1. William Norris Professor and Head, Department of Computer Science
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
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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
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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
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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
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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
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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
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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
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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
11/10/2018

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
11/10/2018

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
11/10/2018