Abstract
We propose an automated method for exploring kinetic parameters of stochastic biochemical systems. The main question addressed is how the validity of an a priori given hypothesis expressed as a temporal logic property depends on kinetic parameters. Our aim is to compute a landscape function that, for each parameter point from the inspected parameter space, returns the quantitative model checking result for the respective continuous time Markov chain. Since the parameter space is in principle dense, it is infeasible to compute the landscape function directly. Hence, we design an effective method that iteratively approximates the lower and upper bounds of the landscape function with respect to a given accuracy. To this end, we modify the standard uniformization technique and introduce an iterative parameter space decomposition. We also demonstrate our approach on two biologically motivated case studies.
This work has been supported by the Czech Science Foundation grant No. GAP202/11/0312. M. Češka has been supported by Ministry of Education, Youth, and Sport project No. CZ.1.07/2.3.00/30.0009 – Employment of Newly Graduated Doctors of Science for Scientific Excellence. D. Šafránek has been supported by EC OP project No. CZ.1.07/2.3.00/20.0256.
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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.P.: Model Checking Continuous-Time Markov Chains by Transient Analysis. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 358–372. Springer, Heidelberg (2000)
Ballarini, P., Forlin, M., Mazza, T., Prandi, D.: Efficient Parallel Statistical Model Checking of Biochemical Networks. In: PDMC 2009. EPTCS, vol. 14, pp. 47–61 (2009)
Barbuti, R., Levi, F., Milazzo, P., Scatena, G.: Probabilistic Model Checking of Biological Systems with Uncertain Kinetic Rates. Theor. Comput. Sci. 419, 2–16 (2012)
Bernardini, F., Biggs, C., Derrick, J., Gheorghe, M., Niranjan, M., Sanguinetti, G.: Parameter Estimation and Model Checking in a Model of Prokaryotic Autoregulation. Tech. rep., University of Sheffield (2007)
Daigle, B., Roh, M., Petzold, L., Niemi, J.: Accelerated Maximum Likelihood Parameter Estimation for Stochastic Biochemical Systems. BMC Bioinformatics 13(1), 68–71 (2012)
Degasperi, A., Gilmore, S.: Sensitivity Analysis of Stochastic Models of Bistable Biochemical Reactions. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 1–20. Springer, Heidelberg (2008)
Didier, F., Henzinger, T.A., Mateescu, M., Wolf, V.: Fast Adaptive Uniformization of the Chemical Master Equation. In: HIBI 2009, pp. 118–127. IEEE Computer Society (2009)
El Samad, H., Khammash, M., Petzold, L., Gillespie, D.: Stochastic Modelling of Gene Regulatory Networks. Int. J. of Robust and Nonlinear Control 15(15), 691–711 (2005)
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)
Golightly, A., Wilkinson, D.J.: Bayesian Parameter Inference for Stochastic Biochemical Network Models Using Particle Markov Chain Monte Carlo. Interface Focus 1(6), 807–820 (2011)
Grassmann, W.: Transient Solutions in Markovian Queueing Systems. Computers & Operations Research 4(1), 47–53 (1977)
Hahn, E.M., Han, T., Zhang, L.: Synthesis for PCTL in Parametric Markov Decision Processes. In: NASA Formal Methods, pp. 146–161 (2011)
Henzinger, T.A., Mateescu, M., Wolf, V.: Sliding Window Abstraction for Infinite Markov Chains. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 337–352. Springer, Heidelberg (2009)
Jha, S.K., Clarke, E.M., Langmead, C.J., Legay, A., Platzer, A., Zuliani, P.: A Bayesian Approach to Model Checking Biological Systems. In: Degano, P., Gorrieri, R. (eds.) CMSB 2009. LNCS, vol. 5688, pp. 218–234. Springer, Heidelberg (2009)
Koh, C.H., Palaniappan, S., Thiagarajan, P., Wong, L.: Improved Statistical Model Checking Methods for Pathway Analysis. BMC Bioinformatics 13(suppl. 17), S15 (2012)
Kwiatkowska, M., Norman, G., Pacheco, A.: Model Checking Expected Time and Expected Reward Formulae with Random Time Bounds. Compu. Math. Appl. 51(2), 305–316 (2006)
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)
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)
Mikeev, L., Neuhäußer, M., Spieler, D., Wolf, V.: On-the-fly Verification and Optimization of DTA-properties for Large Markov Chains. Form. Method. Syst. Des., 1–25 (2012)
Reinker, S., Altman, R., Timmer, J.: Parameter Estimation in Stochastic Biochemical Reactions. IEEE Proc. Syst. Biol. 153(4), 168–178 (2006)
Schlögl, F.: Chemical Reaction Models for Non-Equilibrium Phase Transitions. Zeitschrift fur Physik 253, 147–161 (1972)
Swat, M., Kel, A., Herzel, H.: Bifurcation Analysis of the Regulatory Modules of the Mammalian G1/S transition. Bioinformatics 20(10), 1506–1511 (2004)
Vellela, M., Qian, H.: Stochastic Dynamics and Non-Equilibrium Thermodynamics of a Bistable Chemical System: the Schlögl Model Revisited. Journal of The Royal Society Interface 6(39), 925–940 (2009)
Yang, E., van Nimwegen, E., Zavolan, M., Rajewsky, N., Schroeder, M.K., Magnasco, M., Darnell, J.E.: Decay Rates of Human mRNAs: Correlation With Functional Characteristics and Sequence Attributes. Genome Research 13(8), 1863–1872 (2003)
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Brim, L., Češka, M., Dražan, S., Šafránek, D. (2013). Exploring Parameter Space of Stochastic Biochemical Systems Using Quantitative Model Checking. In: Sharygina, N., Veith, H. (eds) Computer Aided Verification. CAV 2013. Lecture Notes in Computer Science, vol 8044. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39799-8_7
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DOI: https://doi.org/10.1007/978-3-642-39799-8_7
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