applying bayesian networks to modeling of cell signaling pathways

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