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Analysis of microarray data

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1 Analysis of microarray data

2

3 HTS Using Hybridization
Microarray Chip Probe: oligos/cDNA (gene templates) + Target: cDNA (variables to be detected) Samples Hybridization Analysis of outcome Pathways Targets/Leads Disease Class. Functional Annotation Physiological states

4 Timeline for drug discovery
Discovery (5 yrs) Gene expression study Pre-Clinical (1 yr) 50 Clinical (6 yrs) 5 Review (2 yrs) 1 Marketed

5 Microarray for Yeast Figure from DeRisi et al. (See next slide).

6 cDNA Microarrays Use robot to spot glass slides at precise points with complete gene/EST sequences Able to measure qualitatively relative expression levels of genes Differential expression by use of simultaneous, two-colour fluorescence hybridisation

7 Microarray Experiment
RT-PCR DNA “Chip” High glucose RT-PCR LASER Low glucose

8 Microarray for Yeast Figure from DeRisi et al. (See next slide).

9 cDNA Microarrays Use robot to spot glass slides at precise points with complete gene/EST sequences Able to measure qualitatively relative expression levels of genes Differential expression by use of simultaneous, two-colour fluorescence hybridisation

10 Microarray Experiment
RT-PCR DNA “Chip” High glucose RT-PCR LASER Low glucose

11 Raw data – images Red (Cy5) dot overexpressed or up-regulated
Green (Cy3) dot underexpressed or down-regulated Yellow dot equally expressed Intensity - “absolute” level red/green - ratio of expression x overexpressed x underexpressed log2( red/green ) - “log ratio” x overexpressed x underexpressed cDNA plotted microarray

12 Microarray Expression Value Representation
expression value types composite spots primary spots primary measurements derived values composite images e.g., green/red ratios primary images Source: MGED

13 Analysing Expression Data
Measure gene expression levels under various conditions The more experiments the finer the classification Clustering reveals groupings of genes and/or experiments / tissues / treatments Hypothesize similar regulatory mechanisms and perhaps role Analysis of expression data needs to be integrated with other types of biological analysis and knowledge Gene 1 Gene 2 Gene n Condition 1 Condition m

14 Gene expression database – a conceptual view
Sample annotations Samples Gene annotations Gene expression matrix Genes Gene expression levels

15 Gene Expression Profiles
Measure gene expression of many genes Repeat under various conditions Which genes are behaving similarly co-regulated co-expressed

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17 Bioinformatics in microarray data
Array design Data extraction (Pixel to matrix) Background correction Data normalization Data analysis

18 Data normalization expression of gen x in experiment i
expression of gen x in reference Logarithm of ratio - treats induction and repression of identical magnitude as numerical equal but with opposite sign.

19 Levels of analysis Level 1: Which genes are induced / repressed?
Gives a good understanding of the biology. Methods: Factor-2 rule, t-test. Level 2: Which genes are co-regulated? Inference of function. -Clustering algorithms, -Support Vector Machines. Level 3: Which genes regulate others? Reconstruction of networks. - Transcriptions factor binding sites, - Bayesian networks.

20 Analysis of multiple experiments
Expression of gene x in m experiments can be represented by an exression vector with m elementer 1) The vector can be normalized so that m = 0, s2 = 1 Gener whith low expression and low variation can be correlated to gens with high expression and high variation. 2) Discretization: up regulation: +1 no regulation: 0 down regulation: -1

21 Clustering Hierachical clustering:
- Transforms n (genes) * m (experiments) matrix into a diagonal n * n similarity (or distance) matrix Similarity (or distance) measures: Euclidic distance Pearsons correlation coefficent Ud fra denne matrix kan man bygge et dendrogram, ved Eisen et al PNAS 95:

22 Key Terms in Cluster Analysis
Distance & Similarity measures Hierarchical & non-hierarchical Single/complete/average linkage Dendrograms & ordering

23 Distance Measures: Minkowski Metric

24 Most Common Minkowski Metrics

25 An Example x 3 y 4

26 Taken from http://www. icgeb. trieste

27 Similarity Measures: Correlation Coefficient

28 Similarity Measures: Correlation Coefficient
Expression Level Expression Level Gene A Gene B Gene B Gene A Time Time Expression Level Gene B Gene A Time

29 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

30 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.

