Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
The fundamental goal of molecular cell biology is to understand cell physiology
in terms of its underlying molecular mechanisms. In making this connection, a
progression of analyses must be undertaken: from gene sequence to protein
sequence , then to protein structure and function, and on to characterize the
networks of interacting proteins in the cell. Finally, the dynamic consequences
of these molecular networks determine the physiology of the cell.
Computational methods play crucial roles at each step in connecting different
levels of descriptions. However, the final step, going from the molecular
mechanism to cell physiology, is often neglected.
Computational molecular biology
gene sequence
protein sequence
protein structure
protein function
protein network
cell physiology
1
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
The problem related to this final step is nicely described by Dennis Bray:
Bray, D. (1997): TiBS 22: 325-326.
"What are we to do with the enormous cornucopia of
genes and molecules we have found in living cells?…
[One] road to salvation is through the keyboard of
a computer… If we can use computer-based graphical
elements to understand the world of protein structure,
why should we not do the same for the universe of cells?
The data are accumulating and the computers are
humming. What we lack are the words, the grammar
and the syntax of the new language."
I want to show, by using the cell division cycle as an example, that the language
does exist and it is called biochemical kinetics. The "words" are the rate laws
and the "sentences" are the differential equations. I will also show that we can
understand the sentences written in biochemical kinetics with the tools of
dynamical systems theory.
To understand the regulation of the eukaryotic cell cycle is a major goal in
present day molecular cell biology. During the cell division cycle, the cell must
replicate all of its components and divide them into two nearly identical
daughter cells. Since DNA stores the genetic information of the cell, it has a
particular importance among the cellular constituents. For this reason, DNA
must be accurately replicated and chromosomes must be precisely segregated.
2
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
These two events
happen at
different phases
cell division
of the cell cycle.
mitosis
(M phase)
The phase of
G1
DNA replication
is called S
phase. The
G2
DNA replication
(S phase)
phase of
chromosome
segregation is
called mitosis or
M phase. The gaps between DNA replication and mitosis are called G1 and G2,
respectively.
To keep the genetic information intact and at constant level, it is crucial that the
phase of DNA replication (S phase) and the phase of chromosome segregation
(M phase) alternate
during the normal
DNA replication
mitotic cycle. Each
DNA replication is
followed by a
chromosome segregation
and a new DNA
replication can start only
chromosome
segregation
after previous
chromosome segregation
has finished.
Rule: replication and segregation of chromosomes must alternate.
3
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
Molecules regulating the cell cycle
The central
elements for cell
cycle control are
the cyclin-
+
Cdk
+
Cyclin
dependent kinases
(Cdks for short).
-
-
Cdks are a family
of special protein
C
AP
kinases, whose
activities depend on
the availability of
their regulatory subunits, called cyclins (they are only active in complex with
cyclin). Cdk activity is needed for DNA replication and even higher activity is
required for mitosis.
After DNA is completely replicated and chromosomes properly aligned on the
metaphase plate, cells are driven into anaphase by the Anaphase Promoting
Complex. The APC is a huge enzyme complex that attach a “eat- me label” to
proteins that are to be degraded. APC promotes anaphase, because it causes
degradation of the glue (represented here by yellow lines) that holds together
sister-chromatids, so they can separate. APC also causes degradation of the
cyclin subunits of the Cdks, thus inactivating the Cdks. When Cdk activity is
decreased, then chromosomes can decondense and cells can leave mitosis. Cells
enter G1 and the cycle repeats itself.
It turns out that the Cdk/cyclin complex also has a negative effect on APC,
because Cdk phosphorylates components of the APC and turns off its activity.
For this reason, APC and Cdk are antagonists and this antagonism between Cdk
4
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
and APC is important to create two characteristic states in the cell cycle, as we
will see now.
This slide shows a hypothetical cell cycle control mechanism that we think may
have been used by the most primitive eukaryotic cell. Cyclins are synthesized in
the cytoplasm, they combine with kinase subunits, and the active dimers are
transported and accumulated in the nucleus. As I mentioned before, we assume
that the Cdk activity inhibits APC and APC degrades the cyclin subunits.
