More Analysis of Gene Expression Data

1. More Analysis of Gene Expression Data Brent D. Foy, Ph.D. Wright State University

2. Overview • Types of Data Sets • Data Analysis • Clustering • Hierarchical • Self-Organizing Maps • Principal Components Analysis • Statistical Hypothesis Testing (ANOVA)

3. Types of Data – 1D, 2 Conditions • Many genes • 2 conditions • A few replicates per condition

4. Types of Data – 1D, 2 Conditions (cont) • Conditions can be control vs treated, different cell types, different time points, etc. • Typical Question – Which genes’ expression levels change due to condition? • T-test, Mann-Whitney, Comparison Analysis

5. Types of Data – 1D, Multiple Conditions • Many genes • Multiple conditions • A few replicates per condition

6. Types of Data – 1D, Multiple Conditions (cont)

7. Types of Data – 1D, Multiple Conditions (cont) • Again, conditions can be treatments or chemicals, cell types, time points, etc. • Typical question – Which genes’ expression levels change due to one or more conditions? • 1-way ANOVA, Kruskal-Wallis

8. Types of Data – 1D, Multiple Conditions (cont) • Typical question – Which genes’ expression levels behave similarly for all the conditions? • Self-Organizing Maps, Hierarchical Clustering, Principal Components Analysis • Typical question – Which conditions show similar expression levels among genes? (Toxicogenomic Fingerprint) • Hierarchical Clustering, Principal Components Analysis, (Self-Organizing Maps)

9. Types of Data – 2D, Multiple x Multiple Conditions • Many genes • 2 Factors, multiple conditions per factor • For example, Factor 1 could be dose of a chemical, and Factor 2 could be time point after dosing • Multiple replicates per condition

10. Types of Data – 2D, Multiple x Multiple Conditions (cont)

11. Types of Data – 2D, Multiple x Multiple Conditions (cont) • Typical Question – Which genes’ expression levels change due to time? Due to dose? Due to an interaction between the two? • 2-way ANOVA • Or, eliminate one of the dimensions and ask the same questions as before – At time 1, which doses show similar expression levels among genes?

12. Typical Applications of Clustering Algorithms Many samples/cell lines/chemicals, Principal components of genes Many samples/cell lines/chemicals, Many genes chem3 chem3 6 6 chem2 chem2 4 4 chem6 chem6 chem1 Gene B chem1 Principal component 2 2 2 chem5 chem5 chem4 chem4 0 0 0 2 4 6 0 2 4 6 Principal component 1 Gene A Number of axes can be very large here

13. Typical Applications of Clustering Algorithms Many genes, multiple time points. (Different letters represent different genes.) Many genes, multiple doses B C 8 6 B 6 C A 4 F E Dose 2 A 4 T2 D 2 F 2 E D 0 0 0 2 4 6 8 0 2 4 6 Dose 1 T1 Number of dimensions (time points) can be greater than 2 Reasons to cluster genes of similar behavior together?

14. Hierarchical Clustering • Focus on 1D, multiple conditions type of data • Here, group cell types according to similar gene response

15. chem3 6 chem2 4 chem6 chem1 Gene B 2 chem5 chem4 0 0 2 4 6 Gene A Hierarchical Clustering (cont) Construct pairwise groupings of data elements based on similarity. Definition of similarity is typically the separation of data elements in n-dimensional space. Chem 2 Chem 3 Chem 1 Chem 6 Chem 4 Chem 5 Generation 3 2 1 0 # clusters 6 3 2 1

16. C B F A E D Hierarchical clustering - chooses pairwise groupings based on distances between pairs of points Once the two closest points are found, the two are grouped together, and a new point is placed at the average location of the old 2 points.

17. Hierarchical clustering • Advantages • Computationally efficient • Produces tree-like structure • Disadvantage • Clusters are not optimal. Once branches split, it’s permanent. There is no way to reevaluate whether it was the best division based on whole data set.

