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Gene expression

Gene expression. Statistics 246, Week 3, 2002. 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)

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Gene expression

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  1. Gene expression Statistics 246, Week 3, 2002

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

  4. 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. Transcription RNA polymerase G U A A U C C mRNA Biological background DNA G T A A T C C T C | | | | | | | | | C A T T A G G A G

  6. Idea: measure the amount of mRNA to see which genes are being expressedin (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 mRNA Reverse transcriptase T T A G G A G 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 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

  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 PRINT cDNA from one gene on each spot SAMPLES cDNA labelled red/green Compare the genetic expression in two samples of cells 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. Experimental design Microarray experiment 16-bit TIFF files Image analysis (Rfg, Rbg), (Gfg, Gbg) Normalization R, G Estimation Testing Clustering Discrimination Biological verification and interpretation

  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 Fixed Circle SRG Inside the boundary is spot (foreground), outside is not.

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

  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 Log2(Red intensity / Green intensity)

  21. Gene Expression Data On p genes for nslides:p is O(10,000), n is O(10-100), but growing, Slides 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 ... Genes Gene expression level of gene 5 in slide 4 = Log2(Red intensity / Green intensity) These values are conventionally displayed on a red(>0)yellow (0)green (<0) scale.

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

  23. The red/green ratios can be intensity-biased M = log2R/G = log2R - log2G Values should scatter about zero. = (log2R + log2G )/2

  24. Normalization: how we “fix” the previous problem The curved line becomes the new zero line Orange: Schadt-Wong rank invariant set Red line: lowess smooth Yellow:GAPDH, tubulin Light blue: MSP pool / titration

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

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

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

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

  29. 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.

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

  31. 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 pg1 pg2

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

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

  34. An Important Aspect of Our Design D A 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) M L P V How do we combine these?

  35. 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.

  36. The Olfactory Bulb Experiments completed so far

  37. 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

  38. 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.

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

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

  41. Patterns, More Globally... Can we identify genes with interesting patterns of expression across the bulb? Two approaches: 1. Find the genes whose expression fits specific, predefined patterns. 2. Perform cluster analysis - see what expression patterns emerge.

  42. 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.

  43. Plots guiding choice of clusters of genes Number of genes Number of clusters (patterns) Cluster heterogeneity h (max of 15 SDs)

  44. PA DA VA MA LA MP LA VP DP LP VD MD LD MV LA LM LV Red :genes chosen Blue:controls 15 p/w effects

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

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

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