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## PowerPoint Slideshow about ' Circadian Rhythms' - nyx

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Presentation Transcript

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?

- ‘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?

- 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

- 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

- 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

- 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)

- 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 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?

- 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

- Nonlinear systems are ubiquitous

Basic concepts

- ODE(ordinary differential equation)
Ex) pendulum

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 : a point where
- Give a small disturbance, then watch linear terms
- Stable, unstable, saddle

Stable limit cycle

Limit cycle “clock”- Isolated closed trajectory
- Only in nonlinear system(linear systems won’t be isolated)

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

- 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 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)

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

Synchronization of “the clocks”

- Clock Limit cycle or oscillator
- Interacting clocks coupled oscillators

Sync in nonlinear oscillators

- Winfree model
- Modified general model(Kuramoto)

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

- 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?

- 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

- 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)

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

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)

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)

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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