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A simple model for the eukaryoticcell cycle
Andrea Ciliberto
The cell division cycle
Start
S(DNA Replication)
cell divis
ion
G1
Fini
sh
G2G2/MM(mitosis)
Kohn, Mol. Biol. Cell., 1999
How did we get to this mess??
Murray and Kirschner, Science, 1989
Xenopus and the clock paradigm
Cell mass decreases during early divisions
Alberts et a., Molecular Biology of the Cell.2002
In Xenopus oscillations progress independentlyof DNA presence and cell cycle events
Autonomous oscillations!
Alberts et a., Molecular Biology of the Cell.2002
MPF, the mitosis promoting factor
Murray and Kirschner, Science, 1989
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
CDK
CycCyc
CDK
APCa APCi
CDK is activated by cyclin binding and onceactivated it induces cyclin degradation
‘X’
CDK
CycCyc
CDK
APCa APCi
But something else must be at work...
‘X’
Cyclin threshold
Solomon et al, Cell, 1990
Yeast and the domino paradigm
S
G1
G2Metaphase
Anaphase
Balanced growth and division
Size control
TDTC
Cell cycleengine
Cytoplasmicgrowth
Cyt
opla
smic
mas
s
exponentialbalancedgrowth
0 1 2 3 40
1
2
3
4
TC > TD
TC < TD
TC = TD
Cell division cycle (cdc) mutants are temperature sensitive
Alberts et a., Molecular Biology of the Cell.2002
Hartwell, Genetics, 1991
wee1wild type cdc25
Wee1 controls a rate limiting step in the cell cycle
Cell division and cell growth are coupled
unreplicated DNA
Nurse, Noble lecture, 2000
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).
Dominoes and clocks: Cdc28 is thebudding yeast homologous of MPF’s
catalytic subunit
MPF Cdc28
Clb2= Cdc2
Cdc13= = CDK1
CycB
Cdc2
Cyc
P
Cdc25P
Wee1
Cdc2
CycCyc
Cdc2
APCaAPCi
Phosphorylation as well as cyclin binding controls MPF activity
‘X’
mass
Cdc25
Cdc2
Cyc
P
Cdc25P
Wee1 Wee1P
Cdc2
CycCyc
Cdc2
APCaAPCi
‘X’
mass
Phosphorylation as well as cyclin binding controls MPF activity
Cdc2
Cyc
P
Wee1 Wee1P
Isolation and analysis of a positive feedback: the network...
G2
M
Cdc2
Cyc
Notice, here no cyclin synthesis, no cyclin degradation!!
...and the physiology
Solomon et al, Cell, 1990
Part IIStandard laws of biochemical kinetics
applied to molecular networks
pMPF MPF
�
dMPF
dt= ka ! pMPF
pMPF =MPFtot -MPF
dMPF
dt= ka ! (MPFtot -MPF)
ka
dMPF
dt= 0
MPFSS=MPF
tot
Steady State solution (MPFSS)
Law of Mass Action: forward reaction
Notice: no dimer, only MPF. Cdk is supposed to be present in excess throughoutthe cycle. Increasing MPF total mimics an increase in cyclin total.
0 0.2 0.4 0.6 0.8 1-0.1
0
0.1
0.2
MPF
�
dMPF
dt
�
dMPF
dt> 0
�
dMPF
dt= 0
0 4 8 12 16 200
0.2
0.4
0.6
0.8
1
timeM
PF
MPFtot
dMPF
dt= ka ! (MPF
tot-MPF)
�
dMPF
dt= ka ! pMPF - ki !MPF
ki
dMPF
dt= 0
MPFSS=ka !MPF
tot
ka + ki
Steady State solution
Law of Mass Action: reversible reaction
pMPF MPFka
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
MPF
�
dMPF
dt> 0
�
dMPF
dt< 0
�
dMPF
dt= ka ! (MPFtot "MPF) - ki !MPF
production+
elimination-
�
dMPF
dt= 0
ki
pMPF MPFka
�
dMPF
dt
0 4 8 12 16 200
0.2
0.4
0.6
0.8
1
time
MPF
t
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
1
2
34
5
pMPF MPFka
ki
Wee1
MPF
rate
12345
Law of Mass Action: catalyzed reversible reaction
�
dMPF
dt= ka ! (MPFtot "MPF) - ki !MPF !Wee1
production+
elimination-
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
1
2
34
5
MPF
rate
12345 0 2.5 50
0.5
1MPFSS
Wee11 2 3 4
�
dMPF
dt= 0
�
dMPF
dt< 0
�
dMPF
dt> 0
Nullclines
pMPF MPFka
ki
Wee1
�
dMPF
dt= ka ! (MPFtot "MPF) - ki !MPF !Wee1
production+
elimination-
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
1
2
34
5
MPF
rate
12345 0 2.5 50
0.5
1MPFSS
Wee11 2 3 4
�
dMPF
dt= 0
�
dMPF
dt< 0
�
dMPF
dt> 0
What happens if MPF total increases?
