20100509 bioinformatics kapushesky_lecture03-04_0
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  • This is an MA plot from one of the TIGR loop expt arrays I removed the zeros It is a beauty. Very slight curvature reflect a mild dye effect that we can correct by shifting before taking logs Bulk of genes lie on zero-line but there is evidence of differential expression
  • For sake of comparison this an array from an anonymous source This MA plots shows several of the ‘bad’ things can happen with an array There is low-end truncation High end saturation There are three ‘pin groups’ in different colors and each has it’s own unique curvature -> dye effect is pin group specific Amazingly enough - as part of a larger experiment with replication of samples across arrays there is information here that can extracted - albeit with some effort required. PS This is worst case of the 48 arrays in the expt.
  • affymetrix arrays uses 25 base-pairs Oligonucleotides to probe genes. There are two types of probes, the perfect match and the mismatch probes. 11-20 of these probe pairs of PP and MM represent a genes.
  • The MM probes are designed to measure non-specific binding and optical noise components in PM. Many expression measures are based on PM-MM, with the intention of correcting for non-specific binding and background noise. • Problems: – MMsare PMsfor some genes, – removing the middle base does not make a difference for some probes . – Subtracting MM adds variance. Especially at low end.
  • Y-axis, log intensity of individual probe The G-C information could be accounted for in the analysis
  • RPKM – reads per kilo base of exon per million mapped reads Estimation of gene expression (RPKM) values was performed as follows:1. Count the number of reads which map to constitutive exon bodies. The set of constitutive exons was derived from Ensembl genes (hg18, UCSC genome browser), where an exon was defined to be constitutive if present in all transcripts for a given gene.2. Determine the number of uniquely mappable positions in the same set of constitutive exons. "Uniquely mappable" was defined as being a unique 32-mer in the genome and our junction database.3. Count the total number of uniquely mapping reads in each tissue or sample.4. Compute RPKM as the number of reads which map per kilobase of exon model per million mapped reads for each gene, for each tissue or sample.
  • RPKM – reads per kilo base of exon per million mapped reads Estimation of gene expression (RPKM) values was performed as follows:1. Count the number of reads which map to constitutive exon bodies. The set of constitutive exons was derived from Ensembl genes (hg18, UCSC genome browser), where an exon was defined to be constitutive if present in all transcripts for a given gene.2. Determine the number of uniquely mappable positions in the same set of constitutive exons. "Uniquely mappable" was defined as being a unique 32-mer in the genome and our junction database.3. Count the total number of uniquely mapping reads in each tissue or sample.4. Compute RPKM as the number of reads which map per kilobase of exon model per million mapped reads for each gene, for each tissue or sample.

20100509 bioinformatics kapushesky_lecture03-04_0 Presentation Transcript

  • 1. Gene Expression - Microarrays Misha Kapushesky European Bioinformatics Institute, EMBL St. Petersburg, Russia May 2010
  • 2.  
  • 3.  
  • 4.  
  • 5.  
  • 6. Compare gene expression in this cell type… … after drug treatment … at a later developmental time … in a different body region … after viral infection … in samples from patients … relative to a knockout
  • 7.
    • • by region (e.g. brain versus kidney)
    • • in development (e.g. fetal versus adult tissue)
    • • in dynamic response to environmental signals
    • (e.g. immediate-early response genes)
    • in disease states
    • by gene activity
    Gene expression is context-dependent, and is regulated in several basic ways Page 297
  • 8. Outline: microarray data analysis Gene expression Microarrays Preprocessing normalization scatter plots Inferential statistics t-test ANOVA Exploratory (descriptive) statistics distances clustering principal components analysis (PCA)
  • 9. Microarrays: tools for gene expression A microarray is a solid support (such as a membrane or glass microscope slide) on which DNA of known sequence is deposited in a grid-like array. Page 312
  • 10. Microarrays: tools for gene expression The most common form of microarray is used to measure gene expression. RNA is isolated from matched samples of interest. The RNA is typically converted to cDNA, labeled with fluorescence (or radioactivity), then hybridized to microarrays in order to measure the expression levels of thousands of genes.
