i=1,2,...N data points = vertices of graph

neighbors i,j connected by edges

5

1

8

J i,j – weight associated with edge i,jJ 5,8

J i,j depends on distance D i,j

J i,j

D i,j

weighted graph

partitions

weights

correlated pairs

clusters

C i,j > 0.5

how many clusters?

3 LARGEMANY small (SPC)

toy problem SPC

TSS vs K

Iris setosa

Iris versicolor

Iris virginica

50 specimes from each group4 numbers for each flower150 data points in 4-dimensional space

irises

150 points in d=4

3 large clusters

d=4

comparison Iris

3circles:

N=4800 POINTS IN D=2

identifying stable clusters

Same data - Average Linkage

No analog for No analog for

Same data - Average Linkage

Examining this cluster

Examining this cluster

Advantages of SPC

• RELIES ON PROXIMITY

• SCANS ALL RESOLUTIONS (T)

• ROBUST AGAINST NOISE AND INITIALIZATION -

CALCULATES COLLECTIVE CORRELATIONS.

• IDENTIFIES STABLE CLUSTERS (T)

• NO NEED TO PRE-SPECIFY NUMBER OF CLUSTERS

Samples

Genes5 10 15 20 25

5

10

15

20

25

30

350

10

20

30

40

50

60

70

80

90

100

%

ProtocolA

a

b

-

+ A B

5 10 15 20 25 30 35

5

10

15

20

25

30

35

C

S1G3 stability

larger T - tighter, more stable cluster

T

YEAST CELL-CYCLE EXPRESSION DATA

• EXPRESSION DATA: SIMULTANEOUS MEASUREMENT OF MRNA CONCENT-

RATION OF THOUSANDS OF GENES.

• DATA: N=2467 GENES OF KNOWN

FUNCTION MEASURED AT 18 TIME

INTERVALS (18*7 MIN) DURING CELL

CYCLE OF YEAST. .

• CELLS SYNCHRONIZED BY ALPHA FACTOR ARREST AND RELEASE.

SPELLMAN ET. AL. (1998) MOL. BIOL. CELL

CELL CYCLE

G1 –gap, decide whether to proliferate, wait

or cross to non-dividing stage G0

S -- DNA Synthesis

G2– gap, allow DNA repair

M – Mitosis, cell division

Yeast data dendrogram

500 1000 1500 2000

5

10

15

20

25

30

35

40

45

50T

- R

esol

utio

n

Genes

• WE APPLIED FILTERS TO SELECT CLUSTERS OF CELL-CYCLE RELATED GENES. THE MEAN EXPRESSION PROFILE OF A CLUSTER SHOULD HAVE – SMOOTH, LOW FREQUENCY TEMPORAL

VARIATION.– SIGNIFICANT DEVIATION FROM

CONSTANT VALUE

Choosing clusters to examine

500 1000 1500 2000

5

10

15

20

25

30

35

40

45

50T

- R

esol

utio

n

Genes

432 1

Chosen clusters

Cell-cycle clusters

0 2 4 6 8 10 12 14 16 18-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Time0 2 4 6 8 10 12 14 16 18

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Time

0 2 4 6 8 10 12 14 16 18-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Time

0 2 4 6 8 10 12 14 16 18-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Time

Late G1Cln1,2Clb5,6Swi4

G2/MClb1,2Swi5Ace2

SHistones

Progression of the cell-cycle

0 2 4 6 8 10 12 14 16 18-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Late G1 clusterS cluster G2/M cluster

Other stable clusters

500 1000 1500 2000

5

10

15

20

25

30

35

40

45

50T

- R

esol

utio

n

Genes

56

7

89

10

11

Analyzing promoters of the genes

• Mostly ribosomal proteins(Artifact - freezer)

• General metabolismA novel conserved DNA motif GCGATGAGNT in 90% of genes

• Dip at the endA novel conserved DNAmotif RNNGCWGCNNC

0 2 4 6 8 10 12 14 16 18 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Cluster #5

0 2 4 6 8 10 12 14 16 18 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Cluster #6

0 2 4 6 8 10 12 14 16 18 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Cluster #8

0 2 4 6 8 10 12 14 16 18 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Cluster #7

