Abstract
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.
Keywords
- 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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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)
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)
Murphy, K.P.: Dynamic Bayesian Networks: Representation, Inference and Learning. PhD thesis, University of California, Berkeley (2002)
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)
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)
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)
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)
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)
Ciocchetta, F., Degasperi, A., Hillston, J., Calder, M.: CTMC with levels models for biochemical systems. Elsevier, Amsterdam (2009) (preprint submitted)
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)
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)
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)
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)
Geisweiller, N., Hillston, J., Stenico, M.: Relating continuous and discrete PEPA models of signalling pathways. Theor. Comput. Sc. 404(2), 97–111 (2008)
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)
Supplementary Materials, http://www.comp.nus.edu.sg/~rpsysbio/cmsb09
Ammann, H.: Ordinary Differential Equations: An Introduction to Nonlinear Analysis. Walter de Gruyter, Berlin (1990)
Durrett, R.: Probability: Theory and Examples. Duxbury Press (2004)
Nunez, L.M.: On the relationship between temporal Bayes networks and Markov chains. Master’s thesis, Brown University (1989)
Kholodenko, B.N.: Untangling the signalling wires. Nat. Cell Biol. 9(3), 247–249 (2007)
Banga, J.R.: Optimization in computational systems biology. BMC Syst. Biol. 2(47), 1–7 (2008)
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)
Hooke, R., Jeeves, T.A.: “Direct search” solution of numerical and statistical problems. J. ACM. 8(2), 212–229 (1961)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, B., Thiagarajan, P.S., Hsu, D. (2009). Probabilistic Approximations of Signaling Pathway Dynamics. In: Degano, P., Gorrieri, R. (eds) Computational Methods in Systems Biology. CMSB 2009. Lecture Notes in Computer Science(), vol 5688. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03845-7_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-03845-7_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03844-0
Online ISBN: 978-3-642-03845-7
eBook Packages: Computer ScienceComputer Science (R0)