Transcript Document

Modelling of Cell Cycle
Edda Klipp, Humboldt-Universität zu Berlin
Budding yeast biology
The cell cycle is the succession of events
whereby a cell grows and divides into two
daughter cells that each contain the information
and machinery necessary to repeat the process.
Between one cell division and the next, all
essential components of the cell must be
duplicated. The most important component is the
genetic material (DNA molecules present in
chromosomes), which must be accurately
replicated and the two copies carefully
segregated to the two daughter cells.
The processes of DNA replication and sister
chromatid separation occur in temporally
distinct phases of the eukaryotic cell
cycle. These are known as S-phase (DNA
synthesis) and M-phase (mitosis), In general, S
and M phases separated by two gaps, known as
G1 and G2.
Edda Klipp, Humboldt-Universität zu Berlin
Budding yeast biology
The unicellular budding yeast, Saccharomyces cerevisiae, is a
model system to study cell cycle regulation.
As a yeast cell progresses through the cell cycle, it halts at two
major checkpoints:
•the G1 checkpoint: If DNA damage is detected, mating
pheromone is present, or the cell has not reached the critical size,
the cell arrests in G1 and is unable to undergo the Start transition
which commits the cell to a new round of DNA synthesis and
mitosis.
•the spindle assembly checkpoint: If DNA damage is detected,
DNA is not replicated completely, or chromosomes are not
aligned on the metaphase plate, the cell arrests in metaphase and
is unable to undergo the Finish transition, whereby sister
chromatids are separated and the cell divides.
Edda Klipp, Humboldt-Universität zu Berlin
Cell cycle
Passage through the eukaryotic cell cycle is strictly regulated by
-the periodic synthesis and destruction of cyclins
-that bind and activate cyclin-dependent kinases (CDKs).
The notion kinase expresses that their function is phosphorylation of proteins with
controlling functions.
-Cyclin-dependent kinase inhibitors (CKI) also play important roles in cell cycle
control by coordinating internal and external signals and impeding proliferation at
several key checkpoints.
Edda Klipp, Humboldt-Universität zu Berlin
Cell cycle – evolutionary conserved
Edda Klipp, Humboldt-Universität zu Berlin
Checkpoints
They ensure that all processes connected with
-cell cycle progression,
-DNA doubling and
-separation
occur correctly.
At checkpoints, the cell cycle
can be aborted or arrested
They involve checks
-on completion of S phase,
-on DNA damage, and
-on failure of spindle behavior.
If the damage is irreparable, apoptosis is triggered.
Edda Klipp, Humboldt-Universität zu Berlin
Checkpoints
These checkpoints are enforced by the Cdk/cyclin complexes, a family of protein kinases.
The catalytic subunit of these complexes, the cyclin-dependent kinase (Cdk), is only active
when combined with a regulatory cyclin subunit.
In budding yeast, there is only one Cdk (called Cdc28); and nine different cyclins (Cln1-3,
Clb1-6). Depending on the cyclin partner, Cdc28/cyclin dimers accomplish specific and
different tasks. Proper progression through the cell cycle requires the successive activation
and inactivation of these Cdc28/cyclin dimers.
There are several different mechanisms for regulating Cdc28 activity in the cell, namely:
•through the synthesis of cyclins by various transcription factors (SBF, MBF and Mcm1).
•through the degradation of cyclins (promoted by Cdc20/APC, Cdh1/APC, and Grr1/SCF).
•through association with stoichiometric CDK inhibitors (Sic1 and Cdc6, and Far1).
•through phosphorylation and dephosphorylation of Cdc28 by Swe1 and Mih1.
Edda Klipp, Humboldt-Universität zu Berlin
Cell cycle progression
Edda Klipp, Humboldt-Universität zu Berlin
Minimal Model
One of the first genes to be identified as being an important regulator of the cell
cycle in yeast was cdc2/cdc28 (Nurse and Bissett, 1981), where cdc2 refers to
fission yeast and cdc28 to budding yeast.
Activation of the cdc2/cdc28 kinase requires association with a regulatory
subunit referred to as a cyclin.
A minimal model for the mitotic oscillator involving a cyclin and the Cdc2
kinase has been presented by Goldbeter (Goldbeter, 1991). It covers the cascade
of post-translational modifications that modulate the activity of Cdc2 kinase
during cell cycle.
In the first cycle of the bicyclic cascade model, the cyclin promotes the activation
of the Cdc2 kinase by reversible dephosphorylation, and in the second cycle, the
Cdc2 kinase activates a cyclin protease by reversible phosphorylation.
The model was used to test the hypothesis that cell cycle oscillations may arise
from a negative feedback loop, i.e. the cyclin activates the Cdc2 kinase while the
Cdc2 kinase triggers the degradation of the cyclin.
Edda Klipp, Humboldt-Universität zu Berlin
Minimal cascade model
A
vi
M+
vd
Cyclin
v1
v2
M
v3
X+
v4
X
dC
X C
 vi  v d
 kd C
dt
K md  C
V  1  M 
V M
dM
 m1
 m2
dt
K m1  1  M  K m 2  M
V  1  X 
V X
dX
 m3
 m4
dt K m3  1  X  K m4  X
Only two main actors: cyclin and cyclin dependent kinase.
Cyclin - synthesized at constant rate, vi,
- triggers the transformation of inactive (M+) into
active (M) Cdc2 kinase by enhancing the rate of a
phosphatase, v1.
A kinase with rate v2 reverts this modification.
Cdc2 kinase - phosphorylates a protease (v3) shifting it
from the inactive (X+) to the active (X) form.
The activation of the cyclin protease is reverted by a
further phosphatase with rate v4.
C - cyclin concentration;
M and X - fractional concentrations of active cdc2 kinase and
active cyclin protease,
1-M, 1-X - fractions of inactive kinase and phosphatase
Km values - Michaelis constants.
Vm1  V1C K mc  C  and Vm3  V3  M - effective maximal rates
Differential equations for the changes of M and X are modeled
with the so-called Goldbeter-Koshland switch
Edda Klipp, Humboldt-Universität zu Berlin
Model application
A
vi
M+
vd
Cyclin
v1
v2
This model involves only Michaelis-Menten type kinetics,
but no form of positive cooperativity.
M
v3
X+
v4
X
dC
X C
 vi  v d
 kd C
dt
K md  C
It can be used to test whether oscillations can arise solely as
a result of the negative feedback provided by the cdc2induced cyclin degradation and of the threshold and time
delay involved in the cascade.
The time delay is implemented by considering posttranslational modifications
(phosphorylation/dephosphorylation cycles v1/v2 and v3/ v4).
V  1  M 
V M
dM
 m1
 m2
dt
K m1  1  M  K m 2  M
V  1  X 
V X
dX
 m3
 m4
dt K m3  1  X  K m4  X
Edda Klipp, Humboldt-Universität zu Berlin
A
vi
M+
vd
Cyclin
v1
v2
Model behavior
M
Cdc2 kinase, M
1
v3
X+
v4
X
For certain parameters: threshold in the dependence
of steady state values for M on C and for X on M.
0.8
0.6
0.4
0.2
0
0
0
Vm1  1  M 
V M
V M
V1  C  1  M 
 m2

