1. Analysis of microarray data

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

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

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

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:

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:

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

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