Humboldt- Universität zu Berlin Edda Klipp Systembiologie 9 – Signal Transduction Sommersemester...
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Transcript of Humboldt- Universität zu Berlin Edda Klipp Systembiologie 9 – Signal Transduction Sommersemester...
Humboldt-Universität
zu Berlin
Edda Klipp
Systembiologie 9 – Signal Transduction
Sommersemester 2010
Humboldt-Universität zu BerlinInstitut für BiologieTheoretische Biophysik
Humboldt-Universität
zu Berlin
Modeling of Signal Transduction
Before: Metabolismus - Mass transferNow: Signal transduction - Information transfer
Typical Signals:• Hormones, pheromones• Heat, cold, osmotic pressure• concentration of certain substances (K, Ca, cAMP,..)• nutrient availability
http://www.bio.davidson.edu/courses/Immunology/Flash/MAPK.html
Interactive Animation of MAP Kinase Signal Transduction
http://www.idp.mdh.se/personal/bfg02/forskning/quasi/quasi12.htmlwww.apple.com/quicktime
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Typical Mechanism“Signal”
Activation of receptor at membran
Internalization of signalsG-Protein, Phosphorelay
Signal transmission
Activation of transcription factors
Transcription,Translation,Protein function biochemical response
Gen
mRNA Protein
Downregulation of signal
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Yeast Signaling Pathways
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Signaling Pathway Components
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Rezeptors
• transmembrane • receive signal and transmit it• conformation change• active or inactive form
Simple concept:
H + R HR
KD = H R HR
.
H - HormoneR - ReceptorHR - Hormone-receptor-complex
Typical values :KD = 10-12 M ….10-6 M
Ligand
Extrazellular space
Intrazellular space
Membrane
Receptor,Binding site
Rezeptor,zytosolische Domaine
inactive active
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Receptor, Extended Model
Ri Rs Ra
L
vis
vsi
vsa
vas
vpi
vdivai
vps
vds vda
aisiisdipii vvvvvRdt
d
assasiisdspss vvvvvvRdt
d
aiassadaa vvvvRdt
d
xxyxy Rkv
LRkv ssasa
nb
nb
ssasaLK
LKRkv
1
Differential equationsRate expressions ??
Mass action
Hill kinetics
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Receptor, Model of Yi et al.
Ri Rs Ra
L
vis
vsi
vsa
vas
vpi
vdi vai
vps
vds vda
0 10 20 30
0
2000
4000
6000
8000
10000
Time
Rs
Ra
Num
ber
of
Mol
ecul
es
0iR
0 ** ii vv
-1s cellper molecules 4pskpsps kv
sdsds Rkv
adada Rkv
LRkv ssasa
aasas Rkv
14 s104 dsk
13 s104 dak
116 sM102 sak
12 s101 ask
+L
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G-Proteine: „small G-proteins“
21
21
vvRasdt
d
vvRasdt
d
GTP
GDP
RasRasRas GTPGDPtotal
Differential equationsConservation relations
GDP GTP
GTPGDP+ +
z.B. Ras-Protein
GDPRas GTPRas
GDPGTPGEF
GAPPi
v1
v2
GEF – Guanine nucleotide exchange factorGAP – GTPase-activating protein
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G-Proteine: „small G-proteins“
e.g. Ras-Protein
GDPRas GTPRas
GDPGTP
GEF
GAPPi
v1
v2
GAPRaskv
GEFRaskv
GTP
GDP
22
11
GAPkGEFk
GEFkRasRas total
GTP
21
1
2 4 6 8 10
0.2
0.4
0.6
0.8
1
0.5 1 1.5 2
0.2
0.4
0.6
0.8
1
RasK
RasGAPkv
RasK
RasGEFkv
GTPm
GTP
GDPm
GDP
2
22
1
11
GT
PR
asG
TPR
as
GAP
GEF
GAP
GEF
21
21
vvRasdt
d
vvRasdt
d
GTP
GDP
RasRasRas GTPGDPtotal
Differential equations
1121 totalRaskk ;
111 2121 mmtotal KKRaskk ;;
Mass action
Michaelis Menten
GEF or GAP =1 (const.), other varying from 0 to 10
Enzyme concentration
Enzyme concentration
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G-Proteins: „small G-proteins“
21
21
vvRasdt
d
vvRasdt
d
GTP
GDP
RasRasRas GTPGDPtotal
Differential equations
e.g. Ras-Protein
GDPRas GTPRas
GDPGTP
GEF
GAPPi
v1
v2
0.5 1 1.5 2
0.2
0.4
0.6
0.8
1
RasK
RasGAPkv
RasK
RasGEFkv
GTPm
GTP
GDPm
GDP
2
22
1
11
GT
PR
as
GEF
GAP
„sigmoidal dependence“
„Ultrasensitivity“
„Switch-like regulation“
0.5 1 1.5 2
0.2
0.4
0.6
0.8
1
01021 . mm KK
1021 mm KK
GT
PR
as
Enzyme: GEF
Enzyme concentration111 2121 mmtotal KKRaskk ;;
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G-Proteins: „small G-proteins“
e.g. Ras-Protein
GDPRas GTPRas
GDPGTP
GEF
GAPPi
v1
v2
RasK
RasGAPkv
RasK
RasGEFkv
GTPm
GTP
GDPm
GDP
2
22
1
11
0.5 1 1.5 2
0.2
0.4
0.6
0.8
1
01021 . mm KK
1021 mm KK
GT
PR
as
Enzym: GEF
010
11
21
21
.
