Transcript Bose_Goldstein

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  4DC R
I m  4R 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 
t diffusion
t advection
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
d1
 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