Download - Sequence analysis. Cluster analysis. · 2010-09-30 · Sequence analysis. Cluster analysis. Meelis Kull [email protected] Lecture 5 Bioinformatics MTAT.03.239 University of Tartu

Sequence analysis.Cluster analysis.

Meelis [email protected]

Lecture 5Bioinformatics MTAT.03.239

University of Tartu2010 Fall

mailto:[email protected]

mailto:[email protected]

Sequence Analysis:DNA, RNA, Protein

Aperiodic crystals store information

• Erwin Schrödinger“What is Life? The Physical Aspect of the Living Cell”1944

• In the book, Schrödinger introduced the idea of an "aperiodic crystal" that contained genetic information in its configuration of covalent chemical bonds

• Note that this is before discovery of the helical structure of DNA in 1953 by Watson & Crick

http://en.wikipedia.org/wiki/Chemical_bond

http://en.wikipedia.org/wiki/Chemical_bond

Sequence Information

• How is the sequence information used/read? How is it converted into working machinery? Why is it important to have A instead of T in some locus?

• Different nucleotides in DNA/RNA and amino acids in proteins have different physical (and chemical) properties

Chemical bindingExample: protein-DNA

Protein GCN4 binds on DNA at TGASTCA, (S is G or C)

Transcription regulation:Information processing

DNA

Sequence annotation

• How do the nucleotides in the genome contribute to the life of the cell?

• One of the main objectives in bioinformatics (and biology)

• Sequence annotation is the next major challenge for the Human Genome Project

• ENCyclopedia Of DNA Elements (ENCODE)

Sequence annotation

How to get annotations for the genome?

• Evidence from case studies (Biology)

• Large scale experiments (Biology with Bioinformatics support)

• Predictions based on existing annotations (Bioinformatics)

• Experimental verification of predictions (Biology)

Finding TFBS - Transcription Factor Binding Sites

DNA

Transcription Factor binding on DNA

Protein GCN4 binds on DNA at TGASTCA, (S is G or C)

Substrings, k-mers, k-lets

• GCN4 prefers to bind on 7-mers TGACTCA and TGAGTCA

Terminology:

• 1-mer, monomer, nucleotide, base

• 2-mer, dimer, duplet, dinucleotide

• 3-mer, trimer, triplet, trinucleotide

• ...

• k-mer, k-let, substring/subsequence of length k

IUPAC ambiguity codes

Transcription factor binding site examples

Models for aDNA sequence

• Consensus sequence

• k-mer

• IUPAC k-mer

• RegExp - Regular expression

• e.g. CG[GT]N{5,10}CCG

• PWM - Position Weight Matrix

• HMM - Hidden Markov Model

PWM - Position Weight Matrix• TBP - TATA-binding protein

Binding TATAWAW where W is T or A

A [ 61 16 352 3 354 268 360 222 155 56 83 82 82 68 77 ]C [145 46 0 10 0 0 3 2 44 135 147 127 118 107 101 ]G [152 18 2 2 5 0 20 44 157 150 128 128 128 139 140 ]T [ 31 309 35 374 30 121 6 121 33 48 31 52 61 75 71 ]-----------------------------------------------------------------SUM 389 389 389 389 389 389 389 389 389 389 389 389 389 389 389

PWM logoCount matrix,

not PWM

Count matrix to PWM (1)

• Count matrixA [ 61 16 352 3 354 268 360 222 155 56 83 82 82 68 77 ]C [145 46 0 10 0 0 3 2 44 135 147 127 118 107 101 ]G [152 18 2 2 5 0 20 44 157 150 128 128 128 139 140 ]T [ 31 309 35 374 30 121 6 121 33 48 31 52 61 75 71 ]-----------------------------------------------------------------SUM 389 389 389 389 389 389 389 389 389 389 389 389 389 389 389

