Network Dynamics andNetwork Dynamics andCell PhysiologyCell Physiology

John J. Tyson John J. Tyson

Biological Sciences Biological Sciences

Virginia TechVirginia Tech

CollaboratorCollaboratorss

Kathy ChenKathy ChenJill SibleJill SibleBela Novak Bela Novak Attila CsikaszAttila Csikasz

Funding Funding AgenciesAgencies

DARPADARPAMcDonnell FoundMcDonnell Found

Hanahan & Weinberg (2000)

Cell signaling

Externalsignals

InformationProcessing System

Death

DivisionReproduction

GrowthDevelopment

InternalSignals

Information Processing Systems

Laptop CellSilicon Carbon

Solid state Watery

Programmable Hard-wired

Precise Sloppy

Digital Analog

Sequential Parallel

Manufactured Self-reproducing

Designed Evolved

Silicon Carbon

BrainCarbon

Membrany

Learning

Accurate

Analog/digital

Parallel

Soma/germ

Evolved

Carbon

$$

Hanahan & Weinberg (2000)

Signal Transduction Network

p21

Smad

MAPK

MKK

MAPK-P

PP2A

R

S

0

0.5

0 1 2 3

res

po

ns

e (

R)

signal (S)

linear

0

5

0 0.5 1

S=1

R

rate

(d

R/d

t)

rate of degradation

rate of synthesis

S=2

S=3

Gene Expression

Signal-ResponseCurve

1 2

d,

d

Rk S k R

t 1

ss2

k SR

k

R

Kinase

RP

ATP ADP

H2OPi

Protein Phosphorylation

0

1

2

0 0.5 1

RP

rate

(d

RP

/dt)

0.25

0.5

1

1.5

2

Phosphatase 0

0.5

1

0 1 2 3

res

po

ns

e (

RP

)

Signal (Kinase)

“Buzzer”

Goldbeter & Koshland, 1981

1 R 0

R

S

EP E0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.5R

rate

(d

R/d

t) S=0

S=8

S=16

0

0.5

0 10

res

po

ns

e (

R)

signal (S)

Protein Synthesis:Positive Feedback

“Fuse”Bistability

Closed

Open

Griffith, 1968

Example: Fuse

0

0.5

0 10

resp

on

se (

R)

signal (S)

dying

Apoptosis(Programmed Cell Death)

living

Eissing et al. (2004) J Biol Chem 279:36892

R

S = Rtotal

E EP0

0.5

1

0 0.5 1 1.5

R

E

Coupled Buzzers

0

0.5

1

0 1 2

res

po

ns

e (

R)

signal (S)

SN

SN

“Toggle”Bistability

RP

S=0.5 S=1.5S=1

Frog egg

MPF

Cdc25-PCdc25

MPF-P

Wee1

0

0.5

1

0 1 2

resp

on

se (

MP

F)

signal (cyclin)

interphase

met

apha

se

(inactive)

S = Total Cyclin

CycBMPF =

M-phase Promoting Factor

02468

101214

0 6 12 18 24 30 60

MPF activity depends on total cyclin concentration

and on the history of the extract

Cyclin concentration increasing

inactivation threshold at 90 min

MP

F a

ctiv

ity

nM cyclin B

M

IIIIII

02468

101214

0 6 12 18 24 30 60

MP

F a

ctiv

ity

nM cyclin B

M

M

MI/MIII

Cyclin concentration decreasing

I M

bistabilityWei Sha & Jill Sible (2003)

Oscillations

0

0.5

1

0 1 2

MP

F

cyclin

MPF

Cdc25-PCdc25

MPF-P(inactive)

cyclin synthesis

cyclin degradationAPC

negative feedback loop

0.0 0.5

0

1

signal (rate of cyclin synthesis)

Hopf Hopf

res

po

ns

e (

MP

F)

sss

sssuss

Pomerening, Kim & FerrellCell (2005)

If knock-out positive feedback loop, then oscillations become faster and smaller amplitude…

Figure 4. Pomerening, Kim and Ferrell

With + feedback Without + feedback

P Wee1

Wee1P

Cdc25

CycB

PCdc20

Cdc20

CycB

APC-PAPCTFBI

TFBA

Cdc14

Cdc14

Cdc14

Cdc25

MPF

P Wee1

Wee1P

Cdc25

CycB

PCdc20

Cdc20

Cdh1

CK

I

CycB

CycBCK

I

CK

I

CycA

CycA

APC-PAPCTFBI

TFBA

TFEA

TFEI

CycE

TFIA

TFII

Cdc20

Cdc14

Cdc14

Cdc14

CycA

CycB

CycD

Cdh1CycD

Cdc25

SPF

primed RC

fired RC primed MEN

fired MEN

Cdk1

CycB

high MPF

low MPF

high SPF

low SPF

Cdk2

CycA

Cell Cycle Regulation

Cdk2

CycA

LicensingFactor

ReplicationComplex time

Csikasz-Nagy & Novak, 2005

SPF

“Cock-and-Fire”

