How cells make decisions?
The cell is a (bio)chemical computer
outputs
External
signals
Information
Processing
System
Hanahan & Weinberg (2000)
?
?
Signal transduction networks
Smad
p21
MKK
MAPK
MAPK-P
PP
Hanahan & Weinberg (2000)
‘Birth control’ for proteins
DNA
transcription
factor
transciption
RNA
translation
protein
d [protein]
= synthesis - degradation
dt
Gene expression
S = mRNA
R = protein
R
k2
rate (dR/dt)
k1
3
2
S=1
synthesis
0
0
dR
= k 1 . S – k2 . R
dt
synthesis
degradation
response (R)
S
linear
degradation
5
0.5
k1 . S
Rss =
k2
R
0.5
0
1
0
1
2
signal (S)
Signal-response
curve
3
Protein phosphorylation-dephosphorylation
Michaelis-Menten enzyme kinetics
d [ ES ]
 k1[ E ][ S ]  k 1[ ES ]  kcat [ ES ]
dt
since [Eo] = [E] + [ES]
d [ ES ]
 k1 ([ Eo ]  [ ES ])[ S ]  k 1[ ES ]  kcat [ ES ]  0
dt
[ ES ] 
V
[ Eo ][ S ]
k 1  k cat
 [S ]
k1
k [ E ][ S ]
V [S ]
d [ P]
 k 2 [ ES ]  cat o
 max
k 1  kcat
dt
 [S ] K M  [S ]
k1
Protein phosphorylation
Signal-response
curve
2
k1
R
k2
Pi
RP
2
1.5
1
1
dephosphorylation
phosphorylation
0.5
H 2O
sigmoidal
1
response (RP)
ADP
ATP
rate (dRP/dt)
S
0.25
0.5
0
0
0
1
dR
k S(R  R )
k R
P 1
T P  2 P
dt K  R  R K  R
m1 T P m2 P
phosphorylation dephosphorylation
0.5
R
RP
1
0
1
2
signal (S)
3
0
‘Buzzer’
graded and reversible
zero order ultrasensitivity
Goldbeter & Koshland, 1981
Multiple phosphorylation
R
k
p
k
RP  R
p
RP
k
p
RP2
RPn
……
k
k2
RP2  RP  2 R ........
p
p
RT  R  RP  RP2  ....  R(1  K  K2  .....)
where K=k/p
for n=2
RT
R
1  K  K2
K  RT
RP  K  R 
1  K  K2
K 2  RT
RP2  K  R 
1  K  K2
2
Multiple phosphorylation
n=2
1
RP2
0.8
RP3
0.8
0.6
0.6
0.4
0.4
R
0.2
n=3
1
R
0.2
0
0
0
2
4
6
8
K=k/p
10
1
0.8
4
6
8
10
Hill equation:
0.8
RP4
0.6
0.6
0.4
0.4
R
0.2
2
K=k/p
n=4
1
0
K5
RP5  5
J  K5
0.2
0
0
0
2
4
6
8
K=k/p
10
0
2
4
6
8
K=k/p
10
Coupling of modules
Two linear modules
k4
X
k1
R
rate (dR/dt)
1.9
k3
S
adapted
synthesis
3
5
4
S
R
3
5
2
X
2
1.4
1
1
k2
0
0
0.9
0
dR  k S  k X R
2
dt 1
dX  k S  k X
4
dt 3
R
1
Response is
independent
of Signal
kk
Rss  1 4
k k
23
k S
Xss  3
k
4
2
-1
0
10
time
Perfect
adaptation
20
Feed-forward loop
S
S
+
X
+
R
-
R increases for S increase
R decreases for S decrease
+
X
-
R
+
R decreases for S increase
R increases for S decrease
Feed-forward loop with two buzzers
X
S
+
XA
R
+
RA
Cock and fire
RA
S
XA
Another way to get perfect adaptation
k0
R’
k1
dR'
 k0  k1 S R'  k2 R 
dt
dR 
 k1 S R'  k2 R   k3 R 
dt
dR' dR