for any i = 1, 2, . . . , nS = cAi + cCi + cGi + cTi

cA1 cA2 . . . cAn

cC1 cC2 . . . cCn

cG1 cG2 . . . cGn

cT1 cT2 . . . cTn


• Probability matrixA [ .16 .05 .87 .02 .88 .67 .89 .56 .39 .15 .22 .21 .21 .18 .20 ]C [ .37 .12 .01 .04 .01 .01 .02 .02 .12 .34 .37 .32 .30 .27 .26 ]G [ .38 .06 .02 .02 .02 .01 .06 .12 .40 .38 .33 .33 .33 .35 .35 ]T [ .09 .77 .10 .93 .09 .31 .03 .31 .09 .13 .09 .14 .16 .20 .19 ]-----------------------------------------------------------------SUM 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

for anyi = 1, 2, . . . , n

X = A,C,G,T

pA1 pA2 . . . pAn

pC1 pC2 . . . pCn

pG1 pG2 . . . pGn

pT1 pT2 . . . pTn

bAbCbGbT

pXi =cXi + bX

√S

S +√S


• Position weight matrixA [ -0.6 -2.3 +1.8 -3.7 +1.8 +1.4 +1.8 +1.2 +0.6 -0.7 -0.2 -0.2 -0.2 -0.5 -0.3 ]C [ +0.6 -1.0 -4.4 -2.8 -4.4 -4.4 -3.7 -3.9 -1.1 +0.5 +0.6 +0.4 +0.3 +0.1 +0.1 ]G [ +0.6 -2.2 -3.9 -3.9 -3.4 -4.4 -2.0 -1.1 +0.7 +0.6 +0.4 +0.4 +0.4 +0.5 +0.5 ]T [ -1.5 +1.6 -1.4 +1.9 -1.5 +0.3 -3.2 +0.3 -1.4 -0.9 -1.5 -0.8 -0.6 -0.4 -0.4 ]

for anyi = 1, 2, . . . , n

X = A,C,G,T

wA1 wA2 . . . wAn

wC1 wC2 . . . wCn

wG1 wG2 . . . wGn

wT1 wT2 . . . wTn

wXi = log2pXi

bX

Matching a PWM on DNA

• Position weight matrix

A [ -0.6 -2.3 +1.8 -3.7 +1.8 +1.4 ]C [ +0.6 -1.0 -4.4 -2.8 -4.4 -4.4 ]G [ +0.6 -2.2 -3.9 -3.9 -3.4 -4.4 ]T [ -1.5 +1.6 -1.4 +1.9 -1.5 +0.3 ]

C C T T A T +0.6 -1.0 -1.4 +1.9 +1.8 +0.3 = +2.2

Sequence:Score:

PWM of length k gives a score to each k-mer in the DNA

Information content in PWM

• Information content - how different is a PWM from uniform distribution

IC

IC = log2 4−�

i=1,...,nX=A,C,G,T

−pXi log2(pXi)

Observations: Sunny, Rainy, Sunny, Sunny, Rainy, Snowy, Snowy, ...Hidden states: Summer, Fall, Fall, Fall, Fall, Winter, Winter,...

HMMs - Hidden Markov Models

http://webdocs.cs.ualberta.ca/~colinc/cmput606/606FinalPres.ppt



Tasks with HMMsScoring task:

• Given an existing HMM and observed sequence, what is the probability that the HMM generates the sequence

Alignment task:

• Given a sequence, what is the optimal state sequence that the HMM would use to generate it

Training task:

• Given a large amount of data how can we estimate the structure and the parameters of the HMM that best accounts for the data

Hidden Markov Models in Sequence Analysis

ACA---ATG TCAACTATCACAC--AGCAGA---ATCACCG--ATC

http://www.evl.uic.edu/shalini/coursework/hmm.ppt

ACANNNATC

ACA[ACGT]{0,3}ATC

Task: represent the following sequences in a model IUPAC consensus:

Regular expression:PWMHMM



HMMs in gene finding• S - gene start

• D - donor splice site

• E - exon

• I - intron

• A - acceptor splice site

• T - gene termination

DNA sequence analysis

... is mostly about:

• building a model for some DNA feature (or often just learning the parameters)

• searching for sites which match a model (or match it well enough)

• statistical analysis about what features are over-represented in some region of DNA

Common tasks in DNA sequence analysis• GC-content

• CpG islands

• Masking repeats

• Melting temperature

• PCR primer design

• TFBS motif discovery

• TFBS search

• Gene search

• Codon usage

• Sequence alignment

• and many more

Clustering

What is Cluster Analysis?

