1. Analysis of Gene Expression Data
Rainer Breitling
Bioinformatics Research Centre and Institute of Biomedical and Life Sciences
University of Glasgow

2. Outline Gene expression biology Measuring gene expression levels
two technologies: Two-color cDNA arrays and single-color Affymetrix genechips
Finding and understanding differentially expressed genes
Advanced analysis (clustering and classification)
Cutting-edge uses of microarray technology

3. Gene expression biology

4. The central dogma of biology

5. Genome information is complete for hundreds of organisms...

6. ...but the complexity and diversity of the resulting phenotype is challenging
whole-mount in situ hybridization of X. laevis tadpoles

7. The dramatic consequences of gene regulation in biology
Same genome 
Different tissues
Different physiology
Different proteome
Different expression pattern
Anise swallowtail, Papilio zelicaon

8. The complexity of eukaryotic gene expression regulation

9. Regulatory Networks – integrating it all together
Genetic regulatory network controlling the development of the body plan of the sea urchin embryo Davidson et al., Science, 295(5560):

10. Gene expression distinguishes...
...physiological status (nutrition, environment)
...sex and age
...various tissues and cell types
...response to stimuli (drugs, signals, toxins)
...health and disease
underlying pathogenic diversity
progression and response to treatment
patient classes of varying prospects

11. Measuring gene expression levels
total amount of mRNA = optical density at appropriate (UV) wavelength
mass separation and specific probing, one gene at a time = Northern blot
comprehensive “molecular sorting” = microarray technology
two-color cDNA or oligo arrays
single-color Affymetrix genechips

12. cDNA microarray schema
color code for relative expression
From Duggan et al. Nature Genetics 21, 10 – 14 (1999)

13. cDNA microarray raw data
can be custom-made in the laboratory
always compares two samples
relatively cheap
up to about 20,000 mRNAs measured per array
probes about 50 to a few hundred nucleotides
Yeast genome microarray. The actual size of the microarray is 18 mm by 18 mm. (DeRisi, Iyer & Brown, Science, 268: , 1997)

15. GeneChip® Affymetrix

16. GeneChip® Hybridization
Image courtesy of Affymetrix.

17. Affymetrix genearrays
single color (color code indicates only hybridization intensity)
high density, perfectly addressable probes
multiple probes per gene/mRNA

18. Affymetrix genechips contain “probe sets” instead of single probes per gene  better reliability of the results (each probe is [almost] an independent test)

19. Mismatch probes allow present/absence calls for every single probe set
PM probes
MM probes
Wilcoxon Signed Rank Test : non-parametric test; Take the paired observations (PM-MM), calculate the differences, and rank them from smallest to largest by absolute value. Add all the ranks associated with positive differences, giving the T+ statistic. Finally, the p-value associated with this statistic is found from an appropriate table. (MathWorld)

20. Finding and understanding differentially expressed genes

23. Scatter plots classical scatter plot M-A plot for microarray analysis
Differentially expressed genes are higher (or lower) in one of the samples
Use an appropriate cut-off (‘distance’ from diagonal) to select relevant genes  highly arbitrary!

24. t-test = statistical significance of observed difference
requires independent experimental replication
assumes the data are identically normally distributed

25. Testing an intrinsic hypothesis
Frequency
Sample 2
Sample 1
Two samples (1, 2) with mean expression that differ by some amount d.
If H0 : d = 0 is true, then the expected distribution of the test statistic t is -3 -2 -1 1 2 3
Probability

26. Volcano plot
A volcano plot is a scatter plot of -log (p-value) from a t-test or one-way ANOVA, versus log ratio. It allows you to visualize fold-change and statistical significance at the same time, so that one can find genes that are significant and have large fold change, or genes that are significant but have small fold change.
Scatter plot of -log(p-value) from a t-test vs. log ratio. Visualises fold-change and statistical significance at the same time: Find genes that are significant and have large fold change, and genes that are significant but have small fold change.