18. Principal Component Analysis • - Each data point is a single condition • Each axis is a linear combination of hundreds or • thousands of gene expression levels

19. Principal Component Analysis • Reduces the dimensionality of the data set • Thousands of genes are combined in a few linear combinations to make 2 or 3 Principal Components (PC). Going from thousands of axes, with each axis representing the expression level for a gene, to 2 or 3 axes. • These few PCs may capture most of the variability of the original data set • Hope is that the first few PCs extract or expose the cluster structure of the original data set • i.e. Another clustering algorithm still needed after PCA

20. Principal Component Analysis – A Simple Example PC1

21. Self Organizing Maps • Partition data into specified number of groupings. • Iterative procedure, so seeks to produce optimal clusters. • K-means clustering is a specific form of the self-organizing map

22. Self Organizing Maps - General Procedure Consider n data points in d-dimensional space. In the hypothetical data set, there are 6 data points (gene expression levels) in 2-dimensional space (2 time points). Say you want k = 3 clusters. 1. Select k of your data points to each be the original center of a cluster 2. Place the next data point in the nearest cluster 3. Compute the new location of the cluster center 4. Repeat the previous 2 steps for each data point 5. After all data is placed in a cluster, use final cluster centers as starting point for another iteration beginning at step 2.

23. C B A F E D Self Organizing Maps – Simple Example

24. Let Genes A, B, and C be initial cluster centers. Clusters after 1st pass C C B B F A F A E E D D Clusters after 2nd pass C B F A E D

25. Self Organizing Maps – Simple Example

26. Self Organizing Maps – Larger example • X-axis is time after dose • Y-axis is normalized gene expression level • Group ~1000 genes into 24 categories

27. Self Organizing maps - details to consider • Several methods exist for choosing initial data points for clusters. • How to choose the initial number of clusters. • Method of recalculating cluster center after adding a new data point can be varied. How much ‘weight’ is given to new data point. • Routines for merging and dividing clusters and detecting outliers can be added at each iteration.

28. Self Organizing maps • Advantages • Able to come closer to ‘optimal’ clustering through iterations. • Doesn’t force a tree-structure on data • Disadvantage • Larger number of options for clustering means that details of process may be hidden.

29. Data Preprocessing • Filter data • Remove genes with expression levels in the noise • Focus on a group of genes with a particular function • Normalize data • Subtract a control condition • Scale so that a gene whose expression level changes from 5000 to 10000 looks the same as a gene whose expression level changes from 500 to 1000. One possibility is to scale all genes to mean of 0 and standard deviation of 1.

30. Detecting Statistically Significant Changes • Consider 1D, multiple conditions • 1-way ANOVA • Similar tests for 1D, 2 condition data: • Fold changes • Tests Steve described in previous talk (Mann-Whitney, Comparison Analysis)

31. 1D, Multiple Condition Data

32. 1-Way ANOVA • Question being asked is whether the expression level for each gene (taken one at a time) changes significantly as a function of dose. • More specifically, it compares the variability within replicates for a given dose to the variability caused by changing the dose. • If gene chip contains 1000 genes, then do 1000 ANOVAs. • Consider “repeated measures ANOVA” if multiple measurements done on same animal

33. ANOVA for Hepatocytes exposed to Hydrazine, time 0

34. 2-way ANOVA • Apply to 2D, multiple x multiple condition data sets • Consider 3 doses, 5 time points per dose, 2 replicates per condition • Can reveal significant effect of time, significant effect of dose, or a significant interaction between the two • A “2-way repeated measures ANOVA” also exists

35. 2-way ANOVA for Hydrazine Data – Output for 1 gene

36. 2-Way ANOVA – p-value Summary for 10 Genes

37. 2-Way ANOVA – Dose effect Red, 0 mM Green, 50 mM Blue, 75 mM

38. 2-way ANOVA – Time x Dose effect

39. Software • Free • Eisen’s software Cluster, Treeview • Hierarchical clustering, SOM • http://rana.lbl.gov/ • Genecluster • SOM • http://www-genome.wi.mit.edu/cancer/software/software.html

40. Software (cont) • Commercial, gene-specific • Genelinker Gold • PCA, clustering, SOM, statistics • http://microarray.genelinker.com/products.html#GeneLinkerGold • GeneSpring • PCA, clustering, SOM, statistics • http://www.sigenetics.com/cgi/SiG.cgi/Products/GeneSpring/index.smf • Rosetta • PCA, clustering, SOM, ANOVA • http://www.rosettabio.com/products/resolver/default.htm • Several others

41. Software (cont) • Tools, not gene specific • Matlab • SPSS • SAS • A useful web site, briefly summarizes many software packages, up-to-date • http://ihome.cuhk.edu.hk/~b400559/arraysoft.html

42. Collaborators AFIT Dr. Dennis Quinn Rebecca Olson Tom Hopkins 2Lt Matt Campbell WSU Dr. Nick Reo Dr. Steve Berberich Dr. Tatiana Karpinets AFRL Dr. John Frazier Dr. Charles Wang Dr. Victor Chan AFOSR Dr. Walt Kozumbo

43. Questions?