positive feedback and bistability
DESCRIPTION
Positive Feedback and Bistability. BIOE 423: 2013. Stable state. Transient state. Stable state. Simulation of biochemical network. Stable steady state. Multiple stable states. Different starting points lead to different steady states. Positive Feedback. v1 = ? v2 = ? dS/dt = ?. v2. - PowerPoint PPT PresentationTRANSCRIPT
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Positive Feedback and Bistability
BIOE 423: 2013
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Stable state
0 2 4 6 8 10
1.0
1.5
2.0
t
[s]
Simulation of biochemical network
Stable steady state
Transient state Stable state
0 10 20 30 40
0.5
1.0
1.5
2.0
2.5
3.0
t
[s]
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Multiple stable states
0 10 20 30 40 50
68
1012
t
[s]
0 10 20 30 40 50
68
1012
t
[s]
Different starting points lead to different steady states
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Positive Feedback
v1 = ?
v2 = ?
dS/dt = ?v1
v2
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Positive Feedback
p = defn cell $Xo -> S1; 0.5 + Vmax*S1^n/(15 + S1^n); S1 -> $X1; k1*S1;end;p.Xo = 1;p.X1 = 0;p.S1 = 1;p.n = 4;p.Vmax = 10;p.k1 = 2;
5
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Positive Feedback
Time
S1
High State
Low State
6
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Positive Feedback
S1
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
k1
v2
v1
v1 v2
Perturbations around a stable point
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Positive Feedback
S1
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
k1
v2
v1
v1 v2
Perturbations around a stable point
S1
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Positive Feedback
S1
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
k1
v2
v1
v1 v2
v2 > v1
Perturbations around a stable point
S1
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Positive Feedback
S1
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
k1
v2
v1
v1 v2
v2 > v1
Therefore: dS1/dt is negative
Perturbations around a stable point
S1
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Positive Feedback
S1
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
k1
v2
v1
v1 v2
Perturbations around a unstable point
S1
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Positive Feedback
S1
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
k1
v2
v1
v1 v2
v1 > v2
Perturbations around a unstable point
S1
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Positive Feedback
S1
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
k1
v2
v1
v1 v2
Therefore: dS1/dt is positive
Perturbations around a unstable point
v1 > v2 S1
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Positive Feedback
S1
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5 6
k1
v2
v1
v1 v2
Therefore: dS1/dt is positive
Perturbations around a unstable point
v1 > v2 S1
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Where in nature do we find multiple steady states?
http://weirdscience.ca/2007/ www.phri.org/research/res_pidubnau.asp
Eukaryotic cell differentiation Bacterial differentiation and adaptation
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Bistability of the lac operon
Where is the positive feedback?
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Genetic Toggle Switch
Where is the positive feedback?
dA/dt = ?
dB/dt = ?
Gardner, T. S. Cantor, C. R. Collins, J. J. Construction of a genetic toggle switch in Escherichia coli. Nature (2000) 6767, pages 339-342
Synthetic toggle switch has been built using lacI and tetR repressors.
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Flip-Flop (Latch)
A B
1 0 1 0
0 0 1 0
0 1 0 1
0 0 0 1
1 1 ? ?
Flip-flops can be made either from NAND or NOR gates.In synthetic biology it is probably easier to constructOR like gates than AND gates.
In addition an OR based flip-flop is quiescent when both inputs are low, meaning low protein levels. Latching occurswhen one or other of the inputs is brought to a high state. 18
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Flip-Flop0
0
1
0
0
NOR
NOR
A B NOR
1 1 0
0 1 0
1 0 0
0 0 1
1
0 0
Making NOR gates is ‘relatively’ easy and requires only two operator sitesdownstream of the RNA polymerase binding site (promoter).
19
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Flip-Flop0
0
1
0
0
NOR
NOR
A B NOR
1 1 0
0 1 0
1 0 0
0 0 1
1
0 0
20
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Flip-Flop0
0
1
0
0
NOR
NOR
A B NOR
1 1 0
0 1 0
1 0 0
0 0 1
1
0 0
1
0
1
0
0
NOR
NOR1
0 0
21
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Flip-Flop0
0
1
0
0
NOR
NOR
A B NOR
1 1 0
0 1 0
1 0 0
0 0 1
1
0 0
1
0
1
0
0
NOR
NOR1
1 0
22
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Flip-Flop0
0
1
0
0
NOR
NOR
A B NOR
1 1 0
0 1 0
1 0 0
0 0 1
1
0 0
1
0
0
0
0
NOR
NOR1
1 0
23
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Flip-Flop0
0
1
0
0
NOR
NOR
A B NOR
1 1 0
0 1 0
1 0 0
0 0 1
1
0 0
1
0
0
0
0
NOR
NOR0
1 0
24
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Flip-Flop0
0
1
0
0
NOR
NOR
A B NOR
1 1 0
0 1 0
1 0 0
0 0 1
1
0 0
1
1
0
0
0
NOR
NOR0
1 0
25
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Flip-Flop0
0
1
0
0
NOR
NOR
A B NOR
1 1 0
0 1 0
1 0 0
0 0 1
1
0 0
1
1
0
0
0
NOR
NOR0
1 1
26
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Flip-Flop0
0
1
0
0
NOR
NOR
A B NOR
1 1 0
0 1 0
1 0 0
0 0 1
1
0 0
1
1
0
0
0
NOR
NOR0
1 1
0
1
0
0
0
NOR
NOR0
0 1
27
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Flip-Flop0
0
1
0
0
NOR
NOR
A B NOR
1 1 0
0 1 0
1 0 0
0 0 1
1
0 0
0
0
1
1
1
NOR
NOR1
0 0
0
0
1
0
0
NOR
NOR1
0 0
Toggle A to reset P1Toggle B to set P1
28
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Network structures involving toggle switches
Developmental Switch
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Bifurcation Diagram
h
Steady state value of A
Stable Unstable
Stable
Stable
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Bistability with Hysteresis
One of the parameters in the model
Unstable state
Stable state
Stable state
Gianluca M. Guidi, and Albert Goldbeter. Bistability without Histeresis in Chemical Reaction Systems: A Theoretical Analysis of Irreversible Transitions between Multiple Steady States. Journal of Physical Chemistry (1997), 101 (49).
State Variable
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Bistability with Irreversibility
Gianluca M. Guidi, and Albert Goldbeter. Bistability without Histeresis in Chemical Reaction Systems: A Theoretical Analysis of Irreversible Transitions between Multiple Steady States. Journal of Physical Chemistry (1997), 101 (49).