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BioInformatics (3). Computational Issues. Data Warehousing: Organising Biological Information into a Structured Entity (World’s Largest Distributed DB) Function Analysis (Numerical Analysis) :

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computational issues
Computational Issues
  • Data Warehousing:
    • Organising Biological Information into a Structured Entity (World’s Largest Distributed DB)
  • Function Analysis (Numerical Analysis) :
    • Gene Expression Analysis : Applying sophisticated data mining/Visualisation to understand gene activities within an environment (Clustering )
    • Integrated Genomic Study : Relating structural analysis with functional analysis
  • Structure Analysis (Symbolic Analysis) :
    • Sequence Alignment: Analysing a sequence using comparative methods against existing databases to develop hypothesis concerning relatives (genetics) and functions (Dynamic Programming and HMM)
    • Structure prediction : from a sequence of a protein to predict its 3D structure (Inductive LP)
structure analysis alignments scores
Structure Analysis :Alignments & Scores

Local (motif)

ACCACACA

::::

ACACCATA

Score= 4(+1) = 4

Global (e.g. haplotype)

ACCACACA

::xx::x:

ACACCATA

Score= 5(+1) + 3(-1) = 2

Suffix (shotgun assembly)

ACCACACA

:::

ACACCATA

Score= 3(+1) =3

slide5
A comparison of the homology search and the motif search for functional interpretation of sequence information.

Homology Search

Motif Search

New sequence

New sequence

Knowledge

acquisition

Motif library

(Empirical rules)

Sequence database

(Primary data)

Retrieval

Similar

sequence

Inference

Expert

knowledge

Expert

knowledge

Sequence interpretation

Sequence interpretation

whole genome gene expression analysis
(Whole genome) Gene Expression Analysis
  • Quantitative Analysis of Gene Activities (Transcription Profiles)

Gene

Expression

slide8

Biotinylated RNA

from experiment

Each probe cell contains

millions of copies of a specific

oligonucleotide probe

GeneChip expression

analysis probe array

Streptavidin-

phycoerythrin

conjugate

Image of hybridized probe array

sub cellular inhomogeneity
(Sub)cellular inhomogeneity

Cell-cycle differences in expression.

XIST RNA localized on inactive

X-chromosome

( see figure)

cluster analysis
Cluster Analysis

Protein/protein complex

Genes

DNA regulatory elements

functional analysis via gene expression
Functional Analysis via Gene Expression

Pairwise Measures

Clustering

Motif Searching/...

clustering algorithms
Clustering Algorithms

A clustering algorithm attempts to find natural groups of components (or data) based on some similarity. Also, the clustering algorithm finds the centroid of a group of data sets.To determine cluster membership, most algorithms evaluate the distance between a point and the cluster centroids. The output from a clustering algorithm is basically a statistical description of the cluster centroids with the number of components in each cluster.

key terms in cluster analysis
Key Terms in Cluster Analysis
  • Distance & Similarity measures
  • Hierarchical & non-hierarchical
  • Single/complete/average linkage
  • Dendrograms & ordering
manhattan distance is called hamming distance when all features are binary
Manhattan distance is called Hamming distance when all features are binary.

Gene Expression Levels Under 17 Conditions (1-High,0-Low)

similarity measures correlation coefficient1
Similarity Measures: Correlation Coefficient

Expression Level

Expression Level

Gene A

Gene B

Gene B

Gene A

Time

Time

Expression Level

Gene B

Gene A

Time

distance based clustering
Assign a distance measure between data

Find a partition such that:

Distance between objects within partition (i.e. same cluster) is minimized

Distance between objects from different clusters is maximised

Issues :

Requires defining a distance (similarity) measure in situation where it is unclear how to assign it

What relative weighting to give to one attribute vs another?

Number of possible partition is super-exponential

Distance-based Clustering
hierarchical non
hierarchical & non-

Normalized Expression Data

hierarchical clustering
Hierarchical Clustering

Given a set of N items to be clustered, and an NxN distance (or similarity) matrix, the basic process hierarchical clustering is this:

1.Start by assigning each item to its own cluster, so that if you have N items, you now have N clusters, each containing just one item. Let the distances (similarities) between the clusters equal the distances (similarities) between the items they contain.