;;
mm
total
KK
Raskk
GT
PR
as
Zeit
GEF: 0 x
2 4 6 8 10
0.2
0.4
0.6
0.8
1
x=0.5
x=1.0
x=1.5
x=2.5x=2.0
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G-Protein
GDPG
GTPG
GDPG
GDP
activereceptor
Pi
signalG
Pi
slow fast
RGS
GTP
vga
vh1vh0
vsr
srga vvGdt
d
10 hhga vvvGTPGdt
d GDPGGTPGGGt
GGGtotal
0 10 20 30
0
2000
4000
6000
8000
10000
Time
G
Num
ber
of
Mol
ecul
es
G
GDPG
GTPG
Differential equationsConservation relations
GDP
GTP
+
GDP
+
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Phosphorelay-System
AspHis
Sln1 ATP
ADP
Pii
Ypd1
Ssk1-P
Pi
Pi
Pi
high osmolarity
?
Ypd1-P
Ssk1
Asp
12
3
4
5
Example: Sln1 pathway, Phosphorelay system
His
Asp
1111 31 YpdPASlnkSlnkSlndt
d
PHSlnkSlnkPHSlndt
d 111 21
1111 32 YpdPASlnkPHSlnkPASlndt
d
11111 34 YpdPASlnkSskPYpdkYpddt
d
11111 34 YpdPASlnkSskPYpdkPYpddt
d
1111 45 SskPYpdkPSskkSskdt
d
1111 45 SskPYpdkPSskkPSskdt
d
PASlnPHSlnSlnSln total 1111
PYpdYpdYpd total 111
PskSSskSsk total 111
- Transmits individual phosphate groups
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Phosphorelay-System
total
total
total
CCPC
BBPB
AAPA
CPkBPCkCdt
d
CBPkAPBkBdt
d
BAPkATPAkAdt
d
43
32
21
0 1 2 3 4 5
k1
0.2
0.4
0.6
0.8
1
A, B
, C
A-P A
ADP ATP
B B-P
C-P CP
k1
k2
k3
k4
Three component system
Two components
One component
0 50 100
0.02
0.04
0.06
0.08
0.1
Time
Dependence ofsteady state valuesOf stress strength
Temporal behavior,Stress – no Stress
A, B
, C
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Phosphorelay-System
B
C-P
B-P
C
v3
v4
A-P Av2
v1
0 100 200 300 400 500 600
0
0.2
0.4
0.6
0.8
1.
0.001 0.01 0.1 1. 10.
0
0.2
0.4
0.6
0.8
1.
Co
nce
ntr
atio
n C
Co
nce
ntr
atio
n,
a.u
.
