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Applying Bayesian networks to modeling of cell signaling pathways Kathryn Armstrong and Reshma Shetty

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Outline Biological model system (MAPK) Overview of Bayesian networks Design and development Verification Correlation with experimental data Issues Future work

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MAPK Pathway K-PP KK-PP KKK*KKK E1E2 KKKK-P KK-PKK’ase K’ase

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Overview of Bayesian Networks BurglaryEarthquake Alarm P(A)P(^A)BE 0.010.99No 0.800.20YesNo 0.100.90NoYes 0.900.10Yes Givens:

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Bayesian network model K-PP KK-PP KKK*KKK E1E2 KKKK-P KK-PKK’ase K’ase

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Normalized concentrations of all species Discretized continuous concentration curves at 20 states Considered steady-state behavior Simplifying Assumptions

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The key factor in determining the performance of a Bayesian network is the data used to train the network. Training data Probability tables Bayesian network

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Network training I: Data source Current experimental data sets were not sufficient to provide enough information Relied on ODE model to generate training set (Huang et al.) Captured the essential steady-state behavior of the MAPK signaling pathway

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Network training II: Poor data variation

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Network training III: incomplete versus complete data sets 4D Time = (# samples) 4 E1 1D x 4 E2 MAPKPase MAPKKPase Time = (# samples) x 4

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Verification: P(Kinase | E1, P’ases) Huang et al. Bayesian network

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Verification: P(E1 | MAPK-PP, P’ases)

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C.F. Huang and J.E. Ferrell, Proc. Natl. Acad. Sci. USA 93, 10078 (1996). Correlation with experimental data

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J.E. Ferrell and E.M. Machleder, Science 280, 895 (1998).

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Where does our Bayesian network fail?

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Inference from incomplete data K-PP KK-PP KKK*KKK E1E2 KKKK-P KK-PKK’ase K’ase

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Future work Time incorporation to represent signaling dynamics Continuous or more finely discretized sampling and modeling of node values Priors Bayesian posterior Structure learning

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Open areas of research Should steady state behavior be modeled with a directed acyclic graph? Cyclic networks Hard, but doable Theoretically impossible Need an alternate way to represent feedback loops

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Why use a Bayesian network? ODE’s require detailed kinetic and mechanistic information on the pathway. Bayesian networks can model pathways well when large amounts of data are available regardless of how well the pathway is understood.

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Acknowledgments Kevin Murphy Doug Lauffenburger Paul Matsudaira Ali Khademhosseini BE400 students

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References http://www.cs.berkeley.edu/~murphyk/Bayes/bayes.html http://www.ai.mit.edu/~murphyk/Software/BNT/usage.html A.R. Asthagiri and D.A. Lauffenburger, Biotechnol. Prog. 17, 227 (2001). A.R. Asthagiri, C.M. Nelson, A.F. Horowitz and D.A. Lauffenburger, J. Biol. Chem. 274, 27119 (1999). J.E. Ferrell and R.R. Bhatt, J. Biol. Chem. 272, 19008 (1997). J.E. Ferrell and E.M. Machleder, Science 280, 895 (1998). C.F. Huang and J.E. Ferrell, Proc. Natl. Acad. Sci. USA 93, 10078 (1996). F. V. Jensen. Bayesian Networks and Decision Graphs. Springer: New York, 2001. K.A. Gallo and G.L. Johnson, Nat. Rev. Mol. Cell Biol. 3, 663 (2002). K.P. Murphy, Computing Science and Statistics. (2001). S. Russell and P. Norvig. Artificial Intelligence: A Modern Approach. Prentice Hall: New York, 1995. K Sachs, D. Gifford, T. Jaakkola, P. Sorger and D.A. Lauffenburger, Science STKE 148, 38 (2002).

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Network training IV: final data set E1E2 (P’ase)MAPKKPaseMAPKPaseMAPK-PP 00000 00010 00100 00110 01000 01010 01100 01110 10001 10011 10101 10110 11001 11010 11100 11110

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Network training V: Final concentration ranges

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Network training III: Observation of all input combinations E1 MAPKKPase E2 4D Visualization 3D Visualization 2D Visualization Time = (# samples) 4 1D Visualization E2 MAPKPase MAPKKPase

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