Tue Sep 18 Intro 1: Computing, statistics, Perl, Mathematica Tue Sep 25 Intro 2: Biology, comparative genomics, models & evidence, applications Tue Oct

Tue Sep 18 Intro 1: Computing, statistics, Perl, MathematicaTue Sep 25 Intro 2: Biology, comparative genomics, models & evidence, applications Tue Oct 02 DNA 1: Polymorphisms, populations, statistics, pharmacogenomics, databasesTue Oct 09 DNA 2: Dynamic programming, Blast, multi-alignment, HiddenMarkovModelsTue Oct 16 RNA 1: 3D-structure, microarrays, library sequencing & quantitation concepts Tue Oct 23 RNA 2: Clustering by gene or condition, DNA/RNA motifs. Tue Oct 30 Protein 1: 3D structural genomics, homology, dynamics, function & drug designTue Nov 06 Protein 2: Mass spectrometry, modifications, quantitation of interactionsTue Nov 13 Network 1: Metabolic kinetic & flux balance optimization methodsTue Nov 20 Network 2: Molecular computing, self-assembly, genetic algorithms, neural-netsTue Nov 27 Network 3: Cellular, developmental, social, ecological & commercial modelsTue Dec 04 Project presentationsTue Dec 11 Project PresentationsTue Jan 08 Project PresentationsTue Jan 15 Project Presentations

Bio 101: Genomics & Computational Biology

RNA1: Last week's take home lessons

• Integration with previous topics (HMM for RNA structure)

• Goals of molecular quantitation (maximal fold-changes, clustering & classification of genes & conditions/cell types, causality)

• Genomics-grade measures of RNA and protein and how we choose (SAGE, oligo-arrays, gene-arrays)

• Sources of random and systematic errors (reproducibilty of RNA source(s), biases in labeling, non-polyA RNAs, effects of array geometry, cross-talk).

• Interpretation issues (splicing, 5' & 3' ends, editing, gene families, small RNAs, antisense, apparent absence of RNA).

• Time series data: causality, mRNA decay, time-warping

RNA2: Today's story & goals

• Clustering by gene and/or condition

• Distance and similarity measures

• Clustering & classification

• Applications

• DNA & RNA motif discovery & search

Data- Ratios- Log Ratios- Absolute Measurement

- Euclidean Dist.- Manhattan Dist.- Sup. Dist.- Correlation Coeff.

- Single- Complete- Average- Centroid

Unsupervised | Supervised

- SVM- Relevance NetworksHierarchical | Non-hierarchical

- Minimal Spanning Tree - K-means- SOM

Data Normalization | Distance Metric | Linkage | Clustering Method

Gene Expression Clustering Decision Tree

How to normalize- Variance normalize- Mean center normalize- Median center normalize

What to normalize- genes- conditions

(Whole genome) RNA quantitation objectives

RNAs showing maximum changeminimum change detectable/meaningful

RNA absolute levels (compare protein levels)minimum amount detectable/meaningful

Classification: drugs & cancers

Network -- direct causality-- motifs

Clustering vs. supervised learning

K-means clusteringSOM = Self Organizing MapsSVD = Singular Value decompositionPCA = Principal Component Analysis

SVM = Support Vector Machine classification and Relevance networksBrown et al. PNAS 97:262 Butte et al PNAS 97:12182

http://www.pnas.org/cgi/content/full/97/1/262



Cluster analysis of mRNA expression data

By gene (rat spinal cord development, yeast cell cycle):

Wen et al., 1998; Tavazoie et al., 1999; Eisen et al., 1998; Tamayo et al., 1999

By condition or cell-type or by gene&cell-type (human cancer): Golub, et al. 1999; Alon, et al. 1999; Perou, et al. 1999; Weinstein, et al. 1997

Cheng, ISMB 2000.