Rate constant k4
Time a.u.
k1=10
k1=10.10.010.001
C
BA
Dynamics
Steady State
total
total
total
CCPC
BBPB
AAPA
CPkBPCkCdt
d
CBPkAPBkBdt
d
BAPkATPAkAdt
d
43
32
21
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MAP Kinase Cascade= Mitogen activated protein kinase cascade
MAPKKKK
MAPKKKinactive
MAPKKKactive
MAPKKinactive
MAPKKactive
MAPKinactive
MAPKactive
Signal
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MAP Kinase Cascade - Equations
ATPMAPKKKPkATPMAPKKKKMAPKKKkMAPKKKPdt
d
MAPKKKPkATPMAPKKKKMAPKKKkMAPKKKdt
d
21
41
MAPKKPPkATPMAPKKKPMAPKKPkMAPKKPPdt
d
MAPKKPkMAPKKPPkATPMAPKKKPMAPKKPkATPMAPKKKPMAPKKkMAPKKPdt
d
MAPKKPkATPMAPKKKPMAPKKkMAPKKdt
d
86
8765
85
MAPKPPkATPMAPKKPPMAPKPkMAPKPPdt
d
MAPKPkMAPKPPkATPMAPKKPPMAPKPkATPMAPKKPPMAPKkMAPKPdt
d
MAPKPkATPMAPKKPPMAPKkMAPKdt
d
1110
1211109
109
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MAP Kinase Cascade - Equations
totaltotal
totaltotal
totaltotal
MAPKKKCCPPCPC
MAPKKKBBPPBPB
MAPKKKAAPPAPA
CPPpBPPCPkCPPdt
d
CPpBPPCkCdt
d
BPPpAPBPkBPPdt
d
BPpAPBkBdt
d
APPpAPkAPPdt
d
APpSAkAdt
d
k – Kinase, p - Phosphatase Steady state
101234
10244
pSSSSS
kCBASCPP totaltotaltotal
...............
Sigmoidale dependence of concentrationof activated MAP kinase on concentration of input signal.
0 0.5 1 1.5 2kp0
0.05
0.1
0.15
0.2
PP
C
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MAPK Cascade: Impact of Kinases and Phosphatase
0 10 20 30 40 500
0.005
0.01
0.015
0.02
0.025
0 10 20 30 40 500
0.2
0.4
0.6
0.8
0 10 20 30 40 500
0.0025
0.005
0.0075
0.01
0.0125
0.015
0.0175
0 10 20 30 40 500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
k=1
k=2
k=3k=4 k=5
k=1
0.9
0.8
0.7
0.6
p=1
p=1
p=1
1.1
1.2
1.3
1.4
k=1
p=0.5
p=0.3
p=0.4
p=0.1
p=0.2
Time, a.u. Time, a.u.
MA
PK
-PP
, a
.u.
MA
PK
-PP
, a
.u.
Time, a.u. Time, a.u.
A
B
C
D
MA
PK
-PP
, a
.u.
MA
PK
-PP
, a
.u.
k – Kinase, p - Phosphatase
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71 vvMAPKKKdt
d
8271 vvvvPMAPKKKdt
d
822 vvPMAPKKKdt
d
....
0 20 40 60 80 1000
0.05
0.1
0.15
0.2
0.25
0 2 4 6 8 10
0.02
0.04
0.06
0.08
MA
PK
P2
MA
PK
P2(t
)
Time
MAPKKKK=0.1
k = 0.04
k = 0.36
k = 0.16
k = 0.64k = 1
k/p
MAPKKKK=0.01
1262 vvPMAPKdt
d
- Sigmoide input/output dependence
- Signal amplification
Time courses Steady states
MAP Kinase Cascade – Parameter Dependence
k – Kinase, p - Phosphatase
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MAPK Cascade: Control
P1,0 P1
1
2
P0
P2,0 P2
3
4
P3,0 P3
5
6
1 2 3 4 5 6
Rates
P1,0
P1
P2,0
P2
P3,0
P3
1
2
3
4
5
6
positive
none
negative
k
j
j
kJv v
J
J
vC j
k
k
i
i
kSv v
S
S
vC i
k
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MAPK Cascade: Control
P1,0
P0P1,0
P1X
P0
P1
P2,0
P1P2,0
P2X
P2
P3,0
P2P3,0
P3X
P3
with complex formation
1 2 3 4 5 6 7 8 9 10 11 12
Rates
P1,0
P0 P1,0
P1
P1X
P2,0
P1 P2,0
P2
P2X
P3,0
P2 P3,0
P3
P3X
1
2
3
4
5
6
7
8
9
10
11
12
1 2
4 3
5 6
8 7
9 10
12 11X – phosphatase
positive
none
negative
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MAPK-Cascade with Feedbackand Michaelis-Menten Kinetics: Oscillations
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MAP Kinase Cascade – Scaffolding
MAPKKK
MAPKK
MAPK
Ste5Ste11
Ste7Fus3
Sca
ffol
d
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MAP Kinase Cascade – Scaffolding
Ste5Ste11
Ste7Fus3
Double Phosphorylation of each protein
000 001 002
010 011 012
020 021 022100 101 102
110 111 112
120 121 122200 201 202
210 211 212
220 221 222
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Quantitative Measures for Signaling
0 1 2 3 4 50
0.1
0.2
0.3P1,0 P1
v1f
v1r
P2,0 P2
P3,0 P3
v2r
P0
v2f
v3f
v3r
Time, a.u.C
on
cen
tra
tion
, a
.u.