The primitive APC-CDK controller
AA
Cyclin
Cdk
(fast)
Cyclin
Cdk
Cdk
Nucleus
Cdk
Cyclin
+
OFF
+
C
AP
APC
degraded
cyclin
ON
The interaction of CDK and APC can be described by a pair of kinetic
equations. The synthesis and degradation of cyclins are described by law of
mass action. The activation and inactivation of APC is described by MichaelisMenten kinetics. These DE’s can be best illustrated in terms of nullclines in a
phase plane. The phase plane is a simple coordinate system with two dynamic
variables (CDK and APC) plotted on the axes. Along the CDK nullcline, the rate
of cyclin synthesis is exactly balanced by the rate of cyclin degradation, so the
5
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
concentration of
d CDK
= k 1 . m as s - [v 2 ’ (1 - A P C ) + v 2 ” . A P C ) ] . C D K
dt
.
.
(k 3 ’ + k 3 ” A C T ) ( 1 - A P C ) (k 4 ’ + k 4 ” C D K ) A P C
d A PC
=
J3 + 1 - A P C
J4 + A P C
dt
CDK/cyclin
complex is not
changing, and its
G1
stable node
Phase Plane Portrait
value is
APC
determined by the
rate of cyclin
synthesis divided
saddle point
by the rate of
S/M
stable node
CDK
degradation. The
rate of synthesis is
constant, whereas the rate of degradation increases with APC activity. If APC is
high, then CDK is low and vice versa. So we get a simple hyperbola for the
CDK nullcline.
The APC nullcline has a sigmoidal shape. When CDK is low, APC is active and
vice versa. There is a critical level of CDK activity to turn off APC.
Wherever the two nullclines intersect, the system will be in a steady state. In this
slide, they intersect at three steady states. The two outside ones are stable steady
states (stable nodes). The intermediate one is unstable, a so called "saddle
point”. The stable steady state at the upper left corner has APC switched on and
CDK activity low, and it corresponds to the "G1" state of the primordial cell
cycle. The one at the lower right corner has APC switched off and CDK activity
high, and it corresponds to an "S/M" like state of the cell cycle. Depending on
the initial conditions, the control system will be in either th G1 or the S/M
steady state.
6
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
Imagine that the
Start
us see how the
G1
0.8
G1
0.8
APC
the "G1" state and let
1.2
APC
regulatory system is in
Finish
1.2
0.4
0.4
S/M
S/M
primitive eukaryote
0.0
0.01
0.1
0.0
0.01
CDK 1
could move into an
CDK 1
Cdk
degraded
cyclin
Cdk
mass
Cyclin
+
"S/M" like state. As
OFF
the cell grows, the rate
of cyclin accumulation
0.1
APC
ACT
unreplicated DNA
+
unaligned Xsomes
+
+
C
AP
+
ON
degraded
activator
apoACT
in the nucleus
increases proportional to cell mass. This causes the Cdk nullcline to move to the
right. When the cell reaches a critical mass, the "G1" state disappears by
coalescing with the saddle point (saddle-node bifurcation), and the only
remaining steady state is now the "S/M" steady state, and the cell must move
toward it. So the cell will switch off APC and activate CDK in an irreversible
way. This is the Start transition in the cycle.
How could the cell leave the "S/M" state and go back to the "G1" state? This
transition happens at the end mitosis, when DNA replication is completed and
all chromosomes are properly aligned on the mitotic spindle. It happens by
turning on APC. The details of how APC turns on is very complicated and here
we propose a simple scheme. We assume that an activator of APC is synthesized
in an inactive form at a constant rate and degraded in an APC-dependent
fashion. The distribution of the activator between its active and inactive forms is
regulated by a checkpoint mechanism: if DNA replication is not complete or
chromosomes are not aligned, most of the hypothetical activator is kept in the
inactive form. However, when the checkpoint is lifted, the activator gets
activated, the APC nullcline moves to the right, first recreating the G1 steady
7
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
state and then eliminating the S/M steady state. The cell must now leave mitosis
and enter G1. This is the Finish transition in the cell cycle.
This graph shows the
Simulation of the primitive eukaryotic cell cycle
2
numerical simulation
of the primordial cell
mass
cycle. In "G1", APC is
1
active and little cyclin
1.5
and activator are
Cdk
1.0
Cyclin
C
AP
present, because APC
degrades both of them.
0.5
However the cell is
growing and
0.0
G1
S/M
G1
S/M
1.5
cyclin/CDK dimers are
accumulating in the
1.0
ACTT
nucleus. When the cell
0.5
reaches a critical mass,
ACT
there is enough CDK
0.0
0
40
80
120
160
200
Time (min)
240
activity in the nucleus
to switch off APC.
After APC gets switched off, the levels of cyclin and the activator rise rapidly.
