1. Introduction to Microarray Data Analysis 11/17/08 – 11/24/08
CS 5263 Bioinformatics
Introduction to Microarray Data Analysis
11/17/08 – 11/24/08

2. Outline What is microarray
Basic categories of microarray
How can microarray be used
Computational and statistical methods involved in microarray
Probe design
Image processing
Pre-processing
Differentially expressed gene identification
Clustering and classification
Network / pathway modeling

3. Gene expression
Reverse transcription (in lab)
Product is called cDNA
Genes have different activities at different time / environment
DNA Microarrays
Measure gene transcription (amount of mRNA) in a high-throughput fashion
A surrogate of gene activity

4. (an old technique for measuring mRNA expression)
Northern Blot
(an old technique for measuring mRNA expression)
1. mRNA extracted and purified.
4. mRNA are transferred from the gel to a membrane.
2. mRNA loaded for electrophoresis.
Lane 1: size standards.
Lane 2: RNA to be tested.
5. A labeled probe specific for the RNA fragment is incubated with the blot. So the RNA of interest can be detected. -
3. The gel is charged and RNA “swim” through gel according to weight.
Hybridization
Need relatively large amount of mRNA +

5. RT-PCR (reverse transcription-polymerase chain reaction)
RNA is reverse transcribed to DNA.
PCR procedures can be used amplify DNA at exponential rate.
Gel quantification for the amplified product.
---- an semi-quantitative method. Smaller amount of sample needed.
See animation of RT-PCR:
real-time RT-PCR
The PCR amplification can be monitored by fluorescence in “real time”.
The fluorescence values recorded in each cycle represent the amount of amplified product.
---- a quantitative method. The current most advanced and accurate analysis for mRNA abundance. Usually used to validate microarray result.
Often used to validate microarray

6. Limitation of the old techniques
Labor intensive
Can only detect up to dozens of genes.
(gene-by-gene analysis)

7. What is a microarray
A 2D array of DNA sequences from thousands of genes
Each spot has many copies of same gene (probe)
Allow mRNAs from a sample to hybridize
Form RNA-DNA double-strand
Measure number of hybridizations per spot

8. What is a Microarray (2) Gene 9
Conceptually similar to (reverse) Northern blot
(Many) probes, rather than mRNAs, are fixed on some surface, in an ordered way

9. Microarray categories
cDNAs microarray
Each probe is the cDNA of a gene (length: hundreds to thousands nucleotides)
Stanford, Brown Lab
Oligonucleotide microarray
Each probe is a synthesized short DNA (uniquely corresponding to a substring of a gene)
Affymetrix: ~ 25mers
Agilent: ~ 60 mers
Others

10. Spotted cDNA microarray

11. Array Manufacturing
Each tube contains cDNAs corresponding to a unique gene. Pre-amplified, and spotted onto a glass slide

12. Experiment
cy3
cy5

13. Data acquisition
Computer programs are used to process the image into digital signals.
Segmentation: determine the boundary between signal and background
Results: gene expression ratios between two samples

14. cDNA Microarray Methodology Animation

15. Affymetrix GeneChip®

16. Array Design 25-mer unique oligo mismatch in the middle nuclieotide
multiple probes (11~16) for each gene
from Affymetrix Inc.

17. Array Manufacturing In situ synthesis of oligonucletides
Technology adapted from semiconductor industry.
(photolithography and combinatorial chemistry)
                                                            
In situ synthesis of oligonucletides
from Affymetrix Inc.

18. GeneChip® Probe Arrays
Hybridized Probe Cell * *
GeneChip Probe Array * * *
Single stranded,
labeled RNA target *
Oligonucleotide probe
24µm
Millions of copies of a specific
oligonucleotide probe
1.28cm
>200,000 different
complementary probes
Image of Hybridized Probe Array

19. Overview of the Affymetrix GeneChip technology
Each probe set combines to give an absolute expression level.
Image segmentation is relatively easy.
But how to use MM signal is debatable
from Affymetrix Inc.