A11
1
P1
P1maxt1max
(a) (b)
Transition time
0
0
dttX
dttXt
i
i
i
2
0
0
2
i
i
i
i
dttX
dttXt
i
i
i
dttX
S
20
Signal duration Amplitude
Heinrich et al., T.A. Mol.Cell, 2002
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Crosstalk & Signal Integration
Schaber, Kofahl, Kowald & Klipp, 2006, FEBS J.
Signal Signal
Receptor A Receptor B
Target A Target BX – function of amplitude, timing or integral of response
AX
BXC
BAX
AXSi ,
Measures of crosstalk
BAX
BXSe ,
Se > 1 Se < 1
Si > 1
Si < 1
Mutual signalinhibition
Mutual signalamplification
Dominance ofextrinsic signal
Dominance ofintrinsic signal
PheromonePathway
FilamentousGrowth Pathway
Crossactivation
Mutual signalamplification
Crossinhibition
Dominance of intrinsic signal
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Crosstalk
0 1 2 3 4 50
0.1
0.2
0.3
0 1 2 3 4 50
0.1
0.2
0.3
0 1 2 3 4 50
0.1
0.2
0.3
0 1 2 3 4 50
0.1
0.2
0.3
P1A,0 P1A
v1Af
v1Ar
P2A,0 P2A
P3A,0 P3A
v2Ar
= P0A
v2Af
v3Af
v3Ar
P1B,0P1B
v1Bf
v1Br
P2B,0P2B
P3B,0P3B
= P0B
v2Bf
v3Bf
v3Br
(a)
v2Br
P1A
P2A
P3A
P1B
P2B
P3BP1A P2A
P3A
P1A
P2A
P3A
Time a.u
Co
nce
ntr
atio
n a
.u.
Time a.u
Co
nce
ntr
atio
n a
.u.
0 1 2 3 4 50
0.1
0.2
0.3
P1B
P2B
P3B
ki = 1 ki = 10
0 1 2 3 4 50
0.1
0.2
0.3
Co
nce
ntr
atio
n a
.u.
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Crosstalk
0 1 2 3 4 50
0.1
0.2
0.3
0 1 2 3 4 50
0.1
0.2
0.3
0 1 2 3 4 50
0.1
0.2
0.3
P1A,0 P1A
v1Af
v1Ar
P2A,0 P2A
P3A,0 P3A
v2Ar
= P0A
v2Af
v3Af
v3Ar
P1B,0P1B
v1Bf
v1Br
P2B,0P2B
P3B,0P3B
= P0B
v2Bf
v3Bf
v3Br
v2Br
P1A
P2A
P3A
P1A P2AP3A
P1A
P2A
P3A
Co
nce
ntr
atio
n a
.u.
Time a.u
Co
nce
ntr
atio
n a
.u.
ki = 1 ki = 10
Co
nce
ntr
atio
n a
.u.
