Physics and Biology of Multicellularity

1
Physics and Biology of Multicellularity
R E Goldstein
www.damtp.cam.ac.uk/user/gold
www.youtube.com/Goldsteinlab
2
The Life of Bacteria
3
The Size-Complexity Relation
Amoebas, Ciliates, Brown Seaweeds Green Algae and
Plants Red Seaweeds Fungi Animals
Bell Mooers (1997) Bonner (2004)
4
Multicellularity
Populations of individuals
Truly multicellular organisms
REG
Park, et al. (2003)
Chara corallina
Vibrio harveyi
Signaling, adaptation, chemotaxis, quorum
sensing (e.g., Berg Purcell)
Advantages of size, complexity, differentiation,
transport (e.g., Bonner, Niklas)
5
Some Terminology
(D.L. Kirk)
Homocytic assembly of prokaryotic or
eukaryotic cells that are structurally and
functionally equivalent Heterocytic
differentiation of structure/function
Mendelson (1976)
Colonial physical association without
cytoplasmic connections Multicellular with
cytoplasmic connections
Lee, Cox, G (1996)
Colonialism need not precede heterocytic
lifestyle
D. discoideum
6
Case Studies Lectures 2-4
Multicellular Algae
Costs/benefits of increasing size Driving force
for differentiation Collective dynamics of
flagella Phototaxis Collective behaviour
Cytoplasmic Streaming
Internal Circulation Wall-Driven Flows at
Re0 Chirality/Transverse Flows Metabolic
Link? Vacuolar Membrane Dynamics
7
Advection, Dissipation Diffusion Reynolds and
Peclet Numbers
Navier-Stokes equations
Passive scalar dynamics
Reynolds number
Peclet number
If U10 mm/s, L10 mm, Re 10-4, Pe 10-1 At
the scale of an individual bacterium, dissipation
dominates inertia, and diffusion dominates
advection. The second relation breaks down with
multicellularity
8
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
This is like the Reynolds number
comparing inertia to viscous dissipation
If U10 mm/s, L10 mm, Re 10-4, Pe 10-1 At
the scale of an individual cell, diffusion
dominates advection. The opposite holds for
multicellularity
9
Bacterial Swimming
Real-time Imaging of Fluorescent Flagella
1-4 mm
Macnab and Ornstein (1977)
Turner, Ryu, and Berg (2000)
20 nm
10-20 mm
B. subtilis
C. Dombrowski
10
Nanostructure of Flagella
11 protofilaments

• Nanoscale bistability of monomer packing produces
  microscale polymorphism
• Asakura, Adv. Biophys. 1, 99 (1970).
• Calladine, J. Mol. Biol. 118, 457 (1996).
• Yamashita, et al., Nature Struct. Biol. 5, 92
  (1998).
• Samatey, et al., Nature 410, 331 (2001).

11
The Bacterial Flagellum
Namba, et al. (Osaka)
12
Self-Concentration via Bioconvection
1 cm
Dombrowski, et al., PRL (2004) Tuval, et al.,
PNAS (2005)
13
Diffusion, Chemotaxis, and Flow
Oxygen diffusion/advection
Pedley Kessler (1992)
Chemotaxis
Navier-Stokes/Boussinesq
depletion layer D/v
n(z)
C(z)
z
z
14
Side Views Reveal Large-Scale Flows
drop
laser (532 nm)
ring light
Keplerian telescope
shutter
dichroic
longpass filter
ccd camera
Tuval, et al. (2005)
15
Side Views Depletion and Flow
2 mm
Video 100x actual speed
16
Persistent Vortex Large Peclet Number
1 mm
Experiment (PIV)
If U10 mm/s, L10 mm, Re 10-4, Pe 10-1 At
the scale of individual bacteria, advection
is unimportant. Collective dynamics can lead to
very large Pe. Here, L1000 mm, U100 mm/s so Pe
100.
Numerics (FEM)
Vortex in wedge Moffatt (1964).
17
The Zooming Bio-Nematic (ZBN)
Petri dish
contact line
brightfield
epi-fluorescence
300 mm
A bacterial bath with enormously enhanced
diffusion (even superdiffusion)
Kessler (98) Wu Libchaber (00) Soni, et
al., (03/4) Microfluidic applications Kim
Breuer (04), Darnton, Turner, Breuer Berg
(04)
18
Velocity Field from PIV (pendant drop)
Peclet number 10-100 (vs. 0.01-0.1 for
individual bacterium)
35 mm
Like a van Kármán vortex street, but the Reynolds
number is 10-2 (!) Phenomenology like that of
recurring jets and swirls in sedimentation.
19
Velocity Correlation Functions in Space Time
oscillations due to multiple vortices (individual
images)
space
sequence average
What determines these length and time scales?
time
oscillations due to recurring vortices (individual
images)
spatial average
20
Historical threads

