Network Dynamics and Cell Physiology · John J. Tyson Department of Biological Sciences & Virginia...

Network Dynamics andNetwork Dynamics andCell PhysiologyCell Physiology

John J. Tyson John J. Tyson Department of Biological Sciences Department of Biological Sciences & Virginia Bioinformatics Institute& Virginia Bioinformatics Institute

Outline

1. Cell Signaling: Physiology2. Cell Signaling: Molecular Biology3. Chemical Kinetics4. Sniffers, Buzzers & Toggles5. Bistability & Oscillations in Frog Eggs6. Dynamical Perspective7. Example: Fission Yeast Cell Cycle

nutrients

repellants

damage

hormones

heat shock

growth & division

movement

geneexpression

death

BacteriaGlucose

Lactose

lactosemetabolizing

enzymes

1

0 0

Fission Yeast

14 mm

7 mm

Wild type Mutant(wee1D)

Fibroblast

Growth Factor

PROLIFERATION

Extracellular Matrix

Cell-Cell Contact

Fibroblast

ProgrammedCell Death

http://www.youtube.com/watch?v=I_xh-bkiv_c&NR=1

Suprachiasmatic Nucleus12hL:12hD

ActivityBody temp

Outline


Hanahan & Weinberg (2000)

Signal Transduction Network

Cdk

C K

I C d k

Cyclin

C K

I

C d k

Cycl in

Cdk

Cycl in

P

Cyclin

Cdk

Each icon represents a chemical species. Each arrow represents a chemical reaction that occurs at a certain rate.

CyclinMPF =

M-phase Promoting Factor

X(t) = [cyclin]

1 0

0 1

, (0)

( )

dXk X X

dtX t X k t

= =

= +

T i m e ( m i n )

Cycl in(nM )

20

40

402 0 60

In te rphase arres tedFel ix e t a l . (1990)Nature 346 :379 , F ig . 1

Metaphase r e l easedTang e t a l . (1993)E M B O J 1 2 : 3 4 2 7 , F i g . 2

1. Synthesis

Estimate k1 from the “red” data:

2

2 1 / 2

2 1 / 2

2 1 / 2

2 0

0

1 / 2 0 0 0

1 / 22 2

, ( 0 )

( )

1 1( )

2

ln 2 0.72 , or

k t

k tk t

k t

d Xk X X X

d t

X t X e

X t X X e Xe

e tk k

−

−

= − =

=

= = =

= = ≅

2. Degradation

Estimate k2 from the “blue” and “green” data above.How can it be that cyclin has different half-lives in different phases of the cell cycle?

3 3 0 0

0 03 0 0

0 0

( ) ( ) ( )( ), (0) 0

(1 )( ) , where ( )

t

t

dMk C t X t k C M X M M

dt

C X eM t k C X

C X e

α

α α−

−

= = − − =

−= = −

−

3. Dimerization

X(t) = [cyclin], C(t) = [Cdc2], M(t) = [dimer],

Estimate k3 from the data below, given that C0 = 100 nM.

T i m e ( m i n )

D i m e r s(n M )

20

40

1 05 1 5

K u m a g a i & D u n p h y ( 1 9 9 5 )M o l B i o l Cel l 6 :199, F ig . 3B

( )2

1 2

1

2

1

2

, (0) 0 ,

( ) 1

Note: as , ( ) (stable steady state)

k t

dXk k X X

dt

kX t e

k

kt X t

k

−

= − =

= −

→ ∞ →

From your previous estimates of k1 and k2, estimate the steady stateconcentrations of cyclin in interphase and late anaphase (end of mitosis).

4. Synthesis and Degradation

Phase k1 k2 Xss

Interphase

Anaphase

This case is unusual in that one can write down an “exact” solution of the differential equation in terms of elementary functions. When an exact solution is not available, one canalways take other approaches…

Numerical1 2

1 2

( ) ( )( )

( ) ( ) ( ( ))

X t t X tk k X t

tX t t X t k k X t t

+ ∆ −≅ −

∆+ ∆ ≅ + − ⋅ ∆

This always works, but doesn’t provide much insight.