  • 11. [email_address] Measuring RNA abundances
  • 12. [email_address] How it works
    • Complementary hybridization:
    • Put a part of the gene sequence on the array
    • convert mRNA to cDNA using reverse transcriptase
  • 13. [email_address] Spotted Arrays
    • Robot puts little spots of DNA on glass slides
    • Each spot is a DNA analog of the mRNA we want to detect
  • 14. [email_address] Spotted Arrays
    • Two channel technology for comparing two samples – relative measurements
    • Two mRNA samples (reference, test) are reverse transcribed to cDNA, labeled with fluorescent dyes (Cy3, Cy5) and allowed to hybridize to array
  • 15. [email_address] Spotted Arrays
    • Read out two images by scanning array with lasers, one for each dye
  • 16. [email_address] Oligonucleotide Arrays
    • One channel technology – absolute measurements
    • Instead of putting entire genes on array, put multiple oligonucleotide probes: short, fixed length DNA sequences (25-60 nucleotides)
    • Oligos are synthesized in situ
      • Affymetrix uses a photolithography process, similar to that used to make semiconductor chips
      • Other technologies available (e.g. mirror arrays)
  • 17. [email_address] Oligonucleotide Arrays
    • For each gene, construct a probeset – a set of n-mers to specific to this gene
  • 18. Fast Data on >20,000 transcripts within weeks Comprehensive Entire yeast or mouse genome on a chip Flexible Custom arrays can be made to represent genes of interest Easy Submit RNA samples to a core facility Cheap? Chip representing 20,000 genes for $300 Advantages of microarray experiments
  • 19. Cost ■ Some researchers can’t afford to do appropriate numbers of controls, replicates RNA ■ The final product of gene expression is protein significance ■ “Pervasive transcription” of the genome is poorly understood (ENCODE project) ■ There are many noncoding RNAs not yet represented on microarrays Quality ■ Impossible to assess elements on array surface control ■ Artifacts with image analysis ■ Artifacts with data analysis ■ Not enough attention to experimental design ■ Not enough collaboration with statisticians Disadvantages of microarray experiments
  • 20. Biological insight Sample acquisition Data acquisition Data analysis Data confirmation
  • 21. Stage 1: Experimental design Stage 3: Hybridization to DNA arrays Stage 2: RNA and probe preparation Stage 4: Image analysis Stage 5: Microarray data analysis Stage 6: Biological confirmation Stage 7: Microarray databases
  • 22. Stage 1: Experimental design [1] Biological samples: technical and biological replicates: determine the data analysis approach at the outset [2] RNA extraction, conversion, labeling, hybridization: except for RNA isolation, routinely performed at core facilities [3] Arrangement of array elements on a surface: randomization can reduce spatially-based artifacts Page 314
  • 23. Stage 2: RNA preparation For Affymetrix chips, need total RNA (about 5 ug) Confirm purity by running agarose gel Measure a260/a280 to confirm purity, quantity One of the greatest sources of error in microarray experiments is artifacts associated with RNA isolation; appropriately balanced, randomized experimental design is necessary.
  • 24. Stage 3: Hybridization to DNA arrays The array consists of cDNA or oligonucleotides Oligonucleotides can be deposited by photolithography The sample is converted to cRNA or cDNA (Note that the terms “probe” and “target” may refer to the element immobilized on the surface of the microarray, or to the labeled biological sample; for clarity, it may be simplest to avoid both terms.)
  • 25. Stage 4: Image analysis RNA transcript levels are quantitated Fluorescence intensity is measured with a scanner.
  • 26. Rett Control Differential Gene Expression on a cDNA Microarray  B Crystallin is over-expressed in Rett Syndrome
  • 27.  
  • 28. Fig. 8.21 Page 319
  • 29.  
  • 30. Fig. 8.21 Page 319
  • 31. Stage 5: Microarray data analysis Page 318
    • Hypothesis testing
    • How can arrays be compared?