The rise in CDK activity initiates DNA replication. However, the activator
molecules are kept inactive by the inhibitory signals from unreplicated DNA and
unaligned chromosomes, as I described before. When these signals disappear,
the activator is rapidly transformed into its active form, which leads to abrupt
activation of APC, which in turn, degrades both cyclin and the activator and
pushes the cell back into the G1 state and the cycle repeats itself.
8
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
The simple
Addition of stochiometric Cdk inhibitor (CKI)
CKI
network described
above, based on
CKI
regulation of
degraded
CKI
+
Cdk
Cyclin
cyclin availability
only, could be the
Cdk
mass
Cyclin
+
heart of the
eukaryotic cell
OFF
APC
unreplicated DNA
cycle. However
present day
unaligned Xsomes
ACT
+
Cdk
+
C
AP
+
+
degraded
cyclin
ON
degraded
activator
apoACT
eukaryotes use
additional mechanisms to regulate Cdk activity as well. One of the mechanisms
uses a stochiometric Cdk inhibitor (CKI), which binds to the Cdk/cyclin
complex and inhibits its kinase activity during the G1 phase. We know such
kind of an inhibitor in both budding and fission yeasts. Of course, the inhibitor
must be present only transiently during the cycle. It must be eliminated at Start
so that Cdk activity can drive DNA synthesis and mitosis. The inhibitor is
eliminated, when it is phosphorylated by the Cdk. Notice that, CKI inhibits Cdk
and Cdk promotes the degradation of CKI: another antagonistic relationship.
Now, Cdk has two enemies, both CKI and APC. Therefore at the Start
transition, Cdk must win against both enemies, and its job is much harder now.
The network you saw on the previous diagram is very similar to the present day
budding yeast cell cycle control. The only missing components are the starter
kinases, which helps Cdk in fighting against its enemies at Start transition. The
cyclins, I was talking before belong to the B-type class and they are called Clb’s
in budding yeast. The starter kinases that help Clb-kinases are also Cdk/cyclin
complexes, in which the Cdk subunits are the same, but the cyclins belong to a
different class, called Cln’s. One of the Cln’s, Cln3, is present at low and
9
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
Budding yeast
constant concentration
throughout the cycle. Its
major role is to turn on
Cdk
transcription factor
degraded
Cln3
Cln3
SBF, which is
Cdk
SBF
Cdk
+
responsible for
+
transcription of another
+
Clb
P
Cdk
SBF
Cln type cyclin called
degraded
Cln2
Cln2
Cln2. Cln2 can also
Cdk2
Cdk
activate SBF, thereby
Sic1
Sic1
+
P
degraded
Sic1
transcription, creating a
+
-
activating its own
positive feedback loop.
Cdk
degraded
Clb
Clb
+
+
Cdk
+
AP
APC
Because Cln/Cdk
complexes are not
inhibited by the CKI,
C
ACT
and not degraded by
APC, a burst of the Cln2 kinase activity is a very efficient way to help Clbkinases to eliminate CKI, (called Sic1) and to turn off APC, thus enabling cells
to pass Start.
Budding yeast cells divide in an asymmetric fashion, by producing a large
mother cell and a small daughter cell. This graph shows you the simulation of
the small daughter cell. It has a long G1 phase with low Clb kinase activity. As
the cell is growing, Cln3 kinase accumulates in the nucleus and when the cell
reaches a critical size, it turns on the transcription of Cln2 through SBF. The
rising Cln2 level turns off APC and eliminates CKI by phosphroylation. As a
consequence Clb level can increase. The rising Clb kinase activity initiates first
10
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
DNA replication and later
on mitosis. At the end of
Simulation of the budding yeast cell cycle
2
mitosis the activator gets
activated and the two
mass
1
enemies of Clb kinase
(CKI and APC) make a
SBF
Sic1
1.0
come back.
Cln2
0.5
Now we can connect the
model with cell
0.0
G1
S/M
Clb
1.5
physiology. Let me show
you one such example. On
this graph we plot the
APC
1.0
0.5
concentrations as a
0.0
function of cell mass.
0
50
100
150
Time (min)
Wild type cell does Start
at around one mass unit (top panel), when it inactivates APC and destroys CKI
(the molecule Sic1) with the help of Cln2 starter kinase. If we take Cln2 starter
kinase out of the model, as in a cln2- mutants, then cell passes Start at a much
larger mass (see middle panel). This is because the Clb-kinase must fight against
both CKI and APC alone. However, if we also eliminate CKI, as in a cln2- sic1double mutant, then mass at Start moves back to almost normal value (see
bottom panel). This clearly shows that the major role of the Cln2 starter kinase
is to eliminate the CKI. Also observe that in this double mutant, where there is
no CKI and no starter kinase, the cell cycle regulation is almost the same as the
primitive eukaryote.
