Daiki Nishiguchi 1 Department of Physics, The University of Tokyo PhD student (D3) at Sano Lab. Ken H. Nagai (JAIST) Hugues Chaté (CEA-Saclay, CSRC-Beijing) Masaki Sano (The University of Tokyo) Big Waves of Theoretical Sciences in Okinawa @ OIST (arXiv:1604.04247) Long-range nematic order & anomalous fluctuations in collective motion of filamentous bacteria
Collective motion of self-propelled particles ・Consume some kind of energy at the particle level (intrinsically nonequilibrium) ・Direction of motion is determined not solely by external force, but by internal degree of freedom. 2 ■Examples of “Collective motion” H. P. Zhang (2010) school of jack tuna (www.youtube.com/watch?v=D6HdoIsLMFg) bird flock (www.youtube.com/watch?v=_tEFRAI9WSE) polarity・shape・cell cycle... ■Characteristics of “self-propelled particles” Bacillus subtilis ( 枯草菌 )
A big wave in theoretical active matter noise ↘ transition order-disorder →We want to realize such experiments, if possible, with biological systems! ・However, no corresponding experiments yet. ・Many studies on Vicsek-like models regarding collective behavior. ■Vicsek model or 3 density ↗ uniformly distributed on : white noise ↑average angle of particles inside radius R ■Our motivation Vicsek, et al. Phys. Rev. Lett. 75, 6 (1995) (1st order)
A big wave in theoretical active matter noise ↘ transition order-disorder →We want to realize such experiments, if possible, with biological systems! ・However, no corresponding experiments yet. ・Many studies on Vicsek-like models regarding collective behavior. ■Vicsek model or 3 density ↗ uniformly distributed on : white noise ↑average angle of particles inside radius R ■Our motivation Vicsek, et al. Phys. Rev. Lett. 75, 6 (1995) (1st order)
A big wave in theoretical active matter noise ↘ transition order-disorder →We want to realize such experiments, if possible, with biological systems! ・However, no corresponding experiments yet. ・Many studies on Vicsek-like models regarding collective behavior. ■Vicsek model or 3 density ↗ uniformly distributed on : white noise ↑average angle of particles inside radius R ■Our motivation Vicsek, et al. Phys. Rev. Lett. 75, 6 (1995) (1st order)
A big wave in theoretical active matter noise ↘ transition order-disorder →We want to realize such experiments, if possible, with biological systems! ・However, no corresponding experiments yet. ・Many studies on Vicsek-like models regarding collective behavior. ■Vicsek model or 3 density ↗ uniformly distributed on : white noise ↑average angle of particles inside radius R ■Our motivation Vicsek, et al. Phys. Rev. Lett. 75, 6 (1995) (1st order)
4 ■What is number fluctuation? Goldstone modes in the ordered state. ・Note: GNF is associated with Nambu- ・Due to numerics and continuum theory: →giant number fluctuation (GNF) in the homogeneous ordered state. ・Exponent larger than 0.5 Chaté, et al. Eur. Phys. J. B 64, 451 (2008), Toner and Tu Phys. Rev. E 58, 4 (1998) ■What about in Vicsek model? (Central limit theorem) in equilibrium or random systems (standard deviation) ：fluctuation ：mean value Properties: Giant Number Fluctuations (GNF) at time t. ：# of observed particles Giant fluctuations Normal fluctuations
Vicsek-like models with different symmetry 5 Phys. Rev. Lett. 104, 184502 (2010) Ginelli, et al. nematic ordered state→ ■Self-propelled rods Phys. Rev. Lett. 113, 038302 (2014) Ngo, et al. cf：Vicsek model ■Active nematics e.g.: Bacteria e.g. ： shaken rods Narayan, et al. Science, 317, 6 (2007). Vicsek'model ac-ve'nema-cs self1propelled'rods mo-lity polar apolar polar interac-on polar nema-c nema-c GNF'(numerics) ~'0.8 ~'0.8 ~'0.75 GNF'(con-nuum) 0.8'(exact) 1'(linear'theory) controversial order True'LRO Quasi1LRO True1LRO
Exponents in continuum theories ■Vicsek model (Toner-Tu theory) ■Active nematics (Ramaswamy, et al) ・From symmetry arguments, hydrodynamic equations can be written: ・Dynamical renomalization group method can derive the exponent in 2D. ・Exponents of GNF is only known for linear theory. ・Some theoreticians believes that phenomenologies on active nematics and self-propelled rods should be the same. 6 Vicsek'model ac-ve'nema-cs self1propelled'rods mo-lity polar apolar polar interac-on polar nema-c nema-c GNF'(numerics) ~'0.8 ~'0.8 ~'0.75 GNF'(con-nuum) 0.8'(exact) 1'(linear'theory) controversial order True'LRO Quasi1LRO True1LRO Toner & Tu, PRL, 75, 23 (1995). Ramaswamy, et al. EPL, 62(2), 196, (2003). Mishra, et al., J. Stat. Mech., (2010) P02003. ↑ Symmetric Traceless part
