CS262 Lecture 16, Win07, Batzoglou Gene Recognition Credits for slides: Serafim Batzoglou Marina Alexandersson Lior Pachter Serge Saxonov

CS262 Lecture 16, Win07, Batzoglou

Gene Recognition

Credits for slides:Serafim BatzoglouMarina AlexanderssonLior PachterSerge Saxonov


Gene structure

exon1 exon2 exon3intron1 intron2

transcription

translation

splicing

exon = protein-codingintron = non-coding

Codon:A triplet of nucleotides that is converted to one amino acid


GTCAGATGAGCAAAGTAGACACTCCAGTAACGCGGTGAGTACATTAA

exon exon exonintronintronintergene intergene

Hidden Markov Models for Gene Finding

Intergene State

First Exon State

IntronState


GTCAGATGAGCAAAGTAGACACTCCAGTAACGCGGTGAGTACATTAA

exon exon exonintronintronintergene intergene

Hidden Markov Models for Gene Finding

Intergene State

First Exon State

IntronState


TAA A A A A A A A A A A AA AAT T T T TT TT T T TT T T TG GGG G G G GGGG G G G GCC C C C C C

Exon1 Exon2 Exon3

Duration d

Duration HMM for Gene Finding

iPINTRON(xi | xi-1…xi-w)

PEXON_DUR(d)iPEXON((i – j + 2)%3)) (xi | xi-1…xi-w)

j+2

P5’SS(xi-3…xi+4)

PSTOP(xi-4…xi+3)


HMM-based Gene Finders

• GENMARK (Borodovsky & McIninch 1993)

• GENIE (Kulp 1996)

• GENSCAN (Burge 1997) Big jump in accuracy of de novo gene finding Currently, one of the best HMM with duration modeling for Exon states

• FGENESH (Solovyev 1997) Currently one of the best

• HMMgene (Krogh 1997)

• VEIL (Henderson, Salzberg, & Fasman 1997)


Better way to do it: negative binomial

• EasyGene:

Prokaryotic

gene-finder

Larsen TS, Krogh A

• Negative binomial with n = 3


GENSCAN’s hidden weapon

• C+G content is correlated with: Gene content (+) Mean exon length (+) Mean intron length (–)

• These quantities affect parameters of model

• Solution Train parameters of model in four

different C+G content ranges!


Evaluation of Accuracy

(Slide by NF Samatova)

Sensitivity (SN) Fraction of exons (coding nucleotides) whose boundaries are predicted exactly (that are predicted as coding)

•Specificity (Sp) Fraction of the predicted exons (coding nucleotides) that are exactly correct (that are coding)

•Correlation Coefficient (CC)

Combined measure of Sensitivity & Specificity Range: -1 (always wrong) +1 (always right)

TP FP TN FN TP FN TN

Actual

Predicted

Coding / No Coding

TNFN

FPTP

Pre

dic

ted

Actual

No

Co

din

g /

Co

din

g


Results of GENSCAN

• On the initial test dataset (Burset & Guigo) 80% exact exon detection

• 10% partial exons• 10% wrong exons

• In general

HMMs have been best in de novo prediction In practice they overpredict human genes by ~2x


Comparison-based Methods


Cross-species gene finding

5’ 3’

Exon1 Exon2 Exon3Intron1 Intron2

[human]

[mouse]

GGTTTT--ATGAGTAAAGTAGACACTCCAGTAACGCGGTGAGTAC----ATTAA | ||||| ||||| ||| ||||| ||||||||||||| | |C-TCAGGAATGAGCAAAGTCGAC---CCAGTAACGCGGTAAGTACATTAACGA-


Comparison of 1196 orthologous genes(Makalowski et al., 1996)

• Sequence identity between genes in human/mouse– exons: 84.6%– protein: 85.4%– introns: 35%– 5’ UTRs: 67%– 3’ UTRs: 69%

• 27 proteins were 100% identical



Not always: HoxA human-mouse


Patterns of Conservation

30% 1.3%

0.14%

58%14%

10.2%

Genes Intergenic

Mutations Gaps Frameshifts

Separation

2-fold10-fold75-fold


Twinscan

• Twinscan is an augmented version of the Gencscan HMM.