11
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
G1
S/M
1.5
Clb
Sic1
Wild type
SBF
1.0
APC
0.5
0.0
G1
2.5
2.0
S/M
cln2-
Sic1
Clb
1.5
1.0
APC
SBF
0.5
0.0
G1
2.0
S/M
1.5
Clb
APC
1.0
SBF
cln2- sic1-
0.5
0.0
0.5
1.0
1.5
2.0
2.5
cell mass
Now I would like to turn to higher eukaryotes and talk about control of cell
cycle in multicellular organisms like mammalian cells. Normal, individual cells
in a multicellular organism can proliferate only in the presence of growth
factors. If growth factors are deprived, cells early in G1 phase leave the cycle
and enter into a G0 (G-zero) resting state; cells later in the cycle, however, finish
their ongoing cycle and stop in the next cycle. The point in G1, which
determines whether cells can enter into this G0 resting state is called the
restriction point.
The control machinery for the mammalian cell cycle is very complex. They have
many different Cdks, cyclins and CKIs. Cdks can combine with cyclins and
12
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
CKIs in various
Cell cycle control in multicellular organisms
combinations that
Cell divides
(mitosis)
affect various
cellular events.
There are enormous
Cell
rests
G0
efforts by
molecular
Restriction point:
cell decides whether
to commit itself to
the complete cycle
Cell replicates
its DNA
biologists trying to
sort out this
network, and data
are accumulating at
a tremendously fast rate. What I want to do today, is to show you a very
simplified model of the mammalian cell cycle. Using this simple model, we can
study the behavior of a normal mammalian cell cycle and how deprivation of
growth factor may affect it. By doing that, I hope to demonstrate to you how
mathematical modeling helps us in understanding cell physiology from
molecular mechanisms.
How does the cell sense
How growth factors work
the presence of growth
growth
factor
growth factor
receptor
GF
factors? Growth factors
kSE
bind to specific receptors
ERG
kDE
-
activated
intracellular
signalling
proteins
kLV +
LRG
kSL
+
in the plasma membrane
kDL
+
k10
Cdk4
k9
CycD
and they activate
Cdk4
k SE
d ERG
= ε . 1 + (LRG/V )2 - k DE . ERG
dt
0
intracellular signal
ERG
d LRG
=ε
dt
LRG
mRNA
transduction pathways.
degraded
CycD
.
k
.
(LRG/L0) 2
{ k LV . ERG + 1 SL+ (LRG / L0)2 )} - k DL . LRG
d cycD T
= ε . k 9 . LRG - k 10 . cycD T
dt
The end result of this
time
activation is twofold:
13
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
1. the transcription of certain genes is turned on (as shown on this diagram).
2. there is a general increase in the rate of protein translation on the ribosomes
(which is not shown here).
Two groups of genes are activated in succession after GF addition. The so called
early response genes (ERG) are activated in a few minutes, and their mRNA
level reaches a peak soon and then falls off. The ERG proteins induce
transcription of a second group of genes, called late response genes, which in
turn, inhibit the transcription of ERG’s. One of the late response genes is a
cyclin gene, namely cycD. CycD level is high only in the presence of growth
factor, so it can be considered as a growth factor sensor. CycD combines with a
special Cdk, called Cdk4.
The mechanism of transcriptional activation of CycD by growth factor is not
fully understood. We propose that GF activates ERG, which activate LRG,
which in turn activates CycD transcription. In addition, LRG is activated
autocatalytically. The system can be described by these 3 DE’s and the
dynamics of their interaction will be discussed later.
Just like budding yeast, mammalian cells also use another starter kinase, which
is a complex of cycE and another Cdk, called Cdk2. The transcription factor for
CycE belongs to the E2F family. E2F has an inhibitor named Rb
(retinoplastoma protein), which binds to it and inhibits its activity. However,
CycE can activate its own transcription because CycE-kinase can phosphorylate
Rb, which releases E2F, resulting an increase of CycE transcription. The role of
CycD/Cdk4 complexes is to help CycE/Cdk2 in starting this positive feedback
loop if growth factor is present.
