systems biology 9 – signal...

Humboldt-Universität

zu Berlin

Edda Klipp

Systems biology 9 – Signal Transduction

Sommersemester 2011

Humboldt-Universität zu BerlinInstitut für BiologieTheoretische Biophysik


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.htmlInteractive Animation of MAP Kinase Signal Transduction

http://www.idp.mdh.se/personal/bfg02/forskning/quasi/quasi12.htmlwww.apple.com/quicktime


zu Berlin

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


zu Berlin

Yeast Signaling Pathways


zu Berlin

Signaling Pathway Components


zu Berlin

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


zu Berlin

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


zu Berlin

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


zu Berlin

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


zu Berlin


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


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


zu Berlin


21

21

vvRasdtd

vvRasdtd

GTP

GDP


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 ;;


zu Berlin


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


zu Berlin

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+


zu Berlin

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


zu Berlin

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


zu Berlin

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


zu Berlin

MAP Kinase Cascade= Mitogen activated protein kinase cascade

MAPKKKK

MAPKKKinactive

MAPKKKactive

MAPKKinactive

MAPKKactive

MAPKinactive

MAPKactive

Signal

Alternative: SAP = stress activated protein …


zu Berlin

MAP Kinase Cascade - Equations

ATPMAPKKKPkATPMAPKKKKMAPKKKkMAPKKKPdtd

MAPKKKPkATPMAPKKKKMAPKKKkMAPKKKdtd

21

41

MAPKKPPkATPMAPKKKPMAPKKPkMAPKKPPdtd

MAPKKPkMAPKKPPkATPMAPKKKPMAPKKPkATPMAPKKKPMAPKKkMAPKKPdtd

MAPKKPkATPMAPKKKPMAPKKkMAPKKdtd

86

8765

85

MAPKPPkATPMAPKKPPMAPKPkMAPKPPdtd

MAPKPkMAPKPPkATPMAPKKPPMAPKPkATPMAPKKPPMAPKkMAPKPdtd

MAPKPkATPMAPKKPPMAPKkMAPKdtd

1110

1211109

109


zu Berlin

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


zu BerlinMAPK 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

0.00250.005

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


zu Berlin

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


zu Berlin

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


zu Berlin

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


zu BerlinMAPK-Cascade with Feedback and Michaelis-Menten Kinetics: Oscillations


zu Berlin

MAP Kinase Cascade – Scaffolding

MAPKKK

MAPKK

MAPK

Ste5Ste11Ste7

Fus3Sc

affo

ld


zu Berlin

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


zu Berlin

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


zu Berlin

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?


zu Berlin

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


zu Berlin

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


zu Berlin

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


zu Berlin

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


zu Berlin

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.


zu Berlin

Crosstalk Model

1

2

3

4

7

5

6


zu Berlin

1

2

3

4

7

5

6


zu Berlin

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


zu Berlin

Pathway Interaction upon Cell Cycle Regulation


zu Berlin

gTOW Method


zu Berlin

Growth Rates for Signal Pathway Mutants


zu Berlin

gToW – Sensitivity to Overexpression

Krantz et a., MSB, 2009


zu Berlin

Ca2+ oscillations

Cytosolic Ca2+ oscillationsSpatio-temporal dynamicsControl variety of cell processes


zu Berlin

Calcium Oscillation - Equations


zu Berlin

Calcium Oscillation - Simulations

Thul et al., 2009

… for different parameter values


zu Berlin

Ca2+ oscillations

Interspike interval

Calcium oscillations - limit cycle oscillations?- sequences of random spikes?

Problem: Channels form tetramers, tetramers form cluster.


zu Berlin

Ca2+ oscillations

Thurley & Falcke, PNAS, 2011

Hierarchic stochastic modeling

systems biology 9 – signal...

Documents