Lesson 11. Functional Genomics I: Microarray Analysis

Transcription

1 Lesson 11 Functional Genomics I: Microarray Analysis

2 Transcription of DNA and translation of RNA vary with biological conditions

3 3 kinds of microarray platforms Spotted Array - 2 color - Pat Brown (Stanford) Synthesized Oligonucleotide - 1 color Affymetrix Synthesized Oligonucleotide - 2 color Agilent

4 Spotted (2 Color) Arrays

5 Agilent 2 color Arrays Synthesized oligonucleotides like Affymetrix arrays but 2 colors like spotted arrays.

6 Concentrations from 2 Color Experiments RNA(Experiment) RNA(Control) = IntensityRed IntensityGreen

7

8 Gene Expression Arrays Measurement of mrna levels for all genes.

9 Gene Expression Arrays

10 Affymetrix 1 Color Arrays

11 Spotted vs Affymetrix vs Agilent Spotted Arrays: Advantages: Long pieces. Disadvantages: Uncertainties in spot reading. Affymetrix Arrays: Advantages: Probes in same place, can be read precisely. Disadvantages: Short pieces. Must assemble probe information. Agilent: Advantages: Medium pieces. Advantages of Affymetrix and Agilent. Disadvantages: None in principle.

12 Concentrations from 1 Color Experiments RNA experiment RNA control = Intensity experiment Intensity control

13 Probeset intensity as an average of probe intensities Iprobeset = j=1,k log 2 (PM j MM j ) k

14 Problems with averaging probes 1. Var(probes within probeset) > Var(The same probe across slides) 2. MM>PM (40% of slides)

15 Problems to be solved in chip reading 1. Highly variable probe intensities compared to probes set intensity. 2. Correct for nonspecific binding realistically. 3. Correct for background within chips. 4. Correct for intensity variation between chips.

16 Steps in RMA 1. Background correction- in each chip. 2. Normalization - between chips. 3. Summarization of probes to probe sets.

17 RMA Background Correction

18 Boxplot of Unnormalized Chips

19 Quantile Normalization

20 Intensity Plots

21 Contributions to probe intensity Y ijn = µ in +α jn +ε ijn

22 Constraint on probe-effects α 0 jn j =1, J

23 1 probeset, 3 probes/probeset 2 chips Simple Example Y 11 =µ 1 + α 1 "Y 21 =µ 2 + α 1" Y 12 =µ 1 + α 2 " Y 22 =µ 2 + α 2" Y 13 =µ 1 + α 3 " Y 23 =µ 2 + α 3" α 1 + α 2 + α 3 =0 5 unknowns, 7 equations

24 Median polish algorithm Y ijn = µ in +α jn +ε ijn

25 GCRMA Similar to RMA but has a probe composition dependent background correction. GC base-pair 3 hydrogen bonds. AT base-pair 2 hydrogen bonds. Non-specific binding to GC higher than to AT. GCRMA implements RMA-type background correction dependent on GC content. Mismatch intensities of probes with the same GC content are pooled.

26 Expression ratios x 2 2,OR x 2 1 x x 2 1 1

27 Need for a measure of variability Experiment Replicate A Replicate B Average 1 2 x x 2 x 1 = " 1+15 % $ ' # 2 & = " % $ ' # 2 & " 16 % $ ' # 2 & = 8 " 8 % 4 = 2 $ ' # 2 &

28 Approximation of the normal distribution

29 Equation of the normal distribution σ 1 2π e µ= mean(average) σ= (x µ ) 2 2σ standard deviation

30 Effect of the standard deviation

31 Standard deviation and percent

32 Estimates of the mean and standard deviation of the mean x = x i i =1, N N s x = (x i x ) 2 i =1, N N( N 1)

33 Standard deviation of the mean σ = x σ n 68% of all of the means within 1 standard deviation of the mean. 95% of all of the means within 2 standard deviation of the mean.

34 The z distribution z = x µ s x

35 x Does experimental CO 2 =10.00mg/m 3 = 10.43( mg µ = 10.00( mg s x = 0.24( mg / m 3 / m / m 3 3 ) ) ) z = = 1.79 p( z 1.79 AND z 1.79) =

36 The t-distribution t = x µ s x

37 The t-distribution of the difference of 2 means t = x 2 x 1 s p 2 2 N 1 + s p N 2 s 2 p = i=1,n 1 (x i1 x 1 ) 2 N 1 + N i=1,n 2 (x i2 x 2 ) 2 N 1 + N 2 2 t = # % $ 1 N N 2 # &% (% '% $ i =1, N 1 x 2 x 1 (x i1 x 1 ) 2 N 1 + N (x i 2 x 2 ) 2 & i =1, N 2 ( ( N 1 + N 2 2 ( '

38 Problems applying t-test to microarrays 1. Multiple tests - thousands of genes. 2. Multiple conditions- more than 2 conditions. Solution: LIMMA LInear Models for Microarray Analysis.

39 The log transformation of x > log 2 (x) intensities # x m = log x log x = log % $ x 1 & ( '

40 The t-distribution of the difference of 2 means t = x 2 x 1 s p 2 2 N 1 + s p N 2 s 2 p = i=1,n 1 (x i1 x 1 ) 2 N 1 + N i=1,n 2 (x i2 x 2 ) 2 N 1 + N 2 2 t = # % $ 1 N N 2 # &% (% '% $ i =1, N 1 x 2 x 1 (x i1 x 1 ) 2 N 1 + N (x i 2 x 2 ) 2 & i =1, N 2 ( ( N 1 + N 2 2 ( '

41 Empirical Bayesian correction t = x 2 x 1 s 2 2 p + s p + s N N Adding S 0 Denominator increases. t decreases. p increases. #false positives decreases.

42 Empirical Bayesian Correction Frequentist Statistics- Standard deviation estimated from data. Bayesian Statistics- Prior estimate of standard deviation modifed from data. Empirical Bayesian Statistics- Prior estimate of standard deviation obtained from from all data and modified for individual data.

43 Benjamini-Hochberg False Discovery Correction Uncorrected p-value= rate of false discovery if only 1 test. Corrected p-value= rate of false discovery if all of the genes above it on the p-value list were tested and accepted.

44 False Discovery vs Raw Pvalue Raw p-value is the probability of getting the t-statistic or a larger one by chance if there is no difference. False discovery rate is the proportion of differences that are accepted at or above a given p-value for which there is really no difference.

45 Multiple Conditions t = # % $ 1 N N 2 # &% (% '% $ i =1, N 1 x 2 x 1 (x i1 x 1 ) 2 N 1 + N i =1, N 2 (x i 2 x 2 ) 2 N 1 + N 2 2 & ( ( ( '

46 Comparing 2 conditions out of 3 t = # % $ 1 N N 2 # &% (% '% $ i =1, N 1 (x i1 x 1 ) 2 N 1 + N 2 + N x 2 x 1 i =1, N 2 (x i 2 x 2 ) 2 N 1 + N 2 + N (x i 3 x 3 ) 2 & i =1, N 3 ( ( N 1 + N 2 + N 3 3( '

47 Cutoffs for differential expression B = ln(odds of differential expression) Cutoff1: p fdr.05 Cutoff2: B = ln(odds) 0 (Cutoff2: odds 1) Cutoff3: p raw.001 But take FDR into account!

48 AffylmGUI R (Statistical Programming Language) Bioconductor (R Programs for Biology) LIMMA AffylmGUI 1 Color Limma GUI 2 Color