14
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
ERG
+
LRG
+
In addition to Rb, CycE
Mammalian cells
GF
has another enemy, which
is a CKI, called p27. They
+
are antagonistic also. p27
Cdk4
CycD
Rb
Cdk4
E2F
degraded
CycD
binds to CycE/Cdk2
+
Cdk1
P
P Rb
Rb
CycA/B
complex and inhibits its
P
activity; whereas
+
-
Cdk2
E2F
degraded
CycE
CycE
CycE/Cdk2 phosphorylate
Cdk2
-
p27 and renders it for
p27
p27
+
rapid degradation.
P
degraded
p27
+
synthesis and works as a
Cdk1
degraded
CycA/B
CycA/B
+
+
CycE/Cdk2 initiate DNA
starter kinase for cyclin B.
Cdk1
+
In mammalian cells, BC
AP
APC
types cyclins combine
ACT
with Cdk1 to initiate
mitosis. The only enemy for CycB/Cdk1 is the APC. Interestingly, no CKI,
specific for CycB-kinase has been found in mammalian cells so far. CycE/Cdk2
turns off APC, so CycB can accumulate. Rising levels of CycB, hence the
activity of CycB/Cdk1 drives the cell into mitosis.
Summarizing this minimum model of the mammalian cell cycle: in the presence
of growth factors, CycD transcription is activated. CycD/Cdk4 complexes then
help CycE in turning on its own transcription. The rising cycE kinase eliminates
its inhibitor p27. In addition, CycE/Cdk2 activity also helps CycB by turning off
APC. High CycE-kinase activity triggers DNA synthesis and higher CycBkinase activity drives the cell into mitosis.
15
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
Notice the similarity in cell cycle controls between mammalian cells and
budding yeast cells. cycD corresponds to Cln3, while cycE is the Cln2 analogue.
Both cycE and Cln2 synthesis is regulated by a positive feedback loop. The only
difference is that the positive feedback in CycE transcription is achieved by
inactivation of an inhibitor (Rb) for its transcription factor E2F. In contrast, in
Budding yeast
GF
Mammalian cells
the Cln2 case, its transcription factor (SBF) is activated by Cln2 itself.
ERG
+
LRG
+
+
degraded
Cln3
Cdk
Cln3
Cdk4
Rb
Cdk
Cdk4
E2F
SBF
+
+
Cdk
Cdk1
+
Clb
degraded
CycD
CycD
P
P Rb
Rb
CycA/B
+
-
P
Cdk
SBF
Cdk2
degraded
Cln2
Cln2
E2F
degraded
CycE
CycE
Cdk
Cdk2
Cdk2
degraded
Sic1
+
Cdk
Cdk1
degraded
Clb
degraded
p27
Cdk
+
+
AP
degraded
CycA/B
CycA/B
+
APC
P
+
Clb
+
+
p27
P
p27
Sic1
Sic1
+
-
P
+
C
+
APC
ACT
Cdk1
+
AP
C
ACT
The other difference is in the CKI. In mammalian cells, the inhibitor, p27,
inhibits CycE-kinase; whereas in budding yeast, Sic1 inhibits Clb-kinases.
This figure shows the simulation of a normal mammalian cell, growing
exponentially in the presence of growth factors. At the end of mitosis, the cell
divides into two daughter cells and we follow one of them. Because APC is
activated at that time, CycB is degraded, which causes Rb to be active, which
16
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
inhibits CycE synthesis,
Simulation of mammalian cell cycle
which allows p27 to rise.
Therefore in the early G1
4
mass
3
phase, CycD/Cdk4 represents
the only Cdk activity, CycE-
2
2
Cdk2
their enemies Rb, p27 and
APC.
p27
and CycB-kinases all lose to
CycE
1
0
2
CycE
Rb
About 3 hours after cell
total
1
division, CycD/Cdk4 comes
to the rescue. As CycD/Cdk4
0
3
Cdk1
accumulates in the nucleus to
2
high enough levels, Rb
1
phosphorylation reaches a
CycA/B
C
AP
0
0
4
8
12
16
20
24
28
Time (h)
threshold, and positive
feedback loop in CycE transcription turns on. The rising cycE kinase wins over
p27 and p27 goes away, and CycE kinase is not inhibited anymore. At about
half-way through the cycle, APC gets switched off by the continuously rising
CycE kinase activity. This marks the G1/S transition as high CycE-kinase
activity triggers initiation of S phase. As APC is off, CycB starts to accumulate.
The rising level of cycB-kinase later drives cells into mitosis. When all the
chromosomes are properly aligned, APC is activated and cells exit from
mitosis.
