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Complex Functional Rates in Rule-Based Languages for Biochemistry

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Part of the Lecture Notes in Computer Science book series (TCSB,volume 7625)

Abstract

Rule-based languages (like, for example, Kappa, BioNetGen, and BioCham) have emerged as successful models for the representation, analysis, and simulation of bio-chemical systems. In particular Kappa, although based on reactions, differs from traditional chemistry as it allows for a graph-like representation of complexes. It follows the “don’t care, don’t write” approach: a rule contains the description of only those parts of the complexes that are actually involved in a reaction. Hence, given any possible combination of complexes that contain the reactants, such complexes can give rise to the reaction. In this paper we address the problem of extending the “don’t care, don’t write” approach to cases in which the actual structure of the complexes involved in the reaction could affect it (for instance, the mass of the complexes could influence the rate). The solutions that we propose is κ F , an extension of the Kappa-calculus in which rates are defined as functions of the actually involved complexes.

Keywords

  • Functional Rate
  • Label Transition System
  • Continuous Time Markov Chain
  • Binding Rate
  • System Biology Markup Language

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. KaSim: kappa language simulator, http://www.kappalanguage.org

  2. Badjić, J.D., Balzani, V., Credi, A., Silvi, S., Stoddart, J.F.: A molecular elevator. Science 303(5665), 1845–1849 (2004)

    CrossRef  Google Scholar 

  3. Balzani, V., Credi, A., Venturi, M.: Molecular devices and machines - Concepts and perspectives for the nano world, 2nd edn. Wiley-VCH, Weinheim (2008)

    Google Scholar 

  4. Blinov, M., Faeder, J., Goldstein, B., Hlavacek, W.: Bionetgen: software for rule-based modeling of signal transduction based on the interactions of molecular domains. Bioinformatics 20(17), 3289–3291 (2004)

    CrossRef  Google Scholar 

  5. Cao, Y., Li, H., Petzold, L.: Efficient formulation of the stochastic simulation algorithm for chemically reacting systems. J. Chem. Phys. 121(9), 4059–4067 (2004)

    CrossRef  Google Scholar 

  6. Cardelli, L.: Brane Calculi. In: Danos and Schächter [14], pp. 257–278

    Google Scholar 

  7. Ciocchetta, F., Duguid, A., Gilmore, S., Guerriero, M.L., Hillston, J.: The bio-pepa tool suite. In: QEST, pp. 309–310. IEEE Computer Society (2009)

    Google Scholar 

  8. Credi, A., Garavelli, M., Laneve, C., Pradalier, S., Silvi, S., Zavattaro, G.: nanok: A calculus for the modeling and simulation of nano devices. Theor. Comput. Sci. 408(1), 17–30 (2008)

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Danos, V., Feret, J., Fontana, W., Harmer, R., Krivine, J.: Rule-Based Modelling of Cellular Signalling. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 17–41. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  10. Danos, V., Feret, J., Fontana, W., Harmer, R., Krivine, J.: Rule-Based Modelling, Symmetries, Refinements. In: Fisher, J. (ed.) FMSB 2008. LNCS (LNBI), vol. 5054, pp. 103–122. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  11. Danos, V., Feret, J., Fontana, W., Harmer, R., Krivine, J.: Abstracting the differential semantics of rule-based models: Exact and automated model reduction. In: LICS, pp. 362–381. IEEE Computer Society (2010)

    Google Scholar 

  12. Danos, V., Feret, J., Fontana, W., Krivine, J.: Abstract Interpretation of Cellular Signalling Networks. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 83–97. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  13. Danos, V., Laneve, C.: Formal molecular biology. Theoretical Computer Science 325(1), 69–110 (2004)

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Danos, V., Schachter, V. (eds.): CMSB 2004. LNCS (LNBI), vol. 3082. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  15. Degano, P., Gorrieri, R. (eds.): CMSB 2009. LNCS, vol. 5688. Springer, Heidelberg (2009)

    MATH  Google Scholar 

  16. Delzanno, G., Giusto, C.D., Gabbrielli, M., Laneve, C., Zavattaro, G.: The kappa-lattice: Decidability boundaries for qualitative analysis in biological languages. In: Degano and Gorrieri [15], pp. 158–172

