BioInformatics (3)

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)

Data Warehousing : Mapping Biologic into Data Logic

Structure Analysis :Alignments & Scores

Global (e.g. haplotype) ACCACACA ::xx::x: ACACCATAScore= 5(+1) + 3(-1) = 2

Suffix (shotgun assembly) ACCACACA ::: ACACCATAScore= 3(+1) =3

Local (motif) ACCACACA ::::ACACCATAScore= 4(+1) = 4

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

Homology Search Motif Search

New sequence

Retrieval

Similarsequence

Expertknowledge

Sequence interpretation

Sequence database(Primary data)

Knowledgeacquisition

Motif library(Empirical rules)

Expertknowledge

New sequence

Inference

Sequence interpretation

Search and learning problems in sequence analysisProblems in Biological Science Math/Stat/CompSci method

Similarity search Pairwise sequence alignmentDatabase search for similarsequencesMultiple sequence alignmentPhylogenetic treereconstructionProtein 3D structurealignment

Optimization algorithms Dynamic programming

(DP) Simulated annealing (SA) Genetic algorithms (GA) Markov Chain Monte

Carlo (MCMC:Metropolis and Gibbssamplers)

Hopfield neural networkStructure/functionprediction

ab initio prediction RNA secondary structurepredictionRNA 3D structure predictionProtein 3D structure prediction

Knowledge basedprediction

Motif extractionFunctional site predictionCellular localization predictionCoding region predictionTransmembrane domainpredictionProtein secondary structurepredictionProtein 3D structure prediction

Pattern recognition andlearning algorithms Discriminant analysis Neural networks Support vector machines Hidden Markov models

(HMM) Formal grammar CART

Molecular classification Superfamily classificationOrtholog/paralog grouping ofgenes3D fold classification

Clustering algorithms Hierarchical, k-means, etc PCA, MDS, etc Self-organizing maps, etc

(Whole genome) Gene Expression Analysis

• Quantitative Analysis of Gene Activities (Transcription Profiles)

Gene Expression

Biotinylated RNAfrom experiment

GeneChip expressionanalysis probe array

Image of hybridized probe array

Each probe cell containsmillions of copies of a specific oligonucleotide probe

Streptavidin-phycoerythrinconjugate

(Sub)cellular inhomogeneity

( see figure)

Cell-cycle differences in expression.

XIST RNA localized on inactive X-chromosome

Cluster Analysis

General Purpose: To divide samples intohomogeneous groups based on a set of features.

Gene Expression Analysis: To find co-regulatedgenes.

Protein/protein complex

Genes

DNA regulatory elements

Functional Analysis via Gene Expression

Gene Expression Data

Distance/Similarity Matrix

Gene Clusters

Regulatory Elements / Gene Functions

Pairwise Measures

Clustering

Motif Searching/...

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.

Clusters of Two-Dimensional Data

Key Terms in Cluster Analysis

• Distance & Similarity measures

• Hierarchical & non-hierarchical

• Single/complete/average linkage

• Dendrograms & ordering

Distance Measures: Minkowski Metric

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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

Normalized Expression Data

hierarchical & non-

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Hierarchical Clustering Techniques

At the beginning, each object (gene) isa cluster. In each of the subsequentsteps, two closest clusters will mergeinto one cluster until there is only onecluster left.

Hierarchical ClusteringGiven 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

• Single-Link Method / Nearest Neighbor

• Complete-Link / Furthest Neighbor

• Their Centroids.

• Average of all cross-cluster pairs.

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

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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

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Which clustering methods do you suggest for the following two-dimensional data?

Nadler and Smith, Pattern Recognition Engineering, 1993

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.

Normalized Expression Data

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

Non-hierarchical clustering

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

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Evaluate Cluster contents