Presentation is loading. Please wait.

Presentation is loading. Please wait.

DNA Chips and Their Analysis Comp

Similar presentations


Presentation on theme: "DNA Chips and Their Analysis Comp"— Presentation transcript:

1 DNA Chips and Their Analysis Comp
DNA Chips and Their Analysis Comp. Genomics: Lecture 13 based on many sources, primarily Zohar Yakhini

2 DNA Microarras: Basics
What are they. Types of arrays (cDNA arrays, oligo arrays). What is measured using DNA microarrays. How are the measurements done?

3 DNA Microarras: Computational Questions
Design of arrays. Techniques for analyzing experiments. Detecting differential expression. Similar expression: Clustering. Other analysis techniques (mmmmmany). Machine learning techniques, and applications for advanced diagnosis.

4 What is a DNA Microarray (I)
A surface (nylon, glass, or plastic). Containing hundreds to thousand pixels. Each pixel has copies of a sequence of single stranded DNA (ssDNA). Each such sequence is called a probe.

5 What is a DNA Microarray (II)
An experiment with k elements. Way to concurrently explore the function of multiple genes. A snapshot of the expression level of k genes under given test conditions

6 Some Microarray Terminology
Probe: ssDNA printed on the solid substrate (nylon or glass). These are short substrings of the genes we are going to be testing Target: cDNA which has been labeled and is to be washed over the probe

7 Back to Basics: Watson and Crick
James Watson and Francis Crick discovered, in 1953, the double helix structure of DNA. From Zohar Yakhini

8 Watson-Crick Complimentarity
A binds to T C binds to G AATGCTTAGTC TTACGAATCAG Perfect match AATGCGTAGTC TTACGAATCAG One-base mismatch From Zohar Yakhini

9 Array Based Hybridization Assays (DNA Chips)
Array of probes Thousands to millions of different probe sequences per array. Unknown sequence or mixture (target). Many copies. From Zohar Yakhini

10 Array Based Hyb Assays Target hybs to WC complimentary probes only
Therefore – the fluorescence pattern is indicative of the target sequence. From Zohar Yakhini

11 DNA Sequencing Sanger Method
Generate all A,C,G,T – terminated prefixes of the sequence, by a polymerase reaction with terminating corresponding bases. Run in four different gel lanes. Reconstruct sequence from the information on the lengths of all A,C,G,T – terminated prefixes. The need for 4 different reactions is avoided by using differentially dye labeled terminating bases. From Zohar Yakhini

12 Central Dogma of Molecular Biology (reminder)
Transcription mRNA Translation Protein Cells express different subset of the genes in different tissues and under different conditions Gene (DNA) From Zohar Yakhini

13 Expression Profiling on MicroArrays
Differentially label the query sample and the control (1-3). Mix and hybridize to an array. Analyze the image to obtain expression levels information. From Zohar Yakhini

14 Microarray: 2 Types of Fabrication
cDNA Arrays: Deposition of DNA fragments Deposition of PCR-amplified cDNA clones Printing of already synthesized oligonucleotieds Oligo Arrays: In Situ synthesis Photolithography Ink Jet Printing Electrochemical Synthesis By Steve Hookway lecture and Sorin Draghici’s book “Data Analysis Tools for DNA Microarrays”

15 cDNA Microarrays vs. Oligonucleotide Probes and Cost
cDNA Arrays Oligonucleotide Arrays Long Sequences Spot Unknown Sequences More variability Arrays cheaper Short Sequences Spot Known Sequences More reliable data Arrays typically more expensive By Steve Hookway lecture and Sorin Draghici’s book “Data Analysis Tools for DNA Microarrays”

16 Photolithography (Affymetrix)
Photodeprotection Similar to process used to generate VLSI circuits Photolithographic masks are used to add each base If base is present, there will be a “hole” in the corresponding mask Can create high density arrays, but sequence length is limited mask C From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

17 Photolithography (Affymetrix)
From Zohar Yakhini

18 Ink Jet Printing Four cartridges are loaded with the four nucleotides: A, G, C,T As the printer head moves across the array, the nucleotides are deposited in pixels where they are needed. This way (many copies of) a base long oligo is deposited in each pixel. By Steve Hookway lecture and Sorin Draghici’s book “Data Analysis Tools for DNA Microarrays”