0 2 4 6 8 10 12 14 16 18 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Cluster #10

G.Getz, E.Levine, E.Domany and M.Zhang Physica A279, 457 (2000)

0 2 4 6 8 10 12 14 16 18 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Cluster #5

0 2 4 6 8 10 12 14 16 18 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Cluster #6

0 2 4 6 8 10 12 14 16 18 20-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Cluster #8

oscillations – by eye

PRIMARY TARGETS OF P53

TEMPERATURE SENSITIVE MUTANT P53, ACTIVATE - 32 C (t=0)

MEASURE EXPRESSION AT t=0,2,6,12,24 h (use t=0 as control)

REPEAT IN PRESENCE OF CYCLOHEXIMIDE (CHX) t=0,2,4,6,9,12

(CHX INHIBITS PROTEIN SYNTHESIS)

IDENTIFY UPREGULATED GENES USING FILTER:

AT LEAST 2.5 FOLD INCREASE AT 3 OR MORE TIME POINTS

(SEPARATELY IN EACH OF THE

TWO EXPTS, -CHX AND +CHX)

38 CANDIDATE PRIMARIES:EFFECT OF FILTERING??? RELEASE FILTER FROM +CHXCLUSTERING: 38 47 (31)

REDUCE EFFECT OF FILTERING BY CLUSTERING

X – 38 candidate primary targets

% candidate primary targets

c

a

K.Kannan et al, Oncogene

COLON CANCER DATA:

Colon Cancer Data

Two-way clustering

S1(G1)

G1(S1)

TWO-WAYCLUSTERING:

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Experiments

Ge

ne

s

Colon cancer data (normalized genes)

10 20 30 40 50 60

200

400

600

800

1000

1200

1400

1600

1800

2000

TWO-WAYCLUSTERING:

Two way clustering-ordered

S1(G1)

G1(S1)

TWO-WAY CLUSTERING – TISSUES - S1(G1)

1.IDENTIFY TISSUE CLASSES (TUMOR/NORMAL)

EACH TISSUE = POINT IN 2000 DIMENSIONAL SPACE

2-way clustering - tissues

Ribosomal proteins Cytochrome C

HLA2

metabolism

2-way clustering –genes Erel

TWO-WAY CUSTERING – GENES - G1(S1)

2. FIND DIFFERENTIATING AND CORRELATED GENES EACH GENE = POINT IN 62 DIMENSIONAL SPACE

TWO-WAYCLUSTERING:

Two-way clustering

football

COUPLED TWO-WAY CLUSTERING

C2WC - Motivation

MOTIVATION:

ONLY A SMALL SUBSET OF GENES PLAY A ROLE

IN A PARTICULAR BIOLOGICAL PROCESS; THE

OTHER GENES INTRODUCE NOISE, WHICH MAY

MASK THE SIGNAL OF THE IMPORTANT PLAYERS.

ONLY A SUBSET OF SAMPLES EXHIBIT THE

EXPRESSION PATTERNS OF INTEREST.

SHOULD USE A SUBSET OF GENES TO STUDY A

SUBSET OF THE SAMPLES (AND VICE VERSA)

PROBLEM: ENORMOUS NUMBER OF SUBMATRICES

COUPLED TWO-WAY CLUSTERING

PICK ONE STABLE GENE CLUSTER. REPRESENT

TISSUES BY THE EXPRESSION LEVELS OF THESE

GENES ONLY. ANALYZE ALL TISSUE CLUSTERS

BY USING ALL GENE CLUSTERS, ONE AT A TIME.

LOOK FOR INTERNAL STRUCTURE, SUB-CLUSTERS.

USE ALL STABLE TISSUE CLUSTERS TO CLASSIFY

GENES; IDENTIFY GENE CLUSTERS THAT GOVERN

BIOLOGICAL PROCESSES.

