A simple model for the eukaryotic cell cycle. Andrea Ciliberto

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1 A simple model for the eukaryotic cell cycle Andrea Ciliberto

2 The cell division cycle G1 cell division Start S (DNA Replication) Finish M (mitosis) G2/M G2

3 Kohn, Mol. Biol. Cell., 1999

4 How did we get to this mess??

5 Murray and Kirschner, Science, 1989

6 Xenopus and the clock paradigm Cell mass decreases during early divisions Alberts et a., Molecular Biology of the Cell.2002

7 In Xenopus oscillations progress independently of DNA presence and cell cycle events Autonomous oscillations! Alberts et a., Molecular Biology of the Cell.2002

8 MPF, the mitosis promoting factor Murray and Kirschner, Science, 1989

9 MPF is a heterodimer CDK Cyc cyclin dependent kinase cyclin (regulatory subunit) Only cyclin synthesis and degradation are required for Xenopus early cycles. Alberts et a., Molecular Biology of the Cell.2002

10 CDK is activated by cyclin binding and once activated it induces cyclin degradation CDK Cyc CDK Cyc X APCa APCi

11 But something else must be at work... CDK Cyc CDK Cyc X APCa APCi

12 Cyclin threshold Solomon et al, Cell, 1990

13 Yeast and the domino paradigm G1 Anaphase S Metaphase G2

14 Balanced growth and division Cell cycle engine T C Size control T D Cytoplasmic growth 4 Cytoplasmic mass T C > T D T C = T D exponential balanced growth T C < T D

15 Cell division cycle (cdc) mutants are temperature sensitive Hartwell, Genetics, 1991 Alberts et a., Molecular Biology of the Cell.2002

16 Wee1 controls a rate limiting step in the cell cycle Cell division and cell growth are coupled wild type wee1 cdc25 unreplicated DNA Nurse, Noble lecture, 2000

17 Basic cell cycle properties - Cell physiology- - Coupling of mass growth and cell division. - Once the cell enters the cycle,it is commited to finish it: irreversibility. - The cell halts during cell cycle progression if something has gone wrongly. -Molecular network- -Oscillations of MPF drive cells into and out of mitosis. - Cdc28 activity is controlled by Wee1 (negative) and Cdc25 (positive).

18 Dominoes and clocks: Cdc28 is the budding yeast homologous of MPF s catalytic subunit MPF = Cdc28 = Cdc2 = Clb2 Cdc13 CDK1 CycB

19 Phosphorylation as well as cyclin binding controls MPF activity Wee1 Cdc2 P Cdc2 Cyc Cdc2 Cyc Cyc mass Cdc25P X APCi APCa

20 Phosphorylation as well as cyclin binding controls MPF activity Wee1 Wee1P Cdc2 P Cdc2 Cyc Cdc2 Cyc Cyc mass Cdc25P Cdc25 X APCi APCa

21 Isolation and analysis of a positive feedback: the network... Wee1 Wee1P P Cdc2 Cyc Cdc2 Cyc G2 M Notice, here no cyclin synthesis, no cyclin degradation!!

22 ...and the physiology Solomon et al, Cell, 1990

23 Part II Standard laws of biochemical kinetics applied to molecular networks

24 Law of Mass Action: forward reaction pmpf k a MPF = ka! pmpf pmpf = MPF tot - MPF = ka! (MPF tot - MPF) Steady State solution (MPF SS ) = 0 MPF SS = MPF tot Notice: no dimer, only MPF. Cdk is supposed to be present in excess throughout the cycle. Increasing MPF total mimics an increase in cyclin total.

25 = ka! (MPF tot -MPF) > 0 = 0 MPF MPF tot MPF time

26 Law of Mass Action: reversible reaction pmpf k a k i MPF = ka! pmpf - ki! MPF Steady State solution = 0 MPF SS = ka! MPF tot ka + ki

27 pmpf k a MPF k i = ka! (MPF tot " MPF) - ki! MPF production + elimination = 0 > 0 < MPF

28 MPF time t

29 Law of Mass Action: catalyzed reversible reaction pmpf k a k i Wee1 MPF = ka! (MPF tot " MPF) - ki! MPF! Wee1 production + elimination rate MPF

30 Nullclines pmpf k a k i Wee1 MPF = ka! (MPF tot " MPF) - ki! MPF! Wee1 production + elimination rate MPF MPF SS < 0 > Wee1 = 0