E I

transitions

duration

emissionsACUAUACAGACAUAUAUCAU


Twinscan Algorithm

1. Align the two sequences (eg. from human and mouse)

2. Mark each human base as gap ( - ), mismatch ( : ), match ( | )

New “alphabet”: 4 x 3 = 12 letters = { A-, A:, A|, C-, C:, C|, G-, G:, G|, U-, U:, U| }

3. Run Viterbi using emissions ek(b) where b { A-, A:, A|, …, T| }

Emission distributions ek(b) estimated from real genes from human/mouse

eI(x|) < eE(x|): matches favored in exonseI(x-) > eE(x-): gaps (and mismatches) favored in introns


Example

Human: ACGGCGACGUGCACGU

Mouse: ACUGUGACGUGCACUU

Alignment: ||:|:|||||||||:|

Input to Twinscan HMM:A| C| G: G| C: G| A| C| G| U| G| C| A| C| G: U|

Recall, eE(A|) > eI(A|)

eE(A-) < eI(A-)

Likely exon


HMMs for simultaneous alignment and gene finding:

Generalized Pair HMMs


The SLAM hidden Markov model


Exon GPHMM

d

e

1.Choose exon lengths (d,e).2.Generate alignment of length d+e.


Approximate alignment


Measuring Performance


Example: HoxA2 and HoxA3

SLAM

SGP-2

TwinscanGenscan

TBLASTXSLAM CNS

VISTARefSeq


Gene Regulation and Gene Regulation and MicroarraysMicroarrays


Overview

• A. Gene Expression and Regulation

• B. Measuring Gene Expression: Microarrays

• C. Finding Regulatory Motifs


Cells respond to environment

Cell responds toenvironment—various external messages


Genome is fixed – Cells are dynamic

• A genome is static

Every cell in our body has a copy of same genome

• A cell is dynamic

Responds to external conditions Most cells follow a cell cycle of division

• Cells differentiate during development

• Gene expression varies according to:

Cell type Cell cycle External conditions Location

slide credits: M. Kellis


Where gene regulation takes place

• Opening of chromatin

• Transcription

• Translation

• Protein stability

• Protein modifications


Transcriptional Regulation

• Efficient place to regulate:

No energy wasted making intermediate products

• However, slowest response time

After a receptor notices a change:

1. Cascade message to nucleus

2. Open chromatin & bind transcription factors

3. Recruit RNA polymerase and transcribe

4. Splice mRNA and send to cytoplasm

5. Translate into protein


Transcription Factors Binding to DNA

Transcription regulation:

Certain transcription factors bind DNA

Binding recognizes DNA substrings:

Regulatory motifs


Promoter and Enhancers

• Promoter necessary to start transcription

• Enhancers can affect transcription from afar


Regulation of Genes

GeneRegulatory Element

RNA polymerase(Protein)

Transcription Factor(Protein)

DNA


Regulation of Genes

Gene

RNA polymerase

Transcription Factor(Protein)

