Probabilistic Approximations of Signaling Pathway Dynamics

  • Bing Liu
  • P. S. Thiagarajan
  • David Hsu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5688)


Systems of ordinary differential equations (ODEs) are often used to model the dynamics of complex biological pathways. We construct a discrete state model as a probabilistic approximation of the ODE dynamics by discretizing the value space and the time domain. We then sample a representative set of trajectories and exploit the discretization and the structure of the signaling pathway to encode these trajectories compactly as a dynamic Bayesian network. As a result, many interesting pathway properties can be analyzed efficiently through standard Bayesian inference techniques. We have tested our method on a model of EGF-NGF signaling pathway [1] and the results are very promising in terms of both accuracy and efficiency.


Model Check Probabilistic Approximation Latin Hypercube Sampling Dynamic Bayesian Network Global Sensitivity Analysis 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Brown, K.S., Hill, C.C., Calero, G.A., Lee, K.H., Sethna, J.P., Cerione, R.A.: The statistical mechanics of complex signaling networks: nerve growth factor signaling. Phys. Biol. 1, 184–195 (2004)CrossRefPubMedGoogle Scholar
  2. 2.
    Matsuno, H., Tanaka, Y., Aoshima, H., Doi, A., Matsui, M., Miyano, S.: Biopathways representation and simulation on hybrid functional Petri net. Silico Biol. 3(3), 389–404 (2003)Google Scholar
  3. 3.
    Murphy, K.P.: Dynamic Bayesian Networks: Representation, Inference and Learning. PhD thesis, University of California, Berkeley (2002)Google Scholar
  4. 4.
    Antoniotti, M., Policriti, A., Ugel, N., Mishra, B.: XS-systems: extended s-systems and algebraic differential automata for modeling cellular behavior. In: Sahni, S.K., Prasanna, V.K., Shukla, U. (eds.) HiPC 2002. LNCS, vol. 2552, pp. 431–442. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. 5.
    de Jong, H., Page, M.: Search for steady states of piecewise-linear differential equation models of genetic regulatory networks. IEEE/ACM T. Comput. Bi. 5(2), 208–223 (2008)CrossRefGoogle Scholar
  6. 6.
    Ghosh, R., Tomlin, C.: Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta-notch protein signalling. Systems Biol. 1(1), 170–183 (2004)CrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    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
  9. 9.
    Ciocchetta, F., Degasperi, A., Hillston, J., Calder, M.: CTMC with levels models for biochemical systems. Elsevier, Amsterdam (2009) (preprint submitted)Google Scholar
  10. 10.
    Nodelman, U., Shelton, C.R., Koller, D.: Continuous time Bayesian networks. In: Proceedings of the 18th Conference in Uncertainty in Artificial Intelligence, Alberta, Canada, pp. 378–387 (2002)Google Scholar
  11. 11.
    Langmead, C., Jha, S., Clarke, E.: Temporal logics as query languages for dynamic Bayesian networks: Application to D. Melanogaster embryo development. Technical report, Carnegie Mellon University (2006)Google Scholar
  12. 12.
    Clarke, E.M., Faeder, J.R., Langmead, C.J., Harris, L.A., Jha, S.K., Legay, A.: Statistical model checking in BioLab: Applications to the automated analysis of T-Cell receptor signaling pathway. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 231–250. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Heath, J., Kwiatkowska, M., Norman, G., Parker, D., Tymchyshyn, O.: Probabilistic model checking of complex biological pathways. Theor. Comput. Sc. 319(3), 239–257 (2008)CrossRefGoogle Scholar
  14. 14.
    Geisweiller, N., Hillston, J., Stenico, M.: Relating continuous and discrete PEPA models of signalling pathways. Theor. Comput. Sc. 404(2), 97–111 (2008)CrossRefGoogle Scholar
  15. 15.
    Murphy, K.P., Weiss, Y.: The factored frontier algorithm for approximate inference in DBNs. In: Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence, San Francisco, CA, USA, pp. 378–385 (2001)Google Scholar
  16. 16.
  17. 17.
    Ammann, H.: Ordinary Differential Equations: An Introduction to Nonlinear Analysis. Walter de Gruyter, Berlin (1990)CrossRefGoogle Scholar
  18. 18.
    Durrett, R.: Probability: Theory and Examples. Duxbury Press (2004)Google Scholar
  19. 19.
    Nunez, L.M.: On the relationship between temporal Bayes networks and Markov chains. Master’s thesis, Brown University (1989)Google Scholar
  20. 20.
    Kholodenko, B.N.: Untangling the signalling wires. Nat. Cell Biol. 9(3), 247–249 (2007)CrossRefPubMedPubMedCentralGoogle Scholar
  21. 21.
    Banga, J.R.: Optimization in computational systems biology. BMC Syst. Biol. 2(47), 1–7 (2008)Google Scholar
  22. 22.
    Gutenkunst, R.N., Waterfall, J.J., Casey, F.P., Brown, K.S., Myers, C.R., Sethna, J.P.: Universally sloppy parameter sensitivities in systems biology. PLoS Comput. Biol. 3(10), 1871–1878 (2007)CrossRefPubMedGoogle Scholar
  23. 23.
    Hooke, R., Jeeves, T.A.: “Direct search” solution of numerical and statistical problems. J. ACM. 8(2), 212–229 (1961)CrossRefGoogle Scholar
  24. 24.
    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)CrossRefPubMedGoogle Scholar
  25. 25.
    Cho, K.H., Shin, S.Y., Kolch, W., Wolkenhauer, O.: Experimental design in systems biology, based on parameter sensitivity analysis using a monte carlo method: A case study for the TNFα-mediated NF-κB signal transduction pathway. Simulation 79(12), 726–739 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Bing Liu
    • 1
  • P. S. Thiagarajan
    • 1
    • 2
  • David Hsu
    • 1
    • 2
  1. 1.NUS Graduate School for Integrative Sciences and EngineeringNational University of SingaporeSingapore
  2. 2.Department of Computer ScienceNational University of SingaporeSingapore

Personalised recommendations