    • Which RNA transcripts (genes) are regulated?
    • Are differences authentic?
    • What are the criteria for statistical significance?
    • Clustering
    • Are there meaningful patterns in the data (e.g. groups)?
    • Classification
    • Do RNA transcripts predict predefined groups, such as disease subtypes?
  • 32. Stage 6: Biological confirmation Page 320 Microarray experiments can be thought of as “ hypothesis-generating” experiments. The differential up- or down-regulation of specific RNA transcripts can be measured using independent assays such as -- Northern blots -- polymerase chain reaction (RT-PCR) -- in situ hybridization
  • 33. Stage 7: Microarray databases There are two main repositories: Gene Expression Omnibus (GEO) at NCBI ArrayExpress at the European Bioinformatics Institute (EBI)
  • 34. Microarray Overview I Microbial ORFs Design PCR Primers PCR Products Eukaryotic Genes Select cDNA clones PCR Products For each plate set, many identical replicas Microarray Slide (with 60,000 or more spotted genes) + Microtiter Plate Many different plates containing different genes
  • 35. Microarray Overview II Prepare Fluorescently Labeled Probes Control Test Hybridize, Wash Measure Fluorescence in 2 channels red / green Analyze the data to identify patterns of gene expression
  • 36. Affymetrix GeneChip™ Expression Analysis Obtain RNA Samples Prepare Fluorescently Labeled Probes Control Test Scan chips Analyze PM MM Hybridize and wash chips
  • 37. Gene Microarray Expression Analysis Spots on an Array Fluorescence Intensity Expression Measurement Tissue Selection Differential State/Stage Selection RNA Preparation and Labeling Competitive Hybridization
  • 38. Steps in the Process
    • Select array elements and annotate them
    • Build a database to manage stuff
    • Print arrays and manage the lab
    • Hybridize and analyze images; manage data
    • Analyze hybridization data and get results
  • 39. MIAME In an effort to standardize microarray data presentation and analysis, Alvis Brazma and colleagues at 17 institutions introduced Minimum Information About a Microarray Experiment (MIAME). The MIAME framework standardizes six areas of information: ► experimental design ► microarray design ► sample preparation ► hybridization procedures ► image analysis ► controls for normalization Visit http://www.mged.org
  • 40. Interpretation of RNA analyses The relationship of DNA, RNA, and protein: DNA is transcribed to RNA. RNA quantities and half-lives vary. There tends to be a low positive correlation between RNA and protein levels. The pervasive nature of transcription: The Encyclopedia of DNA Elements (ENCODE) project identified functional features of genomic DNA, initially in 30 megabases (1% of the human genome). One of its observations was the “pervasive nature of transcription”: the vast majority of DNA is transcribed, although the function is unknown.
  • 41. Outline: microarray data analysis Gene expression Microarrays Preprocessing normalization scatter plots Inferential statistics t-test ANOVA Exploratory (descriptive) statistics distances clustering principal components analysis (PCA)
  • 42. Microarray data analysis • begin with a data matrix (gene expression values versus samples) genes (RNA transcript levels)
  • 43. Microarray data analysis • begin with a data matrix (gene expression values versus samples) Typically, there are many genes (>> 20,000) and few samples ( ~ 10) Fig. 9.1 Page 333
  • 44. Microarray data analysis • begin with a data matrix (gene expression values versus samples) Preprocessing Inferential statistics Descriptive statistics
  • 45. Microarray data analysis: preprocessing
    • Observed differences in gene expression could be
    • due to transcriptional changes, or they could be
    • caused by artifacts such as:
    • different labeling efficiencies of Cy3, Cy5
    • uneven spotting of DNA onto an array surface
    • variations in RNA purity or quantity
    • variations in washing efficiency
    • variations in scanning efficiency
  • 46. Microarray data analysis: preprocessing The main goal of data preprocessing is to remove the systematic bias in the data as completely as possible, while preserving the variation in gene expression that occurs because of biologically relevant changes in transcription. A basic assumption of most normalization procedures is that the average gene expression level does not change in an experiment.