I = 0.628748Pmax = 0.132872tmax = 2.85456
I = 0.067494Pmax = 0.0459428tmax = 0.538455
I = 0.688995Pmax = 0.136802tmax = 2.73227
Integrated Response
Timing of Response
,A
Ai X
XAS
,A
Ae X
XAS
Si(Pmax) = 0.97
Se(I) = 0.097
Si(I) = 0.91
Se(Pmax) = 0.34
Se(tmax) = 0.197
Si(tmax) = 1.04
Mutual amplification
Mutual amplification
Dominance ofintrinsic signal
Maximal Response
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Integration of Signaling Pathways
m24; FRE, medium Responses: 9,10,11
0 10 20 30 40 500
0.0005
0.001
0.0015
0.002
0.0025
m20; PRE, large Responses: 5,17,19,20
0 10 20 30 40 500
0.2
0.4
0.6
0.8
m20; PRE, medium negative Responses: 7,9,12,18,21
0 10 20 30 40 500.2
0.15
0.1
0.05
0
5
79
11
12
17
18
1920
21
5
9
10
11
4 -Fus3 phosphorylation in MAPKcascade6 -repeated Fus3 phosphorylation10-Kss1 phosphorylation in MAPKcascade21-Kss1 release from Ste12Tec1 complex
Response coefficients of
m24; FRE, large negative Responses: 6,16,30,31,39
0 10 20 30 40 50
0.01
0.008
0.006
0.004
0.002
0
6
Time/min Time/min
m24; FRE, plus minus Responses: 2,4,5,21,22
0 10 20 30 40 500.006
0.004
0.002
0
0.002
0.004
0.006
2
4
21
22
m20; PRE, medium Responses: 3,4,6,10,11,40
0 10 20 30 40 500
0.025
0.05
0.075
0.1
0.125
0.15
0.175
46
10
PREs FREs
l
i
i
lSp p
tS
tS
pR i
l
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Putting all together : the Pheromone pathway
a
a
a
a
MATa-cells MAT-cells
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MATa-cells MAT-cells
Putting all together: the Pheromone pathway
a
a
a
a
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Pheromone pathway
Ste50
Cdc
42
Ste5
G
G
PP
NucleusCytoplasm
Bem1
Cdc24
Plasma membrane
Extracellular space
Ste20
Ste2G
G
G
G Ste11
Ste7
Fus3
Fus3Fus3
Far1Cdc24 P
P
ClnCdc28
Far1Cdc24
Far1
Actin
GSte20
Cdc
42
G
Cdc24
Bem1
Bar1
active
GTP
GDP
GGDP
Sst2
Ste12
Dig1Dig2
Kss1
Ste12
Dig1Dig2
Kss1
Ste12
Ste12
Ste2
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Pheromone pathway
Cdc
42
Ste5
GG
Bem1
Cdc24
Extracellular space
Ste20
Ste2G
G
G
G
GTP
GDP
GGDP
Sst2
Ste2
NucleusCytoplasm
Far1Cdc24 P
P
ClnCdc28
Far1Cdc24
Bar1
active
Ste12
Dig1Dig2
Kss1
Ste12
Dig1Dig2
Kss1
Ste12
Ste12
PPFus3
Fus3
Plasma membrane
Far1
Actin
GSte20
Cdc
42
G
Cdc24
Bem1
Ste50 Ste11
Ste7
Fus3
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Pheromone pathway
Ste50
Cdc
42
Ste5
GG
PP
Bem1
Cdc24
Plasma membrane
Extracellular space
Ste20
Ste2G
G
G
G Ste11
Ste7
Fus3
Fus3Fus3
Far1
Actin
GSte20
Cdc
42
G
Cdc24Bem1GTP
GDP
GGDP
Sst2
Ste2
NucleusCytoplasm
Far1Cdc24 P
P
ClnCdc28
Far1Cdc24
Bar1
active
Ste12
Dig1Dig2
Kss1
Ste12
Dig1Dig2
Kss1
Ste12
Ste12
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Pheromone pathway
Ste50
Cdc
42
Ste5
GG
PP
NucleusCytoplasm
Bem1
Cdc24
Plasma membrane
Extracellular space
Ste20
Ste2G
G
G
G Ste11
Ste7
Fus3
Fus3Fus3
Far1Cdc24 P
P
ClnCdc28
Far1Cdc24
Far1
Actin
GSte20
Cdc
42
G
Cdc24Bem1
Bar1active
GTP
GDP
GGDP
Sst2
Ste12
Dig1Dig2
Kss1
Ste12
Dig1Dig2
Kss1
Ste12
Ste12
Ste2
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Pheromone pathway: structural parts
Ste2
G
Fus3 Sst2
Ste12Bar1
MAPKscaffold
Far1Cdc28
Plasma membrane
Gene expression Complex formation
Signalingcascade
G proteincycle
Receptor activation
Pheromone
Humboldt-Universität
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Ste2
G
Fus3 Sst2
Ste12Bar1
MAPKscaffold
Far1Cdc28
Plasma membrane
Gene expression Complex formation
Signalingcascade
G proteincycle
Receptor activation
Pheromone
Yu et al., Nature, 2008
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Pheromone pathway: time courses
In comprehensive model: regulatory feedback loops are consideredmutant phenotypes can be investigated
10-3 10-2 10-1 100 101 102 103 104
0
0.2
0.4
0.6
0.8
1
Ste12active
Fus3PP
G-Far1
Rel
ativ
e C
once
ntra
tion
-factor / nM
Far1-Cdc28
Graded response depending on concentration of -factor
Polarized growth
CellCyclearrest
Kofahl & Klipp, Yeast, 2004
Humboldt-Universität
zu Berlin
Pheromone pathway: time coursesF
us3
-PP
G
0 10 20 300
1.2
0.025
0.05
1.17
0 10 20 300
0.20.4
0.60.8
1.