20. Comparison of cDNA array and GeneChip cDNA GeneChip
Probe preparation
Probes are cDNA fragments, usually amplified by PCR and spotted by robot.
Probes are short oligos synthesized using a photolithographic approach.
colors
Two-color
(measures relative intensity)
One-color
(measures absolute intensity)
Gene representation
One probe per gene
11-16 probe pairs per gene
Probe length
Long, varying lengths
(hundreds to 1K bp)
25-mers
Density
Maximum of ~15000 probes.
38500 genes * 11 probes = probes

21. Why the difference? Affymetrix GeneChip One color design
cDNA microarray
Two color design
Why the difference?

22. Affymetrix GeneChip cDNA microarray Photolithography Robotic spotting
(The amount of oligos on a probe is well controlled)
cDNA microarray
Robotic spotting
(The amount of cDNA spotted on a probe may vary greatly)

23. Advantage and disadvantage of cDNA array and GeneChip
cDNA microarray
Affymetrix GeneChip
The data can be noisy and with variable quality
Specific and sensitive. Result very reproducible.
Cross(non-specific) hybridization can often happen.
Hybridization more specific.
May need a RNA amplification procedure.
Can use small amount of RNA.
More difficulty in image analysis.
Image analysis and intensity extraction is easier.
Need to search the database for gene annotation.
More widely used. Better quality of gene annotation.
Cheap. (both initial cost and per slide cost)
Expensive (~$400 per array+labeling and hybridization)
Can be custom made for special species.
Only several popular species are available
Do not need to know the exact DNA sequence.
Need the DNA sequence for probe selection.

24. Typical Microarray Analysis
Preprocess
Normalize
Filter
Raw data
•Present/Absent •Minimum value •Fold change
Significance
Classification
Clustering
Function (Gene Ontology)
Regulation (Motif finding)

25. Preprocessing Garbage in => Garbage out Background subtraction
Account for non-specific hybridization
Transformation (e.g. to log scale)
Convenience
Convert data into a certain distribution (e.g. normal) assumed by many statistical procedures
Normalization
Remove systematic biases
Make data from different samples comparable
Filtering, averaging, etc.
Remove random noises
Order may be different.
May be combined.
Garbage in => Garbage out

26. Background subtraction
For cDNA array, relatively straightforward
Raw data contain foreground and background values
Foreground values obtained from detected spots
Background values obtained from surrounding area
It may occur that background > foreground
For oligo array, probes are densely packed, so cannot be used directly. Hope: MM captures non-specific hybridization?
Recent studies suggest that PM and MM
are correlated.
Better ignore MM entirely or use with caution
Available software tools
MAS 5 (by affymetrix)
dChIP
GCRMA

27. Normalization Where errors could come from? Random noises
Repeat the same experiment twice, get diff results
Using multiple replicates reduces the problem
Systematic errors
Arrays manufactured at different time
On the same array, probes printed with different printer tips may have different biases
Dye effect: difference between Cy5 and Cy3 labeling
Experimental factors
Array A being applied more mRNAs than array B
Sample preparation procedure
Experiments carried out at different time, by different users, etc.

28. cDNA microarray data preprocessing

29. Typical experiments Probes (genes) Wide-type cells vs mutated cells
Diseased cells with normal cells
Cells under normal growth condition vs cells treated with chemicals
Typically repeated for several times
Ratios
Probes (genes)

30. Transforming cDNA microarray data
Data: Cy5/Cy3 ratios as well as raw intensities
Most common is log2 transformation
2 fold increase => log2(2) = 1
2 fold decrease => log2(1/2) = -1

31. Dye effect Solution: dye swapping.
cDNA microarray experiments using two identical samples.
Observation: Cy5 consistently lower than Cy3. (mean log (cy5/cy3) < 0)
Solution: dye swapping.

32. Dye swapping ½ log2 (cy5/cy3 on chip 1) + ½ log2 (cy3/cy5 on chip 2)
Chip 1: label test by cy5 and control by cy3
Chip 2: label test by cy3 and control by cy5
Ideally cy5/cy3 = cy3/cy5
Not so due to dye effect
Compute average ratio:
½ log2 (cy5/cy3 on chip 1)
+ ½ log2 (cy3/cy5 on chip 2)

33. Total intensity normalization
Even after dye-swapping, may still see systematic biases
Assume the total amount of mRNAs should not change between two samples
Rescale so that the two colors have same total intensity
Assumption not necessarily true
Rescale according to a subset of genes
House-keeping genes
Middle 90% (for example) of genes
Spike-in genes

