Transcript From molecular regulatory networks to cell physiology

Modeling the Cell Cycle
Engine of Eukaryotes
John J. Tyson & Bela Novak
Virginia Polytechnic Institute & State Univ.
Budapest Univ. Technology & Economics
The cell cycle is the sequence of events by which a growing
cell replicates all its components and divides them moreor-less evenly between two daughter cells...
…so that the two daughter cells contain all the information
and machinery necessary to repeat the process.
G1
S
(DNA
synthesis)
M
(mitosis)
G2
G1
Too small?
DNA damage?
G1/S checkpoint
S
1. Alternation of S and M phases
Unaligned
chromosomes?
Metaphase
checkpoint
2. Balanced growth and division
(DNA
synthesis)
Unreplicated DNA?
Too small?
M
(mitosis)
G2
G2/M checkpoint
G1
cell division
Cyclin-dependent kinase
Cdk1
CycB
Tar
M
(mitosis)
S
DNA
replication
Tar- P
G2
G1
cell division
S
Cdk1
CycB
M
(mitosis)
G2/M
DNA
replication
G2
Wee1-P
Wee1
less active
less active
P- Cdk1
Cdk1
CycB
CycB
Cdc25-P
cyclin B
degradation
cyclin B
synthesis
Cdc25
less active
active MPF
cyclin B
degradation
Solomon’s protocol for cyclin-induced activation of MPF
Cyclin
centrifuge
M
Ca2+
Cycloheximide
Cdk1
Cyclin
cytoplasmic extract
pellet
no synthesis of cyclin
no degradation of cyclin
Threshold
120
100
MPF
80
60
40
20
0
0
10
20
30
Cyclin (nM)
Solomon et al. (1990)
Cell 63:1013.
Frog egg
active MPF
Novak & Tyson (1993)
J. Cell Sci. 106:1153
no synthesis or
degradation
of cyclin
total cyclin
non-hysteretic
MPF activity
MPF activity
hysteretic
Ti
Ta
cyclin level
T
cyclin level
Prediction: The threshold concentration of cyclin B
required to activate MPF is higher than the threshold
concentration required to inactivate MPF.
Norel & Agur (1991). “A model for the adjustment of the mitotic
clock by cyclin and MPF levels,” Science 251:1076-1078.
Tyson (1991). “Modeling the cell division cycle: cdc2 and cyclin
interactions,” PNAS 88:7328-7332.
Goldbeter (1991). “A minimal cascade model for the mitotic
oscillator involving cyclin and cdc2 kinase,” PNAS 88:9107-9111.
Novak & Tyson (1993). “Numerical analysis of a comprehensive
model of M-phase control in Xenopus oocyte extracts and intact
embryos,” J. Cell Sci. 106:1153-1168.
Thron (1996). “A model for a bistable biochemical trigger of
mitosis,” Biophys. Chem. 57:239-251.
Thron (1997). “Bistable biochemical switching and the control of
the events of the cell cycle,” Oncogene 15:317-325.
G1
S
DNA
replication
M
(mitosis)
G2/M
G2
G1
CKI
Cdh1
Cdc20
APC
Cln2
S
APC
Clb5
Cdk
DNA
replication
Clb2
M
(mitosis)
G2/M
G2
Cdk
Cdk
CycB
CycB
Cdk
Cdk
Cln2
Cdk
CycB
Cdc14
AA
CKI
Cdh1
CKI
CKI
AA
Cdc14
P
P
The mathematical model
d[Cln2]
 k1  k1' [SBF]  k2 [Cln2]
dt
synthesis

degradation

d[Clb2]
 k3  k3' [Mcm1]  k4  k4' [Cdh1] [Clb2]  k5 [Sic1][Clb2]
dt
synthesis

binding
degradation



k6  k6' [Cdc20] [Cdh1]T  [Cdh1] 
k7  k7' [Clb5] [Cdh1]
d[Cdh1]