Wee1P Wee1
�
dWee1
dt=kwa !Wee1P
J +Wee1P
dWee1
dt=kwa ! (Wee1tot -Wee1)
J + (Wee1tot -Wee1)
kwa
dWee1
dt= 0
Wee1SS= Wee1
tot
Steady State solution
Michaelis-Menten: forward reaction
0 4 8 12 16 200
0.2
0.4
0.6
0.8
1
�
Wee1tot
time
b
0 0.2 0.4 0.6 0.8 1-0.1
0
0.1
0.2
Wee1
�
dWee1
dt
�
dWee1
dt= 0�
dWee1
dt> 0
Michaelis-Menten: reversible reaction
Wee1P Wee1kwa
kwi
Wee1P Enzyme1:Wee1Pk1
Enzyme1 Enzyme1
Wee1k1r
k2
Wee1 Enzyme2:Wee1k3
Enzyme2 Enzyme2
Wee1Pk3r
k4
dWee1
dt=kwa ! (Wee1
tot"Wee1)
J +Wee1tot-Wee1
-kwi !Wee1
J +Wee1
production+
elimination-
if [enzym1TOT], [enzyme2TOT] << [Wee1TOT]
kwa=[enzyme1TOT]k2
kwi=[enzyme2TOT]k4
Michaelis-Menten: reversible reaction
dWee1
dt=kwa ! (Wee1
tot"Wee1)
J +Wee1tot-Wee1
-kwi !Wee1
J +Wee1
production+
elimination-
Wee1P Wee1kwa
kwi
0.0 0.2 0.4 0.6 0.8 1.00.0
0.1
0.2
0.3
0.4
0.5
Wee1*
rate
�
dWee1
dt< 0
�
dWee1
dt> 0
�
dWee1
dt= 0
0.0 0.2 0.4 0.6 0.8 1.00.0
0.1
0.2
0.3
0.4
0.5
Wee1SS
rate
�
dWee1
dt< 0
�
dWee1
dt> 0
�
dWee1
dt= 0
Nullclines
dWee1
dt=kwa ! (Wee1
tot"Wee1)
J +Wee1tot-Wee1
-kwi !Wee1
J +Wee1
production+
elimination-
Wee1P Wee1kwa
kwi
0 2.5 50
0.5
1Wee1SS
MPF1 2 3 4
�
dWee1
dt< 0
�
dWee1
dt> 0
Wee1P Wee1kwi
MPF pMPFka
ki
Phase plane analysis
�
dMPF
dt= ka ! (MPFtot "MPF) - ki !MPF !Wee1
dWee1
dt=kwa ! (Wee1
tot"Wee1)
J +Wee1tot-Wee1
-kwi !Wee1
J +Wee1
0 0.5 1
Wee1SS
MPF
02.5
5
�
dWee1
dt< 0
�
dWee1
dt> 0
0 2.5 50
0.5
1MPFSS
Wee11 2 3 4
�
dMPF
dt= 0
�
dMPF
dt< 0
�
dMPF
dt> 0
0 2.5 50
0.5
1
Wee1
MP
F
0 0.5 1
Wee1SS
MP
F
02.5
5
�
dWee1
dt< 0
�
dWee1
dt> 0
0 2.5 50
0.5
1
MP
FSS
Wee1
�
dMPF
dt= 0
�
dMPF
dt< 0
�
dMPF
dt> 0
How does MPF increases with Cyclin total?
0
MPFtot
MPF
MPFSS=ka !MPF
tot
ki !Wee1+ka
0 2.5 50
0.5
Wee1
MP
F
Solomon et al, Cell, 1990
Not quite the same!
Wee1P Wee1kwi
MPF pMPFka
ki
Michaelis-Menten: catalyzed reversible reaction
dWee1
dt=kwa ! (Wee1
tot"Wee1)
J +Wee1tot-Wee1
-kwi !Wee1 !MPF
J +Wee1
production+
elimination-
Wee1P Wee1kwa
kwi
MPF
0 1 2 3 4 50
0.2
0.4
0.6
0.8
1
Wee1SS
MPF
�
dWee1
dt= 0
�
dWee1
dt< 0
�
dWee1
dt> 0
Nullclines
0.0 0.2 0.4 0.6 0.8 1.00.0
0.1
0.2
0.3
0.4
0.5
1
2
3
4
5
.1
Wee1SS
rate
Wee1P Wee1kwi
MPF
dWee1
dt=kwa ! (Wee1
tot"Wee1)
J +Wee1tot-Wee1
-kwi !Wee1 !MPF
J +Wee1
production+
elimination-
0 2.5 50
0.5
1MPFSS
Wee10 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1Wee1SS
MPF
�
dWee1
dt< 0
�
dMPF
dt< 0
�
dMPF
dt> 0
�
dWee1
dt> 0
�
dWee1
dt= 0
�
dMPF
dt= 0
Phase plane analysis
0 0.5 10
2.5
5Wee1
MPFSS0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1Wee1SS
MPF
�
dWee1
dt< 0
�
dMPF
dt< 0
�
dMPF
dt> 0
�
dWee1
dt> 0
�
dWee1
dt= 0
�
dMPF
dt= 0
Phase plane analysis
0 0.4 0.8 1.2 1.60
0.2
0.4
0.6
0.8
1
Wee1
MPF
First solution, MPF wins, Wee1 loses
MPFtot=1.5
0 0.4 0.8 1.2 1.60
0.2
0.4
0.6
0.8
1
Wee1
MPF
Second solution, Wee1 wins, MPF loses
MPFtot=0.5
0 0.4 0.8 1.2 1.60
0.2
0.4
0.6
0.8
1
Wee1
MPF
Third solution, both can win: hysteresis
MPFtot=1
How does MPF increases with Cyclin total?
Wee1Wee1
MPFMPF
Wee1
MPF
MPFtot=0.5MPFtot=1.5MPFtot=1
Hysteresis in the Xenopus early cycles: simulationof an experimental result
From Sha et al, PNAS, 2003
What happens if cyclin total increases with cell mass?
Cdc25
Cdc2
Cyc
P
Cdc25P
Wee1 Wee1P
Cdc2
CycCyc
Cdc2
APCaAPCi
‘X’
mass
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.
