systems biology 9 – signal...
TRANSCRIPT
Humboldt-Universität
zu Berlin
Edda Klipp
Systems biology 9 – Signal Transduction
Sommersemester 2011
Humboldt-Universität zu BerlinInstitut für BiologieTheoretische Biophysik
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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.htmlInteractive 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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Receptors
• transmembrane• receive signal and transmit it• conformation change• active or inactive form
Simple concept:
H + R HR
KD = H RHR.
H - HormoneR - ReceptorHR - Hormone-receptor-complex
Typical values :KD = 10-12 M ….10-6 M
LigandExtracellular space
Intracellular space
Membrane
Receptor,Binding site
Receptor,cytosolicdomain inactive active
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Receptor, Extended Model
Ri Rs Ra
L
vis
vsi
vsa
vas
vpi
vdivai
vps
vds vda
aisiisdipii vvvvvRdtd
assasiisdspss vvvvvvRdtd
aiassadaa vvvvRdtd
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
bero
f 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 dak116 sM102 sak
12 s101 ask
+L
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G-Proteins: „small G-proteins“
21
21
vvRasdtd
vvRasdtd
GTP
GDP
RasRasRas GTPGDPtotal
Differential equations Conservation relations
GDP GTP
GTPGDP+ +
e.g. Ras-Protein
GDPRas GTPRas
GDPGTPGEF
GAPPi
v1
v2
GEF –
Guanine
nucleotide
exchange
factorGAP –
GTPase-activating
protein
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G-Proteins: „small G-proteins“
e.g. Ras-Protein
GDPRas GTPRas
GDPGTP
GEF
GAPPi
v1
v2
GAPRaskv
GEFRaskvGTP
GDP
22
11
GAPkGEFkGEFkRasRas 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
RasKRasGAPkv
RasKRasGEFkv
GTPm
GTP
GDPm
GDP
2
22
1
11
GTP
Ras
GTP
Ras
GAP
GEF
GAP
GEF
21
21
vvRasdtd
vvRasdtd
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
vvRasdtd
vvRasdtd
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
RasKRasGAPkv
RasKRasGEFkv
GTPm
GTP
GDPm
GDP
2
22
1
11
GTP
Ras 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
GTP
Ras
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
RasKRasGAPkv
RasKRasGEFkv
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
GTP
Ras
Enzym: GEF
01011
21
21.
;;
mm
totalKK
Raskk
GTP
Ras
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
RGSGTP
vga
vh1vh0
vsr
srga vvGdtd
10 hhga vvvGTPGdtd
GDPGGTPGGGt
GGGtotal
0 10 20 30
0
2000
4000
6000
8000
10000
Time
G
Num
bero
f Mol
ecul
es
G
GDPG
GTPG
Differential equations Conservation relations
GDP
GTP
+
GDP+
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Phosphorelay-System
AspHisSln1 ATP
ADP
Pii
Ypd1
Ssk1-P
Pi
Pi
Pi
high osmolarity
?
Ypd1-P
Ssk1
Asp1
2
3
4
5
Example: Sln1 pathway, Phosphorelay system
His
Asp
1111 31 YpdPASlnkSlnkSlndtd
PHSlnkSlnkPHSlndtd
111 21
1111 32 YpdPASlnkPHSlnkPASlndtd
11111 34 YpdPASlnkSskPYpdkYpddtd
11111 34 YpdPASlnkSskPYpdkPYpddtd
1111 45 SskPYpdkPSskkSskdtd
1111 45 SskPYpdkPSskkPSskdtd
PASlnPHSlnSlnSln total 1111
PYpdYpdYpd total 111
PskSSskSsk total 111
- Transmits individual phosphate groups
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Phosphorelay-System
total
total
total
CCPCBBPBAAPA
CPkBPCkCdtd
CBPkAPBkBdtd
BAPkATPAkAdtd
43
32
21
0 1 2 3 4 5k1
0.2
0.4
0.6
0.8
1
A, B
, CA-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 6000
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.
