III. Flagellar Synchronization
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III. Flagellar Synchronization and Eukaryotic Random Walks. R E Goldstein. www.damtp.cam.ac.uk/user/gold www.youtube.com/Goldsteinlab. Metachronal Waves in Volvox (Side View). Huygens’ Clock Synchronization (1665). Pendulum clocks hung on a common wall synchronize out of phase!.

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III. Flagellar Synchronization

and Eukaryotic Random Walks

R E Goldstein

www.damtp.cam.ac.uk/user/gold

www.youtube.com/Goldsteinlab


Metachronal waves in volvox side view
Metachronal Waves in Volvox (Side View)


Huygens clock synchronization 1665
Huygens’ Clock Synchronization (1665)

Pendulum clocks hung on a common

wall synchronize out of phase!

Modern version of experiment confirms

that vibrations in the wall cause the

synchronization.

Schatz, et al. (Georgia Tech)


Bacterial swimming e coli
Bacterial Swimming (E. coli)

Turner, Ryu and Berg (Harvard)


trans

%

cis

85 %

complete

synchrony

10 %

5 %

Rüffer and Nultsch,Cell Motility and the Cytoskeleton7, 87 (1987)

Early Study of Flagella Synchronisation in Chlamydomonas

For different cells:

sporadic asynchronies

different frequencies


Historical background
Historical Background

  • R. Kamiya and E. Hasegawa [Exp. Cell. Res. (‘87)]

  • (cell models – demembranated)

  • intrinsically different frequencies of two flagella

  • U. Rüffer and W. Nultsch [Cell Motil. (‘87,’90,’91,’98)]

  • short observations (50-100 beats at a time, 1-2 sec.)

  • truly heroic – hand drawing from videos

  • synchronization, small phase shift, occasional “slips”

Key issue:

control of

phototaxis

“Phase oscillator” model used in e.g. circadian rhythms, etc.

strokes of

flagella

natural

frequencies

amplitudes

“phases”

or angles

Without coupling, the phase difference simply grows in time

So, is this seen?


The experiment
The Experiment

Polin, Tuval, Drescher, Gollub, Goldstein, Science (this Friday) (2009)

Goldstein, Polin, Tuval, submitted (2009)


Noisy synchronization
Noisy Synchronization

  • Experimental methods:

  • Micropipette manipulation

  • with a rotating stage

  • for precise alignment

  • Up to 2000 frames/sec

  • Long time series

  • (50,000 beats or more)

  • Can impose external

  • fluid flow

Frame-subtraction

Cell body

Micropipette

Polin, Tuval, Drescher, Gollub, Goldstein, in press (2009)


A Phase Slip

Goldstein, Polin, Tuval, submitted (2009)


slips

synchrony

drift

Interflagellar phase difference Δ of a

Chlamydomonas cell at 500 frames/sec

Δ

Polin, Tuval, Drescher, Gollub, Goldstein, in press (2009)


Model for Phase Evolution

Spheres forced in circular

orbits by an azimuthal force,

with elasticity to maintain

orbit radius, and sphere-sphere

hydrodynamic interactions

(deterministic)

Niedermayer, Eckhardt, and Lenz, Chaos (2008)

We see clear evidence of stochasticity …

which suggests the stochastic Adler equation:

biochemical noise

Quasi-universal

form for phase oscillators

(Kuramoto)

Intrinsic

frequency

mismatch

coupling

Strength

(hydrodynamics?)


Slips

diffusion

Δ(t2)

Δ(t1)

Model for Phase Evolution

Synchrony

Relative probability of +/- slips

Yields the frequency difference dn

Veff(Δ)

Amplitude and autocorrelation function of fluctuations in the synchronised state yields Teff and B

Δ


Model parameters
Model Parameters

Two “gears”

estimate of

hydrodynamic

coupling

expected value for intrinsic frequency difference


Direct Demonstration of Chlamydomonas Diffusion

Polin, Tuval, Drescher, Gollub, Goldstein, in press (2009)

Dexp ~ (0.68±0.11)x10-3 cm2/s

and u~100 µm/s, there must be a time t~10 s

Since


Dual-View Apparatus Free of Thermal Convection

White LED

& shutter

White LED

& shutter

Capable of imaging protists from 10 μm

to 1 mm, with tracking precision of

~1 micron, @ 20 fps.

Drescher, Leptos, Goldstein,

Review of Scientific Instruments 80, 014301 (2009)



Statistics of sharp turns origin of diffusion
Statistics of Sharp Turns: Origin of Diffusion

Mean free-flight time

is ~11 s

Turns and drifts have identical statistics,

much longer than slips.


Geometry of turning

Angular velocity

Angular change

Geometry of Turning

Chlamy w/single flagellum,

rotating near a surface

Probability (angle)

Turning angle (degrees)

90

Angle per beat -

Frequency difference -

Dest~ (0.47±0.05)x10-3 cm2/s

“Drift” duration-




A phototurn v barberi
A Phototurn (V. barberi)

Drescher, Leptos, Goldstein, Rev. Sci. Instrum. (2009)


Adaptive flagellar dynamics and the fidelity of multicellular phototaxis
Adaptive Flagellar Dynamics and the Fidelity of Multicellular Phototaxis

Drescher, Goldstein, Tuval, preprint (2009)


Flagellar response and eyespot size
Flagellar Response and Eyespot Size Multicellular Phototaxis

eyespot diameter (microns)

flagellar response probability

angle from anterior (degrees)



Angular dependence of the transient response
Angular Dependence of the Transient Response Multicellular Phototaxis

anterior is sensitive

posterior is not


Velocity ratio vs radius
Velocity Ratio vs. Radius Multicellular Phototaxis


Systematics of volvox
Systematics of Multicellular PhototaxisVolvox

Upswimming

speed

Spinning

frequency

Settling speed

Reorientation time

Drescher, Leptos, Tuval, Ishikawa, Pedley, Goldstein,PRL (2009)


Frequency dependent response
Frequency-Dependent Response Multicellular Phototaxis

Phototactic

Colonies have

Rotational

Frequencies

In this band

Tuning!


Metachronal waves in volvox side view1
Metachronal Waves in Multicellular PhototaxisVolvox (Side View)


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