Cell-Signaling Dynamics in Time and Space

Boris N. KholodenkoDepartment of Pathology, Anatomy and Cell Biology

Thomas Jefferson UniversityPhiladelphia, PA

Systems Biology of Signaling Networks

Systems biology studies living organisms in terms of their underlying network structure rather than their individual molecular components

Combinatorial Complexity Presents Problems for Models

• Signaling proteins have multiple “sites” and many “states”

• Each combination is a different species that requires its own differential equation

Example: The ErbB family

L Ligand Binding

Sites StatesBound or Not1 2

Kinase Domain 1

Active or Inactive

2

Y

Y

Y

Y

Y

Y

Y

Y

Y

Docking (pY) 10

Y, pY, Bound

3

Y

21*51*21*310=

1,180,980!!TOTAL SPECIES:

Dimer-ization

1 None or 1,2,3,4 5

Yarden and Sliwkowski, Nat. Rev. Mol. Cell Biol. 2:127 (2001)

p

p

pp

pA1

A2

Y: Tyrosine

pY: Phospho-Y

L: Ligand

A: Adapter

Macro-state is a sum of micro-states:

∑∑==

==1

1

2

2 02122

02111 ),,(),(,),,(),(

m

a

m

a

haarhaRhaarhaR

Reducing Combinatorial Complexity of Multi-Domain Proteins

RPlasma membrane

A2

A1

L L

1

Tyrosine kinase domain

–pY–

–pY–

0 (Y, free unphosphorylated)

1 (pY, free phosphorylated)

2 (pY-A1, partner A1 bound)

0 (Y) 1 (pY)

2 (pY-A2)

3 (pY-pA2, phosphorylated partner A2 bound)

11

2 2

Ligand-binding domain

0 (free domain)

1 (ligand-occupied)

A1

A2

R

Y– –pY –|Y

|pY

I

A1

Sh=1

S h=0

0 (Y)

1 (pY)

2 (pY-A2)

3 (pY-pA2)

0 (Y)

1 (pY)

2 (pY-A1)

3 (pY-pA1)

A2

Plasma membrane

Y– –pY –|Y

|pY

I

A1

Sh=1

Tyrosine kinase domain

S h=0

Site 1 Site 2

0 (Y)

1 (pY)

2 (pY-A2)

3 (pY-pA2)

0 (Y)

1 (pY)

2 (pY-A1)

3 (pY-pA1)

A2

∑ ∑ ∑ ∑= = = =

−

−

+

+

=1

1

1

1

1

10 0 0 01 ),,...,(......),(

m

a

m

a

m

a

m

anii

i

i

i

i

n

n

haashaS

)(

),( ) ;,,( 1

11 hS

haShaas n

tot

n

iii

n −=∏

≈…

Tim e (s)0 100 200 300 400

Con

cent

ratio

n (n

M)

0.0

0.5

1.0

1.5

+ Approxim ate solution

• Exact micro-state concentration s(2,2,1)

For the EGFR signaling network (GAB scaffold), the number of equations reduces from hundreds of thousands to ≈ 350.

Borisov et al (2005) Biophys. J. 89:951. Conzelmann et al (2006) BMC Bioinformatics, 7:34Kiyatkin et al. J Biol Chem, (2006) 281:19925. Borisov et al (2006) Biosystems. 83:152

Micro- and Macro-Models of Scaffold Proteins

Interactions between the Ras/ERK and PI3K/Akt pathways

Distinct Operational Ranges of Different Feedback Loops Shape Signaling Outcome

Disruption of GAB1-PI3K-GAB1 Positive Feedback: Experiment and Theory

Time (min)0 5 10 15 20 25 30

ppM

EK (A

rbitr

ary

Uni

ts)

0

1

2

3

4

5

Control Gab1 siRNA WM

Experiment

Time (min)0 5 10 15 20 25 30

ppM

EK (%

of t

otal

pro

tein

)

0

5

10

15

20

25

Control

WM GAB1 down

Theory

Kiyatkin et al. J Biol Chem, (2006) 281:19925

Context-Dependent Responses to EGF and HRG

Time(min): 0 1 2 5 10 30 0 1 2 5 10 30

Treatment: EGF HRG

p-ERK

ERK

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25 30 35

Time (min)

Nor

mal

ized

ER

K A

ctiv

atio

n

EGFHRG

Time (min)

ER

K A

ctiv

atio

n

Yarden and Sliwkowski, Nat. Rev. Mol. Cell Biol. 2:127 (2001)

Data from M. Hatakeyama’s lab

See Poster #269 by M. Birtwistle et al. ER

K A

ctiv

atio

n

Akt

Act

ivat

ion

Time (sec) Time (sec)

ErbB2 Overexpression Transforms a Transient into Sustained Response

ErbB2 Up

Wild TypeWild Type

ErbB2 Up

Time (sec)

ER

K A

ctiv

atio

n

10 nM EGF

10 nM HRG

10 nM10 nM

S

En−1

1E 1E

T T

2E 2E

I

I

I

How to Quantify the Control Exerted by a Signal over a Target?

