Bioinformatics: Network Analysis
Kinetics of Regulatory Networks: Basic Building Blocks
COMP 572 (BIOS 572 / BIOE 564) - Fall 2013
Luay Nakhleh, Rice University
1
Basic Building Blocks
✤
Here we show how simple signaling pathways can be embedded in
networks using positive and negative feedback to generate more
complex behaviors - toggle switches and oscillators - which are the
basic building blocks of the dynamic behavior shown by non-linear
control systems.
2
hnology about
curves
en remarkably
Let’s start with two simple examples of protein d
chanisms that
synthesis and degradation (Figure 1a), and pho
cells. Stunning
tion and dephosphorylation (Figure 1b). Using t
h of viruses [1],
mass action, we can write rate equations for t
ision cycle of
mechanisms,
as
follows:
Using
the
law
of
mass
action, we have: Linear
5
y development
S
0.5
ammalian cells
dR
3
¼
k
þ
k
S
%
k
R;
0
1
2
e cases is laid
2
dt
R
1
nih.gov/kohnk/
dRP
0 :
0¼ k SðR
u:82/Inst/gorb_
%
R
Þ
%
k
R
1
T
P
2
P
0
1
2
3
0
0.5
1
dt
Signal (S)
R
w.biocarta.com/
In case
(a),of SmRNA)
¼ signal strength (e.g. concen
ooks
strikingly
2
S: signal
strength
(concentration
S
1
Hyperbolic
2
mRNA) and
R 4¼ 8response magnitude (e.g. conc
ern electronic
ATP
ADP
Rate (dR/dt)
Response (R)
Protein Synthesis and
Degradation: Linear Response
RP
Pi
Response (RP)
R
Rate (dRP/dt)
R: response magnitude (concentration of protein)
1
0.5
Current Opinion
in Cell Biology 2003,
H2O
0
0
0.5
R
1
0
0
5
Signal (S)
10
3
hnology about
en remarkably
chanisms that
cells. Stunning
h of viruses [1],
ision cycle of
y development
S
ammalian cells
e cases is laid
R
nih.gov/kohnk/
u:82/Inst/gorb_
w.biocarta.com/
ooks strikingly
S
ern electronic
ATP
ADP
curves
Protein Synthesis and
Degradation: Linear Response
Pi
H2O
Response (R)
Rate (dR/dt)
dRP
Steady-state
solution:
¼0 k1 SðR0.5T % RP1Þ % k2 RP0 0:
0
k0 þ Rk1 S
Signal (S)
Rss ¼
k2 S ¼ signal strength (e.g. concen
In case
(a),
2
1
Hyperbolic
2
mRNA) and
RRT4¼
S 8response magnitude (e.g. conc
:
RP;ss ¼
ðk2 =k1 ÞCurrent
þ S Opinion
1
0.5
in Cell Biology 2003,
dt
1
2
3
Response (RP)
RP
of the response element.
A steady-state
0.5
dR
differential
¼ k0 þ k1 Sequation,
% k322 R; dR=dt ¼ f ðRÞ, is a con
dt
satisfies the algebraic
equation f ðRss Þ ¼ 0.
1
Rate (dRP/dt)
R
Let’s start with two simple examples of protein d
synthesis and degradation (Figure 1a), and pho
of
protein).
In
case
(b),
RP
is
the
phosphor
tion and dephosphorylation (Figure 1b). Using t
the response
element
(which
we suppose
mass
action, we
can write
rate equations
for tt
¼
½RP#,
and
R
¼
R
þ
R
¼
tota
form),
R
mechanisms,
as
follows:
P
T
P
Linear
Using5 the law of mass action, we have:
These equations correspond to the linear a
0
0
signal-response
curves
in
1. In10 mo
0
0.5
1
0 Figure
5
R
Signal (S)
4
i
2
Response (RP)
Rate (dRP/dt)
HO
P
ooks strikingly
dern electronic
In case
(a),
S
¼
signal
strength
(e.g.
concentr
0
0
0
1
0
5
10
mRNA)
and 0.5
R
¼
response
magnitude
(e.g.
conce
R
Signal (S)
P
2
ADP
ATP
RT: total concentration
R
RP
Pi
of the1.5response element
1
1
0.5
0.25
H2 O
0
0
0.5
1
Response (RP)
RP: concentration
of the phosphorylated
form
of the
element
Sigmoidal
Opinion
in Cell
Biology
2003, 1
2 Current
1 response
S
Rate (dRP/dt)
)
Response
Rate (dR
echanisms that
3
synthesis and degradation
(Figure 1a), and phos
cells. Stunning
2
tion and dephosphorylation
(Figure
1b).
