Comparative Gene Expression Analysis: Data Analysis Issues and Solutions

1. Comparative Gene Expression Analysis: Data Analysis Issues and Solutions Vipin Kumar William Norris Professor and Head, Department of Computer Science

2. Problem Definition • Goal: gain biological insights by analyzing which genes have the same or divergent behavior across the two organisms • Techniques can identify pairs of orthologous genes between two organisms • C. albicans and S cerevisiae have 4000 such pairs

3. One Approach (Judith Berman, et al.) • Step 1: Identify clusters of functionally related orthologous genes within one organism • Select a functionally related group of genes • Find clusters using similarities computed from the gene expression data of the organism • Step 2: Split each cluster into two clusters • Use the similarities computed from the gene expression data of the second organism • Analyze for similarities and differences

4. Problems With Step 1 • Clustering techniques may produce incorrect clusters due to • Noise • Varying cluster sizes • Varying cluster density • Non-globular cluster shape • High-dimensional data • Clusters that exist in subsets of the attributes • Clusters may be overlapping • Normalization • Choice of similarity measure

5. Problems With Step 2 • Given a decomposition of genes into functionally coherent clusters for two organisms, A and B, there are a wide variety of relationships between the clusters of the two organisms • Some relationships are not captured by current approach • Example: a cluster of genes in organism A may (1) be split into two standalone clusters, or (2) be split into two groups that are just a part of larger clusters • Focusing on one cluster at a time does not take into account cross-talk between functional categories

6. Alternative #1: Similarity-Based Approach • Directly compare the pattern of similarities of a gene g in both organisms • Idea is that the function of a gene is conserved if its relationship to other genes is similar in both organisms • Degree of similarity reflects the degree of overlap • Assign a value between 0 and 1 to each pair that indicates the divergence or conservation of functionality • A value of 0 implies divergence of function • A value of 1 implies conservation of function • Intermediate values indicate intermediate degrees of conservation/divergence Orthologous pair of genes

7. Shared Nearest Neighbor Approach Idea is that the function of a gene is conserved if its relationship to other genes is similar in both organisms

8. Shared Nearest Neighbor Approach • For each pair of orthologues of a gene g in organisms A and B • Assign a measure based on the overlap of the k nearest neighbor list • Various possibilities • Fraction of overlap in k nearest neighbor list (0 indicates no overlap, 1 indicates complete overlap) • Use a weighted measure (high weight for high ranks) • A pair of orthologues that have a high value of the measure are likely to have conserved behavior

9. Alternative #2: Contrast Sets (motivated by Bay and Pazzani, KDD 99) A set of genes that have very high similarity (in expression patterns) for one organisms and low similarity for the other organism • Contrast sets can be overlapping • Set of candidates are exponentially large • Recent advantages make it possible to prune the search space and compute them efficiently

10. Alternatives for Step 2 • Assume that the output of step 1 is accurate • Could apply statistical tests for comparing distributions • T-test commonly used for comparing individual genes • Issues for comparing clusters using this scheme • Need to define a multi-dimensional version of the T-test • Only tests equality of the sample means • Assumes that the conditions are the same for the samples • Could apply techniques developed for comparing partitions (Strehl and Ghosh, 2002) • Measures of distance between partitions • Evaluate which clusters contribute most to the distance • Catch: Works only for the same data set (Correlation matrices for the two organisms in this case) • Need a more general solution

11. General solution to step 2 • Compare sets of clusters derived from two different but related data sets • Biologically-inspired overlap-based approach: • Consider cluster C1 of genes for first organism and C2 for second • |C1∩C2|/|C2|>α1 implies genes in C2 still working together for a function similar to C1 • Else, |C1∩C2|/|C2|<α2 implies genes in C2 have diverged into some other functional category • Guidelines for choosing the α’s: • Ideally, α1→1 and α2→0 • α1 should be small enough to allow splits into more than two clusters • Similarly, α2 should be just high enough to be able to identify outliers