34. M-A plot Also know as ratio-intensity plot
M: log2(cy5 / cy3) = log2(cy5) – log2(cy3)
A: ½ log2(cy5 * cy3) = (log2(cy5) + log2(cy3)) / 2
Ideal:
M centered at zero
variance does not depend on A.
However:
Systematic dependence between M and A
High variance of M for smaller A M A

35. Lowess normalization Lowess: Locally Weighted Regression
Fit local polynomial functions
M adjusted according to fitted line M M’ A A

36. Replicate filtering Experiments repeated
Genes with very high variability is questionable
Ratio 1
Ratio 2
Log2(ratio2)
Log2(ratio1)

37. oligo microarray data preprocessing
(Affymetrix chip)

38. Typical experiments Multiple microarrays For example
n samples (from different time, location, condition, treatment, etc.)
k replicates for each samples
For example
Samples collected from 100 healthy people and 100 cancer patients
Cells treated with some drugs, take samples every 10 minutes
Repeat on 3 – 5 microarrays for each sample
Improve reliability of the results
Often averaged after some preprocessing

39. Main characteristics
For each gene, there are multiple PM and MM probes (11-16 pairs)
how to obtain overall intensities from these probe-level intensities?
Array outputs are absolute values rather than ratios
Cross-array normalization is important for them to be comparable

40. Transformation Log transformation for one-color array
When get a data set from someone, be careful with the scale

41. Normalization Ideas similar to cDNA microarrays
For cDNA microarray arrays, normalize on log ratios.
May have one or more arrays.
Here, normalize absolute expression values.
Usually multiple array.
Total intensity normalization
Each array has the same mean intensity
Can be based on all genes or a selected subset of genes
House-keeping genes
Middle 90% (for example) of genes
Spike-in genes
Lowess: using a common reference, or cyclic
Many useful tools implemented in R (Bioconductor)

42. Quantile normalization
Normalize multiple arrays
Assume the distribution of the values obtained from each array is the same or similar
Quantile
normalization

43. Quantile normalization
Restore
order
Sort col
mean
X 3

44. An example data set
J DeRisi, V Iyer, and P Brown, “Exploring the Metabolic and Genetic Control of Gene Expression on a Genomic Scale”, Science, 278: 680 – 686, 1997
Yeast cells grow in glucose medium
When glucose was depleted, cells change their metabolic pathways
cDNA microarray
Test: 2, 4, 6, 8, 10, 12, 14 hours after growth
Control: 0 hour
Total data points: ~6000 x 7
No replicates!
No normalization!
Use fold-change to get differentially expressed genes!

45. Histogram of log ratios
Median = -0.27
Two possibilities:
Dye effect
Sample difference

46. Total intensity normalization
Median = -0.1
mean(cy3) = 3141
mean(cy5) = 2838
3141 / 2838 = 1.11
Other options:
use median
use subset of genes
Exclude 10% extreme
House-keeping genes
Spike-in genes
Etc.
Net effect: constant factor for every gene

47. Intensity-intensity plot
Total intensity
normalization
Total intensity normalization worked well here

48. Intensity-intensity plot
Total intensity
normalization
Did not work well for this experiment
Dye-swapping can probably help

49. M-A plot A: log2(cy5 * cy3) = log2(cy5)+log2(cy3)
M: log2(cy5 / cy3) = = log2(cy5)-log2(cy3)

50. M-A plot
Dependency of M on A

52. Box plot

53. Conclusions
Microarray provides a way to measure thousands of genes simultaneously and make the global monitoring of cellular activities possible.
The method produces noisy data and normalization is crucial.
Real Time RT-PCR for validation of small number of genes.

54. Limitation
Measures mRNA instead of proteins. Actual protein abundance and post-translation modification can not be detected.
Suitable for global monitoring and should be used to generate further hypothesis or should combine with other carefully designed experiments.

