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

2. 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.

3. G1
cell division S
(DNA
synthesis) M
(mitosis) G2

4. 1. Alternation of S and M phases (DNA synthesis) Unaligned
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

5. Cyclin-dependent kinase SG1
cell division
Cyclin-dependent kinase S
Cdk1
CycB
DNA
replication
Tar
Tar- P M
(mitosis) G2

6. G1 G1/S cell division S DNA replication Exit M G2 (mitosis) G2/M Cdk1
CycB
DNA
replication
Exit M
(mitosis) G2
G2/M

8. cyclin B synthesis cyclin B degradation cyclin B degradation Wee1-P
less active
Wee1
Cdk1
CycB P-
less active
cyclin B
degradation
Cdk1
CycB
active MPF
Cdc25-P
Cdc25
cyclin B
degradation
less active

9. no degradation of cyclin
Solomon’s protocol for cyclin-induced activation of MPF
Cyclin M
Ca2+
centrifuge
Wee1
Cyclo-
heximide
Cyclin
Cdk1
Cdk1
Cdc25
cytoplasmic extract
no synthesis of cyclin
pellet
no degradation of cyclin

10. Threshold
MPF
Cyclin (nM)
Solomon et al. (1990)
Cell 63:1013.

11. Novak & Tyson (1993) J. Cell Sci. 106:1153 active MPF no synthesis or
Frog egg
Novak & Tyson (1993)
J. Cell Sci. 106:1153
active MPF
no synthesis or
degradation
of cyclin
total cyclin

12. 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.

13. Norel & Agur (1991). “A model for the adjustment of the mitotic clock by cyclin and MPF levels,” Science 251:
Tyson (1991). “Modeling the cell division cycle: cdc2 and cyclin interactions,” PNAS 88:
Goldbeter (1991). “A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase,” PNAS 88:
Novak & Tyson (1993). “Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos,” J. Cell Sci. 106:
Thron (1996). “A model for a bistable biochemical trigger of mitosis,” Biophys. Chem. 57:
Thron (1997). “Bistable biochemical switching and the control of the events of the cell cycle,” Oncogene 15:

14. G1
Start
cell division S
DNA
replication
Finish M
(mitosis) G2
G2/M

15. G1 Start S DNA replication Finish M G2 (mitosis) G2/M CKI Cdh1 Cln2
cell division
APC
Cdh1
CKI
Cln2 S
APC
Cdc20
Clb5
DNA
replication
Cdk
Finish
Clb2 M
(mitosis) G2
G2/M

16. Cdk Cdk CycB Cdk CycB Cdk Cln2 CycB P
Cdc20
Cdk
Cdk AA
CycB
Cdk
CycB
Cdh1
Cdh1 P
Cdk
Cln2
Cdc14
CKI
Cdk
CycB AA P
CKI
CKI
Cdc14

17. The mathematical model
synthesis
degradation
binding
activation
inactivation

18. Simulation of the budding yeast cell cycle
mass
CKI
Cln2 G1
S/M
Cdh1
Clb2
Cdc20
Time (min)

19. 30 equations 100 parameters fitted by brute force
These are the “brutes”
Kathy Chen
Laurence Calzone

20. Is the model yeast-shaped?
“With four parameters
I can fit an elephant…”
Is the model yeast-shaped?

21. Differential equations Parameter values
k1 = , 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, …

22. CKI
Cln
Cdk
CKI
+APC
Cdh1
+APC
Cdk
Cdc20
Cln
Cdk
CycB

23. Mutual antagonism and bistability...
Cdk
CycB
Cdc14
CKI
Cdh1
Cln2

24. S/G2/M
A/B
Start
Clb2/Cdk
activity
Finish G1
A + Cln2
B+Cdc14
time
Cln2
Cdc14

25. From molecular networks to cell physiology…
Wee1
0.2
0.4
0.6
0.8
1.0 10 20 30
time (min)
MPF
differential equations
simulation & analysis P
Wee1 P
Cdc2
Cdc2
CycB
CycB
Cdc25 P
G2/M
Cdc25
???
molecules
physiology

26. Our thanks to... National Science Foundation (USA)
National Science Foundation (Hungary)
National Institutes of Health
James S. McDonnell Foundation
Defense Advanced Research Project Agency