Abstract
In this paper, we apply the probabilistic symbolic model checker PRISM to the analysis of a biological system – the Platelet-Derived Growth Factor (PDGF) signaling pathway, demonstrating in detail how this pathway can be analyzed in PRISM. Moreover, we compare the results from verification and ODE simulation on the PDGF pathway and demonstrate by examples the influence of model structure, parameter values and pathway length on the two analysis methods.
An extended abstract appears in the proceedings of CompMod 2011 [1]. The first two authors made equal contributions to this work.
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
Yuan, Q., Pang, J., Mauw, S., Trairatphisan, P., Wiesinger, M., Sauter, T.: A study of the PDGF signaling pathway with PRISM. In: Proc. 3rd Workshop on Computational Models for Cell Processes. EPTCS, vol. 67, pp. 65–81 (2011)
Regev, A., Shapiro, E.: Cellular abstractions: Cells as computation. Nature 419, 343 (2002)
Bonzanni, N., Anton Feenstra, K., Fokkink, W., Krepska, E.: What Can Formal Methods Bring to Systems Biology? In: Cavalcanti, A., Dams, D.R. (eds.) FM 2009. LNCS, vol. 5850, pp. 16–22. Springer, Heidelberg (2009)
Fisher, J., Henzinger, T.A.: Executable cell biology. Nature Biotechnology 25(11), 1239–1249 (2007)
Sadot, A., Fisher, J., Barak, D., Admanit, Y., Stern, M.J., Jane Albert Hubbard, E., Harel, D.: Toward verified biological models. IEEE/ACM Transactions on Computational Biology Bioinformatics 5(2), 223–234 (2008)
Fisher, J., Piterman, N.: The executable pathway to biological networks. Briefings in Functional Genomics and Proteomics 9(1), 79–92 (2010)
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)
Baier, C., Katoen, J.P.: Principles in Model Checking. MIT Press (2008)
Hart, S., Sharir, M., Pnueli, A.: Termination of probabilistic concurrent programs. ACM Transactions on Programming Languages and Systems 5(3), 356–380 (1983)
Kwiatkowska, M.Z., Norman, G., Parker, D.: Quantitative Verification Techniques for Biological Processes. In: Algorithmic Bioprocesses, pp. 391–409. Springer (2009)
Kwiatkowska, M.Z., Norman, G., Parker, D.: Probabilistic Model Checking for Systems Biology. In: Symbolic Systems Biology, pp. 31–59. Jones and Bartlett (2010)
Aldridge, B.B., Haller, G., Sorger, P.K., Lauffenburger, D.A.: Direct lyapunov exponent analysis enables parametric study of transient signalling governing cell behaviour. Systems Biology 153(6), 425–432 (2006)
Yu, J., Ustach, C., Kim, H.R.: Platelet-derived growth factor signaling and human cancer. Journal of Biochemistry and Molecular Biology 36(1), 49–59 (2003)
Golub, T.R., Barker, G.F., Lovett, M., Gilliland, D.G.: Fusion of PDGF receptor beta to a novel ets-like gene, tel, in chronic myelomonocytic leukemia with t(5;12) chromosomal translocation. Cell 77(2), 307–316 (1994)
Anan, K., Morisaki, T., Katano, M., Ikubo, A., Kitsuki, H., Uchiyama, A., Kuroki, S., Tanaka, M., Torisu, M.: Vascular endothelial growth factor and platelet-derived growth factor are potential angiogenic and metastatic factors in human breast cancer. Surgery 119(3), 333–339 (1996)
Cools, J., DeAngelo, D.J., Gotlib, J., Stover, E.H., Legare, R.D., Cortes, J., Kutok, J., Clark, J., Galinsky, I., Griffin, J.D., Cross, N.C., Tefferi, A., Malone, J., Alam, R., Schrier, S.L., Schmid, J., Rose, M., Vandenberghe, P., Verhoef, G., Boogaerts, M., Wlodarska, I., Kantarjian, H., Marynen, P., Coutre, S.E., Stone, R., Gilliland, D.G.: A tyrosine kinase created by fusion of the PDGFRA and FIP1L1 genes as a therapeutic target of imatinib in idiopathic hypereosinophilic syndrome. The New England Journal of Medicine 348(13), 1201–1214 (2003)