19 Ink Jet Printing (Agilent)
The array is a stack of images in the colors A, C, G, T. A G T C From Zohar Yakhini

20 Inkjet Printed Microarrays
Inkjet head, squirting phosphor-ammodites From Zohar Yakhini

21 Electrochemical Synthesis
Electrodes are embedded in the substrate to manage individual reaction sites Electrodes are activated in necessary positions in a predetermined sequence that allows the sequences to be constructed base by base Solutions containing specific bases are washed over the substrate while the electrodes are activated From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

22 Preparation of Samples
Use oligo(dT) on a separation column to extract mRNA from total cell populations. Use olig(dT) initiated polymerase to reverse transcribe RNA into fluorescence labeled cDNA. RNA is unstable because of environment RNA-digesting enzymes. Alternatively – use random priming for this purpose, generating a population of transcript subsequences From Zohar Yakhini

23 Expression Profiling on MicroArrays
Differentially label the query sample and the control (1-3). Mix and hybridize to an array. Analyze the image to obtain expression levels information. From Zohar Yakhini

24 Expression Profiling: a FLASH Demo
URL:

25 Expression Profiling – Probe Design Issues
Probe specificity and sensitivity. Special designs for splice variations or other custom purposes. Flat thermodynamics. Generic and universal systems From Zohar Yakhini

26 Hybridization Probes Sensitivity: Strong interaction between the probe and its intended target, under the assay's conditions. How much target is needed for the reaction to be detectable or quantifiable? Specificity: No potential cross hybridization. From Zohar Yakhini

27 Specificity Symbolic specificity
Statistical protection in the unknown part of the genome. Methods, software and application in collaboration with Peter Webb, Doron Lipson. From Zohar Yakhini

28 Reading Results: Color Coding
Campbell & Heyer, 2003 Numeric tables are difficult to read Data is presented with a color scale Coding scheme: Green = repressed (less mRNA) gene in experiment Red = induced (more mRNA) gene in experiment Black = no change (1:1 ratio) Or Green = control condition (e.g. aerobic) Red = experimental condition (e.g. anaerobic) We usually use ratio

29 Thermal Ink Jet Arrays, by Agilent Technologies
In-Situ synthesized oligonucleotide array mers. cDNA array, Inkjet deposition

30 Application of Microarrays
We only know the function of about 30% of the 30,000 genes in the Human Genome Gene exploration Functional Genomics First among many high throughput genomic devices By Steve Hookway lecture and Sorin Draghici’s book “Data Analysis Tools for DNA Microarrays”

31 A Data Mining Problem On a given microarray, we test on the order of 10k elements in one time Number of microarrays used in typical experiment is no more than 100. Insufficient sampling. Data is obtained faster than it can be processed. High noise. Algorithmic approaches to work through this large data set and make sense of the data are desired.

32 Informative Genes in a Two Classes Experiment
Differentially expressed in the two classes. Identifying (statistically significant) informative genes - Provides biological insight - Indicate promising research directions - Reduce data dimensionality - Diagnostic assay From Zohar Yakhini

33 Scoring Genes Expression pattern and pathological diagnosis information (annotation), for a single gene a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 a13 a14 a15 Permute the annotation by sorting the expression pattern (ascending, say). Informative genes etc Non-informative genes From Zohar Yakhini

34 Separation Score Compute a Gaussian fit for each class  (1 , 1) , (2 , 2) . The Separation Score is (1 - 2)/(1+ 2)

35 Threshold Error Rate (TNoM) Score
Find the threshold that best separates tumors from normals, count the number of errors committed there. Ex 1: # of errors = min(7,8) = 7. 6 7 Ex 2: A perfect single gene classifier gets a score of 0. From Zohar Yakhini

36 p-Values Relevance scores are more useful when we can compute their significance: p-value: The probability of finding a gene with a given score if the labeling is random p-Values allow for higher level statistical assessment of data quality. p-Values provide a uniform platform for comparing relevance, across data sets. p-Values enable class discovery From Zohar Yakhini