  • 47. Data analysis: global normalization Global normalization is used to correct two or more data sets. In one common scenario, samples are labeled with Cy3 (green dye) or Cy5 (red dye) and hybridized to DNA elements on a microrarray. After washing, probes are excited with a laser and detected with a scanning confocal microscope.
  • 48. Data analysis: global normalization Global normalization is used to correct two or more data sets Example: total fluorescence in Cy3 channel = 4 million units Cy 5 channel = 2 million units Then the uncorrected ratio for a gene could show 2,000 units versus 1,000 units. This would artifactually appear to show 2-fold regulation.
  • 49. Data analysis: global normalization Global normalization procedure Step 1: subtract background intensity values (use a blank region of the array) Step 2: globally normalize so that the average ratio = 1 (apply this to 1-channel or 2-channel data sets)
  • 50. Scatter plots Useful to represent gene expression values from two microarray experiments (e.g. control, experimental) Each dot corresponds to a gene expression value Most dots fall along a line Outliers represent up-regulated or down-regulated genes
  • 51. Brain Astrocyte Astrocyte Fibroblast Differential Gene Expression in Different Tissue and Cell Types
  • 52. expression level high low up down Expression level (sample 1) Expression level (sample 2)
  • 53. Log-log transformation
  • 54. Scatter plots Typically, data are plotted on log-log coordinates Visually, this spreads out the data and offers symmetry raw ratio log 2 ratio time behavior value value t=0 basal 1.0 0.0 t=1h no change 1.0 0.0 t=2h 2-fold up 2.0 1.0 t=3h 2-fold down 0.5 -1.0
  • 55. expression level high low up down Mean log intensity Log ratio
  • 56. You can make these plots in Excel… … but for many bioinformatics applications use R. Visit http://www.r-project.org to download it.
  • 57.  
  • 58. There are limits to what you can measure
  • 59. The Limits of log-ratios: The space we explore
  • 60. The Limits of log-ratios: The space we explore
  • 61. The Limits of log-ratios: The space we explore
  • 62. Good Data
  • 63. Bad Data from Parts Unknown Gary Churchill Each “pin group” is colored differently
  • 64. Lowess Normalization
    • Why LOWESS?
    • Intensity-dependent structure
    • Data not mean centered at log 2 (ratio) = 0
    A SD = 0.346
  • 65. Ratio Cy3/Cy5 for the same RNA sorted from least most expressed
  • 66. LOWESS Results
  • 67. Affymetrix Chips
  • 68. Mismatch (MM) probes
    • MM probes are used to measure background signals due to non-specific sources and scanner offset.
    • Using a MM probe as an estimate of background seems wrong and often the MM signal >= the PM signal
    • Some would claim that subtraction of the mismatch probe adds noise for little gain.
  • 69. Computing expression summaries: a three-step process
    • Background/Signal adjustment
    • Normalization (can happen at the probe-pair or the probe-set level).
    • Summarization of probe-pairs into probe-set or gene level information
  • 70. Background/Signal Adjustment
    • A method which does some or all of the following
      • Corrects for background noise, processing effects
      • Adjusts for cross hybridization
      • Adjust estimated expression values to fall on proper scale
    • Probe intensities are used in background adjustment to compute correction (unlike cDNA arrays where area surrounding spot might be used)
  • 71. Normalization Methods
    • Complete data (no reference chip, information from all arrays used)
      • Quantile normalization (Bolstadt al 2003)
    • Baseline (normalized using reference chip)
      • Scaling (Affymetrix)
      • Non linear (Li-Wong)
  • 72. Summarization
    • Reduce the 11-20 probe intensities on each array to a single number for gene expression
    • Main Approaches
      • Single chip
        • AvDiff (Affymetrix) – no longer recommended for use due to many flaws
        • Mas5.0 (Affymetrix) –use a 1 step Tukey biweight to combine the probe intensities in log scale
      • Multiple Chip
        • • MBEI (Li-Wong dChip) –a multiplicative model
        • • RMA –a robust multi-chip linear model fit on the log scale
  • 73. Robust multi-array analysis (RMA)
    • Developed by Rafael Irizarry (Dept. of Biostatistics), Terry Speed, and others
    • Available at www.bioconductor.org as an R package
    • Also available in various software packages (including Partek, www.partek.com and Iobion Gene Traffic)
    • See Bolstad et al. (2003) Bioinformatics 19;
    • Irizarry et al. (2003) Biostatistics 4
    • There are three steps:
    • [1] Background adjustment based on a normal plus exponential model (no mismatch data are used)
    • [2] Quantile normalization (nonparametric fitting of signal intensity data to normalize their distribution)
    • [3] Fitting a log scale additive model robustly. The model is additive: probe effect + sample effect
  • 74. GCRMA
    • GC-RMA is a modified version of RMA that models intensity of probe level data as a function of GC-content
    • expect to see higher intensity values for probes that are GC rich due to increased binding
  • 75.  
