Abstract
This paper examines the influence of the Raf Kinase Inhibitor Protein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signalling pathway [5] through modelling in a Markovian process algebra, PEPA [11]. Two models of the system are presented, a reagent-centric view and a pathway-centric view. The models capture functionality at the level of subpathway, rather than at a molecular level. Each model affords a different perspective of the pathway and analysis. We demonstrate the two models to be formally equivalent using the timing-aware bisimulation defined over PEPA models and discuss the biological significance.
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References
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. 169–276. Springer, Heidelberg (1996)
Calder, M., Gilmore, S., Hillston, J.: Modelling the influence of RKIP on the ERK signalling pathway using the stochastic process algebra PEPA. In: Proc. of BioConcur 2004, Danmarks Tekniske Universitet, pp. 26–41 (2004) (to appear in ENTCS)
Calder, M., Gilmore, S., Hillston, J.: Automatically deriving ODEs from process algebra models of signalling pathways. In: Computational Methods in Systems Biology 2005. LFCS, University of Edinburgh, pp. 204–215 (2005)
Calder, M., Vyshemirsky, V., Orton, R., Gilbert, D.: Analysis of signalling pathways using the PRISM model checker. In: Computational Methods in Systems Biology 2005. LFCS, University of Edinburgh, pp. 179–190 (2005)
Cho, K.-H., Shin, S.-Y., Kim, H.-W., Wolkenhauer, O., McFerran, B., Kolch, W.: Mathematical modeling of the influence of RKIP on the ERK signaling pathway. In: Priami, C. (ed.) CMSB 2003. LNCS, vol. 2602, pp. 127–141. Springer, Heidelberg (2003)
Colom, J.M., Silva, M.: Convex geometry and semiflows in P/T nets. a comparative study of algorithms for computation of minimal P-semiflows. In: Rozenberg, G. (ed.) APN 1990. LNCS, vol. 483, pp. 79–112. Springer, Heidelberg (1991)
Elliot, W.H., Elliot, D.C.: Biochemistry and Molecular Biology, 2nd edn. Oxford University Press, Oxford (2002)
Fisher, J., Harel, D., Hubbard, E.J.A., Piterman, N., Stern, M.J., Swerdlin, N.: Combining state-based and scenario-based approaches in modeling biological systems. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 236–241. Springer, Heidelberg (2005)
Gilmore, S., Hillston, J.: The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In: Haring, G., Kotsis, G. (eds.) TOOLS 1994. LNCS, vol. 794, pp. 353–368. Springer, Heidelberg (1994)
Heiner, M., Koch, I.: Petri net based model validation in systems biology. In: 25th International Conference on Application and Theory of Petri Nets, Bologna, Italy (2004)
Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press, Cambridge (1996)
Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic symbolic model checking with PRISM: A hybrid approach. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 52–66. Springer, Heidelberg (2002)
Matheiss, T.H., Rubin, D.S.: A survey and comparison of methods for finding all the vertices of convex polyhedral sets. Mathematics of Operational Research 5(2), 167–185 (1980)
Papin, J.A., Price, N.D., Wiback, S.J., Fell, D.A., Palsson, B.O.: Metabolic pathways in the post-genome era. TRENDS in Biochemical Sciences 28(5), 250–258 (2003)
Priami, C., Regev, A., Silverman, W., Shapiro, E.: Application of a stochastic name passing calculus to representation and simulation of molecular processes. Information Processing Letters 80, 25–31 (2001)
Regev, A.: Computational Systems Biology: a Calculus for Biomolecular Knowledge. PhD thesis, Tel Aviv University (2002)
Regev, A., Panina, E.M., Silverman, W., Cardelli, L., Shapiro, E.: BioAmbients: an abstraction for biological compartments. Theoretical Computer Science 325(1), 141–167 (2004)
Regev, A., Silverman, W., Shapiro, E.: Representation and simulation of biochemical processes using the pi-calculus process algebra. In: Proceedings of the Pacific Symposium of Biocomputing (PSB 2001), pp. 459–470 (2001)
Stewart, W.: Numerical Solution of Markov Chains. Princeton University Press, Princeton (1994)
Vissers, C.A., Scollo, G., van Sinderen, M., Brinksma, E.: Specification styles in distributed systems design and verification. Theoretical Computer Science 89, 179–206 (1991)
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Calder, M., Gilmore, S., Hillston, J. (2006). Modelling the Influence of RKIP on the ERK Signalling Pathway Using the Stochastic Process Algebra PEPA. In: Priami, C., Ingólfsdóttir, A., Mishra, B., Riis Nielson, H. (eds) Transactions on Computational Systems Biology VII. Lecture Notes in Computer Science(), vol 4230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11905455_1
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DOI: https://doi.org/10.1007/11905455_1
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