Using
th
R
1
h ofPhosphorylation
viruses [1],
andwe can write rate equations for th
mass action,
vision cycle of
0
0
0
1
2
3
0
0.5as follows:
1
mechanisms,
Dephosphorylation:R Hyperbolic Response
Signal (S)
y development
ammalian cells
dR 2
)
¼ k0 þ k1 S % k2 R;
S
1
Hyperbolic
se cases
is
laid
8 action, we have:
Using
of mass
2
4
dt the law
ATP
ADP
nih.gov/kohnk/
dRP 1
u:82/Inst/gorb_
¼ k1 SðRT % RP Þ % k2 R0.5
R
RP
P:
dt
w.biocarta.com/
0.5
0
0
1
2
3
5
Response (RP)
Rate (dRP/dt)
Response
Rate (dR
echanisms that
3
synthesis and degradation
(Figure 1a), and phos
cells. Stunning
2
tion and dephosphorylation
(Figure
1b).
Using
th
R
1
h ofPhosphorylation
viruses [1],
and
of protein).
Inwe
casecan
(b),write
RP israte
the phosphorylated
fo
mass
action,
equations for th
vision cycle of
0
0
0
1
2 to be
3 the
0
0.5
1 (which we
the
response
element
suppose
mechanisms,
as
follows:
Dephosphorylation:
Signal (S)
R Hyperbolic Response
y development
form), RP ¼ ½RP#, and RT ¼ R þ RP ¼ total concen
ammalian cells
dR
2
of
the
response
element.
A1 steady-state
solution
)
¼
k
þ
k
S
%
k
R;
S
Hyperbolic
0
1
2
se cases
is
laid
8 action,
Using
of mass
2 equation,
4
dt the law
ATP
differential
dR=dtwe
¼ have:
f ðRÞ, is a constant, R
ADP
nih.gov/kohnk/
satisfies
the algebraic equation f ðRss Þ ¼ 0. In our c
dR
P 1
u:82/Inst/gorb_
¼ k1 SðRT % RP Þ % k2 R0.5
R
RP
P:
dt
k0 þ k1 S
w.biocarta.com/
Rss ¼
HO
P
k(a),
Steady-state
In case
S
¼
signal
strength
(e.g.
concentr
ooks strikingly
2 solution:
0
0
0
0.5
1
0
5
10
mRNA)
and
R
¼
response
magnitude
(e.g.
conce
dern electronic
RTRS
Signal (S)
:
RP;ss ¼
ðk2 =k1 Þ þ S
2
2
i
P
2 Current
ATP
R
ADP
RP
Pi
H2 O
Sigmoidal
Opinion
Biology 2003, 1
1 in Cell
These equations
correspond to the linear and hype
1.5
signal-response curves in Figure 1. In most cases,
1
1
0.5
simple components are embedded
in more complex
0.5
ways, to generate
signal-response curves of more ad
value. 0.25
Response (RP)
S
Rate (dRP/dt)
)
0
0
0.5
1
0
0
1
2
3
6
Linear and Hyperpolic Responses
✤
Linear and hyperbolic curves share the properties of being graded
and reversible:
✤
Graded means that the response increases continuously with signal
strength. A slightly stronger signal gives a slightly stronger
response.
✤
Reversible means that if the signal strength is changed from Sinitial
to Sfinal, the response at Sfinal is the same whether the signal is being
increased (Sinitial>Sfinal) or decreased (Sinitial>Sfinal).
7
RP Gðu; v; J; KÞ
Pi
H2 O
Response
Response (RP)
Rate (dR
Rate (dRP/dt)
T
T
m1
m2
the
‘Goldbeter-Koshland’
function, G, is(
1
¼ Gðk1 ; S; k2 ;
;
Þ; 0.5
T
P;ss
where
1
R
Response (RP)
)
Phosphorylation and
Dephosphorylation: Buzzer
Rate (dRP/dt)
)
simpleways,
components
are embedded
in more complex
path- of cisely
to generate
signal-response
curves
morethe
adapti
same
Case
(c)
of
Figure
1
is
a
modification
of
case
(b),
wh
3
ways, to
generate
signal-response
curves
of
more
adaptive
value.
