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Pattern Formation in Model Active Systems
Igor AronsonArgonne National Laboratory
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• Introduction
• patterns in granular systems
• in vitro cytoskeletal networks • suspensions of swimmers
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• Tomorrow: simple kinetic theory for inelastic rods, application to microtubules/motors systems
• Then: models of collective swimming, viscosity reduction
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Where in the World is Argonne?
World-Class Science Unique Scientific Facilities Free and Abundant Parking25 min from Downtown ChicagoWhite Deer
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Energy Sciences Building Stephen Chu
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Collective Behavior in Living and Inanimate Matter
swarming hungry locusts
Schaller et al, Nature 2010I. Cousin et al, Science, 2005
• simple interactions – complex emergent behavior• different mechanisms – similar patterns
swirling actin
Blair, Kudrolli, 2003
granular rods
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1. Polar orienting interaction in a noisy environment
2. Streaming: motion along the polar direction
•More complicated continuum hydrodynamic models (Tu, Toner, Ramaswamy)
Vicsek Model: A Major Theoretical Milestone •Point particles (boids) move off-lattice
• Driven overdamped (no inertia effects) dynamics
•Strictly local interaction range
•Alignment according to average direction of the neighbors
•Simple update algorithm for the position/orientation of particles•Not necessarily reproduce observed phenomenology
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Simulations of Vicsek model
at large size, discontinuous transition
Order parameter:(similar to magnetization)
Chate and Gregoire,PRL 2004
1,000,000 boids
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Fundamental Issues (Physicist Point of View)
Similarity between collective behaviors in living and inanimate systems
Role of long-range interactions vs short-range collisions
Derivation of mathematical models from simple interaction rules
Relation between collective behavior and the mechanisms of self-propulsion
Modeling of emergent collective behavior in the lab
Applications for dynamic self-assembly/materials design
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Active Systems are Very Complex
Focus on simple yet non-trivial systems such as in vivo cytoskeletal networks, bacterial suspensions
Fundamental interactions are simple and well-characterized
Interactions are mostly of the “physical nature”: inelastic collisions, self-propulsion, hydrodynamic entrainment, vs chemotaxis, signaling etc
Derive continuum description from elementary interaction roles and connect observed patterns with experiment
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Approach is mesoscopic and is complementary
Direct simulations of complex systems
Concept of Active Gels (extension of liquid crystal theory to active systems near thermodynamic equilibrium) by Prost, Joanny, Kruse, Julicher
Phenomenological theory by John Toner, Sriram Ramaswamy, Yuhai Tu
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US DOE Materials Science and Engineering, Biomolecular Program
Major thrust areas: understanding, controlling, and building complex hierarchical structures by mimicking nature’s self- and directed-assembly approaches
design and synthesis of environmentally adaptive, self-healing systems
http://science.energy.gov/bes/mse/research-areas/biomolecular-materials/
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Active Systems – A Unique Opportunity for Materials Science
Design of active self-assembled structures with functionality not available under equilibrium conditions self-assembled colloidal robot
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Blair-Neicu-Kudrolli experiment
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long Cu cylinders
# of particles 104 6.2 mm0.5 mm
vibration of long rods
top view
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Phase transitions and vortices
•Weakly vibrated layer of rods
• Phase transition
• Coarsening
• Vortex motion
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Long-Term Evolution
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Origin of Motion
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Experiment Simulations
D Volfson, L Tsimring, A. Kudrolli
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Swarming in Quasi-2D Experiments Experiment, 500 asymmetric rods Simulations, 500 rods
Lumay, D Volfson, L Tsimring, A. Kudrolli PRL 2008
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Vibrated Polar Disks Experiment, 1000 asymmetric disks
re-injecting boundary conditions
Deseigne, Dauchot, Chate, PRL 2010
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Recruiting Nanofabrication: micron-size AuPt rods swim in H2O2
AuPt & AuRu microrods are provided by
Ayusman Sen and Tom Mallouk, PSU
Movie: Argonne
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Actin-Myosin Motility Assay
V Schaller et al. Nature 467, 73-77 (2010)
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Moving Clusters and Swirls