Now I would like to focus on the following questions:
1. Where is the restriction point in the cycle?
2. How do cells regulate the progression through the cycle after growth factor
deprivation?
17
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
It is a nice place to
Zetterberg & Larsson experiment
discuss these topics
Where is the restriction point?
What is the effect of transient GF deprivation on cycle time?
in Sweden, because
these questions have
been analyzed
carefully by
cycle time
Zetterberg and
Larsson at the
division delay
treatment
Karolinska Institute.
- GF
+ GF
They cultivated
mouse fibroblast
(Zetterberg, A. & Larsson, O. (1985): Kinetic analysis of regulatory events in G1 leading to
proliferation or quiescence of Swiss 3T3 cells. Proc. Natl. Acad. Sci. U. S. A., 82: 5365-5369)
cells under the microscope equipped with a camera. Thereby they could measure
the cycle time of individual cells. They analyzed the effect of transient growth
factor deprivation and protein synthesis inhibition on cycle time for cells at
different ages in the cycle. Would cell division be delayed? If so, by how
much?
What Zetterberg and Larsson found is shown in left panel. For cells treated
early in the cycle (age 3h or less at the time of serum deprivation), their first
mitotic cycle was delayed by 8 hours, but their 2nd cycle was normal. For cells
treated late in the cycle (ages 3-14h), however, their 1st cycle was not affected
by the GF deprivation. Their first division was on schedule, but their second
mitotic cycle was lengthened.
The right panel shows our simulation of the Zetterberg & Larsson experiments.
To simulate growth factor deprivation we reduced the rate of synthesis for all
components by 50%. The two dotted lines on the upper panel represents the
effect due to 10% variation in cell size.
18
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
First cell cycle
30
Intermitotic time (h)
Experiment
Simulation
mean cell size
+/- 10%
20
10
0
0
4
8
12
Cell age (h)
Second cell cycle
Experiment
Simulation
30
Intermitotic time (h)
26
22
18
14
10
6
0
4
8
12
Cell age (h)
You can see that the simulation results resemble the experiments. The main
conclusion is that all the cells are responding to GF deprivation. What is the
restriction point then? Cells before the restriction point respond to transient GF
deprivation in their ongoing cycle, while cells after the restriction point respond
in their subsequent cycle. Why is that ?
This figure shows the numerical simulations for 1 hr of GF deprivation. On the
left panel, the treatment is applied in G1 phase, between 2-3 hours after cell
division. On the right panel, it is applied in G2 phase, between 10-11 hours. In
both cases, the level of cycD drops quickly to zero and returns to its normal
19
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
steady state value about 8 hours after the treatment. The fast drop in cycD level
is the consequence of LRG disappearance. Once LRG has disappeared, it takes a
lot of time to come back, because the ERG level is low.
Effect of transient (1h) serum deprivation
Age 2h
4
Age 10h
4
mass
mass
3
3
2
2
1
1
ERG
LRG
LRG
ERG
0
2
p27
0
2
Cdk2
p27
Cdk2
CycE
1
CycE
1
Cdk4
Cdk4
CycD
CycD
0
0
3
3
Cdk1
Cdk1
CycA/B
2
CycA/B
2
Rb
1
Rb
1
C
AP
0
0
C
AP
0
10
20
30
40
0
Time (h)
10
20
30
Time (h)
The lack of cycD has very different effect in G1 and in G2 cells. Since in G1
cells, cycD is the only cyclin to phosphorylate Rb; when cycD level drops, Rb
gets dephosphorylated at once. The dephosphorylated form of Rb inactivates all
the transcription factors and cells growth dramatically slowing down. As a
consequence, cells enter into a G0 state. Since it takes 8 hrs for CycD to come
back after GF has been restored, so the first cycle is delayed by additional 8 hrs.
In G2 cells, however, other cyclins and Cdk/cyclin complexes are present as
well, which can keep Rb phosphorylated even in the absence of cycD. For this
reason, cells keep on growing in mass until they finish their cycle. However at
the end mitosis, if CycD has not made a come back yet (i.e., if it has not been 8
20
Bela Novak:
Bioinformatics ’99
Modeling the eukaryotic cell division cycle
Lund (Sweden) ‘99
hrs since the GF restoration), when cycB gets destroyed, Rb gets rapidly
dephosphorylated. As a consequence, cells will slow down growth for a while
until cycD makes a comes back. This period of reduced growth in G1 induces a
delay in the second mitotic cycle. The later cells are treated in their first cycle,
the longer will be the delay in their second cycle.
21