Con
cent
ratio
n C
Con
cent
ratio
n, a
.u.
Rate constant k4
Time a.u.
k1
=10
k1
=10.10.010.001
C
BA
Dynamics
Steady State
total
total
total
CCPCBBPBAAPA
CPkBPCkCdtd
CBPkAPBkBdtd
BAPkATPAkAdtd
43
32
21
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MAP Kinase Cascade= Mitogen activated protein kinase cascade
MAPKKKK
MAPKKKinactive
MAPKKKactive
MAPKKinactive
MAPKKactive
MAPKinactive
MAPKactive
Signal
Alternative: SAP = stress activated protein …
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MAP Kinase Cascade - Equations
ATPMAPKKKPkATPMAPKKKKMAPKKKkMAPKKKPdtd
MAPKKKPkATPMAPKKKKMAPKKKkMAPKKKdtd
21
41
MAPKKPPkATPMAPKKKPMAPKKPkMAPKKPPdtd
MAPKKPkMAPKKPPkATPMAPKKKPMAPKKPkATPMAPKKKPMAPKKkMAPKKPdtd
MAPKKPkATPMAPKKKPMAPKKkMAPKKdtd
86
8765
85
MAPKPPkATPMAPKKPPMAPKPkMAPKPPdtd
MAPKPkMAPKPPkATPMAPKKPPMAPKPkATPMAPKKPPMAPKkMAPKPdtd
MAPKPkATPMAPKKPPMAPKkMAPKdtd
1110
1211109
109
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MAP Kinase Cascade - Equations
totaltotal
totaltotal
totaltotal
MAPKKKCCPPCPCMAPKKKBBPPBPBMAPKKKAAPPAPA
CPPpBPPCPkCPPdtd
CPpBPPCkCdtd
BPPpAPBPkBPPdtd
BPpAPBkBdtd
APPpAPkAPPdtd
APpSAkAdtd
k – Kinase, p - Phosphatase Steady state
101234
10244
pSSSSSkCBASCPP totaltotaltotal
...............
Sigmoidale dependence of concentrationof activated MAP kinase on concentrationof input signal.
0 0.5 1 1.5 2k�p0
0.05
0.1
0.15
0.2
PP
C
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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
0.00250.005
0.00750.01
0.01250.015
0.0175
0 10 20 30 40 500
0.10.20.30.40.50.60.7
k=1
k=2
k=3k=4 k=5
k=1
0.9
0.80.70.6
p=1
p=1
p=1
1.1
1.21.3
1.4
k=1
p=0.5
p=0.3
p=0.4
p=0.1p=0.2
Time, a.u. Time, a.u.
MA
PK
-PP
, a.u
.M
AP
K-P
P, a
.u.
Time, a.u. Time, a.u.
A
B
C
D
MA
PK
-PP
, a.u
.M
AP
K-P
P, a
.u.
k – Kinase, p - Phosphatase
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71 vvMAPKKKdtd
8271 vvvvPMAPKKKdtd
822 vvPMAPKKKdtd
....
0 20 40 60 80 1000
0.050.1
0.150.2
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 = 0.36k = 0.16
k = 0.64k = 1
k/p
MAPKKKK=0.01
1262 vvPMAPKdtd
- 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
61 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
JJvC j
k
k
i
i
kSv v
SSvC i
k
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MAPK Cascade: Control
P1,0
P0
P1,0
P1
X
P0
P1
P2,0
P1
P2,0
P2
X
P2
P3,0
P2
P3,0
P3
X
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
Humboldt-Universität
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MAP Kinase Cascade – Scaffolding
MAPKKK
MAPKK
MAPK
Ste5Ste11Ste7
Fus3Sc
affo
ld
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MAP Kinase Cascade – Scaffolding
Ste5Ste11Ste7
Fus3
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
v3rTime, a.u.
Con
cent
ratio
n, a
.u.