  • 76. A A M M After RMA (a normalization procedure), the median is near zero, and skewing is corrected. Scatterplots display the effects of normalization.
  • 77. vsn: variance stabilizing normalization
    • Variance depends on signal intensity in microarray data
    • A transformation can be found after which the variance is approximately constant
    • Like the logarithm at the upper end of, approximately linear at the lower end
    • Also incorporates the estimation of "normalization" parameters (shift and scale)
    • Assumes that less than half of the genes on the arrays are differentially transcribed across the experiment.
  • 78. vsn: post-normalization plot
  • 79. array log signal intensity array log signal intensity Histograms of raw intensity values for 14 arrays (plotted in R) before and after RMA was applied.
  • 80. RMA can adjust for the effect of GC content GC content log intensity
  • 81. Robust multi-array analysis (RMA) RMA offers a large increase in precision (relative to Affymetrix MAS 5.0 software). precision average log expression log expression SD RMA MAS 5.0
  • 82. Robust multi-array analysis (RMA) RMA offers comparable accuracy to MAS 5.0. log nominal concentration observed log expression accuracy
  • 83. Outline: microarray data analysis Gene expression Microarrays Preprocessing normalization scatter plots Inferential statistics t-test ANOVA Exploratory (descriptive) statistics distances clustering principal components analysis (PCA)
  • 84. Inferential statistics Inferential statistics are used to make inferences about a population from a sample. Hypothesis testing is a common form of inferential statistics. A null hypothesis is stated, such as: “ There is no difference in signal intensity for the gene expression measurements in normal and diseased samples.” The alternative hypothesis is that there is a difference. We use a test statistic to decide whether to accept or reject the null hypothesis. For many applications, we set the significance level  to p < 0.05.
  • 85. [1] Obtain a matrix of genes (rows) and expression values columns. Here there are 20,000 rows of genes of which the first six are shown. There are three control samples and three disease samples. Calculate the mean value for each gene (transcript) for the controls and the disease (experimental) samples. Analyzing expression data Question: for each of my 20,000 transcripts, decide whether it is significantly regulated in some disease. control disease
  • 86. [2] Calculate the ratios of control versus disease. Also note that some ratios, such as 2.00, appear to be dramatic while others are not. Some researchers set a cut-off for changes of interest such as two-fold. Analyzing expression data
  • 87. A significant difference Probably not
  • 88. Inferential statistics A t-test is a commonly used test statistic to assess the difference in mean values between two groups. t = = Questions Is the sample size (n) adequate? Are the data normally distributed? Is the variance of the data known? Is the variance the same in the two groups? Is it appropriate to set the significance level to p < 0.05? x 1 – x 2 SE difference between mean values variability (standard error of the difference)
  • 89. Inferential statistics
    • A t-test is a commonly used test statistic to assess
    • the difference in mean values between two groups.
    • t = =
    • Notes
    • t is a ratio (it thus has no units)
    • We assume the two populations are Gaussian
    • The two groups may be of different sizes
    • Obtain a P value from t using a table
    • For a two-sample t test, the degrees of freedom is N - 2.
