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Statistical model checking for biological applications

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Abstract

In this paper, we survey recent work on the use of statistical model checking techniques for biological applications. We begin with an overview of the basic modelling techniques for biochemical reactions and their corresponding stochastic simulation algorithm—the Gillespie algorithm. We continue by giving a brief description of the relation between stochastic models and continuous (ordinary differential equation) models. Next, we present a literature survey, divided into two general areas. In the first area, we focus on works addressing verification of biological models, while in the second area we focus on papers tackling the parameter synthesis problem. We conclude with some open problems and directions for further research.

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Notes

  1. http://www.prismmodelchecker.org/casestudies/index.php#biology.

References

  1. Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P.: Model-checking algorithms for continuous-time Markov chains. IEEE Trans. Softw. Eng. 29(6), 524–541 (2003)

    Article  Google Scholar 

  2. Ballarini, P., Djafri, H., Duflot, M., Haddad, S., Pekergin, N.: COSMOS: a statistical model checker for the hybrid automata stochastic logic. In: QEST, pp. 143–144 (2011)

  3. Ballarini, P., Mäkelä, J., Ribeiro, A.S.: Expressive statistical model checking of genetic networks with delayed stochastic dynamics. In: CMSB, volume 7605 of LNCS, pp. 29–48 (2012)

  4. Bartocci, E., Bortolussi, L., Nenzi, L., Sanguinetti, G.: On the robustness of temporal properties for stochastic models. In: HSB, volume 125 of EPTCS, pp. 3–19 (2013)

  5. Boyer, B., Corre, K., Legay, A., Sedwards, S.: PLASMA-lab: a flexible, distributable statistical model checking library. In: QEST, volume 8054 of LNCS, pp. 160–164 (2013)

  6. Brim, L., Česka, M., Šafránek, D.: Model checking of biological systems. In: SFM, volume 7938 of LNCS, pp. 63–112 (2013)

  7. Bulychev, P.E., David, A., Larsen, K.G., Mikucionis, M., Poulsen, D.B., Legay, A., Wang, Z.: UPPAAL-SMC: statistical model checking for priced timed automata. In: QAPL, volume 85 of EPTCS, pp. 1–16 (2012)

  8. Calzone, L., Chabrier-Rivier, N., Fages, F., Soliman, S.: Machine learning biochemical networks from temporal logic properties. In: Transactions on Computational Systems Biology, volume 4220 of LNCS, pp. 68–94 (2006)

  9. Clarke, E.M., Faeder, J.R., Langmead, C.J., Harris, L.A., Jha, S.K., Legay, A.: Statistical model checking in BioLab: applications to the automated analysis of T-cell receptor signaling pathway. In: CMSB, volume 5307 of LNCS, pp. 231–250 (2008)

  10. David, A., Larsen, K.G., Legay, A., Mikucionis, M., Poulsen, D.B., Sedwards, S.: Runtime verification of biological systems. In: ISoLA (1), volume 7609 of LNCS, pp. 388–404 (2012)

  11. Donaldson, R., Gilbert, D.: A model checking approach to the parameter estimation of biochemical pathways. In: CMSB, volume 5307 of LNCS, pp. 269–287 (2008)

  12. Donzé, A., Ferrère, T., Maler, O.: Efficient robust monitoring for STL. In: CAV, volume 8044 of LNCS, pp. 264–279 (2013)

  13. Gao, S., Avigad, J., Clarke, E.M.: Delta-decidability over the reals. In: LICS, pp. 305–314 (2012)

  14. Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403–434 (1976)

    Article  MathSciNet  Google Scholar 

  15. Gillespie, D.T.: A rigorous derivation of the chemical master equation. Phys. A 188, 404–425 (1992)

    Article  Google Scholar 

  16. Gillespie, D.T.: Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115(4), 1716–1733 (2001)

    Article  Google Scholar 

  17. Hucka, 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)

    Article  Google Scholar 

  18. Jha, S.K., Clarke, E.M., Langmead, C.J., Legay, A., Platzer, A., Zuliani, P.: A Bayesian approach to model checking biological systems. In: CMSB, volume 5688 of LNCS, pp. 218–234 (2009)

  19. Jha, S.K., Dutta, R.G., Langmead, C.J., Jha, S., Sassano, E.: Synthesis of insulin pump controllers from safety specifications using Bayesian model validation. IJBRA 8(3/4), 263–285 (2012)

