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Biological Rhythms :

Biological Rhythms :. From Clocks to Chaos. Henri Poincaré started it all. Norbert Wiener & Cybernetics. Late 1975. ****************************************************. Outline. Homeostasis -- in many forms Biological oscillators

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Biological Rhythms :

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  1. Biological Rhythms : From Clocks to Chaos

  2. Henri Poincaré started it all

  3. Norbert Wiener & Cybernetics

  4. Late 1975 ****************************************************

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

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

  7. Homeostasis

  8. Externally Induced Fluctuations

  9. Ion Channel Current Fluctuations

  10. “Spontaneous” Fluctuations

  11. Noise vs. Chaos

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

  13. Maintained by a periodic process

  14. Different Perturbations Different Effects

  15. Homeostatis in the Kidney

  16. Islets of Langerhorns: Constant Glucose Stimulus

  17. Mutual Inhibition in the LobsterCells 1 & 2 both active but they inhibit each other

  18. Same in the Mouse Spinal CordReciprocal Neural Oscillators

  19. Making the Pupil OscillateA negative feedback system

  20. Neural Inhibition

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

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

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

  24. Schematically

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

  26. Fictive swimming Arterial occlusion Still More Soft Excitation

  27. Visual HysteresisHard Excitation?

  28. Squid activity Hard Excitation(Subcritical Hopf Bifurcation)

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

  30. Single Pulse Perturbation--Heart

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

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

  33. 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

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