1. Gene expression Terry Speed Lecture 4, December 18, 2001

2. Thesis: the analysis of gene expression data is going to be big in 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)*

3. 1995 1996 1997 1998 1999 2000 2001 0 100 200 300 400 500 600 (projected) Year Number of papers Total microarray articles indexed in Medline

4. themes Common 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

5. Biological 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

6. 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.

7. Reverse transcription Clone 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 T T A G G A G C A T T A G G A G

8. cDNA 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).

9. cDNA microarrays cDNA clones

10. cDNA microarrays Compare the genetic expression in two samples of cells PRINT cDNA from one gene on each spot SAMPLES cDNA labelled red/green e.g. treatment / control normal / tumor tissue

11. HYBRIDIZE Add equal amounts of labelled cDNA samples to microarray. SCAN Laser Detector

12. Biological question Differentially expressed genes Sample 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)

13. Some 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.

14. Some 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.

15. Some 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.

16. 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

17. Does one size fit all?

18. Segmentation: limitation of the fixed circle method SRG Fixed Circle Inside the boundary is spot (foreground), outside is not.

19. Some local backgrounds We use something different again: a smaller, less variable value. Single channel grey scale

20. Quantification 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 Log 2 ( Red intensity / Green intensity)

21. Gene 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 = Log 2 ( Red intensity / Green intensity) slide 1slide 2slide 3slide 4slide 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.

23. The red/green ratios can be spatially biased. Top 2.5%of ratios red, bottom 2.5% of ratios green

24. The red/green ratios can be intensity-biased M = log 2 R/G = log 2 R - log 2 G = (log 2 R + log 2 G )/2 Values should scatter about zero.

25. 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

26. Normalizing: before 2 0 -2 -4 6 8 10 12 14 16 M

27. Normalizing: after 2 0 -2 -4 M normalised 6 8 10 12 14 16

28. SCIENTIFIC: To determine which genes are differentially expressed between two sources of mRNA (trt, ctl). STATISTICAL: To assign appropriately adjusted p-values to thousands of genes. A basic problem

29. 8 treatment mice and 8 control mice 16 hybridizations: liver mRNA from each of the 16 mice (T i, C i ) is labelled with Cy5, while pooled liver mRNA from the control mice (C*) is labelled with Cy3. Probes: ~ 6,000 cDNAs (genes), including 200 related to lipid metabolism. Goal. To identify genes with altered expression in the livers of Apo AI knock-out mice (T) compared to inbred C57Bl/6 control mice (C). Apo AI experiment (Callow et al 2000, LBNL)

30. Leukemia experiments (Golub et al 1999,WI) Leukemia experiments (Golub et al 1999,WI) Goal. To identify genes which are differentially expressed in acute lymphoblastic leukemia (ALL) tumours in comparison with acute myeloid leukemia (AML) tumours. 38 tumour samples: 27 ALL, 11 AML. Data from Affymetrix chips, some pre-processing. Originally 6,817 genes; 3,051 after reduction. Data therefore a 3,051  38 array of expression values.

31. Univariate hypothesis testing Initially, focus on one gene only. We wish to test the null hypothesis H that the gene is not differentially expressed. In order to do so, we use a two sample t-statistic:

32. Single-step adjustments of Single-step adjustments of p i Bonferroni: min (mp i, 1), m= #genes Sid á k: 1 - (1 - p i ) m minP method of Westfall and Young: Pr( min P l ≤ p i | H) 1≤l≤m maxT method of Westfall and Young: Pr( max |T l | ≥ | t i | | H 0 C ) 1≤l≤m

33. More powerful methods: step-down adjustments The idea: S Holm’s modification of Bonferroni. Also applies to Sidák, maxT, and minP. We illustrate this last adjustment.

