微生物の集団遊泳と懸濁液内の輸送現象 石川拓司. 東北大学大学院工学研究科 URL :

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1 微生物の集団遊泳と懸濁液内の輸送現象 石川拓司 東北大学大学院工学研究科 ishikawa@pfsl.mech.tohoku.ac.jp URL :

2 Introduction The role of the infinitely small in nature is infinitely large. Louis Pasteur ( ) Micro-organisms in the ocean 50% of biomass Bottom of food chain Oceanic ecosystem Absorption of CO Nitrogen cycle Global environment Plankton blooms around Australia and New Zealand Picture from Byatt et al. (001)

3 Micro-organisms in bioreactors Making food Yeast, Lactic acid bacterium Introduction Food industry Sewage treatment Plant industry Algae fuel an alternative to fossil fuel Energy revolution?

4 Introduction Micro-organisms in human body Helicobacter pylori in the stomach hundreds of species about cells Digestion helped by enterobacteria (vitamin K) from Introduction to Microbiology Infection by salmonella Reproduction owed to sperm swimming from Introduction to Microbiology from Introduction to Microbiology

5 Artificial Micro-swimmers Introduction Sanchez, et al. (011) Thutupalli, et al. (011) Dreyfus et al. (005)

6 Introduction In order to understand variety of micro-organisms phenomena Ecology, Biology & Chemistry have been used. One example of bacterial phenomena In this suspension, chemical substances spread 10 3 times more than the Brownian diffusion. Can we explain this by ecology, biology or chemistry? Biophysics & biomechanics can contribute more in this field A suspension of Escherichia coli

7 Bottom-up Strategy Macroscopic level Rheological and Diffusion properties Strong influence Mesoscale level Collective motions, Coherent structures Strong influence Cellular level Cell-cell interactions Bottom-up Strategy

8 Outline of the talk Introduction Biomechanics of an individual and a pair of micro-organisms Collective swimming in meso-scale Macroscopic properties of a suspension of micro-organisms Conclusions

9 Classification of micro-organisms In terms of swimming motion Ciliate Flagellate (eukaryote) Volvox Paramecium Euglena wave relative to body body wave Bacteria w x E. coli body W

10 Hydrodynamics of a single cell Flow field Size of a single cell: 1-100mm Swimming speed: 1-10 body length / sec Re = Stokes flow (Inertia-free) Force-Torque condition of a cell Force is almost free g Torque may not be free (bottom-heaviness) Review paper Brennen & Winet, Ann. Rev. Fluid Mech. (1977) Lauga & Powers, Rep. Prog. Phys. (009) When two cells come close, what happens? e h

11 Experiment of Paramecia Paramecium caudatum Approximately 50mm in length 50mm in width Experimental Setup Digital video camera Light source Light source Macro lens Inner dish Paramesium swim between flat plats with 70mm gap. Test fluid Outer dish 70mm

12 Biological reaction Avoiding Reaction (AR) Anterior end: Ca + channel Escape Reaction (ER) Posterior end: K + channel Ishikawa and Hota, J. Exp. Biol. (006)

13 Hydrodynamic interaction Initially facing each other Two orientation vectors initially have a large angle Ishikawa and Hota, J. Exp. Biol. (006)

14 Experimental results Ratio of three kinds of interaction The total number of experimental cases recorded in this study is 301, and the total number of cells is 60. Kinds of interaction Number of cells Percent [%] Hydrodynamic Interaction (HI) Avoiding Reaction (AR) Escape Reaction (ER) Ishikawa and Hota, J. Exp. Biol. (006) Mainly hydrodynamic interaction

15 How to model Paramecium? Squirmer model assumed to propel itself by generating tangential velocities on its surface. Surface velocity is given as a B.C. Velocity field around Paramecium 1.5 PIV u s experimental results 0 1 3

16 Flow Field: Boundary Element Method u i Numerical Methods Paramecium: Force-free, Torque-free Ishikawa et al., J. Fluid Mech. (006) ( x) u i ( x) 1 8m N 1 A J ij ( x y) q j ( y) da q : single-layer potential A : surface of a particle u : velocity J : Green function y

17 Numerical Results 1 500mm 500mm Agree with the experiment Ishikawa and Hota, J. Exp. Biol. (006) 1

18 Waltzing motion of Volvox A waltzing motion was found by R.E.Goldstein s group. Mechanism: Biological? Hydrodynamical? for fertilization?

19 Resluts : effect of Bottom-heaviness G bh =50 : bottom-heavy (l = 5deg) Waltzing motion does appear

20 Waltzing motion of Volvox The waltzing motion can be reproduced by introducing: (a) A wall boundary (b) Bottom-heaviness (c) Swirl velocity Mechanism = Hydrodynamics Drescher et al., Phys. Rev. Lett. (009)

21 Outline of the talk Introduction Biomechanics of an individual and a pair of micro-organisms Collective swimming in meso-scale Macroscopic properties of a suspension of micro-organisms Conclusions

22 Bio-convection A suspension of Chlamydomonas Mechanism: upswimming of cells that are slightly denser than water generates unstable density stratification which leads to overturning

23 Other collective motions Band formation Slow turbulence Band formation of magnetotactic bacteria. Picture from Guell et al., J. Theor. Biol. (1988) Colonies on agar gel Complex patten of bacterial colonies. Picture from Ben- Jacob & Levine (006) Cell motions of Bacillus subtilis. Movie from Goldstein Lab, Mechanism = Physics? Mechanics?

