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R E Goldstein

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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R E Goldstein

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  1. III. Flagellar Synchronization and Eukaryotic Random Walks R E Goldstein www.damtp.cam.ac.uk/user/gold www.youtube.com/Goldsteinlab

  2. Metachronal Waves in Volvox (Side View)

  3. 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)

  4. Bacterial Swimming (E. coli) Turner, Ryu and Berg (Harvard)

  5. 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

  6. 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?

  7. The Experiment Polin, Tuval, Drescher, Gollub, Goldstein, Science (this Friday) (2009) Goldstein, Polin, Tuval, submitted (2009)

  8. 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)

  9. A Phase Slip Goldstein, Polin, Tuval, submitted (2009)

  10. slips synchrony drift Interflagellar phase difference Δ of a Chlamydomonas cell at 500 frames/sec Δ Polin, Tuval, Drescher, Gollub, Goldstein, in press (2009)

  11. 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?)

  12. 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

  13. Model Parameters Two “gears” estimate of hydrodynamic coupling expected value for intrinsic frequency difference

  14. 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

  15. 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)

  16. Tracking in Detail – A Sharp Turn

  17. Statistics of Sharp Turns: Origin of Diffusion Mean free-flight time is ~11 s Turns and drifts have identical statistics, much longer than slips.

  18. 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-

  19. Details of Slips

  20. Details of Slips

  21. A Phototurn (V. barberi) Drescher, Leptos, Goldstein, Rev. Sci. Instrum. (2009)

  22. Adaptive Flagellar Dynamics and the Fidelity of Multicellular Phototaxis Drescher, Goldstein, Tuval, preprint (2009)

  23. Flagellar Response and Eyespot Size eyespot diameter (microns) flagellar response probability angle from anterior (degrees)

  24. Dynamic PIV Measurements – Step Response

  25. Angular Dependence of the Transient Response anterior is sensitive posterior is not

  26. Velocity Ratio vs. Radius

  27. Systematics of Volvox Upswimming speed Spinning frequency Settling speed Reorientation time Drescher, Leptos, Tuval, Ishikawa, Pedley, Goldstein,PRL (2009)

  28. Frequency-Dependent Response Phototactic Colonies have Rotational Frequencies In this band Tuning!

  29. Metachronal Waves in Volvox (Side View)

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