.

http://www.ncbi.nlm.nih.gov/htbin-post/Entrez/query?uid=9419376&form=6&db=m&Dopt=b








http://www.pubmedcentral.nih.gov/b.cgi?pubmedid=10077610


http://www.ncbi.nlm.nih.gov/htbin-post/Entrez/query?db=m&form=6&uid=10521349&db=m

http://www.ncbi.nlm.nih.gov/htbin-post/Entrez/query?db=m&form=6&uid=10521349&db=m

http://www.ncbi.nlm.nih.gov/htbin-post/Entrez/query?uid=10359783&form=6&Dopt=b






ftp://ftp.sdsc.edu/pub/sdsc/biology/ISMB00/157.pdf

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

Clustering hierarchical & non-

•Hierarchical: a series of successive fusions of data until a final number of clusters is obtained; e.g. Minimal Spanning Tree: each component of the population to be a cluster. Next, the two clusters with the minimum distance between them are fused to form a single cluster. Repeated until all components are grouped.• Non-: e.g. K-mean: K clusters chosen such that the points are mutually farthest apart. Each component in the population assigned to one cluster by minimum distance. The centroid's position is recalculated and repeat until all the components are grouped. The criterion minimized, is the within-clusters sum of the variance.

Clusters of Two-Dimensional Data

Key Terms in Cluster Analysis

• Distance measures

• Similarity measures

• Hierarchical and non-hierarchical

• Single/complete/average linkage

• Dendrogram

Distance Measures: Minkowski Metric

r rp

iii

p

p

yxyxd

yyyy

xxxx

pyx

||),(

)(

)(

1

21

21

by defined is metric Minkowski The

:features have both and objects two Suppose

Most Common Minkowski Metrics

||max),(

||),(

1

||),(

2

1

1

2 2

1

iipi

p

iii

p

iii

yxyxd

r

yxyxd

r

yxyxd

r

) distance sup"(" 3,

distance) (Manhattan 2,

) distance (Euclidean 1,

An Example

.4}3,4{max

.734

.5342 22

:distance sup"" 3,

:distance Manhattan 2,

:distance Euclidean 1,

4

3

x

y

Manhattan distance is called Hamming distance when all features are binary.

1101111110000111010011100100100110

1716151413121110987654321

GeneBGeneA

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

. :Distance Hamming 5141001 )#()#(

Similarity Measures: Correlation Coefficient

.

)()(

))((),(

1

1

1

1

1 1

22

1

p

iip

p

iip

p

i

p

iii

p

iii

yyxx

yyxx

yyxxyxs

and where

1),( yxs

(1) s(x,y)=1, (2) s(x,y)=-1, (3) s(x,y)=0

What kind of x and y givelinear CC

?

Similarity Measures: Correlation Coefficient

Time

Gene A

Gene B

Gene A

Time

Gene B

Expression LevelExpression Level

Expression Level

Time

Gene A

Gene B

Hierarchical Clustering Dendrograms

Alon et al. 1999

Clustering tree for the tissue samplesTumors(T) and normal tissue(n).

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.

The distance between two clusters is defined as the distance between

• Single-Link Method / Nearest Neighbor: their closest members.

• Complete-Link Method / Furthest Neighbor: their furthest members.

• Centroid: their centroids.

• Average: average of all cross-cluster pairs.

Single-Link Method

ba

453652

cba

dcb

Distance Matrix

Euclidean Distance

453,

cba

dc

453652

cba

dcb4,, cbad

(1) (2) (3)

a,b,ccc d

a,b

d da,b,c,d

Complete-Link Method

ba

453652

cba

dcb

Distance Matrix

Euclidean Distance

465,

cba

dc

453652

cba

dcb6,,

badc

(1) (2) (3)

a,b

cc d

a,b

d c,da,b,c,d

Dendrograms

a b c d a b c d

2

4

6

0

Single-Link Complete-Link

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

Nadler and Smith, Pattern Recognition Engineering, 1993

Data- Ratios- Log Ratios- Absolute Measurement

- Euclidean Dist.- Manhattan Dist.- Sup. Dist.- Correlation Coeff.

