1932

Abstract

In the past decade, the volvocine green algae, spanning from the unicellular to multicellular , have emerged as model organisms for a number of problems in biological fluid dynamics. These include flagellar propulsion, nutrient uptake by swimming organisms, hydrodynamic interactions mediated by walls, collective dynamics and transport within suspensions of microswimmers, the mechanism of phototaxis, and the stochastic dynamics of flagellar synchronization. Green algae are well suited to the study of such problems because of their range of sizes (from 10 μm to several millimeters), their geometric regularity, the ease with which they can be cultured, and the availability of many mutants that allow for connections between molecular details and organism-level behavior. This review summarizes these recent developments and highlights promising future directions in the study of biological fluid dynamics, especially in the context of evolutionary biology, that can take advantage of these remarkable organisms.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-010313-141426
2015-01-03
2024-06-20
Loading full text...

Full text loading...

/deliver/fulltext/fluid/47/1/annurev-fluid-010313-141426.html?itemId=/content/journals/10.1146/annurev-fluid-010313-141426&mimeType=html&fmt=ahah

Literature Cited

  1. Acrivos A, Taylor TD. 1962. Heat and mass transfer from single spheres in Stokes flow. Phys. Fluids 5:387–94 [Google Scholar]
  2. Adler R. 1946. A study of locking phenomena in oscillators. Proc. IRE 34:351–57 [Google Scholar]
  3. Adrian RJ. 1991. Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech. 23:261–304 [Google Scholar]
  4. Angelani L, Leonardo RD, Ruocco G. 2009. Self-starting micromotors in a bacterial bath. Phys. Rev. Lett. 102:048104 [Google Scholar]
  5. Bell G, Mooers AO. 1997. Size and complexity among multicellular organisms. Biol. J. Linn. Soc. 60:345–63 [Google Scholar]
  6. Bennett M, Schatz MF, Rockwood H, Wiesenfeld K. 2002. Huygen's clocks. Proc. R. Soc. Lond. A 458:563–79 [Google Scholar]
  7. Bennett RR, Golestanian R. 2013. Emergent run-and-tumble behavior in a simple model of Chlamydomonas with intrinsic noise. Phys. Rev. Lett. 110:148102 [Google Scholar]
  8. Berg HC. 1971. How to track bacteria. Rev. Sci. Instrum. 42:868–71 [Google Scholar]
  9. Berg HC, Brown DA. 1972. Chemotaxis in Escherichia coli analysed by three-dimensional tracking. Nature 239:500–4 [Google Scholar]
  10. Berg HC, Purcell EM. 1977. Physics of chemoreception. Biophys. J. 20:193–219 [Google Scholar]
  11. Berke AP, Turner L, Berg HC, Lauga E. 2008. Hydrodynamic attraction of swimming microorganisms by surfaces. Phys. Rev. Lett. 101:038102 [Google Scholar]
  12. Blake JR. 1971a. A note on the image system for a stokeslet in a no-slip boundary. Math. Proc. Camb. Philos. Soc. 70:303–10 [Google Scholar]
  13. Blake JR. 1971b. A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46:199–208 [Google Scholar]
  14. Blake JR, Chwang AT. 1974. Fundamental singularities of viscous flow. 1. Image systems in the vicinity of a stationary no-slip boundary. J. Eng. Math. 8:23–29 [Google Scholar]
  15. Bonner JT. 1998. The origins of multicellularity. Integr. Biol. 1:27–36 [Google Scholar]
  16. Bonner JT. 2004. Perspective: the size-complexity rule. Evolution 58:1883–90 [Google Scholar]
  17. Brennen C. 1974. Oscillating-boundary-layer theory for ciliary propulsion. J. Fluid Mech. 65:799–824 [Google Scholar]
  18. Brennen C, Winet H. 1977. Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9:339–98 [Google Scholar]
