1. Lecture 3 From Images to Data
A lot of this is not so relevant NOW, but I think its good basic knowledge.

2. Recap of: How Microarrays are used to measure gene expression
Basic idea: measure the activity level of a gene (its expression level), in a particular cell at a particular time, by measuring the concentration of that gene’s mRNA transcript in the cell’s total RNA.
Immobilize DNA probes (oligos, cDNA) onto glass
Hybridize labelled target mRNA (in reality cDNA equivalent) with probes on glass,
Measure how much binds to each probe (i.e. forms ds DNA). (In two-channel arrays, equal amounts of two differently labelled target cDNAs are hybridized to the probes.)
Recall:Dyes are chosen to have different peak emission wavelengths, Cy3’s is 532 nm and Cy5’s is 635 nm.

3. What is measured in Microarrays?
We measure the amount of labeled target cDNA which is bound to the immobilized probe by exciting the labeling molecules (the dye) with a laser, and collecting and counting the photons emitted.
In practice the entire glass slide or chip is scanned (excitation emission counting of emitted photons), and the result is a digital image.This then needs to be processed to locate the probes in the image and assign intensity measurements to each of them. There can be from hundreds to millions of different probes on each slide/chip.

4. The AFFY Chip

5. Affymetrix GeneChips®
Probes = 25 bp sequences
Probe Sets = set of probes corresponding to a particular gene or EST.
In the past there has been 20 probes/probe set on human chips, 16 on mouse, while there are 11 on Human GeneChips® HG-U133A.
Most genes or ESTs contain one probe set, but quite a few have > 1.

9. DATA AND NOTATION
PMijg, MMijg: Intensity for perfect match and mismatch probe in cell j for gene g in chip I
i=1…n: From one to hundreds of chips
J=1…J: from probe pairs
g=1…G: from probe sets
Compute SIGNAL/ Expression measure

10. DATA AND NOTATION
PROBE SET 1
PROBE SET 2
Probe Cell
Probe Pair

11. Expression Value Calculation (Signal)
The signal represents the amount of transcript in solution
Signal is calculated as follows (in brief):
- Cell intensities are preprocessed for global background
- An ideal mismatch value is calculated and subtracted to adjust PM intensity
- The adjusted PM intensities are log transformed to stabilize the variance
- The Tukey’s biweight estimator is used to provide a robust mean of the signal
- Signal is output as the antilog of the mean signal value
- Finally the signal is scaled to generated a normalized data

12. DETECTION ALGORITHM
BACKGROUND: Average of the lowest 2% of the intensities subtracted.

13. Algorithm
First calculate R: ability to detect intended target for each probe
R = (PM-MM)/(PM+MM)
R near 1 means PM>>MM
R near or below 0 means PM <= MM
Define: t (default 0.015) as cutoff for R to be “present” for each probe pair

14. Algorithm contd…
Calculate (R-t) for each Probe.
Rank Probes according to their (R-t) Values
Apply Wilcoxin’s Sign test (non-parametric) to generate the detection p-value.

15. Wilcoxon Signed Rank Test
To test if the median of a distribution q >,<, ≠, q0.
Non-parametric equivalent of one sample mean problem.
Model: yi = q + ei
Procedure for greater than 0 alternative.
Subtract q0 from the yi as zi=yi-q0
Calculate absolute values |zi| and
define yi = 1 if zi is positive and 0 otherwise
Rank the absolute values, Ri
Test Statistic, sum of positive ranks, S=
Find the corresponding p-value P(S > s) and reject if p-value is small.

16. Calculating p-values
Logic: Lets find the distribution of the Test Statistic.
If there are n observations the total number of possible configurations for the ranks is 2n
For n=8, there are 256 possible outcomes
All positive, S=1+2+…+8 =36
One negative: ( 8 options) with S=35,…,28
Two negative: (28 options) S= 33,…,1
And so on
All we need are the extreme outcomes and see how extreme our test statistic is.