- Single- Complete- Average- Centroid

Unsupervised | Supervised

- SVM- Relevance NetworksHierarchical | Non-hierarchical

- Minimal Spanning Tree - K-means- SOM

Data Normalization | Distance Metric | Linkage | Clustering Method

Gene Expression Clustering Decision Tree

How to normalize- Variance normalize- Mean center normalize- Median center normalize

What to normalize- genes- conditions

Normalized Expression Data

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

Time-point 1

Tim

e-po

int 3

Tim

e-po

int 2

Gene 1Gene 2

Normalized Expression Data from microarrays

T1 T2 T3Gene 1

Gene N.

Representation of expression data

dij

Identifying prevalent expression patterns (gene clusters)

Time-point 1

Tim

e-po

int 3

Tim

e-po

int 2

-1.8

-1.3

-0.8

-0.3

0.2

0.7

1.2

1 2 3

-2

-1.5

-1

-0.5

0

0.5

1

1.5

1 2 3

-1.5

-1

-0.5

0

0.5

1

1.5

1 2 3

Time -pointTime -point

Time -point

Nor

mal

ized

Exp

ress

ion

Nor

mal

ized

Exp

ress

ion

Nor

mal

ized

Exp

ress

ion

gpm1HTB1RPL11ARPL12BRPL13ARPL14ARPL15ARPL17ARPL23ATEF2YDL228cYDR133CYDR134CYDR327WYDR417CYKL153WYPL142C

GlycolysisNuclear Organization

Ribosome

Translation

Unknown

Genes MIPS functional category

Cluster contents

Eisen et al. (1998):

FIG. 1. Cluster display of data from time course of serumstimulation of primary human fibroblasts.

Expemeriments:Foreskin fibroblasts were grown in culture and weredeprived of serum for 48 hr. Serum was added back andsamples taken at time 0, 15 min, 30 min, 1hr, 2 hr, 3 hr, 4hr, 8 hr, 12 hr, 16 hr, 20 hr, 24 hr.

Clustering:Correlation Coefficient + Centroid Hierarchical Clustering

Clusters:(A) cholesterol biosynthesis,(B) the cell cycle,(C) the immediate-early response,(D) signaling and angiogenesis,(E) wound healing and tissue remodeling.

Weinstein et al. (1997)

Figure 2. "Clusteredcorrelation" (ClusCor)map of the relationbetween compoundstested and moleculartargets in the cells.





• Applications


Motif-finding algorithms

• oligonucleotide frequencies

• Gibbs sampling (e.g. AlignACE)

• MEME

• ClustalW

• MACAW

Transcription control sites(~7 bases of information)

Genome:(12 Mb)

• 7 bases of information (14 bits) ~ 1 match every 16000 sites.• 1500 such matches in a 12 Mb genome (24 * 106 sites).• The distribution of numbers of sites for different motifs is Poisson with mean 1500, which can be approximated as normal with a mean of 1500 and a standard deviation of ~40 sites.• Therefore, ~100 sites are needed to achieve a detectable signal above background.

Feasibility of a whole-genome motif search?Feasibility of a whole-genome motif search?

• Whole-genome mRNA expression data: two-way comparisons between different conditions or mutants, clustering/grouping over many conditions/timepoints.

• Shared phenotype (functional category).

• Conservation among different species.

• Details of the sequence selection: eliminate protein-coding regions, repetitive regions, and any other sequences not likely to contain control sites.

Sequence Search Space ReductionSequence Search Space Reduction

• Whole-genome mRNA expression data: two-way comparisons between different conditions or mutants, clustering/grouping over many conditions/timepoints.

• Shared phenotype (functional category).

• Conservation among different species.

• Details of the sequence selection: eliminate protein-coding regions, repetitive regions, and any other sequences not likely to contain control sites.

Sequence Search Space ReductionSequence Search Space Reduction

• Modification of Gibbs Motif Sampling (GMS), a routine for motif finding in protein sequences (Lawrence, et al. Science 262:208-214, 1993).