  19. Brokaw CJ. 1975. Molecular mechanism for oscillation in flagella and muscle. Proc. Natl. Acad. Sci. USA 72:3102–6 [Google Scholar]
  20. Brown R. 1828. A brief account of microscopical observations made in the months of June, July and August, 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies. Philos. Mag. 4:161–73 [Google Scholar]
  21. Brumley DR, Polin M, Pedley TJ, Goldstein RE. 2012. Hydrodynamic synchronization and metachronal waves on the surface of the colonial alga Volvox carteri. Phys. Rev. Lett. 109:268102 [Google Scholar]
  22. Brumley DR, Wan KY, Polin M, Goldstein RE. 2014. Flagellar synchronization through direct hydrodynamic interactions. eLife 3:02750
  23. Bruot N, Kotar J, de Lillo F, Lagomarsino MC, Cicuta P. 2012. Driving potential and noise level determine the synchronization state of hydrodynamically coupled oscillators. Phys. Rev. Lett. 109:164103 [Google Scholar]
  24. Camalet S, Jülicher F, Prost J. 1999. Self-organized beating and swimming of internally driven filaments. Phys. Rev. Lett. 82:1590–93 [Google Scholar]
  25. Catton KB, Webster DR, Brown J, Yen J. 2007. Quantitative analysis of tethered and free-swimming copepod flow fields. J. Exp. Biol. 210:299–310 [Google Scholar]
  26. Croft MT, Lawrence AD, Raux-Deery E, Warren MJ, Smith AG. 2005. Algae acquire vitamin B12 through a symbiotic relationship with bacteria. Nature 438:90–93 [Google Scholar]
  27. Crowdy DG, Samson O. 2011. Hydrodynamic bound states of a low-Reynolds-number swimmer near a gap in a wall. J. Fluid Mech. 667:309–35 [Google Scholar]
  28. Darwin C. 1953. Note on hydrodynamics. Math. Proc. Camb. Philos. Soc. 49:342–54 [Google Scholar]
  29. Dombrowski C, Cisneros L, Chatkaew S, Goldstein RE, Kessler JO. 2004. Self-concentration and large-scale coherence in bacterial dynamics. Phys. Rev. Lett. 93:098103 [Google Scholar]
  30. Drescher K, Dunkel J, Cisneros LH, Ganguly S, Goldstein RE. 2011. Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering. Proc. Natl. Acad. Sci. USA 108:10940–45 [Google Scholar]
  31. Drescher K, Goldstein RE, Michel N, Polin M, Tuval I. 2010a. Direct measurement of the flow field around swimming microorganisms. Phys. Rev. Lett. 105:168101 [Google Scholar]
  32. Drescher K, Goldstein RE, Tuval I. 2010b. Fidelity of adaptive phototaxis. Proc. Natl. Acad. Sci. USA 107:11171–76 [Google Scholar]
  33. Drescher K, Leptos K, Goldstein RE. 2009a. How to track protists in three dimensions. Rev. Sci. Instrum. 80:014301 [Google Scholar]
  34. Drescher K, Leptos K, Tuval I, Ishikawa T, Pedley T, Goldstein R. 2009b. Dancing Volvox: hydrodynamic bound states of swimming algae. Phys. Rev. Lett. 80:014301 [Google Scholar]
  35. Dunkel J, Heidenreich S, Drescher K, Wensink HH, Bar M, Goldstein RE. 2013. Fluid dynamics of bacterial turbulence. Phys. Rev. Lett. 110:228102 [Google Scholar]
  36. Dunkel J, Putz VB, Zaid IM, Yeomans JM. 2010. Swimmer-tracer scattering at low Reynolds number. Soft Matter 6:4268–76 [Google Scholar]
  37. Eckhardt B, Zammert S. 2012. Non-normal tracer diffusion from stirring by swimming microorganisms. Eur. Phys. J. E 35:96 [Google Scholar]
  38. Elfring GJ, Lauga E. 2011. Synchronization of flexible sheets. J. Fluid Mech. 674:163–73 [Google Scholar]
  39. Evans E, Rawicz W. 1990. Entropy-driven tension and bending elasticity in condensed-fluid membranes. Phys. Rev. Lett. 64:2094–97 [Google Scholar]
  40. Fauci LJ. 1990. Interaction of oscillatory filaments: a computational study. J. Comput. Phys. 86:294–313 [Google Scholar]
  41. Foster KW, Smyth RD. 1980. Light antennas in phototactic algae. Microbiol. Rev. 44:572–630 [Google Scholar]