Graphical

+

dX/dt

X

k1

k1/ k2

dX/dt = 0 at X = k1/k2, called a “steady state” solutionX(t) approaches k1/k2 for t large (“stable” steady state)

Outline


R

S

0

0.5

0 1 2 3

resp

on

se (R

)

signal (S)

linear

0

5

0 0.5 1

S=1

R

rate

(dR

/dt)

rate of degradation

rate of synthesis

S=2

S=3

Gene Expression

Signal-ResponseCurve1 2

d,

dR

k S k Rt

= − 1ss

2

k SR

k=

R

Kinase

RP

ATP ADP

H2OPi

Protein Phosphorylation

0

1

2

0 0.5 1RP

rate

(dR

P/d

t)

0.25

0.5

1

1.5

2

Phosphatase 0

0.5

1

0 1 2 3

resp

on

se (R

P)

Signal (Kinase)

1 R 0

R

S

EP E0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.5R

rate

(dR

/dt) S=0

S=8

S=16

0

0.5

0 10

resp

on

se (R

)

signal (S)

Protein Synthesis:Positive Feedback

Example: Fuse

0

0.5

0 10

resp

onse

(R)

signal (S)

dying

Apoptosis(Programmed Cell Death)

living

Outline


0

0.5

1

0 1 2

resp

on

se (M

PF

)

signal (cyclin)

MPF

Cdc25-PCdc25

MPF-P

Wee1

(inactive)

0

0.5

1

0 0.5 1 1.5MPF

Cd

c25-

P

0

0.5

1

0 1 2 3

Cd

c25-

P

MPF

S = Total Cyclin

centrifuge

Solomon’s protocol for cyclin-induced activation of MPF

cytoplasmic extract

pellet

Ca2+ M

Cyclin

Cyclo-heximide

Cyclin

Cdk1

Cell 63:1013 (1990)

Threshold

0

20

40

60

80

100

120

0 10 20 30

Cyclin (nM)

CD

K a

ctiv

ity

Solomon et al. (1990)Cell 63:1013.

Novak & Tyson (1993) J. Cell Sci. 106:1153

Pomerening et al., Nature Cell Biology 5:346-351 (2003)

Sha et al., PNAS 100:975-980 (2003)

Testing activation threshold for Mitosis I

Interphase

Mitosis I

∆90Cyclin B1 and 100 µg/ml CHX

Testing Thresholds in Cycling Extracts

Testing inactivation threshold for Mitosis I

Interphase Interphase

Mitosis I

∆90Cyclin B1

100 µg/ml CHX

MPFactivity

time

16 24 32 400∆90 cyclin B (nM) :

90 min

0 min

60 min

140 min

0∆90 cyclin B (nM) : 16 3224 40

M

M M M

The activation threshold for Mitosis I is between 32 and 40 nM.

The inactivation threshold for Mitosis I is between 16 and 24 nM.

0

0.5

1

0 1 2

MP

F

cyclin

MPF

Cdc25-PCdc25

MPF-P(inactive)

cyclin synthesis

cyclin degradationAPC

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

Figure 4. Pomerening, Kim and Ferrell

With + feedback Without + feedback

• 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

Outline


Cdk

C K

I C d k

Cyclin

C K

I

C d k

Cycl in

Cdk

Cycl in

P

Cyclin

Cdk

Wee1Cdc25

= k1 - (kwee + k2) * MPF + k25 (cyclin - MPF)

= k1 - k2 * cyclin

d MPFdt

d cyclindt

MPF

Cyclin

Phase Plane dx/dt=f(x,y)dy/dt=g(x,y)

(xo,yo)

∆x=f(xo,yo) ∆t

∆y=g(xo,yo) ∆t

One-parameter bifurcation diagram

parameter

variable

stable steady stateunstable steady state

saddle-nodesaddle-node

Signal Responset t

p x

OFF

ON

(signal)

(response)

x

y

One-parameter bifurcation diagram

parameter

variable

stable steady stateunstable steady state

saddle-nodesaddle-node Hopf

(signal)

(response)

MPF

Cyclin


MPF

Cyclin


MPF

Cyclin


Hopf BifurcationHopf Bifurcation

x2

p1

stable limit cycle

sssuss

slc max

min

Hopf BifurcationHopf Bifurcation

x2

p1

sssuss

slc

parameter(signal)

variable(response)

Hopf

Second Parameter

subcritical

Second Parameter

CF

parameter(signal)

variable(response)

SNIC

Second Parameter

SL

SNIC BifurcationSNIC Bifurcation

Invariant Circle

Limit Cycle

x2

p1

node

saddle

Saddle-Node on anInvariant Circle

max

min

maxSNIC

Signal-Response Curve = One-parameter Bifurcation Diagram

•Saddle-Node•Supercritical Hopf•Subcritical Hopf•Cyclic Fold•Saddle-Node Invariant Circle

Outline


S

G1

DNAreplication

G2Mmitosis

cell division

1) Alternation ofS phase and M phase.

