Biology Reference
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stimulates production of a CKI (Far1) that specifically
inhibits Cln1,2,3-dependent kinase activities.
In the presence of
steady states of the full system (
Figure 14.5
A
รพ
B, with
EP
0), and one can readily guess the stability of each
steady state and the temporal evolution of the dynamical
system when the steady states are removed by saddle-node
bifurcations.
z
factor, the Start switch is perma-
nently arrested in the Cln2-low position. In the absence of
a
a
factor, a small cell is arrested in the Cln2-low position; but
as the cell grows, Cln3:Cdk1 activity increases. By phos-
phorylating Whi5, Cln3-kinase partially inactivates Whi5
and helps the Cln2 self-activation loop to engage
[57]
. The
Cln2-low state is lost by a saddle-node bifurcation
(
Figure 14.8
, left), and Cln2 begins to accumulate in a self-
accelerating manner
[20]
. The Start switch is moving
toward the Cln2-high position, but before it reaches this
state, Cln2:Cdk1 flips the G1/S switch to the Clb2-high
position, and Clb2:Cdk1 inactivates SBF (see
Figure
14.5
B). The Start switch never reaches the stable Cln2-high
position, but instead drops back to the Cln2-low state
(
Figure 14.8
, left). After Cln2 has done its job as a starter
kinase to activate the B-type cyclins (DNA synthesis and
mitosis), it drops back to the Cln2-low state in order not to
interfere with mitotic exit
[58]
.
Aword about the interpretation of
Figure 14.8
. The left
and right sides, considered separately, should be thought
of as 'pseudo-phase planes'. The control system in
Figure 14.5
has dozens of dynamical variables, and its
vector field cannot be represented on a two-dimensional
phase plane. Instead, we have plotted one-parameter
bifurcation diagrams for subsets of the reaction network.
For example, consider the left side of
Figure 14.8
(similar
reasoning applies to the right side). The black curve is the
one-parameter bifurcation diagram for the bistable network
in
Figure 14.5
A, treating Cln2-kinase as the bifurcation
parameter and setting Cdc20
Mitotic Checkpoint
The M/G1 transition is guarded by the mitotic checkpoint,
which controls activation of APC:Cdc20 and the exit
phosphatase, Cdc14
[59]
.
Figure 14.5
D diagrams the
mitotic checkpoint proper, which controls activation of
APC:Cdc20, and
Figure 14.5
C indicates how active Cdc20
initiates the activation of Cdc14 and the re-establishment of
cells in G1.
The role of the mitotic checkpoint (the 'anaphase
switch') is to prevent cells from cleaving cohesin rings until
all replicated chromosomes are properly aligned on the
mitotic spindle
[60]
. Alignment is judged, it seems, by
tension within the centromeric region of bi-oriented chro-
mosomes (one kinetochore attached by microtubules to one
pole of the spindle, and the other kinetochore to the other
pole). Unaligned, tensionless chromosomes generate
a signal that activates Mad2, and active Mad2 binds to
APC:Cdc20
[40]
, holding it in an inactive complex (the
mitotic checkpoint complex, MCC, which is inactive with
respect to degradation of separase and Clb2, but active on
the degradation of Clb5). The signal from tensionless
chromosomes to Mad2 depends on Clb-kinase activity,
which is high in prometaphase. As soon as all chromo-
somes are properly aligned and under tension, the rate of
Mad2 activation becomes 0, and the MCC begins to
dissociate, releasing active APC:Cdc20.
The network in
Figure 14.5
C has two positive feedback
loops. (1) Clb2:Cdk1 (via tensionless chromosomes) acti-
vates Mad2, which inactivates APC:Cdc20; whereas APC:
Cdc20 degrades Clb2, thereby inactivating the kinase. This
double-negative feedback loop creates a bistable switch at
0. The red
curve is the one-parameter bifurcation diagram for the
bistable network in
Figure 14.5
B, with Cln2-kinase as the
variable and Clb2-kinase as the bifurcation parameter.
Strictly speaking, these bifurcation curves are not null-
clines on a phase plane, but they can be thought of as
pseudo-nullclines. Their intersection points are certainly
0 and Cdc14
z
z
FIGURE 14.8
Checkpoints in budding yeast. We identify SK
with Cln2:Cdk1 and EP with a combination of activities of Cdc20
and Cdc14. Left: the G1/S transition is guarded by a checkpoint
called Start (Figure 14.5B), which creates a stable steady state of
low Cln2 abundance. As the cell grows, the checkpoint is lifted
(red arrow) and the stable G1 state is lost by a saddle-node
bifurcation. Subsequently, Cln2 production induces the G1/S
transition as in
Figure 14.6
. Right: the M/A transition is guarded by
the mitotic checkpoint. When all chromosomes are properly
aligned on the metaphase plate, the checkpoint is lifted (green
arrow) and the stable metaphase-arrested state is lost by a saddle-
node bifurcation. Subsequently, Cdc20 and Cdc14 are activated
and they drive exit from mitosis and return to G1 phase.
