications of reactive systems. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372, pp. 1–17. Springer, Heidelberg (1989)
Aoshima, T., Sakuma, K., Yonezaki, N.: An efficient verification procedure supporting evolution of reactive system specifications. In: Proceedings of the 4th International Workshop on Principles of Software Evolution, IWPSE 2001, pp. 182–185. ACM, New York (2001)
Barringer, H.: Up and down the temporal way. Comput. J. 30(2), 134–148 (1987)
Barringer, H., Kuiper, R., Pnueli, A.: Now you may compose temporal logic specifications. In: Proceedings of the Sixteenth Annual ACM Symposium on Theory of Computing, STOC 1984, pp. 51–63. ACM, New York (1984)
Batt, G., Ropers, D., de Jong, H., Geiselmann, J., Mateescu, R., Page, M., Schneider, D.: Validation of qualitative models of genetic regulatory networks by model checking: analysis of the nutritional stress response in Escherichia coli. Bioinformatics 21(suppl. 1), i19–i28 (2005)
Bernot, G., Comet, J., Richard, A., Guespin, J.: Application of formal methods to biological regulatory networks: extending Thomas’ asynchronous logical approach with temporal logic. J. Theor. Biol. 229(3), 339–347 (2004)
Bloem, R., Cimatti, A., Greimel, K., Hofferek, G., Könighofer, R., Roveri, M., Schuppan, V., Seeber, R.: RATSY – a new requirements analysis tool with synthesis. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 425–429. Springer, Heidelberg (2010)
Emerson, E.A.: Temporal and modal logic. In: Handbook of Theoretical Computer Science. Formal Models and Sematics (B), vol. B, pp. 995–1072. MIT Press, Cambridge (1990)
Fages, F., Soliman, S., Chabrier-Rivier, N.: Modelling and querying interaction networks in the biochemical abstract machine BIOCHAM. J. Biol. Phys. Chem. 4, 64–73 (2004)
Filiot, E., Jin, N., Raskin, J.-F.: An antichain algorithm for LTL realizability. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 263–277. Springer, Heidelberg (2009)
Hagihara, S., Kitamura, Y., Shimakawa, M., Yonezaki, N.: Extracting environmental constraints to make reactive system specifications realizable. In: Proceedings of the 2009 16th Asia-Pacific Software Engineering Conference, APSEC 2009, pp. 61–68. IEEE Computer Society, Washington, DC (2009)
Hagihara, S., Yonezaki, N.: Completeness of verification methods for approaching to realizable reactive specifications. In: Completeness of Verification Methods for Approaching to Realizable Reactive Specifications, vol. 348, pp. 242–257 (2006)
Ito, S., Ichinose, T., Shimakawa, M., Izumi, N., Hagihara, S., Yonezaki, N.: Modular analysis of gene networks by linear temporal logic. J. Integr. Bioinform. 10(2), 216 (2013)
Ito, S., Ichinose, T., Shimakawa, M., Izumi, N., Hagihara, S., Yonezaki, N.: Qualitative analysis of gene regulatory networks using network motifs. In: Proceedings of the 4th International Conference on Bioinformatics Models, Methods and Algorithms (BIOINFORMATICS 2013), pp. 15–24 (2013)
Ito, S., Izumi, N., Hagihara, S., Yonezaki, N.: Qualitative analysis of gene regulatory networks by satisfiability checking of linear temporal logic. In: Proceedings of the 10th IEEE International Conference on Bioinformatics & Bioengineering, pp. 232–237 (2010)
Jobstmann, B., Bloem, R.: Optimizations for LTL synthesis. In: Proceedings of the Formal Methods in Computer Aided Design, FMCAD 2006, pp. 117–124. IEEE Computer Society, Washington, DC (2006)
Jobstmann, B., Galler, S., Weiglhofer, M., Bloem, R.: Anzu: a tool for property synthesis. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 258–262. Springer, Heidelberg (2007)
de Jong, H., Geiselmann, J., Hernandez, G., Page, M.: Genetic network analyzer: qualitative simulation of genetic regulatory networks. Bioinformatics 19(3), 336–344 (2003)
Mori, R., Yonezaki, N.: Several realizability concepts in reactive objects. In: Information Modeling and Knowledge Bases IV, pp. 407–424 (1993)
Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: POPL 1989: Proceedings of the 16th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 179–190. ACM, New York (1989)
Tomita, T., Hagihara, S., Yonezaki, N.: A probabilistic temporal logic with frequency operators and its model checking. In: INFINITY. EPTCS, pp. 79–93 (2011)
Tomita, T., Hiura, S., Hagihara, S., Yonezaki, N.: A temporal logic with mean-payoff constraints. In: Aoki, T., Taguchi, K. (eds.) ICFEM 2012. LNCS, vol. 7635, pp. 249–265. Springer, Heidelberg (2012)
Vanitha, V., Yamashita, K., Fukuzawa, K., Yonezaki., N.: A method for structuralisation of evolutional specifications of reactive systems. In: ICSE 2000, The Third International Workshop on Intelligent Software Engineering (WISE3), pp. 30–38 (2000)
Vardi, M.Y.: An automata-theoretic approach to fair realizability and synthesis. In: Wolper, P. (ed.) CAV 1995. LNCS, vol. 939, pp. 267–278. Springer, Heidelberg (1995)
Wong-Toi, H., Dill, D.L.: Synthesizing processes and schedulers from temporal specifications. In: Larsen, K.G., Skou, A. (eds.) CAV 1991. LNCS, vol. 575, pp. 272–281. Springer, Heidelberg (1992)
Zhang, Q., Andersen, M.E.: Dose response relationship in anti-stress gene regulatory networks. PLoS Comput. Biol. 3(3), e24 (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Ito, S., Hagihara, S., Yonezaki, N. (2015). Formulation of Homeostasis by Realisability on Linear Temporal Logic. In: Plantier, G., Schultz, T., Fred, A., Gamboa, H. (eds) Biomedical Engineering Systems and Technologies. BIOSTEC 2014. Communications in Computer and Information Science, vol 511. Springer, Cham. https://doi.org/10.1007/978-3-319-26129-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-26129-4_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26128-7
Online ISBN: 978-3-319-26129-4
eBook Packages: Computer ScienceComputer Science (R0)