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Motility, Mixing, and Multicellularity

Motility, Mixing, and Multicellularity. Raymond E. Goldstein Department of Physics & Program in Applied Mathematics & BIO5 Institute University of Arizona. The Zooming Bio- Nematic, a non- equilibrium phase with turbulent dynamics. Large-scale coherent flows from chemotaxis,

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Motility, Mixing, and Multicellularity

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  1. Motility, Mixing, and Multicellularity Raymond E. Goldstein Department of Physics & Program in Applied Mathematics & BIO5 Institute University of Arizona The Zooming Bio- Nematic, a non- equilibrium phase with turbulent dynamics Large-scale coherent flows from chemotaxis, with diffusion dom- Inated by advection Physical driving forces underlying evolutionary transitions to multicellularity in Volvox

  2. Macnab and Ornstein, J. Mol. Biol. (1977) Bacterial Swimming and Chemotaxis Real-time Imaging of Fluorescent Flagella 1-4mm 10-20mm Turner, Ryu, and Berg, J. Bacteriol. (2000) 20 nm “normal = LH helix “curly” = RH helix “straight” = straight Swimming speed ~10mm/s Propulsive force ~1 pN

  3. Advection, Dissipation & Diffusion: Reynolds and Peclet Numbers Navier-Stokes equations: Passive scalar dynamics: Reynolds number: Peclet number: If U=10 mm/s, L=10 mm, Re ~ 10-4, Pe ~ 10-1 At the scale of an individual bacterium, dissipation dominates inertia, and advection dominates diffusion. The second relation breaks down with multicellularity…

  4. Part I. Bacterial Self-Concentration 1 cm Dombrowski, Cisneros, Chatkaew, Goldstein & Kessler, “Self-concentration and large-scale coherence in bacterial dynamics,” PRL 93, 098103 (2004) Tuval, Cisneros, Dombrowski, Wolgemuth, Kessler & Goldstein, “Bacterial swimming and oxygen transport near contact lines,” PNAS102, 2277 (2005)

  5. Mechanism of Self-Concentration Dombrowski, et al. (2004)

  6. The Boycott Effect (in Sedimentation) g A.E. Boycott, Nature102, 532 (1920). A.A. Acrivos and E. Herbolzheimer, J. Fluid Mech.92, 435 (1979).

  7. Side Views: Depletion and Flow 2 mm Video ~100x actual speed Dombrowski, et al. (2004)

  8. Diffusion and Chemotaxis Oxygen diffusion/advection Chemotaxis Navier-Stokes/Boussinesq depletion layer: D/v n(z) C(z) z z

  9. Experiment vs. Theory Tuval, et al. PNAS (2005)

  10. Moffat Vortex 1 mm Experiment (PIV) Numerics (FEM) Tuval, et al. (2005)

  11. Chemotactic Singularities & Mixing Stirring re-oxygenates the entire drop Tuval, et al. (2005)

  12. Part II. The Zooming Bio-Nematic Phase contact line Petri dish 300mm Dombrowski, Cisneros, Chatkaew, Goldstein & Kessler, “Self-concentration and large-scale coherence in bacterial dynamics,” PRL 93, 098103 (2004)

  13. Peclet number ~10-100 (vs. 0.01-0.1 for individual bacterium) Velocity Field from PIV (pendant drop) 35mm Dombrowski, et al. (2003). See also Wu and Libchaber (2000)

  14. Velocity Correlation Functions in Space & Time space oscillations due to multiple vortices (individual images) sequence average time oscillations due to recurring vortices (individual images) spatial average

  15. Advection of Microspheres contact line

  16. Flocking models (Toner and Tu, 1995, …; traffic flow…) Historical Ideas A Landau theory in the velocity field – clever but not at all faithful to the physics of Stokes flow • Sedimentation (interacting Stokeslets) as few as three particles exhibit chaotic trajectories (Janosi, et al., 1997) • Conventional chemotaxis picture (e.g. Keller-Segel) - MISSES ADVECTION Velocity field must be determined self-consistently with density field • A synthesis is emerging from coarse-grained models of sedimentation • (Bruinsma, et al.) and of self-propelled objects (Ramaswamy, et al.)… IMPLICATIONS FOR QUORUM SENSING…

  17. Part III. Driving Forces for Multicellularity (consider the Volvocalean green algae) Chlamydomonas V. carteri Discovered by van Leeuwenhoek (1700), name means “fierce roller”

  18. The Diffusional Bottleneck Smoluchowski result – diffusion to an absorbing sphere Number of peripheral cells, and hence their requirements, scale as R2 Fluxes Organism radius R

  19. Volvox On A Stick S. Ganguly Solari, Ganguly, Kessler, Michod & Goldstein, “Multicellularity and the Functional Interdependence Of Motility and Molecular Transport,” preprint (2005).

  20. Stirring by Volvox carteri

  21. A Closer View

  22. Even Closer (Flagellar Motions Visible)

  23. Locally Chaotic Advection

  24. High-Speed Movie (125 fps) of Volvox Flagella

  25. Flow Field Viewed On Axis

  26. Fluid Velocities During Life Cycle • Hatch • Division • Daughter • Pre-Hatch Solari, et al. (2005)

  27. Peclet Number During Life Cycle (Large!) Solari, et al. (2005)

  28. Flagellar-Driven Flows and Scaling Laws Specified shear stress t at surface Detailed calculation: (Gegenbauer polynomials, etc.) yields: This implies that the Peclet number scales as: Finally, large Pe scaling (Flux~RPe1/3) yields: This almost eliminates the bottleneck!

  29. Velocity Profile Solari, et al. (2005a)

  30. Issues Transport, mixing, and chemical signaling at high concentrations – quorum sensing, etc. (biology, nonequilibrium statistical mechanics, …) Mixing, metabolism, and evolutionary transitions to multicellularity – germ-soma differentiation, vascularization, morphological transformations

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