Biological Rhythms :

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Nov 30, 2013 (3 years and 9 months ago)

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Biological Rhythms

:

From Clocks to Chaos

Henri Poincaré started it all

Norbert Wiener & Cybernetics

****************************************************

Late 1975

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

Electrical

Mechanical

Soft Excitation

(Supercritical Hopf Bifurcation)

Cardiac Cell Model


(McAllister, 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

Annihilation of action potentials

with residual signs of limit cycles

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)

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