37 BRCA1 Differential Expression
Genes over-expressed in BRCA1 wildtype Genes over-expressed in BRCA1 mutants Collab with NIH NEJM 2001 Sporadic sample s14321 With BRCA1-mutant expression profile BRCA1 mutants BRCA1 Wildtype From Zohar Yakhini

38 Data Analysis: Leave One Out Cross Validation (LOOCV)
Repeat, for each tissue (tumor/normal) “Hide” the label of the test tissue Diagnose the test tissue based on the remaining data Compare the diagnosis to the hidden label Perform this using different choices of genes subsets sizes Small, efficient diagnostic assays From Zohar Yakhini

39 BRCA1 LOOCV Results 95% success rate (21/22)
Sporadic tissue (14321) consistently classified as BRCA1 BRCA1 gene is normal, but silenced in the patient’s DNA From Zohar Yakhini

40 Lung Cancer Informative Genes
Data from Naftali Kaminski’s lab, at Sheba. 24 tumors (various types and origins) 10 normals (normal edges and normal lung pools) From Zohar Yakhini

41 And Now: Global Analysis of Gene Expression Data
First (but not least): Clustering either of genes, or of experiments

42 Example data: fold change (ratios)
What is the pattern? Name 0 hours 2 hours 4 hours 6 hours 8 hours 10 hours Gene C 1 8 12 16 Gene D 3 4 2 Gene E Gene F 0.25 0.1 Gene G Gene H 0.5 0.33 Gene I Gene J Gene K Gene L Gene M Gene N 0.125 0.0833 0.0625 Campbell & Heyer, 2003

43 Example data 2 Name 0 hours 2 hours 4 hours 6 hours 8 hours 10 hours
Gene C 3 3.58 4 Gene D 1.58 2 1 Gene E Gene F -2 -3.32 Gene G Gene H -1 -1.60 Gene I Gene J Gene K Gene L Gene M Gene N -3 -3.59 -4 Campbell & Heyer, 2003

44 Pearson Correlation Coefficient, r. values in [-1,1] interval
Gene expression over d experiments is a vector in Rd, e.g. for gene C: (0, 3, 3.58, 4, 3.58, 3) Given two vectors X and Y that contain N elements, we calculate r as follows: Cho & Won, 2003

45 Example: Pearson Correlation Coefficient, r
X = Gene C = (0, 3.00, 3.58, 4, 3.58, 3) Y = Gene D = (0, 1.58, 2.00, 2, 1.58, 1) ∑XY = (0)(0)+(3)(1.58)+(3.58)(2)+(4)(2)+(3.58)(1.58)+(3)(1) = ∑X = = 17.16 ∑X2 = = ∑Y = = 8.16 ∑Y2 = = N = 6 ∑XY – ∑X∑Y/N = – (17.16)(8.16)/6 = ∑X2 – (∑X)2/N = – (17.16)2/6 = ∑Y2 – (∑Y)2/N = – (8.16)2/6 = r = / sqrt(( )(2.8952)) = 0.944

46 Example data: Pearson correlation coefficients
Gene C Gene D Gene E Gene F Gene G Gene H Gene I Gene J Gene K Gene L Gene M Gene N 1 0.94 0.96 -0.40 0.95 -0.95 0.41 0.36 0.23 -0.94 -1 0.84 -0.10 0.68 0.24 -0.07 -0.57 0.89 -0.89 0.21 0.30 0.43 -0.84 -0.96 -0.35 0.35 0.60 -0.43 -0.79 0.10 0.40 0.48 0.22 0.11 -0.48 -0.21 -0.11 -0.75 -0.68 -0.41 -0.24 -0.36 0.07 -0.23 Campbell & Heyer, 2003

47 Example: Reorganization of data
Name 0 hours 2 hours 4 hours 6 hours 8 hours 10 hours Gene M 1 0.33 0.25 0.5 Gene N 0.125 0.0833 0.0625 Gene H Gene K 3 Gene J 2 Gene E 4 8 Gene C 12 16 Gene L Gene G Gene D Gene I Gene F 0.1 Campbell & Heyer, 2003

