Propulsion and Evolution of Algae

R E GoldsteinDAMTPCambridge

The Size-Complexity Relation

Amoebas, Ciliates, Brown SeaweedsGreen Algae and PlantsRed SeaweedsFungiAnimals

Bell & Mooers (1997)Bonner (2004)?

Volvox

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

(1758)

A Family PortraitChlamydomonas reinhardtii

Volvox carteri

Gonium pectorale Eudorina elegans

Pleodorina californica

Volvox aureus

daughter colonies somatic cellsGerm-soma differentiation

Altruism, apoptosis

The Diffusional Bottleneck

Organism radius R

Cu

rren

ts

RCDI

r

RCC

4

1

d

Diffusion to an absorbing sphere

PO42- and O2 estimates yield

bottleneck radius ~50-200 m(~Pleodorina, start of germ-somadifferentiation)

DCRb

Metabolic requirements scale with surface somatic cells

2m 4 RI

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…

D

UL

t

tPe

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:

D

Lt

U

Lt

diffusion

advection

2

We define the Péclet number as the ratio:

Microscopy & Micromanipulation

motorized microscope stage

micro-manipulator

micro-manipulator

Stirring by Volvox carteri P

seu

do-

da

rkfie

ld (

4x o

bje

ctiv

e, P

h4

rin

g)

To

ols

of t

he

tra

de –

mic

ropi

pet

te

pre

pa

ratio

n

1 mm

A Closer ViewF

luo

resc

enc

e

Fluid Velocities During Life Cycle

Hatch Division Daughter Pre-Hatch

This is “Life at High Péclet Numbers”

D

RuPe max2

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

Micropipette

Cell body

Frame-subtraction

22

11

dt

ddt

d

)](cos[A)(

)](cos[A)(

222

111

ttS

ttS

“Phase oscillator” model used in e.g. circadian rhythms, etc.

t2121

strokes offlagella

amplitudes “phases”or angles

naturalfrequencies

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 ofphototaxis

A Phase Slip

Dynamics of Phase Slips (Both Directions!)

Drifts and Slips are Controlled by the Cell

frequency (arb)

Po

wer

sp

ectr

um

“Random” Swimming of Chlamydomonas reinhardtii

Red light illumination – no phototactic cues45 s. track – note many changes of directionVolume explored is ~1 mm3 very far from chamber walls

Geometry of Turning

beat

rad4.0

beats16~

2

s

beats10-5

rad/s 4-2

s1-0.5

beats5025

driftT 90rad21driftT

Turning angle (degrees)

~100o

90

Pro

bab

ility

(a

ngle

)

Chlamy w/single flagellum,rotating near a surface

Angle per beat -

Frequency difference -

“Drift” duration-

Angular velocity

Angular change

Walzing Volvox: Orbiting “Bound State”

Dual Views

Dominant physics: downwardgravitational 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

Numerical solution of a model:Based on hovering, negativelybuoyant, bottom-heavy swimmers.

Bottom-heaviness confers stability.

Side view

Chamber bottom

Marco PolinIdan TuvalKyriacos LeptosKnut Drescher

Sujoy Ganguly

Cristian Solari

Timothy J. PedleyTakuji Ishikawa

Jerry P. Gollub

www.damtp.cam.ac.uk/user/gold

Our Team