1.2
0 10 20 300
0.2
0.4
0.6
0.8
1.
1.2
0 10 20 300
0.2
0.4
0.6
0 10 20 30
0.01
0.02
0.03
0.04
0 10 20 300
0.01
0.02
0.03
0.04
0 10 20 300
0.01
0.02
0.03
0 10 20 300
0.02
0.04
0.06
0 10 20 30
0.1
0.2
0.3
0.4
0 10 20 30
0.1
0.2
0.3
0.4
0 10 20 30
0.1
0.2
0.3
0 10 20 30
0.1
0.2
0.3
0.4
Overexpression G
G defect in binding G
Overexpression G
sst2
Sst2 mutant
Sst2 gain of function
Humboldt-Universität
zu Berlin
Yu & Brent et al.: Experimental Data
Humboldt-Universität
zu Berlin
Yu & Brent et al.: Experimental Data
DoRA – Dose Response Alignment
Humboldt-Universität
zu Berlin
Yeast Cell as an Osmometer
Eriksson, Lab on Chip, 2006
Serge Pelet, ETH, Zürich
Yeast cells shrink upon osmoshock
Stress adaptation requires glycerol accumulation.
MAPK Hog1 is considered a key player.
Humboldt-Universität
zu Berlin
Osmotic Stress Response
Ypd1
High osmolarity
Ssk1
Sln1
Ssk2
Pbs2
Hog1 mRNA
Protein
Glycerol
Turgor Fps1
Construct network from literature data and experts‘ knowledge
Study properties of small modules, e.g. MAPK cascade, G protein cycles, …
MKKK-P
MKK-PPMKK
MK-PPMK
k
p
MKKKK
MKKK
0 10 20 30 40 500
0.005
0.01
0.015
0.02
0.025
0 10 20 30 40 500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
k/p=1
k/p=2
k/p=3
k/p=4k/p=5
k/p=1
0.9
0.8
0.70.6
Time, a.u.
MA
PK
-PP
, a
.u.
MA
PK
-PP
, a
.u.
Parameter change
Amplitude
Duration
Collect experimental data (time series!!!)Estimate model parametersSimulate: Agreement of model/experiment?Sensitivity analysis
Prediction of hitherto untested scenarios- Deletion mutants- Compound overexpression- New experimental scenarios
Transcriptome data – mRNA levelsProteome data – phosphorylation, concentration changesMetabolome data – concentration changes
MA
PK
casc
adeP
hosp
hore
lay
Gene regulation
Metabolism
Systems equations (Set of ODEs)
r – number of reactionsSi – metabolite concentrationsvj – reaction ratesnij – stoichiometric coefficients
Network properties
Individual reaction properties
r
jjij
i vndt
dS
1
Humboldt-Universität
zu Berlin
Osmostress Response – Full Model
Klipp, Nordlander, Krüger, Gennemark & Hohmann, Nature Biotechn, 2005
Humboldt-Universität
zu BerlinTwo Pathways for Stress Osmotic Response
Ypd1
High osmolarity
Ssk1
Sln1
Ssk2
Pbs2
Hog1 mRNA
Protein
Glycerol
Turgor Fps1
0 30 60 90 120
0
0.2
0.4
0.6
0.8
1.
Time / min
mRNA
Ssk1
Co
nce
ntr
atio
n,
rela
tive
Hog1P2
Gpd1
A
WT
Hog
1P2
Time / min0 30 60 90 120
00.20.40.60.8
1.1.2
wild type
Fps1 open
Ptp2 over
Fps open+Ptp2 over
0 30 60 90 120
0
0.5
1.