• Advantages of GMS: • stochastic sampling• variable number of sites per input sequence• distributed information content per motif

• AlignACE modifications: • considers both strands of DNA simultaneously • efficiently returns multiple distinct motifs • various other tweaks

Motif FindingMotif FindingAlignACE

(Aligns nucleic Acid Conserved Elements)

5’- TCTCTCTCCACGGCTAATTAGGTGATCATGAAAAAATGAAAAATTCATGAGAAAAGAGTCAGACATCGAAACATACAT

5’- ATGGCAGAATCACTTTAAAACGTGGCCCCACCCGCTGCACCCTGTGCATTTTGTACGTTACTGCGAAATGACTCAACG

5’- CACATCCAACGAATCACCTCACCGTTATCGTGACTCACTTTCTTTCGCATCGCCGAAGTGCCATAAAAAATATTTTTT

5’- TGCGAACAAAAGAGTCATTACAACGAGGAAATAGAAGAAAATGAAAAATTTTCGACAAAATGTATAGTCATTTCTATC

5’- ACAAAGGTACCTTCCTGGCCAATCTCACAGATTTAATATAGTAAATTGTCATGCATATGACTCATCCCGAACATGAAA

5’- ATTGATTGACTCATTTTCCTCTGACTACTACCAGTTCAAAATGTTAGAGAAAAATAGAAAAGCAGAAAAAATAAATAA

5’- GGCGCCACAGTCCGCGTTTGGTTATCCGGCTGACTCATTCTGACTCTTTTTTGGAAAGTGTGGCATGTGCTTCACACA

…HIS7

…ARO4

…ILV6

…THR4

…ARO1

…HOM2

…PRO3

300-600 bp of upstream sequence per gene are searched in

Saccharomyces cerevisiae.

AlignACE ExampleAlignACE ExampleInput Data SetInput Data Set








AAAAGAGTCA

AAATGACTCA

AAGTGAGTCA

AAAAGAGTCA

GGATGAGTCA

AAATGAGTCA

GAATGAGTCA

AAAAGAGTCA

**********MAP score = 20.37 (maximum)

…HIS7

…ARO4

…ILV6

…THR4

…ARO1

…HOM2

…PRO3

AlignACE ExampleAlignACE ExampleThe Target MotifThe Target Motif







**********

TGAAAAATTC

GACATCGAAA

GCACTTCGGC

GAGTCATTAC

GTAAATTGTC

CCACAGTCCG

TGTGAAGCAC






**********

TGAAAAATTC

GACATCGAAA

GCACTTCGGC

GAGTCATTAC

GTAAATTGTC

CCACAGTCCG

TGTGAAGCACMAP score = -10.0

…HIS7

…ARO4

…ILV6

…THR4

…ARO1

…HOM2

…PRO3

AlignACE ExampleAlignACE ExampleInitial SeedingInitial Seeding








**********

TGAAAAATTC

GACATCGAAA

GCACTTCGGC

GAGTCATTAC

GTAAATTGTC

CCACAGTCCG

TGTGAAGCAC

Add?

**********

TGAAAAATTC

GACATCGAAA

GCACTTCGGC

GAGTCATTAC

GTAAATTGTC

CCACAGTCCG

TGTGAAGCAC

TCTCTCTCCA

How much better is the alignment with this site as opposed to without?

…HIS7

…ARO4

…ILV6

…THR4

…ARO1

…HOM2

…PRO3

AlignACE ExampleAlignACE ExampleSamplingSampling








**********

TGAAAAATTC

GACATCGAAA

GCACTTCGGC

GAGTCATTAC

GTAAATTGTC

CCACAGTCCG

TGTGAAGCAC

Add?

**********

TGAAAAATTC

GACATCGAAA

GCACTTCGGC

GAGTCATTAC

GTAAATTGTC

CCACAGTCCG

TGTGAAGCAC


Remove.