2) Balanced growth anddivision.

3) Checkpoints

P

Cdc25

Wee1

Wee1P

Cdc25

CycB

P

Cdc20

CK

I

CycB

CycBCK

I

CK

I

CycA

CycA

APC-PAPCTFBI

TFBA

CycE

CycD

TFEA

TFEI

Cyc E,A,B

CycE

TFIA

TFII

CK

I

CycE

Cdc14

Cdc14

Cdc14

CycA

CycA

CycB

CycD

Cdh1CycD

0 50 100 150 200 250 300

0

1

2

3

4

5

mass/nucleus

P Cdk1CycB

Cdk1CycB

CKI

Cdh1

Cdc20

Wee1

Cdc25

Time (min)

S G2 MG1 S G2 MG1 S

Gene Viable? Traitcdc2 − No block in G2cdc13 − No block in G2rum1 − Yes sterileste9 − Yes sterileslp1 − Yeswee1 − Yes smallcdc25 − No block in G2

cdc2 OP Yes wtcdc13 OP Yes wtrum1 OP No endoreplic.ste9 OP Yes wtwee1 OP Yes largecdc25 OP Yes small

wee1 − rum1∆ No extremely smallwee1 − cdc25∆ Yes quantized cycleswee1 − cdc25 OP No cutwee1 OP cdc25 − No block in G2

Mutants in Fission YeastMutants in Fission Yeast

P

Cdc25

Wee1

Wee1P

Cdc25

CycB

P

Cdc20

CK

I

CycB

CycBCK

I

CK

I

CycA

CycA

APC-PAPCTFBI

TFBA

CycE

CycD

TFEA

TFEI

Cyc E,A,B

CycE

TFIA

TFII

CK

I

CycE

Cdc14

Cdc14

Cdc14

CycA

CycA

CycB

CycD

Cdh1CycD

mass/DNA

0.0 0.5 1.0 1.5

Cdc2

/Cdc

13

10-5

10-4

10-3

10-2

10-1

100

G1

Mmass/DNA

0 1 2

Cdc2

/Cdc

13

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

/Cdc

13

0.1

1

M

0 1 2 3 4 5

0

0.4

0.8

3.0

mass/nucleus

Cdk1

:Cyc

B

G1S/G2

M

SNICHopf SN1SN2SN3

P

Cdc25

Wee1

Wee1P

Cdc25

CycB

P

Cdc20

CK

I

CycB

CycBCK

I

CK

I

CycA

CycA

APC-PAPCTFBI

TFBA

CycE

CycD

TFEA

TFEI

Cyc E,A,B

CycE

TFIA

TFII

CK

I

CycE

Cdc14

Cdc14

Cdc14

CycA

CycA

CycB

CycD

Cdh1CycD

mass/nucleus

wee1∆

mass/nucleus

Cdk1

:Cyc

B

0 1 2 3 4 5

0

0.4

0.8

1.2

G1

S/G2

M

P

Cdc25

Wee1

Wee1P

CycB

P

Cdc20

CK

I

CycB

CycBCK

I

CK

I

CycA

CycA

APC-PAPCTFBI

TFBA

CycE

CycD

TFEA

TFEI

Cyc E,A,B

CycE

TFIA

TFII

CK

I

CycE

Cdc14

Cdc14

Cdc14

CycA

CycA

CycB

CycD

Cdh1CycD

Cdc25

mass/nucleus

mass/nucleus

Cdk1

:Cyc

B

G1 S/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

P

Cdc20

CK

I

CycBCK

I

CK

I

CycA

CycA

APC-PAPCTFBI

TFBA

CycE

CycD

TFEA

TFEI

Cyc E,A,B

CycE

TFIA

TFII

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∆ wee1ts

mass/nucleus

Cdk1

:Cyc

B

Unbalanced Growthand Division …

is Lethal !

Date post:	13-Oct-2020
Category:	Documents
Upload:	others
View:	1 times
Download:	0 times

Network Dynamics and Cell Physiology · John J. Tyson Department of Biological Sciences & Virginia...

Documents