Modeling the Cell CycleModeling the Cell CycleEngine of EukaryotesEngine of Eukaryotes

John J. Tyson & Bela NovakJohn J. Tyson & Bela Novak

Virginia Polytechnic Institute & State Univ.Virginia Polytechnic Institute & State Univ.

Budapest Univ. Technology & EconomicsBudapest 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.

S

cell d

ivision

G1

(DNAsynthesis)

G2M(mitosis)

S

cell d

ivision

G1

(DNAsynthesis)

G2M(mitosis)

1. Alternation of S and M phases

2. Balanced growth and division

G1/S checkpoint

Too small?DNA damage?

Unreplicated DNA?Too small?

G2/M checkpoint

Metaphase checkpoint

Unalignedchromosomes?

S

G1

DNAreplication

G2M(mitosis)

cell division

Cdk1

CycB

Cyclin-dependent kinase

Tar Tar- P

Cdk1

CycB

G1/S

S

G2

Exi

t

G1

DNAreplication

G2/MM

(mitosis)

cell division

Cdk1

CycB

Wee1-P

Cdc25

Cdc25-P

Wee1

active MPF

less active

less activecyclin Bsynthesis

cyclin Bdegradation

Cdk1

CycB

P-less active

cyclin Bdegradation

centrifuge

Solomon’s protocol for cyclin-induced activation of MPF

cytoplasmic extract

pellet

Ca2+ M

Cyclin

Cyclo-heximide

Cdk1Wee1

Cdc25

Cyclin

Cdk1

no synthesis of cyclin

no degradation of cyclin

Threshold

0

20

40

60

80

100

120

0 10 20 30

Cyclin (nM)

MPF

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

total cyclin

acti

ve M

PF

Frog egg

no synthesis ordegradation

of cyclin

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

Ti Ta Tcyclin level cyclin level

MP

F a

ctiv

ity

MP

F a

ctiv

ity

hysteretic non-hysteretic

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,” Science 251:1076-1078.

Tyson (1991). “Modeling the cell division cycle: cdc2 and cyclin interactions,” PNAS 88:7328-7332.

Goldbeter (1991). “A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase,” PNAS 88:9107-9111.

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,” Oncogene 15:317-325.

Start

S

cell d

ivision

Fin

ish

G1

DNAreplication

G2G2/M

M(mitosis)

Start

S

cell d

ivision

Fin

ish

G1

DNAreplication

G2G2/M

M(mitosis)

APC

Cdc20APC

Cdh1CKI

Cdk

Clb2

Clb5

Cln2

AACdk

CycB

Cdh1

CK

I Cdk

CycB

CK

I

AAP

CK

I

CycB

Cdk

Cdk

Cdc14

Cdc14

Cdh1 P

Cdc20

CdkCln2

The mathematical model

'1 1 2

d[Cln2][SBF] [Cln2]

dk k k

t

' '3 3 4 4 5

d[Clb2][Mcm1] [Cdh1] [Clb2] [Sic1][Clb2]

dk k k k k

t

' '6 6 T 7 7

6 T 7

[Cdc20] [Cdh1] [Cdh1] [Clb5] [Cdh1]d[Cdh1]

d [Cdh1] [Cdh1] [Cdh1]

k k k k

t J J

synthesis degradation

synthesis degradation binding

activation inactivation

0 50 100 150

0.0

0.5

1.0

1.5

0.0

0.5

0.0

0.5

1.0

1

2

Time (min)

CKI

mass

Clb2

Cln2

Cdh1

Simulation of the budding yeast cell cycle

G1 S/M

Cdc20

30 equations30 equations100 parameters100 parameters

fitted by brute forcefitted by brute force

These are the “brutes”These are the “brutes”

Kathy ChenKathy Chen Laurence CalzoneLaurence Calzone

Is the model yeast-shaped?

“With four parametersI can fit an elephant…”

Table 6. Properties of clb, sic1, and hct1 mutants

mass at birth

mass at

SBF 50%

mass at

DNA repl.

mass at bud ini.

mass at division

TG1

(min)

changed

parameter

Comments

1 wild type

(daughter) 0.71 1.07

(71’) 1.15 (84’)

1.15 (84’)

1.64 (146’)

84 CT 146 min (time of occurrence of event)

2 clb1 clb2

0.71 1.07 1.16 1.16 No mit k's,b2 = 0

k"s,b2 = 0 Surana 1991 Table 1, G2 arrest.

