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Circadian Rhythms. 안용열 (물리학과). Index. Intro - What is the circadian rhythm? Mechanism in reality How can we understand it?  Nonlinear dynamics Limit cycle Linearization and stability Stochastic resonance Coupled nonlinear oscillators Summary - What have we learned?.

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Circadian rhythms

Circadian Rhythms

안용열

(물리학과)


Index
Index

  • Intro - What is the circadian rhythm?

  • Mechanism in reality

  • How can we understand it?

     Nonlinear dynamics

    • Limit cycle

    • Linearization and stability

    • Stochastic resonance

    • Coupled nonlinear oscillators

  • Summary - What have we learned?


Circadian rhythm
Circadian’ rhythm?

  • ‘circa’ means ‘round about’

  • ‘dies’ means ‘a day’

     ‘About-a-day-period behavioral rhythm’

  • Sleep-wake cycle, Insect eclosion, …

  • Circadian rhythm vs. cell cycle?(ref)


Is 24 hours a long time
Is 24 hours a long time?

  • If we think that a day is long time…

     A trap!-Two short period oscillator model

     long period is extremely sensitive to changes in the short period.

  • ‘because long periods are inconvenient in the laboratory’ (Winfree)

     aging, female endocrine cycle, replacement of membrane phospholipids


What we know about circadian rhythms i
What we know about circadian rhythms I

  • Scale

    • In temporal scale  About 24 hours(ref)

    • In spatial scale  From a single cell to complex multicelluar organisms in synchrony

    • In the kingdom of life  from bacteria to mammals (synechococcus, neurospora, drosophila, mouse, human,…)


What we know about circadian rhythms ii
What we know about circadian rhythms II

  • Reliability

    • Period conservation under temperature variation (temperature compensation)

    • Immunity to many kinds of chemical perturbation

    • Sensitivity to visible light of an appropriate color

    • Slow entrainment to outside environment


Dunlap s viewpoint about circadian clock research
Dunlap’s viewpoint about circadian clock research

  • Mechanism - how does the clock work?

  • Input – how does outer world entrain the clock?

  • Output – how does the clock control the entire organism?


Viewpoint of this presentation mech specific
Viewpoint of this presentation(mech-specific)

  • First, How can we make a 24-hours clock in a single cell?

  • We get a clock, then how do cells in a tissue synchronize with each other?

  • We get tissues in synchrony, then how do tissues synchronize all over the body?


Discovered mechanism in a cell
Discovered Mechanism ina cell

  • Positive element vs. negative element

    • Positive element enhance both

    • Negative element inhibit positive element

    • Negative element has ‘slower’ dynamics

  • This mechanism is fundamental in the neuron interaction model(ref)

    • Simplest example which has a limit cycle


Mechanism in a diagram

Positive element

Negative element

Mechanism in a diagram


How can we understand it
How can we understand it?

  • Nonlinear dynamics!

  • Why nonlinear?

    • Nonlinear systems are ubiquitous

      • Zoology Metaphor

    • Linear systems can be broken down into parts (superposition principle. 2+2=4) nonlinear  emergence, holism, stability…

    • Noise tolerance


Basic concepts
Basic concepts

  • ODE(ordinary differential equation)

    Ex) pendulum


Basic concepts1

Trajectory

Basic concepts

  • Phase space


Geometric paradigm of dynamics
Geometric paradigm of dynamics

  • Classical method

    • Find analytical solution

    • Approximations (linearization)

  • With trajectory in phase space,

     Find “Geometry” of phase space



Fixed point and stability analysis
Fixed point and stability analysis

  • Fixed point : a point where

  • Give a small disturbance, then watch linear terms

    • Stable, unstable, saddle


Limit cycle clock

Linear system

Stable limit cycle

Limit cycle  “clock”

  • Isolated closed trajectory

  • Only in nonlinear system(linear systems won’t be isolated)


Slaving principle pseudo steady state
Slaving principle(pseudo-steady state)

  • For “fast” variable and “slow” variable

  • Fast variable is a “slave” of slow variable

     reduction of number of variables


Poincare bendixson theorem
Poincare-Bendixson theorem

  • If an annulus region in 2d

    • Has no stable fixed point

    • Has only trajectories which are confined in it

       There exist limit cycles


Noise induced dynamics stochastic resonance
noise-induced dynamics(Stochastic resonance)

  • Noise  what is to be removed

  • Noise  what is important in dynamics

  • Noise “enhance” signal (stochastic resonance, coherent resonance)

    • Climate change (Phys.Rev.Lett., 88,038501)

    • Sensory system(PRL, 88,218101)