27. Is this gene changed? Rank Product:
Comparison with all other genes on the array
Expression of gene A
Rank Product:
RP = (3/10) * (1/10) * (2/10) * (5/10)
intuitive
non-parametric, powerful test statistic
more reliable detection of changed genes in noisy data with few replicates
Significance estimate based on random permutations:
Probability that gene A shows such an effect by chance: p ≤ 0.03
Expectation to see any gene (out of 10) with such a effect: E-value ≈ 0.5
Breitling et al., FEBS Letters, 2004

28. Multiple Testing Problem
microarrays measure expression of >10,000 genes at the same time  many thousands of statistical tests are performed
type 1-error: Calling a gene significantly changed, even if it’s just by chance  protect yourself by Bonferroni correction
type 2-error: Missing a significantly changed gene  reduce this problem by Benjamini-Hochberg false-discovery rate procedure

29. Multiple Testing Problem
Bonferroni correction. n independent tests, control the probability that a spurious result passes the test at signficance level α  adjust acceptance level for each individual test as:
Benjamini-Hochberg False Discovery Rate. Control the number of false positives (N1|0) among the top R genes at the significance level α.

30. The result of “differential expression” statistical analysis  a long list of genes!
Fold-Change
Gene Symbol
Gene Title 1
26.45
TNFAIP6
tumor necrosis factor, alpha-induced protein 6 2
25.79
THBS1
thrombospondin 1 3
23.08
SERPINE2
serine (or cysteine) proteinase inhibitor, clade E (nexin, plasminogen activator inhibitor type 1), member 2 4
21.5
PTX3
pentaxin-related gene, rapidly induced by IL-1 beta 5
18.82 6
16.68
CXCL10
chemokine (C-X-C motif) ligand 10 7
18.23
CCL4
chemokine (C-C motif) ligand 4 8
14.85
SOD2
superoxide dismutase 2, mitochondrial 9
13.62
IL1B
interleukin 1, beta 10
11.53
CCL20
chemokine (C-C motif) ligand 20 11
11.82
CCL3
chemokine (C-C motif) ligand 3 12
11.27 13
10.89
GCH1
GTP cyclohydrolase 1 (dopa-responsive dystonia) 14
10.73
IL8
interleukin 8 15
9.98
ICAM1
intercellular adhesion molecule 1 (CD54), human rhinovirus receptor 16
9.97
SLC2A6
solute carrier family 2 (facilitated glucose transporter), member 6 17
8.36
BCL2A1
BCL2-related protein A1 18
7.33
TNFAIP2
tumor necrosis factor, alpha-induced protein 2 19
6.97
SERPINB2
serine (or cysteine) proteinase inhibitor, clade B (ovalbumin), member 2 20
6.69
MAFB
v-maf musculoaponeurotic fibrosarcoma oncogene homolog B (avian)

31. Biological Interpretation Strategy
Are certain types of genes more common at the top of the list and is that significant?
Challenges:
Some types of genes are more common in the genome/on the array
The list of genes usually stops at an arbitrary cut-off (“significantly changed genes”)
Classifying genes according to “gene type” is a tedious task
Expectations and focused expertise might bias the interpretation
Early discoveries might restrict further analysis
Solution: Automated procedure using available annotations

32. iterative Group Analysis (iGA)
iGA uses a simple hypergeometric distribution to obtain p-values
Breitling et al. (2004), BMC Bioinformatics, 5:34.

33. Possible sources of classification
adjacency in metabolic networks
shared biological processes
co-expression in microarray experiments
co-occurrence in the biomedical literature
gene ontology annotations (shared terms from a controlled vocabulary)

34. Graph-based iGA
exploits the overlap of annotations to produce a comprehensive picture of the microarray results

35. Graph-based iGA
1. step: build the network

36. Graph-based iGA
2. step: assign experimentally determined ranks to genes

37. Graph-based iGA 3. step: find local minima p = 1/8 = 0.125

38. Graph-based iGA 4. step: extend subgraph from minima p=0.014 p=0.018

39. Graph-based iGA 5. step: select p-value minimum p=0.014 p=0.018

40. small ribosomal subunit large ribosomal subunit nucleolar rRNA
processing
translational
elongation
Breitling et al., BMC Bioinformatics, 2004