17. Discrimination Score [R]80 PM MM 10
100
Increasing Tau: reduces false positives but also reduces the number of present calls 1 R t
-0.2
MM Intensity/probe pair

18. Detection Call
Detection Call is based on p-value cut offs: Alpha1 and Alpha2 provide boundaries for P,M,A calls
Default: a1=0.04, a2=0.06
p<a1: P, p>a2: A, intermediate: M a1 a2 P M A
0.04
0.06
1.00
0.00

19. Example: s=35 P(S>35)= 1/256=.003 PRESENT PM MM R Zi= R-.15 |Zi|
Rank
Pos or not
283.3
.992
0.842
5.5 1
-.02
-.170
.170
239.0
.842
286.0
.991
.841 4
190.8
.994
.844 8
6314.0
.792
.642 2
265.0
.990
.840 3
218.0
.993
.843 7
s=35
P(S>35)=
1/256=.003
PRESENT

20. SIGNAL
Calculated using One –step Tukey’s Biweight estimate: robust weighted mean, insensitive to outliers
One STEP Tukey’s Biweight Algorithm
Let data be xi, let m represent the median of the data.
Calculate: Median Absolute Deviation
(MAD)= Med |x-m|
Ui = (xi –m)/(cMAD+e)
Here c is the tuning constant (set at 5), e=.0001 (so that we don’t have division by zero)

21. Tukey Bi-weight
Weights are calculated as:
Tukey-Biweight is:

22. Comments on Biweight
Generally used for multiple interations, but here we are using just one iteration of it.
Supposedly very robust as an estimator.

23. Signal Calculation Signal= Tukey Biweight{log(PMj-IM)j}
IM= Idealized mismatch which is never greater than PM
If MM<PM them IM=MM
If MM>PM, then use IM
Calculate SB (Specific Background)
SB = [ Tbi( log2 (PM) – log2 (MM)) ]

24. Signal Calculation What is the Idealized Mismatch (IM)?
According to Affymetrix
the reason for including the MM probe is to provide a value that comprises of most of the cross-hybridizations and stray signals affecting the PM probe.
It does contain a portion of the true signal. If MM is less than PM then it can be directly used.
If not we calculate the IM. To do so, first calculate the Specific Background (SB) for each probe pair in a probe set:

25. Specific Background Calculations
Calculate y=log2 (PM/MM)
Find Median(y) = m
Calculate MAD=Median|y-m|
Define u= (y-m)/(c*MAD+e) with c=5 and e=.0001
Define w= (1-u2)2 if |u| ≤1, 0 otherwise
Tb(y) = Syiwi/ Swi

26. Example: Specific Background calculations

27. Signal Calculation First we need to define Idealized Mismatch
By default
t=.03
v=10

28. Signal Calculation Contd
Vij=Max(PMij-IMij, d)
The d is a small positive constant.
Signal=Tbi(log2(Vij))
Keep in mind here we are SUBTRACTING IM from PM and not taking a ratio as we did for SB.

29. Example for Signal Calculation
Signal= , P

30. Program for Signal Calculation for PM and MM data.
Have the data in a csv file called signal1.csv
setwd("/myRfolder")
hwdata<-read.table(“signal1.csv",header=TRUE,sep=",",na.strings=" ")
#SB calculation
p1<-hwdata$PM
m1<-hwdata$MM
y<-log2(p1/m1)
md<-median(y)
z<-abs(y-md)
mz<-median(z)
u<-(y-md)/(5*mz+.0001)
w<-ifelse(abs(u)<=1,(1-u^2)^2,0)
sb=sum(y*w)/sum(w)
 sb

31. #signal calculation begins
IM<-ifelse(m1>p1,p1/(2^sb),m1)
i1<-IM
ys<-log2(p1-i1)
ms<-median(ys)
zs<-abs(ys-ms)
ss<-median(zs)
us<-(ys-ms)/(5*ss+.0001)
ws<-ifelse(abs(us)<=1,(1-us^2)^2,0)
tbs<-sum(ws*ys)/sum(ws)
sgnl<-2^tbs

32. AFFY: SINGLE CHIP EXPRESSION

33. AFFY: TREATMENT COMPARISON: TWO CHIPS