Gene Expression Arrays

1
Gene Expression Arrays

• EPP 245
• Statistical Analysis of
• Laboratory Data

2
Basic Design of Expression Arrays

• For each gene that is a target for the array, we
  have a known DNA sequence.
• mRNA is reverse transcribed to DNA, and if a
  complementary sequence is on the on a chip, the
  DNA will be more likely to stick
• The DNA is labeled with a dye that will fluoresce
  and generate a signal that is monotonic in the
  amount in the sample

3
Intron
Exon
TAAATCGATACGCATTAGTTCGACCTATCGAAGACCCAACACGGATTCGA
TACGTTAATATGACTACCTGCGCAACCCTAACGTCCATGTATCTAATACG
ATTTAGCTATGCGTAATCAAGCTGGATAGCTTCTGGGTTGTGCCTAAGC
TATGCAATTATACTGATGGACGCGTTGGGATTGCAGGTACATAGATTATG
C
Probe Sequence

• cDNA arrays use variable length probes derived
  from expressed sequence tags
• Spotted and almost always used with two color
  methods
• Can be used in species with an unsequenced genome
• Long oligoarrays use 60-70mers
• Agilent two-color arrays
• Spotted arrays from UC Davis or elsewhere
• Usually use computationally derived probes but
  can use probes from sequenced ESTs

4

• Affymetrix GeneChips use multiple 25-mers
• For each gene, one or more sets of 8-20 distinct
  probes
• May overlap
• May cover more than one exon
• Affymetrix chips also use mismatch (MM) probes
  that have the same sequence as perfect match
  probes except for the middle base which is
  changed to inhibitbinding.
• This is supposed to act as a control, but often
  instead binds to another mRNA species, so many
  analysts do not use them

5
Probe Design

• A good probe sequence should match the chosen
  gene or exon from a gene and should not match any
  other gene in the genome.
• Melting temperature depends on the GC content and
  should be similar on all probes on an array since
  the hybridization must be conducted at a single
  temperature.

6

• The affinity of a given piece of DNA for the
  probe sequence can depend on many things,
  including secondary and tertiary structure as
  well as GC content.
• This means that the relationship between the
  concentration of the RNA species in the original
  sample and the brightness of the spot on the
  array can be very different for different probes
  for the same gene.
• Thus only comparisons of intensity within the
  same probe across arrays makes sense.

7
Affymetrix GeneChips

• For each probe set, there are 8-20 perfect match
  (PM) probes which may overlap or not and which
  target the same gene
• There are also mismatch (MM) probes which are
  supposed to serve as a control, but do so rather
  badly
• Most of us ignore the MM probes

8
Expression Indices

• A key issue with Affymetrix chips is how to
  summarize the multiple data values on a chip for
  each probe set (aka gene).
• There have been a large number of suggested
  methods.
• Generally, the worst ones are those from Affy, by
  a long way worse means less able to detect real
  differences

9
Usable Methods

• Li and Wongs dCHIP and follow on work is
  demonstrably better than MAS 4.0 and MAS 5.0, but
  not as good as RMA and GLA
• ArrayAssist can use dCHIP, RMA, gcRMA, and
  others.
• The GLA method (Durbin, Rocke, Zhou) can be
  imported into ArrayAssist.

10
Steps in Expression Index Construction

• Background correction is the process of adjusting
  the signals so that the zero point is similar on
  all parts of all arrays.
• We like to manage this so that zero signal after
  background correction corresponds approximately
  to zero amount of the mRNA species that is the
  target of the probe set.

11

• Data transformation is the process of changing
  the scale of the data so that it is more
  comparable from high to low.
• Common transformations are the logarithm and
  generalized logarithm
• Normalization is the process of adjusting for
  systematic differences from one array to another.
• Normalization may be done before or after
  transformation, and before or after probe set
  summarization.

12

• One may use only the perfect match (PM) probes,
  or may subtract or otherwise use the mismatch
  (MM) probes
• There are many ways to summarize 20 PM probes and
  20 MM probes on 10 arrays (total of 200 numbers)
  into 10 expression index numbers

13
The RMA Method

• Background correction that does not make 0 signal
  correspond to 0 amount
• Quantile normalization makes the overall
  distribution of intensity values across probes
  the same on each array
• Log2 transform
• Median polish summary of PM probes

14

• Analysis by means
• Remove Row Means
• Remove Column Means
• Rows and Columns have mean 0
• Influence of an outlier spreads

15

• Median Polish
• Remove Row Medians
• Remove Column Medians
• Rows and Columns may not
• have median 0
• Outliers contained
• May have to be iterated

16
Example Probe Set

• Using the Affy HG U133 Plus 2.0 GeneChip with
  54675 probe sets, from 604258 PM probes.
• Four chips derived from human IR exposed skin at
  0, 1, 10, and 100 cGy
• Probe set number 10067/54675 has Affy ID
  200618_at
• Gene is LASP1, LIM and SH3 protein 1, LIM protein
  subfamily, Src homology, actin binding.

