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Applying Bayesian networks to modeling of cell signaling pathways. Kathryn Armstrong and Reshma Shetty. Outline. Biological model system (MAPK) Overview of Bayesian networks Design and development Verification Correlation with experimental data Issues Future work. MAPK Pathway. E2. E1. - PowerPoint PPT Presentation
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Applying Bayesian networks to modeling of cell signaling pathwaysKathryn Armstrong and Reshma Shetty
Outline
Biological model system (MAPK) Overview of Bayesian networks Design and development Verification Correlation with experimental data Issues Future work
MAPK Pathway
K-PP
KK-PP
KKK*KKK
E1E2
KK KK-P
K K-PKK’ase
K’ase
Overview of Bayesian Networks
Burglary Earthquake
Alarm
€
P Burglary | Alarm( ) =P B,E,A( ) + P B,^E,A( )
P B,E,A( ) + P B,^E,A( ) + P ^B,E,A( ) + P ^B,^E,A( )€
P Burglary( ) = 0.01
P Earthquake( ) = 0.01
P(A) P(^A) B E0.01 0.99 No No0.80 0.20 Yes No0.10 0.90 No Yes0.90 0.10 Yes Yes
Givens:
Bayesian network model
K-PP
KK-PP
KKK*KKK
E1E2
KK KK-P
K K-PKK’ase
K’ase
Normalized concentrations of all species
Discretized continuous concentration curves at 20 states
Considered steady-state behavior
Simplifying Assumptions
The key factor in determining the performance of a Bayesian
network is the data used to train the network.
Trainingdata
Probabilitytables
Bayesiannetwork
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
Network training II: Poor data variation
Network training III: incomplete versus complete data sets
4D
Time = (# samples)4
E1
1D x 4
E2
MAPKPase MAPKKPase
Time = (# samples) x 4
Verification: P(Kinase | E1, P’ases)Huang et al. Bayesian network
Verification: P(E1 | MAPK-PP, P’ases)
C.F. Huang and J.E. Ferrell, Proc. Natl. Acad. Sci. USA 93, 10078 (1996).
Correlation with experimental data
Correlation with experimental data
J.E. Ferrell and E.M. Machleder, Science 280, 895 (1998).
Where does our Bayesian network fail?
Where does our Bayesian network fail?
Inference from incomplete data
K-PP
KK-PP
KKK*KKK
E1E2
KK KK-P
K K-PKK’ase
K’ase
Future work Time incorporation to represent signaling
dynamics Continuous or more finely discretized
sampling and modeling of node values Priors Bayesian posterior Structure learning
Open areas of research
Should steady state behavior be modeled with a directed acyclic graph?
Cyclic networks
Hard, but doable
Theoretically impossibleNeed an alternate way to represent feedback loops
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.
Acknowledgments
Kevin Murphy Doug Lauffenburger Paul Matsudaira Ali Khademhosseini BE400 students
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).
Network training IV: final data set
E1 E2 (P’ase) MAPKKPase MAPKPase MAPK-PP0 0 0 0 00 0 0 1 00 0 1 0 00 0 1 1 00 1 0 0 00 1 0 1 00 1 1 0 00 1 1 1 01 0 0 0 11 0 0 1 11 0 1 0 11 0 1 1 01 1 0 0 11 1 0 1 01 1 1 0 01 1 1 1 0
Network training V: Final concentration ranges
Network training III: Observation of all input combinations
E1E1
MAPKKPase
E2
4D Visualization
3D Visualization
2D Visualization Time = (# samples)4
1D Visualization
E2
MAPKPase MAPKKPase