1. Computational Modeling of the Cell Cycle
Eric Sobie
Pharmacology and Systems Therapeutics
Mount Sinai School of Medicine 1

2. Outline Lecture Workshop Biological background
Regulation of mitosis-promoting factor (MPF)
Steps that occur during rapid, post-fertilization cell cycles
The Tyson (1991) cell cycle model
Biology captured by the model
Important model results
Simplifications of the Tyson model
Comparison with biology taught by Dr. Hirsch
Improvements made over the years
Workshop
Implementation of the Tyson cell cycle model
Simulations of disruptions to normal cell division
Adding complexity to the model 2

3. Basics of the cell cycle
G2M transition driven by increase in MPF
MPF = Mitosis-Promoting Factor
pre-MPF
Active MPF
Cyc = cyclin
Cdk = cyclin-dependent kinase
Two obvious ways to regulate Cdk/MPF activity:
synthesis/degradation of cyclin
Phosphorylation/dephosphorylation of Cdk 3

4. Basics of the cell cycle
cyclin is alternately synthesized and degraded
We will only consider M-type cyclins (aka cyclinB), not others 4

5. Basics of the cell cycle
Positive feedback in activation of MPF
Greater MPF activity  Greater cdc25 activity
Greater cdc25 activity  Greater MPF activity
Positive feedback also referred to as: autocatalysis 5

6. The Tyson (1991) cell cycle model
Active MPF
cdc2 = name of yeast gene
cdk1 = name of protein
k for kinase
This minimal, and old, cell cycle model contains several simplifications compared with what we now know. 6

7. The Tyson (1991) cell cycle model
Active MPF
Plus 3 additional ODEs
Each ODE reflects:
rate of appearance –
rate of disappearance
Pre-MPF 7

8. Simplifications of the Tyson model
1) Autocatalytic activation of MPF
Model
Current knowledge
Active MPF
Inactive MPF
Alberts et al., Molecular Biology of the Cell 8

9. Simplifications of the Tyson model
2) What triggers degradation of cyclin?
Current knowledge
Model
Active MPF
Tyson considers two possibilities:
1) degradation occurs at a constant rate (k6 = constant)
2) degradation is time-dependent, presumably reflecting changes in cell size.
Alberts et al., Molecular Biology of the Cell 9

10. Simplifications of the Tyson model
3) Does not include wee1
Boutros et al. (2007) Nature Reviews Cancer 7:
wee1 opposes MPF activation
MPF opposes wee1 activation
Therefore MPF regulates both:
activation of MPF (de-phosphorylation of CDK)
inactivation of MPF (phosphorylation of CDK) 10

11. What did the Tyson model show?
1) The model can oscillate spontaneously
Whether this oscillation occurs depends on k4 and k6
This result confirms the experimental observations that (1) de-phosphorylation of cdc-2 (k4) and (2) degradation of cyclin (k6), are the two key steps 11

12. What did the Tyson model show?
2) Nonoscillating regimes show two types of behavior
In region (A), [MPF] is high, as in metaphase arrest of mature oocytes.
In region (C), [MPF] is low, as in nondividing somatic cells. 12

13. What did the Tyson model show?
3) The model can show "excitability"
In this regime, oscillations do not occur at fixed k6, but periodic changes in k6 can cause periodic changes in [MPF]
This was considered analogous to growth control of cell division. 13

14. Good models typically evolve
Compare 1991 model with 1993 model
Tyson (1991) PNAS 88:100:
Novak & Tyson (1993) J. Cell Science 106:
diagram from Sible & Tyson (2007)
Between 1991 and 1993, new processes were added to the model 14

15. Autocatalytic activation of MPF
1991 model versus 1993 model
Autocatalytic activation of MPF
Tyson (1991)
Novak & Tyson (1993)
Active MPF
Inactive MPF
Active MPF
Occurs through cdc25
Inactive MPF
Direct effect of [MPF] 15

16. 1991 model versus 1993 model Degradation of cyclin Tyson (1991)
Novak & Tyson (1993)
Active MPF
Active MPF
Degradation occurs at a constant rate (k6 = constant)
[MPF] indirectly activates APC 16

17. Good models typically evolve
Since 1993, more components have been included
Generic model of cell cycle regulation
Csikász-Nagy et al. (2006) Biophysical Journal 90:4361 – 4379. 17

18. Good models typically evolve
Since 1993, more components have been included
A model specific to budding yeast
Chen et al. (2004) Mol. Biol. Cell 15: 18

19. Implementing the Tyson model
Variable definitions
Matlab variable name
Biochemical name Y YP C2 CP M pM
cyclin
cyclin-P
cdc2
cdc2-P
MPF = cyclin-P/cdc2
preMPF = cyclin-P/cdc2-P 19

20. Implementing the Tyson model
Complete Equations
Tyson (1991) PNAS 88:100: 20

21. Implementing the Tyson model
Notation
1) The equations are given in Table 1 on the paper.
2) Some rate constants are defined as kx[~P], where [~P] is the constant phosphate concentration. Thus, k5 and k8 in the model represent k5[~P] and k8[~P], respectively.
3) Similarly, Tyson defines the rate of cyclin synthesis as k1[aa], where [aa] stands for amino acids. We will just refer to this as k1.
4) The differential equations for [M] and [pM] contain an additional function, F([M]), that is listed in the Table 1 legend. This equation, which is also provided in the notes, is critical for the proper functioning of the model.
Assignments
1) Get the model to run
2) Plot all variables separately
3) Plot more informative ratios of variables
4) Explore changes in rate of cyclin degradation
5) Homework assignment: incorporate effects of wee1. 21

22. Slides from a lecture in the course Systems Biology—Biomedical Modeling
Citation: E. A. Sobie, Computational modeling of the cell cycle. Sci. Signal. 4, tr11 (2011).