  42. Friedrich BM, Jülicher F. 2007. Chemotaxis of sperm cells. Proc. Natl. Acad. Sci. USA 104:13256–61 [Google Scholar]
  43. Friedrich BM, Jülicher F. 2012. Flagellar synchronization independent of hydrodynamic interactions. Phys. Rev. Lett. 109:138102 [Google Scholar]
  44. Geyer VF, Jülicher F, Howard J, Friedrich BM. 2013. Cell-body rocking is a dominant mechanism for flagellar synchronization in a swimming alga. Proc. Natl. Acad. Sci. USA 110:18058–63 [Google Scholar]
  45. Ghose S, Adhikari R. 2014. Irreducible representations of oscillatory and swirling flows in active soft matter. Phys. Rev. Lett. 112:118102 [Google Scholar]
  46. Goldstein R, Polin M, Tuval I. 2009. Noise and synchronization in pairs of beating eukaryotic flagella. Phys. Rev. Lett. 103:168103 [Google Scholar]
  47. Goldstein RE, Polin M, Tuval I. 2011. Emergence of synchronized beating during the regrowth of eukaryotic flagella. Phys. Rev. Lett. 107:148103 [Google Scholar]
  48. Gray J. 1928. Ciliary Movement Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  49. Guasto JS, Johnson KA, Gollub JP. 2010. Oscillatory flows induced by microorganisms swimming in two dimensions. Phys. Rev. Lett. 105:168102 [Google Scholar]
  50. Guasto JS, Rusconi R, Stocker R. 2012. Fluid mechanics of planktonic microorganisms. Annu. Rev. Fluid Mech. 44:373–400 [Google Scholar]
  51. Guirao B, Joanny JF. 2007. Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia. Biophys. J. 92:1900–17 [Google Scholar]
  52. Guirao B, Meunier A, Mortaud S, Aguilar A, Corsi JM. et al. 2010. Coupling between hydrodynamic forces and planar cell polarity orients mammalian motile cilia. Nat. Cell Biol. 12:341–50 [Google Scholar]
  53. Hand WG, Haupt W. 1971. Flagellar activity of the colony members of Volvox aureus Ehrbg. during light stimulation. J. Protozool. 18:361–64 [Google Scholar]
  54. Harris EH. 2009. The Chlamydomonas Sourcebook: Introduction to Chlamydomonas and Its Laboratory Use New York: Academic [Google Scholar]
  55. Hiatt JDF, Hand WG. 1972. Do protoplasmic connections function in phototactic coordination of the Volvox colony during light stimulation?. J. Protozool. 19:488–89 [Google Scholar]
  56. Higdon JJL. 1979. The generation of feeding currents by flagellar motions. J. Fluid Mech. 94:305–30 [Google Scholar]
  57. Hirokawa N, Okada Y, Tanaka Y. 2009. Fluid dynamic mechanism responsible for breaking the left-right symmetry of the human body: the nodal flow. Annu. Rev. Fluid Mech. 41:53–72 [Google Scholar]
  58. Holmes SJ. 1903. Phototaxis in Volvox. Biol. Bull. 4:319–26 [Google Scholar]
  59. Hoops HJ, Brighton MC, Stickles SM, Clement PR. 1999. A test of two possible mechanisms for phototactic steering in Volvox carteri (Chlorophyceae). J. Phycol. 35:539–47 [Google Scholar]
  60. Horst CJ, Witman GB. 1993. ptx1, a nonphototactic mutant of Chlamydomonas, lacks control of flagellar dominance. J. Cell Biol. 120:733–41 [Google Scholar]
  61. Huygens C. 1893. Oeuvres complétes de Christiaan Huygens The Hague: Martinus Nijhoff [Google Scholar]
  62. Ibañez-Tallon I, Heintz H, Omran H. 2003. To beat or not to beat: roles of cilia in development and disease. Hum. Mol. Genet. 12:R27–35 [Google Scholar]
  63. Ishikawa T, Pedley TJ. 2008. Coherent structures in monolayers of swimming particles. Phys. Rev. Lett. 100:088103 [Google Scholar]
  64. Jékely G. 2009. Evolution of phototaxis. Philos. Trans. R. Soc. B 364:2795–808 [Google Scholar]
  65. Jékely G, Columbelli J, Hausen H, Guy K, Stelzer E. et al. 2008. Mechanism of phototaxis in marine zooplankton. Nature 456:395–99 [Google Scholar]
