Living at low Reynold 's numbersKatherine Richardson ChristensenFacultyof Science, Universityof Copenhagen, Denmark

WednesdaY,4 May-1:10 p.m.

It is becoming increasinglyclearthatlifeon Earth (the'biosphere') impacts global geochemica lprocesses. Thus, anunderstanding ofhowthebiosphere functions is critica l forunderstandinghowtheEarthsystem itselffunctions. It is ironic inthat context- given theocean covers 71%of theEarth 'ssurface - thatmostof ourunderstandingofNature andecological processes comesfrom observingecosystems onland.The 'ground rules' that structure ecosystems on landarevery different from thosegoverning life in theocean - andboth onlandandin thesea, these 'ground rules' areestablished byphysics. One of themostobviousdifferences between ecosystems onland andin thesea isthefactthatmuch oftheplantlifeonland is comprisedof relatively large organismswhile, intheocean , over95%ofthephotosynthesisoccurring iscarried outbyplantsthataretoosmallto even beseen bythenakedeye.These plantsfonnthebasis of thefoodweb intheocean. Therefore , mostof theanimals livingthere arealsoverysmall. Thus, these plantsandanimals liveat Reynold'snumbers that arevery muchlower thanisthe case forourselves, andmostoftheotherorganisms we observe in nature. Living at lowReynold'snumbers presents anumber of challengesthat larger plants andanimals donot experience.These challenges demand different solutionsforcarrying outsuchcritical tasks ascatchingprey,movingaboutand nutrient uptake. Some ofNature 'sfantastic solutions formeeting these challengesaredescribed. In addition , thevarious physical processes that may contributeto establishing andmaintaining plankton biodiversity in theoceanareconsidered.

Living at low Reynolds numbernumber

Katherine RichardsonKatherine RichardsonProfessor, Center for Macroecology, Evolution and Climate

University of Copenhagen

Differences in Terrestrial and Marine ecosystems

Photo: Norman Nichols

Victor Hensen

”Father” of Biological oceanography

Coined the term ”plankton” (1887)

And recognised that plankton are the ”blood of the sea”

Our starting point:

Purcell, E.M. American Journal

Our starting point:

of Physics vol 45, pages 3-11, 1977.

“… I want to take you into the world of very low Reynolds number--a world which is inhabited by the overwhelming majority of the organisms

This world is quite different form the one that ….This world is quite different form the one that we have developed our intuitions in…”

31-05-2011

Reynolds number:

Osborne Reynolds: Osborne Reynolds: 1842 - 1912British Physicist famousfor his study of the for his study of the transition fram laminar to turbulent flow.

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Purcell, 1977

F t iFor most organismsin the ocean ,

Re< 1

That means viscousforces > intertialfforces

= challenges we have

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Purcell, 1977

challenges we have never even imagined!

1. Locomotion

This leads to otherchallenges…

P ll 1977

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Purcell, 1977

Purcell’s ”Scallop Theorem”

”If the sequence of shapes displayed by shapes displayed by the swimmer is identical to the sequences of shapessequences of shapeswhen seen in reverse*, then the a e age position of average position of the body cannotchange over one

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period” (Lauga 2010)

* recriprocal motion

At l RAt low Reswimmers must have more thanhave more thanone degree of freedom in orderto move…

” t i l”a geometricalapproach to locomotion”

Dias 1031-05-2011 Purcell, 1977

locomotion

Locomotion at low Re: A question of qbreaking symmetry

Whips,

hairs

paddlesMaximum weight-specific force in escapejump more than order of magnitudehigher than other organsims (Kiørboe et al 2010)

After Visser, 2011

Locomotion at low Re is NOT only of interest for tiny organisms living of interest for tiny organisms living in fluids!

Nano technologyNano technology

”Pushmepullyou” (A 2005)”Pushmepullyou” (Avron, 2005)

Drag on twospheres close

together istogether is less than

when they arefar apartp

”Three sphere creeper” (Najafi and Golestinian, 2004)

d ”Th h

Drag oninflated

sphere greaterthan for non- and ”Three-sphere-

rotator” (Dreyfus et al. 2005)

than for noninflated

After Visser, 2011

2. Finding food

Why?

Dias 1331-05-2011 Purcell, 1977

Which is about 20 x about 20 x faster th ththan theseorganismsgcan swim!

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Purcell, 1977

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Purcell, 1977

It’s hard to shake off yourIt s hard to shake off yourenvironment at low Re!

• Small cells have a competetive advantage at p glow nutrient concentrations

• It’s easy to ”lose yourlover” (and reproduction is lover (and reproduction is essential to survival!)