Regulatory Element

DNA


Regulation of Genes

Gene

RNA polymerase

Transcription Factor

Regulatory Element

DNA

New protein

TTATATTGAATTTTCAAAAATTCTTACTTTTTTTTTGGATGGACGCAAAGAAGTTTAATAATCATATTACATGGCATTACCACCATATACATATCCATATCTAATCTTACTTATATGTTGTGGAAATGTAAAGAGCCCCATTATCTTAGCCTAAAAAAACCTTCTCTTTGGAACTTTCAGTAATACGCTTAACTGCTCATTGCTATATTGAAGTACGGATTAGAAGCCGCCGAGCGGGCGACAGCCCTCCGACGGAAGACTCTCCTCCGTGCGTCCTCGTCTTCACCGGTCGCGTTCCTGAAACGCAGATGTGCCTCGCGCCGCACTGCTCCGAACAATAAAGATTCTACAATACTAGCTTTTATGGTTATGAAGAGGAAAAATTGGCAGTAACCTGGCCCCACAAACCTTCAAATTAACGAATCAAATTAACAACCATAGGATGATAATGCGATTAGTTTTTTAGCCTTATTTCTGGGGTAATTAATCAGCGAAGCGATGATTTTTGATCTATTAACAGATATATAAATGGAAAAGCTGCATAACCACTTTAACTAATACTTTCAACATTTTCAGTTTGTATTACTTCTTATTCAAATGTCATAAAAGTATCAACAAAAAATTGTTAATATACCTCTATACTTTAACGTCAAGGAGAAAAAACTATAATGACTAAATCTCATTCAGAAGAAGTGATTGTACCTGAGTTCAATTCTAGCGCAAAGGAATTACCAAGACCATTGGCCGAAAAGTGCCCGAGCATAATTAAGAAATTTATAAGCGCTTATGATGCTAAACCGGATTTTGTTGCTAGATCGCCTGGTAGAGTCAATCTAATTGGTGAACATATTGATTATTGTGACTTCTCGGTTTTACCTTTAGCTATTGATTTTGATATGCTTTGCGCCGTCAAAGTTTTGAACGATGAGATTTCAAGTCTTAAAGCTATATCAGAGGGCTAAGCATGTGTATTCTGAATCTTTAAGAGTCTTGAAGGCTGTGAAATTAATGACTACAGCGAGCTTTACTGCCGACGAAGACTTTTTCAAGCAATTTGGTGCCTTGATGAACGAGTCTCAAGCTTCTTGCGATAAACTTTACGAATGTTCTTGTCCAGAGATTGACAAAATTTGTTCCATTGCTTTGTCAAATGGATCATATGGTTCCCGTTTGACCGGAGCTGGCTGGGGTGGTTGTACTGTTCACTTGGTTCCAGGGGGCCCAAATGGCAACATAGAAAAGGTAAAAGAAGCCCTTGCCAATGAGTTCTACAAGGTCAAGTACCCTAAGATCACTGATGCTGAGCTAGAAAATGCTATCATCGTCTCTAAACCAGCATTGGGCAGCTGTCTATATGAATTAGTCAAGTATACTTCTTTTTTTTACTTTGTTCAGAACAACTTCTCATTTTTTTCTACTCATAACTTTAGCATCACAAAATACGCAATAATAACGAGTAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTTGGATACCTATTCTTGACATGATATGACTACCATTTTGTTATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAG...TTGCGAAGTTCTTGGCAAGTTGCCAACTGACGAGATGCAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTTGGATACCTATTCTTGACATGATATGACTACCATTTTGTTATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAGTCATTTGCGAAGTTCTTGGCAAGTTGCCAACTGACGAGATGCAGTTTCCTACGCATAATAAGAATAGGAGGGAATATCAAGCCAGACAATCTATCATTACATTTAAGCGGCTCTTCAAAAAGATTGAACTCTCGCCAACTTATGGAATCTTCCAATGAGACCTTTGCGCCAAATAATGTGGATTTGGAAAAAGAGTATAAGTCATCTCAGAGTAATATAACTACCGAAGTTTATGAGGCATCGAGCTTTGAAGAAAAAGTAAGCTCAGAAAAACCTCAATACAGCTCATTCTGGAAGAAAATCTATTATGAATATGTGGTCGTTGACAAATCAATCTTGGGTGTTTCTATTCTGGATTCATTTATGTACAACCAGGACTTGAAGCCCGTCGAAAAAGAAAGGCGGGTTTGGTCCTGGTACAATTATTGTTACTTCTGGCTTGCTGAATGTTTCAATATCAACACTTGGCAAATTGCAGCTACAGGTCTACAACTGGGTCTAAATTGGTGGCAGTGTTGGATAACAATTTGGATTGGGTACGGTTTCGTTGGTGCTTTTGTTGTTTTGGCCTCTAGAGTTGGATCTGCTTATCATTTGTCATTCCCTATATCATCTAGAGCATCATTCGGTATTTTCTTCTCTTTATGGCCCGTTATTAACAGAGTCGTCATGGCCATCGTTTGGTATAGTGTCCAAGCTTATATTGCGGCAACTCCCGTATCATTAATGCTGAAATCTATCTTTGGAAAAGATTTACAATGATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAGTCATTTGCGAAGTTCTTGGCAAGTTGCCAACTGACGAGATGCAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTTGGATACCTATTCTTGACATGATATGACTACCATTTTGTTATTGTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAAT

