PIV Studies of the Zooming Bionematic Phase

Luis CisnerosDepartment of PhysicsUniversity of Arizona

NSF: MCB (NER)

Earlier work: Dombrowski, et al., PRL 93, 098103 (2004)

Chris Dombrowski John O. Kessler Raymond E. Goldstein

Advection, Dissipation & Diffusion: Reynolds and Peclet Numbers

nfupuuut 2)(

Re/

/2

2

2

UL

LU

LU

u

uu

If U=10 m/s, L=10 m, Re ~ 10-4, Pe ~ 10-1

At the scale of an individual bacterium, dissipation dominates inertia, and diffusion dominates.

With multicellularity, Pe > or >> 1.

cDcuct2

Navier-Stokes equations:

Passive scalar dynamics:

Pe/

/22

D

UL

LDC

LUC

cD

cu

Reynolds number: Peclet number:

Self-Concentration and the Chemotactic Boycott Effect

2 mm

Dombrowski, et al. (2004); Tuval, et al. (2005)

Video ~100x actual speed

Experimental Details

Bacterial protocols using B. subtilis strain 1085 (and various mutants)

Simple: Overnight growth in Terrific Broth in a still petri dish

More controlled: Start with -20o C stock, prepared from spores stored on sand. [Add to TB at RT, 24h of growth, 1 ml + 50 ml TB, incubated for 18 h. Then 1 ml + 50 ml TB, incubated for 5 hrs. 0.75 ml + 0.25 ml glycerol].

1 ml of -20o stock + 50 ml TB, incubate for 18 h (shaker bath, 37o, 100 rpm), then 1 ml + 50 ml TB (5 hr), then into chamber

Fluorescent microspheres (Molecular Probes, Nile Red, 0.1-2.0 m)

The ZBN in Brightfield and Fluorescence

210 m

Velocity Field from Cinemagraphic PIV

Dombrowski, et al. (2004). See also Wu and Libchaber (2000)

35 m

Peclet number ~10-100 (vs. 0.01-0.1 for individual bacterium)

The ZBN in Brightfield and Fluorescence

210 m

PIV Velocity Field

210 m

Streamlines (Note intermittency)

210 m

Velocity-Velocity Correlation Function (spatial)

I(r)

r (m)

22

2),(),(

)(xx

xx

vv

vxvrxv

ttrI

Velocity-Velocity Correlation Function (temporal)

22

2),(),(

)(ss

sssts

tJvv

vxvxv

J(t)

t (s)

Vorticity (homage a Miró)

210 m

Summary: Peclet Number Revisited

In the Zooming Bionematic (ZBN) phase, there are large coherent regions of high-speed swimming, whose internal fluid velocities and scale generate an effective diffusion constant DZBN =L2/T~10-4 cm2/s which is an order of magnitude larger than the molecular oxygen diffusion constant. Alternatively, the (chaotic) Peclet number is >> 1.

In the ZBN, the bacterial concentration is so high that dissolved oxygen is used up in the time T~1 s, matching the time scale of the coherent structures.

Side Views of Sessile Drops

Tuval, et al. PNAS 102, 227 (2005)

drop

t

Bacterial Swimming and Chemotaxis(Macnab and Ornstein, 1977)

Turner, Ryu, and Berg, J. Bacteriol. 182, 2793 (2000)

Real-time Imaging of Fluorescent Flagella

“normal = LH helix“curly” = RH helix“straight” = straight

1-4 m

10-20 m

20 nm

Swimming speed ~10 m/sPropulsive force ~1 pN

Swimming Near the Contact Line

Bacterial Bioconvection

J.O. Kessler

The Chemotactic Boycott Effect

Dombrowski, Cisneros, Chatkaew, Goldstein, and Kessler, PRL 93, 098103 (2004)1 cm

Mechanism of Self-Concentration

Dombrowski, et al. (2004)

Historical Ideas

)()(

)(),(

2

2t

ucrD

cuccfcDc

tt

tc

•Flocking models (Toner and Tu, 1995, …; traffic flow…)

•Sedimentation (interacting Stokeslets)

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

Velocity field must bedetermined self-consistentlywith density field

0)(

||)( 21

2t

v

vvvvvvv

t

Dp

3

00

)(

4

3)(

)(v

rr

a

an

ijjii

rreerU

rrUvras few as three particles exhibit chaotictrajectories (Janosi, et al., 1997)

A Landau theory in the velocity field – clever butnot relevant to the physics of Stokes flow

•A synthesis is emerging from coarse-grained models of sedimentation (Bruinsma, et al.) and self-propelled objects (Ramaswamy, et al. 2002, 2004)…

IMPLICATIONS FOR QUORUM SENSING…

Side Views of Sessile Drops

Tuval, Cisneros, Dombrowski, Wolgemuth, Kessler & Goldstein, preprint (2004)

Side Views: Depletion and Flow

2 mm

Dombrowski, et al. (2004)

Circulation Near the “Nose”

Self-trapping in the corner

Diffusion and Chemotaxis

zngupuuu

crnnDnun

cnfcDcuc

t

nt

ct

ˆ))((

)(

)(

2

2

2

Oxygen diffusion/advection

Navier-Stokes/Boussinesq

Chemotaxis

C(z) n(z)

z z

depletion layer: D/v

Experiment vs. Theory

Tuval, Cisneros, Dombrowski, Wolgemuth, Kessler & Goldstein, preprint (2004)

Moffat Vortex

Tuval, et al. (2004)

Exp

erim

ent

(PIV

)N

um

eric

s (F

EM

)

Depletion Layers

Geometry of the Contact Line Region

Tuval, Cisneros, Dombrowski, Wolgemuth, Kessler & Goldstein, preprint (2004)

)(

)2/cos(),(

2

1

2/

crnnDnun

mracrc

nt

m

mms

Chemotactic Singularities & Mixing

Tuval, et al. (2004)

Supported Drops

Tuval, et al. (2004)