Analysis of microarray data. Gene expression database – a conceptual view Samples Genes Gene...
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Analysis of microarray data
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Gene expression database – a conceptual view
SamplesG
enes
Gene expression levels
Sample annotations
Gene annotations
Gene expression matrix
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An Example
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Distance-based Clustering
• Assign a distance measure between data • Find a partition such that:
– Distance between objects within partition (i.e. same cluster) is minimized
– Distance between objects from different clusters is maximised
• Issues :– Requires defining a distance (similarity) measure in situation
where it is unclear how to assign it– What relative weighting to give to one attribute vs another?– Number of possible partition is super-exponential
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Hierarchical Clustering Techniques
At the beginning, each object (gene) is a cluster. In each of the subsequent steps, two closest clusters will merge into one cluster until there is only one cluster left.
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Hierarchical ClusteringGiven a set of N items to be clustered, and an NxN distance (or similarity) matrix, the basic process hierarchical clustering is this:
1.Start by assigning each item to its own cluster, so that if you have N items, you now have N clusters, each containing just one item. Let the distances (similarities) between the clusters equal the distances (similarities) between the items they contain.
2.Find the closest (most similar) pair of clusters and merge them into a single cluster, so that now you have one less cluster.
3.Compute distances (similarities) between the new cluster and each of the old clusters.
4.Repeat steps 2 and 3 until all items are clustered into a single cluster of size N.
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The distance between two clusters is defined as the distance between
• Single-Link Method / Nearest Neighbor (NN): minimum of pairwise dissimilarities
• Complete-Link / Furthest Neighbor (FN): maximum of pairwise dissimilarities
• Unweighted Pair Group Method with Arithmetic Mean (UPGMA): average of pairwise dissimilarities
• Their Centroids.• Average of all cross-cluster pairs.
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Computing Distances• single-link clustering (also called the connectedness or minimum method) : we consider the distance between one cluster and another cluster to be equal to the shortest distance from any member of one cluster to any member of the other cluster. If the data consist of similarities, we consider the similarity between one cluster and another cluster to be equal to the greatest similarity from any member of one cluster to any member of the other cluster.
• complete-link clustering (also called the diameter or maximum method): we consider the distance between one cluster and another cluster to be equal to the longest distance from any member of one cluster to any member of
the other cluster.
• average-link clustering : we consider the distance between one cluster and another cluster to be equal to the average distance from any member of one cluster
to any member of the other cluster.
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Single-Link Method
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Distance Matrix
Euclidean Distance
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Complete-Link Method
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Distance Matrix
Euclidean Distance
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Compare Dendrograms
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Single-Link Complete-Link
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Ordered dendrograms
2 n-1 linear orderings of n elements (n= # genes or conditions)
Maximizing adjacent similarity is impractical. So order by:•Average expression level, •Time of max induction, or•Chromosome positioning
Eisen98
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Self organizing maps
Tamayo et al. 1999 PNAS 96:2907-2912
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1. centroide 2. centroide 3. centroide
4. centroide 5. centroide 6. centroide
k = 6
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k = 6
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k = 6
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k = 6
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Partitioning vs. Hierarchical
• Partitioning– Advantage: Provides clusters that satisfy some
optimality criterion (approximately)– Disadvantages: Need initial K, long computation
time
• Hierarchical– Advantage: Fast computation (agglomerative)– Disadvantages: Rigid, cannot correct later for
erroneous decisions made earlier
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Generic Clustering Tasks
• Estimating number of clusters
• Assigning each object to a cluster
• Assessing strength/confidence of cluster assignments for individual objects
• Assessing cluster homogeneity