55. Mechanisms in microarray
Important mechanisms that make microarray work:
Reverse transcription: mRNA => cDNA. This is usually also the step to label dyes.
(Protein can not be reverse translated to mRNA or to another form. So difficult to label dyes.)
Double strand binding of complimentary DNA sequences.
(Protein does not enjoy such a good property; there are 20 amino acids without complementary binding)

56. Typical Microarray Analysis
Normalize
Filter
Raw data
•Present/Absent •Minimum value •Fold change
Significance
Classification
Clustering
Function (Gene Ontology)
Regulation (Motif finding)

57. Identify differentially expressed genes
Two samples: one normal, one cancer
Which set of genes have significantly different expression levels between the two samples?
Naïve approach: fold change threshold (e.g. two fold)
Log2 (cy5 / cy3) > 1: up-regulated / induced
Log2(cy5 / cy3) < -1: down-regulated / repressed
Still widely used – very simple
Main problem: genes with low expression levels may have a large fold change by chance
From 10 to 100: ten fold
From 1000 to 3000: three fold
However: low-intensity => relatively high variance

58. Problem with fold change
The most “differentially” expressed genes are the ones with the lowest average expression levels

59. More robust estimation of differentially expression
Estimate variance as a function of average expression
Compute a Z-score depending on location: Z(x) = (x - <x>) / (x)
x : log2(R/G) value.
<x> : local mean
(x): local standard deviation
Reference: Quackenbush, Nat Gen, 2002

60. SAM (Significance Analysis of Microarrays)
Tusher et. al. PNAS 2001, 98:
Excel add-in (free download, technical details)
Most cited method of microarray data analysis
Example: Test - 3 reps; Control - 3 reps T1 T2 T3 C1 C2 C3
Ratio
Gene1
1000
2000
1500
200
300
250 6
Gene2
3000
500 2
Gene3
100 20 80 50 8
Gene4
1800
1700
1900
800
900
Which one is more significantly differentially expressed?

61. Gene 2
Ratio = 2000/1000 = 2
Gene 4
Ratio = 1800/900 = 2

62. SAM (Significance Analysis of Microarrays)
Basic idea: compute a statistic (e.g. Student’s t-test)
Larger t => higher significance
P-value can be directly computed for t-test or estimated from permutation test
+ S0
To avoid small sample problem T1 T2 T3 C1 C2 C3
Ratio t
Gene1
1000
2000
1500
200
300
250 6
4.3
Gene2
3000
500 2
1.5
Gene3
100 20 80 50 8
1.2
Gene4
1800
1700
1900
800
900
11.0

63. Permutation test to determine significance
Gene1
1000
2000
1500
200
300
250
4.3
Perm1
0.17
Perm2
-1.3 …
Perm-n
0.7
Number of unique permutations: (6 choose 3) = 20.
Smallest possible p-value: 1/20 = 0.05
With 5 samples on each side: (10 choose 5) = 252
With 10 samples on each side: (20 choose 10) ~ 200k
For small sample size: pool all genes

64. Permutation test
Sorted
Real t t1 t2 … tn
tavg
Treal - tavg  -

65. SAM

66. False Discovery Rate (FDR)
Multiple testing problem
P-value cutoff = 0.05
We tested genes
Would expect 500 genes by chance at this significance level
Found 600 genes with p < Many might be due to noise.
Bonferroni correction
Use p-value cutoff 0.05 / 10000
Among all genes selected, P(at least one false positive) <= 0.05
Too conservative. Very few genes can be selected.
False Discovery Rate (FDR)
FDR = 0.1, meaning among all genes selected, (say 100), we would expect 10 to be false positive
FDR as high as 0.5 may be acceptable to biologists
Several different approaches to estimate (Most popular: Benjamini & Hochberg)

67. FDR in SAM Real t t1 t2 … tn tavg Treal - tavg Sorted  -
FDR = the median number of “significant” ones in permuted columns
number of significant ones in real
Small : more genes selected; higher FDR.
Large : less genes selected; lower FDR.

68. FDR in SAM
FDR = 1855/5065=36%
FDR = 1.5/209<1%

69. Typical Microarray Analysis
Normalize
Filter
Raw data
•Present/Absent •Minimum value •Fold change
Significance
Classification
Clustering
Function (Gene Ontology)
Regulation (Motif finding)

70. Source: “Practical Microarray Analysis”, Presentation by Benedikt Brors, German Cancer Research Center

71. Classification (Supervised learning)
(Clustering: unsupervised learning)
Classification: separate items into groups based on features of the items and based on a training set of previously labeled items
Many classification algorithms:
Decision tree, SVM, naïve bayes, nearest neighbors, neural networks, etc.
Some tell you how the classification is made, which might help biologists to understand the molecular mechanisms
Some are black boxes
In most cases, performance by different algs is similar. Having the right features (predictor variables) is the key.