ATGAAAAAAT

…HIS7

…ARO4

…ILV6

…THR4

…ARO1

…HOM2

…PRO3

AlignACE ExampleAlignACE ExampleContinued SamplingContinued Sampling








**********

GACATCGAAA

GCACTTCGGC

GAGTCATTAC

GTAAATTGTC

CCACAGTCCG

TGTGAAGCAC

Add?

**********

TGAAAAATTC

GACATCGAAA

GCACTTCGGC

GAGTCATTAC

GTAAATTGTC

CCACAGTCCG

TGTGAAGCAC


…HIS7

…ARO4

…ILV6

…THR4

…ARO1

…HOM2

…PRO3

AlignACE ExampleAlignACE ExampleContinued SamplingContinued Sampling








**********

GACATCGAAA

GCACTTCGGC

GAGTCATTAC

GTAAATTGTC

CCACAGTCCG

TGTGAAGCAC

********* *

GACATCGAAAC

GCACTTCGGCG

GAGTCATTACA

GTAAATTGTCA

CCACAGTCCGC

TGTGAAGCACA

How much better is the alignment with this new

column structure?

…HIS7

…ARO4

…ILV6

…THR4

…ARO1

…HOM2

…PRO3

AlignACE ExampleAlignACE ExampleColumn SamplingColumn Sampling








AAAAGAGTCA

AAATGACTCA

AAGTGAGTCA

AAAAGAGTCA

GGATGAGTCA

AAATGAGTCA

GAATGAGTCA

AAAAGAGTCA

**********MAP score = 20.37

…HIS7

…ARO4

…ILV6

…THR4

…ARO1

…HOM2

…PRO3

AlignACE ExampleAlignACE ExampleThe Best MotifThe Best Motif

5’- TCTCTCTCCACGGCTAATTAGGTGATCATGAAAAAATGAAAAATTCATGAGAAAAXAGTCAGACATCGAAACATACAT5’- ATGGCAGAATCACTTTAAAACGTGGCCCCACCCGCTGCACCCTGTGCATTTTGTACGTTACTGCGAAATXACTCAACG

5’- CACATCCAACGAATCACCTCACCGTTATCGTGACTXACTTTCTTTCGCATCGCCGAAGTGCCATAAAAAATATTTTTT

5’- TGCGAACAAAAXAGTCATTACAACGAGGAAATAGAAGAAAATGAAAAATTTTCGACAAAATGTATAGTCATTTCTATC

5’- ACAAAGGTACCTTCCTGGCCAATCTCACAGATTTAATATAGTAAATTGTCATGCATATGACTXATCCCGAACATGAAA

5’- ATTGATTGACTXATTTTCCTCTGACTACTACCAGTTCAAAATGTTAGAGAAAAATAGAAAAGCAGAAAAAATAAATAA

5’- GGCGCCACAGTCCGCGTTTGGTTATCCGGCTGACTXATTCTGACTXTTTTTTGGAAAGTGTGGCATGTGCTTCACACA

AAAAGAGTCA

AAATGACTCA

AAGTGAGTCA

AAAAGAGTCA

GGATGAGTCA

AAATGAGTCA

GAATGAGTCA

AAAAGAGTCA

**********

…HIS7

…ARO4

…ILV6

…THR4

…ARO1

…HOM2

…PRO3

• Take the best motif found after a prescribed number of random seedings.• Select the strongest position of the motif.• Mark these sites in the input sequence, and do not allow future motifs to sample those sites.• Continue sampling.

AlignACE ExampleAlignACE ExampleMasking (old way)Masking (old way)








AAAAGAGTCA

AAATGACTCA

AAGTGAGTCA

AAAAGAGTCA

GGATGAGTCA

AAATGAGTCA

GAATGAGTCA

AAAAGAGTCA

**********

…HIS7

…ARO4

…ILV6

…THR4

…ARO1

…HOM2

…PRO3

• Maintain a list of all distinct motifs found.• Use CompareACE to compare subsequent motifs to those already found.• Quickly reject weaker, but similar motifs.

