Biological Rhythms:

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Biological Rhythms

• From Clocks to Chaos

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Henri Poincaré started it all
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Norbert Wiener Cybernetics
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Late 1975


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Outline

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

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Outline

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

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Homeostasis
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Externally Induced Fluctuations
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Ion Channel Current Fluctuations
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Spontaneous Fluctuations
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Noise vs. Chaos
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Outline

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

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Maintained by a periodic process
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Different Perturbations Different Effects
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Homeostatis in the Kidney
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Islets of Langerhorns Constant Glucose Stimulus
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Mutual Inhibition in the LobsterCells 1 2 both
active but they inhibit each other
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Same in the Mouse Spinal CordReciprocal Neural
Oscillators
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Making the Pupil OscillateA negative feedback
system
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Neural Inhibition
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Outline

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

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Gut Tapping in to an Oscillator
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Soft Excitation(Supercritical Hopf Bifurcation)
Cardiac Cell Model (McAllister, Noble, Tsien)
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Schematically
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More Soft Excitation
Lung volume Phrenic activity
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Still More Soft Excitation
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Female orgasm
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Visual HysteresisHard Excitation?
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Hard Excitation(Subcritical Hopf Bifurcation)
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Male orgasm
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Outline

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

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Single Pulse Perturbation--Heart
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Single Pulse Perturbation--Squid
Annihilation of action potentials
Annihilation of action potentials with residual
signs of limit cycles
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Periodic Perturbation/Forcing
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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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Next LecturePeriodic Dynamic Diseases
Bifurcations at the Bedside