41. oxidative phosphorylation (complex V)
respiratory chain
complex II
glyoxylate
cycle
citrate (TCA) cycle
oxidative phosphorylation
(complex V)
respiratory chain
complex III
Breitling et al., BMC Bioinformatics, 2004

42. Advanced analysis (clustering and classification)

43. Classical study of cancer subtypes
Golub et al. (1999)
identification of diagnostic genes

44. Similarity between microarray experiments or expression patterns
 distance between points in high dimensional space
Pearson correlation (looks for similarity in shape of the response profile, not the absolute values)
Euclidean distance (shortest direct path), takes absolute expression level into account
There are many ways of conceptualizing the correlation coefficient. If you were to make a scatterplot of the values of x against y (pairing x1 with y1, x2 with y2, etc), then r reports how well you can fit a line to the values.
The simplest way to think about the correlation coefficient is to plot x and y as curves, with r telling you how similar the shapes of the two curves are. The Pearson correlation coefficient is always between -1 and 1, with 1 meaning that the two series are identical, 0 meaning they are completely uncorrelated, and -1 meaning they are perfect opposites. The correlation coefficient is invariant under linear transformation of the data. That is, if you multiply all the values in y by 2, or add 7 to all the values in y, the correlation between x and y will be unchanged. Thus, two curves that have identical shape, but different magnitude, will still have a correlation of 1.
The Euclidean distance takes the difference between two gene expression levels directly. It should therefore only be used for expression data that are suitably normalized, for example by converting the measured gene expression levels to log-ratios. Unlike the correlation-based distance measures, the Euclidean distance takes the magnitude of changes in the gene expression levels into account. It therefore preserves more information about the gene expression levels than the other distance measures mentioned above. An example of the Euclidean distance applied to k-means clustering can be found in De Hoon, Imoto, and Miyano (2002).
The city-block distance, alternatively known as the Manhattan distance, is related to the Euclidean distance. Whereas the Euclidean distance corresponds to the length of the shortest path between two points, the city-block distance is the sum of distances along each dimension:
This is equal to the distance you would have to walk between two points in a city, where you have to walk along city blocks. The city-block distance is a metric, as it satisfies the triangle inequality. As for the Euclidean distance, the expression data are subtracted directly from each other, and we should there fore make sure that they are properly normalized.
Manhattan (or city-block) distance

45. Gene expression data analysis
(Ramaswamy and Golub 2002)

46. Hierarchical clustering
Combine most similar genes into agglomerative clusters, build tree of genes
Do the same procedure along the second dimension to cluster samples
Display the sorted expression values as a heatmap

47. Hierarchical clustering results
Chi et al., PNAS | September 16, 2003 | vol. 100 | no. 19 |
“Endothelial cell diversity revealed by global expression profiling”

48. Biologically Valid Linear Factor Models of Gene Expression
expression level of gene g in array a
expression level of gene x in hypothetical process p
contribution of process p to expression pattern in array a
experiment- and gene-specific noise
M. Girolami & R. Breitling (2004), Bioinformatics, 20(17):

49. Biologically Valid Linear Factor Models of Gene Expression
M. Girolami & R. Breitling (2004), Bioinformatics, 20(17):

50. Support Vector Machines (SVM) for supervised classification
Find separating hyperplane that maximizes the margin between the two classes  use this to classify new samples (e.g. in a microarray-based diagnostic test)

51. Excursus: Experimental design
common
reference
loop
Kerr & Churchill, Biostatistics Jun;2(2):
A-Optimality = minimize

