2. Biological Rhythms: From Clocks to Chaos

3. Henri Poincaré started it all

4. Norbert Wiener & Cybernetics

5. **************************************************** Late 1975

6. Outline Homeostasis -- in many forms Biological oscillators Starting and stopping oscillators (Bifurcations in physiological dynamics) Forcing oscillators: Single vs. Periodic Conclusions

7. Outline Homeostasis in all of its forms Biological oscillators Starting and stopping oscillators (Bifurcations in physiological dynamics) Forcing oscillators: Single vs. Periodic

8. Homeostasis

9. Externally Induced Fluctuations

10. Ion Channel Current Fluctuations

11. “Spontaneous” Fluctuations

12. Noise vs. Chaos

13. Outline Homeostasis in all of its forms Biological oscillators Starting and stopping oscillators (Bifurcations in physiological dynamics) Forcing oscillators: Single vs. Periodic

14. Maintained by a periodic process

15. Different Perturbations Different Effects

16. Homeostatis in the Kidney

17. Islets of Langerhorns: Constant Glucose Stimulus

18. Mutual Inhibition in the Lobster Cells 1 & 2 both active but they inhibit each other

19. Same in the Mouse Spinal Cord Reciprocal Neural Oscillators

20. Making the Pupil Oscillate A negative feedback system

21. Neural Inhibition

22. Outline Homeostasis in all of its forms Biological oscillators Starting and stopping oscillators (Bifurcations in physiological dynamics) Forcing oscillators: Single vs. Periodic

23. Gut: Tapping in to an Oscillator Electrical Mechanical Electrical Mechanical

24. Soft Excitation (Supercritical Hopf Bifurcation) Cardiac Cell Model (McAllister, Noble, Tsien)

25. Schematically

26. More Soft Excitation Lung volume Phrenic activity Uterine pressure waves in dysmenorrhea

27. Still More Soft Excitation Arterial occlusion Fictive swimming

28. Female orgasm

29. Visual Hysteresis Hard Excitation?

30. Hard Excitation (Subcritical Hopf Bifurcation) Squid activity

31. Male orgasm

32. Outline Homeostasis in all of its forms Biological oscillators Starting and stopping oscillators (Bifurcations in physiological dynamics) Forcing oscillators: Single vs. Periodic

33. Single Pulse Perturbation--Heart

34. Single Pulse Perturbation--Squid Annihilation of action potentials with residual signs of limit cycles

35. Periodic Perturbation/Forcing Control 2:1 3:2 1:1 2:2 2:3 “Chaos” 3:1 2:1 3:2 (walking) 3:2 (running)

36. Conclusions Homeostasis can be like a (mathematical) steady state Varieties of homeostasis: steady, oscillating, ??chaotic?? Types of bifurcations: Soft and Hard Direct analogies between behaviour and mathematical properties Understanding normal biological properties ↔ understand disease Every example has been studied mathematically