    Google Scholar 

  17. Faeder, J.R., Blinov, M.L., Hlavacek, W.S.: Rule-based modeling of biochemical systems with bionetgen. Methods in Molecular Biology 500, 113–167 (2009)

    CrossRef  Google Scholar 

  18. Fages, F., Soliman, S.: Formal Cell Biology in Biocham. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 54–80. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  19. Gibson, M., Bruck, J.: Efficient exact stochastic simulation of chemical systems with many species and many channels. Journal of Physical Chemistry A 104(9), 1876–1889 (2000)

    CrossRef  Google Scholar 

  20. Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)

    CrossRef  Google Scholar 

  21. Hlavacek, W.S., Faeder, J.R., Blinov, M.L., Posner, R.G., Hucka, M., Fontana, W.: Rules for modeling signal-transduction systems. Science Signaling 2006(344) (2006)

    Google Scholar 

  22. Hoops, S., Sahle, S., Gauges, R., Lee, C., Pahle, J., Simus, N., Singhal, M., Xu, L., Mendes, P., Kummer, U.: Copasi – a complex pathway simulator. Bioinformatics 22(24), 3067–3074 (2006)

    CrossRef  Google Scholar 

  23. Hucka, M., Finney, A., Sauro, H., Bolouri, H., Doyle, J., Kitano, H., Arkin, A., Bornstein, B., Bray, D., Cornish-Bowden, A., et al.: The systems biology markup language (sbml): a medium for representation and exchange of biochemical network models. Bioinformatics 19(4), 524–531 (2003)

    CrossRef  Google Scholar 

  24. Hucka, M., Finney, A., Sauro, H., Bolouri, H., Doyle, J., Kitano, H., Arkin, A., Bornstein, B., Bray, D., Cornish-Bowden, A., et al.: The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models (2003)

    Google Scholar 

  25. John, M., Lhoussaine, C., Niehren, J.: Dynamic compartments in the imperative pi-calculus. In: Degano and Gorrieri [15], pp. 235–250

    Google Scholar 

  26. John, M., Lhoussaine, C., Niehren, J., Uhrmacher, A.M.: The Attributed Pi Calculus. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 83–102. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  27. John, M., Lhoussaine, C., Niehren, J., Versari, C.: Biochemical Reaction Rules with Constraints. In: Barthe, G. (ed.) ESOP 2011. LNCS, vol. 6602, pp. 338–357. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  28. Marsan, M.A.: Stochastic Petri Nets: An Elementary Introduction. In: Rozenberg, G. (ed.) APN 1989. LNCS, vol. 424, pp. 1–29. Springer, Heidelberg (1990)

    CrossRef  Google Scholar 

  29. Meyer, R.: A theory of structural stationarity in the π-calculus. Acta Inf. 46(2), 87–137 (2009)

    CrossRef  MATH  Google Scholar 

  30. Meyer, R., Gorrieri, R.: On the Relationship between π-Calculus and Finite Place/Transition Petri Nets. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 463–480. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  31. Phillips, A., Cardelli, L.: Efficient, Correct Simulation of Biological Processes in the Stochastic Pi-calculus. In: Calder, M., Gilmore, S. (eds.) CMSB 2007. LNCS (LNBI), vol. 4695, pp. 184–199. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  32. Priami, C., Quaglia, P.: Beta binders for biological interactions. In: Danos and Schächter [14], pp. 20–33

    Google Scholar 

  33. Regev, A., Panina, E.M., Silverman, W., Cardelli, L., Shapiro, E.Y.: BioAmbients: an abstraction for biological compartments. Theor. Comput. Sci. 325(1), 141–167 (2004)

    CrossRef  MathSciNet  MATH  Google Scholar 

  34. Sneddon, M.W., Faeder, J.R., Emonet, T.: Efficient modeling, simulation and coarse-graining of biological complexity with NFsim. Nature Methods 8, 177–183 (2011)

    CrossRef  Google Scholar 

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Versari, C., Zavattaro, G. (2012). Complex Functional Rates in Rule-Based Languages for Biochemistry. 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_6

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  • DOI: https://doi.org/10.1007/978-3-642-35524-0_6

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