ITERATE THE PROCEDURE UNTIL NO NEW STABLE

CLUSTERS EMERGE

C2WC - method

A

B

A

B

10 20 30 40 50 60

200

400

600

800

1000

1200

1400

1600

1800

2000

COUPLED TWO-WAY CLUSTERING OF COLON CANCER: TISSUES

G4

G12

S1(G4)

S1(G12)

A

B

A

B

10 20 30 40 50 60

200

400

600

800

1000

1200

1400

1600

1800

2000

0 10 20 30 40 50 60

0

10

20

30

40

50

60

COUPLED TWO-WAY CLUSTERING OF COLON CANCER: TISSUES

CTWC colon cancer - tissues

S1(G4)

S1(G12)

0 10 20 30 40 50 60

0

10

20

30

40

50

60

S17

0 10 20 30 40 50 60

0

10

20

30

40

50

60

genes1

S17

G1(S17)

COUPLED TWO WAY CLUSTERING OF COLON CANCER - GENES

USING ONLY THE TUMOR TISSUES TO CLUSTERGENES, REVEALS CORRELATION BETWEEN TWO GENE CLUSTERS; CELL GROWTH AND EPTHELIAL

COLON CANCER - ASSOCIATED WITH EPITHELIAL CELLS

CTWC of colon cancer - genes

G1(S17)G1(S1)

COLON CANCER: 18 PAIRED CARCINOMA/NORMAL 4 PAIRED ADENOMA/NORMALNotterman et al Cancer Res. (2001)

tumor/normal distance matrix

COLON CANCER: 18 PAIRED CARCINOMA/NORMAL 4 PAIRED ADENOMA/NORMALNotterman et al Cancer Res. (2001)

protocol A /protocol B distance matrix

A(II)ScGBM

PrGBMCL

GE

NE

S

S2S3

T

S1(G1)

G12

G5

Coupled Two-Way Clustering (CTWC)

of 358 Genes and 36 Samples

Fig. 2A

GLIOBLASTOMA: M. HEGI et al CHUV, CLONTECH ARRAYS

glioblastoma

AB004904 STAT-induced STAT inhibitor 3

M32977 VEGF

M35410 IGFBP2

X51602 VEGFR1

M96322 gravin

AB004903 STAT-induced STAT inhibitor 2

X52946 PTN

J04111 c-jun

X79067 TIS11B

S11S12

S14

S10

S13S1(G5)

Super-Paramagnetic Clustering of All Samples

Using Stable Gene Cluster G5

Fig. 2B

S1(G5)

G5Ver

LGAAIIIScGBMPrGBMRecPrGBMnew sample

validation

Induction of IGFBPs under Hypoxic Conditions in

Glioblastoma Cell Lines

Fig. 4

IGFBP EXPT

BREAST CANCER DATA (BOTSTEIN/BROWN LAB PEROU ET AL, NATURE 2000)

20 patients before/after chemotherapy. 10 of the “before” samples are in cluster b; all 3 successful treatments’ samples in this group.

Intermediate expression level of the G46 genes may serve as a marker for a relatively high success rate of the doxorubicin treatment

Predicting response to doxorubicin treatment;successful for 3/20 patients

survival S1(G33) Sorlie

BREAST CANCER DATA (BOTSTEIN/BROWN LAB),

Sorlie et al, PNAS (2001)

Cluster (a): high expression levels of the genes of G33,low survival, mutant p53.

predictor of survival.

S1(G36) Sorlie

BREAST CANCER DATA (BOTSTEIN/BROWN LAB),

Sorlie et al, PNAS (2001)

Gene cluster G36 inducesclear partition to two classes of no known clinical interpretation

signature algorithmJ. Ihmels, G. Friedlander,S. Bergmann,O. Sarig, Y Ziv, N. Barkai

((a) Ncore = 37,73,145 genes for ribosomal proteins 132 genes for biosynthesis Each used as input GI

ref, returns (nearly same) gene signature Sref

add Nrand randomly picked genes GI input set of Ncore + Nrand genes, returns gene signatures SI

Recurrence of Sref is measured by Overlap = Fraction of shared genes by Sref and SI

(b) Use as GIref sets of genes with shared regulatory sequences.

Only the truely coregulated ones are returned in Sref; recurrent.

yeast genome: 6400 genes, 1000 “conditions” (chips)

recurrence

pathways

(a) Tricarboxyl acid (TCA) cycle: known genes in E.coli, find (34) homologues in yeast used as GI ; produce SI which excludes the wrong genes and misses only few correct ones(b,c) Identify two autonomous subparts of the cycle