2
signal-response
curvesPerfectly
value.Sigmoidal
phosphorylation
and
dephosphorylation
reactions
ada
R
1 a modification of case
By(b),
supplement
Case
(c)
of
Figure
1
is
where
erned
by
Michaelis-Menten
kinetics:
Sigmoidal
signal-response
curves (Figure 1a) wit
Sigmoidal
signal-response
curves
0
0
phosphorylation
and dephosphorylation
0
1 reactions
2
3 are g
0 1 is a modification
0.5
1of case (b), where
Case (c)
of
Figure
the
Case
(c) ofkFigure
1
is
a
modification
of
case
(b),
where
th
species
X in Fig
dR
SðR
'
R
Þ
k
R
Signal
(S)
R T
1dephosphorylation
P reactions
2 areP governedP byandMichaelis-Menten
kinetics:
phosphorylation
ism that are
exhibit
¼
'
;
phosphorylation
and
dephosphorylation
reactions
go
erned by dt
Michaelis-Menten
kinetics:
adaptation mea
K
þ
R
'
R
k
þ
R
m1
T
P
m2
P
2
erned
by
Michaelis-Menten
kinetics:
dR
k
SðR
'
R
Þ
k
RP1
P
1
T
P
2
exhibits a transi
S
Hyperbolic
Assuming
Michaelis-Menten
kinetics:
dRP
k1 SðR
'
R
Þ
k
R
T
P
2
P
¼
; (c) its steady-state
8; '
2 ' the
4 steady-state
ATP
¼ dt
In
this
case,
concentration
of
th
ADP
K
þ
R
'
R
k
þ
R
m1
m2
Km1P þ RTk'
dt dR
RP TkT
' þRR
k2 RP P
m2
PP
1 SðR
PÞ
behaviour iseq
t(
phorylated
form
is
a
solution
of
the
quadratic
¼
'
;
In thisIn
case,
the
steady-state
concentration
ofconcentration
the
phosrespond
to anph
a
1K
this
case,
the
steady-state
of
the
dt
þ
R
'
R
k
þ
R
m1
T
P
m2
P
0.5
R
RP
phorylated form is a solution of the quadratic equation:
but then
adapt
phorylated
form
is
a
solution
of
the
quadratic
equatio
k1this
SðRcase,
Þ ¼concentration
k2 RP ðKm1 sense
þofRTof
'
RPo
T 'R
PaÞðK
m2 þ R
Steady-state
is
solution
ofPthe
equation:
In
the
steady-state
the
pho
smell
k1 SðRT ' RP ÞðKm2 þ RP Þ ¼ k2 RP ðKm1 þ RT ' RP Þ:
O
H
response
as a ‘s
Pi
2
phorylated
form
is
a
solution
of
the
quadratic
equatio
k
SðR
'
R
ÞðK
þ
R
Þ
¼
k
R
ðK
þ
R
'
R
Þ:
acceptable
1TheT
P
m2 solution
P (0 < 2RP0P< Rsolution
m1
T (0 <P RP <
0 biophysically
)
of
The biophysically
acceptable
T
0
0.5
1
0
5
10
this equation
isequation
[30]:
[30]:
The
hyperbolic
RP is þ
Signal
k1this
SðRbiophysically
RP Þ ¼ k2 Rsolution
RT(S)
'RR
T ' RP ÞðK
m2 acceptable
P ðKm1 þ
P Þ:
< RT )
The
(0
<
P
The biophysically acceptable solution (0<RP<RT) of this equation
is:
made perfectly
RP;ss this equation
K
K
m2 [30]:
2 k ; m1 ; is
pathway
that
d
<
R
)
biophysically
solution
(0
<
R
¼The
Gðk
;
S;
Þ;2 acceptable
(d)
R
K
K
1
2
P
T
P;ss
m1
m2
Sigmoidal
1
S
RT
RT R;TS; k ;
¼
Gðk
;
Þ;
and Iglesias [31
1is [30]:
2
this
equation
ADP
ATP
R‘Goldbeter-Koshland’
RTKm2RG,
1.5
Km1function,
P;ss
T
T is defined
whereRthe
model phospho
¼ Gðk1 ; S; k2 ;
;
Þ;
as:
neutrophils.