Miettinen, M., Lasota, J.: Gastrointestinal stromal tumors: Pathology and prognosis at different sites. Seminars in Diagnostic Pathology 23(2), 70–83 (2006)
Calder, M., Vyshemirsky, V., Gilbert, D., Orton, R.: Analysis of Signalling Pathways Using Continuous Time Markov Chains. In: Priami, C., Plotkin, G. (eds.) Transactions on Computational Systems Biology VI. LNCS (LNBI), vol. 4220, pp. 44–67. Springer, Heidelberg (2006)
Kwiatkowska, M.Z., Norman, G., Parker, D.: Using probabilistic model checking in systems biology. SIGMETRICS Performance Evaluation Review 35, 14–21 (2008)
Pronk, T., de Vink, E., Bosnacki, D., Breit, T.: Stochastic modeling of codon bias with PRISM. In: Proc. 3rd Workshop on Methods and Tools for Coordinating Concurrent, Distributed and Mobile Systems, Computer Science Department, University of Cyprus, Nicosia (2007)
Bošnački, D., Pronk, T.E., de Vink, E.P.: In Silico Modelling and Analysis of Ribosome Kinetics and aa-tRNA Competition. In: Priami, C., Back, R.-J., Petre, I. (eds.) Transactions on Computational Systems Biology XI. LNCS, vol. 5750, pp. 69–89. Springer, Heidelberg (2009)
Heath, J., Kwiatkowska, M., Norman, G., Parker, D., Tymchyshyn, O.: Probabilistic model checking of complex biological pathways. Theoretical Computer Science 319(3), 239–257 (2008)
Owens, N.D.L., Timmis, J., Greensted, A.J., Tyrrell, A.M.: Modelling the Tunability of Early T Cell Signalling Events. In: Bentley, P.J., Lee, D., Jung, S. (eds.) ICARIS 2008. LNCS, vol. 5132, pp. 12–23. Springer, Heidelberg (2008)
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)
Liò, P., Merelli, E., Paoletti, N.: Multiple verification in computational modeling of bone pathologies. In: Proc. 3rd International Workshop on Computational Models for Cell Processes. EPTCS, vol. 68, pp. 82–96 (2011)
Zhang, R., Shah, M.V., Yang, J., Nyland, S.B., Liu, X., Yun, J.K., Albert, R., Loughran, T.P.: Network model of survival signaling in large granular lymphocyte leukemia. Proceedings of the National Academy of Sciences of the United States of America 105(42), 16308–16313 (2008)
Wang, C.C., Cirit, M., Haugh, J.M.: PI3K-dependent cross-talk interactions converge with Ras as quantifiable inputs integrated by Erk. Molecular Systems Biology 5, 246 (2009)
Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model checking continuous time markov chains. ACM Transactions on Computational Logic 1(1), 162–170 (2000)
Baier, C., Hermanns, H., Haverkort, B.R., Katoen, J.P.: Model-checking algorithms for continuous-time markov chains. IEEE Transactions on Software Engineering 29(6), 524–541 (2003)
Krauss, G.: Biochemistry of Signal Transduction and Regulation. Wiley-VCH, Weinheim (2008)
Bhalla, U.: Understanding complex signaling networks through models and metaphor. Progress in Biophysics & Molecular Biology 81(1), 45–65 (2003)
Heldin, C.H., Westermarkt, B., Wasteson, A.: Platelet-derived growth factor. Molecular and Celluar Endocrinology 39(3), 169–187 (1985)
Tallquist, M., Kazlauskas, A.: PDGF signaling in cells and mice. Cytokine & Growth Factor Review 15(4), 205–213 (2004)
Yokote, K., Hellman, U., Ekman, S., Saito, Y., Roennstrand, L., Saito, Y., Heldin, C.H., Mori, S.: Identification of Tyr-762 in the platelet-derived growth factor alpha-receptor as the binding site for Crk proteins. Oncogene 16(10), 1229–1239 (1998)
Gutiérrez-Uzquiza, A., Arechederra, M., Molina, I., Banos, R., Maia, V., Benito, M., Guerrero, C., Porras, A.: C3G down-regulates p38 MAPK activity in response to stress by Rap-1 independent mechanisms: involvement in cell death. Cellualar Signalling 22(3), 533–542 (2010)