S11
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
dttXS
20
Signal duration Amplitude
Heinrich et al., T.A. Mol.Cell, 2002
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Crosstalk in Signaling Pathways
Are signaling pathways linear structures?
Are signals transmitted in signaling networks?
How can we measure the transfer of signal between different branches of the network?
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Crosstalk & Signal Integration
Signal Signal
Receptor A Receptor B
Target A Target B X – function of amplitude, timing or integral of response
AXBXC
BAXAXSi ,
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,0 P1B
v1Bf
v1Br
P2B,0 P2B
P3B,0 P3B
= P0B
v2Bf
v3Bf
v3Br
(a)
v2Br
P1A
P2A
P3A
P1B
P2B
P3BP1A P2A
P3A
P1A
P2A
P3A
Time a.u
Con
cent
ratio
n a.
u.
Time a.u
Con
cent
ratio
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
Con
cent
ratio
n a.
u.
left cascade right cascade
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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,0 P1B
v1Bf
v1Br
P2B,0 P2B
P3B,0 P3B
= P0B
v2Bf
v3Bf
v3Br
v2Br
P1A
P2A
P3A
P1A P2AP3A
P1A
P2A
P3A
Con
cent
ratio
n a.
u.
Time a.u
Con
cent
ratio
n a.
u.
ki = 1 ki = 10
Con
cent
ratio
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) = 0.097Si (I) = 0.91
Se (Pmax ) = 0.34
Se (tmax ) = 0.197Si (tmax ) = 1.04
Mutual amplification
Mutual amplification
Dominance ofintrinsic signal
Maximal Response
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Integration of Signaling Pathways
m@24D; FRE, medium Responses: 9,10,11
0 10 20 30 40 500
0.0005
0.001
0.0015
0.002
0.0025
m@20D; PRE, large Responses: 5,17,19,20
0 10 20 30 40 500
0.2
0.4
0.6
0.8
m@20D; PRE, medium negative Responses: 7,9,12,18,21
0 10 20 30 40 50- 0.2
- 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
m@24D; 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
m@24D; FRE, plus minus Responses: 2,4,5,21,22
0 10 20 30 40 50- 0.006- 0.004- 0.002
00.0020.0040.006
2
4
21
22
m@20D; PRE, medium Responses: 3,4,6,10,11,40
0 10 20 30 40 500
0.0250.05
0.0750.1
0.1250.15
0.175
46
10
PREs FREs
l
i
i
lSp p
tStS
pR il
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Yeast Signaling Pathways
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,70
0,80
0,90
1,00
0 20 40 60 80 100 120 140 160 180 200
0,00
0,20
0,40
0,60
0,80
1,00
1,20
0 20 40 60 80 100 120 140 160 180 200
0,00
0,20
0,40
0,60
0,80
1,00
1,20
0 20 40 60 80 100 120 140 160 180 200
Crosstalk Opportunities
+Pheromone
+Salt
+Pheromone +Salt
Fus3 Kss1 Hog1
Waltermann in prep., Hoffman-Sommer in prep.
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Hog1 activity as timer for filamentous differentiation under exposure to simultaneous osmo-stress and nutrient-limitation
Nutrient limitation only
Osmo-stress and nutrient-limitationsimultaneously: increase of Tec1 activity delayed (transcriptional activator of filamentation(FRE) genes)
In mutants with altered crosstalk the timer function of Hog1 is
disrupted or enhanced.
TimeTime
Time Time
Activ
ityAc
tivity
Nutrient limitation + osmostress
Nutrient limitation + osmostressReduced crosstalk from Hog1 to Tec1
Nutrient limitation + osmostressReduced inhibition of Hog1 by Kss1
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Ca2+ oscillations
Cytosolic Ca2+ oscillationsSpatio-temporal dynamicsControl variety of cell processes
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Calcium Oscillation - Simulations
Thul et al., 2009
… for different parameter values
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Ca2+ oscillations
Interspike interval
Calcium oscillations - limit cycle oscillations?- sequences of random spikes?
Problem: Channels form tetramers, tetramers form cluster.