RR
KR G,KRis defined as:
where the Goldbeter-Koshland
function,
Ras:
RT RT
T
h
where
the ‘Goldbeter-Koshland’
function,Many
G, authors
is defin
0.5
2uK
tion (see [32–35
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
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ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
q
¼ as:
:
where
the
‘Goldbeter-Koshland’
function,
G,
is
define
0.25
2
J;þKÞðv ' u þ vJ þ uKÞ ' 4ðv ' uÞuK
v ' uGðu;
þ vJ þv;uK
0
0
as:
Positive
feed
0 KÞ
0.5
1
Gðu; v; J;
1
2
3
0
8
Response (RP
Rate (dRP/dt
1
Phosphorylation and
Dephosphorylation: Buzzer
0
0
0.5
0.5
0
1
0
RP
2
1
0.5
0.25
0
0
0.5
Sigmoidal
1
1.5
1
10
Signal (S)
Response (RP)
Rate (dRP/dt)
2
5
1
0.5
0
0
RP
1
2
3
Signal (S)
5
Rate (dR/dt)
Adapted and reversible, but abrupt.
A sigmoidal response is 1.9continuous
4
3
S
R
The element
behaves like a buzzer, where one3 must push hard enough
5
X
2
2
on the button to activate the1.4response. In terms
of phosphorylation, the
1
1
signal S must be strong enough to create a noticeable
change of the
0
–1
0.9equilibrium.
0
0
1
R
0.6
2
0
10
20
Time
9
RP
5
0
1
1
10
0.5
Perfect Adaptation:
Sniffer
Box 1 Mathematical
models of signal-response
Signal (S)
0.5
0.25
H2 O
Pi
0
Sigmoidal
1
0
0.5
0
1
0
RP
1
2
3
Signal (S)
Figure 1d. Perfectly adapted
)
k4
k1
R
k
2
feed-forward
Signal (S)
0
1.9
1 2
S
R
X
1.4
EP
0
E
10
Time
0
0
1
0.9
2
0
10
3
2
1
0
–1
20
Time
ObserveR that Rss is independent
of S.
Adapted
S
R
0.9
3
4
The response mechanism exhibits perfect adaptation to the signal.
5 0.6
16
Although the signaling
pathwayMutual
responds
transiently to changes
activation
Figure
1e.
Mutual
activation
8
4 0.5
in signal strength,
its steady-state
response RSS is independent of S
0.5
0
0.4
3dRand is only controlled by the ratio of the four kinetic rates of the
E
ðRÞ
þ
k
S
#
k
X
$
R
¼
k
0.3
0
P
1
2
system.
Scrit
2 dt
0.2
Such behavior is typical of chemotactic systems, which respond to
1
0.1 ðRÞ ¼ Gðk R; k ; J ; J Þ
E
Pan abrupt change
3 in 4attractants
3 4 or repellents, but then adapt to a
0 0
0
constant
level
of
the
signal.
0
10
0
0.5
R
Signal (S)
–1
Figure
1f.
Mutual
inhibition
Our
own
sense
of
smell
operates
this
way; hence, this element is
20
0.1 termed a sniffer.
1
dR
Response (R)
0
1.8
S
¼ ko þ k1 S # k2 R #
)
X
S
Rate (dR/dt)
k3
dR
k1 k4 S
3
R
¼ k1 S # k2 X $ R
Rss ¼
5
k2 k3X
dt
2
1.4
dX
k3 S
1
Xss ¼
¼ k3 S # k4 X
dt
k4
Rate (dR/dt)
0.5
5
Adapted
1.9
)
)
Response (
Rate (dRP/dt
Re
Response (RP)
0
R
0 Mutual inhibition
k2 EðRÞ $ R
10
1.9
4
S
R
3
5
Positive Feedback: One-way
Switch
X
0
1
Signal (S)
k2
R
1.4
k4
k3
EP
0.6
4
0.3
2
0.2
1
0.1
E
0
feedback
0
0.9
10
0
0.1
0.5
0.05
E
S
0
Scrit
0
10
1
Signal (S)
R
0
dR/dt)
Response (R)
R
0
10
20
Time
R
Scrit
0
–1
R
0.5
0
10
Signal (S)
1
1.8
Mutual activation
EP
–1
0
a Goldbeter-Koshland function
Mutual inhibition
Rate (dR/dt)
S
0.9
2
0
20
Time
)
1
16
Mutual activation
R
enzyme
E
(by
phosphorylation),
and EP
8
3
0.5
0
0.4
enhances
the synthesis of R:
X
Rate (dR/dt)
k1
0
S 0.5
activates
R
S
0
5
Adapted
1.9
3
0
1
1
Response (R)
R
2
2
1.4
Response (R)
0
X
2
In the response
curve, the control system is found to be bistable
1.2
Scrit1 there are two stable steadybetween 0 and Scrit. In 0.5
this regime,
Scrit2
0.6
state response
values (on the upper and
lower branches, the solid
lines). The is called a one-parameter bifurcation. Which value is
0
taken
depends
on
the
history
of the
system.