24 Stokesian-dynamics simulation Micro-organism : Spherical squirmer model Multipole Expansion of the boundary integral equation m m klj ij l k jk ijk j ij j ij N y j A ij i i Q J S K a L R F J a da q J u u ) ( ) ( 8 1 ) ( ) ( y y x x x ( ( ) ( ) ( ) ( ) ( 1 8 ) ( ) ( ) ( m m m w m x x x x x x x j i i j ij j i ij ij k j ijk i i i i i i i i u u a e e B a a S E u a L u a e B a F u U W Faxen Laws + : Ewald sumation Ishikawa et al., J. Fluid Mech. (008)

25 Stokesian-dynamics simulation Then, inclusion of near-field lubrication forces ( near sq near sq near sq sq far B far near B far B far B B S L F I ee Q e R R E ω Ω u U R R R S L F Effect of squirming motion Database compiled by BEM cf. Brady & Bossis, Annu. Rev. Fluid Mech. (1988) For details : Ishikawa et al., J. Fluid Mech. (008)

26 Results: Aggregation Monolayer Non-bottom-heavy a =0.1 Periodic B.C. Hydrodynamic interaction only Ishikawa & Pedley Phys. Rev. Lett. (008)

27 Results: Band formation Monolayer Bottom-heavy a =0.5, G bh =100 G bh gah mb 1 Ishikawa & Pedley Phys. Rev. Lett. (008)

28 Results: 3D Large scale Bioconvection Bottom-Heavy Sedimentation Periodic B.C.

29 Coherent structures Various collective motions observed in former experiments can be expressed Meso-scale spatiotemporal motion Ordered motion How coherent structures affect transport phenomena? Diffusion of particles Wu & Libchaber (000) Energy is transported towards larger scale?

30 Energy transport in a bacterial bath Confocal mpiv system E. coli : MG1655 (wildtype) Lima, et al., Meas. Sci. Technol. (006) Sample confocal image 3D velocity field can be measured with high spacial and time resolusions

31 Energy transport in a bacterial bath In-plane vorticity Iso-surfaces of W z = 1.3 and -1.3 s -1 are drawn by red and blue, respectively. Energy dissipation on meso-scale n rot v J/(s.mL) / number density of = individual bacteria dissipate energy of J/(s.cell) on the meso-scale. Is this a large portion of energy input?

32 Energy transport in a bacterial bath Energy dissipation of a solitary bacteria BEM model Cell body: ellipsoid ( 1 μm) Flagella length: 6 μm Swimming velocity: 0 μm/s Energy input: J/s Used for swimming: J/s (=0.36pN 0μm/s) Used for the coherent structure: J/s Giacche et al., PRE (010) Gain from the coherent structure: Enhanced diffusion High swimming velocity Useful to expand the biosphere? Ishikawa, et al., Phys. Rev. Lett. (011)

33 Outline of the talk Introduction Biomechanics of an individual and a pair of micro-organisms Collective swimming in meso-scale Macroscopic properties of a suspension of micro-organisms Conclusions

34 Rheological properties Stress field generated by a solitary cell Stress field is opposite A bottom-heavy cell in a shear flow g g Orientation changes

35 Rheological properties Shear viscosity (compared to dead cell suspensions) Horizontal shear Increase Vertical shear Decrease Decrease Increase

36 apparent viscosity Rheological properties Shear viscosity : Suspension of Squirmers vertical, harizontal xy, xy yx, yx Ishikawa & Pedley, J. Fluid Mech. (007)

37 Diffusion properties Cell Conservation (continuum model) Dn ( nv c Jr Dt [+ birth, death, etc] where V c = mean cell swimming velocity, J r = flux due to random cell swimming J r D n? Definition of D D r( t t ) r( t ) r( t t ) ( t ) r lim t t 0

38 square displacement Self-diffusion of cells 10 3 Diffusion properties translational rotational (b 5, 0.1 y = c x y = c x time interval Ishikawa & Pedley, J. Fluid Mech. (007) The spreading is correctly described as a diffusive process

39 y Large Scale Example in Nature Thin layers of plankton are important hotspots of ecological activity Red tide Durham et al., Science (009) Continuum model: c. ( V Ud c. D. c t Thin layer is also formed in this system c = 0.1 t = 0 t = 500 t = 1000 t = 10

40 Horizontal Poiseuille Flow Engineering settings: Horizontal Poiseuille flow Flow: D, parabolic Cells: Bottom-heavy squirmers Inlet concentration: uniform (c = 0.0) g High concentration appears near the upper wall. Volume fraction of bottom-heavy cells in the channel becomes larger than that at the inlet. Ishikawa, J. Fluid Mech. (01)

41 Applications: Population dynamics Microbial flora in the intestine 50a Simultaneously solving: - Flow field generated by peristalsis - Concentrations of oxygen and nutrient - Densities of anaerobes and aerobes flow direction flow direction flow direction (a) aerobe (b) anaerobe (c) oxygen x10 7 [cell/ l ] 1.5x10 4 [cell/ l ] 8x10-3 [mol / l ] flow direction 0 0.1[mol / l ] Ishikawa et al., J. Theor. Biol. (011) (d) nutrient

42 Conclusions By using the bottom-up strategy, suspension biomechanics of swimming microbes can be clarified much further. Such mathematical modeling should be expanded to various phenomena in nature.

43 Acknowledgements Collaborators on this topic T. J. Pedley (Cambridge) R. E. Goldstein (Cambridge) E. Lauga (UCSD) S. Herminghaus (Max Planck) Prof. T. Yamaguchi (Tohoku Univ.) Lab members Grant NEXT Program by the JSPS Tohoku Univ. Global COE Program Thank you for your listening