TTATATTGAATTTTCAAAAATTCTTACTTTTTTTTTGGATGGACGCAAAGAAGTTTAATAATCATATTACATGGCATTACCACCATATACATATCCATATCTAATCTTACTTATATGTTGTGGAAATGTAAAGAGCCCCATTATCTTAGCCTAAAAAAACCTTCTCTTTGGAACTTTCAGTAATACGCTTAACTGCTCATTGCTATATTGAAGTACGGATTAGAAGCCGCCGAGCGGGCGACAGCCCTCCGACGGAAGACTCTCCTCCGTGCGTCCTCGTCTTCACCGGTCGCGTTCCTGAAACGCAGATGTGCCTCGCGCCGCACTGCTCCGAACAATAAAGATTCTACAATACTAGCTTTTATGGTTATGAAGAGGAAAAATTGGCAGTAACCTGGCCCCACAAACCTTCAAATTAACGAATCAAATTAACAACCATAGGATGATAATGCGATTAGTTTTTTAGCCTTATTTCTGGGGTAATTAATCAGCGAAGCGATGATTTTTGATCTATTAACAGATATATAAATGGAAAAGCTGCATAACCACTTTAACTAATACTTTCAACATTTTCAGTTTGTATTACTTCTTATTCAAATGTCATAAAAGTATCAACAAAAAATTGTTAATATACCTCTATACTTTAACGTCAAGGAGAAAAAACTATAATGACTAAATCTCATTCAGAAGAAGTGATTGTACCTGAGTTCAATTCTAGCGCAAAGGAATTACCAAGACCATTGGCCGAAAAGTGCCCGAGCATAATTAAGAAATTTATAAGCGCTTATGATGCTAAACCGGATTTTGTTGCTAGATCGCCTGGTAGAGTCAATCTAATTGGTGAACATATTGATTATTGTGACTTCTCGGTTTTACCTTTAGCTATTGATTTTGATATGCTTTGCGCCGTCAAAGTTTTGAACGATGAGATTTCAAGTCTTAAAGCTATATCAGAGGGCTAAGCATGTGTATTCTGAATCTTTAAGAGTCTTGAAGGCTGTGAAATTAATGACTACAGCGAGCTTTACTGCCGACGAAGACTTTTTCAAGCAATTTGGTGCCTTGATGAACGAGTCTCAAGCTTCTTGCGATAAACTTTACGAATGTTCTTGTCCAGAGATTGACAAAATTTGTTCCATTGCTTTGTCAAATGGATCATATGGTTCCCGTTTGACCGGAGCTGGCTGGGGTGGTTGTACTGTTCACTTGGTTCCAGGGGGCCCAAATGGCAACATAGAAAAGGTAAAAGAAGCCCTTGCCAATGAGTTCTACAAGGTCAAGTACCCTAAGATCACTGATGCTGAGCTAGAAAATGCTATCATCGTCTCTAAACCAGCATTGGGCAGCTGTCTATATGAATTAGTCAAGTATACTTCTTTTTTTTACTTTGTTCAGAACAACTTCTCATTTTTTTCTACTCATAACTTTAGCATCACAAAATACGCAATAATAACGAGTAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTTGGATACCTATTCTTGACATGATATGACTACCATTTTGTTATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAG...TTGCGAAGTTCTTGGCAAGTTGCCAACTGACGAGATGCAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTTGGATACCTATTCTTGACATGATATGACTACCATTTTGTTATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAGTCATTTGCGAAGTTCTTGGCAAGTTGCCAACTGACGAGATGCAGTTTCCTACGCATAATAAGAATAGGAGGGAATATCAAGCCAGACAATCTATCATTACATTTAAGCGGCTCTTCAAAAAGATTGAACTCTCGCCAACTTATGGAATCTTCCAATGAGACCTTTGCGCCAAATAATGTGGATTTGGAAAAAGAGTATAAGTCATCTCAGAGTAATATAACTACCGAAGTTTATGAGGCATCGAGCTTTGAAGAAAAAGTAAGCTCAGAAAAACCTCAATACAGCTCATTCTGGAAGAAAATCTATTATGAATATGTGGTCGTTGACAAATCAATCTTGGGTGTTTCTATTCTGGATTCATTTATGTACAACCAGGACTTGAAGCCCGTCGAAAAAGAAAGGCGGGTTTGGTCCTGGTACAATTATTGTTACTTCTGGCTTGCTGAATGTTTCAATATCAACACTTGGCAAATTGCAGCTACAGGTCTACAACTGGGTCTAAATTGGTGGCAGTGTTGGATAACAATTTGGATTGGGTACGGTTTCGTTGGTGCTTTTGTTGTTTTGGCCTCTAGAGTTGGATCTGCTTATCATTTGTCATTCCCTATATCATCTAGAGCATCATTCGGTATTTTCTTCTCTTTATGGCCCGTTATTAACAGAGTCGTCATGGCCATCGTTTGGTATAGTGTCCAAGCTTATATTGCGGCAACTCCCGTATCATTAATGCTGAAATCTATCTTTGGAAAAGATTTACAATGATTGTACGTGGGGCAGTTGACGTCTTATCATATGTCAAAGTCATTTGCGAAGTTCTTGGCAAGTTGCCAACTGACGAGATGCAGTAACACTTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCACAAACTTTAAAACACAGGGACAAAATTCTTGATATGCTTTCAACCGCTGCGTTTTGGATACCTATTCTTGACATGATATGACTACCATTTTGTTATTGTTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATAATGTTTTCAATGTAAGAGATTTCGATTATCTTATAGTTCATACATGCTTCAACTACTTAATAAATGATTGTATGATTT