17
Mean Summarization
18
Mean Summarization of the Logs
19
The GLA Method

• The Glog Average (GLA) method is simpler than the
  RMA method, though it can require estimation of a
  parameter
• Background correction is intended to make a
  measured value of zero correspond to a zero
  quantity in the sample
• Transformation uses the glog ln for large
  values
• Normalization via lowess
• Summary is a simple average of PM probes

20
Probe Sets not Genes

• It is unavoidable to refer to a probe set as
  measuring a gene, but nevertheless it can be
  deceptive
• The annotation of a probe set may be based on
  homology with a gene of possibly known function
  in a different organism
• Only a relatively few probe sets correspond to
  genes with known function and known structure in
  the organism being studied

21
Two-Color Arrays

• Two-color arrays are designed to account for
  variability in slides and spots by using two
  samples on each slide, each labeled with a
  different dye.
• If a spot is too large, for example, both signals
  will be too big, and the difference or ratio will
  eliminate that source of variability

22
Dyes

• The most common dye sets are Cy3 (green) and Cy5
  (red), which fluoresce at approximately 550 nm
  and 649 nm respectively (red light 700 nm,
  green light 550 nm)
• The dyes are excited with lasers at 532 nm (Cy3
  green) and 635 nm (Cy5 red)
• The emissions are read via filters using a CCD
  device

23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
File Format

• A slide scanned with Axon GenePix produces a file
  with extension .gpr that contains the
  resultshttp//www.axon.com/gn_GenePix_File_Forma
  ts.html
• This contains 29 rows of headers followed by 43
  columns of data (in our example files)
• For full analysis one may also need a .gal file
  that describes the layout of the arrays

27
"Block" "Column" "Row" "Name" "ID" "X" "Y"
"Dia." "F635 Median" "F635 Mean" "F635 SD"
"B635 Median" "B635 Mean" "B635 SD" " gt
B6351SD" " gt B6352SD" "F635 Sat."
28
"F532 Median" "F532 Mean" "F532 SD" "B532
Median" "B532 Mean" "B532 SD" " gt B5321SD"
" gt B5322SD" "F532 Sat."
29
"Ratio of Medians (635/532)" "Ratio of Means
(635/532)" "Median of Ratios (635/532)" "Mean
of Ratios (635/532)" "Ratios SD (635/532)" "Rgn
Ratio (635/532)" "Rgn R² (635/532)" "F Pixels"
"B Pixels" "Sum of Medians" "Sum of Means"
"Log Ratio (635/532)" "F635 Median -
B635" "F532 Median - B532" "F635 Mean - B635"
"F532 Mean - B532" "Flags"
30
Analysis Choices

• Mean or median foreground intensity
• Background corrected or not
• Log transform (base 2, e, or 10) or glog
  transform
• Log is compatible only with no background
  correction
• Glog is best with background correction

31
DDR1
32
(No Transcript)
33
Issues with Two-Color Arrays

• Chips have different overall intensities, so
  normalization across chips is needed.
• The overall intensity on the red channel may be
  greater or less than on the green channel, so
  normalization across dyes is needed.
• The red/green difference is can be different at
  different intensity levels

34
Array normalization

• Array normalization is meant to increase the
  precision of comparisons by adjusting for
  variations that cover entire arrays
• Without normalization, the analysis would be
  valid, but possibly less sensitive
• However, a poor normalization method will be
  worse than none at all.

