Physical Aspects of Evolutionary Transitions
to Multicellularity
R E Goldstein
DAMTP
Cambridge
C A Solari
S Ganguly
M B Short
T R Powers
J O Kessler
R E Michod
NSF: PHYS
DOE: BES
Multicellularity
Populations of individuals
Chemotaxis & quorum sensing
Park, et al. (2003)
E. coli
V. harveyi
Signaling, adaptation,
chemotaxis,
(e.g., Berg & Purcell)
Uni- to multicellular organisms
Cellularization
D. Mandoli (U. Washington)
Acetabularia crenulata
Advantages of size, complexity,
differentiation, transport
(e.g., Bonner, Niklas)
Some Terminology
(D.L. Kirk)
Lee, Cox, G (1996)
Homocytic – 1,2, or 3-dimensional assembly of prokaryotic or
eukaryotic cells that are structurally and functionally equivalent
Heterocytic – differentiation of structure/function
Colonial – physical association without cytoplasmic connections
Multicellular – … with cytoplasmic connections
Colonialism need not precede heterocytic lifestyle
D. discoideum
Volvox as a Model Organism
Weismann (1892), Kirk (1998)
van Leeuwenhoek (1700)
Named by Linnaeus (1758)
1. Extant collection, spanning from
unicellular to differentiated multicellular
2. Readily obtainable in nature, cultured
under a wide range of conditions
3. Studied from differing perspectives
(biochemical, developmental, genetic)
4. Broad ecological studies, with information
on distribution, environmental effects
5. Recent enough that genome may retain
traces of genetic changes in organization
6. Evidence of repeated genetic changes,
with hope that key ones are modest
7. Amenable to modern molecular-genetic
methods, such as 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
Life Cycles of the Rich and Famous
division
Maturation
of gonidia
inversion
hatching
of juveniles
cytodifferentiation
and expansion
A Place in the Sun
Hatching of Daughter Colonies (V. barberi)
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.
Advection, Dissipation & Diffusion:
Reynolds and Peclet Numbers
Navier-Stokes equations:

  
2
 (ut  u  u )  p   u
Passive scalar dynamics:

2
ct  u  c  D c
Reynolds number:
 
 u  u U 2 / L UL


 Re
2
2
 u
U / L

Peclet number:
 
u  c UC / L UL


 Pe
2
2
D c DC / L
D
If U=10 mm/s, L=10 mm, Re ~ 10-4, Pe ~ 10-1
At the scale of an individual bacterium, dissipation dominates
inertia, and advection dominates diffusion.
The second relation breaks down with multicellularity…
Currents
The Diffusional Bottleneck
Metabolic requirements
scale with surface
somatic cells: ~R2
Diffusion to an
absorbing sphere
 R
C  C 1  
r

I d  4DC R
I m  4  R2
PO42- and O2 estimates yield
bottleneck radius ~50-200 mm
(~Pleodorina, start of germ-soma
differentiation)
Rb 
DC

Organism radius R
Biological Considerations
Source-Sink Hypothesis (Bell & Koufopanou, ’85,’93)
The extracellular matrix is a source of nutrients, germ cells are sinks.
• this enhances nutrient uptake rates over that possible with
isolated germs cells.
• experimental demonstration – liberated germ cells grow more slowly
than those within ECM
Flagellation Constraint
Anchoring structures of flagella (“basal bodies”) serve as
microtubule organizing centers (MTOCs) during cell division
Hence, flagella beating stops during cell division, the time of
high metabolic activity
Other aspects of Flagella/Cilia/Undulipodia
Left-Right symmetry breaking in embryonic development, mucus clearing,
oocyte transport, kidney function, eyes, … (Ibanez-Tallon, et al., 2003)
Highly-conserved nature of proteins from Chlamydomonas to humans
(Pazour, et al., 2005)
[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
Pseudo-darkfield (4x objective, Ph4 ring)
Stirring by Volvox carteri
micropipette
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)
Phase contrast
High-Speed Movie (125 fps) of Volvox Flagella
+/- cytoplasmic connections between somatic cells:
same flagellar coordination (Hiatt & Hand, 1972)
Flow Field Viewed On Axis, Showing Swirl
Fluid Velocities During Life Cycle
Solari, et al. (2006)
Hatch
Division
Daughter
Pre-Hatch
Peclet Number During Life Cycle
Division
Pre-hatch
Daughter
Hatch
This is “Life at High Peclet Numbers”
Biological Version of Millikan Oil Drop Experiment
(Or, how to measure the average force per flagellum)
Colonies are pH sensitive – they will throw off their flagella
when the pH is transiently lowered - regrowth takes 90 minutes
Regrowth can be in inhibited with colchicine (binds to tubulin)
Flagellar-Driven Flows and Scaling Laws
Specified shear stress f at surface



R3 
ur  U  c  3  P1 cos    Al ( r )Pl cos 
r 
l 2





R3  1
1
u  U  d  3  P1 cos    Bl ( r )Pl cos 
2r 
l 2


 fR
U
8
Free-swimming colonies:
Colonies held in place:
Larger colonies swim faster
Measure <f> by deflagellation expt.
c  d 1
R
R
c ; d 
r
2r
Velocity Profile (Experiment & Theory)
Short, Solari, Ganguly, Powers, Kessler & Goldstein, PNAS (2006)
Metabolite Exchange
Acrivos & Taylor (1962) – heat transport from a solid sphere:
1/ 3
Current ~ R Pe
Magar, Goto & Pedley (2003) – prescribed tangential velocity in a
model of “squirmers”
Current ~ R Pe1/ 2
Near surface:
C
C
ur
D 2
y
y
 C
C
U
D 2
R

2
y
ur  U
R
Boundary layer scale:
 UR 
 ~

 D 
1 / 2
~ Pe1/ 2
In dimensionful terms,
the boundary layer is Ra
Finite-Element Calculations

u  c  D2c
Boundary Layer Scaling
1 / 2
~ Pe
The Peclet number scales as:
2
1/ 2
 4 D 
2 Ru  R 

Pe 
   ; Ra  
D
 f 
 Ra 
 10 mm  Rb
“Solute plumes” – like those of marine snow (Kiørboe & Jackson, 2001)
(Roman Stocker, MIT – microfluidic studies of these plumes)
Bottleneck Bypassed (!)
C
2 C
I a   DR  d
 4DR
 4DC RPe1/ 2 ~ R 2 (!)
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 (!)
Some Next Steps
Further test of the scaling laws
rotational frequency, swimming velocity
Direct measurements of photosynthesis
with/without flagella-driven stirring
Flagella synchronization via hydrodynamic coupling
a general problem involving molecular motors
phototactic steering via a network of somatic cells