Microarray Data Analysis

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Microarray Data Analysis

• Angela Burr
• Divya Rao

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Microarray Data Analysis

• Objectives
• Identify genes with differential gene expression
  between two experimental conditions
• Identifying patterns of gene expression of a
  sample at a particular state
• Understanding biological systems

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Normalization

• Adjust raw intensity values to correct for
  intensity differences due to the procedure
• Methods
• Global adjustment
• Intensity dependent
• Housekeeping normalization
• Print run normalizations
• Between slides

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Preliminary Analysis

• General distribution information
• Scatterplots (log R vs log G)
• MA plots (Mlog (R/G))
• Histograms
• Boxplots

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Histogram of distribution
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Differential Expression

• Goal Identify significant differences in gene
  expression from the background
• Problems
• Microarray experiments with many variables and
  few replicates are not conducive for traditional
  statistical tests
• Possible Solution
• Use statistical models
• Concerns
• High variability among levels gene expressions
  making it difficult to identify up-regulation or
  down-regulation of a single gene
• False negatives and false positives

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Parametric Methods

• T-test approaches
• Bayesian approach pool genes with similar
  expression levels to better estimate the variance
• Compute probability of gene expression from a
  uniform distribution vs non-uniform distribution
• ANOVA

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t-tests Comparison
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Non-Parametric Methods

• Nonparametric t-test
• Permutations
• Not very sensitive
• Wilcoxon rank sum test

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Xu and Li, Bioinformatics Vol 19(10) 2003
p1284-1289
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CLUSTER ANALYSIS

• Genes that belong to a particular pathway are
  generally co-regulated and have similar
  expression patterns
• Correlating gene expression changes to identify
  sets of genes with similar profiles
• Method of organizing gene expression data, and
  developing phylogenetic trees

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Terminology

• Vector Position of the gene in expression
  space, a geometric coordinate
• Expression space - The log2 ratios from the
  experiment with n arrays, plotted in n dimensions
• Clustering algorithms group genes based on their
  separation in expression space

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• Mean Centring Subtract the basal expression
  level of a gene from each experimental
  measurement
• Distance Metric Measure of distance between
  gene expression vectors
• Metric distances
• Semi-Metric distances

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Distance Metrics

• Metric distances (dij between vectors i and j)
• dij positive definite
• dij symmetric
• dij zero distance from itself
• Triangle rule dik lt dij djk
• Euclidean distance d v S ( xi yi) 2 over i
  1 to n.
• Semi Metric distances
• Do not obey triangle rule

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Classification of Clustering Algorithms

• Hierarchical
• Produces a hierarchy of clusters
• Non-Hierarchical
• Partitions objects into different clusters
• Divisive
• Breaks down parent cluster into smaller clusters
• Agglomerative
• Fuses single-member clusters

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Classification continued

• Supervised
• Use known biological information to guide the
  algorithm
• Example SVM
• Unsupervised
• Make use of gene expression information to reveal
  patterns in the data
• Example Hierarchical, k-Means, SOM, PCA

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Hierarchical Clustering

• Most widely used
• Agglomerative approach, produces a single
  hierarchical tree
• Typically average linkage clustering is used.
• Disadvantages
• If a bad assignment is made, it cannot be
  corrected
• Expression patterns of genes become less relevant
  with progress in clustering

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Hierarchical Clustering Algorithms

• Single Linkage Clustering
• Minimum distance between members of two clusters
• Complete Linkage Clustering
• Greatest distance between members of relevant
  clusters
• Average Linkage Clustering
• UPGMA
• Centroid or Median

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Visualization of Hierarchical clustering

• average linking
• complete linkage
• single linkage

• Quackebush J

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k-means Clustering

• Used when prior biological knowledge regarding
  the number of clusters is known.
• Partitions objects into fixed number (k) of
  clusters.
• No dendrograms produced

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Self-organizing Maps

• Neural network based divisive clustering
• Assigns genes to partitions based on the
  similarity of their expression vectors to
  pre-defined reference vectors
• Requires prior knowledge

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Principal Component Analysis

• Provides a projection of complex data sets onto a
  reduced, easily visualized space
• Difficult to accurately define the precise
  boundaries of distinct clusters in the data
• Powerful when used with another classification
  technique such as k-means clustering or SOM

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PCA and Hierarchical analysis

• Hierarchical (average linkage) clustering
• PCA
• Quackenbush J

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Supervised Methods - SVM

• Require previous information about which genes
  are expected to cluster together
• Support Vector Machines (SVM)
• Binary classifier
• Kernel function
• Classification of samples
• Molecular expression fingerprinting

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Comparison of clustering methods

• Hierarchical clustering with correlation
• Clustering by k-means
• Diana
• Fanny
• Model-based clustering
• Hierarchical clustering with partial least squares

