Gene expressionGene expression
Statistics 246, Week 3, 2002
Thesis:Thesis: the analysis of gene the analysis of gene expression data is going to be big expression data is going to be big
in 21st century statisticsin 21st century statistics
Many different technologies, including
High-density nylon membrane arrays
Serial analysis of gene expression (SAGE)
Short oligonucleotide arrays (Affymetrix)
Long oligo arrays (Agilent)
Fibre optic arrays (Illumina)
cDNA arrays (Brown/Botstein)*
1995 1996 1997 1998 1999 2000 2001
0
100
200
300
400
500
600
(projected)
Year
Num
ber
of
papers
Total microarray articles indexed in Medline
Common themes themes
• Parallel approach to collection of very large amounts of data (by biological standards)
• Sophisticated instrumentation, requires some understanding
• Systematic features of the data are at least as important as the random ones
• Often more like industrial process than single investigator lab research
• Integration of many data types: clinical, genetic, molecular…..databases
Biological backgroundBiological background
G T A A T C C T C | | | | | | | | | C A T T A G G A G
DNA
G U A A U C C
RNA polymerase
mRNA
Transcription
Idea: measure the amount of mRNA to see which genes are being expressed in (used by) the cell.
Measuring protein might be better, but is currently harder.
Reverse transcriptionReverse transcriptionClone cDNA strands, complementary to the mRNA
G U A A U C C U C
Reverse transcriptase
mRNA
cDNA
C A T T A G G A G C A T T A G G A G C A T T A G G A G C A T T A G G A G
T T A G G A G
C A T T A G G A G C A T T A G G A G C A T T A G G A G
C A T T A G G A G
C A T T A G G A G
cDNA microarray experimentscDNA microarray experiments
mRNA levels compared in many different contexts
Different tissues, same organism (brain v. liver) Same tissue, same organism (ttt v. ctl, tumor v. non-tumor) Same tissue, different organisms (wt v. ko, tg, or mutant)
Time course experiments (effect of ttt, development)
Other special designs (e.g. to detect spatial patterns).
cDNA microarrayscDNA microarrays
cDNA clones
cDNA microarrayscDNA microarraysCompare the genetic expression in two samples of cells
cDNA from one gene on each spot
SAMPLES
cDNA labelled red/green
e.g. treatment / control
normal / tumor tissue
HYBRIDIZE
Add equal amounts of labelled cDNA samples to microarray.
SCAN
Laser Detector
Biological questionDifferentially expressed genesSample class prediction etc.
Testing
Biological verification and interpretation
Microarray experiment
Estimation
Experimental design
Image analysis
Normalization
Clustering Discrimination
R, G
16-bit TIFF files
(Rfg, Rbg), (Gfg, Gbg)
Some statistical questionsSome statistical questions
Image analysis: addressing, segmenting, quantifying Normalisation: within and between slides
Quality: of images, of spots, of (log) ratios
Which genes are (relatively) up/down regulated?
Assigning p-values to tests/confidence to results.
Some statistical questions, ctdSome statistical questions, ctd
Planning of experiments: design, sample size
Discrimination and allocation of samples
Clustering, classification: of samples, of genes
Selection of genes relevant to any given analysis
Analysis of time course, factorial and other special experiments…..…...& much more.
Some bioinformatic questionsSome bioinformatic questions
Connecting spots to databases, e.g. to sequence, structure, and pathway databases
Discovering short sequences regulating sets of genes: direct and inverse methods
Relating expression profiles to structure and function, e.g. protein localisation
Identifying novel biochemical or signalling pathways, ………..and much more.
Part of the image of one channel false-coloured on a white (v. high) red (high) through yellow and green (medium) to blue (low) and black scale
Does one size fit all?
Segmentation: limitation of the Segmentation: limitation of the fixed circle methodfixed circle method
SRG Fixed Circle
Inside the boundary is spot (foreground), outside is not.
Some local backgroundsSome local backgrounds
We use something different again: a smaller, less variable value.
Single channelgrey scale
Quantification of expressionQuantification of expression
For each spot on the slide we calculate
Red intensity = Rfg - Rbg
fg = foreground, bg = background, and
Green intensity = Gfg - Gbg
and combine them in the log (base 2) ratio
Log2( Red intensity / Green intensity)
Gene Expression DataGene Expression Data On p genes for n slides: p is O(10,000), n is O(10-100), but growing,
Genes
Slides
Gene expression level of gene 5 in slide 4
= Log2( Red intensity / Green intensity)
slide 1 slide 2 slide 3 slide 4 slide 5 …
1 0.46 0.30 0.80 1.51 0.90 ...2 -0.10 0.49 0.24 0.06 0.46 ...3 0.15 0.74 0.04 0.10 0.20 ...4 -0.45 -1.03 -0.79 -0.56 -0.32 ...5 -0.06 1.06 1.35 1.09 -1.09 ...
