Modeling the cell cycle engine of eukaryotes
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Modeling the Cell Cycle Engine of Eukaryotes. John J. Tyson & Bela Novak Virginia Polytechnic Institute & State Univ. Budapest Univ. Technology & Economics.

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Modeling the Cell Cycle Engine of Eukaryotes

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Modeling the Cell CycleEngine of Eukaryotes

John J. Tyson & Bela Novak

Virginia Polytechnic Institute & State Univ.

Budapest Univ. Technology & Economics


The cell cycle is the sequence of events by which a growing cell replicates all its components and divides them more-or-less evenly between two daughter cells...

…so that the two daughter cells contain all the information and machinery necessary to repeat the process.


G1

cell division

S

(DNA

synthesis)

M

(mitosis)

G2


G1

Too small?

DNA damage?

G1/S checkpoint

cell division

S

1. Alternation of S and M phases

(DNA

synthesis)

Unaligned

chromosomes?

2. Balanced growth and division

Metaphase

checkpoint

Unreplicated DNA?

Too small?

M

(mitosis)

G2

G2/M checkpoint


Cdk1

CycB

Tar

Tar- P

G1

cell division

Cyclin-dependent kinase

S

DNA

replication

M

(mitosis)

G2


Cdk1

CycB

G1

G1/S

cell division

S

DNA

replication

Exit

M

(mitosis)

G2

G2/M


Wee1-P

Wee1

Cdk1

Cdk1

CycB

CycB

P-

less active

Cdc25-P

Cdc25

cyclin B

degradation

cyclin B

synthesis

less active

active MPF

cyclin B

degradation

less active


Cyclin

Cdk1

Cyclin

M

Solomon’s protocol for cyclin-induced activation of MPF

Ca2+

centrifuge

Wee1

Cyclo-

heximide

Cdk1

Cdc25

cytoplasmic extract

no synthesis of cyclin

pellet

no degradation of cyclin


Threshold

MPF

Cyclin (nM)

Solomon et al. (1990)

Cell 63:1013.


Frog egg

Novak & Tyson (1993)

J. Cell Sci.106:1153

active MPF

no synthesis or

degradation

of cyclin

total cyclin


hysteretic

non-hysteretic

MPF activity

MPF activity

Ti

Ta

T

cyclin level

cyclin level

Prediction: The threshold concentration of cyclin B required to activate MPF is higher than the threshold concentration required to inactivate MPF.


Norel & Agur (1991). “A model for the adjustment of the mitotic clock by cyclin and MPF levels,” Science251:1076-1078.

Tyson (1991). “Modeling the cell division cycle: cdc2 and cyclin interactions,” PNAS88:7328-7332.

Goldbeter (1991). “A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase,” PNAS88:9107-9111.

Novak & Tyson (1993). “Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos,” J. Cell Sci.106:1153-1168.

Thron (1996). “A model for a bistable biochemical trigger of mitosis,” Biophys. Chem.57:239-251.

Thron (1997). “Bistable biochemical switching and the control of the events of the cell cycle,” Oncogene15:317-325.


G1

Start

cell division

S

DNA

replication

Finish

M

(mitosis)

G2

G2/M


CKI

Cdh1

APC

Cdc20

APC

G1

Start

cell division

Cln2

S

Clb5

DNA

replication

Cdk

Finish

Clb2

M

(mitosis)

G2

G2/M


Cdc20

P

Cdk

Cln2

P

Cdh1

CKI

AA

Cdk

Cdk

AA

CycB

Cdk

CycB

Cdh1

Cdc14

Cdk

CKI

CycB

CKI

Cdc14


synthesis

synthesis

binding

degradation

degradation

inactivation

activation

The mathematical model


G1

S/M

Simulation of the budding yeast cell cycle

mass

CKI

Cln2

Clb2

Cdh1

Cdc20

Time (min)


These are the “brutes”

Kathy Chen

Laurence Calzone

30 equations

100 parameters

fitted by brute force


“With four parameters

I can fit an elephant…”

Is the model yeast-shaped?


k1 = 0.0013, v2’ = 0.001, v2” = 0.17,

k3’ = 0.02, k3” = 0.85, k4’ = 0.01, k4” = 0.9,

J3 = 0.01, J4 = 0.01, k9 = 0.38, k10 = 0.2,

k5’ = 0.005, k5” = 2.4, J5 = 0.5, k6 = 0.33,

k7 = 2.2, J7 = 0.05, k8 = 0.2, J8 = 0.05,

Parameter values

Differential equations


Cdk

Cln

CKI

CKI

+APC

Cdh1

+APC

Cdk

Cdc20

Cln

Cdk

CycB


Cdc14

Cln2

Mutual antagonism and bistability...

Cdk

CycB

CKI

Cdh1


Start

Finish

A/B

Cdc14

Cln2

time

S/G2/M

Clb2/Cdk

activity

G1

A + Cln2

B+Cdc14


From molecular networks to cell physiology…

1.0

0.8

MPF

0.6

0.4

0.2

0

0

10

20

30

time (min)

differential equations

simulation & analysis

Wee1

P

Wee1

P

Cdc2

Cdc2

CycB

CycB

Cdc25

P

G2/M

Cdc25

???

molecules

physiology


Our thanks to...

National Science Foundation (USA)

National Science Foundation (Hungary)

National Institutes of Health

James S. McDonnell Foundation

Defense Advanced Research Project Agency


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