72. AML: acute myeloid leukemia ALL: acute lymphoblastic leukemia
Classification is critical
for successful treatment.
Clinical distinction involves an experienced hematopathologist’s interpretation of tumor morphology, histochemistry, immunophenotyping, and cytogenetic analysis. each performed in a separate, highly specialized laboratory
Still imperfect and errors do occur.
Golub et. al., Molecular Classification of Cancer: Class Discovery and Class Prediction by Gene Expression Monitoring, Science 286: 531 – 537, 1999
Method: weighted vote (similar to centroid classifier)

73. Centroid-based classifierG1 x?
Model Training: Based on the training data calculate the centroid for each class.
Classification:
Given a data point, calculate the distance between the point and each of the class centroids.
Assign the point to the closest class d1 * * * d2 * c1 * * * * o o o o c2 o o o o G2
ALL centroid
AML centroid ?

74. K-Nearest-Neighbour classifier
Model Training: none
Classification:
Given a data point, locate K nearest points.
Returns the most common class label among the k points nearest to x
We usually set K > 1 to avoid outliers
Variations:
Can also use a radius threshold rather than K.
We can also set a weight for each neighbour that takes into account how far it is from the query point . _ + x

75. Cancer classification
Tons of papers have been published. Many claimed high accuracy.
Be careful when evaluating those papers.
Very easy to overfit: much more number of genes than number of samples
Simple methods often outperform fancy ones
SVM and KNN among best
Simple methods usually also mean robustness and easy to interpret
In most cases, performance by different algs is similar. Having the right features (predictor variables) is the key.

76. Clustering microarray data
Unsupervised learning
Group genes into co-expressed sets
Genes with similar expression patterns across multiple experiments may be co-regulated
Group experiments into clusters
Experiments within the same group may have similar “gene expression” signature
For example, disease sub-types that can be classified from gene expression data

77. Clustering microarray data
How to tell if two expression vectors are similar?
Define the (dis)-similarity measure between two vectors
How to group multiple profiles into meaningful subsets ?
Describe the clustering procedure
Are the results meaningful ?
Evaluate biological meaning of a clustering

78. (Dis)-similarity measures
Two genes, X=(x1,…, xm) and Y=(y1…,ym).
Euclidean distance
Pearson correlation coefficient
Cosine similarity
Mutual information
Etc.

79. Clustering algorithms
Hierarchical clustering
K-means clustering
Self Organizing Maps (SOMs)
Spectral clustering
Model-based
Graph-based
Etc.
Jiang and Zhang, Cluster Analysis for Gene Expression Data: A Survey, IEEE Transactions on Knowledge and Data Engineering, Vol. 16, No. 11. (2004), pp

80. Hierarchical clustering
Agglomerative or divisive (less popular)
Agglomerative basic idea:
Given n genes
Initially every gene in a single cluster
for each iteration
find two most similar genes (or gene groups), combine into one cluster
Terminate when only one cluster is left
(how to define similarity between two groups?)

81. Hierarchical clusteringb c d e f
Exact behavior depends on how to compute the distance between two clusters
No need to specify number of clusters
A distance cutoff is often chosen to break tree into clusters

82. Distance between clusters
Single-linkage
Not recommended
Can be reduced to MST
Complete-linkage
Average-linkage
(very similar to UPGMA)
Centroid method

83. An example
Genes
Experiments

84. Hierarchical clustering
Average linkage. Cluster genes only.

85. Average linkage. Cluster both genes and experiments.

86. Leaf ordering a b c d e f a b c f d e

87. Optimal leaf ordering
Idea: maximize sum of similarities of adjacent leaves in the ordering.
Algorithm: Dynamic Programming.
Bar-Joseph, Gifford and Jaakkola, Fast optimal leaf ordering for hierarchical clustering, Bioinformatics Vol. 17 no

88. K-means Basic idea: Given n genes Guess number of clusters: k
(Randomly) choose k genes as cluster centers
Assign each gene to the closest center
Re-compute center for each cluster
Until assignment is stable
Similarity to EM. Objective function: minimize total distance to cluster centers.
May be trapped by local optima. Multiple runs with different random starting points are generally needed.