48 Spearman Rank Order Coefficient
Replace each entry xi by its rank in vector x. Then compute Pearson correlation coefficients of rank vectors. Example: X = Gene C = (0, 3.00, 3.41, 4, 3.58, 3.01) Y = Gene D = (0, 1.51, 2.00, 2.32, 1.58, 1) Ranks(X)= (1,2,4,6,5,3) Ranks(Y)= (1,3,5,6,4,2) Ties should be taken care of: (1) rare (2) randomize (small effect)

49 Grouping and Reduction
Grouping: Partition items into groups. Items in same group should be similar. Items in different groups should be dissimilar. Grouping may help discover patterns in the data. Reduction: reduce the complexity of data by removing redundant probes (genes).

50 Unsupervised Grouping: Clustering
Pattern discovery via clustering similarly expressed genes together Techniques most often used: k-Means Clustering Hierarchical Clustering Biclustering Alternative Methods: Self Organizing Maps (SOMS), plaid models, singular value decomposition (SVD), order preserving submatrices (OPSM),……

51 Clustering Overview Different similarity measures in use:
Pearson Correlation Coefficient Cosine Coefficient Euclidean Distance Information Gain Mutual Information Signal to noise ratio Simple Matching for Nominal

52 Clustering Overview (cont.)
Different Clustering Methods Unsupervised k-means Clustering (k nearest neighbors) Hierarchical Clustering Self-organizing map Supervised Support vector machine Ensemble classifier Data Mining

53 Clustering Limitations
Any data can be clustered, therefore we must be careful what conclusions we draw from our results Clustering is often randomized and can and will produce different results for different runs on same data

54 K-means Clustering Given a set of m data points in
n-dimensional space and an integer k. We want to find the set of k “centers” in n-dimensional space that minimizes the Euclidean (mean squared) distance from each data point to its nearest center. No exact polynomial-time algorithms are known for this problem (no wonder, NP-hard!). “A Local Search Approximation Algorithm for k-Means Clustering” by Kanungo et. al

55 K-means Heuristic (Lloyd’s Algorithm)
Has been shown to converge to a locally optimal solution But can converge to a solution arbitrarily bad compared to the optimal solution Data Points Optimal Centers Heuristic Centers K=3 “K-means-type algorithms: A generalized convergence theorem and characterization of local optimality” by Selim and Ismail “A Local Search Approximation Algorithm for k-Means Clustering” by Kanungo et al.

56 Euclidean Distance Now to find the distance between two points, say the origin and the point (3,4): Simple and Fast! Remember this when we consider the complexity!

57 Finding a Centroid We use the following equation to find the n dimensional centroid point (center of mass) amid k (n dimensional) points: Example: Let’s find the midpoint between three 2D points, say: (2,4) (5,2) (8,9)

58 K-means Iterative Heuristic
Choose k initial center points “randomly” Cluster data using Euclidean distance (or other distance metric) Calculate new center points for each cluster, using only points within the cluster Re-Cluster all data using the new center points (this step could cause some data points to be placed in a different cluster) Repeat steps 3 & 4 until no data points are moved from one cluster to another (stabilization), or till some other convergence criteria is met From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

59 An example with 2 clusters
We Pick 2 centers at random We cluster our data around these center points Figure Reproduced From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

60 K-means example with k=2
We recalculate centers based on our current clusters Figure Reproduced From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

61 K-means example with k=2
We re-cluster our data around our new center points Figure Reproduced From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

62 K-means example with k=2
5. We repeat the last two steps until no more data points are moved into a different cluster Figure Reproduced From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

63 Choosing k Run algorithm on data with several different values of k
Use advance knowledge about the characteristics of your test (e.g. Cancerous vs Non-Cancerous Tissues, in case the experiments are being clustered)

64 From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici
Cluster Quality Since any data can be clustered, how do we know our clusters are meaningful? The size (diameter) of the cluster vs. the inter-cluster distance Distance between the members of a cluster and the cluster’s center Diameter of the smallest sphere containing the cluster From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