    • For any value of t, P gets smaller as df gets larger
    x 1 – x 2 SE difference between mean values variability (standard error of the difference)
  • 90. [3] Perform a t-test. Hypothesis is that the transcript in the disease group is up (or down) relative to controls. Analyzing expression data
  • 91. [3] Note the results: you can have… a small p value (<0.05) with a big ratio difference a small p value (<0.05) with a trivial ratio difference a large p value (>0.05) with a big ratio difference a large p value (>0.05) with a trivial ratio difference Analyzing expression data
  • 92. Inferential statistics Is it appropriate to set the significance level to p < 0.05? If you hypothesize that a specific gene is up-regulated, you can set the probability value to 0.05. You might measure the expression of 10,000 genes and hope that any of them are up- or down-regulated. But you can expect to see 5% (500 genes) regulated at the p < 0.05 level by chance alone. To account for the thousands of repeated measurements you are making, some researchers apply a Bonferroni correction. The level for statistical significance is divided by the number of measurements, e.g. the criterion becomes: p < (0.05)/10,000 or p < 5 x 10 -6 The Bonferroni correction is generally considered to be too conservative.
  • 93. Inferential statistics: false discovery rate The false discovery rate (FDR) is a popular multiple corrections correction. A false positive (also called a type I error) is sometimes called a false discovery. The FDR equals the p value of the t-test times the number of genes measured (e.g. for 10,000 genes and a p value of 0.01, there are 100 expected false positives). You can adjust the false discovery rate. For example: FDR # regulated transcripts # false discoveries 0.1 100 10 0.05 45 3 0.01 20 1 Would you report 100 regulated transcripts of which 10 are likely to be false positives, or 20 transcripts of which one is likely to be a false positive?
  • 94. Inferential statistics: other methods used
    • t-test for two sample groups, SAM and t-tests with permutation testing
    • ANOVA for multiple factors
    • Linear models with Bayesian moderation of variance Smyth G. (2004) “ Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments”
    • Simultaneous inference: multivariate t-distributions for simultaneous confidence intervals
        • Hsu et al. (1996) “Multiple Comparisons: Theory and Methods”
        • Hsu et al. (2006) “Screening for Differential Gene Expressions from Microarray Data”
  • 95. log fold change (treated/untreated) p value (treated versus control) A volcano plot displays both p values and fold change
  • 96. Outline: microarray data analysis Gene expression Microarrays Preprocessing normalization scatter plots Inferential statistics t-test ANOVA Exploratory (descriptive) statistics distances clustering principal components analysis (PCA)
  • 97.  
  • 98.  
  • 99.  
  • 100. Descriptive statistics Microarray data are highly dimensional: there are many thousands of measurements made from a small number of samples. Descriptive (exploratory) statistics help you to find meaningful patterns in the data. A first step is to arrange the data in a matrix. Next, use a distance metric to define the relatedness of the different data points. Two commonly used distance metrics are: -- Euclidean distance -- Pearson coefficient of correlation
  • 101. What is a cluster? A cluster is a group that has homogeneity (internal cohesion) and separation (external isolation). The relationships between objects being studied are assessed by similarity or dissimilarity measures.
  • 102. Data matrix (20 genes and 3 time points from Chu et al., 1998) Software: S-PLUS package genes samples (time points)
  • 103. 3D plot (using S-PLUS software) t=0 t=0.5 t=2.0
  • 104. Descriptive statistics: clustering Clustering algorithms offer useful visual descriptions of microarray data. Genes may be clustered, or samples, or both. We will next describe hierarchical clustering. This may be agglomerative (building up the branches of a tree, beginning with the two most closely related objects) or divisive (building the tree by finding the most dissimilar objects first). In each case, we end up with a tree having branches and nodes. Page 355
  • 105. Distance Is Defined by a Metric Euclidean Pearson* Distance Metric: 6.0 1.4 +1.00 -0.05 D D
  • 106. Distance is Defined by a Metric 4.2 1.4 -1.00 -0.90 Euclidean Pearson(r*-1) Distance Metric: D D
  • 107.