AlignACE ExampleAlignACE ExampleMasking (new way)Masking (new way)

= standard Beta & Gamma functionsN = number of aligned sites; T = number of total possible sitesFjb = number of occurrences of base b at position j (Fsum)Gb = background genomic frequency for base bb = n x Gb for n pseudocounts (sum)W = width of motif; C = number of columns in motif (W>=C)

MAP ScoreMAP Score

N = number of aligned sitesR = overrepresentation of those sites.

MAP N log R

MAP ScoreMAP Score

188.38578.116320.620128.1044117.52831.101

73.42768.2458619.379

55.0993

89.42922.78973

MAP score Motif

AlignACE Example: Final Results

(alignment of upstream regions from 116 amino acid biosynthetic

genes in S. cerevisiae)

Indices used to evaluate motif significance

• Group specificity

• Functional enrichment Positional bias

• Palindromicity

• Known motifs (CompareACE)

Searching for additional motif instances in the entire genome sequence

Searches over the entire genome for additional high-scoring instances of the motif are done using the ScanACE program, which uses the Berg & von Hippel weight matrix (1987).

M

l l

lB

n

nE

0 0 5.0

5.0ln

M = length of binding site motifB = base at position l within the motifnlB= number of occurrences of base B at position l in the input alignmentnlO= number of occurrences of the most common base at position l in the

input alignment

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

Replication & DNA synthesis (2)

s.d

. fr

om

mean

MCB SCB

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3005

101520253035

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

CLUSTERCLUSTER

Nu

mb

er o

f O

RF

s

05

1015

2025

3035

Distance from ATG (b.p.)

Nu

mb

er o

f si

tes

02468

1012141618


Nu

mb

er o

f si

tes

Nu

mb

er o

f O

RF

s

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

MIPS Functional category (total ORFs) ORFs withinfunctional category

(k)

P-value-Log10

DNA synthesis and replication (82)Cell cycle control and mitosis (312)Recombination and DNA repair (84)Nuclear organization (720)

23301140

16854

N = 186

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Organization of centrosome (14)s.

d. f

rom

mea

n

0

10

20

30

40

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

M14a

CLUSTER

0

10

20

30

40

50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

M14b

CLUSTER

0

5

10

15

20


Nu

mb

er o

f si

tes

0

5

10

15

20

25


Nu

mb

er o

f si

tes

Nu

mb

er o

f O

RF

s

Nu

mb

er o

f O

RF

s

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5


(k)

P-value-Log10

Organization of centrosome (28)Nuclear biogenesis (5)Organization of cytoskeleton (93)

637

654*

N = 74

-1.5

-0.5

0.5

1.5

2.5

3.5

Ribosome (1)s.

d. f

rom

mea

n

Rap1

CLUSTER

Nu

mb

er o

f O

RF

s

0

10

20

30

40

50

60

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

M1a

CLUSTER

02468

10121416


Nu

mb

er o

f si

tes

02

46

810

1214


Nu

mb

er o

f si

tes

Nu

mb

er o

f O

RF

s


(k)

P-value-Log10

Ribosomal proteins (206)Organization of cytoplasm (555)Organization of chromosome structure (41)

64797

54394

N = 164

Separate, Tag, Quantitate RNAs or interactions

ClusteringPrevious

FunctionalAssignments

Periodicity

InteractionMotifs

Interactionpartners

•Group specificity•Positional bias

•Palindromicity

•CompareACE

Metrics of motif significance

N genes total; s1 = # genes in a cluster; s2= # genes in a particular functional category (“success”); p = s2/N; N=s1+s2-xWhich odds of exactly x in that category in s1 trials?Binomial: sampling with replacement.

or Hypergeometric: sampling without replacement:Odds of getting exactly x = intersection of sets s1 & s2:

Functional category enrichment odds

2

2

11

s

N

xs

sN

x

s

H

ref

)1()1(1 xsx ppx

sB

(Wrong!)

