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Trend-Based Analysis of a Population Model of the AKAP Scaffold Protein

  • Oana Andrei
  • Muffy Calder
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7625)

Abstract

We formalise a continuous-time Markov chain with multi-dimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system.

Keywords

Model Check Biochemical System Biochemical Network State Formula Stochastic Trend 
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. 1.
    Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  2. 2.
    Ciocchetta, F., Degasperi, A., Hillston, J., Calder, M.: Some Investigations Concerning the CTMC and the ODE Model Derived From Bio-PEPA. Electr. Notes Theor. Comput. Sci. 229(1), 145–163 (2009)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bartlett, M.S.: An introduction to stochastic processes, with special reference to methods and applications, 3rd edn. Cambridge University Press (1978)Google Scholar
  4. 4.
    Kingman, J.F.C.: Markov Population Processes. Journal of Applied Probability 6, 1–18 (1969)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Cohen, J.E.: Markov population processes as models of primate social and population dynamics. Theoretical Population Biology 3(2), 119–134 (1972)CrossRefGoogle Scholar
  6. 6.
    Henzinger, T.A., Jobstmann, B., Wolf, V.: Formalisms for Specifying Markovian Population Models. In: Bournez, O., Potapov, I. (eds.) RP 2009. LNCS, vol. 5797, pp. 3–23. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Fages, F.: Temporal Logic Constraints in the Biochemical Abstract Machine BIOCHAM. In: Hill, P.M. (ed.) LOPSTR 2005. LNCS, vol. 3901, pp. 1–5. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Rizk, A., Batt, G., Fages, F., Soliman, S.: On a Continuous Degree of Satisfaction of Temporal Logic Formulae with Applications to Systems Biology. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 251–268. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Chabrier-Rivier, N., Chiaverini, M., Danos, V., Fages, F., Schächter, V.: Modeling and querying biomolecular interaction networks. Theoretical Computer Science 325(1), 25–44 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Ballarini, P., Mardare, R., Mura, I.: Analysing Biochemical Oscillation through Probabilistic Model Checking. Electr. Notes Theor. Comput. Sci. 229(1), 3–19 (2009)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Spieler, D., Hahn, E.M., Zhang, L.: Model Checking CSL for Markov Population Models. CoRR abs/1111.4385 (2011)Google Scholar
  12. 12.
    Júlvez, J., Kwiatkowska, M.Z., Norman, G., Parker, D.: A Systematic Approach to Evaluate Sustained Stochastic Oscillations. In: Al-Mubaid, H. (ed.) Proc. of the ISCA 3rd International Conference on Bioinformatics and Computational Biology (BICoB 2011). ISCA, pp. 134–139 (2011)Google Scholar
  13. 13.
    Ballarini, P., Guerriero, M.L.: Query-based verification of qualitative trends and oscillations in biochemical systems. Theoretical Computer Science 411(20), 2019–2036 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Andrei, O., Calder, M.: A Model and Analysis of the AKAP Scaffold. Electr. Notes Theor. Comput. Sci. 268, 3–15 (2010)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.P.: Model-Checking Algorithms for Continuous-Time Markov Chains. IEEE Trans. Software Eng. 29(6), 524–541 (2003)CrossRefGoogle Scholar
  16. 16.
    Baier, C., Katoen, J.P.: Principles of Model Checking. The MIT Press (2008)Google Scholar
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    Kleinrock, L.: Queueing Systems, vol I: Theory. John Wiley, New York (1975)zbMATHGoogle Scholar
  19. 19.
    Bolch, G., Greiner, S., de Meer, H., Trivedi, K.S.: Queueing networks and Markov chains: modeling and performance evaluation with computer science applications, 2nd edn. Wiley Interscience (2006)Google Scholar
  20. 20.
    Ciocchetta, F., Gilmore, S., Guerriero, M.L., Hillston, J.: Integrated Simulation and Model-Checking for the Analysis of Biochemical Systems. Electr. Notes Theor. Comput. Sci. 232, 17–38 (2009)CrossRefGoogle Scholar
  21. 21.
    Calder, M., Gilmore, S., Hillston, J.: 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. LNCS (LNBI), vol. 4230, pp. 1–23. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  22. 22.
    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)CrossRefGoogle Scholar
  23. 23.
    Kurtz, T.G.: Limit Theorems for Sequences of Jump Markov Processes Approximating Ordinary Differential Processes. Journal of Applied Probability 8(2), 344–356 (1971)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Alur, R., Henzinger, T.A.: Reactive Modules. Formal Methods in System Design 15(1), 7–48 (1999)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Kwiatkowska, M.Z., Norman, G., Parker, D.: PRISM: probabilistic model checking for performance and reliability analysis. SIGMETRICS Performance Evaluation Review 36(4), 40–45 (2009)CrossRefGoogle Scholar
  26. 26.
    Calder, M., Hillston, J.: Process Algebra Modelling Styles for Biomolecular Processes. T. Comp. Sys. Biology 11, 1–25 (2009)Google Scholar
  27. 27.
    James, E., Ferrell, J.: What Do Scaffold Proteins Really Do? Sci. STKE (52), 1–3 (2000)Google Scholar
  28. 28.
    Andrei, O., Calder, M.: Modelling Scaffold-mediated Crosstalk between the cAMP and the Raf-1/MEK/ERK Pathways. In: Proceedings of the PASTA 2009 (2009)Google Scholar
  29. 29.
    Monteiro, P.T., Ropers, D., Mateescu, R., Freitas, A.T., de Jong, H.: Temporal logic patterns for querying dynamic models of cellular interaction networks. Bioinformatics 24(16), 227–233 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Oana Andrei
    • 1
  • Muffy Calder
    • 1
  1. 1.School of Computing ScienceUniversity of GlasgowUK

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