Positive Feedback and Bistability

# Positive Feedback and Bistability

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## Positive Feedback and Bistability

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1. Positive Feedback and Bistability BIOE 423: 2013

2. Stable state Transient state Stable state Simulation of biochemical network Stable steady state

3. Multiple stable states Different starting points lead to different steady states

4. Positive Feedback v1 = ? v2 = ? dS/dt = ? v2 v1

5. 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

6. Positive Feedback High State S1 Low State Time 6

7. Positive Feedback v1 v2 Perturbations around a stable point v2 S1 v1 k1

8. Positive Feedback v1 v2 Perturbations around a stable point v2 S1  S1 v1 k1

9. Positive Feedback v1 v2 Perturbations around a stable point v2 S1 v2 > v1  S1 v1 k1

10. Positive Feedback v1 v2 Perturbations around a stable point v2 S1 v2 > v1  S1 v1 Therefore: dS1/dt is negative k1

11. Positive Feedback v1 v2 Perturbations around a unstable point v2 S1 v1  S1 k1

12. Positive Feedback v1 v2 Perturbations around a unstable point v2 S1 v1  S1 v1 > v2 k1

13. Positive Feedback v1 v2 Perturbations around a unstable point v2 S1 v1 Therefore: dS1/dt is positive  S1 v1 > v2 k1

14. Positive Feedback v1 v2 Perturbations around a unstable point v2 S1 v1 Therefore: dS1/dt is positive  S1 v1 > v2 k1

15. Where in nature do we find multiple steady states? Eukaryotic cell differentiation Bacterial differentiation and adaptation www.phri.org/research/res_pidubnau.asp http://weirdscience.ca/2007/

16. Bistability of the lac operon Where is the positive feedback?

17. Genetic Toggle Switch dA/dt = ? dB/dt = ? Where is the positive feedback? Synthetic toggle switch has been built using lacI and tetR repressors. Gardner, T. S. Cantor, C. R. Collins, J. J.Construction of a genetic toggle switch in Escherichia coli. Nature (2000) 6767, pages 339-342

18. Flip-Flop (Latch) Flip-flops can be made either from NAND or NOR gates. In synthetic biology it is probably easier to construct OR like gates than AND gates. In addition an OR based flip-flop is quiescent when both inputs are low, meaning low protein levels. Latching occurs when one or other of the inputs is brought to a high state.

19. Flip-Flop 0 0 NOR 1 0 0 0 NOR 0 1 Making NOR gates is ‘relatively’ easy and requires only two operator sites downstream of the RNA polymerase binding site (promoter).

20. Flip-Flop 0 0 NOR 1 0 0 0 NOR 0 1

21. Flip-Flop 0 0 NOR 1 0 0 0 NOR 0 1 0 0 NOR 1 1 0 0 NOR 0 1

22. Flip-Flop 0 0 NOR 1 0 0 0 NOR 0 1 1 0 NOR 1 1 0 0 NOR 0 1

23. Flip-Flop 0 0 NOR 1 0 0 0 NOR 0 1 1 0 NOR 0 1 0 0 NOR 0 1

24. Flip-Flop 0 0 NOR 1 0 0 0 NOR 0 1 1 0 NOR 0 1 0 0 NOR 0 0

25. Flip-Flop 0 0 NOR 1 0 0 0 NOR 0 1 1 0 NOR 0 1 0 1 NOR 0 0

26. Flip-Flop 0 0 NOR 1 0 0 0 NOR 0 1 1 1 NOR 0 1 0 1 NOR 0 0

27. Flip-Flop 0 0 NOR 1 0 0 0 NOR 0 1 0 1 1 1 NOR NOR 0 0 0 1 0 0 1 1 NOR NOR 0 0 0 0

28. Flip-Flop 0 0 NOR 1 0 0 Toggle A to reset P1 Toggle B to set P1 0 NOR 0 1 0 0 0 0 NOR NOR 1 1 0 0 0 1 0 0 NOR NOR 0 1 1 1

29. Network structures involving toggle switches Developmental Switch

30. Bifurcation Diagram Stable Steady state value of A Stable Unstable Stable h

31. Bistability with Hysteresis Stable state State Variable Unstable state Stable state One of the parameters in the model 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).

32. 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).