V Schaller et al. Nature 467, 73-77 (2010)
moderate density higher density
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§ Simplified system with only few purified components § Experiments performed in 2D glass container: diameter 100 µm,
height 5µm § Controlled tubulin/motor concentrations and fixed temperature§ MT have fixed length 5µm due to fixation by taxol
F. Nedelec, T. Surrey, A. Maggs, S. Leibler, Self-Organization of Microtubules and Motors, Nature, 389 (1997) T. Surray, F. Nedelec, S. Leibler & E. Karsenti, Physical Properties Determining Self-Organization of Motors & Microtubules, Science, 292
(2001)
in-vitro Self-Assembly of MT and MM
Cell with MT & MM
CCD camera
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Patterns in MM-MT mixtures Formation of asters, large kinesin concentration (scale 100 m)
100 µ
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Vortex – Aster Transitions
Ncd – gluththione-S-transferase-nonclaret disjunctional fusion protein
Ncd walks in opposite direction to kinesin
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Dynamics of Aster/Vortex Formation
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Kinesin Ncd
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Rotating Vortex Kinesin
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Summary of Experimental Results
2D mixture of MM & MT exhibits pattern formation Kinesin: vortices for low density of MM and asters for higher density Ncd: only asters are observed for all MM densities For very high MM density asters disappear and bundles are formed
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Self-Propelled BioParticlesswimming aerobic bacteria Bacillus Subtilislength 5 µm, speed 20 µm/sec, Re=10-4collective flows up to 100 µm/secneed Oxygen (oxygentaxis)
5 µµ
Turner, Ryu, and Berg (E. coli)
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Swimming Algae Eukaryotic Clamydomonas reinhardtiiSize: 10 mm, two flagella ~10 mm Swimming speed: 50-100 mm/sec Highly asocial animals
Single Alga Algae Suspension
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Bacillus subtilis primary behaviors
Collision of two bacteria in thin films
Confining wall
Liquid
Concentration of bacteria near the surface due to gradient of dissolved Oxygen
To
p v
iew
Sid
e vi
ew
Ο2
Air
•Excellent swimmers •No tumbling
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Bacterial Turbulence
Goldstein, Kessler, et al PRL 2004
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Schematics of Experimental Setup
Thin free-standing film concept
Adjustable thickness
Adjustable concentration of bacteria
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pH-Taxis & concentration of cells
1sec 20sec 80sec
concentration vs. time Bacteria crowd control
pH indicator (bromothynol blue) was added field of view
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Bacterial Turbulence
Sokolov, Goldstein, Kessler, I.A PRL (2007)
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7-fold reduction of viscosity
viscosity is extracted from the vortex decay time viscosity is extracted from the magnetic torqueviscosity vs concentration and swimming speed of bacteria
vortex probe micro-rheometerLiquid film with
bacteria
Supporting frame
Magnetic deflecting system
Movable probe
Probe induced vortex
rotational micro-rheometer
Collective behavior
Magnetic coils
Nickel
particle
Liquid film
with bacteria
viscosity vs concentration
Sokolov & I.A, PRL 2009
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Mixing and self-diffusivity in bacterial suspensionsOptical coherence tomography
Technical parameters
In-depth resolution = 15μm
Lateral resolution = 25μm
low coherence light source
photo detector
vertical scanning
reference mirror
beam splitter
deflecting system
3D concentration distribution
collective swimming enhances mixing by a factor of 10 confinement reduces mixing ratesnontrivial 3D patterns result in enhanced transport
Sokolov, Feldstein, Goldstein, I.A, PRE 2009
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Machines Powered by Bacteria:Rectification of Chaotic Motion
Sokolov, Apodaca, Grzybowski, I.A, PNAS, December 2009
Size of gears: 350 µm, SU-8 photoresist
Photolithography technique
Mass of Gear ~106 mass of bacteria
Collaboration with Bartosz Grzybowski, Northwestern University
0.5 mm
Lithographic Mask
Featured in NY Times,
Forbes, Wired, WDR, Sci American
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Gears Turned by Bacteria Click to edit Master text styles
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1 mm
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•1-2 rotations per minute •Power about 1 femtowatt=10-15 Watt
•About 300 bacteria power the gear
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Control of Rotation
•Rotation rate controlled by Oxygen/Nitrogen •Rotation rate depends on concentration
•Rotation enhanced by collective swimming
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Ratchet Mechanism of Rotation
•Bacteria slide along slanted edges •Trapped in junctions formed by the teeth
•Consistent with simulations by Angelini et al, PRL 2008
Trajectory of fluorescent tracers
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