35
Possible normalization methods

• We can equalize the mean or median intensity by
  adding or multiplying a correction term
• We can use different normalizations at different
  intensity levels (intensity-based normalization)
  for example by lowess or quantiles
• We can normalize for other things such as print
  tips

36
Example for Normalization
37
. list Array Group Gene Expression
--------------------------------- Array
Group Gene Expresn
--------------------------------- 1. 1
1 1 1100 2. 2 1
1 900 3. 3 2 1
425 4. 4 2 1 550
5. 1 1 2 110
--------------------------------- 6. 2
1 2 95 7. 3 2
2 85 8. 4 2 2
110 9. 1 1 3 80
10. 2 1 3 65
--------------------------------- 11. 3
2 3 55 12. 4 2
3 80 --------------------------
-------
38
. sort Gene . by Gene anova Expression
Group -------------------------------------------
------------------------------------- -gt Gene
1 Number of obs
4 R-squared 0.9042
Root MSE 117.925 Adj
R-squared 0.8564 Source
Partial SS df MS F Prob gt
F ---------------------------------
------------------------------
Model 262656.25 1 262656.25 18.89
0.0491
Group 262656.25 1 262656.25
18.89 0.0491
Residual 27812.5 2
13906.25 -----------------------
----------------------------------------
Total 290468.75 3 96822.9167

39
-gt Gene 2 Number of
obs 4 R-squared 0.0556
Root MSE 14.5774
Adj R-squared -0.4167 Source
Partial SS df MS F Prob
gt F -------------------------------
--------------------------------
Model 25 1 25
0.12 0.7643
Group 25 1 25
0.12 0.7643
Residual 425 2
212.5 --------------------------
-------------------------------------
Total 450 3 150
-------------------------------------------------
------------------------------ -gt Gene 3
Number of obs 4
R-squared 0.0556
Root MSE 14.5774 Adj R-squared
-0.4167 Source Partial SS
df MS F Prob gt F
-----------------------------------------------
---------------- Model
25 1 25 0.12 0.7643
Group
25 1 25 0.12
0.7643
Residual 425 2 212.5
-----------------------------------------
---------------------- Total
450 3 150
40
Additive Normalization by Means
41
. mean Expression . ereturn list scalars
e(df_r) 11 e(N_over) 1
e(N) 12 e(k_eq)
1 e(k_eform) 0 macros
e(cmd) "mean" e(title) "Mean
estimation" e(estat_cmd)
"estat_vce_only" e(varlist)
"Expression" e(predict)
"_no_predict" e(properties) "b
V" matrices e(b) 1 x 1
e(V) 1 x 1 e(_N)
1 x 1 e(error) 1 x
1 functions e(sample)
. matrix ExpMeanMat e(b) . matlist
ExpMeanMat Expressn
------------------------ y1
304.5833 . scalar ExpMean ExpMeanMat1,1 .
display ExpMean 304.58333 . anova Expression
Array . predict ArrayMean . generate
NormExp1Expression-ArrayMean ExpMean
42
. list Array Group Gene Expression ArrayMean
NormExp1 ----------------------------------
---------------------- Array Group
Gene Expresn ArrayMn NormExp1
-------------------------------------------------
------- 1. 1 1 1 1100
430 974.5833 2. 2 1
1 900 353.3333 851.25 3.
3 2 1 425 188.3333
541.25 4. 4 2 1 550
246.6667 607.9167 5. 1 1
2 110 430 -15.41667
-------------------------------------------------
------- 6. 2 1 2 95
353.3333 46.24999 7. 3 2
2 85 188.3333 201.25 8.
4 2 2 110 246.6667
167.9167 9. 1 1 3 80
430 -45.41667 10. 2 1
3 65 353.3333 16.24999
-------------------------------------------------
------- 11. 3 2 3 55
188.3333 171.25 12. 4 2
3 80 246.6667 137.9167
-------------------------------------------------
-------
43
. by Gene anova NormExp1 Group -----------------
--------------------------------------------------
----------------- -gt Gene 1
Number of obs 4 R-squared
0.9209 Root MSE
70.0991 Adj R-squared 0.8814
Source Partial SS df MS
F Prob gt F
-------------------------------------------------
-------------- Model
114469.431 1 114469.431 23.30
0.0403
Group 114469.431 1 114469.431
23.30 0.0403
Residual 9827.77662 2
4913.88831 ---------------------
------------------------------------------
Total 124297.207 3 41432.4024

44
-gt Gene 2 Number of
obs 4 R-squared 0.9209
Root MSE 35.0496
Adj R-squared 0.8814 Source
Partial SS df MS F Prob
gt F -------------------------------
--------------------------------
Model 28617.3614 1 28617.3614
23.30 0.0403
Group 28617.3614 1
28617.3614 23.30 0.0403
Residual 2456.9441
2 1228.47205
-------------------------------------------------
-------------- Total
31074.3055 3 10358.1018 -----------------
--------------------------------------------------
------------------ -gt Gene 3
Number of obs 4 R-squared
0.9209 Root MSE
35.0496 Adj R-squared 0.8814
Source Partial SS df MS
F Prob gt F
-------------------------------------------------
-------------- Model
28617.3612 1 28617.3612 23.30
0.0403
Group 28617.3612 1 28617.3612
23.30 0.0403
Residual 2456.94427 2
1228.47214 ---------------------
------------------------------------------
Total 31074.3055 3 10358.1018