http://library.thinkquest.org/10030/statcon.htm

)2,1min(

2

2

11ss

xis

N

is

sN

i

s

functionS

N = Total # of genes (or ORFs) in the genomes1 = # genes in the clusters2 = # genes found in a functional categoryx = # ORFs in the intersection of these groups(hypergeometric probability distribution)

x s2s1N = 6226

(S. cerevisiae)

Functional category enrichment

)2,1min(

2

2

11ss

xis

N

is

sN

i

s

groupS

N = Total # of genes (ORFs) in the genomes1 = # genes whose upstream sequences were used to align the motif (cluster)s2 = # genes in the target list (~ 100 genes in the genome with the best sites for

the motif near their translational starts)x = # genes in the intersection of these groups

x s2s1N = 6226

(S. cerevisiae)

Group Specificity Score (Sgroup)

t

mi

it

s

wi

s

w

i

tP 1

t = number of sites within 600 bp of translational start from among the best 200 being considered

m = number of sites in the most enriched 50-bp windows = 600 bpw = 50 bp

Start -600 bp

50 bp

Positional Bias

Comparisons of motifs

• The CompareACE program finds best alignment between two motifs and calculates the correlation between the two position-specific scoring matrices

• Similar motifs: CompareACE score > 0.7

Clustering motifs by similarity

motif Amotif Bmotif Cmotif D

A B C DA 1.0 0.9 0.1 0.0 B 1.0 0.2 0.1C 1.0 0.8D 1.0

Cluster motifs using a similarity matrix consisting of all pairwise CompareACE scores

cluster 1: A, Bcluster 2: C, D

CompareACE

HierarchicalClustering

Palindromicity

0.97

0.92

0.92

0.39

• CompareACE score of a motif versus its reverse complement

• Palindromes: CompareACE > 0.7

• Selected palindromicity values:

Crp

PurR ArgR

CpxR

S. cerevisiae AlignACE Test Set

Functional categories (248 groups 3313 motifs) MIPS (135 goups) YPD (17 groups) names (96 groups)

Negative controls (250 groups 3692 motifs) 50 each of randomly selected sets of 20, 40, 60,

80, or 100 genes

Positive controls (29 groups) Cold Spring Harbor website -- SCPD 29 sets of genes controlled by a TF with 5 or

more known binding sites

S. cerevisiae AlignACE test set

Most specific motifs(ranked by Sgroup)

Most positionally biased motifs

• 250 AlignACE runs on 50 groups each of 20, 40, 60, 80,and 100 orfs, resulting in 3692 motifs.

• Allows calibration of an expected false positive rate for a set of hypotheses resulting from any chosen cutoffs.

MAP > 10.0Spec. < 1e-5

Example:

Functional Categories

Random Runs82 motifs (24 known)41 motifs

Negative Controls

Computational identification of cis-regulatory elements associated with groups of functionally related genes in S. cerevisiae Hughes, et al JMB, 1999.

Positive Controls• 29 transcription factors listed on the CSH web

site have five or more known binding sites. AlignACE was run on the upstream regions of the corresponding genes.

• An appropriate motif was found in 21/29 cases.• 5/8 false negatives were found in appropriate

functional category AlignACE runs.• False negative rate = ~ 10-30 %

Establishing regulatory connections

• Generalizing & reducing assumptions:• Motif Interactions: (Pilpel et al 2001 Nat Gen )

• Which protein(s): in vivo crosslinking • Interdependence of column in weight

matrices: array binding (Bulyk et al 2001PNAS 98: 7158)

http://arep.med.harvard.edu/pdf/Pilpel01.pdf

http://arep.med.harvard.edu/pdf/Bulyk01.pdf

http://arep.med.harvard.edu/pdf/Bulyk01.pdf





• Applications


Documents

Tue Sep 18 Intro 1: Computing, statistics, Perl, Mathematica Tue Sep 25 Intro 2: Biology, comparative genomics, models & evidence, applications Tue Oct