31 Hierarchical Clustering
Given 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.

32 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.

33 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.

34 Single-Link Method Euclidean Distance a a,b b a,b,c a,b,c,d c d c d d
(1) (2) (3) Distance Matrix

35 Complete-Link Method Euclidean Distance a a,b a,b b a,b,c,d c,d c d c
(1) (2) (3) Distance Matrix

36 Compare Dendrograms Single-Link Complete-Link 2 4 6

37 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

38 Serum stimulation of human fibroblasts (24h) Cholesterol biosynthesis
Celle cyclus I-E response Signalling/ Angiogenesis Wound healning

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40 k-means clustering Tavazoie et al Nature Genet. 22:

41 Which clustering methods do you suggest for the following two-dimensional data?

42 Clustering by K-means Given a set S of N p-dimension vectors without any prior knowledge about the set, the K-means clustering algorithm forms K disjoint nonempty subsets such that each subset minimizes some measure of dissimilarity locally. The algorithm will globally yield an optimal dissimilarity of all subsets. K-means algorithm has time complexity O(RKN) where K is the number of desired clusters and R is the number of iterations to converges. Euclidean distance metric between the coordinates of any two genes in the space reflects ignorance of a more biologically relevant measure of distance. K-means is an unsupervised, iterative algorithm that minimizes the within-cluster sum of squared distances from the cluster mean. The first cluster center is chosen as the centroid of the entire data set and subsequent centers are chosen by finding the data point farthest from the centers already chosen iterations.

43 K-Means Clustering Algorithm
1) Select an initial partition of k clusters 2) Assign each object to the cluster with the closest center: 3) Compute the new centers of the clusters: 4) Repeat step 2 and 3 until no object changes cluster

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45 1. centroide

46 k = 6 6. centroide 5. centroide 3. centroide 1. centroide 2. centroide

47 k = 6 6. centroide 5. centroide 3. centroide 1. centroide 2. centroide

48 k = 6 6. centroide 3. centroide 5. centroide 1. centroide 2. centroide

49 Self organizing maps Tamayo et al PNAS 96:

50

51 k = 6 1. centroide 2. centroide 3. centroide 4. centroide 5. centroide

52 k = 6

53 k = 6

54 k = 6

55 Partitioning vs. Hierarchical
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

56 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

57 Clustering and promoter elements
Harmer et al Science 290:

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59 An Example Cluster (DeRisi et al, 1997)

60 Cluster of co-expressed genes, pattern discovery in regulatory regions
600 basepairs Expression profiles Retrieve Upstream regions Pattern over-represented in cluster

61 Some Discovered Patterns
Vilo et al. 2001 Pattern Probability Cluster No. Total ACGCG E ACGCGT E CCTCGACTAA E GACGCG E TTTCGAAACTTACAAAAAT 2.08E TTCTTGTCAAAAAGC E ACATACTATTGTTAAT E GATGAGATG E TGTTTATATTGATGGA E GATGGATTTCTTGTCAAAA 5.04E TATAAATAGAGC E GATTTCTTGTCAAA E GATGGATTTCTTG E GGTGGCAA E TTCTTGTCAAAAAGCA E

62 Results Jaak Vilo Over 6000 “interesting” patterns
Many from homologous upstreams - Removed Leaves 1500 patterns These patterns clustered into 62 groups Found alignments, consensus, and profiles Of 62 clusters - 48 had patterns matching SCPD (experimentally mapped) binding site database Jaak Vilo

63 The "GGTGGCAA" Cluster Jaak Vilo

64 From Gifford 2001 Science 293:2049-2050
34 genes, 140 experiments

65 Two sided clustering Alizadeh et al Nature 403:

66 Diffuse large B-cell lymphoma

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70 Principal Component Analysis
(Singular Value Decomposition) Alter et al PNAS 97:

71 Bayesian Networks Analysis
Friedman et al J. Comp. Biol., 7:

72 - Kan kun representere acykliske relationer.

73 Principal Component Analysis

74 Clustering methods Hierarchical clustering: Distance measures:
complete linkage average linkage single linkage Distance measures: Euclidean Correlation based Rank correlation Manhattan ... Partition-based K-means Specify K Randomly select “centers” Assign genes to centers Recalculate centers to “gravity center” Iterate until stabilizes Can get to local minimum Fast for large datasets Initial selection of centers


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