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Transcript
Propulsion and Evolution of Algae R E Goldstein DAMTP Cambridge The Size-Complexity Relation Amoebas, Ciliates, Brown Seaweeds Green Algae and Plants Red Seaweeds Fungi Animals ? Bell & Mooers (1997) Bonner (2004) Volvox Phil. Trans. Roy. Soc. 22, 509-518 (1700) (1758) A Family Portrait Chlamydomonas reinhardtii Gonium pectorale Pleodorina californica Volvox carteri Germ-soma differentiation Eudorina elegans Volvox aureus daughter colonies Altruism, apoptosis somatic cells Currents The Diffusional Bottleneck Metabolic requirements scale with surface somatic cells Diffusion to an absorbing sphere R C C 1 r I d 4DC R I m 4R 2 PO42- and O2 estimates yield bottleneck radius ~50-200 mm (~Pleodorina, start of germ-soma differentiation) Rb DC Organism radius R Advection & Diffusion 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: Pe tdiffusion tadvection L t advection U L2 t diffusion D UL D If U=10 mm/s, L=10 mm, Pe ~ 10-1 At the scale of an individual cell, diffusion dominates advection. The opposite holds for multicellularity… Microscopy & Micromanipulation micromanipulator micromanipulator 1 mm Tools of the trade – micropipette preparation Pseudo-darkfield (4x objective, Ph4 ring) Stirring by Volvox carteri Fluorescence A Closer View Fluid Velocities During Life Cycle Pe Hatch Division 2 Ru max D Daughter Pre-Hatch This is “Life at High Péclet Numbers” Metabolite Exchange Flagella Beating/Symmetry (2000 frames/s background subtraction) 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 Cell body Micropipette Frame-subtraction 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 S1 (t ) A1 cos[1 (t )] S 2 (t ) A 2 cos[ 2 (t )] amplitudes d1 1 dt d 2 2 dt natural frequencies “phases” or angles Without coupling, the phase difference simply grows in time 1 2 1 2 t So, is this seen? A Phase Slip Dynamics of Phase Slips (Both Directions!) Power spectrum Drifts and Slips are Controlled by the Cell frequency (arb) “Random” Swimming of Chlamydomonas reinhardtii Red light illumination – no phototactic cues 45 s. track – note many changes of direction Volume explored is ~1 mm3 very far from chamber walls Geometry of Turning ~100o Probability (angle) Chlamy w/single flagellum, rotating near a surface Turning angle (degrees) Angle per beat - 2 rad 0.4 ~ 16 beats beat beats Frequency difference - 5 - 10 s “Drift” duration- Tdrift 25 50 beats 0.5 - 1s 90 Angular velocity 2 - 4 rad/s Angular change Tdrift 1 2 rad 90 Walzing Volvox: Orbiting “Bound State” 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) The Minuet Bound State Side view Chamber bottom Numerical solution of a model: Based on hovering, negatively buoyant, bottom-heavy swimmers. Bottom-heaviness confers stability. Our Team 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