circadian rhythms
Download
Skip this Video
Download Presentation
Circadian Rhythms

Loading in 2 Seconds...

play fullscreen
1 / 37

Circadian Rhythms - PowerPoint PPT Presentation


  • 209 Views
  • Uploaded on

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?.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Circadian Rhythms' - nyx


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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
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

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

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)
ad