3 clb1 clb2

1X GAL-CLB2 0.65 1.10 1.19 1.19 1.50 105 k's,b2 = 0.1

k"s,b2 = 0 Surana 1993 Fig 4, 1X GAL-CLB2 is OK, 4X GAL-CLB2 (or 1X GAL-CLB2db) causes telophase arrest.

4 clb5 clb6 0.73 1.07

(65’) 1.30 (99’)

1.17 (80’)

1.70 (146’)

99 k's,b5 = 0 k"s,b5 = 0

Schwob 1993 Fig 4, DNA repl begins 30 min after SBF activation.

5 clb5 clb6

GAL-CLB5 0.61 0.93 0.92 0.96 1.41 73 k's,b5 = 0.1

k"s,b5 = 0 Schwob 1993 Fig 6, DNA repl concurrent with SBF activation in both GAL-CLB5 and GAL-CLB5db.

6 sic1 0.66 1.00

(73’) 0.82 (37’)

1.06 (83’)

1.52 (146’)

38 k's,c1 = 0 k"s,c1 = 0

Schneider 1996 Fig 4, sic1 uncouples S phase from budding.

7 sic1 GAL-SIC1 0.80 1.07 1.38 1.17 1.86 94 k's,c1 = 0.1 k"s,c1 = 0

Verma 1997 Fig3B, Nugroho & Mendenhall 1994 Fig 2, most cells are viable.

8 hct1 0.73 1.08 1.17 1.18 1.69 82 k"d,b2 = 0.01 Schwab 1997 Fig 2, viable, size like WT, Clb2 level high

throughout the cycle. 9 sic1 hct1

0.71 No SBF 0.72 No bud No mit k's,c1 = 0

k"d,b2 = 0.01 Visintin 1997, telophase arrest.

10 sic1 GAL-CLB5

first cycle second cycle

0.71 0.52

0.74

0.73

No repl

0.76

1.20

k's,b5 = 0.1 k"s,b5 = 0 k's,c1 = 0

Schwob 1994 Fig 7C, inviable. First cycle OK, DNA repl advanced; but pre-repl complexes cannot form and cell dies after the first cycle.

d CDK dt = k1 - (v2’ + v2” . Cdh1 ) . CDK

d Cdh1dt =

(k3’ + k3” . Cdc20A) (1 - Cdh1) J3 + 1 - Cdh1 -

(k4’ + k4” . CDK . M) Cdh1 J4 + Cdh1

d IEPdt = k9

. CDK . M . (1 – IEP ) – k10 . IEP

d Cdc20T

dt = k5’ + k5” (CDK . M)4

J54 + (CDK . M)4 - k6

. Cdc20T

d Cdc20A

dt = k7

. IEP (Cdc20T - Cdc20A) J7 + Cdc20T - Cdc20A

- k8

. MAD Cdc20A

J8 + Cdc20A - k6

. Cdc20T

Differential equations Parameter values

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,

…

CdkCycB

Cdh1 CK

I

Cdc20 ClnCdk

+APC ClnCdk

+APC CK

I

Cdk

CycB

CKICdh1

Cln2

Cdc14

Mutual antagonism and bistability...

Clb2/Cdkactivity

A + Cln2B+Cdc14

A/B

G1

S/G2/M

Start

Finish

time

Cln2 Cdc14

P

Wee1P

Cdc25

Cdc25

Wee1

G2/

M

Cdc2

CycBP

Cdc2

CycB

???molecules

physiology

From molecular networks to cell physiology…From molecular networks to cell physiology…

0

0.2

0.4

0.6

0.8

1.0

0 10 20 30time (min)

MP

F

d CDK dt = k1 - (v2’ + v2” . Cdh1 ) . CDK

d Cdh1dt =

(k3’ + k3” . Cdc20A) (1 - Cdh1) J3 + 1 - Cdh1 -

(k4’ + k4” . CDK . M) Cdh1 J4 + Cdh1

d IEPdt = k9

. CDK . M . (1 – IEP ) – k10 . IEP

d Cdc20T

dt = k5’ + k5” (CDK . M)4

J54 + (CDK . M)4 - k6

. Cdc20T

d Cdc20A

dt = k7

. IEP (Cdc20T - Cdc20A) J7 + Cdc20T - Cdc20A

- k8

. MAD Cdc20A

J8 + Cdc20A - k6

. Cdc20T

differential equations

simulation & analysis

National Science Foundation (USA)National Science Foundation (Hungary)National Institutes of HealthJames S. McDonnell FoundationDefense Advanced Research Project Agency

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