Abstract
The paper presents the Stochastic Calculus of Looping Sequences (SCLS) suitable to describe microbiological systems, such as cellular pathways, and their evolution. Systems are represented by terms. The terms of the calculus are constructed by basic constituent elements and operators of sequencing, looping, containment and parallel composition. The looping operator allows tying up the ends of a sequence, thus creating a circular sequence which can represent a membrane.
The evolution of a term is modelled by a set of rewrite rules enriched with stochastic rates representing the speed of the activities described by the rules, and can be simulated automatically.
As applications, we give SCLS representations of the regulation process of the lactose operon in Escherichia coli and of the quorum sensing in Pseudomonas aeruginosa.
A prototype simulator (SCLSm) has been implemented in F# and used to run the experiments. A public version of the tool is available at the url: http://www.di.unipi.it/~milazzo/biosims/.
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References
Alur, R., Belta, C., Ivancic, F., Kumar, V., Mintz, M., Pappas, G.J., Rubin, H., Schug, J.: Hybrid modeling and simulation of biomolecular networks. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 19–32. Springer, Heidelberg (2001)
Barbuti, R., Caravagna, G., Maggiolo-Schettini, A., Milazzo, P., Pardini, G.: The Calculus of Looping Sequences. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 387–423. Springer, Heidelberg (2008)
Barbuti, R., Maggiolo-Schettini, A., Milazzo, P.: Extending the Calculus of Looping Sequences to Model Protein Interaction at the Domain Level. In: Măndoiu, I.I., Zelikovsky, A. (eds.) ISBRA 2007. LNCS (LNBI), vol. 4463, pp. 638–649. Springer, Heidelberg (2007)
Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Troina, A.: A calculus of looping sequences for modelling microbiological systems. Fund. Inform. 72, 21–35 (2006)
Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Troina, A.: Bisimulation congruences in the calculus of looping sequences. In: Barkaoui, K., Cavalcanti, A., Cerone, A. (eds.) ICTAC 2006. LNCS, vol. 4281, pp. 93–107. Springer, Heidelberg (2006)
Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Troina, A.: Bisimulations in Calculi Modelling Membranes. Formal Aspects of Computing (to appear, 2008)
Cardelli, L.: Brane calculi. Interactions of biological membranes. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 257–280. Springer, Heidelberg (2005)
Chabrier-Rivier, N., Chiaverini, M., Danos, V., Fages, F., Schachter, V.: Modeling and querying biomolecular interaction networks. Theor. Comput. Sci. 325, 25–44 (2004)
Ciocchetta, F., Hillston, J.: Bio-PEPA: a framework for the modelling and analysis of biological systems. Theor. Comput. Sci. (to appear, 2008)
Curti, M., Degano, P., Priami, C., Baldari, C.T.: Modelling Biochemical Pathways through Enhanced pi-calculus. Theor. Comput. Sci. 325, 111–140 (2004)
Danos, V., Feret, J., Fontana, W., Krivine, J.: Scalable modelling of biological pathways. In: Shao, Z. (ed.) APLAS 2007. LNCS, vol. 4807, pp. 139–157. Springer, Heidelberg (2007)
Danos, V., Laneve, C.: Formal molecular biology. Theor. Comput. Sci. 325, 69–110 (2004)
Dockery, J.D., Keener, J.P.: A mathematical model for quorum sensing in Pseudomonas aeruginosa. Bulletin of Mathematical Biology 63, 95–116 (2001)
Gillespie, D.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340–2361 (1977)
Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press, Cambridge (1996)
James, S., Nilsson, P., James, G., Kjelleberg, S., Fagerstroem, T.: Luminescence Control in the Marine Bacterium Vibrio fischeri: An Analysis of the Dynamics of lux Regulation. Journal of Molecular Biology 296, 1127–1137 (2000)
Krivine, J., Milner, R., Troina, A.: Stochastic Bigraphs. In: Proc. of the 24th Conference on Mathematical Foundations of Programming Semantics (MFPS 2008). ENTCS. Elsevier, Amsterdam (to appear, 2008)
Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic symbolic model checking with PRISM: a hybrid approach. Int. J. on Software Tools for Technology Transfer 6, 128–142 (2004)
Matsuno, H., Doi, A., Nagasaki, M., Miyano, S.: Hybrid Petri net representation of gene regulatory network. In: Prooceedings of Pacific Symposium on Biocomputing, pp. 341–352. World Scientific Press, Singapore (2000)
Milazzo, P.: Qualitative and quantitative formal modeling of biological systems. Ph.D. Thesis, University of Pisa (2007)
Pǎun, G.: Membrane computing. An introduction. Springer, Heidelberg (2002)
Pérez-Jiménez, M.J., Romero-Campero, F.J.: Modelling Vibrio fischeri’s behaviour using P systems. In: Proc. of the 8th European Conference on Artificial Life, Systems Biology Workshop (2005)
Priami, C.: Stochastic π-calculus. The Computer Journal 38, 578–589 (1995)
Priami, C., Quaglia, P.: Beta Binders for Biological Interactions. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 20–33. Springer, Heidelberg (2005)
Priami, C., Regev, A., Shapiro, E., Silverman, W.: Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Inform. Process. Lett. 80, 25–31 (2001)
Regev, A., Panina, E.M., Silverman, W., Cardelli, L., Shapiro, E.: BioAmbients: an abstraction for biological compartments. Theor. Comput. Sci. 325, 141–167 (2004)
Regev, A., Shapiro, E.: Cells as computation. Nature 419, 343 (2002)
Regev, A., Shapiro, E.: The π-calculus as an abstraction for biomolecular systems. In: Modelling in Molecular Biology. Natural Computing Series, pp. 219–266. Springer, Heidelberg (2004)
Regev, A., Silverman, W., Shapiro, E.Y.: Representation and simulation of biochemical processes using the pi-calculus process algebra. In: Proc. of Pacific Symposium on Biocomputing, pp. 459–470. World Scientific Press, Singapore (2001)
Stevens, A.M., Greenberg, E.P.: Quorum sensing in Vibrio fischeri: essential elements for activation of the luminescence genes. J. of Bacteriology 179, 557–562 (1997)
Van Delden, C., Iglewski, B.H.: Cell-to-cell signaling and Pseudomonas aeruginosa infections. Emerg. Infect. Dis. 4, 551–560 (1998)
Ward, J.P., King, J.R., Koerber, A.J., Croft, J.M., Sockett, R.E., Williams, P.: Early development and quorum sensing in bacterial biofilms. Journal of Mathematical Biology 47, 23–55 (2003)
Wilkinson, D.: Stochastic modelling for Systems Biology. Chapman & Hall/CRC, Boca Raton (2006)
Wong, P., Gladney, S., Keasling, J.D.: Mathematical model of the lac operon: inducer exclusion, catabolite repression, and diauxic growth on glucose and lactose. Biotechnology Progress 13, 132–143 (1997)
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Barbuti, R., Maggiolo-Schettini, A., Milazzo, P., Tiberi, P., Troina, A. (2008). Stochastic Calculus of Looping Sequences for the Modelling and Simulation of Cellular Pathways. In: Priami, C. (eds) Transactions on Computational Systems Biology IX. Lecture Notes in Computer Science(), vol 5121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88765-2_3
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