Dynamics of concentrated swimming micro-organisms. John O Kessler. Bacillus subtilis , from individuals to great, concentrated populations: What we see, what we suspect, what we think we know, and at least some of what we ought to know. Physics Dept, University of Arizona, Tucson, AZ
John O Kessler
Bacillus subtilis, from individuals to great, concentrated populations: What we see, what we suspect, what we think we know, and at least some of what we ought to know.
Physics Dept, University of Arizona, Tucson, AZ
DOE W31-109-ENG38; NSF PHY 0551742
ANL SO 2007
Martin Bees................. Glasgow
Luis Cisneros.............. Arizona
Ricardo Cortez.............. Tulane
Chris Dombrowski....... Arizona
Ray Goldstein.............. DAMTP
Igor Aronson............... Argonne
Andrey Sokolov........... Argonne
(near cell division)
Width apprx 0.7mm
Pic by C. Dombrowski
& D. Bentley
The plan: Start with single swimmers, proceed to pairs, small groups, finally arrive at phenomena at high concentration—dynamics, self-organization, modification of themselves and their environment
Note that Re<<1, BUT
boundary conditions that change with flow imply nonlinearity
and irreversibility; blinking Stokeslets. Flow generated by a
swimmer is bounded by other moving swimmers. Swimming
exerts force on the fluid; it is a source of energy (bio to mecha-
nical). The collectively generated flow modifies trajectories.
Constraints affect “behavior” of individual organisms
Flippancy: longitudinal symmetry in propulsion
Swim velocity Vx~ -Ux direction when dUx/dy = 0
Intracellular Brownian fluctuations, AND biochemistry:
polymer exudates, autoinducers modify gene expression
(quorum sensing; + feedback); antibiotics; consumption.
Electrostatics: pH taxis (Sokolov/Aronson)
Transverse flows toward axis of a self-propelled “organism”. This quadrupole-like flow field attracts neighbors and nearby surfaces.
Extending rod/rotating helix
W–V(1)=V(2)=velocity relative to fluid
Elongating rod, rotating helix or whatever, resistance R(2).
ATTACHED TO HEAD
Ramia et al (Biophys Jnl, 1993)
Phan-Thien and Nasseri 1997
and Fauci; Hopkins;....
u= 70 mm/s
f=100/s, l =3 mm , R1 =2R2 , w= 300μm/s, v1 = 30 mm/s:
10 “ “ 30 30
including an efficiency factor = 0.1
B. subtilis require oxygen. A population suspended in water, bounded by glass, except at one interface with air, accumu-lates there.
WATER & B. subtilis
Flat glass “microslide”
velocity in the interior of, and around the
periphery of a phalanx?
There is not much flow in the interior. The
push by the flagella is counteracted by the drag of the heads. Fluid is pushed forward by the leading heads, backward by the trailing (propelling) tails, the bundles of flagella.
Do lateral flows stabilize the phalanx?
mistake: a should be ~ 0.0001 cm; 1.8 really = 2
(Analogy with Re)
Ratio of work by n moving “organisms”/volume to the collective shear stress:
The Bs (Bacterial shear) number definition is:
These parameters are typical for the Zooming BioNematic(ZBN)
Note that Bs is not viscosity-dependent
Also need to consider: Quorum sensing,
diffusion sensing, efficiency sensing.
Biofilm production, crowding out (via
production of antibiotics), topology...
S Park, P Wolanin et al, PNAS 03; B L Bassler (lots); B A Hense et al.,
Nature Reviews Microbiology 2007.
movie 4 (also note Lévy flights and superdiffusion; Kate Remick). movie 5
The ~chaotic (ZBN) transport region sweeps
auto-connected groups of bacteria (biofilms)
away from the “action” = “upwards”, into
deeper region. Similarly, in deeper layers of
fluid, dominated by bioconvection + ZBN,
that dynamic also concentrates the biofilm,
now downwards, toward shallower fluid.