31 What happens if MPF total increases? rate MPF MPF SS < 0 > Wee1 = 0

32 Michaelis-Menten: forward reaction Wee1P k wa Wee1 = kwa! Wee1P J + Wee1P = kwa! (Wee1 tot - Wee1) J + (Wee1 tot - Wee1) Steady State solution = 0 Wee1 SS = Wee1 tot

33 > 0 b Wee1 tot Wee1 = time

34 Michaelis-Menten: reversible reaction Wee1P k wa k wi Wee1 Wee1P k 1 k 2 Enzyme1:Wee1P k 1r Enzyme1 Enzyme1 Wee1 Wee1 k 3 k 4 Enzyme2:Wee1 k 3r Enzyme2 Enzyme2 Wee1P

35 if [enzym1 TOT ], [enzyme2 TOT ] << [Wee1 TOT ] k wa =[enzyme1 TOT ]k 2 k wi =[enzyme2 TOT ]k 4 = kwa! (Wee1 tot " Wee1) J + Wee1 tot -Wee1 - kwi! Wee1 J + Wee1 production + elimination -

36 Michaelis-Menten: reversible reaction Wee1P k wa k wi Wee1 = kwa! (Wee1 tot " Wee1) J + Wee1 tot -Wee1 - kwi! Wee1 J + Wee1 production + elimination - rate = > 0 < Wee1*

37 Nullclines Wee1P k wa k wi Wee1 = kwa! (Wee1 tot " Wee1) J + Wee1 tot -Wee1 - kwi! Wee1 J + Wee1 production + elimination - rate > 0 = 0 < 0 Wee1 SS 1 < > Wee1 SS MPF

38 Phase plane analysis Wee1P k wi Wee1 MPF k i k a pmpf = ka! (MPF tot " MPF) - ki! MPF! Wee1 = kwa! (Wee1 tot " Wee1) J + Wee1 tot -Wee1 - kwi! Wee1 J + Wee1

39 MPF SS 1 < 0 = 0 MPF 5 > 0 < > Wee Wee1 SS 1

40 1MPFSS MPF < 0 = 0 MPF 5 > 0 < > Wee Wee1 SS Wee

41 MPF How does MPF increases with Cyclin total? MPF SS = ka! MPF tot ki! Wee1+ka MPF Wee MPFtot

42 Not quite the same! Solomon et al, Cell, 1990

43 Wee1P k wi Wee1 MPF k i k a pmpf

44 Michaelis-Menten: catalyzed reversible reaction Wee1P k wa k wi Wee1 MPF = kwa! (Wee1 tot " Wee1) J + Wee1 tot -Wee1 - kwi! Wee1! MPF J + Wee1 production + elimination -

45 Nullclines Wee1P k wi Wee1 = kwa! (Wee1 tot " Wee1) J + Wee1 tot -Wee1 - kwi! Wee1! MPF J + Wee1 MPF production + elimination - rate Wee1 SS Wee1 SS > MPF < 0 = 0

46 Phase plane analysis MPF SS < 0 > Wee1 = 0 Wee1 SS > 0 = 0 < MPF

47 Phase plane analysis Wee > 0 < 0 = 0 Wee1 SS MPF SS MPF > 0 = 0 < 0

48 First solution, MPF wins, Wee1 loses 1 MPFtot=1.5 Wee MPF

49 Second solution, Wee1 wins, MPF loses MPFtot=0.5 Wee MPF

50 Third solution, both can win: hysteresis 1 MPFtot=1 0.8 Wee MPF

51 How does MPF increases with Cyclin total?

52 Wee1 Wee1 Wee1 MPFtot=0.5 MPFtot=1 MPFtot=1.5 MPF MPF MPF

53 Hysteresis in the Xenopus early cycles: simulation of an experimental result From Sha et al, PNAS, 2003

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55 What happens if cyclin total increases with cell mass?

56 Wee1 Wee1P Cdc2 P Cdc2 Cyc Cdc2 Cyc Cyc mass Cdc25P Cdc25 X APCi APCa

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60 Conclusion -Same wiring in different organisms, combination of positive and negative feedbacks. - In Xenopus early development, with large mass, the cell cycle is a limit cycle oscillator, the negative feedback plays the key role. - Artificially, an additional mechanism of control emerges, based on a positive feedback loop. - Both positive and negative feedbacks are at work in yeast. In these organisms, mass growth drives the cell cycle. - Positive feedbacks introduce checkpoints and irreversibility in the cycle. The negative feedback the capability to start a new process.

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