These values are conventionally displayed on a red (>0) yellow (0) green (<0) scale.
The red/green ratios can be spatially biasedThe red/green ratios can be spatially biased
• .Top 2.5%of ratios red, bottom 2.5% of ratios green
The red/green ratios can be intensity-biased
M = log2R/G
= log2R - log2G
= (log2R + log2G )/2
Values should scatter about zero.
Yellow: GAPDH, tubulin Light blue: MSP pool / titration
Orange: Schadt-Wong rank invariant set Red line: lowess smooth
Normalization: how we “fix” the previous problem
The curved line becomes the new zero line
Normalizing: before2
0-2
-4
6 8 10 12 14 16
M
Normalizing: after2
0-2
-4
M n
orm
alis
ed
6 8 10 12 14 16
Olfactory Epithelium
VomeroNasal Organ
Main (Auxiliary)Olfactory Bulb
From Buck (2000)
From a study of the mouse olfactory system
Axonal connectivity between the nose and the mouse olfactory bulb
>2M, ~1,800 types
Two principles: “zone-to-zone projection”, and “glomerular convergence”
Neocortex
Of interest: the hardwiring of the Of interest: the hardwiring of the vertebrate olfactory systemvertebrate olfactory system
• Expression of a specific odorant receptor gene by an olfactory neuron.
• Targeting and convergence of like axons to specific glomeruli in the olfactory bulb.
The biological question in this caseThe biological question in this case
Are there genes with spatially restricted expression patterns within
the olfactory bulb?
Layout of the cDNA MicroarraysLayout of the cDNA Microarrays
• Sequence verified mouse cDNAs• 19,200 spots in two print groups of 9,600 each
– 4 x 4 grid, each with 25 x24 spots– Controls on the first 2 rows of each grid.
77
pg1 pg2
Design: How We Sliced Up the BulbDesign: How We Sliced Up the Bulb
A
P D
V
M
L
Design: Two Ways to Do the Design: Two Ways to Do the ComparisonsComparisons
Goal: 3-D representation of gene expression
P
D
MA
V
L
R
Compare all samples to a common reference sample (e.g., whole bulb)
P
D
MA
V
L
Multiple direct comparisons between different samples (no common reference)
An Important Aspect of Our DesignAn Important Aspect of Our Design
Different ways of estimating the same contrast:
e.g. A compared to P
Direct = A-P
Indirect = A-M + (M-P) or
A-D + (D-P) or
-(L-A) - (P-L)
How do we combine these?
LL
PPVV
DD
MM
AA
Analysis using a linear model
Define a matrix X so that E(M)=X
Use least squares estimates for A-L, P-L, D-L, V-L, M-LIn practice, we use robust regression.
Estimates for other estimable contrasts follow in the usual way.
€
E
m1
m2
M
mn
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ =
0 0 0 −1 1
−1 0 0 0 0
M O M
−1 1 0 0 0
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ •
A−L
P −L
D−L
V −L
M−L
⎛
⎝
⎜ ⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟ ⎟
ˆ = X' X( )−1X'M
The Olfactory Bulb ExperimentsThe Olfactory Bulb Experiments completed so farcompleted so far
Contrasts & PatternsContrasts & Patterns Because of the connectivity of our experiment, we can estimate
all 15 different pairwise comparisons directly and/or indirectly.
For every gene we thus have a pattern based on the 15 pairwise comparisons.
Gene #15,228
Contrasts & patterns:another wayContrasts & patterns:another way Instead of estimating pairwise comparisons between each of the six
effects, we can come closer to estimating the effects themselves by doing so subject to the standard zero sum constraint (6 parameters, 5 d.f.).
What we estimate for A, say, subject to this constraint, is in reality an estimate of
A - 1/6(A + P + D + V + M + L).
This set of parameter estimates gives results similar to, but better than, the ones we would have obtained had we carried out the experiments with whole-bulb reference tissue.
In effect we have created the whole-bulb reference in silico.
Alternative pattern representationAlternative pattern representation
Gene #15,228 once again.
Reconstruction of the Bulb as a Cube:Reconstruction of the Bulb as a Cube:Expression of Gene # 15,228Expression of Gene # 15,228
ExpressionLevel
High
Low
Patterns, More Globally...Patterns, More Globally...
1. Find the genes whose expression fits specific, predefined patterns.
2. Perform cluster analysis - see what expression patterns emerge.
Can we identify genes with interesting patterns of expression across the bulb?
Two approaches:
Clustering procedureClustering procedure
Start with a sets of genes exhibiting some minimal level of differential expression across the bulb; here ~650 were chosen from all 15 contrasts.
Carry out hierarchical clustering, building a dendrogram: Mahalanobis distance and Ward agglomeration (minimum variance) were used.
Now consider all clusters of 2 or more genes in the tree. Singles are added separately.
Measure the heterogeneity h of a cluster by calculating the 15 SDs
across the cluster of each of the pairwise effects, and taking the largest.