 m2
K m1  1  M  K m2  M K mc  C K m1  1  M  K m2  M
0
Vm3  1  X 
V X
V  M  1  X  Vm4  X
 m4
 3

K m3  1  X  K m4  X K m3  1  X  K m4  X
Edda Klipp, Humboldt-Universität zu Berlin
0.2
0.4
0.6
0.8
1
Cyclin, C
Vm1  V1C K mc  C 
Vm3  V3  M
A
vi
M+
vd
Cyclin
v1
v2
Model behavior
M
Cdc2 kinase, M
1
v3
X+
v4
X
Provided that this threshold exists, the evolution of the
bicyclic cascade proceeds in a periodic manner.
B
0.8
0.6
0.4
0.2
0
0
0.2
0.8
Concentraions
As soon as C crosses the activation threshold, M rises.
The resulting oscillations are of the limit cycle type.
0.6
0.8
1
80
100
Cyclin, C
Starting from low initial cyclin concentration, this value
accumulates at constant rate, while M and X stay low.
If M crosses the threshold, X starts to increase sharply. X
in turn accelerates cyclin degradation and consequently,
C, M, and X drop rapidly.
0.4
C
0.6
C
0.4
M
0.2
X
0
0
20
40
60
Time/min
Edda Klipp, Humboldt-Universität zu Berlin
vi
M+
Cyclin
v1
v2
0.8
vd
Concentraions
A
M
C
0.4
M
0.2
X
0
X
20
40
60
80
100
Time/min
B
Cdc2 kinase, M
Cdc2 kinase, M
1
v4
0.6
0
v3
X+
C
0.8
0.6
0.4
0.2
0.8
D
0.6
0.4
0.2
0
0
0
0.2
0.4
0.6
0.8
1
0
Cyclin, C
0.2
0.4
Cyclin, C
Edda Klipp, Humboldt-Universität zu Berlin
0.6
0.8
Yeast Cell Cycle
Start
G1
S

Budding
Cell
division
Cln2
Clb5
SBF
MBF
Sic1Clb5
Sic1P
Sic1
Sic1Clb2
Clb2
Hct1
Ccd20
Ccd20
Hct1
APC
APC