2.Find the closest (most similar) pair of clusters and merge them into a single cluster, so that now you have one less cluster.

3.Compute distances (similarities) between the new cluster and each of the old clusters.

4.Repeat steps 2 and 3 until all items are clustered into a single cluster of size N.

the distance between two clusters is defined as the distance between
The distance between two clusters is defined as the distance between
  • Single-Link Method / Nearest Neighbor
  • Complete-Link / Furthest Neighbor
  • Their Centroids.
  • Average of all cross-cluster pairs.
computing distances
Computing Distances
  • single-link clustering (also called the connectedness or minimum method) : we consider the distance between one cluster and another cluster to be equal to the shortest distance from any member of one cluster to any member of the other cluster. If the data consist of similarities, we consider the similarity between one cluster and another cluster to be equal to the greatest similarity from any member of one cluster to any member of the other cluster.
  • complete-link clustering (also called the diameter or maximum method): we consider the distance between one cluster and another cluster to be equal to the longest distance from any member of one cluster to any member of the other cluster.
  • average-link clustering : we consider the distance between one cluster and another cluster to be equal to the average distance from any member of one cluster to any member of the other cluster.
single link method
Single-Link Method

Euclidean Distance

a

a,b

b

a,b,c

a,b,c,d

c

d

c

d

d

(1)

(3)

(2)

Distance Matrix

complete link method
Complete-Link Method

Euclidean Distance

a

a,b

a,b

b

a,b,c,d

c,d

c

d

c

d

(1)

(3)

(2)

Distance Matrix

compare dendrograms
Compare Dendrograms

Single-Link

Complete-Link

0

2

4

6

ordered dendrograms
Ordered dendrograms
  • 2 n-1 linear orderings of n elements
  • (n= # genes or conditions)
  • Maximizing adjacent similarity is impractical. So order by:
  • Average expression level,
  • Time of max induction, or
  • Chromosome positioning

Eisen98

problems of hierarchical clustering
Problems of Hierarchical Clustering
  • It concerns more about complete tree structure than the optimal number of clusters.
  • There is no possibility of correcting for a poor initial partition.
  • Similarity and distance measures rarely have strict numerical significance.
non hierarchical clustering
Non-hierarchical clustering

Normalized Expression Data

Tavazoie et al. 1999 (http://arep.med.harvard.edu)

clustering by k means
Clustering by K-means
  • Given a set S of N p-dimension vectors without any prior knowledge about the set, the K-means clustering algorithm forms K disjoint nonempty subsets such that each subset minimizes some measure of dissimilarity locally. The algorithm will globally yield an optimal dissimilarity of all subsets.
  • K-means algorithm has time complexity O(RKN) where K is the number of desired clusters and R is the number of iterations to converges.
  • Euclidean distance metric between the coordinates of any two genes in the space reflects ignorance of a more biologically relevant measure of distance. K-means is an unsupervised, iterative algorithm that minimizes the within-cluster sum of squared distances from the cluster mean.
  • The first cluster center is chosen as the centroid of the entire data set and subsequent centers are chosen by finding the data point farthest from the centers already chosen. 200-400 iterations.
k means clustering algorithm
1) Select an initial partition of k clusters

2) Assign each object to the cluster with the closest center:

3) Compute the new centers of the clusters:

4) Repeat step 2 and 3 until no object changes cluster

K-Means Clustering Algorithm
representation of expression data
Representation of expression data

T2

T3

T1

Gene 1

Time-point 1

Time-point 3

dij

Gene N

.

Time-point 2

Normalized Expression Data from microarrays

Gene 1

Gene 2

identifying prevalent expression patterns gene clusters
Identifying prevalent expression patterns (gene clusters)

1.5

1

0.5

0

1

2

3

-0.5

-1

-1.5

1.5

1

1.2

0.5

0.7

0

0.2

1

2

3

-0.5

-0.3

1

2

3

-1

-0.8

-1.5

-2

-1.3

-1.8

Time-point 1

Normalized

Expression

Time-point 3

Time -point

Time-point 2

Normalized

Expression

Normalized

Expression

Time -point

Time -point

evaluate cluster contents
Evaluate Cluster contents

Genes

MIPS functional category

Glycolysis

Nuclear Organization

Ribosome

Translation

Unknown

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