45
Multiplicative Normalization by Means
46
. generate NormExp2 ExpressionExpMean/ArrayMean
. list Array Group Gene Expression ArrayMean
NormExp2 ----------------------------------
--------------------- Array Group
Gene Expresn ArrayMn NormExp2
-------------------------------------------------
------ 1. 1 1 1 1100
430 779.1667 2. 2 1 1
900 353.3333 775.8254 3. 3
2 1 425 188.3333 687.3341
4. 4 2 1 550 246.6667
679.1385 5. 1 1 2 110
430 77.91666 --------------------
----------------------------------- 6. 2
1 2 95 353.3333 81.89268
7. 3 2 2 85
188.3333 137.4668 8. 4 2 2
110 246.6667 135.8277 9. 1
1 3 80 430 56.66667
10. 2 1 3 65 353.3333
56.03184 --------------------------------
----------------------- 11. 3 2
3 55 188.3333 88.94912 12.
4 2 3 80 246.6667 98.78378
------------------------------------------
-------------
47
. by Gene anova NormExp2 Group -----------------
--------------------------------------------------
------------- -gt Gene 1
Source Partial SS df MS F
Prob gt F ------------------------
---------------------------------------
Model 8884.90342 1 8884.90342
453.70 0.0022 ------------------------------
--------------------------------------------------
-gt Gene 2 Source Partial
SS df MS F Prob gt F
------------------------------------------
--------------------- Model
3219.72043 1 3219.72043 696.33
0.0014 ------------------------------------------
-------------------------------------- -gt Gene
3 Source Partial SS df
MS F Prob gt F
-------------------------------------------------
-------------- Model
1407.54019 1 1407.54019 57.97 0.0168
48
Multiplicative Normalization by Medians
49
. sort Array . table Array, contents(p50
Expression) ------------------------- Array
med(Expresn) ------------------------
1 110 2 95
3 85 4
110 ------------------------- . input ArrayMed
ArrayMed 1. 110 2. 110 3. 110 4. 95
5. 95 6. 95 7. 85 8. 85 9. 85 10. 110
11. 110 12. 110
50
. summarize Expression, detail
Expression --------------------------------
----------------------------- Percentiles
Smallest 1 55 55 5
55 65 10 65
80 Obs 12 25
80 80 Sum of Wgt.
12 50 102.5 Mean
304.5833 Largest
Std. Dev. 363.1144 75 487.5
425 90 900 550
Variance 131852.1 95 1100
900 Skewness 1.277954 99
1100 1100 Kurtosis
3.132949 . generate NormExp3
Expression102.5/ArrayMed
51
-gt Gene 1 Source Partial
SS df MS F Prob gt F
------------------------------------------
--------------------- Model
235735.794 1 235735.794 324.00
0.0031 ------------------------------------------
------------------------------------------ -gt
Gene 2 Source Partial SS
df MS F Prob gt F
----------------------------------------------
----------------- Model
0 1 0 ---------------------
--------------------------------------------------
------------- -gt Gene 3
Source Partial SS df MS F
Prob gt F ------------------------
---------------------------------------
Model 3.6253006 1 3.6253006
0.17 0.7228
52
Intensity-based normalization

• Normalize by means, medians, etc., but do so only
  in groups of genes with similar expression
  levels.
• lowess is a procedure that produces a running
  estimate of the middle, like a robustified mean
• If we subtract the lowess of each array and add
  the average of the lowesss, we get the lowess
  normalization

53
(No Transcript)
54
(No Transcript)
55
(No Transcript)
56
Fitting a model to genes

• We can fit a model to the data of each gene after
  the whole arrays have been background corrected,
  transformed, and normalized
• Each gene is then test for whether there is
  differential expression

57
(No Transcript)
58
Multiplicity Adjustments

• If we test thousands of genes and pick all the
  ones which are significant at the 5 level, we
  will get hundreds of false positives.
• Multiplicity adjustments winnow this down so that
  the number of false positives is smaller

59
Types of Multiplicity Adjustments

• The Bonferroni correction aims to detect no
  significant genes at all if there are truly none,
  and guarantees that the chance that any will be
  detected is less than .05 under these conditions
• Generally, this is too conservative
• Less conservative versions include methods due to
  Holm, Hochberg, and Benjamini and Hochberg (FDR)

60
(No Transcript)