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Hydrodynamicsy yAnalytic and Computational fluid dynamics

Streamlines around aFlow around a gravitationally Flow lines around a rapidlyStreamlines around a self-propelled sphere: squirmer model

Flow around a gravitationally tethered copepod

Flow lines around a rapidly swimming copepod

Slide: A. Visser

Copepods create feedingp p gcurrents

Dias 1831-05-2011 Koehl, 1998

Re influences effectivenessRe influences effectivenessof different morphologies

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Koehl, 1998

Hydrodynamicsy yThe question of detection:How do micro-organisms perceive each other?

sinking particle

mate

particleswimming prey

G t h d d i i lGenerate hydrodynamic signals that convey information about the size, speed and location of the approaching encounter partner

approaching Detection distance

approaching encounter partner.

approaching predator

Detection distance

Slide from Andre Visser

Hydrodynamicsy yThe question of detection:How do micro-organisms perceive each other?

Labidocera madurae

200 m

Mechano-receptive setae are velocity detectors

40 mNeurological sensitivity 20 μm / s

5 mSlide: Andre Visser

Hydrodynamicsy ySensing and Information

Signal along antenna for a self propelled

along across

sphere

along across

Slide: Andre Visser

Slide: Andre Visser

Encounter rate is everything to planktony g p

CostCost

Ri k B fitRisk Benefit

Slide: Andre Visser

Encounter rate and turbulence

perception distance

( )1/ 22 2 2 22ij i ij ij i j ijZ C R u v wb p= = + +

is the encounter kernel

preypredator

ijbu

Rw

≈ maximum clearance ratej

v

Rturbulent velocity scale

( )1/ 3w Ra e=Visser & MacKenzie, J Plankton Res 1998

( )ij ijw Ra e

Rothschild & Osborn, J Plankton Res 1988

Evans, J Plankton Res 1989Slide: Andre Visser

Encounter rate and turbulence

( )1/ 22 2 2 22ij i ij ij i j ijZ C R u v wb p= = + +

is the encounter kernelijbu

Rw

≈ maximum clearance ratej

v

R

A simple formulation of the rate of i t ti (th f lif ) i thinteraction (the pace of life) in the planktonic world.

Slide: Andre Visser

Too much of a good thing!

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Visser, 2011

Searching for Eel larvae in the Sargasso Sea:

38

Galathea 3

34

36

110

30

32

ees

nort

h]

515456

106

108

110

515456

106

24

26

28

Latit

ude

[deg

re

17202427313538414851

5860626466676970717576

77828586899091929798

101102

89

7517

6727

76

101

60 356290

102

91

69

51

77 70

64

3831

7182

20

41

66

4858

85

92

86

9798

24

20

22

24

7

8

14

1717

14

7

8

-80 -78 -76 -74 -72 -70 -68 -66 -64 -62 -60

Longitude [degrees east]

18

44

Temperatur (C)0 51E+0011E+0012E+0012E+0012E+0013E+0013E+0013E+0014E+0014E+0015E+0015E+0015E+001

26 00 C

-100

m) 23.00 C

24.50 C

26.00 C

Eel larvae

300

-200

Dyb

de (m

18 50 C

20.00 C

21.50 C

0 100 200 300 400 500 600 700 800 900 1000 1100-400

-300

15.50 C

17.00 C

18.50 C

0 100 200 300 400 500 600 700 800 900 1000 1100Distance (km)

Richardson et al. In prep

Standing stock of phytoplankton

Fluoresens (FSU)

g p y pdoesn’t suggest anything specialhere…

Fluoresens (FSU)0 51E+0011E+0012E+0012E+0012E+0013E+0013E+0013E+0014E+0014E+0015E+0015E+0015E+001

0.42 FSU

0.46 FSU

-200

-100

bde

(m)

0.26 FSU

0.30 FSU

0.34 FSU

0.38 FSU

-300

Dyb

0 06 FSU

0.10 FSU

0.14 FSU

0.18 FSU

0.22 FSU

0 100 200 300 400 500 600 700 800 900 1000 1100

Distance (km)

-400 0.02 FSU

0.06 FSU

Richardson et al. In prep

But the rate of electron transfer in photosynthesis does!

Variabel fluoresens (Fv/Fm)0

0.46 Fv/Fm

-100-50

0

bde

(m)

51E+0011E+0012E+0012E+0012E+0013E+0013E+0013E+0014E+0014E+0015E+0015E+0015E+001

0.28 Fv/Fm

0.34 Fv/Fm

0.40 Fv/Fm

0 100 200 300 400 500 600 700 800 900 1000 1100-200

-150Dyb

0.10 Fv/Fm

0.16 Fv/Fm

0.22 Fv/Fm

Distance (m)

turbulent mixing -> Richardson et al. In prepincreased nutrients (->

inreased encounters)

Life at low Reynolds Life at low Reynolds number is the powerhouse p

for life on Earth…