52. Cutting-edge uses of microarray technology

53. Alternative splicing on microarrays
Alternative Splicing Microarrays Reveal Functional Expression of Neuron-specific Regulators in Hodgkin Lymphoma Cells
Examples of changes in alternative splicing in Hodgkin cell lines. A, changes in expression of p16/p14arf isoforms. The genomic structure of the locus and splicing patterns are represented. Alternative transcription initiation sites are indicated by brown arrows, exons are indicated by boxes, and splicing patterns are indicated by thin lines. Arrows indicate increase (arrows pointing up), decrease (arrows pointing down), or no change (double-headed horizontal arrows) in the detection of exons or splice junctions in RNAs from Hodgkin cell lines (indicated with a color code) as compared with a reference non-tumor B cell line. B, changes in expression of CD44 isoforms. Exons v2–v10 are variable exons that can be included or skipped in various combinations, affecting the cell adhesion properties of the protein product. Genomic structure, splicing patterns, and changes in splicing are indicated as in A.
FIG. 3. Unsupervised clustering analyses of microarray data. Microarray results for splicing events (exons/splice junctions) for 16 RNA preparations were clustered using Gene Spring 6.2 software. Each column represents an RNA sample, and each row represents an exon/splicing event. Colors vary from blue to red with increasing signal intensity and from dark to bright with the confidence on the value observed in multiple measurements. Colors at the bottom row and in dendrograms represent the different cell lines, as indicated.
Relogio et al., J. Biol. Chem., Vol. 280, Issue 6, , February 11, 2005

54. Customised detection of genetic polymorphisms in human patients
individual genotype  personalised medicine
example: ARRAYED PRIMER EXTENSION (APEX)
2.Complementary fragment of PCR amplified sample DNA is annealed to oligos.
1. Up to 6000 known 25-mer oligos are immobilized via 5’ end on a microarray
4. DNA fragments and unused dye terminators are washed off. Signal detection.
3. Template dependent single nucleotide extension by DNA polymerase. Terminator nucleotides are labelled with 4 different fluorescent dyes.

55. Identification of pathogens in environmental (patient) samples – Sequencing by hybridization
Fig. 1. Pathogen screening with oligonucleotide arrays. (A) Scanned image of a portion of the MPID microarray
showing relative fluorescence intensity (in pseudocolor scale, increasing from blue to white) of probes corresponding to
8 Yersinia pestis-diagnostic regions from which amplicons and probes are derived. (B) Magnification of the first 20
probe pairs of probe set Yp5 (from Y. pestis caf1 virulence gene) hybridizing to Y. pestis target DNA (yellow box in A
above); each 20-base perfect match (PM) probe square distinctly matching the pathogen’s diagnostic sequence is paired
with mismatch (MM) partner, physically located in the adjacent, lower position on the microarray. The relative
fluorescence intensity results for each probe pair is graphically displayed with red bars for PM intensity and green bars
for MM intensity. This probe set continues with additional 328 probe pairs. (C) Microarray probe design. Overlapping
sequences advance by one nucleotide over the entire diagnostic sequence, essentially sequencing the entire region by
hybridization. The beginning of the jcaf1 gene sequence (capitalized) is shown, with the first 20 corresponding MM
probes underneath, identical to the PM probes except for a mismatch at position 11 of its partners
20-meroligonucleotide (substitution highlighted in red).
between 3 and 10 probe sets per species, each containing a few hundred probes
sensitivity about 500fg pathogen genomic DNA per sample
Wilson et al. Molecular and Cellular Probes, Volume 16, Issue 2 , April 2002, Pages

56. Global identification of transcription factor target sites using chromatin immunoprecipitation plus whole-genome tiling microarrays (ChIP-chip)
preferably the array should provide continuous genome coverage, not just ORFs
Hanlon & Lieb: Current Opinion in Genetics & Development Volume 14, Issue 6 , December 2004, Pages

