1. Propulsion and Evolution of Algae R E Goldstein DAMTP Cambridge

2. The Size-Complexity Relation Amoebas, Ciliates, Brown Seaweeds Green Algae and Plants Red Seaweeds Fungi Animals Bell & Mooers (1997) Bonner (2004) ?

3. Volvox Phil. Trans. Roy. Soc. 22, 509-518 (1700) (1758)

4. A Family Portrait Chlamydomonas reinhardtii Volvox carteri Gonium pectorale Eudorina elegans Pleodorina californica Volvox aureus daughter colonies somatic cells Germ-soma differentiation Altruism, apoptosis

5. The Diffusional Bottleneck Organism radius R Currents Diffusion to an absorbing sphere PO 4 2- and O 2 estimates yield bottleneck radius ~50-200  m (~Pleodorina, start of germ-soma differentiation) Metabolic requirements scale with surface somatic cells

6. Advection & Diffusion If U=10  m/s, L=10  m, Pe ~ 10 -1 At the scale of an individual cell, diffusion dominates advection. The opposite holds for multicellularity… If a fluid has a typical velocity U, varying on a length scale L, with a molecular species of diffusion constant D. Then there are two times: We define the Péclet number as the ratio:

7. Microscopy & Micromanipulation motorized microscope stage micro- manipulator micro- manipulator

8. Stirring by Volvox carteri Pseudo-darkfield (4x objective, Ph4 ring) Tools of the trade – micropipette preparation 1 mm

9. A Closer View Fluorescence

10. Fluid Velocities During Life Cycle Hatch Division Daughter Pre-Hatch This is “Life at High Péclet Numbers”

11. Metabolite Exchange

12. Flagella Beating/Symmetry (2000 frames/s background subtraction)

13. 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 Micropipette Cell body Frame-subtraction

14. “Phase oscillator” model used in e.g. circadian rhythms, etc. strokes of flagella amplitudes “phases” or angles natural frequencies 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” Without coupling, the phase difference simply grows in time So, is this seen? Key issue: control of phototaxis

15. A Phase Slip

16. Dynamics of Phase Slips (Both Directions!)

17. Drifts and Slips are Controlled by the Cell frequency (arb) Power spectrum

18. “Random” Swimming of Chlamydomonas reinhardtii Red light illumination – no phototactic cues 45 s. track – note many changes of direction Volume explored is ~1 mm 3 very far from chamber walls

19. Geometry of Turning Turning angle (degrees) ~100 o 90 Probability (angle) Chlamy w/single flagellum, rotating near a surface Angle per beat - Frequency difference - “Drift” duration- Angular velocity Angular change

20. Walzing Volvox: Orbiting “Bound State”

21. Dual Views Dominant physics: downward gravitational force on the colony, producing recirculating flows. Fluid flow produced by a point force near a wall: solved exactly by J.R. Blake (1971)

22. The Minuet Bound State Numerical solution of a model: Based on hovering, negatively buoyant, bottom-heavy swimmers. Bottom-heaviness confers stability. Side view Chamber bottom

23. Marco Polin Idan Tuval Kyriacos Leptos Knut Drescher Sujoy Ganguly Cristian Solari Timothy J. Pedley Takuji Ishikawa Jerry P. Gollub www.damtp.cam.ac.uk/user/gold Our Team