Abstract
We consider the problem of synthesising rate parameters for stochastic biochemical networks so that a given time-bounded CSL property is guaranteed to hold, or, in the case of quantitative properties, the probability of satisfying the property is maximised/minimised. We develop algorithms based on the computation of lower and upper bounds of the probability, in conjunction with refinement and sampling, which yield answers that are precise to within an arbitrarily small tolerance value. Our methods are efficient and improve on existing approximate techniques that employ discretisation and refinement. We evaluate the usefulness of the methods by synthesising rates for two biologically motivated case studies, including the reliability analysis of a DNA walker.
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
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Andreychenko, A., Mikeev, L., Spieler, D., Wolf, V.: Parameter Identification for Markov Models of Biochemical Reactions. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 83–98. Springer, Heidelberg (2011)
Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Verifying Continuous Time Markov Chains. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 269–276. Springer, Heidelberg (1996)
Baier, C., Haverkort, B., Hermanns, H., Katoen, J.: Model-Checking Algorithms for Continuous-Time Markov Chains. IEEE Trans. on Soft. Eng. 29(6), 524–541 (2003)
Bortolussi, L., Sanguinetti, G.: Learning and designing stochastic processes from logical constraints. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P.R. (eds.) QEST 2013. LNCS, vol. 8054, pp. 89–105. Springer, Heidelberg (2013)
Bortolussi, L., Sanguinetti, G.: Smoothed model checking for uncertain continuous time markov chains. CoRR ArXiv, 1402.1450 (2014)
Brim, L., Češka, M., Dražan, S., Šafránek, D.: Exploring parameter space of stochastic biochemical systems using quantitative model checking. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 107–123. Springer, Heidelberg (2013)
Chen, T., Hahn, E.M., Han, T., Kwiatkowska, M., Qu, H., Zhang, L.: Model repair for Markov decision processes. In: Theoretical Aspects of Software Engineering (TASE), pp. 85–92. IEEE (2013)
Dannenberg, F., Hahn, E.M., Kwiatkowska, M.: Computing cumulative rewards using fast adaptive uniformisation. In: Gupta, A., Henzinger, T.A. (eds.) CMSB 2013. LNCS, vol. 8130, pp. 33–49. Springer, Heidelberg (2013)
Dannenberg, F., Kwiatkowska, M., Thachuk, C., Turberfield, A.: DNA walker circuits: Computational potential, design, and verification. Natural Computing (to appear, 2014)
Fox, B.L., Glynn, P.W.: Computing Poisson Probabilities. CACM 31(4), 440–445 (1988)
Gillespie, D.T.: Exact Stochastic Simulation of Coupled Chemical Reactions. Journal of Physical Chemistry 81(25), 2340–2381 (1977)
Hahn, E.M., Hermanns, H., Zhang, L.: Probabilistic reachability for parametric Markov models. International Journal on Software Tools for Technology Transfer (STTT) 13(1), 3–19 (2011)
Han, T., Katoen, J., Mereacre, A.: Approximate parameter synthesis for probabilistic time-bounded reachability. In: Real-Time Systems Symposium (RTSS), pp. 173–182. IEEE (2008)
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)
Katoen, J.-P., Klink, D., Leucker, M., Wolf, V.: Three-valued abstraction for continuous-time markov chains. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 311–324. Springer, Heidelberg (2007)
Kermack, W.O., McKendrick, A.G.: Contributions to the mathematical theory of epidemics. ii. the problem of endemicity. Proceedings of the Royal Society of London. Series A 138(834), 55–83 (1932)
Kwiatkowska, M., Norman, G., Parker, D.: Stochastic Model Checking. In: Bernardo, M., Hillston, J. (eds.) SFM 2007. LNCS, vol. 4486, pp. 220–270. Springer, Heidelberg (2007)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: Verification of Probabilistic Real-Time Systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011)
Mateescu, M., Wolf, V., Didier, F., Henzinger, T.A.: Fast Adaptive Uniformization of the Chemical Master Equation. IET Systems Biology 4(6), 441–452 (2010)
Sen, K., Viswanathan, M., Agha, G.: Model-checking markov chains in the presence of uncertainties. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 394–410. Springer, Heidelberg (2006)
Češka, M., Dannenberg, F., Kwiatkowska, M., Paoletti, N.: Precise parameter synthesis for stochastic biochemical systems. Technical Report CS-RR-14-08, Department of Computer Science, University of Oxford (2014)
Wickham, S.F.J., Bath, J., Katsuda, Y., Endo, M., Hidaka, K., Sugiyama, H., Turberfield, A.J.: A DNA-based molecular motor that can navigate a network of tracks. Nature Nanotechnology 7, 169–173 (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Češka, M., Dannenberg, F., Kwiatkowska, M., Paoletti, N. (2014). Precise Parameter Synthesis for Stochastic Biochemical Systems. In: Mendes, P., Dada, J.O., Smallbone, K. (eds) Computational Methods in Systems Biology. CMSB 2014. Lecture Notes in Computer Science(), vol 8859. Springer, Cham. https://doi.org/10.1007/978-3-319-12982-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-12982-2_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12981-5
Online ISBN: 978-3-319-12982-2
eBook Packages: Computer ScienceComputer Science (R0)