Switches, Oscillators, and the Cell Cycle
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Switches, Oscillators, and���the Cell Cycle
What to notice so far
• There are two ways to design a regulatory cell network:
• (1) protein-protein interactions (mutual phosphorylation, etc etc) (time scale: sec- min)
• (2) gene networks (time scale: hrs day)
Gene circuits
Protein circuits
M Mp
Kinase
phosphatase
Protein circuits
Other things to notice
• By building up feedback interactions it is possible to obtain new dynamics :
• (1) Simple decay to steady state • (2) Switch (bistability) • (3) Oscillator (stable cycles)
No feedback
x
Decay to a single stable steady state
No feedback
x
A Decay to a single stable steady state
Positive feedback
x
A Bistability and switch-like behaviour possible
Add negative feedback
x
y Stable cycles possible
Example: Phosphorylation cycle
Active Inactive M Mp
Kinase
phosphatase
Decay to a single stable steady state
Add positive feedback to kinase
M Mp
Kinase
phosphatase
Bistability and switch-like behaviour possible
Add further negative feedback
M Mp
Kinase
phosphatase
Stable cycles possible
Simple mathematical example
x
A
A switch (Generic bistability)
The parameter A controls the switch
A controls the switch
“Switch” (Generic bistability)
The “parameter” y controls the switch
y
y
The curve dx/dt=0
y controls the switch
y
As y varies, we can go around the hysteresis loop
y
Add negative feedback to the switch
x
y
Now y is dynamic
] x
y
Switch becomes an oscillator
] Example: This is the Fitzhugh Nagumo model
“Switch” (Generic bistability)
y
Bifurcation diagram
“Switch” (Generic bistability)
y
Let us flip it over
“Switch” (Generic bistability)
y
y
The xy phase plane
The curve dx/dt=0
The curve dy/dt=0
Oscillator
a=0.7, b=0.8, c=3, j=0.35
Get an oscillator
Application to the Cell Cycle
• Work by John Tyson (Virginia Tech):
• The control of the cell division is maintained by an intricate web of signaling pathways, that incorporates many signals to decide when to divide.
• The cycle has “checkpoints” at which decisions are made.
S
G1
DNA replication
G2 M mitosis
cell division
1) Alternation of S phase and M phase.
2) Balanced growth and division.
Slide by John Tyson
S
G1
DNA replication
G2 M mitosis
cell division
The cell cycle is the sequence of events whereby a growing cell replicates all its components and divides them more-or-less evenly
between two daughter cells ...
Slide by John Tyson
Cdk1
S
G1
DNA replication
G2 M mitosis
cell division
CycB
P P
Cyclin-dependent kinase
Cyclin B
Slide by John Tyson
P
Cdc25
Wee1
Wee1 P
Cdc25
CycB
P
Cdc20
CK
I
CycB
CycB CK
I
CK
I
CycA
CycA
APC-P APC TFBI
TFBA
CycE
CycD
TFEA
TFEI
Cyc E,A,B
CycE
TFIA
TFII
CK
I
CycE
Cdc14
Cdc14
Cdc14
CycA
CycA
CycB
CycD
Cdh1 CycD
Checkpoints
in phase G1 there is low Cdk and low cyclin
buildup of cyclin/Cdk
APC is activated, leading to destruction of cyclin and loss of CdK activity.
Cdk1 CycB
Cyclin is produced and degraded
APC is inactivated by phosphorylation
APC pi
Cyclin
Active form (no phosphate)
Inactive form
APC is inactivated by phosphorylation
This will be modeled by a typical equation that we have already seen.
APC pi
Cyclin
Schematic
APC pi
Cyclin
Cyclin
Negative feedback
APC pi
Cyclin
APC and Cyclin mutually antagonistic
APC pi
Cyclin
Model
Model
Model
Bistable switch
Cell Mass
Cyclin
Cell mass is the parameter that���flips the switch
Cell Mass
Cyclin
P
Cdc25
Wee1
Wee1 P
Cdc25
CycB
P
Cdc20
CK
I
CycB CK
I
CK
I
CycA
CycA
APC-P APC TFBI
TFBA
CycE
CycD
TFEA
TFEI
Cyc E,A,B
CycE
TFIA
TFII
CK
I
CycE
Cdc14
Cdc14
Cdc14
CycA
CycA
CycB
CycD
Cdh1 CycD
CycB
Bistable switch
mass/DNA
0 1 2
Cdc2/Cdc13
10-3
10-2
10-1
100
S/G2
M
[cyclin]
[kin
ase]
Activation of APC by Cdc20 (“A”)
A= Cdc20. It increases sharply during metaphase and activates APC
A
cYclin
A is turned on by cyclin (sigmoidally)
A
cYclin
Activation of APC by Cdc20 (“A”)
A= Cdc20. It increases sharply during metaphase and activates APC
A
cYclin
Three variable model:
Now we get a cell cycle.
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