Finding groups of objects such that the objects are:

• similar (or related) to the objects in the same group and

• different from (or unrelated) to the objects in other groups

Short distance

Long distance

Why to cluster biological data?

• Intuition building

• Hypothesis generation

• Summarizing / compressing large data

Partitional vs Hierarchical

Partitional clustering findsa fixed number of clusters

Hierarchical clustering creates a series of clusterings contained in each other

Fuzzy vs Non-Fuzzy

Each object belongs to eachcluster with some weight(the weight can be zero)

Each object belongs to exactly one cluster

Hierarchical clustering

Hierarchical clustering is usually depicted as a dendrogram (tree)

Hierarchical clustering

• Each subtree corresponds to a cluster• Height of branching shows distance

Hierarchical clustering (0)

Algorithm for Agglomerative Hierarchical Clustering:Join the two closest objects


Join the two closest objects


Keep joining the closest pairs


After 10 steps we have 4 clusters left

Hierarchical clustering (10)Several ways to measure distancebetween clusters:• Single linkage (MIN)

Hierarchical clustering (10)Several ways to measure distancebetween clusters:• Single linkage (MIN) • Complete linkage (MAX)

Hierarchical clustering (10)Several ways to measure distancebetween clusters:• Single linkage (MIN) • Complete linkage (MAX)• Average linkage• Weighted• Unweighted• ...


In this example and at this stage we have the same result as in partitional clustering


In the final step the two remaining clusters are joined into a single cluster

Examples of Hierarchical Clustering in Bioinformatics

PhylogenyGene expression clustering

• Partitional, non-fuzzy

• Partitions the data into K clusters

• K is given by the user

Algorithm:

• Choose K initial centers for the clusters

• Assign each object to its closest center

• Recalculate cluster centers

• Repeat until converges

K-means clustering

K-means (1)

K-means (2)

K-means (3)

K-means (4)

K-means (5)

K-means (6)

• One of the fastest clustering algorithms

• Therefore very widely used

• Sensitive to the choice of initial centres

• many algorithms to choose initial centres cleverly

• Assumes that the mean can be calculated

• can be used on vector data

• cannot be used on sequences (what is the mean of A and T?)

K-means clustering

Distance measuresDistance of vectors and

• Euclidean distance

• Manhattan distance

• Correlation distance

Distance of sequences and

• Hamming distance => 3

• Levenshtein distance

x = (x1, . . . , xn) y = (y1, . . . , yn)

d(x, y) =

��n�

i=1

(xi − yi)2

d(x, y) =n�

i=1

|xi − yi|

d(x, y) = 1− r(x, y)is Pearson

correlation coefficientr(x, y)

ACCTTG TACCTGACCTTGTACCTG

.ACCTTGTACC.TG => 2

• The same as K-means, except that the center is required to be at an object

• Medoid - an object which has minimal total distance to all other objects in its cluster

• Can be used on more complex data, with any distance measure

• Slower than K-means

K-medoids clustering

K-medoids (1)

K-medoids (2)

K-medoids (3)

K-medoids (4)

K-medoids (5)

K-medoids (6)

K-medoids (7)

K-medoids (8)

K-medoids (9)

Examples of K-means and K-medoids in Bioinformatics

Gene expression clustering

Sequence clustering

MCL - Markov CLuster• A method for clustering a graph by flow simulation

• Based on random walks on graphs:a random walk infrequently goes from one cluster to another

• For example, used for clustering proteins by structural similarity

Summary of Clustering• Aims: intuition, hypothesis generation, summarization

• Types:

• Hierarchical/Partitional

• Fuzzy/Non-Fuzzy

• Vector-based/Distance-based

• etc.

• Distance measures

• Euclidean, Manhattan, Correlation

• Hamming, Levenshtein

• etc.

• Applications:

• Clustering genes, sequences, organisms, etc.

Download - Sequence analysis. Cluster analysis. · 2010-09-30 · Sequence analysis. Cluster analysis. Meelis Kull [email protected] Lecture 5 Bioinformatics MTAT.03.239 University of Tartu

Top Related