Biological Rhythms From Clocks to Chaos Henri Poincar

Biological Rhythms : From Clocks to Chaos

Henri Poincaré started it all

Norbert Wiener & Cybernetics

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

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

Homeostasis

Externally Induced Fluctuations

Ion Channel Current Fluctuations

“Spontaneous” Fluctuations

Noise vs. Chaos

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

Maintained by a periodic process

Different Perturbations Different Effects

Homeostatis in the Kidney

Islets of Langerhorns: Constant Glucose Stimulus

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

Same in the Mouse Spinal Cord Reciprocal Neural Oscillators

Making the Pupil Oscillate A negative feedback system

Neural Inhibition

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

Gut: Tapping in to an Oscillator Electrical Mechanical

Soft Excitation (Supercritical Hopf Bifurcation) Cardiac Cell Model (Mc. Allister, Noble, Tsien)

Schematically

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

Still More Soft Excitation Arterial occlusion Fictive swimming

Visual Hysteresis Hard Excitation?

Hard Excitation (Subcritical Hopf Bifurcation) Squid activity

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

Single Pulse Perturbation--Heart

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

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

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