How cells make decisions?

The cell is a (bio)chemical computer

InformationProcessing System

Hanahan & Weinberg (2000)

Externalsignals

outputs

? ?

Signal transduction networks

Hanahan & Weinberg (2000)

p21

Smad

MAPK

MKK

MAPK-P

PP

‘Birth control’ for proteins

d [protein] dt

= synthesis - degradation

DNA

RNA

protein

transcriptionfactor

transciption

translation

Gene expression

R

S

k1 k2

S = mRNAR = protein

0

0.5

0 1 2 3

resp

on

se (

R)

signal (S)

linear

Rss = k1

. Sk2

dRdt = k1

. S – k2 . R

synthesis degradation

0

5

0 0.5 1

S=1

3

2

R

rate

(d

R/d

t)

degradation

synthesis

Signal-responsecurve

Protein phosphorylation-dephosphorylation

Michaelis-Menten enzyme kinetics

][][]][[][

11 ESkESkSEkdt

ESdcat

since [Eo] = [E] + [ES]

0][][]])[[]([][

11 ESkESkSESEkdt

ESdcato

][

]][[][

1

1 Sk

kkSE

EScat

o

][

][

][

]][[][

][ max

1

12 SK

SV

Sk

kkSEk

ESkdt

PdV

Mcat

ocat

Protein phosphorylation

R

S

RP

ATP ADP

H2OPi

k1

k2

0

0.5

1

0 1 2 3

resp

on

se (

RP

)

signal (S)

sigmoidal

PR

m2K

PR

2k

PR

TR

m1K

)P

RT

S(R1

k

dtP

dR

phosphorylationdephosphorylation

R 01

0

1

2

0 0.5 1

rate

(d

RP

/dt)

0.25

0.5

1

1.5

2

RP

dephospho-rylation

phospho-rylation

‘Buzzer’

zero order ultrasensitivityGoldbeter & Koshland, 1981

Signal-responsecurve

graded and reversible

Multiple phosphorylation

........ Rpk

RPpk

RP Rpk

RP 2

2

2

.....) KKR(1RPRPRR 22T ....

R RP RP2 RPn……k

p

k

p

2T

22

22T

2T

KK1RK

RKRP KK1

RKRKRP

KK1R

R

for n=2

where K=k/p

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

n=2

R

RP2

K=k/p

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

n=3

R

RP3

K=k/p

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

n=4

R

RP4

K=k/p

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

55

5

5 KJK

RP

K=k/p

Hill equation:

Multiple phosphorylation

Coupling of modules

PerfectadaptationX

4kS

3k

dtdX

R X2

kS1

kdtdR

0.9

1.4

1.9

0 10 20

-1

0

1

2

3

4

5

S

X

R

time

adapted

3k

2k

4k

1k

ssR 4

k

S3

kssX

R

S X

k1 k2

k3

k4

Two linear modules

0

5

0 1 2R

rate

(d

R/d

t)

1

3

2

synthesis

degr

adat

ion

Response isindependent

of Signal

Feed-forward loop

S

R

X+

+

-

S

R

X-

+

+

R increases for S increaseR decreases for S decrease

R decreases for S increaseR increases for S decrease

Feed-forward loop with two buzzers

X

XARAR

+

+

S

RAS

XA

Cock and fire

R’ R

Sk1

k2

k3k0

Another way to get perfect adaptation

RkRkR'SkdtRd

RkR'SkkdtR'd

321

210

0RkkdtRd

dtR'd

30

3

0

kk

R

R’ R

Sk1

k2k3

k0

RkR'SkdtRd

R'kRkR'SkkdtR'd

21

3210

0R'kkdtRd

dtR'd

30

3

0

kk

'R

The same principle, different deployment

swimming(counter-clockwise)

tumbling(clockwise)

Bacterial chemotaxis

Bacterial chemotaxis

Feedback controls

0

0.5

0 10

resp

on

se (

R)

signal (S)

mutual activation

R

S

EP E

k1

k0

k2

k3

k40

0.1

0.2

0.3

0.4

0.5

0.6

0 0.5R

rate

(d

R/d

t)

08

16

synth

esi

sde

grad

atio

n

Linear module & buzzer

Protein synthesis: positive feedback

‘Fuse’

0

0.5

1

0 1 2

resp

on

se (

R)

signal (S)

Scrit2

Scrit1

‘Toggle’switch

bistability

closed

open

Example: Fuse

0

0.5

0 10

resp

on

se (

R)

signal (S)

dying

Apoptosis(Programmed Cell

Death)

living

The lac operon(‘toggle’ switch)

S (extracellular lactose)

R

S

EP E

k1

k0

k2

k3

k4

R (intracellular lactose)

EP

Nature 427, 737 - 740 (19 February 2004)

Multistability in the lactose utilization network of Escherichia coli

ERTUGRUL M. OZBUDAK1,*, MUKUND THATTAI1,*, HAN N. LIM1, BORIS I. SHRAIMAN2 & ALEXANDER VAN OUDENAARDEN1

Initially uninduced cells grown for 20 hrs in 18 M TMG

Initially uninduced cells (lower panel) and induced cells (upper panel) grown in media containing different concentration of TMG

TMG = thio-methylgalactoside

‘Death control’ for proteins

d [protein] dt

= synthesis - degradation

proteasome

degradedprotein

ubiquitilationsystem

0

0.5

1

0 1 2

resp

on

se (

R)

signal (S)

mutual inhibition

Linear module & buzzer

R

S

EP E

k1

k0

k2

k3

k4

k2'

Protein degradation: mutual inhibition

0

0.05

0.1

0 0.5 1 1.5

R

rate

(d

R/d

t)

0.6

1.2

1.8

synthesisde

grad

atio

n

Oscillators:three modules

0 1

0

1

2

3

X

R

PhasePlane

0.0 0.1 0.2 0.3 0.4 0.5

0

1

2

resp

on

se (

R)

signal (S)

Scrit1 Scrit2

Positive and negative feedback oscillations (activator-inhibitor)

R

S

EP E

X

k0

k1

k2

k2'

k3

k4

k5 k6

p53

Mdm2p53-CFP and Mdm2-YFPlevels in the nucleusafter -irradiation

Period of oscillation: 440 100 min

0 50

1

X

R

0.0 0.5

0

1

resp

on

se (

R)

signal (S)

Scrit1 Scrit2

R

S

EP E

Xk1

k2

k3

k4

k0'

k0

Positive and negative feedback oscillations (substrate depletion)

Negative feedback and oscillation

S

X

Y YP

R RP(1)

k0

k1 k2

(2)

k2'

k3

k4

k5

k6

0

5

0 25 50

0

0.5

1

time

XYP

RP

0 2 4 6

0.0

0.1

0.2

0.3

0.4

0.5

resp

on

se (

RP)

signal (S)

Scrit2Scrit1

R

S

E EP

Negative feedback and homeostasis

k0

k3

k4

k2

0

0.5

1

0 1 2signal (S)

homeostatic

resp

on

se (

R)

0

0.5

1

0 0.5 1

rate

(dR

/dt)

R

0.5

11.5

productionremoval

Typical biosynthetic pathway

protein

demand

aminoacid