1. Making Sense of Complicated Microarray Data Part II Gene Clustering and Data Analysis Gabriel Eichler Boston University Some slides adapted from: MeV documentation slides

2. Why Cluster? Clustering is a process by which you can explore your data in an efficient manner. Visualization of data can help you review the data quality. Assumption: Guilt by association – similar gene expression patterns may indicate a biological relationship.

3. Expression Vectors Gene Expression Vectors encapsulate the expression of a gene over a set of experimental conditions or sample types. -0.8 0.8 1.5 1.8 0.5 -1.3 -0.4 1.5 Line Graph -2 2 Numeric Vector Heatmap

4. Expression Vectors As Points in ‘Expression Space’ Experiment 1 Experiment 2 Experiment 3 Similar Expression -0.8 -0.6 0.91.2 -0.3 1.3 -0.7 t 1t 2t 3 G1 G2 G3 G4 G5 -0.4 -0.8 -0.7 1.30.9 -0.6

5. Distance and Similarity -the ability to calculate a distance (or similarity, it’s inverse) between two expression vectors is fundamental to clustering algorithms -distance between vectors is the basis upon which decisions are made when grouping similar patterns of expression -selection of a distance metric defines the concept of distance

6. Distance: a measure of similarity between gene expression. Exp 1Exp 2Exp 3Exp 4Exp 5Exp 6 Gene A Gene B x 1A x 2A x 3A x 4A x 5A x 6A x 1B x 2B x 3B x 4B x 5B x 6B Some distances: (MeV provides 11 metrics) 1.Euclidean:  i = 1 (x iA - x iB ) 2 6 2.Manhattan:  i = 1 |x iA – x iB | 6 3. Pearson correlation p0p0 p1p1

7. Clustering Algorithms

8. Be weary - confounding computational artifacts are associated with all clustering algorithms. -You should always understand the basic concepts behind an algorithm before using it. Anything will cluster! Garbage In means Garbage Out.

9. Hierarchical Clustering (HCL-1) IDEA: Iteratively combines genes into groups based on similar patterns of observed expression By combining genes with genes OR genes with groups algorithm produces a dendrogram of the hierarchy of relationships. Display the data as a heatmap and dendrogram Cluster genes, samples or both

10. Hierarchical Clustering Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6 Gene 7 Gene 8

11. Hierarchical Clustering Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6 Gene 7 Gene 8

12. Hierarchical Clustering Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6 Gene 7 Gene 8

13. Hierarchical Clustering Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6 Gene 7 Gene 8

14. Hierarchical Clustering Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6 Gene 7 Gene 8

15. Hierarchical Clustering Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6 Gene 7 Gene 8

16. Hierarchical Clustering Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6 Gene 7 Gene 8

17. Hierarchical Clustering Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6 Gene 7 Gene 8

18. Hierarchical Clustering HL

19. The Leaf Ordering Problem: Find ‘optimal’ layout of branches for a given dendrogram architecture 2 N-1 possible orderings of the branches For a small microarray dataset of 500 genes there are 1.6*E150 branch configurations Samples Genes

20. Hierarchical Clustering The Leaf Ordering Problem:

21. Hierarchical Clustering Pros: –Commonly used algorithm –Simple and quick to calculate Cons: –Real genes probably do not have a hierarchical organization

22. Self-Organizing Maps (SOMs) ad b c Idea: Place genes onto a grid so that genes with similar patterns of expression are placed on nearby squares. A D B C

23. Self-Organizing Maps (SOMs) ad b c IDEA: Place genes onto a grid so that genes with similar patterns of expression are placed on nearby squares. A D B C

24. Self-organizing Maps (SOMs)

25. Self-organizing Maps (SOMS)

26. G en e s The Gene Expression Dynamics Inspector – GEDI Group A Group B Group C 1.51.41.71.2.85.65.50.552.52.82.72.1.78.95.75.451.11.21.01.3.56.62.78.89.45.23.15.05.82.71.62.49.11.16.11.95 2.24.56.76.22.22.52.82.9.48.901.51.8 2.12.01.91.64.24.85.25.52.52.62.01.9 1.21.11.62.91.11.81.91.41.71.21.11.6 Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6 … Group A A1A2A3A4 B1 B2 B3B4 C1C2 Group B Group C C3C4 }}} S a m p l e s G en e s 1234 H L Group AGroup B Group C GEDI’s Features: Allows for simultaneous analysis or several time courses or datasets Displays the data in an intuitive and comparable mathematically driven visualization The same genes maps to the same tiles

27. Software Demonstrations MeV available at http://www.tigr.org/software/tm4/mev.html GEDI available at http://www.chip.org/~ge/gedihome.htm

28. Comparison of GEDI vs. Hierarchical Clustering Hierarchical clustering of random data (GIGO) From: CreateGEP_Journal.wpd, random_A G.E.D.I. allows the direct visual assessment of the quality of conventional cluster analysis

29. Questions