System Response: the sensitivity (R) of the target T to a change in the signal S

System response equals the PRODUCT of local responses for a linear cascade:

∏=⋅⋅⋅⋅= − )(... 121 pathrrrrR nnTS

statesteadyTS SdTdR ln/ln=

Local Response: the sensitivity (r) of the level i to the preceding level i-1. Active protein forms (Ei) are “communicating”intermediates:

statesteadyiLeveliii EEr 1ln/ln −∂∂=

Kholodenko et al (1997) FEBS Lett. 414: 430

Functional Implications of the Multiplication Rule: When Does a Signaling Cascade Operate as a Switch?

Signal Strength0 5 10 15

Con

cent

ratio

n of

Act

ive

Form

0

2

4

6

8

10

T*

Signal Strength0 5 10 15

Res

pons

e C

oeffi

cien

t

0

2

4

6

8

r1 r2

R

Cascade responseR = r1 ⋅ r2 ⋅ r3

S

TI T

Kholodenko et al (1997) FEBS Lett., 414: 430

R > 1

1EI1E

2EI2E r3

Cascade responseR = d ln[ERK-PP]/d ln[Ras]

Cascade with feedbackRf = R/(1 – f⋅R)

Feedback strengthf = ∂ ln v/∂ ln[ERK-PP]

Cascade with no feedbackR = r1 ⋅ r2 ⋅ r3

Control and Dynamic Properties of the MAPK Cascades

Raf-PRaf

MEK-PPMEK-PMEK

ERK-PPERK-PERK

Ras f

Kholodenko, B.N. (2000) Europ. J. Biochem. 267: 1583.

Simple motifs displaying complex dynamics

Bistability and hysteresis arise from product activation (destabilizing positive feedback)

Relaxation oscillator is brought about by positive feedback plus negative feedback

Kholodenko, B.N. (2006)Nat. Rev. Mol. Cell Biol.

Simple motifs displaying complex dynamics

32 feedback designs that turn a universal signaling motif into a bistable switch and a relaxation oscillator.

Complex dynamics is a robust design property.

All rates and feedback loops obey simple Michaelis-Menten type kinetics

Kholodenko, B.N. (2006)Nat. Rev. Mol. Cell Biol.

Interaction Map of a Cellular Regulatory Network is Quantified by the Local Response Matrix

A dynamic system: mn pppxxxpxfdtdx ,...,,,...,).,(/ 11 ===

A = (∂f/∂x).The Jacobian matrix:

−+−−−+−+−−

000

000

Signed incidence matrix

If ∂fi/∂xj = 0, there is no connection from variable xj to xi on the network graph.

Local response matrix r

(Network Map)

r = - (dgA)-1⋅A

Relative strength of connections to each xiis given by the ratios,

rij = ∂xi/∂xj = - (∂fi/∂xj)/(∂fi/∂xi)

10010

01001

43

3432

24

1412

−−

−−

rrrrrr

Kholodenko et al (2002) PNAS 99: 12841.

Untangling the Wires: Tracing Functional Interactions in Signaling and Gene Networks.

Goal: To Determine and Quantify Unknown Network Connections

Problem: Network (system) responses (R) can be measured in intact cells, whereas local response matrix, r (network interaction map), cannot be captured unless entire system is reconstituted “in vitro”.

Kholodenko et al (2002) PNAS 99: 12841: Unraveling network structure (including feedback) from responses to gradual perturbations Sachs et al. (2005) Science, 308: Bayesian network algorithm infers connections from perturbation data. No feedback loops are allowed.

Step 1: Determining System Responses to Three Independent Perturbations of the Ras/MAPK Cascade.

a). Measurement of the differences in steady-state variables following perturbations:

4.33.67.129.81.32.67.39.64.7

−−−−−

−

8.214.397.858.563.208.440.253.465.55

−−−−−−

b) Generation of the system response matrix

10% change in parameters 50% change in parameters

(1) (0) (1) (0)ln 2( ) /( )X X X X XΔ ≈ − +

( )( )( )

1

1

1

lnlnln

Raf PMEK PPERK PP

⎛ ⎞Δ −⎜ ⎟Δ −⎜ ⎟⎜ ⎟Δ −⎝ ⎠

1( )

( )( )

2

2

2

lnlnln

Raf PMEK PPERK PP

⎛ ⎞Δ −⎜ ⎟Δ −⎜ ⎟⎜ ⎟Δ −⎝ ⎠

2

( )( )( )

3

3

3

lnlnln

Raf PMEK PPERK PP

⎛ ⎞Δ −⎜ ⎟Δ −⎜ ⎟⎜ ⎟Δ −⎝ ⎠

3

Step 2: Calculating the Ras/MAPK Cascade Interaction Map from the System Responses

r = - (dg(R-1))-1⋅R-1

10.20.06.018.12.10.01

−−−−−

10.20.06.019.11.10.01

−−−−−

10.20.06.019.11.10.01

−−−−−

Known Interaction Map

Two interaction maps (local response matrices) retrieved from two different system response matrices

