Analysis of microarray data

Gene expression database – a conceptual view

SamplesG

enes

Gene expression levels

Sample annotations

Gene annotations

Gene expression matrix

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

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.

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.

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.

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.

Single-Link Method

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Distance Matrix

Euclidean Distance

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Complete-Link Method

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Euclidean Distance

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Compare Dendrograms

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Single-Link Complete-Link

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

Self organizing maps

Tamayo et al. 1999 PNAS 96:2907-2912

1. centroide 2. centroide 3. centroide

4. centroide 5. centroide 6. centroide

k = 6

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

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

Clustering and promoter elements

Harmer et al. 2000 Science 290:2110-2113

An Example Cluster

(DeRisi et al, 1997)

Cluster of co-expressed genes, pattern discovery in regulatory regions

600 basepairs

Expression profiles

Upstream regions

Retrieve

Pattern over-represented in cluster

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

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

Two sided clustering

Alizadeh et al. 2000 Nature 403:505-5011

Diffuse large B-cell lymphoma

Neighborhood analysis

Golub et al 2002

Acute Leukemias

• acute lymphoblastic leukemia, ALL• acute myeloid leukemia, AML

– Not distinguishable, but different clinical outcome

Neighborhood analysis

Class predictor

Regulatory pathway reconstruction

Ideker et al Science 2001

Chromatin IP Chip (ChIP-chip)

Iver et al. 2000

Protein Function Prediction

Jensen et al 2002

NetOGlyc,NetPhos,PEST regions,PSIPRED,SEG filter,SignalP,PSORT,TMHMM.

Protein Function Prediction II

Marcotte & Eisenberg 1999

Biochemical pathways

Dandekar et al 1999

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.

Flux balance analysis

Edwards et al 2000

Comparative genome Comparative genome analysisanalysis