M
anaphase
M
metaphase
Finish
Progression through cell cycle
Activation
Active protein or complex
Production, degradation, complex formation
Inhibition
Inactive protein or complex
Edda Klipp, Humboldt-Universität zu Berlin
Basic mechanism
To understand the basic logic of the cell cycle, to a first approximation, the groups of Tyson
and Novak, and, independently, Kim Nasmyth have envisioned that the cell cycle in budding
yeast is an alternation between two self-maintaining stable steady states (G1 and S/G2/M).
The Start transition carries a cell from G1 to S/G2/M, and the Finish transition from M back
to G1 (Nasmyth, 1996, Tyson et al., 1995, Tyson et al., 2001).
The two self-maintaining steady states arise primarily from the mutual antagonism between
B-type cyclins (Clb1-6, in association with Cdc28) and the G1 stabilizers (Cdh1, Sic1 and
Cdc6).
Cdh1/APC degrades the Clbs, whereas Sic1 and Cdc6, referred to together as the CKIs,
stoichiometrically inhibit Cdc28/Clb complexes.
Clb-kinases, on the other hand, can inactivate Cdh1 and destabilize CKIs.
Since Clb-kinases and the G1 stabilizers mutually inhibit each other, these two classes of
proteins cannot coexist.
In the G1 state, Clb-kinase activities are low because Clb synthesis processes are turned OFF,
their degradation by APC/Cdh1 is ON, and their inhibitors, the CKIs, are abundant. The
reverse is true in the S/G2/M phase.
Edda Klipp, Humboldt-Universität zu Berlin
Transition between states
The transitions between these two alternative steady states
(G1 and S/G2/M) requires helper molecules
(detailed in Chen et al., 2000).
Edda Klipp, Humboldt-Universität zu Berlin
Start transition
The Start transition is facilitated by Cln-kinases
(Cln1-3/Cdc28 complexes) that can
phosphorylate and inactivate CKI and Cdh1, but
are not themselves opposed by CKI and Cdh1.
This transition is driven by cell growth.
When the small daughter cell has grown to a
critical size and Cln-kinase activities have
reached a critical level, CKI and Cdh1 are
inactivated, Clb-kinase activities increase, a bud
emerges, DNA replication commences and
spindle pole is duplicated.
The mother cell executes Start soon after birth
because it has already attained the critical size.
The rising activity of Clb-kinases turns off Cln
synthesis, causing Cln-kinase activities to drop
in preparation for the Finish transition.
Edda Klipp, Humboldt-Universität zu Berlin
Finish transition
The Finish transition is facilitated by Cdc20,
which is activated indirectly by Clb-kinases.
When the spindle assembly checkpoint is lifted
(DNA synthesis is complete and chromosomes
are aligned on the metaphase plate),
- Cdc20 is activated,
- sister chromatids are separated, and
- Clbs are partially degraded.
Cdc20 also initiates the activation of the
phosphatase Cdc14, which reverses the
inhibitory effects of Clb-kinases on Cdh1 and
CKIs, allowing the latter two to overpower the
Clb-kinases and extinguish their activities.
As Clb-kinase activities drop after Finish,
Cdc20 activity also disappears, preparing the
cell for the subsequent Start transition.
Edda Klipp, Humboldt-Universität zu Berlin
Major improvements of the model:
The previous model of the budding yeast by Chen et al., 2000 gives an adequate
description of the Start transition, but, since it was published, many more molecular
details about the Finish transition have come to light.
Also in that paper, Clb2-kinase was assumed to activate Cdc20 directly, making the
checkpoint protein Mad2 essential for cell viability, which is contrary to observation.
Here we introduce an intermediary enzyme, IE, that provides a time delay between Clb2
activation and Cdc20 activation, such that Mad2 is no longer an essential protein. The
new model also accounts for how the MEN pathway facilitates Cdc14 release from the
RENT complex and how the spindle assembly checkpoint impinge on the cell cycle
engine.
Edda Klipp, Humboldt-Universität zu Berlin
Wiring Diagram
Edda Klipp, Humboldt-Universität zu Berlin
Simulations
Simulations compared well with
experimental observations.
For a culture growing exponentially at a MDT=90 min,
(1) Duration of cell cycle phases:
Cycle time, min
G1 length, min
S/G2/M, min
Daughter Cell
97.5 (101.2)*
42 (36)
57 (64)
Mother Cell
81 (80)
22 (28)
59 (52)
•Data for a wild type yeast diploid strain A364A D5 are
obtained from Brewer et al., 1984, simulation results are
shown in parenthesis.
(2) The relative amounts of cyclins and CKIs:
([Cln1]+[Cln2]) : (Clb5]+[Clb6]) : ([Clb1]+[Clb2]) : [Sic1] : [Cdc6]
=15 : 3.8 : 7.5 : 1 : 3 (in experiments)
=15 : 3.3 : 4.7 : 2.8 : 3.7 (in model).
Measurements are made by Cross et al., 2002, and
Archambault et al., 2003.
Edda Klipp, Humboldt-Universität zu Berlin
Phase Plane Representation
Edda Klipp, Humboldt-Universität zu Berlin
Yeast Cell Cycle – Data
Edda Klipp, Humboldt-Universität zu Berlin
Yeast Cell Cycle – Data
Edda Klipp, Humboldt-Universität zu Berlin
Yeast Cell Cycle – Model
Edda Klipp, Humboldt-Universität zu Berlin
Yeast Cell Cycle – Model
Edda Klipp, Humboldt-Universität zu Berlin
Yeast Cell
Cycle – Model
Regulatory interactions of 20 genes
of S.cerevisiae. The full arcs
represent activatory regulation, the
dashed arcs represent inhibitory
regulation.
The relationship between genes
regulating one common gene is
described by ‘OR’-function.
Edda Klipp, Humboldt-Universität zu Berlin