International Conference on Computational Methods in Systems Biology

CMSB 2015: Computational Methods in Systems Biology pp 182-194

BioPSy: An SMT-based Tool for Guaranteed Parameter Set Synthesis of Biological Models

Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9308)

Abstract

The parameter set synthesis problem consists of identifying sets of parameter values for which a given system model satisfies a desired behaviour. This paper presents BioPSy, a tool that performs guaranteed parameter set synthesis for ordinary differential equation (ODE) biological models expressed in the Systems Biology Markup Language (SBML) given a desired behaviour expressed by time-series data. Three key features of BioPSy are: (1) BioPSy computes parameter intervals, not just single values; (2) for the identified intervals the model is formally guaranteed to satisfy the desired behaviour; and (3) BioPSy can handle virtually any Lipschitz-continuous ODEs, including nonlinear ones. BioPSy is able to achieve guaranteed synthesis by utilising Satisfiability Modulo Theory (SMT) solvers to determine acceptable parameter intervals. We have successfully applied our tool to several biological models including a prostate cancer therapy model, a human starvation model, and a cell cycle model.

References

  1. 1.
    Arkin, A.: Setting the standard in synthetic biology. Nature Biotech. 26, 771–774 (2008)CrossRefGoogle Scholar
  2. 2.
    Asarin, E., Dang, T., Frehse, G., Girard, A., Guernic, C.L., Maler, O.: Recent progress in continuous and hybrid reachability analysis. In: IEEE Conference on Computer Aided Control System Design, pp. 1582–1587 (2006)Google Scholar
  3. 3.
    Balsa-Canto, E., Banga, J.R.: AMIGO, a toolbox for advanced model identification in systems biology using global optimization. Bioinformatics 27(16), 2311–2313 (2011)CrossRefGoogle Scholar
  4. 4.
    Barnat, J., Brim, L., Krejci, A., Streck, A., Safranek, D., Vejnar, M., Vejpustek, T.: On parameter synthesis by parallel model checking. IEEE/ACM Trans. Comput. Biol. Bioinform. 9(3), 693–705 (2012)CrossRefGoogle Scholar
  5. 5.
    Batt, G., Yordanov, B., Weiss, R., Belta, C.: Robustness analysis and tuning of synthetic gene networks. Bioinformatics 23(18), 2415–2422 (2007)CrossRefGoogle Scholar
  6. 6.
    Bruchovsky, N., Klotz, L., et al.: Final results of the Canadian prospective phase II trial of intermittent androgen suppression for men in biochemical recurrence after radiotherapy for locally advanced prostate cancer. Cancer 107, 389–395 (2006)CrossRefGoogle Scholar
  7. 7.
    Cimatti, A., Griggio, A., Mover, S., Tonetta, S.: Parameter synthesis with IC3. In: FMCAD, pp. 165–168. IEEE (2013)Google Scholar
  8. 8.
    Donzé, A., Clermont, G., Langmead, C.J.: Parameter synthesis in nonlinear dynamical systems: application to systems biology. J. Comput. Biol. 17(3), 325–336 (2010)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Dötschel, T., Auer, E., Rauh, A., Aschemann, H.: Thermal behavior of high-temperature fuel cells: reliable parameter identification and interval-based sliding mode control. Soft Comput. 17(8), 1329–1343 (2013)CrossRefGoogle Scholar
  10. 10.
    Dreossi, T., Dang, T.: Parameter synthesis for polynomial biological models. In: HSCC 2014, pp. 233–242. ACM (2014)Google Scholar
  11. 11.
    Gao, S., Avigad, J., Clarke, E.M.: Delta-decidability over the reals. In: LICS, pp. 305–314 (2012)Google Scholar
  12. 12.
    Gao, S., Kong, S., Clarke, E.M.: dReal: an SMT solver for nonlinear theories over the reals. In: Bonacina, M.P. (ed.) CADE 2013. LNCS, vol. 7898, pp. 208–214. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  13. 13.
    Hoops, S., Sahle, S., Gauges, R., Lee, C., Pahle, J., Simus, N., Singhal, M., Xu, L., Mendes, P., Kummer, U.: COPASI - a Complex PAthway SImulator. Bioinformatics 22(24), 3067–3074 (2006)CrossRefGoogle Scholar
  14. 14.
    Hucka, M., Finney, A., Sauro, H.M., et al.: The Systems Biology Markup Language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics 19(4), 524–531 (2003)CrossRefGoogle Scholar
  15. 15.
    Ideta, A.M., Tanaka, G., Takeuchi, T., Aihara, K.: A mathematical model of intermittent androgen suppression for prostate cancer. J. Nonlinear Sci. 18(6), 593–614 (2008)CrossRefMATHGoogle Scholar
  16. 16.
    Jha, S.K., Langmead, C.J.: Synthesis and infeasibility analysis for stochastic models of biochemical systems using statistical model checking and abstraction refinement. Theor. Comput. Sci. 412(21), 2162–2187 (2011)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Kitano, H.: Foundations of Systems Biology. MIT Press, Cambridge (2001)Google Scholar
  18. 18.
    Li, C., et al.: BioModels Database: an enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst. Biol. 4, 92 (2010)CrossRefGoogle Scholar
  19. 19.
    Little, M.P., Heidenreich, W.F., Li, G.: Parameter identifiability and redundancy: theoretical considerations. PLoS ONE 5(1), e8915 (2010)CrossRefGoogle Scholar
  20. 20.
    Liu, B., Kong, S., Gao, S., Zuliani, P., Clarke, E.M.: Towards personalized cancer therapy using delta-reachability analysis. In: HSCC, pp. 227–232. ACM (2015)Google Scholar
  21. 21.
    Maiwald, T., Timmer, J.: Dynamical modeling and multi-experiment fitting with PottersWheel. Bioinformatics 24(18), 2037–2043 (2008)CrossRefGoogle Scholar
  22. 22.
    Meslem, N., Ramdani, N., Candau, Y.: Guaranteed parameter set estimation with monotone dynamical systems using hybrid automata. Reliable Comput. 14, 88–104 (2010)MathSciNetGoogle Scholar
  23. 23.
    Schmidt, H., Jirstrand, M.: Systems Biology Toolbox for MATLAB: a computational platform for research in systems biology. Bioinformatics 22(4), 514–515 (2006)CrossRefGoogle Scholar
  24. 24.
    Song, B., Thomas, D.: Dynamics of starvation in humans. J. Math. Biol. 54(1), 27–43 (2007)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Tyson, J.J.: Modeling the cell division cycle: cdc2 and cyclin interactions. Proc. Nat. Acad. Sci. 88(16), 7328–7332 (1991)CrossRefGoogle Scholar
  26. 26.
    Češka, M., Dannenberg, F., Kwiatkowska, M., Paoletti, N.: Precise parameter synthesis for stochastic biochemical systems. In: Mendes, P., Dada, J.O., Smallbone, K. (eds.) CMSB 2014. LNCS, vol. 8859, pp. 86–98. Springer, Heidelberg (2014) Google Scholar
  27. 27.
    Yordanov, B., Belta, C.: Parameter synthesis for piecewise affine systems from temporal logic specifications. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 542–555. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  28. 28.
    Zi, Z., Klipp, E.: SBML-PET: a Systems Biology Markup Language-based parameter estimation tool. Bioinformatics 22(21), 2704–2705 (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of Computing ScienceNewcastle UniversityNewcastle upon TyneUK

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