57. Directed graph of regulatory influences – gene network
Inference of gene regulatory networks from gene expression data (indirect method, in contrast to the direct ChIP-chip approach
remove ambiguous relationships
(remove indirect connections)
(A)
Obtain the gene expression matrix  using several sets of the gene expression patterns resulting from disruption of one gene.
(B)
Binary relation R; Using the gene expression matrix  , if the intensity of gene ` ' is changed higher than a given threshold value  , or is changed lower than a given threshold 1/ resulting from the disruption of gene ` ,' it is defined that gene ` ' affects gene ` ' directly or indirectly. Thus the binary relation  is created by cutting the value of each element in the gene expression matrix  at the threshold ( or 1/ ).
(C)
Adjacency matrix A; The adjacency matrix A is derived directly from the binary relation  . If there is a relation that gene ` ' affects gene ` ', then the value of element  in the adjacency matrix  is set to 1; .
(D)
Equivalence set; If there is the relation, such that gene ` ' and ` ' affect each other, that is , we cannot decide which gene is located upstream or downstream in a gene regulatory network. This is the limitation and disadvantage of this method, however, we introduce an ``equivalence set'', which comprises a group of genes affecting each other and the group is treated as a one-gene node for determining influence on other genes. In Fig. 1, genes G3 and G4 are partitioned into a equivalence set G3**, or a new artificial gene G3**, and the adjacency matrix A is contracted to a matrix. After this process, any two genes, gene ` ' and gene ` ', stand in only one relation, that is ``Gene affects gene ,'' ``Gene affects gene '' or ``Gene and are independent.'' This shows that genes are in a semi-ordered (topologically sorted) matrix.
(E)
Skeleton matrix S; Semi-ordered matrix A( matrix) includes indirect effects between genes. In order to remove them, we process as follows: The value of line and column in semi-ordered matrix  and skeleton matrix  are represented as and , respectively. If equals 1, is set to max{ , 0}( ). Thus, all indirect effects are removed from the semi-ordered matrix. In Fig. 1, the relation between gene G1 and gene G3** are removed, and the skeleton matrix  is constructed.
(F)
Draw multi-level digraph; Arrows are drawn between nodes based on the value of each element in the skeleton matrix. The genes with parentheses indicate an equivalence set of genes. The multi-level digraph method shown in Fig. 1 is consistent with the experiment data E and the binary relation R.
Directed graph of regulatory influences – gene network
ABURATANI et al., DNA Res Feb 28;10(1):1-8.

58. gene expression as a Quantitative Trait
Genetical genomics
gene expression as a Quantitative Trait
qualitative expression
quantitative expression
the combination of genotype and expression information can identify cis- and trans-regulatory sites
Fig. 2. Combined analysis of expression profile and genetic map data from Fig. 1. Four hypothetical cDNAs are given as example. For each, the microarray data is plotted in a histogram and analysed in combination with the molecular marker data, using multifactorial analysis of variance. The types of allele present for the markers A/a, B/b, D/d and F/f are differentiated by colour. The distribution of expression for cDNA1 shows a qualitative expression (a). Consequently, this is a marker in itself. The distribution of expression of cDNA2 (b) gives a quantitative profile, and its components can be resolved by grouping the segregating alleles at the markers A and B. The distribution of expression of cDNA3 (c) also gives a quantitative profile, but its components cannot be resolved despite the segregation of the F/f alleles of marker F. The quantitative expression profile cDNA4 (d) can be resolved based on D/d and F/f. Thus, marker F contributes to information about other cDNAs, whereas F by itself is not informative. Standard one-way analysis of variance of the profile of cDNA2 would distinguish Ab and AB (light shades) from ab and aB (dark shades), but a two-way analysis of variance is more appropriate and allows distinction between the four classes ab, aB, Ab and AB. For cDNA4, the same is true for the classes df, Df, dF and DF. In the case of cDNA2, there is no epistatic interaction, whereas the position of DF relative to the other three classes in case of cDNA4 indicates such an interaction. The multifactorial analysis of variance can easily be extended to three or more markers. It will allow assessing the significance and the strength of the actions and interactions of gene products.
epistatic interaction
Jansen & Nap, Trends Genet Jul;17(7): and
Jansen & Nap, Trends Genet May;20(5):223-5.

59. Further reading
Kerr MK, Churchill GA. Genet Res. 2001; 77: Statistical design and the analysis of gene expression microarray data.
Eisen MB, Spellman PT, Brown PO, Botstein D. Proc Natl Acad Sci U S A. 1998; 95: Cluster analysis and display of genome-wide expression patterns.
Hughes TR, Marton MJ, Jones AR, Roberts CJ, et al. Cell. 2000; 102: Functional discovery via a compendium of expression profiles.
Wit E, McClure J. 2005: Statistics for Microarrays – Design, Analysis and Inference

60. Conclusions
microarrays measure gene expression globally  new post-genomic biology
two principal technologies: one-color (Affymetrix) and two-color (cDNA arrays)
multiple measurements pose particular statistical challenges
interpretation requires combination with previous knowledge
creative application of microarrays opens new avenues for biological insight