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

onse

(R)

signal (S)

linear

Rss = k1 . S

k2

dRdt = k1 . S – k2

. R

synthesis degradation

0

5

0 0.5 1

S=1

32

R

rate

(dR

/dt) degradation

synthesis

Signal-responsecurve

Protein phosphorylation-dephosphorylation

Michaelis-Menten enzyme kinetics

][][]][[][11 ESkESkSEk

dtESd

cat

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

0][][]])[[]([][11 ESkESkSESEk

dtESd

cato

][

]][[][

1

1 SkkkSEES

cat

o

][][

][

]][[][][ max

1

12 SK

SV

Skkk

SEkESkdtPdV

Mcat

ocat

Protein phosphorylation

R

S

RP

ATP ADP

H2OPi

k1

k2

0

0.5

1

0 1 2 3

resp

onse

(RP

)

signal (S)

sigmoidal

PRm2KPR2k

PRTRm1K)PRTS(R1k

dtPdR

phosphorylationdephosphorylation

R 01

0

1

2

0 0.5 1

rate

(dR

P/dt

)

0.250.5

1

1.5

2

RP

dephospho-rylation

phospho-rylation

‘Buzzer’

zero order ultrasensitivityGoldbeter & Koshland, 1981

Signal-responsecurve

graded and reversible

Multiple phosphorylation

........ RpkRPp

kRP RpkRP 2

2

2

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

R RP RP2 RPn……kp

kp

2T

22

22T

2T

KK1RKRKRP KK1

RKRKRP KK1RR

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 KJKRP

K=k/p

Hill equation:

Multiple phosphorylation

Coupling of modules

PerfectadaptationX4kS3kdt

dX

R X2kS1kdtdR

0.9

1.4

1.9

0 10 20-1

0

1

2

3

4

5

S

X

R

time

adapted

3k2k4k1kssR

4kS3kssX

R

S X

k1 k2

k3

k4

Two linear modules

0

5

0 1 2R

rate

(dR

/dt)

1

3

2

synthesis

degra

datio

nResponse 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

XA RAR

+

+

S

RAS

XA

Cock and fire

R’ RS

k1

k2

k3k0

Another way to get perfect adaptation

RkRkR'SkdtRd

RkR'SkkdtR'd

321

210

0RkkdtRd

dtR'd

30

3

0kkR

R’ RS

k1

k2k3

k0

RkR'SkdtRd

R'kRkR'SkkdtR'd

21

3210

0R'kkdtRd

dtR'd

30

3

0kk'R

The same principle, different deployment

swimming(counter-clockwise)

tumbling(clockwise)

Bacterial chemotaxis

Bacterial chemotaxis

Feedback controls

0

0.5

0 10

resp

onse

(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

(dR

/dt)

0816

synt

hesis

degra

datio

n

Linear module & buzzerProtein synthesis: positive feedback

‘Fuse’

0

0.5

1

0 1 2

resp

onse

(R)

signal (S)

Scrit2

Scrit1‘Toggle’switch

bistability

closed

open

Example: Fuse

0

0.5

0 10

resp

onse

(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 proteinsd [protein] dt = synthesis - degradation

proteasome

degradedprotein

ubiquitilationsystem

0

0.5

1

0 1 2

resp

onse

(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

(dR

/dt)

0.6

1.2

1.8

synthesisde

grada

tion

Oscillators:three modules

0 10

1

2

3

X

R

PhasePlane

0.0 0.1 0.2 0.3 0.4 0.50

1

2

resp

onse

(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 0.50

1

resp

onse

(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

k4k5

k6

0

5

0 25 500

0.5

1

time

XYP

RP

0 2 4 60.0

0.1

0.2

0.3

0.4

0.5

resp

onse

(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

onse

(R)

0

0.5

1

0 0.5 1

rate

(dR/

dt)

R

0.5

11.5 production

removal

Typical biosynthetic pathway

protein

demand

aminoacid