1.5
Time / min
mRNA
GlycinC
on
cen
tra
tion
, re
lativ
e
Hog1P2
Protein
A
Gpd1Fps1 mutant
Osmotic stress
Klipp et al.,Nature Biotechn, 2005
Humboldt-Universität
zu Berlin
Osmotic stress model: Test cases
Ypd1
High osmolarity
Ssk1
Sln1
Ssk2
Pbs2
Hog1 mRNA
Protein
Glycerol
Turgor Fps1
0 30 60 90 120
0
0.5
1.
1.5
ŸŸ
Ÿ
Ÿ
Ÿ Ÿ Ÿ
Ÿ Ÿ
ŸŸ Ÿ Ÿ
Cells are competent to respond to a second shock.
0 30 60 90 120
0
0.5
1.
1.5
mR
NA
, rel
ativ
e
60 min
30 min15 minSingle
Time/min
Time/min
mR
NA
, rel
ativ
e
Repeated osmostress
60 min
30 min15 minSingle
x
x
x
x
Klipp et al.,Nature Biotechn, 2005
Humboldt-Universität
zu Berlin
0 20 40 60 80 100 1200
0.1
0.2
0.3
0.4
0.5
Osmotic stress response: What is the impact of specific components over time ?
Ypd1
High osmolarity
Ssk1
Sln1
Ssk2
Pbs2
Hog1 mRNA
Protein
Glycerol
Turgor Fps1
l
i
i
lSp p
tS
tS
pR i
l
Responsecoefficients
0 20 40 60 80 100 1200
2
4
6
8
0 20 40 60 80 100 120
0.4
0.3
0.2
0.1
0
Time-dependent Response CoefficientsRelated to Glycerol Concentration
Closure of Fps1
Inhibition of Sln1
Strength of osmoshockHog1 nuclear import
Ssk1 dephosphorylation
Glycerol export
mRNA degradation
Hog1 dephosphorylation
Hog1 nuclear export
Sln1 phosphorylation
Hog1 phosphorylation
Glycerol influx
mRNA and protein production
Time / min
Time / minTime / min
0 20 40 60 80 100 1200
100
200
300
400
500
600
Time / min
Glycerolconcentration
Ingalls & Sauro, JTB, 2003
Humboldt-Universität
zu Berlin
Signaling Pathways in Yeast
Humboldt-Universität
zu Berlin
Model Selection: Sho branch I
Humboldt-Universität
zu Berlin
Model Selection: Sho branch II
Different architectures – which one explains data best?
Humboldt-Universität
zu Berlin
Model Selection: Sho branch III
Humboldt-Universität
zu Berlin
Model Size – Skeleton Model
Ypd1
High osmolarity
Ssk1
Sln1
Ssk2
Pbs2
Hog1 mRNA
Protein
Glycerol
Turgor Fps1
MA
PK
casc
adeP
hosp
hore
lay
Gene regulation
Metabolism
Hog1P2
Osmolarityex
mRNA
Turgor Glycerol
Fps1
Humboldt-Universität
zu Berlin
Oscillatory Input – Oscillatory Output
Humboldt-Universität
zu Berlin
Oscillatory Input – oscillatory output
x – intracellular osmotic pressurey – nuclear Hog1
Humboldt-Universität
zu Berlin
Oscillatory Input – oscillatory output
x – intracellular osmotic pressurey – nuclear Hog1
3 0 3 5 4 0 4 5 5 0
1 .3
1 .4
1 .5
1 .6
1 .7
Humboldt-Universität
zu Berlin
Simplified, yet Comprehensive Model of Osmotic Stress Response
Zi et al., PLoS ONE, 2010
Data from Mettetal et al., Science, 2008
Humboldt-Universität
zu Berlin
Signal Response Gain
Humboldt-Universität
zu Berlin
Glycerol Accumulation Depends on Stress and Nutritional Conditions
Glycerolt 21
2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0
8 0 0 0 0 0
1 . 0 1 0 6
1 . 2 1 0 6
1 . 4 1 0 6
1 . 6 1 0 6
2 0 4 0 6 0 8 0 1 0 0
1 . 0 1 0 6
1 . 5 1 0 6
2 . 0 1 0 6
2 . 5 1 0 6
5 0 0 0 1 0 0 0 0 1 5 0 0 0
4 0
5 0
6 0
0 . 1 0 . 2 0 . 3 0 . 4
2 5
3 0
3 5
4 0
4 5
5 0
Gly
cero
l
Gly
cero
l
Time Time
stress Glucose
Glycerolt 21
stress Glucose
More stress, stronger response
More stress, slower response
More glucose, stronger response
More glucose, faster response
Humboldt-Universität
zu Berlin
Flows Influencing Glycerol