    • Once a distance metric has been selected, the starting point for all clustering methods is a “distance matrix”
    Distance Matrix Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6
    • Gene 1 0 1.5 1.2 0.25 0.75 1.4
        • Gene 2 1.5 0 1.3 0.55 2.0 1.5
        • Gene 3 1.2 1.3 0 1.3 0.75 0.3
        • Gene 4 0.25 0.55 1.3 0 0.25 0.4
        • Gene 5 0.75 2.0 0.75 0.25 0 1.2
        • Gene 6 1.4 1.5 0.3 0.4 1.2 0
    • The elements of this matrix are the pair-wise distances. Note that the matrix is symmetric about the diagonal.
  • 108. Agglomerative clustering a b c d e a,b 4 3 2 1 0 Adapted from Kaufman and Rousseeuw (1990)
  • 109. a b c d e a,b d,e 4 3 2 1 0 Agglomerative clustering
  • 110. a b c d e a,b d,e c,d,e 4 3 2 1 0 Agglomerative clustering
  • 111. a b c d e a,b d,e c,d,e a,b,c,d,e 4 3 2 1 0 Agglomerative clustering … tree is constructed
  • 112. Divisive clustering a,b,c,d,e 4 3 2 1 0
  • 113. Divisive clustering c,d,e a,b,c,d,e 4 3 2 1 0
  • 114. Divisive clustering d,e c,d,e a,b,c,d,e 4 3 2 1 0
  • 115. Divisive clustering a,b d,e c,d,e a,b,c,d,e 4 3 2 1 0
  • 116. Divisive clustering a b c d e a,b d,e c,d,e a,b,c,d,e 4 3 2 1 0 … tree is constructed
  • 117. divisive agglomerative a b c d e a,b d,e c,d,e a,b,c,d,e 4 3 2 1 0 4 3 2 1 0 Adapted from Kaufman and Rousseeuw (1990)
  • 118.  
  • 119.  
  • 120. 1 1 12 12 Agglomerative and divisive clustering sometimes give conflicting results, as shown here
  • 121. Agglomerative Linkage Methods
    • Linkage methods are rules or metrics that return a value that can be used to determine which elements (clusters) should be linked.
    • Three linkage methods that are commonly used are:
            • Single Linkage
            • Average Linkage
            • Complete Linkage
    (HCL-6)
  • 122. Single Linkage Cluster-to-cluster distance is defined as the minimum distance between members of one cluster and members of the another cluster. Single linkage tends to create ‘elongated’ clusters with individual genes chained onto clusters. D AB = min ( d(u i , v j ) ) where u  A and v  B for all i = 1 to N A and j = 1 to N B (HCL-7) D AB
  • 123. Average Linkage Cluster-to-cluster distance is defined as the average distance between all members of one cluster and all members of another cluster. Average linkage has a slight tendency to produce clusters of similar variance. D AB = 1/(N A N B )  ( d(u i , v j ) ) where u  A and v  B for all i = 1 to N A and j = 1 to N B (HCL-8) D AB
  • 124. Complete Linkage Cluster-to-cluster distance is defined as the maximum distance between members of one cluster and members of the another cluster. Complete linkage tends to create clusters of similar size and variability. D AB = max ( d(u i , v j ) ) where u  A and v  B for all i = 1 to N A and j = 1 to N B (HCL-9) D AB
  • 125. Comparison of Linkage Methods Single Average Complete
  • 126. Two-way clustering of genes (y-axis) and cell lines (x-axis) (Alizadeh et al., 2000)
  • 127. A B x 1 x 2 1 1 0.5 0.5 1.5 A’ B’ a 1 b 1 a’ 1 b’ 1 a’ 2 b 2 a 2 b’ 2    Euclidean distance Chord distance Angle distance
  • 128. K-Means/Medians Clustering – 1 1. Specify number of clusters , e.g., 5. 2. Randomly assign genes to clusters. G1 G2 G3 G4 G5 G6 G7 G8 G9 G10 G11 G12 G13
  • 129. K-Means/Medians Clustering – 2 3. Calculate mean/median expression profile of each cluster. 4. Shuffle genes among clusters such that each gene is now in the cluster whose mean expression profile (calculated in step 3) is the closest to that gene’s expression profile. 5. Repeat steps 3 and 4 until genes cannot be shuffled around any more, OR a user-specified number of iterations has been reached. k -means is most useful when the user has an a priori hypothesis about the number of clusters the genes should belong to. G1 G2 G3 G4 G5 G6 G7 G8 G9 G10 G11 G12 G13
  • 130. K-Means / K-Medians Support (KMS)
    • Because of the random initialization of K-Means/K-Means, clustering results may vary somewhat between successive runs on the same dataset. KMS helps us validate the clustering results obtained from K-Means/K-Medians.