    Article  Google Scholar 

  20. Jha, S.K., Langmead, C.J.: Synthesis and infeasibility analysis for stochastic models of biochemical systems using statistical model checking and abstraction refinement. Theory Comput. Sci. 412(21), 2162–2187 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Jha, S.K., Langmead, C.J.: Exploring behaviors of stochastic differential equation models of biological systems using change of measures. BMC Bioinform. 13(S–5), S8 (2012)

  22. Keating, S.M., Bornstein, B.J., Finney, A., Hucka, M.: SBMLToolbox: an SBML toolbox for MATLAB users. Bioinformatics 22(10), 1275–1277 (2006)

  23. Kitano, H.: Biological robustness. Nat. Rev. Genet. 5(11), 826–837 (2004)

  24. Koh, C.H., Palaniappan, S.K., Thiagarajan, P.S., Wong, L.: Improved statistical model checking methods for pathway analysis. BMC Bioinform. 13(S–17), S15 (2012)

    Article  Google Scholar 

  25. Koymans, R.: Specifying real-time properties with metric temporal logic. Real Time Syst. 2(4), 255–299 (1990)

    Article  Google Scholar 

  26. Kurtz, T.G.: Solutions of ordinary differential equations as limits of pure jump Markov processes. J. Appl. Prob. 7(1), 49–58 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  27. Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: CAV, volume 6806 of LNCS, pp. 585–591 (2011)

  28. Larsen, K.G., Pettersson, P., Yi, W.: UPPAAL in a nutshell. STTT 1(1–2), 134–152 (1997)

    Article  MATH  Google Scholar 

  29. Palaniappan, S.K., Gyori, B.M., Liu, B., Hsu, D., Thiagarajan, P.S.: Statistical model checking based calibration and analysis of bio-pathway models. In: CMSB, volume 8130 of LNCS, pp. 120–134 (2013)

  30. Rathinam, M., Petzold, L.R., Cao, Y., Gillespie, D.T.: Stiffness in stochastic chemically reacting systems: the implicit tau-leaping method. J. Chem. Phys. 119(24), 12784–12794 (2003)

    Article  Google Scholar 

  31. Richardson, D.: Some undecidable problems involving elementary functions of a real variable. J. Symb. Log. 33(4), 514–520 (1968)

    Article  MATH  Google Scholar 

  32. Sankaranarayanan, S., Fainekos, G.E.: Simulating insulin infusion pump risks by in-silico modeling of the insulin-glucose regulatory system. In: CMSB, volume 7605 of LNCS, pp. 322–341 (2012)

  33. Schivo, S., Scholma, J., Wanders, B., Camacho, R.A U., van der Vet, P.E., Karperien, M., Langerak, R., van de Pol, J., Post, J.N.: Modelling biological pathway dynamics with timed automata. In: BIBE, pp. 447–453. IEEE Press, New York (2012)

  34. Česka, M., Šafránek, D., Dražan, S., Brim, L.: Robustness analysis of stochastic biochemical systems. PLoS One 9(4): e94553 (2014)

  35. Wald, A.: Sequential test of stastistical hypotheses. Ann. Math. Stat. 16(2), 117–186 (1945)

    Article  MathSciNet  MATH  Google Scholar 

  36. Wilkinson, D.J.: Stochastic modelling for systems biology, 2nd edn. CRC Press, Boca Raton (2011)

  37. Younes, H.L.S.: Error control for probabilistic model checking. In: VMCAI, volume 3855 of LNCS, pp. 142–156 (2006)

  38. Younes, H.L.S., Simmons, R.G.: Probabilistic verification of discrete event systems using acceptance sampling. In: CAV, volume 2404 of LNCS, pp. 223–235 (2002)

  39. Zhang, F., Yeddanapudi, M., Mosterman, P.: Zero-crossing location and detection algorithms for hybrid system simulation. IFAC World Congress, pp. 7967–7972 (2008)

  40. Zuliani, P., Platzer, A., Clarke, E.M.: Bayesian statistical model checking with application to Simulink/Stateflow verification. In: HSCC, pp. 243–252 (2010)

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Zuliani, P. Statistical model checking for biological applications. Int J Softw Tools Technol Transfer 17, 527–536 (2015). https://doi.org/10.1007/s10009-014-0343-0

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