• Conventional chemotaxis picture e.g.
  Keller-Segel (1971)

Rich and diverse behavior, including singularities
(Childress) from chemical signaling
chemotaxis. But what about the fluid flow??

• Flocking models Vicsek, et al. (1995), Toner and
  Tu, (1995),

A Landau theory predicts long-range swimming
order. Not what we see!!

• Active medium models (Ramaswamy, et al.
  (02,04),
• Kruse, et al. (04) based on ideas from
  liquid crystals
• predict a finite-wavelength instability from
  hydro-
• dynamic interactions long-time behavior
  unknown
• Related swarming models Bertozzi, et al.
  (05)
• Thin-film model Aronson, Sokolov, G (06)
  includes
• effects of shear on orientation vector

21
Challenges

• Direct simulation of a suspension of
  self-propelled swimmers
• Hernandez-Ortiz, Stoltz Graham, PRL 95,
  204501 (05)

rms velocity
0.01
0.1
1
f
Distinct onset of large velocities at transition
length scale increases with f at high f,
fluctuations span box
What is the continuum limit of this system?
22
Simulations of Self-Propelled Rods
Saintillan Shelley (2007) see talks by C.
Hohenegger, Mike Shelley
23
Reversal of Bacterial Locomotion at an Obstacle
                                                
                         
PRE 73, 030901(R) (2006)
24
What if the locomotion of a bacterium is impeded
by an obstacle?
Like a wall, another cell or.
To produce Quorum Polarity at high concentrations
of cells, there might exist some mechanism for
wrong way oriented individuals to join the
majority orientation without turning around
. Reversal of motion, or backing up, is less
costly.
To produce

• Previous work
• Turner Berg PNAS, 1995 E. coli swim with
  either end forward
• Magariyama Biophys, 2005 mono-flagellated
  organisms reverse rotation of flagella

25
Experimental Setup

• Under our particular growth conditions B.s. do
  not display the usual run and tumble behavior
• Petri dish is permeable to O2
• Bacteria swim along the bottom. Trajectories are
  long, slightly curved, runs with essentially no
  tumbles.

Side view
26
Bacterial Reversal

• Cells occasionally approach to the gap near
  spheres contact point (excluded region). They
  generally turn away and keep swimming.
• Close to straight-on docking may produce
  reversal motion, suggesting that the flagellar
  bundle flips from one end of the cell to the
  other.

Gap is less than 1.1mm wide
Top view
27
Bacterial Reversal in flagrante
28
Time dependence of average swimming velocities
29
Asymptotic velocities

• Data points cluster near the equality line
• Histogram shows a Gaussian distribution
• Statistical symmetry between (V?)in and (V?)out
• Swimming ability is independent of the polar
  location of the flagellar bundle

30
Asymmetry between inward and outward motion
Different position of the flagellar bundle with
respect to the gap induces a difference in
viscous drag and hence different net forces over
cell body during docking and undocking processes.
31
Dynamics of Enhanced Tracer Diffusion in
Suspensions of Eukaryotic Microorganisms
Leptos, Guasto, Gollub, Pesci, Goldstein,
submitted (2009)
32
Tracer Trajectories
33
Tracking Tracers
34
Diffusion and Advection of a Tracer
35
Non-Gaussian PDFs
36
Self-Similarity
37
Apparent Functional Form of PDFs
Gaussian contribution
Exponential (Laplace) contribution
Effective volume fraction, obtained from fits to
data
Both lengths display diffusive scaling
38
Diffusive Behaviour of Tracers
39
Effective Diffusivity Volume Fraction
40
Sample Tracer Trajectory
41
Tracers Near a Cell Held on a Micropipette