Fluid Dynamics
and
the Evolution of
Biological Complexity
R E Goldstein
DAMTP
Cambridge
II. Evolutionary Transitions to Multicellularity
Phil. Trans. 22,
509-518 (1700)
(1758)
Volvox as a Model Organism
A. Weismann (1834-1914)
Perhaps second only
to Darwin in impact:
Advocated germ-plasm
theory (anti-Lamarck).
1892: Significance of
Volvocine green algae
D.Kirk (1998)
1. Extant collection, spanning from
unicellular to differentiated multicellular
2. Readily obtainable in nature
3. Studied from differing perspectives
(biochemical, developmental, genetic)
4. Broad ecological studies
5. Recent enough that genome may retain
traces of genetic changes in organization
6. Evidence of repeated genetic changes
7. Amenable to DNA transformation
And, for theorists, it is the proverbial “spherical cow”
A Family Portrait
Chlamydomonas
reinhardtii
Gonium pectorale
Pleodorina
californica
Germ-soma differentiation
Volvox carteri
Eudorina elegans
Volvox aureus
daughter colonies
somatic cells
Evolutionary Aspects
•
Multicellular volvocalean algae may have evolved from a common ancestor
similar to the extant Chlamydomonas reinhardtii.
•
The transition from less complex forms to more complex forms such as
Volvox occurred more than once.
•
Lineages exhibiting different developmental programs are interspersed with each
other and with non-Volvox species.
Chlamydomonas reinhardtii
Eudorina
Eudorina
Eudorina
Volvox
Volvox
Volvox
Germ-Soma Differentiation: regA gene
In e.g. Chlamydomonas, the “ancestral” life cycle is:
vegetative → reproductive → vegetative
Palintomy: reproductive cells first grow and then divide by multiple fission.
8 cells
Grows 2d
8 colonies
d=3 divisions
In e.g. Volvox, there is terminal differentiation, and after birth of daughter
colonies, somatic cells undergo programmed cell death (apoptosis)
“Somatic regenerator” mutants (R. Starr, 1970)
led to discovery that there is a single gene (regA)
whose mutation gives rise Reg phenotype,
in which somatic cells spontaneously revert to
reproductive ones.
In other words, the role of regA in wild-type cells is to suppress all aspects
of reproductive cell development. It is off in gonidia, on in somatic cells.
Currents
The Diffusional Bottleneck
Metabolic requirements
scale with surface
somatic cells: ~R2
Diffusion to an
absorbing sphere
⎛ R⎞
C = C∞ ⎜ 1 − ⎟
r⎠
⎝
I d = 4πDC∞ R
I m = 4π β R 2
PO42- and O2 estimates yield
bottleneck radius ~50-200 μm
(~Pleodorina, start of germ-soma
differentiation)
Rb =
DC∞
β
Organism radius R
Life Cycles of the Green and Famous
division
maturation
of gonidia
inversion
hatching
of juveniles
cytodifferentiation
and expansion
Hatching of Daughter Colonies (V. barberi)
Structure of Flagella & the Flagellation Constraint
Microtubule
Organising Centre
Chromosomes
Basal bodies are microtubule organizing centres
…flagella are resorbed during cell division (no multi-tasking)
(Bell & Koufopanou, ’85,’93)
[Solari, Ganguly, Michod, Kessler, Goldstein, PNAS (2006)]
Stirred, not Shaken
Broken Colonies
Deflagellated Colonies Flagellated Colonies
Colchicine, a flagellar
regeneration inhibitor
(binds to tubulin, prevents
microtubule polymerization)
Consistent with
“Source-sink hypothesis”
Bell & Koufopanou (‘85,’93)
Inhibitor
Liberated Deflagellation
of flagella germ cells +Inhibitor
regeneration
Still medium
Deflagellation
+Inhibitor
Bubbled medium
Liberated
+Inhibitor
Bubbled
Microscopy & Micromanipulation
micromanipulator
microlator
u
p
i
n
a
m
stage
e
p
o
c
s
o
r
ic
m
motorized
1 mm
Tools of the trade – micropipette preparation
Pseudo-darkfield (4x objective, Ph4 ring)
Stirring by Volvox carteri
Sujoy Ganguly, U. Arizona & U. Cambridge
Physics Today, July 2006 (Backscatter)
Measuring Volvox Flows
Time-exposure of Volvox carteri near a surface
Fluorescence
A Closer View
Fluorescence
Even Closer (Flagellar Motions Visible)
Fluorescence
Even Closer (Locally Chaotic Advection)
Fluid Velocities During Life Cycle
Hatch
Division
Daughter Pre-Hatch
This is “Life at High Peclet Numbers”
Solari, et al. (2006)
Flagellar-Driven Flows and Scaling Laws
Specified shear stress f at surface
⎡⎛
u r = −U ⎢ ⎜⎜ c −
⎣⎝
⎡⎛
uθ = −U ⎢ ⎜⎜ d +
⎣⎝
∞
⎤
R3 ⎞
⎟ P (cos θ ) − ∑ Al ( r )Pl (cos θ )⎥
3 ⎟ 1
r ⎠
l =2
⎦
∞
⎤
R3 ⎞ 1
1
⎟ P (cos θ ) + ∑ Bl ( r )Pl (cos θ )⎥
3 ⎟ 1
2r ⎠
l =2
⎦
π fR
U=
8η
Short, Solari, Ganguly, Powers, Kessler & Goldstein, PNAS (2006)
Metabolite Exchange
r
u ⋅ ∇c = D∇2c
Acrivos & Taylor (1962)
heat transport from a solid sphere:
current ~ RPe1/ 3
2
Magar, Goto & Pedley (2003)
prescribed tangential velocity in a
model of “squirmers”
1/ 2
⎛ 4η D ⎞
2 Ruθ ⎛ R ⎞
⎟⎟
Pe =
≈ ⎜⎜ ⎟⎟ ; Ra = ⎜⎜
D
⎝ πf ⎠
⎝ Ra ⎠
≈ 10 μm < Rb
current ~ RPe1/ 2
∂C
∂ 2C
ur
≈D 2
∂y
∂y
ε C
C
≈D 2
U
ε
Rε
The Peclet number scales as:
2
Boundary layer scale:
ε
⎛ UR ⎞
~⎜
⎟
R ⎝ D ⎠
−1 / 2
~ Pe −1/ 2
1/ 2
⎛ 4η D ⎞
2 Ruθ ⎛ R ⎞
⎟⎟
Pe =
≈ ⎜⎜ ⎟⎟ ; Ra = ⎜⎜
D
⎝ πf ⎠
⎝ Ra ⎠
≈ 10 μm < Rb
Bottleneck Bypassed (!)
∂C
2 C∞
≈ 4π DR
≈ 4π DC∞ RPe1/ 2 ~ R 2 (!)
I a = − DR ∫ dΩ
∂r
Ra
2
The Advantage of Size
Phenotypic Plasticity I.
Q: If colonies are deprived of nutrients, how do they adjust?
A: By growing larger (!)
Still medium
Bubbling medium
Phenotypic Plasticity II.
Up velocity
(dilution)
Flow rate/10
(dilution)
Beating rate
(dilution)
Flagella length
(still)
Flagella length
(dilution)
Up velocity
(still)
Q: If colonies are deprived of nutrients, how do they adjust?
A: By growing longer flagella and beating them faster (!)
Hydrodynamic Coupling of Volvox Flagella
Regrowth
after
deflagellation
Changing beat
frequency
125 frames/sec, phase contrast
Regulated self-assembly!