89. K-means
K = 15

90. Another view of clusters
Log ratio
Log ratio
Experiments

91. How to determine number of clusters?
An open problem
Larger K:
More homogeneity within clusters
Less separation between clusters
Small K:
The opposite
Many heuristic methods have been proposed, none is uniformly good

92. Heuristics to determine number of clusters
Tibshirani, Walther and Hastie, Estimating the number of clusters in a dataset via the gap statistic (2000)
Define some statistic with respect to the number of clusters
Gap statistic: (weighted) average log distance to cluster centers  expected

93. Biclustering
Cheng Y, Church GM (2000). "Biclustering of expression data". Proceedings of the 8th International Conference on Intelligent Systems for Molecular Biology: 93–103.
Gene
Condition

94. Evaluating clustering
Do genes in the same cluster share similar functions?
Functional enrichment analysis
Do genes in the same cluster share similar cis-regulatory motifs?
Motif finding

95. Gene Ontology (GO) Gene functions were often defined using free text
Hard to extract, transfer, revise, predict, annotate, comprehend, manage …
The list of vocabularies should be pre-defined and commonly agreed
Gene Ontology provides a controlled vocabulary to describe gene and gene product attribute

96. Gene ontology Two parts Three ontology categories
Ontology: list of vocabularies (terms) to use
Annotations: characterizing genes using ontology terms
Three ontology categories
Biological process
Molecular function
Cellular components

97. Part of a GO graph Each GO category is a directed acyclic graph
A term can have multiple parents, and multiple children.
A gene can be annotated by multiple terms.
If annotated by a child term, automatically annotated by all ascendant terms.

98. Example functional enrichment analysis
Total number of genes in yeast: 7268
65 genes have function in co-enzyme biosynthesis
Cluster A: 100 genes
20 of them have function in co-enzyme biosynthesis
Significance can be computed using cumulative hyper-geometric test:
if we randomly draw 100 genes from the genome, what’s the chance that we’ll see at least 20 co-enzyme biosynthesis genes? 65
100 20
7268

99. Example functional enrichment analysis
If we randomly draw 100 genes from the genome, the prob that we’ll see exactly 20 co-enzyme biosynthesis genes: 65
100 20
7268
P-value of enrichment
Correction for multiple testing problem is usually preferred, as there are many GO terms being tested.
Besides GO, other information can also be used to test for enrichment. E.g. protein complexes, pathways, motifs, etc.

100. Gene Ontology Tools geneontology.org Tools for enrichment analysis
Download ontology files, species-specific annotation files
Links to many useful analysis tools
Tools for enrichment analysis
GO:TermFinder. Downloadable. (Web interface available at SGD for yeast only)
FuncAssociate: Web tool. ~a dozen model organisms (human, mouse, fruit fly, c. elegan, yeast, Arabidopsis, etc).
DAVID Bioinformatics Resources: Web tool. (Downloadable). Mammalian genes.

101. An example application
Tavazoie et al, Systematic determination of genetic network architecture, Nature Genetics, 22, 1999
3000 yeast genes, 15 time points during “cell cycle”
Use k-means clustering, k=30
Clusters correlate well with known function
AlignACE motif finding
From 600-bp upstream regions
Found many known motifs

102. Cell-division cycle
The process that a cell duplicates its genome and divides into two identical cells
Four phases
G1 (preparation)
S (DNA duplication)
G2 (preparation)
M (cell division)

103. Enriched functions in clusters

104. Motifs in Clusters

106. Comparing clustering results
When true clustering is known
Confusion matrix
Jaccard Index, Wallace Index, Rand Index, etc.
M. Meila, Comparing clusterings--an information based distance, Journal of Multivariate Analysis, 2007, 98:
When true clustering is unknown
Use Gene Ontology, e.g.
Total number of enriched GO terms (affected by # of clusters)
Product of enrichment p-values (affected by # of clusters)
Above measurement compared to random (e.g. Z-score)
Gibbons and Roth, Judging the Quality of Gene Expression-Based Clustering Methods Using Gene Annotation, Genome Res, 2002, 12:

107. Jaccard Index Real cluster (c1) K-means cluster (c2) Confusion matrix:3
total 33 31 64 24 52 76
140
Jaccard Index =
# gene-pairs in the same cluster under c1 AND c2
# gene-pairs in the same cluster under c1 OR c2
Real cluster
= 0.54
– N11
K-means cluster