Network Dynamics andNetwork Dynamics andCell PhysiologyCell Physiology

John J. Tyson John J. Tyson

Dept. Biological Sciences Dept. Biological Sciences

Virginia TechVirginia Tech

Budapest Univ. Techn. & Econ.Budapest Univ. Techn. & Econ.

Bela NovakBela Novak

Attila Csikasz-NagyAttila Csikasz-Nagy

Andrea CilibertoAndrea Ciliberto

Virginia TechVirginia Tech

Kathy ChenKathy Chen

Dorjsuren BattogtokhDorjsuren Battogtokh

CollaboratorsCollaborators

FundingFunding

James S. McDonnell FoundationJames S. McDonnell Foundation

DARPADARPA

Computational Molecular BiologyComputational Molecular Biology

DNA

mRNA

Protein

Enzyme

Reaction Network

Cell Physiology

…TACCCGATGGCGAAATGC...

…AUGGGCUACCGCUUUACG...

…Met -Gly -Tyr -Arg -Phe -Thr...

ATP ADP

-P

X Y ZE1

E2

E3E4

Last Step

S

G1

DNAreplication

G2Mmitosis

cell division

The cell cycle is thesequence of events wherebya growing cell replicates allits components and dividesthem more-or-less evenly

between two daughter cells...

Cdk1

S

G1

DNAreplication

G2Mmitosis

cell division

CycB

P P

Cyclin-dependentkinase

Cyclin B

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

Coupled Intra-cellular Networks !

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

R

S

EP E0

0.05

0.1

0 0.5 1 1.5

0

0.5

1

0 1 2R

rate

(d

R/d

t)

res

po

ns

e (

R)

signal (S)

S=0.6

S=1.2

S=1.8

SN

SN

Protein Degradation:Mutual Inhibition

“Toggle”Bistability

R

S

EP E

X

0 50

1

X

R

Positive Feedback & Substrate Depletion

positive

substrate

0.0 0.5

0

1

signal (S)

Hopf Hopf

res

po

ns

e (

R)

“Blinker”

Glycolytic Oscillations

Oscillation

sss

sssuss

Higgins, 1965; Selkov, 1968

S

X

Y YP

R RP

0

5

0 25 50

0

0.5

1

0 2 4 6

0.0

0.1

0.2

0.3

0.4

0.5

time

XYP

RP

res

po

ns

e (

RP

)

signal (S)

HopfHopf

Negative Feedback Loop

Goodwin, 1965

Example: Bacterial Chemotaxis

Barkai & Leibler, 1997 Goldbeter & Segel, 1986

Bray, Bourret & Simon, 1993

R

S X

0

5

0 1 2R

rate

(d

R/d

t)

S=1

S=3

S=2

0.9

1.4

1.9

0 10 20

-1

0

1

2

3

4

5

S

X

R

time

Sniffer

Response isindependent

of Signal

1 2

3 4

d

dd

d

Rk S k XR

tX

k S k Xt

(Levchenko & Iglesias, 2002)

primed RC

fired RC primed MEN

fired MEN

Cdk1

CycB

high MPF

low MPF

high SPF

low SPF

Cdk2

CycA

Example 2: Cell Cycle

(Csikasz-Nagy& Novak, 2005)

LA

Response = F

L

Signal = CDK

Cock-and-Fire

LAL

+

Cdk2

CycA

F+

Signal = MPF

Response = BA

TA T

TABAB

+

+

Cdk1

CycB

Cock-and-Fire-2

P 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

bistable switch

bistable switch

bistable switch

oscillator

oscillator

Cdc25

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

SNIPER

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

cell mass (au.)

Wee

1 ac

tivity

wild-type

wee1-

0 0 50 100 150 200 250 300 350 400 450 500 550

30 60

90

120

150

180

210

240

270 300

period(min)

PHYSIOLOGY

GENETICS

Two-parameter Bifurcation Diagram

SNIPER

P

Cdc25

Wee1

Wee1P

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

Cdc25

mass/nucleus

Cd

k1:C

ycB

G1S/G2

M

0 1 2 3 4 5

0

0.4

0.8

3.0 cki

The Start module is not required during mitotic cyclesThe Start module is not required during mitotic cycles

P

Cdc25

Wee1

Wee1P

Cdc25

CycB

PCdc20

Cdc20

Cdh1

CK

I

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

CycB

0

0.4

0.8

2.0

0 1 2 3 4 5

G1

S/G2

M

cki wee1ts1st

2nd

3rd

4th

mass/nucleus

Cd

k1:C

ycB

Cells become progressively smaller without size controlCells become progressively smaller without size control

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

endoreplication

0 1 2 3 4

0.0001

0.001

0.01

0.1

1

Act

Cyc

A

cdc13

Fission yeast

0 1 2 3 4 5 6

0.000

0.005

0.010

0.015

0.020

0.025

0.030

2 param bifn diag for Cdc13

mitoticcycles

endoreplication

S

G2G1

M

mitotic cycle

mass

Pro

duc

tion

of

Cdc

13

XNo production of cyclin B (Cdc13)

Wild type

cdc13

cdc13 +/??

The Dynamical PerspectiveThe Dynamical Perspective

Molecular MechanismMolecular Mechanism

??

??

??

Physiological PropertiesPhysiological Properties

The Dynamical PerspectiveThe Dynamical Perspective

Molecular MechanismMolecular Mechanism

Kinetic EquationsKinetic Equations

Vector FieldVector Field

Stable AttractorsStable Attractors

Physiological PropertiesPhysiological Properties

d CycBT

dt = k1 . M - (k2' + k2" . Ste9 +k2'" . Slp1A) . CycBT

dSte9

dt = k3' .

1 - Ste9J3 + 1 - Ste9 - (k4'

. SK + k4 . CycB) .

Ste9J4 + Ste9

d Rum1T

dt = k11 - (k12 + k12' . SK + k12" . CycB) . RUM1T

dSlp1A

dt = k7 . IE .

Slp1T - Slp1A

J7 + Slp1T - Slp1A - k8

. Slp1A

J8 + Slp1A - k6

. Slp1A

dMdt = . M

References

• 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).