Using Bayesian Networks to Analyze Expression Data

1. Using Bayesian Networks to Analyze Expression Data N. Friedman M. Linial I. Nachman D. Pe’er Hebrew University, Jerusalem .

2. Transcription mRNA Gene Central Dogma Translation Protein Cells express different subset of the genes In different tissues and under different conditions

3. Microarrays (aka “DNA chips”) • New technological breakthrough: • Measure RNA expression levels of thousands of genes in one experiment • Measure expression on a genomic scale • Opens up new experimental designs • Many major labs are using,or will use this technology in the near future

4. Aij - the mRNA level of gene j in experiment i The Problem Genes Goal: • Learn regulatory/metabolic networks • Identify causal sources of the biological phenomena of interest j Experiments i

5. Our Approach • Characterize statistical relationships between expression patterns of different genes • Beyond pair-wise interactions • Many interactions are explained by intermediate factors • Regulation involves combined effects of several gene-products We build on the language of Bayesian networks

6. Marge Homer Lisa Maggie Bart Network: Example Noisy stochastic process: Example: Pedigree • A node represents an individual’sgenotype • Modeling assumptions: • Ancestors can effect descendants' genotype only by passing genetic materials through intermediate generations

7. Y1 Y2 X Network Structure Ancestor Generalizing to DAGs: • A child is conditionally independent from its non-descendents, given the value of its parents Often a natural assumption for causal processes • if we believe that we capture the relevant state of each intermediate stage. Parent Non-descendent Non-descendent Descendent

8. X P(Y |X) X x 0.9 0.1 x 0.3 0.7 P(Y | X) Y Y X Local Probabilities • Associated with each variable Xi is a conditional probability distribution P(Xi|Pai:) • Discrete variables: Multinomial distribution • Continuous variables: Choice: for example linear gaussian

9. B E R A C Bayesian Network Semantics • Compact & efficient representation: •  k parents  O(2kn) vs. O(2n) params • parameters pertain to local interactions Qualitative part DAG specifies conditional independence statements Quantitative part local probability models Unique joint distribution over domain + = P(C,A,R,E,B) = P(B)*P(E|B)*P(R|E,B)*P(A|R,B,E)*P(C|A,R,B,E) versus P(C,A,R,E,B) = P(B)*P(E) * P(R|E) * P(A|B,E) * P(C|A)

10. Why Bayesian Networks? Bayesian Networks: • Flexible representation of dependency structure of multivariate distributions • Natural for modeling processes with local interactions Learning of Bayesian Networks • Can learn dependencies from observations • Handles stochastic processes: • “true” stochastic behavior • noise in measurements

11. Modeling Regulatory Interactions Variables of interest: • Expression levels of genes • Concentration levels of proteins (proteomics!) • Exogenous variables: Nutrient levels, Metabolite Levels, Temperature, • Phenotype information • … Bayesian Network Structure: • Capture dependencies among these variables

12. Measured expression level of each gene Random variables Probabilistic dependencies Gene interaction A B A X B Examples Interactions are represented by a graph: • Each gene is represented by a node in the graph • Edges between the nodes represent direct dependency

13. A B C More Complex Examples • Dependencies can be mediated through other nodes • Common effects can imply conditional dependence B A B C A C Common cause Intermediate gene

14. B E R A C Outline of Our Approach Bayesian Network Learning Algorithm Expression data Use learned network to make predictions about structure of the interactions between genes

15. Experiment Data from Spellman et al. (Mol.Bio. of the Cell 1998) • Contains 76 samples of all the yeast genome: • Different methods for synchronizing cell-cycle in yeast • Time series at few minutes (5-20min) intervals • Spellman et al. identified 800 cell-cycle regulated genes.

16. 0 - + Log(ratio to control) -0.5 0.5 Methods • Treat samples as IID (ignoring temporal order) Experiment 1: • Discretized into three levels of expression • Learn multinomial probabilities Experiment 2: • Learn linear interactions (w/ Gaussian noise) No prior biological knowledge was used

17. Network Learned

18. Challenge: Statistical Significance Sparse Data • Small number of samples • “Flat posterior” -- many networks fit the data Solution • estimate confidence in network features • Two types of features • Markov neighbors: Xdirectly interacts with Y • Order relations: X is an ancestor of Y

19. B E R A C Confidence Estimates D1 Bootstrap approach[FGW, UAI99] Learn resample D2 E B D Learn resample R A C ... resample E B Dm Learn R A C Estimate:

20. Testing for Significance • We run our procedure on randomized data where we reshuffled the order of values for each gene • Histograms of number of Markov features at each confidence level Randomized Data Original Data

21. 500 Random Real 450 Random Real 400 350 300 250 200 150 100 50 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Testing for Significance • We run our procedure on randomized data where we reshuffled the order of values for each gene Markov w/ Gaussian Models 4000 3500 3000 2500 2000 Features with Confidence above t 1500 1000 500 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t

22. 250 Random Random Real Real 200 150 100 50 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Testing for Significance Markov w/ Multinomial Models 1400 1200 1000 800 Features with Confidence above t 600 400 200 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t

23. Local Map

24. Finding Key Genes Key gene: a gene that preceeds many other genes • YLR183C • MCD1 Mitotic Chromosome Determinant; • RAD27 DNA repair protein • CLN2 role in cell cycle START • SRO4 involved in cellular polarization during budding • YOX1 Homeodomain protein that binds leu-tRNA gene • POL30 required for DNA replication and repair • YLR467W • CDC5 • MSH6 Homolog of the human GTBP protein • YML119W • CLN1 role in cell cycle START

25. Future Work • Finding suitable local distribution models • Correct handling of hidden variables • Can we recognize hidden causes of coordinated regulation events? • Incorporating prior knowledge • Incorporate large mass of biological knowledge, and insight from sequence/structure databases • Abstraction • Combine with cluster analysis of higher confidence conclusions