After the signal
0
1
2
0.5
1
1.5
R
Signal
(S) the system will remain on
threshold
Scrit has been crossed
once,
the upper curve. This is termed a one-way switch. Apoptosis is an
1
1.5
Homeostatic
example for this
behavior, where
the decision to shut down the
1
cell must be clearly a one-way switch.
se (R)
S
e)
g)
Rate (dR/dt)
Res
3
11
0
10
0
0.4
0.3–1
20
8
0
0.5 independent of S.
Observe that Rss is
Response (R)
Rate (dR/dt)
0.9
R
0.5
Scrit
Figure 1e. Mutual activation
dR
0
R
¼ k00.5EP ðRÞ þ k1 S
0 # k2 X $ 10
dt R
Signal (S)
EP ðRÞ ¼ 1.8Gðk3 R; k4 ;1J3 ;Mutual
J4 Þ inhibition
Mutual Inhibition: Toggle Switch
Time
EP
0.2
0.1
E
0
0.5
0
0.1
R
0EP
0
E
Response (R)
The same as the previous case, with the only difference
that E now
stimulates
degradation
of R.
Scrit
1.2 Mutual
Figure
1f.
inhibition
S
Rate (dR/dt)
Response (R)
Mutual activation
0.05
10
0
Signal (S)
0
Scrit1
0.5
Scrit2
E
EP
0
0
0
1
Signal (S)
2
Signal (S)
Response (R)
0.5
1
Rate (dR/dt)
Response (R)
R
crit2
Figure
1g. Negative
feedback: homeostasis
1
This systems
1.5 leads to a discontinuous behavior. This type of
Homeostatic
1
bifurcation is called a toggle-switch. If S is decreased enough after
dR
¼ kfrom
#level,
k2 S the
$ Rswitch will go back to the off-state
0 EðRÞ
starting
a high
dt
0.5
on the lower curve
meaning
a small response R. For intermediate
0.5
EðRÞ
¼strength
Gðk3 ; (S
k4crit1
R;<S<S
J3 ;crit2
J4),Þthe response of the system can be
stimulus
Mutual inhibition
S
Scrit1
dR
S
0
0.6
¼ ko þ k1 S # k2 R # k2 EðRÞ $ R
dt
0
2
EðRÞ
;
k
R;
J
0.5 ¼ 1Gðk1.5
3 4
30 ; J4 Þ 1
R
1
)
0.5
0
either small or large, depending on the history of S(t). This is often
Figure
2a. Negative-feedback
0 examples of suchoscillator
called hysteresis.
Biological
behavior include the
0
1
2
0.5
1
lac operon
in bacteria.
Signal (S)
R
dX
þ k20 Opinion
RP $ inXCell Biology
¼ k0 þ k1 S # k2 X Current
dt
12
R
Scrit
Response (R
Rate (dR/dt)
Response (R)
0.5
1.2
0.05
0.6
Scrit1
0.5
Scrit2
Negative Feedback: Homeostasis
EP
E
0
0
0
0
0
0.5
1
0
1.5
R
10
1
2
Signal (S)
Signal (S)
The response
element,
R, inhibitsHomeostatic
the enzyme E
1
1
Mutual
k1 inhibition
catalyzing its synthesis.
R
k4 k3
0.5
E
k2
S
crit1
Scrit2
0.5
0.5
EP
0
0
0
Response (R)
S
1
Response (R)
1
1.5
Rate (dR/dt)
g)
1
2
Signal (S)
0.5
0
0
0.5
R
1
0
1
2
Signal (S)
Current Opinion in Cell Biology
1
Homeostatic
Response (R)
ogy 2003, 15:221–231
www.current-opin
This type of regulation is called homeostasis. It is sort of an
adaptation, but not a sniffer, because stepwise increases in S do
not generate transient changes in R.
0.5
0
0
1
2
Signal (S)
13
can exhibitisdamped
to a stable
steady
state that the
function
of S,
noting
synthetic pathways,
calledoscillations
nd
but not sustained oscillations [43]. Sustained oscillations
<
S
<
S
.
