ibm research icahn school of medicine at mt sinai … · j.l. borges: el hacedor, 1960. all models...

Introduction to Systems Biology of Cancer

Lecture 4

Gustavo Stolovitzky

IBM Research

Icahn School of Medicine at Mt Sinai

DREAM Challenges

Classification of cancer

From MIT Course: Statstical

Learning Theory and Applications

Modeling in biological processes of

relevance in cancer

Modeling

"… In that Empire the Art of Cartography was so Perfect that the map of a single province occupied a whole city, and the map of the Empire, a whole Province. With the passing of time, these Huge Maps wouldn't be enough and the Colleges of the Cartographers erected a Map of the Empire that equaled in width the Empire itself…”

J.L. Borges: El Hacedor, 1960.

All models are wrong … but some are useful.

Attributed to George Box

Roles of p53

• Transcription factor

• Central role in defending genomic stability

• Decides on cell cycle arrest and apoptosis

• Implicated in over 50% of cancers

Cell cycle

arrest

p53 is highly regulated

ATM

COP-1 PIRH-2

WIP-1

P38

MAPK

MDM-2

p53

MDM-2

ARF E2F-1

Rb

p21

Cyclin E—cdk-2

SIAH-1

b-catenin

PTEN

AKT

Cyclin G

Cyclin G

PP2A

PIP-3

Bar-Or et al., PNAS, 2000

Reflects population but not single cells

Protein level after irradiation (IR)

p53 – MDM2 auto-regulation

Oscillations are not damped at single cell level

Coordinated oscillations of

P53 and MDM2

Lahav et al., Nature Genetics, 2004

P53 protein

Digital Clock: individual cells

Lahav et al., Nature Genetics, 2004

Digital behavior at single cell level: mean number of pulses

but not the amplitude or frequency depends on input signal.

Fraction of cells with zero, one,

two or more pulses as a function

of -IR dose:

Pulse width and height as a function

of -IR dose:

Digital Clock: individual cells

First pulse Second pulse

Pathways to oscillations

From Ciliberto, Novak, Tyson model, cell-cycle, 2005

p53

MDM-2

PTEN

AKT

PIP-3

Modeling digital behavior

From Ciliberto, Novak, Tyson model, cell-cycle, 2005


p53

MDM-2

Cyclin G

Cyclin G

PP2A


p53

MDM-2

mdm2 rna – transport out of nucleus

MDM2 translation – transport into nucleus

x1

a x2

x3

Xn-1

xn

… a

a

w2

a

l

l l

l

l

a

x

1

x

n w2

l l

w1 (time delay t)

nn /)2(

2

1

w

aaw

?

=

( )2/1

2

wlw

t

n

n

n/1

2

a

waw

l/w

tw

w

l

wltw arcsin

)/(1

22/12

Basic structure of the model

DNA

damage

initiation

& repair

ATM:

DNA

damage

detection

P53-

MDM2

oscillator IR

Cell Cycle

Arrest ,

Apoptosis

and DNA

Repair

?

Modeling digital behavior

• Distribution of initial DSBs ~ Poisson Distribution

• Mean of number of DSBs proportional to IR dose (30-40 Gy-1 cell -1)

Rothkamm & Löbrich, PNAS, 2003 DSB

Repair of double strand breaks (DSBs)

3 min

24 h

• Biphasic repair process: rapid repair of simple lesions + slower repair

of complex lesions

• Two repair mechanisms: NHEJ (Non-Homologous End-Joining) & HR

(Homologous Recombination)

Löbrich et al., PNAS, 1995 Rothkamm et al., MCB, 2003

Two-Lesion-Kinetics (TLK)

• Limiting pool of repair proteins

• DSB-enzyme complexes necessary for DNA damage repair

RP: repair protein (Mre11/Rad50/Nbs1 cmplx)

D: intact DSB

C: DSB-enzyme complex

F: fixed DSB

Model: stochastic TLK of DSB repair

A B C

0 500 1000 15000

5

10

15

20

DS

Bc

Time (min)

a b

0 500 1000 15000

0.2

0.4

0.6

0.8

1

DS

B+

DS

Bc

Time (min)

a b

500 1000 15000

20

40

60

80

His

togra

m o

f C

CP

Time (min)

Implemented using Monte-Carlo method:

CCT: critical crossing times

Remaining DSBs DSB complexes Distribution of CCT

Simulation: DNA repair process

DNA

damage

initiation

& repair

ATM:

DNA

damage

detection

P53-

MDM2

oscillatorIrradiation

Cell Cycle

Arrest and

DNA Repair

?

