Computational Modeling of the Cell Cycle

Eric Sobie

Pharmacology and Systems Therapeutics Mount Sinai School of Medicine [email protected]

1

Outline

Lecture 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

Basics of the cell cycle

G 2



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: 1) synthesis/degradation of cyclin 2) Phosphorylation/dephosphorylation of Cdk

3

Basics of the cell cycle

cyclin is alternately synthesized and degraded We will only consider M-type cyclins (aka cyclinB), not others

4

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

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

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

d

[

cyclin



P

] 

k

6 [

MPF

] 

k

7 [

cyclin



P

]

dt d

[

MPF

]

dt d

[

cdc

2 

P

] 

k

8 [

cdc

2 ] 

k

9 [

cdc

2 

P

] 

k

3 [

cdc

2

dt

 

k

6 [

MPF

] 

k

5 [

MPF

]  [

pMPF

]   

k

4 ' 

k

4   

P

[ ][

cyclin MPF

] ([

CDC

2 ]

TOT

] )   2    7

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

8

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 (k 6 = constant) 2) degradation is time-dependent, presumably reflecting changes in cell size. Alberts et al., Molecular Biology of the Cell

9

Simplifications of the Tyson model 3) Does not include wee1 Boutros et al. (2007) Nature Reviews Cancer 7:495-507 wee1 opposes MPF activation MPF opposes wee1 activation Therefore MPF regulates both: 1) activation of MPF (de-phosphorylation of CDK) 2) inactivation of MPF (phosphorylation of CDK)

10

What did the Tyson model show?

1) The model can oscillate spontaneously Whether this oscillation occurs depends on k 4 and k 6 This result confirms the experimental observations that (1) de-phosphorylation of cdc-2 (k 4 ) and (2) degradation of cyclin (k 6 ), are the two key steps

11

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

What did the Tyson model show?

3) The model can show "excitability" In this regime, oscillations do not occur at fixed k 6 , but periodic changes in k 6 can cause periodic changes in [MPF] This was considered analogous to growth control of cell division.

13

Good models typically evolve

Compare 1991 model with 1993 model Tyson (1991) PNAS 88:100:7328-7332 Novak & Tyson (1993) J. Cell Science 106:1153-1168 diagram from Sible & Tyson (2007) Between 1991 and 1993, new processes were added to the model

14

1991 model versus 1993 model Autocatalytic activation of MPF Tyson (1991) Active MPF Novak & Tyson (1993) Inactive MPF Direct effect of [MPF]

J pMPF



MPF

 [

pMPF

]   

k

4 ' 

k

4   [

MPF

] ([

CDC

2 ]

TOT

)   2   

Inactive MPF Active MPF Occurs through cdc25

J pMPF



MPF

 [

pMPF

](

k

' 25 [

CDC

25 ] 

k

25 [

CDC

25 

P

])

J CDC

25 

CDC

25 

P



k a

[

MPF

][

CDC

25 ] [

CDC

25 ] 

K a

15

1991 model versus 1993 model Degradation of cyclin Tyson (1991) Novak & Tyson (1993) Active MPF Degradation occurs at a constant rate (k 6 = constant) Active MPF [MPF] indirectly activates APC

16

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

Good models typically evolve

Since 1993, more components have been included A model specific to budding yeast Chen et al. (2004) Mol. Biol. Cell 15:3841-3862.

18

Implementing the Tyson model

Variable definitions Matlab variable name Y YP C2 CP M pM Biochemical name cyclin cyclin-P cdc2 cdc2-P MPF = cyclin-P/cdc2 preMPF = cyclin-P/cdc2-P

19

Implementing the Tyson model

Complete Equations Tyson (1991) PNAS 88:100:7328-7332

20

Implementing the Tyson model

Notation 1) The equations are given in Table 1 on the paper.

2) Some rate constants are defined as k x [~P], where [~P] is the constant phosphate concentration. Thus, k 5 and k 8 in the model represent k 5 [~P] and k 8 [~P], respectively. 3) Similarly, Tyson defines the rate of cyclin synthesis as k 1 [aa], where [aa] stands for amino acids. We will just refer to this as k 1 .

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

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).

www.sciencesignaling.org