  • Noise can do “work”

    • Molecular ratchet, Parrondo’s paradox(ref)



The clock

0.2

C

1

1

2

0.5

+

10

5

50

A

A

A

A

A

R

50

50

0.01

500

1

1

Gene R

Gene A

50

100

“The clock”


The clock s state

R

mRNAs

Expressed

genes

A

C

R

A

The clock’s state

C

R


Analysis of the clock
Analysis of “the clock”

  • “The Clock” has so many variable.

     pick up two slowest variable : R, C

  • Can the reduced system exhibit ‘clock’– limit cycle – behavior?

     stability analysis of fixed point and application of poincare-bendixon theorem


Analysis of the clock1
Analysis of “the clock”

Null cline

Fixed point


Stochastic resonance in the clock

No noise

With noise

Stochastic resonance in “the clock”


Synchronization of the clocks
Synchronization of “the clocks”

  • Clock  Limit cycle or oscillator

  • Interacting clocks  coupled oscillators



Sync in nonlinear oscillators
Sync in nonlinear oscillators

  • Winfree model

  • Modified general model(Kuramoto)


Scn the master clock
SCN – The master clock

  • In the hypothalamus of the brain

  • Recept light signal from retina

  • About 20000 neuron

  • Negative elements : Period(Per), Cryptochrome(Cry)

  • Positive elements: Clock, Bmal1


Synchronization in scn
Synchronization in SCN

  • SCN  coupled oscillators

  • If f(-x) = -f(x), and if K s are all symmetric,

  • Then collective frequency is mean of all.

  • Cell, 91,855 : hamster SCN’s period determination



What have we learned
What have we learned?

  • Study PHYSICS!

    • Abundant Nonlinearity in biology

    • Nonlinear dynamics is important for dynamical systems (ex. circadian clock)

    • Noise effects are important in life

    • Organisms actively use noise. (muscle, circadian clock)


References
References

  • About nonlinear science and mathematical tools

    • A.T.Winfree, “The Geometry of Biological Time” (1990)

      2nd edition published in 2001

    • S.H.Strogatz, “Nonlinear dynamics and chaos” (1994)

    • J.D.Murray, “Mathematical Biology” (1993)

    • H.R.Wilson, “Spikes, decisions, and actions” (1999)

  • About coupled oscillators

    • A.T.Winfree, “The geometry of biological time” (1990)

    • S.H.Strogatz, “Sync” published in 2003

    • S.H.Strogatz et al., “Coupled oscillators and biological synchronization”, Scientific american vol 269, No. 6 (1993)

    • S.H.Strogatz, From Kuramoto to Crawford, Physica D, 143, 1 (2000)

    • C.L et al. and S.H.Strogatz, Cell, 91,855 (1997)


References1
References

  • About single cell level circadian rhythm

    • J.C.Dunlap, “Molecular bases for Circadian Clocks”, Cell, vol 96, 271 (1999) (Review)

    • N.Barkai and S.Leibler, Nature, 403, 268 (1999)

    • J.M.G.Vilar et al., PNAS, 99, 5988 (2002)

    • N.R.J.Glossop et al., Science, 286, 766 (1999) (mechanism of drosophila clock genes)

    • S.Panda et al., “Circadian rhythm from flies to human”, Nature, 417,329 (2002)

  • Why circadian, circannual rhythms are not precisely one day or one year?

    • H.Daido, Phys. Rev. Lett. 87, 048101 (2001)

  • The circadian oscillator can be synchronized by light without input from eyes

    • U.Schibler, Nature, 404, 25 (2000)


References2
References

  • About synchronization between tissues or organisms

    • U.Schibler, et al., “A web of circadian pacemaker”, Cell, 111,919 (2002)

    • S.M.Reppert et al., “Coordination of circadian timing in mammals”, Nature, 418,935 (2002)

    • M.H.Hastings, nature, 417,391 (2002)

    • K.Stokkan et al., Science, 291,490 (2001)

    • J.D.Levine et al., Science, 298,2010 (2002)

  • Cancer connection

    • M.Rosbash et al., Nature, 420,373 (2002)


References3
References

  • Stochastic resonance

    • L.Gammaitoni et al., Rev. Mod. Phys. 70, 223 (1998)

  • Molecular ratchet & Parrondo’s paradox

    • R.D.Astumian et al., Phys.Rev.Lett.,72,1766 (1994)

    • G.P.Harmer et al., Nature, 402,864(1999)

    • J.M.R.Parrondo et al., Phys.Rev.Lett., 85, 5226 (2000)

    • R.Toral et al., cond-mat/0302324 (2003)


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