DNA

damage

initiation

& repair

ATM:

DNA

damage

detection

P53-

MDM2


Cell Cycle

Arrest and

DNA Repair

?

Ataxia telangiectasia mutated (ATM): mutated in disease AT, a human

genetic disorder characterized by neural degeneration, immunodeficiency,

sterility, cancer predisposition, etc.

Basic structure of model

• Dimer in normal cells

• Intermolecular autophosphorylation

• Direct activation by DSBs

• Nucleation formed by DSB and ATM*

Bakkenist & Kastan, Nature 2003

ATM activation

ATMD

kundim

kdim

ATM ATM*

kaf

kar

DSB complex

ATMD

kundim

kdim

ATM ATM*

kaf

kar

DSB complex

Where

ATMD: ATM dimer

ATM : inactive ATM monomer

ATM* : active ATM monomer

2ATMD+ATM+ATM*=ATMT

and C is DSB complex

Model: ATM activation

10 -2

10 -1

10 0

10 1

0

0.2

0.4

0.6

0.8

1

IR dose ( Gy )

Concentr

ation o

f A

TM

*

0 500 1000 1500 0

0.2

0.4

0.6

0.8

1

Concentr

ation o

f A

TM

*

Time (min)

Bakkenist & Kastan, Nature 2003

Time response:

ON-to-OFF signal

Correlation b/w ATM* & IR

1 2 3 4 5 6 7 8 9 10 111

1.5

2

0

0.1

0

.2

0.3

0

.4

0.5

0

.6

0.7

0

.8

0.9

Gy

Normalized by ATMT

n2.2

sim theo

Simulation: Switch like behavior of ATM*

DNA

damage

initiation

& repair

ATM:

DNA

damage

detection

P53-

MDM2


Cell Cycle

Arrest and

DNA Repair

?

DNA

damage

initiation

& repair

ATM:

DNA

damage

detection

P53-

MDM2


Cell Cycle

Arrest and

DNA Repair

?

Basic structure of model

Delay=t

Mech. 1

Mech. 2

Modified p53 – Mdm2 oscillator

Stommel & Wahl, EMBO 2004

2])([22

53

53253

53

5353

53

5353

53

5325353

53

2)](53[

)](53[2

5353

*

*

2222

**

*

53

***

**

535353

2*

*

22

5353

*

MDMKATM

ATMmdmr

dt

dMDM

KTP

TPMDMTPk

KTP

TPATMk

dt

dTP

KTP

TPATMkTPk

KTP

TPMDMTPpr

dt

dTP

mdmKtTP

tTPks

dt

dmdm

psdt

dp

a

MDMMDMMDMMDM

dTPrp

p

fp

p

fprp

d

TPTPTP

mdmnn

n

mdmmdm

pp

t

t

mRNA: p53, mdm2

Protein: TP53 (inactive), TP53* (active / phosphorylated), MDM2

n=4

p53 – Mdm2 oscillator: equations

Lahav et al., Nature

Genetics 2004

0 500 1000 15000

1

2

3

4

5

TP53

mdm2

MDM2

Time (min)

Mo

lecula

r co

nce

ntr

atio

n (

nM

)

0

20

40

60

80

100

0 1 2

Number of pulses

Pe

rce

nta

ge

of ce

lls 10 Gy

5 Gy

2.5 Gy

0.3 Gy

0 Gy

0 1 2+0

20

40

60

80

100

Number of pulses

Pe

rce

nta

ge

of

ce

lls (

%)

0 500 1000 15000

1

2

3

4

5

Time (min)Mo

lecula

r co

nce

ntr

atio

n (

nM

)

TP53

mdm2

MDM2

0 500 1000 15000

1

2

3

4

5

Time (min)Mo

lecula

r co

nce

ntr

atio

n (

nM

)

TP53

mdm2

MDM2

A B

C D

Mole

cula

r in

ten

sity (

fold

)