Choose a score s (see plots) and take all maximal disjoint clusters with
h < s. Here we used s = 0.46 and obtained 16 clusters.
Plots guiding choice of clusters of genes
Cluster heterogeneity h (max of 15 SDs)
Number ofclusters(patterns)
Number of genes
Red :genes chosenBlue:controls
15 p/w effects
PA DA VA
LA DP VPLA MP
MA
LP VD MD
LA LV LMMV
LD
The 16 groups systematically arranged (6 point representation)
Validation of Gene # 15,228 Expression Validation of Gene # 15,228 Expression Pattern by RNA Pattern by RNA In SituIn Situ Hybridization Hybridization
gluR
CTX
MOB
AOB
#15,228
CTXAOB
MOB
Gene 15,228: another in situ view
384(group 3)
D
V
L M
3-dimension reconstruction from in-situ data
15,228
5,291
8,496
384
Are the pattens we found real?Are the pattens we found real?
Here’s how we attempted to show that the answer is a qualified yes.
Each cluster average (pattern) has a ‘strength’ we can measure by its root-mean-square (RMS). The n=16 clusters we found have an average
RMS of av= 0.3. Both n and av being strongly determined by our heterogeneity cut-off score of s=0.46.
Now consider randomizing the labels (e.g. P-A) on our hybridizations and repeating the entire analysis, keeping the cut-off score at 0.46. We typically get fewer, “weaker” patterns, with less contrast in the red-green patchwork. One such is on the next page.
500 independent random relabellings had a mean av value of 0.18, an SD of 0.07 and a max av value of 0.26, cf. 0.3 in our data. Our clusters are definitely ‘non-random’ in some sense.
Random
Real
ProblemProblem
We later tried all this with a different set of data, one which made use of reference mRNA had generally lower S/N, and where the inveestigator sought fewer interesting patterns.
We found that the patterns the previous method discovered were similarly quite distinct in av values from those in randomly labelled hybs, but this time, the av values were ‘significantly’ lower than random. It all depends where you are on the curve.
Where next?Where next?
I feel that we need a new idea. The previous one doesn’t seem to have worked. Or did it?
Just clustering and taking averages seems too easy….
But maybe clustering is all there is to patterns, once we have decided on the appropriate and context dependent profile to cluster, and selected the genes, but I keep wondering…
Some statistical research stimulated Some statistical research stimulated by microarray data analysisby microarray data analysis
Experimental design : Churchill & Kerr
Image analysis: Zuzan & West, ….
Data visualization: Carr et al
Estimation: Ideker et al, ….
Multiple testing: Westfall & Young , Storey, ….
Discriminant analysis: Golub et al,…
Clustering: Hastie & Tibshirani, Van der Laan, Fridlyand & Dudoit, ….
Empirical Bayes: Efron et al, Newton et al,…. Multiplicative models: Li &Wong
Multivariate analysis: Alter et al
Genetic networks: D’Haeseleer et al and more
In closing:In closing: The pervasiveness of The pervasiveness of microarray technologymicroarray technology
and the statistical problems that go with it
Hybridization of target DNA or RNA to large numbers of probes attached to a solid support in a microarray format has a much wider applicability.
All such applications have their own statistical problems. Here are two relating to the previous lectures.
Meiosis data in which all exchanges are precisely located (from microarrays)
Figure courtesy of J Derisi
Yeast
Predicted exon Predicted exon
Exon Arrays can validate Exon Predictions Exon Arrays can validate Exon Predictions and assemble Gene Structuresand assemble Gene Structures
One or more Probes per Predicted Exon
• Verify predicted exons on a genome-wide scale.• Group exons into genes via co-regulation.
This and the next slide courtesy of Rosetta
Tiling arrays can identify exons and Tiling arrays can identify exons and refine gene structuresrefine gene structures
Oligonucleotides60 bp in length “60-mers”
10 bp steps
Predicted exon Predicted exon
AcknowledgmentsAcknowledgmentsStatistical collaboratorsStatistical collaboratorsYee Hwa Yang (Berkeley)Yee Hwa Yang (Berkeley)Sandrine Dudoit (Berkeley)Sandrine Dudoit (Berkeley)Ingrid Lönnstedt (Uppsala)Natalie Thorne (WEHI)Natalie Thorne (WEHI)Mauro Delorenzi (WEHI)
CSIRO Image Analysis GroupMichael BuckleyMichael BuckleyRyan Lagerstorm
WEHIGlenn BegleySuzie GrantRob Good
PMCIChuang Fong Kong
Ngai Lab (Berkeley)Cynthia DugganJonathan ScolnickDave Lin Vivian Peng Percy LuuElva DiazJohn Ngai
LBNLMatt Callow
RIKEN Genomic Sciences CenterRIKEN Genomic Sciences CenterYasushi OkazakiYoshihide Hayashizaki