Raf-PRaf

MEK-PPMEK-PMEK

ERK-PPERK-PERK

Ras -

+

Raf-P MEK-PP ERK-PP

Raf-P

MEK-PP

ERK-PP

Raf-P MEK-PP ERK-PP

Raf-P

MEK-PP

ERK-PPKholodenko et al (2002) PNAS 99: 12841

Module 3Module 2

PF

EQ-PF

F

MF

F2

F

PE

D2-PE

ME

EQ

D D Q E

Module 1

PD

F2-PD

MD

D2

Promoter

Dimer- Promoter Complex

mRNA

Protein

Dimer

Testing in Silico: Unraveling the Wiring of a Gene Network

Modular description

Yalamanchili et al (2006) IEE Proc Systems Biol, 153, 236-246

Inferring Interaction Maps

D2 EQ F2

D2 -1.00 0.00 0.70

EQ -0.85 -1.00 0.00

F2 0.00 1.17 -1.00

D E F

D -1.00 0.00 0.70

E -1.70 -1.00 0.00

F 0.00 0.59 -1.00

-1.7

0.7

0.59

D

F

E

Protein interaction map

-0.91

0.8

0.92

MD

MF

ME

mRNA interaction map

0.7

1.17

D2

F2

EQ

Interaction Map for Dimers

-0.85

MD ME MF

MD -1.00 0.00 0.80

ME -0.91 -1.00 0.00

MF 0.00 0.92 -1.00

Yalamanchili et al (2006) IEE Proc Systems Biol, 153, 236-246

A

PF

MA

PA

MB

AB

B

PB

[APA]

APBF2PB AF2PB

[EQPF]MF

F

FF2

PEME [D2PE]EQ E

C2PDF2PD C2F2PD

PD D2 MD

APCD2PC AD2PC

C2 C

C MC PC

MG

G

PG

[C2PG]

G2

G

MK

K

PK

[C2PK]

K2

K

[G2PH] MH

HPH

[K2PJ]

J

MJ

PJ

D

D

mRNA

Dimer

Promoter

Protein

Dimer Promoter Complex

33--ggeennee nneettwwoorrkk

Q

1100--GGEENNEE NNEETTWWOORRKK

GENE CASCADE

MUTUAL REPRESSION

AUTO ACTIVATION AND

SEQUESTRATION

AGONIST-INDUCED RECEPTOR DOWN-REGULATION

Testing in Silico: Unraveling the Wiring of a Gene Network

Yalamanchili et al (2006) IEE Proc Systems Biol, 153, 236-246

Unraveling the Wiring Using Time Series Data

Orthogonality theorem: (Fi(t), Gj(t)) = 0 Sontag et al. (2004) Bioinformatics, 20, 1877.

A vector Ai(t) is orthogonal to the linear subspace spanned by responses to perturbations affecting either one or multiple nodes different from i

ΔXi(t)

Time (t) sec0 30 60 90 120 150

PLCγ (

X i)

0

2

4

6

8

10

12

Xi(t, X0, pj+Δpj)

Xi(t, X0, pj)

Vector Gj(t) contains experimentally measured network responses Δxi(t) to parameter pj perturbation,Gj(t) = (∂Δxi/∂t, Δxi , … , Δxn)

dx/dt = f(x,p)F(t) = (∂x/∂p)

Perturbation in pj affects any nodes except node i. The goal is to determine

Fi(t) = (1, Fi1 , … , Fin) the Jacobian elements that quantify connections to xi

Inferring dynamic connections in MAPK pathway successfully

MAPK pathway kinetic diagram Deduced time-dependent strength of a negative feedback for 5, 25, and 50% perturbations

Transition of MAPK pathway from resting to stable activity state

Sontag et al. (2004) Bioinformatics 20, 1877.

Oscillatory dynamics of the feedback connection strengths is successfully deduced

Oscillations in MAPK pathway

Raf-PRaf

MEK-PPMEK-PMEK

ERK-PPERK-PERK

Ras f

The Jacobian element F15 quantifies the negative feedback strength

• (red) - 1%, ♦ (black) - 10% perturbation

Special Thanks Jan HoekMarc Birtwistle Anatoly KiyatkinNick Markevich(Thomas Jefferson University Philadelphia)

Hans WesterhoffFrank Bruggeman(Amsterdam/Manchester)

Guy Brown (Cambridge, UK)

Supported by the NIH

Mariko HatakeyamaYoshiyuki Sakaki(RIKEN, Yokohama Japan)

Holger ConzelmannJulio Saez-RodriguezErnst D Gilles(Max-Plank-Institute, Magdeburg, Germany) Eduardo Sontag (Rutgers, USA)