Cdk1

CycB

Primer

Mitotic ExitNetwork

time

Csikasz-Nagy & Novak, 2005

MPF

P

Cdc25

Wee1

Wee1P

Cdc25

CycB

PCdc20

Cdc20

Cdh1

CK

I

CycB

CycBCK

I

CK

I

CycA

CycA

APC-PAPCTFBI

TFBA

CycE

CycD

TFEA

TFEI

Cyc E,A,B

CycE

TFIA

TFII

Cdc20

CK

I

CycE

Cdc14

Cdc14

Cdc14

CycA

CycA

CycB

CycD

Cdh1CycD

mass/nucleus

Fission Yeast

bistable switch

bistable switch

neg fdbk osc

P

Cdc25

Wee1

Wee1P

Cdc25

CycB

PCdc20

Cdc20

Cdh1

CK

I

CycB

CycBCK

I

CK

I

CycA

CycA

APC-PAPCTFBI

TFBA

CycE

CycD

TFEA

TFEI

Cyc E,A,B

CycE

TFIA

TFII

Cdc20

CK

I

CycE

Cdc14

Cdc14

Cdc14

CycA

CycA

CycB

CycD

Cdh1CycD

mass/ DNA

0.0 0.5 1.0 1.5

Cdc2

/Cdc1

3

10-5

10-4

10-3

10-2

10-1

100

G1

Mmass/ DNA

0 1 2

Cdc2

/Cdc1

3

10-3

10-2

10-1

100

S/G2

M

mass/nucleus

mass/ DNA

0.0 0.5 1.0 1.5 2.0

Cdc2

/Cdc1

3

0.1

1

M

Fission Yeast

0 1 2 3 4 5

0

0.4

0.8

3.0

mass/nucleus

Cd

k1:C

ycB

G1S/G2

MWild type

SNIC

SNICSNIC BifurcationBifurcation

Invariant Circle

Limit Cycle

x2

p1

node

saddle

Saddle-Node on anInvariant Circle

max

min

max

SNIC

0 1 2 3 4 5

0

0.4

0.8

3.0

mass/nucleus

Cd

k1:C

ycB

G1S/G2

MWild type

cell divisionG1

S/G2

enter Mexit M

Genetic control of cell size at cell division in yeastPaul NurseDepartment of Zoology, West Mains Road, Edinburgh EH9 3JT, UK

Nature, Vol, 256, No. 5518, pp. 547-551, August 14, 1975

wild-type wee1

P

Cdc25

Wee1

Wee1P

Cdc25

CycB

PCdc20

Cdc20

Cdh1

CK

I

CycB

CycBCK

I

CK

I

CycA

CycA

APC-PAPCTFBI

TFBA

CycE

CycD

TFEA

TFEI

Cyc E,A,B

CycE

TFIA

TFII

Cdc20

CK

I

CycE

Cdc14

Cdc14

Cdc14

CycA

CycA

CycB

CycD

Cdh1CycD

wee1

mass/nucleus

Cd

k1:C

ycB

0 1 2 3 4 5

0

0.4

0.8

1.2

G1

S/G2

M

wee1wee1 cells are about one-half the size of wild type cells are about one-half the size of wild type

0 1 2 3 4 5 60.0

0.2

0.4

0.6

0.8

1.0

Two-parameter Bifurcation Diagram

cell mass (au.)

Wee

1 ac

tivity

wild-type

B

SN2

SN1

wee1-

<30 60 90

120

150

180 210

240 270 300

period(min)

300<

HB1 2 x wee1+

Gen

etic

s

Physiology

wee1+/-

? ?

• Tyson, Chen & Novak, “Network dynamics and cell physiology,” Nature Rev. Molec. Cell Biol. 2:908 (2001).

• Tyson, Csikasz-Nagy & Novak, “The dynamics of cell cycle regulation,” BioEssays 24:1095 (2002).

• Tyson, Chen & Novak, “Sniffers, buzzers, toggles and blinkers,” Curr. Opin. Cell Biol. 15:221 (2003).

• Csikasz-Nagy et al., “Analysis of a generic model of eukaryotic cell-cycle regulation,” Biophys. J. 90:4361 (2006).

References