34. Step-down adjustment of minP Initialization: Order the unadjusted p-values such that p r 1 ≤ p r 2 ≤  ≤ p r m. The indices r1, r2, r3,.. are fixed for given data. Step-down adjustment: 1.Compare min {P r 1, , P r m } with p r1 ; 2.Compare min {P r 2, , P r m } with p r2 ; 3 Compare min {P r 3 , P r m } with p r i3 ……. m.Compare P r m with p r m Enforce the monotonicity on the adjusted p r i

36. gene tunadj. pminPplowermaxT indexstatistic (  10 4 ) adjust. 2139-221.5.53 8  10 -5 2  10 -4 4117-131.5.53 8  10 -5 5  10 -4 5330-121.5.53 8  10 -5 5  10 -4 1731-111.5.53 8  10 -5 5  10 -4 538-111.5.53 8  10 -5 5  10 -4 1489-9.11.5.53 8  10 -5 1  10 -3 2526-8.31.5.53 8  10 -5 3  10 -3 4916-7.71.5.53 8  10 -5 8  10 -3 941-4.71.5.53 8  10 -5 0.65 2000+3.11.5.53 8  10 -5 1.00 5867-4.23.1.760.540.90 4608+4.86.2.930.870.61 948-4.77.8.960.930.66 5577-4.512.990.930.74

37. Apo AI. Histogram & Q-Q plot ApoA1

39. Brief discussion Not mentioned: strong vs weak control of Type 1 error. The minP adjustment seems more conservative than the maxT adjustment, but is essentially model-free. The adjusted minP values are very discrete; it seems that 12,870 permutations are not enough for 6,000 tests. Extends to other statistics: Wilcoxon, paired t, F, blocked F.. Major question in practice: minP, maxT or something else? Wanted are guidelines for use of minP in terms of sample sizes and number of genes. Other approaches: False Discovery Rate (V/R), Bayes.

40. Olfactory Epithelium VomeroNasal Organ Main (Auxiliary) Olfactory Bulb From Buck (2000) From a study of the mouse olfactory system

41. Axonal connectivity between the nose and the mouse olfactory bulb >2M, ~1,800 types Two principles: “ zone-to-zone projection ”, and “ glomerular convergence ” Neocortex

42. Of interest: the hardwiring of the vertebrate 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.

43. The biological question in this case Are there genes with spatially restricted expression patterns within the olfactory bulb?

45. Layout 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 pg1pg2

46. Design: How We Sliced Up the Bulb A P D V M L

47. Design: Two Ways to Do the Comparisons Goal: 3-D representation of gene expression P D M A V L R Compare all samples to a common reference sample (e.g., whole bulb) P D M A V L Multiple direct comparisons between different samples (no common reference)

48. An 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? L P V D M A

49. 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-L In practice, we use robust regression. Estimates for other estimable contrasts follow in the usual way.

50. The Olfactory Bulb Experiments completed so far completed so far

51. Contrasts & 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

52. Contrasts & 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.

53. Alternative pattern representation Gene #15,228 once again.

54. Reconstruction of the Bulb as a Cube: Expression of Gene # 15,228 Expression Level High Low

55. 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:

56. Clustering 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.

57. Red :genes chosen Blue:controls 15 p/w effects PADA VA LA DP VP LA MP MA LPVD MD LA LV LM MV LD

59. The 16 groups systematically arranged (6 point representation)

61. Validation of Gene # 15,228 Expression Pattern by RNA In Situ Hybridization gluR CTX MOB AOB #15,228 CTX AOB MOB

62. Validation of predicted patterns using in situ hybridization and neurolucida reconstructions from them.

63. Some statistical research stimulated by 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

64. Acknowledgments Statistical collaborators Yee Hwa Yang (Berkeley) Sandrine Dudoit (Berkeley) Ingrid Lönnstedt (Uppsala) Natalie Thorne (WEHI) Mauro Delorenzi (WEHI) CSIRO Image Analysis Group Michael Buckley Ryan Lagerstorm WEHI Glenn Begley Suzie Grant Rob Good PMCI Chuang Fong Kong Ngai Lab (Berkeley) Cynthia Duggan Jonathan Scolnick Dave Lin Vivian Peng Percy Luu Elva Diaz John Ngai LBNL Matt Callow RIKEN Genomic Sciences Center Yasushi Okazaki Yoshihide Hayashizaki

65. Some web sites: Technical reports, talks, software etc. http://www.stat.berkeley.edu/users/terry/zarray/Html/ Statistical software R “GNU’s S” http://lib.stat.cmu.edu/R/CRAN/ Packages within R environment: -- Spot http://www.cmis.csiro.au/iap/spot.htm -- SMA (statistics for microarray analysis) http://www.stat.berkeley.edu/users/terry/zarray/Software /smacode.html