65 Cluster Quality Continued
distance=5 diameter=5 distance=20 Quality of cluster assessed by ratio of distance to nearest cluster and cluster diameter diameter=5 Figure Reproduced From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

66 Cluster Quality Continued
Quality can be assessed simply by looking at the diameter of a cluster (alone????) A cluster can be formed by the heuristic even when there is no similarity between clustered patterns. This occurs because the algorithm forces k clusters to be created. From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

67 Characteristics of k-means Clustering
The random selection of initial center points creates the following properties Non-Determinism May produce clusters without patterns One solution is to choose the centers randomly from existing patterns From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

68 Heuristic’s Complexity
Linear in the number of data points, N Can be shown to have run time cN, where c does not depend on N, but rather the number of clusters, k (not sure about dependence on dimension, n?)  heuristic is efficient From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

69 Hierarchical Clustering
a different clustering paradigm Figure Reproduced From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

70 Hierarchical Clustering (cont.)
Gene C Gene D Gene E Gene F Gene G Gene H Gene I Gene J Gene K Gene L Gene M Gene N 0.94 0.96 -0.40 0.95 -0.95 0.41 0.36 0.23 -0.94 -1 0.84 -0.10 0.68 0.24 -0.07 -0.57 0.89 -0.89 0.21 0.30 0.43 -0.84 -0.96 -0.35 0.35 0.60 -0.43 -0.79 0.10 0.40 0.48 0.22 0.11 1 -0.48 -0.21 -0.11 -0.75 -0.68 -0.41 -0.24 -0.36 0.07 -0.23 Campbell & Heyer, 2003

71 Hierarchical Clustering (cont.)
1 Gene D Gene F Gene G 0.89 -0.485 0.92 -0.10 0.94 -0.35 Gene C Gene D Gene E Gene F Gene G 0.94 0.96 -0.40 0.95 0.84 -0.10 -0.57 0.89 -0.35 C Average “similarity” to Gene D: ( )/2 = 0.89 Gene F: (-0.40+(-0.57))/2 = Gene G: ( )/2 = 0.92 1 D E F 1 G C E

72 Hierarchical Clustering (cont.)
1 Gene D Gene F Gene G 0.89 -0.485 0.92 -0.10 0.94 -0.35 1 2 D C E G D F G

73 Hierarchical Clustering (cont.)
1 2 Gene F 0.905 -0.485 -0.225 3 1 2 C E G D F

74 Hierarchical Clustering (cont.)
4 3 Gene F -0.355 3 F 1 2 F C E G D

75 Hierarchical Clustering (cont.)
algorithm looks familiar? 4 Remember Neighbor-Joining ! 3 1 2 F C E G D

76 Clustering of entire yeast genome
Campbell & Heyer, 2003

77 Hierarchical Clustering: Yeast Gene Expression Data
Eisen et al., 1998

78 A SOFM Example With Yeast
“Interpresting patterns of gene expression with self-organizing maps: Methods and application to hematopoietic differentiation” by Tamayo et al.

79 From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici
SOM Description Each unit of the SOM has a weighted connection to all inputs As the algorithm progresses, neighboring units are grouped by similarity Output Layer Input Layer From “Data Analysis Tools for DNA Microarrays” by Sorin Draghici

80 From http://davis.wpi.edu/~matt/courses/soms/
An Example Using Color Each color in the map is associated with a weight From

81 Cluster Analysis of Microarray Expression Data Matrices
Application of cluster analysis techniques in the elucidation gene expression data

82 Function of Genes ("זבוב בלי רגליים – חרש")
The features of a living organism are governed principally by its genes. If we want to fully understand living systems we must know the function of each gene. Once we know a gene’s sequence we can design experiments to find its function: The Classical Approach of Assigning a function to a Gene ("זבוב בלי רגליים – חרש") Delete Gene X Gene X Conclusion: Gene X = left eye gene. However this approach is too slow to handle all the gene sequence information we have today (HGSP).