Valgeirsdóttir, S., Paukku, K., Silvennoinen, O., Heldin, C.H., Claesson-Welsh, L.: Activation of Stat5 by platelet-derived growth factor (PDGF) is dependent on phosphorylation sites in PDGF beta-receptor juxtamembrane and kinase insert domains. Oncogene 16(4), 505–515 (1998)
Joazeiro, C.A., Wing, S.S., Huang, H., Leverson, J.D., Hunter, T., Liu, Y.C.: The tyrosine kinase negative regulator c-Cbl as a RING-type, E2-dependent ubiquitin-protein ligase. Science 286(5438), 309–312 (1999)
Hanahan, D., Weinberg, R.A.: Hallmarks of cancer: The next generation. Cell 144(5), 646–674 (2011)
Yu, J., Gutkind, J.S., Mahadevan, D., Li, W., Meyers, K.A., Pierce, J.H., Heidaran, M.A.: Biological function of PDGF-induced PI-3 kinase activity: its role in alpha PDGF receptor-mediated mitogenic signaling. Journal of Cell Biology 127(2), 479–487 (1994)
Bazenet, C.E., Gelderloos, J.A., Kazlauskas, A.: Phosphorylation of tyrosine 720 in the platelet-derived growth factor alpha receptor is required for binding of Grb2 and SHP-2 but not for activation of Ras or cell proliferation. Molecular and Cellular Biology 16(12), 6926–6936 (1996)
Reddi, A.L., Ying, G., Duan, L., Chen, G., Dimri, M., Douillard, P., Druker, B.J., Naramura, M., Band, V., Band, H.: Binding of Cbl to a phospholipase Cgamma1-docking site on platelet-derived growth factor receptor beta provides a dual mechanism of negative regulation. Journal of Biological Chemistry 282(40), 29336–293347 (2007)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81(25), 2340–2361 (1977)
Witt, J., Barisic, S., Schumann, E., Allgöwer, F., Sawodny, O., Sauter, T., Kulms, D.: Mechanism of PP2A-mediated IKKβ dephosphorylation: a systems biological approach. BMC Systems Biology 3, 71 (2009)
Schmidt, H., Jirstrand, M.: Systems Biology Toolbox for MATLAB: a computational platform for research in systems biology. Bioinformatics 22(4), 514–515 (2006)
Saltelli, A., Tarantola, S., Chan, K.P.S.: A quantitative model-independent method for global sensitivity analysis of model output. Technometrics 41(1), 39–56 (1999)
Davies, S., Reddy, H., Caivano, M., Cohen, P.: Specificity and mechanism of action of some commonly used protein kinase inhibitors. Biochemical Journal 351(pt. 1), 95–105 (2000)
Stewart, W.J.: Introduction to the Numerical Solution of Markov Chains. Princeton University Press (1994)
Tenenbaum, M., Pollard, H.: Ordinary Differential Equations: An Elementary Textbook for Students of Mathematics, Engineering, and the Science. Harper & Row (1985)
Kwiatkowska, M.Z., Norman, G., Parker, D., Tymchyshyn, O., Heath, J., Gaffney, E.: Simulation and verification for computational modelling of signalling pathways. In: Proc. 38th Winter Simulation Conference, pp. 1666–1674 (2006)
Han, T., Katoen, J.P., Mereacre, A.: Approximate parameter synthesis for probabilistic time-bounded reachability. In: Proc. 29 IEEE Real-Time Systems Symposium, pp. 173–182. IEEE Computer Society (2008)
Hahn, E.M., Hermanns, H., Zhang, L.: Probabilistic Reachability for Parametric Markov Models. In: Păsăreanu, C.S. (ed.) CAV 2011. LNCS, vol. 5578, pp. 88–106. Springer, Heidelberg (2009)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yuan, Q., Trairatphisan, P., Pang, J., Mauw, S., Wiesinger, M., Sauter, T. (2012). Probabilistic Model Checking of the PDGF Signaling Pathway. In: Priami, C., Petre, I., de Vink, E. (eds) Transactions on Computational Systems Biology XIV. Lecture Notes in Computer Science(), vol 7625. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35524-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-35524-0_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35523-3
Online ISBN: 978-3-642-35524-0
eBook Packages: Computer ScienceComputer Science (R0)