Observation of “GNF” 7 Bacillus subtilis Zhang, Beér, Florin & Swinney (PNAS 2010) shaken rods ← These GNF is trivial because of their obvious structures. Narayan, Ramaswamy & Menon (Science 2007)
8 Schaller, et al. Nature, 467, 73 (2008) Schaller and Bausch, PNAS, 110, 4488 (2013) Deseigne, et al. Phys. Rev. Lett. 05,098001 (2010) Observation of “GNF” : variance motility assay shaken polar disks
→Realize experimental systems that exhibit homogeneous ordered states! boundary effects 105, 098001 (2010) Phys. Rev. Lett. Deseigne, et al. PNAS, 110, 4488 (2013) Schaller and Bausch, boundary effects clustering clustering banding not ordered clustering not ordered →Looking at fluctuations not in homogeneous ordered states. ・However, these GNFs came from effects of boundary or clustering. ・Many experiments report GNF, although it’s not their main claims. Observed GNF in previous experiments Bacillus subtilis motility assay shaken rods shaken polar disks Zhang, et al. PNAS, Narayan, et al. 107, 31, 13626 (2010). Science, 317, 6 (2007).
What kind of experiments is required? →Sandwich them between two walls to suppress flow. Phys. Rev. E DN & M. Sano, ■Design principles for homogeneous ordered phases →use higher-aspect-ratio particles ・To realize an ordered state, stronger alignment is required. (The thinner, the more collisions. 2D is easier to observe.) destabilize ordered states. 10 ・Flow fields of bacteria (pusher-type swimmer) →Use bacteria. (→Demonstrations with biological systems is important!) →microswimmers (e.g. self-propelled colloids or bacteria) →µm-scale particles are preferable. ・Far from boundaries, a large number of particles to see statistics. (avoid complicated interactions) ・As simple as possible to compare with numerical models. 92, 052309 (2015) Janus colloids
11 particles：filamentous E. coli High-aspect-ratio bacteria 10μm real speed 20-100 μm
Experimental procedure 12 Making filamentous cells Concentrate the suspension Confine in an observation device Observe and analyze
13 ■procedure ・Add an antibiotic that inhibits cell division to the suspension of E.coli (strain: RP437 or RP4979). ・The length of E.coli can be controlled by changing the incubation time. real speed Making filamentous cells usual E.coli（2-3 µm） filamentous cells（30-40 µm） antibiotic 20 µm
Experimental procedure 14 Making filamentous cells Concentrate the suspension Confine in an observation device Observe and analyze
Experimental procedure 15 Making filamentous cells Concentrate the suspension Confine in an observation device Observe and analyze
What kind of experiments is required? →Sandwich them between two walls to suppress flow. Phys. Rev. E Nishiguchi & Sano, ■Experimental Systems for realizing homogeneous ordered states →use higher-aspect-ratio particles ・To realize an ordered state, stronger alignment is required. (The thinner, the more collisions. 2D is easier to observe.) destabilize ordered states. 16 ・Flow fields of bacteria (pusher-type swimmer) →First introduce bacterial experiments!! (→Demonstrations with biological systems is important!) →microswimmers (e.g. self-propelled colloids or bacteria) →µm-scale particles are preferable. ・Far from boundaries, a large number of particles to see statistics. (avoid complicated interactions) ・As simple as possible to compare with numerical models. 92, 052309 (2015) Janus colloids
Observation Device 17 excitation light ・Oxygen is required for high motility. ・PDMS(polymeric organo silicon) is transparent to oxygen. ・Make patterns on PDMS so that excessive suspension escapes into halls. ・Gap between glass and PDMS: smaller than 2µm O 2 seal PDMS Objective lens Concentrated suspension Coverslip
Experimental procedure 18 Making filamentous cells Concentrate the suspension Confine in an observation device Observe and analyze
Swimming at low density 19 ・Used strain: RP4979(ΔcheY, YFP), chemotactic mutant →no tumbling, swim smoothly, exclude artifacts. some cells swim together after collisions→ 50μm x40 objective lens captured@10fps, real speed wildtype with tumbling mutants without tumbling →motility is polar!
Interactions are nematic! 20 acute angle →parallel alignment obtuse angle →anti-parallel alignment 0 s 0.2 s 0.4 s 0.6 s time 20µm
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