Promoter motifs

3’ UTR motifs

Exons

Introns


Example: A Human heat shock protein

• TATA box: positioning transcription start

• TATA, CCAAT: constitutive transcription

• GRE: glucocorticoid response

• MRE: metal response

• HSE: heat shock element

TATASP1CCAAT AP2HSEAP2CCAATSP1

promoter of heat shock hsp70

0--158

GENE


The Cell as a Regulatory Network

• Genes = wires• Motifs = gates

A B Make DC

If C then D

If B then NOT D

If A and B then D D

Make BD

If D then B

C

gene D

gene B


The Cell as a Regulatory Network (2)


DNA Microarrays

Measuring gene transcription in a high-throughput fashion


What is a microarray



• Measure the level of mRNA messages in a cell

DN

A 1

DN

A 3

DN

A 5

DN

A 6

DN

A 4

DN

A 2

cDNA 4

cDNA 6

Hybridize Gen

e 1

Gen

e 3

Gen

e 5

Gen

e 6

Gen

e 4

Gen

e 2

MeasureRNA 4

RNA 6

RT




• A 2D array of DNA sequences from thousands of genes

• Each spot has many copies of same gene

• Measure number of hybridizations per spot

Result:• Thousands of “experiments” – one per gene –

in one go

• Perform many microarrays for different conditions: Time during cell cycle Temperature Nutrient level


Goal of Microarray Experiments

• Measure level of gene expression across many different conditions:

Expression Matrix M: {genes}{conditions}:

Mij = |genei| in conditionj

• Group genes into coregulated sets

Observe cells under different conditions

Find genes with similar expression profiles

• Potentially regulated by same TF



Clustering vs. Classification

• Clustering Idea: Groups of genes that share similar function have similar expression

patterns• Hierarchical clustering• k-means • Bayesian approaches• Projection techniques

• Principal Component Analysis• Independent Component Analysis

• Classification Idea: A cell can be in one of several states

• (Diseased vs. Healthy, Cancer X vs. Cancer Y vs. Normal) Can we train an algorithm to use the gene expression patterns to

determine which state a cell is in?• Support Vector Machines• Decision Trees• Neural Networks• K-Nearest Neighbors


Clustering Algorithms

b

ed

f

a

c

h

ga b d e f g hc

• K-meansb

ed

f

a

c

h

gc1

c2

c3a b g hcd e f

• Hierarchical



Hierarchical clustering

• Bottom-up algorithm: Initialization: each point in a separate cluster

• At each step: Choose the pair of closest clusters Merge

• The exact behavior of the algorithm depends on how we define the distance CD(X,Y) between clusters X and Y

• Avoids the problem of specifying the number of clusters

b

ed

f

a

c

h

g



Distance between clusters

• CD(X,Y)=minx X, y Y D(x,y)

Single-link method

• CD(X,Y)=maxx X, y Y D(x,y)

Complete-link method

• CD(X,Y)=avgx X, y Y D(x,y)

Average-link method

• CD(X,Y)=D( avg(X) , avg(Y) )

Centroid method

ed

f

h

g

ed

f

h

g

ed

f

h

g

ed

f

h

g



Results of Clustering Gene Expression

• CLUSTER is simple and easy to use

• De facto standard for microarray analysis

Time: O(N2M)

N: #genesM: #conditions


K-Means Clustering Algorithm

• Each cluster Xi has a center ci

• Define the clustering cost criterion

• COST(X1,…Xk) = ∑Xi ∑x Xi |x – ci|2

• Algorithm tries to find clusters X1…Xk and centers c1…ck that minimize COST

• K-means algorithm: Initialize centers Repeat:

• Compute best clusters for given centers

• → Attach each point to the closest center

• Compute best centers for given clusters

• → Choose the centroid of points in cluster

Until the changes in COST are “small”

b

ed

f

a

c

h

g

c1

c2

c3



K-Means Algorithm

• Randomly Initialize Clusters


K-Means Algorithm

• Assign data points to nearest clusters


K-Means Algorithm

• Recalculate Clusters


K-Means Algorithm

• Recalculate Clusters


K-Means Algorithm

• Repeat


K-Means Algorithm

• Repeat


K-Means Algorithm

• Repeat … until convergence

Time: O(KNM) per iteration

N: #genesM: #conditions


Mixture of Gaussians – Probabilistic K-means

• Data is modeled as mixture of K Gaussians N(1, 2I), …, N(K, 2I)

Prior probabilities 1, …, K

• Different i for every Gaussian i, or even different covariance matrices are possible, but learning becomes harder

P(x) = ∑i P(x | N(1, 2I)) i

Use EM to learn parameters


Analysis of Clustering Data

• Statistical Significance of Clusters

Gene Ontology http://www.geneontology.org/

KEGG http://www.genome.jp/kegg/

• Regulatory motifs responsible for common expression

• Regulatory Networks

• Experimental Verification


Evaluating clusters – Hypergeometric Distribution

rm

k

N

mk

pN

m

p

rposP )(

• N experiments, p labeled ++, (N-p) ––• Cluster: k elements, m labeled ++• P-value of single cluster containing k

elements of which at least r are ++

Prob that a randomly chosen set of k experiments would result in m positive and k-m negative

P-value of uniformity

in computed cluster


Documents

CS262 Lecture 16, Win07, Batzoglou Gene Recognition Credits for slides: Serafim Batzoglou Marina Alexandersson Lior Pachter Serge Saxonov