83 Microarray Analysis Microarray analysis allows the monitoring of the activities of many genes over many different conditions. Experiments are carried out on a Physical Matrix like the one below: G1 G2 G3 G4 G5 G6 G7 C1 C2 C3 C4 C5 C6 C7 Low Zero High 1.55 1.05 0.5 2.5 1.75 0.25 0.1 1.7 0.3 2.4 2.9 1.5 1.0 Conditions Genes To facilitate computational analysis the physical matrix which may contain 1000’s of gene’s is converted into a numerical matrix using image analysis equipment. Possible inference: If Gene X’s activity (expression) is affected by Condition Y (Extreme Heat), then Gene X may be involved in protecting the cellular components from extreme heat. Each Gene has its corresponding Expression Profile for a set of conditions. This Expression Profile may be thought of as a feature profile for that gene for that set of conditions (A condition feature profile).

84 Cluster Analysis Cluster Analysis is an unsupervised procedure which involves grouping of objects based on their similarity in feature space. In the Gene Expression context Genes are grouped based on the similarity of their Condition feature profile. Cluster analysis was first applied to Gene Expression data from Brewer’s Yeast (Saccharomyces cerevisiae) by Eisen et al. (1998). 1.55 1.05 0.5 2.5 1.75 0.25 0.1 1.7 0.3 2.4 2.9 1.5 1.0 Conditions Genes X Y A B C Z Clusters A,B and C represent groups of related genes. Clustering Two general conclusions can be drawn from these clusters: Genes clustered together may be related within a biological module/system. If there are genes of known function within a cluster these may help to class this biological/module system.

85 From Data to Biological Hypothesis
Gene Expression Microarray Cluster Set Conditions (A-Z) Cluster C with four Genes may represent System C Relating these genes aids in elucidation of this System C Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6 Gene 7 X Y A B C System C External Stimulus( Condition X) Toxin Cell Membrane Regulator Protein DNA Gene a Gene b Gene c Gene d Gene Expression Toxin Pump

86 Some Drawbacks of Clustering Biological Data
Clustering works well over small numbers of conditions but a typical Microarray may have hundreds of experimental conditions. A global clustering may not offer sufficient resolution with so many features. As with other clustering applications, it may be difficult to cluster noisy expression data. Biological Systems tend to be inter-related and may share numerous factors (Genes) – Clustering enforces partitions which may not accurately represent these intimacies. Clustering Genes over all Conditions only finds the strongest signals in the dataset as a whole. More ‘local’ signals within the data matrix may be missed. X Y A B C Z Inter-related(3) Local Signals(4) May represent more complex system such as:

87 How do we better model more complex systems?
One technique that allows detection of all signals in the data is biclustering. Instead of clustering genes over all conditions biclustering clusters genes with respect to subsets of conditions. This enables better representation of: -interrelated clusters (genes may belong more than one bicluster). -local signals (genes correlated over only a few conditions). -noisy data (allows erratic genes to belong to no cluster).

88 Biclustering A B C D E F G H Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6
Conditions A B C D E F G H Gene 1 Gene 2 Gene 3 Gene 4 Gene 5 Gene 6 Gene 7 Gene 8 Gene 9 Clustering misses local signal {(B,E,F),(1,4,6,7,9)} present over subset of conditions. Gene 1 Gene 4 Gene 6 Gene 7 Gene 9 B E F Biclustering A B D E F G H Biclustering discovers local coherences over a subset of conditions Technique first described by J.A. Hartigan in 1972 and termed ‘Direct Clustering’. First Introduced to Microarray expression data by Cheng and Church(2000)

89 Approaches to Biclustering Microarray Gene Expression
First applied to Gene Expression Data by Cheng and Church(2000). Used a sub-matrix scoring technique to locate biclusters. Tanay et al.(2000) Modelled the expression data on Bipartite graphs and used graph techniques to find ‘complete graphs’ or biclusters. Lazzeroni and Owen Used matrix reordering to represent different ‘layers’ of signals (biclusters) ‘Plaid Models’ to represent multiple signals within data. Ben-Dor et al. (2002) “Biclusters” depending on order relations (OPSM).