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Comparison of clustering methods

• Data used
• Transcriptional program of sporulation in budding
  yeast (Chu et al)
• 7 time points
• 4975 genes
• Simulated data (Quackenbush)
• 10 time points
• 450 genes

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Hierarchical and k-means clustering

• Hierarchical clustering
• Produces a hierarchy of clusters
• Average linkage clustering UPGMA
• d(x, y) 1 - corr(x, y)
• corr(x, y) -gt statistical correlation between
  expression profiles of x and y
• K-means clustering
• Number of clusters determined using Hierarchical
  clustering

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Diana

• Divisive clustering method
• Cluster C with cardinality n(C)
• x1 ? C
• Splits into
• x1, .., xk and
• C \ x1, .., xk

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Fanny

• Fuzzy logic
• Used L1 (Manhattan distance)
• Computes probability vectors for all genes that
  minimize the objective function
• Assigns genes to the group with highest
  probability

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Model-based clustering

• Modeling expression profiles by mixtures of
  multivariate normal distributions
• Density function
• Likelihood of genes with expression profiles
  x1,,xn
• Group levels ? obtained by maximum likelihood
  that maximizes L jointly in ? and ?

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Hierarchical clustering with partial least squares

• xi is the vector of expression ratios for the ith
  gene
• Partial least squared model of x1 on x2,..,xM
• Symmetrized coefficient for any gene pair (i, j),
  i ? j

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Validation

• Average proportion of non-overlap measures
• Average distance between means measure
• Average distance measure
• K number of clusters
• Expect small values

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Results for sporulation data

• Non-overlap measures

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Results of sporulation data

• Average distance between means measure
• Average distance measure

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Results for simulate data

• Hierarchical clustering performed poorly
• Diana and Model based performed best
• K-means and Fanny performed well

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Model profile

• Training set of seven temporal classes
• Model temporal profile
• For each class the average of the log expression
  ratio of all the genes in that class are plotted
  over the seven time points
• Same for 5 algorithms
• Fanny not used

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Comparison with model profiles
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Comparison with model profiles
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Comparison with model profiles
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Obejctive comparison

• Distance measure
• Total distance from model profile

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Discussion

• End result is dependent on clustering method
• Choose based on
• Visual plots
• Validation techniques
• Compare with model profiles
• Application of more than one technique

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Microarray Software

• To assist in management / organization of the
  data and help in the data analysis process
• Commercial and open-source available
• Popular brands
• Gene Spring
• Genesis
• MIDAS

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A Gene-Coexpression Network for Global Discovery
of Conserved Genetic Modules (Stuart et al,
Science Vol. 302 2003)

• Evolutionary divergent organisms
• Home sapien, Drosophia, C. elegans, S. cerevisiae
• Importance
• Only used genes with orthologs to develop
  networks between species
• Dealing with multiple species which found to have
  tighter clusters and more exclusive

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Gene-Coexpression Networks

• Methods
• Group genes by BLAST
• Identify gene groups that are functionally
  related by prior microarray data
• Identify genes with significant Pearson
  correlations indicating conserved coexpression
• Created a coexpression network with based on
  correlations
• Validated by methods of permutations adding
  noise

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Stuart et al, Science Vol 302 Oct 10 , 2003 p
249-255
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Stuart et al, Science Vol 302 Oct 10 , 2003 p
249-255
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Gene-Coexpression Networks

• Results
• Identification of genes involved with particular
  biological processes (that were previously
  unknown) because genes linked in network likely
  to be involved in similar processes
• Selective forces impacting interconnected classes
  of genes over evolution

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References

• Baggerly et al, J. of Comp Bio Vol 8(6) 2001,
  p639-659
• Chen, G. et al., (2002) Evaluation and comparison
  of clustering algorithms in analyzing ES cell
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• Hatfield et al, Molecular Microbiology Vol 47(4)
  2003, p 871-877
• Kerr, M.K. and Churchill, G.A. (2001)
  Bootstrapping cluster analysis assessing the
  resliability of conclusions from microarray
  experiments. Proc. Natl Acad. Sci. USA, 98, 8961
  8965
• Pam, Bioinformatics Vol 19(11) 2003, p 1333-1340
• Sambrook J (ed), DNA Microarrays A Molecular
  Cloning Manual
• Slonim D, Nature Vol 32 2002 p 502-508
• Stuart et al, Science Vol 302 2003 p249-255
• Troyanskaya et al, Bioinformatics Vol 18(11)
  2002, p1454-1461
• Tsodikov et al, Bioinformatics Vol 18(2) 2002, p
  251-260.
• Wilson et al, Bioinformatics Vol 19(11) 2003,
  p1325-1332

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References

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