W
unstable
for
S
of imperfect require
adaptation,
but
it
crit1
crit2
at least three components: X!Y!R––|X. The
Negative Feedback: Oscillation
0
25
S
X
5
X
YP
R
0.5
RP
EP
0
0
E
25
Time
0.5
1
0
50
0.4
2
0.3
R0.2
0.11
0
4
6
Scrit2
Scrit1
Steady-state is unstable
between Scrit1 and Scrit2; it
1
oscillates between RPmin
and RPmax.
6
Signal (S)
0
4
Signal (S)
2
Scrit2
2
2
Time
Scrit1
0.0
0
0
50
Response (R)
Two possible ways
of inhibition
3
Response (RP)
)
Scrit2
Response (RP)
cts the effect
third component (Y) introduces a time delay in the feede element, R,
back loop, causing the control system repeatedly to overs; hence, the
shoot and undershoot its steady state.
sing function
0.5
S
is,
In Figure 2a (column 1), we
present
a
wiring
diagram
)r R — that
1
YP
Scrit1for a
X
Second5scenario:
k1
R. The steady
negative-feedback
control
loop. For intermediate
0.4 signal
k
X
rrow window 2strengths, the system executes sustained oscillations
0.3
k
the supply of3 k(column
2) in the variables X(t), YP(t)
7
0.5and RP(t). In the
(2)
0.2
Y
YP
ulation, comk4 k5signal-response curve (column 3), we plot RP;ss as a
0.1
RP the steady-state response
function of S, noting that
is
ys, is called
RP
R
(1)
RP(t)
for Scrit1
tation, but it k6 unstable
0 this range,
0.0
0 < S < Scrit2 . Within
1
0
0.0
0.1
0.2
0.3
0.4
14
0.5
Putting It All Together:
Cell Cycle Control System
15
Figure 3
(a)
M/G1 mod
ule
Damaged
DNA
Cdc25
Cdk1
P
P
APC
APC
CycB
G2/M
mo
du
le
Cdc25
Unreplicated
DNA
Cdc20
P
Wee1
Misaligned
chromosomes
Cdc20
C
AP
P
Wee1
P
Cdk1
CycB
CKI
CKI
Cdk1
Cdk1
CycB
1/
S
mo
du
le
P
P
Growth
CKI
CKI
G
CKI
CKI
CycB
P
Wiring diagram
for the cyclin-dependent kinase (Cdk) network
(b)
1.2
regulating DNA synthesis and mitosis.
ity
1.0
16
(a)
M/G1 mod
ule
Damaged
DNA
Cdc25
Cdk1
P
P
APC
APC
CycB
G2/M
mo
du
le
Cdc25
Unreplicated
DNA
Cdc20
P
Wee1
Misaligned
chromosomes
Cdc20
C
AP
P
Wee1
P
Cdk1
CycB
CKI
CKI
Cdk1
Cdk1
CycB
1/
S
mo
du
le
P
P
Growth
CKI
CKI
G
CKI
CKI
CycB
P
(b)
1.2
k1–CycB activity
1.0
0.4
toggle-switch
(mutual inhibition
between Cdk1cyclin B and CKI)
17
228
toggle-switch
(mutual activation between Cdk1-cyclin B and Cdc25, and
Cell regulation
mutual inhibition between Cdk1-cyclin B and Wee1)
Figure 3
(a)
M/G1 mod
ule
Damaged
DNA
Cdc25
P
P
APC
APC
Cdk1
CycB
Unreplicated
DNA
Cdc20
P
Wee1
Misaligned
chromosomes
Cdc20
C
AP
P
Wee1
P
Cdk1
CycB
Cdk1
CKI
CKI
Cdk1
CycB
G
1/
S
mo
du
le
P
P
Growth
CKI
CKI
CycB
CKI
CKI
G2/M
mo
du
le
Cdc25
P
18
oscillator, based on negative-feedback loop.
Cdk1-cyclin B activates the APC, which activates Cdc20,
which degrades cyclin B.
228 Cell regulation
Figure 3
(a)
M/G1 mod
ule
Damaged
DNA
Cdc25
Cdk1
P
P
APC
APC
CycB
Unreplicated
DNA
Cdc20
P
Wee1
Misaligned
chromosomes
Cdc20
C
AP
P
Wee1
P
Cdk1
CycB
Cdk1
CKI
CKI
Cdk1
CycB
G
1/
S
mo
du
le
P
P
Growth
CKI
CKI
CycB
CKI
CKI
G2/M
mo
du
le
Cdc25
P
19
Acknowledgment
✤
Material is based on the paper
✤
“Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and
signaling pathways in the cell”, Tyson et al., Current Opinion in Cell
Biology, 15: 221-231, 2003.
20