2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0
5 0 0 0
1 0 0 0 0
1 5 0 0 0
Gly
cero
lflux
Time
Total Production
Transcriptionally regulated
Export
Volume-regulated
Net Production
Humboldt-Universität
zu Berlin
Systembiologie
Systemische Betrachtung von biologischen Sachverhalten und Prozessen
Zusammenspiel von Experiment und Theorie – „iterative cycle“
Häufig: Erzeugung, Analyse und Interpretation großer Datenmengen
Immer öfter: gezielte Erhebung von Daten zur Modellierung
Modellierung: - verschiedene Modellierungsansätze haben ihre
Stärken undSchwächen- ein Sachverhalt kann mit unterschiedlichen
Modellen beschrieben werden- kein sinnvolles Modell ohne sinnvolle Fragestellung
Humboldt-Universität
zu Berlin
Signal-Motive
RSfdt
dR, S – Signal, R – Response
S
R RkSkkdt
dR210
Kinetik
linear
RK
RV
SK
SV
dt
dR
mm
2
2
1
1
Michaelis-Menten
Steady State
2
10
k
SkkR ss
1212
21
VVSKV
SKVR
m
mss
Response
linear
hyperbolic
1 2 3 4 5
1
2
3
4
5
Signal S (arbitrary units)
Re
spo
nse
R (
arb
itra
ry u
nits
)
sigmoid
hyperbolic
linear
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
Humboldt-Universität
zu Berlin
Signal-Motive
RSfdt
dR, S – Signal, R – Response
Kinetik
linear
Michaelis-Menten
Steady State Response
hyperbolic
1 2 3 4 5
1
2
3
4
5
Signal S (arbitrary units)
Re
spo
nse
R (
arb
itra
ry u
nits
)
sigmoid
hyperbolic
linear
S
RR0
RkRRSkdt
dRtotal 21
totalRRR 0
Skk
SkRR totalss
12
1
RK
Rk
RRK
RRSk
dt
dR
mtm
t
2
2
1
1
totalRRR 0
total
m
total
m
totalss
R
K
R
KkSkG
RR
2121 ,,,
sigmoid
One loop
uKuvuKvJuvuKvJuv
uKKJvuG
4
22
,,,
Goldbeter-Koshland-Funktion
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
Humboldt-Universität
zu Berlin
Signal-Motive
RSfdt
dR, S – Signal, R – Response
Kinetik
linear
Steady State Response
1 2 3 4 5
1
2
3
4
5
Signal S (arbitrary units)
Re
spo
nse
R (
arb
itra
ry u
nits
)
sigmoid
hyperbolic
linear
sigmoid
S
R1R0 R
Two loops
RkSRkdt
dR413
RkRSkkSRkdt
dR413201
1
totalRRRR 10
2314142
231
SkkSkkkk
SkkRR totalss
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
Humboldt-Universität
zu Berlin
Signal-Motive
RSfdt
dR, S – Signal, R – Response
Perfect adaptation
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
Humboldt-Universität
zu Berlin
Signal-Motive
RSfdt
dR, S – Signal, R – Response
Mutual activation
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
Humboldt-Universität
zu Berlin
Signal-Motive
RSfdt
dR, S – Signal, R – Response
Mutual inhibition
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
Humboldt-Universität
zu Berlin
Signal-Motive
RSfdt
dR, S – Signal, R – Response
Negative feedback: homeostasis
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
Humboldt-Universität
zu Berlin
Signal-Motive
RSfdt
dR, S – Signal, R – Response
Negative feedback: oscillations
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
Humboldt-Universität
zu Berlin
Signal-Motive
RSfdt
dR, S – Signal, R – Response
Activator – Inhibitor
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003
Humboldt-Universität
zu Berlin
Signal-Motive
RSfdt
dR, S – Signal, R – Response
Substrate-depletion oscillator
Vgl.: Tyson, Chen & Novak, Current Op. Cell Biology, 2003