90 Bipartite Graph Modelling
First proposed in: “Discovering statically significant biclusters in gene expressing data” Tanay et al. Bioinformatics 2000 1 2 3 4 5 6 7 A B C D E F A B C D E F AD Graph G Sub-graph H (Bicluster) Data Matrix M Sub-Matrix (Bicluster) Genes Conditions Within the graph modelling paradigm biclusters are equivalent to complete bipartite sub-graphs. Tanay and colleagues used probabilistic models to determine the least probable sub-graphs (those showing most order and consequently most surprising) to identify biclusters.

91 The Cheng and Church Approach
The core element in this approach is the development of a scoring to prioritise sub-matrices. This scoring is based on the concept of the residue of an entry in a matrix. In the Matrix (I,J) the residue score of element is given by: J j In words, the residue of an entry is the value of the entry minus the row average, minus the column average, plus the average value in the matrix. This score gives an idea of how the value fits into the data in the surrounding matrix. I i a

92 The Cheng and Church Approach(2)
The mean squared residue score (H) for a matrix (I,J) is then calculated : This Global H score gives an indication of how the data fits together within that matrix- whether it has some coherence or is random. A high H value signifies that the data is uncorrelated. - a matrix of equally spread random values over the range [a,b], has an expected H score of (b-a)/12. range = [0,800] then H(I,J) = 53,333 A low H score means that there is a correlation in the matrix - a score of H(I,J)= 0 would mean that the data in the matrix fluctuates in unison i.e. the sub-matrix is a bicluster

93 1 2 3 4 5 6 7 8 9 10 11 12 Worked example of H score:
Matrix (M) Avg. = 6.5 Row Avg. 2 5 8 11 R(1) = = 0.1 R(2) = = 0.1 : : R(12) = = 0.1 Col Avg H (M) = (0.01x12)/12 = 0.01 If 5 was replaced with 3 then the score would changed to: H(M2) = 2.06 If the matrix was reshuffled randomly the score would be around: H(M3) = sqr(12-1)/12 = 10.08

94 The Cheng and Church Approach: Node Deletion Biclustering Algorithm
In order to find all possible biclusters in an Expression Matrix all sub-matrices must be tested using the H score. Node Deletion In a node deletion algorithm all columns and rows are tested for deletion. If removing a row or column decreases the H score of the Matrix than it is removed. This continues until it is not possible to decrease the H score further. This low H score coherent sub-matrix (bicluster) is then returned. The process then masks this located bicluster by inserting random numbers in place of it. And reiterates the process. R Node Deletion

95 The Cheng and Church Approach:
Some results on lymphoma data (402696): No. of genes, no. of conditions 4, 96 10, 29 11, 25 103, 25 127, 13 13, 21 10, 57 2, 96 25, 12 9, 51 3, 96

96 Conclusions: High throughput Functional Genomics (Microarrays) requires Data Mining Applications. Biclustering resolves Expression Data more effectively than single dimensional Cluster Analysis. Cheng and Church Approach offers good base for future work. Future Research/Question’s: Implement a simple H score program to facilitate study if H score concept. Are there other alternative scorings which would better apply to gene expression data? Have unbiclustered genes any significance? Horizontally transferred genes? Implement full scale biclustering program and look at better adaptation to expression data sets and the biological context.

97 References Basic microarray analysis: grouping and feature reduction by Soumya Raychaudhuri, Patrick D. Sutphin, Jeffery T. Chang and Russ B. Altman; Trends in Biotechnology Vol. 19 No. 5 May 2001 Self Organizing Maps, Tom Germano, “Data Analysis Tools for DNA Microarrays” by Sorin Draghici; Chapman & Hall/CRC 2003 Self-Organizing-Feature-Maps versus Statistical Clustering Methods: A Benchmark by A. Ultsh, C. Vetter; FG Neuroinformatik & Kunstliche Intelligenz Research Report 0994

98 References Interpreting patterns of gene expression with self-organizing maps: Methods and application to hematopoietic differentiation by Tamayo et al. A Local Search Approximation Algorithm for k-Means Clustering by Kanungo et al. K-means-type algorithms: A generalized convergence theorem and characterization of local optimality by Selim and Ismail


Download ppt "DNA Chips and Their Analysis Comp"

Similar presentations


Ads by Google