Predict drop of MDM2 at the

beginning of time course

0

1

2

3

4

5

0 100 200 300 400 500 600

MD

M2

Time (min)

MDM2

0 15’30’1h 2h 3h 4h 5h 6h 7h 8h 10h

Experiment

Time (min)

Response to 5Gy

Complete Model Results

0 500 1000 15000

1

2

3

4

5

Time (min)

Mole

cula

r in

ten

sity (

fold

)

TP53

mdm2

MDM2

0 500 1000 15000

1

2

3

4

5

Time (min)

Mole

cula

r in

ten

sity (

fold

)

TP53

mdm2

MDM2

0 500 1000 15000

1

2

3

4

5

Time (min)

Mole

cula

r in

ten

sity (

fold

)

TP53

mdm2

MDM2

Stochasticity in oscillation: IR of 5 Gy

induces one, two or three oscillations

Note: molecular intensity is

normalized by respective

basal concentration.


Lahav et al., Nature

Genetics 2004

Number of pulses increases as IR dose increases

Less stochasticity than experiment


0

20

40

60

80

100

0 1 2

Number of pulses

Pe

rce

nta

ge

of

ce

lls

Number of pulses

Perc

enta

ge o

f cells

(%

)

0 1 2+0

20

40

60

80

1000 Gy

0.3 Gy

2.5 Gy

5 Gy

10 Gy

*

0 2 4 6 8 10 120

100

200

300

400

500

600

Irradiation dose (Gy)

Period (

min

)

0 2 4 6 8 10 120

100

200

300

400

500

600


Period (

min

)

0 2 4 6 8 10 120

0.5

1

1.5


Puls

e h

eig

ht

0 2 4 6 8 10 120

0.5

1

1.5

Irradiaiton dose (Gy)

Puls

e h

eig

ht

* *

A B

C D

Period as function of IR dose:

Pulse height as function of IR dose:

Digital behavior

Pulse width and height as a function of

-IR dose:

P53

GAPDH

0 15’30’1h 2h 3h 4h 5h 6h 7h 8h 10h

Simulation

Simulating a cell population

P53

Mdm2

Fo

ld c

ha

ng

e

0

3

6

9

12

15

0 100 200 300 400 500 600

Time (min) 0 500 1000 1500 2000

0

1

2

3

4

5

Time (min)Mole

cula

r concentr

ation (

nM

)

p53 with PS

Mdm2 with PS

p53 no PS

Mdm2 no PSF

old

ch

an

ge

Lahav et al., Nature Genetics 2004

0 500 1000 15000

1

2

3

4

5

TP53

mdm2

MDM2

Time (min)

Mole

cula

r concentr

ation (

nM

)

0

20

40

60

80

100

0 1 2

Number of pulses

Pe

rce

nta

ge

of

ce

lls 10 Gy

5 Gy

2.5 Gy

0.3 Gy

0 Gy

0 1 2+0

20

40

60

80

100

Number of pulses

Perc

enta

ge o

f cells

(%

)

0 500 1000 15000

1

2

3

4

5

Time (min)Mole

cula

r concentr

ation (

nM

)

TP53

mdm2

MDM2

0 500 1000 15000

1

2

3

4

5

Time (min)Mole

cula

r concentr

ation (

nM

)

TP53

mdm2

MDM2

A B

C D

Mole

cula

r in

ten

sity (

fold

)

Time (min)

Response to 5Gy

DNA

damage

Digital response of tumor suppressor p53 to

IR

Ma, Wagner, Rice, Hu, Levine and Stolovitzky, A plausible model for

the digital response of p53 to DNA damage, Proc. Natl. Acad. Sci. U S A.

102, 14266 (2005).

Wagner; Ma; Rice; Hu; Levine; Stolovitzky, p53-Mdm2 loop

controlled by a balance of its feedback strength and effective dampening

using ATM and delayed feedback, IEE PROCEEDINGS SYSTEMS

BIOLOGY, 152, 3, 109-118 (2005).

Predictions

Basal

Protein

(Fast)

(Slow) ATM*

mRNA

p 53

P53-induced

transcription

53 p

DNA

Mdm2

DNA

Mdm2

Protein

Protein

p53

p53*

Delayt1

Basal

mRNA

Mdm2

Delayt2

Figure 4 (From Ma, Wagner et.al.) - Diagram of the

p53-Mdm2 oscillator. p53 is translated from p53

mRNA and inactive for induction of its targets.