 k0  k3 R  0
dt
dt

k0
R 
k3
S
k2
R
k3
The same principle, different deployment
k0
k3
dR'
 k0  k1 S R'  k2 R   k3 R'
dt
dR 
 k1 S R'  k2 R 
dt
dR' dR

 k0  k3 R'  0
dt
dt
 
k0
R' 
k3
R’
k1
S
k2
R
Bacterial chemotaxis
swimming
(counter-clockwise)
tumbling
(clockwise)
Bacterial chemotaxis
Feedback controls
Linear module & buzzer
k0
EP
rate (dR/dt)
S
k1
16
8
0
0.6
k2
R
k3
E
k4
0.5
0.4
0.3
0
R
response (R)
0.5
bistability
1
‘Toggle’
switch
Scrit1
Scrit2
0
1
signal (S)
0.5
0.1
0
0
mutual activation
0.2
0
0.5
response (R)
Protein synthesis: positive feedback
2
0
10
signal (S)
‘Fuse’
response (R)
Example: Fuse
dying
0.5
0
0
10
signal (S)
Apoptosis
(Programmed Cell Death)
The lac operon
(‘toggle’ switch)
S
k1
k0
EP
k2
R
k3
k4
S (extracellular lactose)
E
EP
R (intracellular
lactose)
Multistability in the lactose utilization network of Escherichia coli
ERTUGRUL M. OZBUDAK1,*, MUKUND THATTAI1,*, HAN N. LIM1, BORIS I. SHRAIMAN2 & ALEXANDER VAN OUDENAARDEN1
Nature 427, 737 - 740 (19 February 2004)
Initially uninduced cells grown
for 20 hrs in 18 M TMG
TMG = thio-methylgalactoside
Initially uninduced cells (lower panel)
and induced cells (upper panel) grown
in media containing different
concentration of TMG
‘Death control’ for proteins
d [protein]
= synthesis - degradation
dt

ubiquitilation
system

proteasome
degraded
protein
Linear module & buzzer
k1
k0
EP
k2
R
k2'
k4
k3
0.1
1.8
response (R)
S
rate (dR/dt)
Protein degradation: mutual inhibition
1.2
0.05
mutual inhibition
0.5
0.6
synthesis
E
1
0
0
0
0.5
R
1
1.5
0
1
signal (S)
2
Oscillators:
three modules
PhasePlane
k5
S
k1
k0
EP
k2'
2
R
Scrit1
Scrit2
2
1
k2
k3
k4
k6
X
R
3
response (R)
Positive and negative feedback oscillations (activator-inhibitor)
1
E
0
0
X
1
0
0
.
0
0
.
1
0
.
2
0
.
3
0
.
4
signal (S)
0
.
5
p53
p53-CFP and Mdm2-YFP
levels in the nucleus
after -irradiation
Mdm2
Period of oscillation: 440  100 min
Positive and negative feedback oscillations (substrate depletion)
Scrit1
k1
X
k0'
k0
EP
k2
R
response (R)
S
1
R
k3
k4
Scrit2
1
E
0
0
X
5
0
0
.
0
signal (S)
0
.
5
S
X
5
k1
k0
Y
X
k3
k4
R
YP
1
k2
k2'
YP
k5
k6
response (RP)
Negative feedback and oscillation
5
.
0
Scrit1
Scrit2
4
.
0
3
.
0
0.5
(2)
2
.
0
RP
RP
1
.
0
(1)
0
0
0
25
time
50
0
.
0
0
2
4
signal (S)
6
Negative feedback and homeostasis
S
k4
k3
k2
EP
1.5
production
removal
1
1
0.5
0.5
0
0
0.5
R
1
1
homeostatic
response (R)
E
R
rate (dR/dt)
k0
0.5
0
0
1
signal (S)
2
Typical biosynthetic pathway
aminoacid
demand
protein