    • Run K-Means / K-Medians multiple times.
    • The KMS module generates clusters in which the member genes frequently group together in the same clusters (“consensus clusters”) across multiple runs of K-Means / K-Medians .
    • T he consensus clusters consist of genes that clustered together in at least x % of the K-Means / Medians runs, where x is the threshold percentage input by the user.
  • 131. An exploratory technique used to reduce the dimensionality of the data set to 2D or 3D For a matrix of m genes x n samples, create a new covariance matrix of size n x n Thus transform some large number of variables into a smaller number of uncorrelated variables called principal components (PCs). Principal components analysis (PCA)
  • 132. Principal components analysis (PCA): objectives • to reduce dimensionality • to determine the linear combination of variables • to choose the most useful variables (features) • to visualize multidimensional data • to identify groups of objects (e.g. genes/samples) • to identify outliers
  • 133. http://www.okstate.edu/artsci/botany/ordinate/PCA.htm
  • 134. http://www.okstate.edu/artsci/botany/ordinate/PCA.htm
  • 135. http://www.okstate.edu/artsci/botany/ordinate/PCA.htm
  • 136. http://www.okstate.edu/artsci/botany/ordinate/PCA.htm
  • 137.  
  • 138.  
  • 139. 1 12
  • 140. [email_address] High-throughput methods beyond microarrays
  • 141. [email_address] RNA-seq
    • Sequencing technology is making fast progress
    • Idea: sequencing is so cheap that we can sequence mRNA molecules directly “Digital Gene Expression”
  • 142. [email_address] RNA-seq
    • After two rounds of poly(A) selection, RNA is fragmented to an average length of 200 nt by magnesium-catalyzed hydrolysis and then converted into cDNA by random priming. The cDNA is then converted into a molecular library for Illumina/Solexa 1G sequencing, and the resulting 25-bp reads are mapped onto the genome. Normalized transcript prevalence is calculated with an algorithm from the ERANGE package.
    • ( b ) Primary data from mouse muscle RNAs that map uniquely in the genome to a 1-kb region of the Myf6 locus, including reads that span introns. The RNA-Seq graph above the gene model summarizes the quantity of reads, so that each point represents the number of reads covering each nucleotide, per million mapped reads (normalized scale of 0–5.5 reads).
    • ( c ) Detection and quantification of differential expression. Mouse poly(A)-selected RNAs from brain, liver and skeletal muscle for a 20-kb region of chromosome 10 containing Myf6 and its paralog Myf5 , which are muscle specific. In muscle, Myf6 is highly expressed in mature muscle, whereas Myf5 is expressed at very low levels from a small number of cells. The specificity of RNA-Seq is high: Myf6 expression is known to be highly muscle specific, and only 4 reads out of 71 million total liver and brain mapped reads were assigned to the Myf6 gene model.
  • 143. [email_address] RNA-seq
  • 144. Acknowledgements
    • This presentation uses slides/graphics from:
      • J. Pevsner (Johns Hopkins, http://www.bioinfbook.org)
      • J. Quackenbush (DFCI, Harvard)
      • C. Dewey (Wisconsin, http:// www.biostat.wisc.edu/bmi576)
    [email_address]