Phosphorylated by ATM*, p53 becomes active (p53*),

and able to transcribe (after a time delay) Mdm2 which

also has a basal transcription rate. Mdm2 protein

promotes a fast degradation of p53 and a slow

degradation of p53*. In addition to a basal self-

degradation, Mdm2 is degraded by a mechanism

stimulated by ATM*.

Figures 4 and 8 from Ma, Wagner et al.,

A B

Figure 8 (From Ma, Wagner, et. al.) - One-

dimensional bifurcation diagrams of steady-state

p53 versus single parameter variation of Mdm2

basal transcription rate (A) or p53 basal

transcription rate (B). The stable equilibrium is

represented by solid line. The lower and upper

bounds of stable oscillation are represented by

paired dotted lines.

0 2 4 6 80

5

10

15

20

25

30

p5

3 c

on

ce

ntr

atio

n (

fold

)

equilibrium

oscillation

p53 basal transcription (fold)0 1 2 3

0

2

4

6

8

mdm2 basal transcription (fold)

p53 c

oncentr

atio

n (

fold

)

equilibrium

oscillation

Specific Predictions About Bifurcations

0 1 2 30

2

4

6

8


p53 c

oncentr

atio

n (

fold

)

equilibrium

oscillationA

0 2 4 6 80

5

10

15

20

25

30

p5

3 c

on

ce

ntr

atio

n (

fold

)

equilibrium

oscillation

p53 basal transcription (fold)

B

Fig. 8 of Ma et al., PNAS, 2005

P53 b

asal tr

anscription

Mdm2 basal transcription

Low High

Lo

w

Hig

h

Oscillatory region

Non-oscillatory region

WP

Mdm2 SNP309: T → G SNP Increases Mdm2

•Quantitative data at cellular level

explained by a point mutation.

•T → G increases affinity for Sp1

•MCF-7 cell line is T/G

•SNP status correlates with cancer risk

Bond et al, Cell, 2004.

Frequency

T/T 48%

G/T 40%

G/G 12%

T/T T/G G/G

Mdm2

mRNA

1X 8X

Mdm2

Protein

1X 2X 4X

Predictions T/T & T/G Oscillate, G/G Does Not P

53 b

asal tr

anscription


Low High

Lo

w

Hig

h

Oscillatory region


0 1 2 30

2

4

6

8


p53

conc

entra

tion

(fold

)

equilibrium

oscillation

T/T

1X

T/G

2X

G/G

4X

T/T

1X

T/G

2X G/G

4X

T/T & T/G Cell Lines H460 and MCF-7 Oscillate

T/T

T/G

Cells wild type (T/T, H460) or heterozygous (T/G, MCF-7) for SNP309

oscillate in response to 5Gy IR.

NB: First p53 peak at 2 hours, second peak at 7 to 8 hours.

G/G Cell Lines A875 and Manca Do Not Oscillate

Two cell lines homozygous (G/G) for SNP309 do NOT oscillate in response to

5Gy IR.

Manca A875

NB: p53 peaks at 10 to 12 hours.

Model Predicts Hopf Bifurcations WRT p53 Production P

53 b

asal tr

anscription


Low High

Lo

w

Hig

h

Oscillatory region


0 2 4 6 80

5

10

15

20

25

30

p5

3 c

on

ce

ntr

atio

n (

fold

)

equilibrium

oscillation

p53 basal transcription (fold)

Oscillations Require Intermediate p53 Production Rates

P53-null H1299-SW24 cells expressing p53 under tetracycline-

dependent promoter.

0 2 4 6 8 10 120

0.5

1

1.5

2

2.5

3

Re

lative

in

du

ction

fo

ld o

f M

dm

2

0 2 4 6 8 10 120

1

2

3

4

5

Re

lative

in

du

ction

fo

ld o

f p

53

h

h h

h

Low Tetracycline

High P53

Medium Tetracycline

Medium P53

High Tetracycline

Low P53

p53 Mdm2

Experi

ment

Model

ibm research icahn school of medicine at mt sinai … · j.l. borges: el hacedor, 1960. all models...

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