how cells make decisions?
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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
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