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Clustering and promoter elements
Harmer et al. 2000 Science 290:2110-2113
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An Example Cluster
(DeRisi et al, 1997)
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Cluster of co-expressed genes, pattern discovery in regulatory regions
600 basepairs
Expression profiles
Upstream regions
Retrieve
Pattern over-represented in cluster
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Some Discovered PatternsPattern Probability Cluster No. TotalACGCG 6.41E-39 96 75 1088ACGCGT 5.23E-38 94 52 387CCTCGACTAA 5.43E-38 27 18 23GACGCG 7.89E-31 86 40 284TTTCGAAACTTACAAAAAT 2.08E-29 26 14 18TTCTTGTCAAAAAGC 2.08E-29 26 14 18ACATACTATTGTTAAT 3.81E-28 22 13 18GATGAGATG 5.60E-28 68 24 83TGTTTATATTGATGGA 1.90E-27 24 13 18GATGGATTTCTTGTCAAAA 5.04E-27 18 12 18TATAAATAGAGC 1.51E-26 27 13 18GATTTCTTGTCAAA 3.40E-26 20 12 18GATGGATTTCTTG 3.40E-26 20 12 18GGTGGCAA 4.18E-26 40 20 96TTCTTGTCAAAAAGCA 5.10E-26 29 13 18
Vilo et al. 2001
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Jaak Vilo
The "GGTGGCAA" Cluster ORF Gene Description
YBL041W PRE7 20S proteasome subunit(beta6) YBR170C NPL4 nuclear protein localization factor and ER translocation component YDL126C CDC48 microsomal protein of CDC48/PAS1/SEC18 family of ATPases YDL100C similarity to E.coli arsenical pump-driving ATPase YDL097C RPN6 subunit of the regulatory particle of the proteasome YDR313C PIB phosphatidylinositol(3)-phosphate binding protein YDR330W similarity to hypothetical S. pombe protein YDR394W RPT3 26S proteasome regulatory subunit YDR427W RPN9 subunit of the regulatory particle of the proteasome YDR510W SMT3 ubiquitin-like protein YER012W PRE1 20S proteasome subunit C11(beta4) YFR004W RPN11 26S proteasome regulatory subunit YFR033C QCR6 ubiquinol--cytochrome-c reductase 17K protein YFR050C PRE4 20S proteasome subunit(beta7) YFR052W RPN12 26S proteasome regulatory subunit YGL048C RPT6 26S proteasome regulatory subunit YGL036W MTC2 Mtf1 Two hybrid Clone 2 YGL011C SCL1 20S proteasome subunit YC7ALPHA/Y8 (alpha1) YGR048W UFD1 ubiquitin fusion degradation protein YGR135W PRE9 20S proteasome subunit Y13 (alpha3) YGR253C PUP2 20S proteasome subunit(alpha5) YIL075C RPN2 26S proteasome regulatory subunit YJL102W MEF2 translation elongation factor, mitochondrial YJL053W PEP8 vacuolar protein sorting/targeting protein YJL036W weak similarity to Mvp1p YJL001W PRE3 20S proteasome subunit (beta1) YJR117W STE24 zinc metallo-protease YKL145W RPT1 26S proteasome regulatory subunit YKL117W SBA1 Hsp90 (Ninety) Associated Co-chaperone YLR387C similarity to YBR267w YMR314W PRE5 20S proteasome subunit(alpha6) YOL038W PRE6 20S proteasome subunit (alpha4) YOR117W RPT5 26S proteasome regulatory subunit YOR157C PUP1 20S proteasome subunit (beta2) YOR176W HEM15 ferrochelatase precursor YOR259C RPT4 26S proteasome regulatory subunit YOR317W FAA1 long-chain-fatty-acid--CoA ligase YOR362C PRE10 20S proteasome subunit C1 (alpha7) YPR103W PRE2 20S proteasome subunit (beta5) YPR108W RPN7 subunit of the regulatory particle of the proteasome
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Two sided clustering
Alizadeh et al. 2000 Nature 403:505-5011
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Diffuse large B-cell lymphoma
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Neighborhood analysis
Golub et al 2002
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Acute Leukemias
• acute lymphoblastic leukemia, ALL• acute myeloid leukemia, AML
– Not distinguishable, but different clinical outcome
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Neighborhood analysis
Class predictor
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Regulatory pathway reconstruction
Ideker et al Science 2001
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Chromatin IP Chip (ChIP-chip)
Iver et al. 2000
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Protein Function Prediction
Jensen et al 2002
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NetOGlyc,NetPhos,PEST regions,PSIPRED,SEG filter,SignalP,PSORT,TMHMM.
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Protein Function Prediction II
Marcotte & Eisenberg 1999
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Biochemical pathways
Dandekar et al 1999
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Standard resolution | High resolution
Figure 1 Pathway alignment for glycolysis, Entner–Doudoroff pathway and pyruvate processingEnzymes for each pathway part (top; EC numbers and enzyme subunits are given below these) are compared in 17 organisms and represented as small rectangles. Filled and empty rectangles indicate the presence and absence respectively of enzyme-encoding genes in the different species listed at the left. Further details are given in the text; different isoenzymes and enzyme families are listed in Table 2.
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Flux balance analysis
Edwards et al 2000
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Comparative genome Comparative genome analysisanalysis
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