dt
J 6  [Cdh1]T  [Cdh1]
J 7  [Cdh1]
activation
inactivation
Simulation of the budding yeast cell cycle
2
mass
1
1
.
0
CKI
Cln2
0
.
5
0
.
0
G1
1
.
5
Cdh1
1
.
0
0
.
5
S/M
Clb2
0
.
5
Cdc20
0
.
0
0
.
0
0
5
0
1
0
0
Time (min)
1
5
0
30 equations
100 parameters
fitted by brute force
These are the “brutes”
Kathy Chen
Laurence Calzone
“With four parameters
I can fit an elephant…”
Is the model yeast-shaped?
d CDK
= k1 - (v2’ + v2” . Cdh1 ) . CDK
dt
k1 = 0.0013, v2’ = 0.001, v2” = 0.17,
d Cdh1 (k3’ + k3” . Cdc20A) (1 - Cdh1) (k4’ + k4” . CDK . M) Cdh1
=
dt
J3 + 1 - Cdh1
J4 + Cdh1
k3’ = 0.02, k3” = 0.85, k4’ = 0.01, k4” = 0.9,
J3 = 0.01, J4 = 0.01, k9 = 0.38, k10 = 0.2,
d IEP
= k9 . CDK . M . (1 – IEP ) – k10 . IEP
dt
k5’ = 0.005, k5” = 2.4, J5 = 0.5, k6 = 0.33,
d Cdc20T
(CDK . M)4
= k5’ + k5” 4
- k6 . Cdc20T
dt
J5 + (CDK . M)4
k7 = 2.2, J7 = 0.05, k8 = 0.2, J8 = 0.05,
…
d Cdc20A k7 . IEP (Cdc20T - Cdc20A) k8 . MAD Cdc20A
=
- k6 . Cdc20T
dt
J7 + Cdc20T - Cdc20A
J8 + Cdc20A
Differential equations
Parameter values
Table 6. Properties of clb, sic1, and hct1 mutants
mass at
birth
mass at
SBF 50%
mass at
DNA repl.
mass at
bud ini.
mass at
division
TG1
(min)
84
changed
parameter
Comments
1
wild type
(daughter)
0.71
1.07
(71’)
1.15
(84’)
1.15
(84’)
1.64
(146’)
CT 146 min
(time of occurrence of event)
2
clb1 clb2
0.71
1.07
1.16
1.16
No mit
3
clb1 clb2
1X GAL-CLB2
0.65
1.10
1.19
1.19
1.50
105
k's,b2 = 0.1
k"s,b2 = 0
Surana 1993 Fig 4, 1X GAL-CLB2 is OK, 4X GAL-CLB2
(or 1X GAL-CLB2db) causes telophase arrest.
4
clb5 clb6
0.73
1.07
(65’)
1.30
(99’)
1.17
(80’)
1.70
(146’)
99
k's,b5 = 0
k"s,b5 = 0
Schwob 1993 Fig 4, DNA repl begins 30 min after SBF
activation.
5
clb5 clb6
GAL-CLB5
0.61
0.93
0.92
0.96
1.41
73
k's,b5 = 0.1
k"s,b5 = 0
6
sic1
0.66
1.00
(73’)
0.82
(37’)
1.06
(83’)
1.52
(146’)
38
k's,c1 = 0
k"s,c1 = 0
Schneider 1996 Fig 4, sic1 uncouples S phase from
budding.
7
sic1 GAL-SIC1
0.80
1.07
1.38
1.17
1.86
94
k's,c1 = 0.1
k"s,c1 = 0
Verma 1997 Fig3B, Nugroho & Mendenhall 1994 Fig 2,
most cells are viable.
8
hct1
0.73
1.08
1.17
1.18
1.69
82
9
sic1 hct1
0.71
No SBF
0.72
No bud
No mit
10
sic1 GAL-CLB5
first cycle
second cycle
0.71
0.52
0.74
0.73
No repl
0.76
1.20
k's,b2 = 0
k"s,b2 = 0
Surana 1991 Table 1, G2 arrest.
Schwob 1993 Fig 6, DNA repl concurrent with SBF
activation in both GAL-CLB5 and GAL-CLB5db.
k"d,b2 = 0.01 Schwab 1997 Fig 2, viable, size like WT, Clb2 level high
throughout the cycle.
k's,c1 = 0
Visintin 1997, telophase arrest.
k"d,b2 = 0.01
k's,b5 = 0.1
k"s,b5 = 0
k's,c1 = 0
Schwob 1994 Fig 7C, inviable.
First cycle OK, DNA repl advanced; but pre-repl complexes
cannot form and cell dies after the first cycle.
CKI
Cdk
Cln
Cdk
CycB
Mutual antagonism and bistability...
Cdk
CycB
CKI
Cdh1
Cln2
Cdc14
S/G2/M
Start
Clb2/Cdk
activity
Finish
G1
A + Cln2
B+Cdc14
A/B
Cln2
Cdc14
time
From molecular networks to cell physiology…
P Wee1
d CDK
= k1 - (v2’ + v2” . Cdh1 ) . CDK
dt
d Cdh1 (k3’ + k3” . Cdc20A) (1 - Cdh1) (k4’ + k4” . CDK . M) Cdh1
=
dt
J3 + 1 - Cdh1
J4 + Cdh1
d IEP
= k9 . CDK . M . (1 – IEP ) – k10 . IEP
dt
Wee1
P Cdc2
Cdc25 P
CycB
d Cdc20A k7 . IEP (Cdc20T - Cdc20A) k8 . MAD Cdc20A
=
- k6 . Cdc20T
dt
J7 + Cdc20T - Cdc20A
J8 + Cdc20A
differential equations
Cdc25
molecules
???
1.0
MPF
G2/M
CycB
d Cdc20T
(CDK . M)4
= k5’ + k5” 4
- k6 . Cdc20T
dt
J5 + (CDK . M)4
Cdc2
0.8
0.6
0.4
0.2
0
physiology
0
10
20
time (min)
simulation & analysis
30
Our thanks to...
National Science Foundation (USA)
National Science Foundation (Hungary)
National Institutes of Health
James S. McDonnell Foundation
Defense Advanced Research Project Agency