  66. Jennings HS. 1901. On the significance of the spiral swimming of organisms. Am. Nat. 35:369–78 [Google Scholar]
  67. Kamiya R, Witman GB. 1984. Submicromolar levels of calcium control the balance of beating between the two flagella in demembranated models of Chlamydomonas. J. Cell Biol. 98:97–107 [Google Scholar]
  68. Kantsler V, Dunkel J, Polin M, Goldstein RE. 2013. Ciliary contact interactions dominate surface scattering of swimming eukaryotes. Proc. Natl. Acad. Sci. USA 110:1187–92 [Google Scholar]
  69. Kim MJ, Bird JC, Parys AJV, Breuer KS, Powers TR. 2003. A macroscopic scale model for bacterial flagellar bundling. Proc. Natl. Acad. Sci. USA 100:15481–85 [Google Scholar]
  70. King N. 2004. The unicellular ancestry of animal development. Dev. Cell 7:313–25 [Google Scholar]
  71. Kirk DL. 1998. Volvox: Molecular-Genetic Origins of Multicellularity and Cellular Differentiation Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  72. Knight-Jones EW. 1954. Relations between metachronism and the direction of ciliary beat in metazoa. Q. J. Microsc. Sci. 95:503–21 [Google Scholar]
  73. Kotar J, Debono L, Bruot N, Box S, Phillips D. et al. 2013. Optimal hydrodynamic synchronization of colloidal rotors. Phys. Rev. Lett. 111:228103 [Google Scholar]
  74. Koufopanou V, Bell G. 1993. Soma and germ: an experimental approach using Volvox. Proc. R. Soc. B 254:107–13 [Google Scholar]
  75. Kurtuldu H, Guasto JS, Johnson KA, Gollub JP. 2011. Enhancement of biomixing by swimming algal cells in two-dimensional films. Proc. Natl. Acad. Sci. USA 108:10391–95 [Google Scholar]
  76. Lauga E, Goldstein RE. 2012. Dance of the microswimmers. Phys. Today 65:30–35 [Google Scholar]
  77. Lauga E, Powers TR. 2009. The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72:096601 [Google Scholar]
  78. Lechtreck KF, Melkonian M. 1991. An update on fibrous flagellar roots in green algae. Protoplasma 164:38–44 [Google Scholar]
  79. Leoni M, Liverpool TB. 2012. Hydrodynamic synchronization of nonlinear oscillators at low Reynolds number. Phys. Rev. E 85:040901 [Google Scholar]
  80. Leptos KC, Guasto JS, Gollub JP, Pesci AI, Goldstein RE. 2009. Dynamics of enhanced tracer diffusion in suspensions of swimming eukaryotic microorganisms. Phys. Rev. Lett. 103:198103 [Google Scholar]
  81. Leptos KC, Wan KY, Polin M, Tuval I, Pesci AI, Goldstein RE. 2013. Antiphase synchronization in a flagellar-dominance mutant of Chlamydomonas. Phys. Rev. Lett. 111:158101 [Google Scholar]
  82. Li G, Tang JX. 2009. Accumulation of microswimmers near a surface mediated by collision and rotational Brownian motion. Phys. Rev. Lett. 103:078101 [Google Scholar]
  83. Lighthill MJ. 1952. On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun. Pure Appl. Math. 5:109–18 [Google Scholar]
  84. Lin Z, Thiffeault JL, Childress S. 2011. Stirring by squirmers. J. Fluid Mech. 669:167–77 [Google Scholar]
  85. Linnaeus C. 1758. Systema Naturae Holmiae: Impensis Laurentii Salvii [Google Scholar]
  86. Magar V, Goto G, Pedley TJ. 2003. Nutrient uptake by a self-propelled steady squirmer. Q. J. Mech. Appl. Math. 56:65–91 [Google Scholar]
  87. Magar V, Pedley TJ. 2005. Average nutrient uptake by a self-propelled unsteady squirmer. J. Fluid Mech. 539:93–112 [Google Scholar]
  88. Michelin S, Lauga E. 2010. Efficiency optimization and symmetry-breaking in a model of ciliary locomotion. Phys. Fluids 22:111901 [Google Scholar]
  89. Michelin S, Lauga E. 2011. Optimal feeding is optimal swimming for all Péclet numbers. Phys. Fluids 23:101901 [Google Scholar]
  90. Mitchison TJ, Mitchison HM. 2010. Cell biology: how cilia beat. Nature 463:308–9 [Google Scholar]
  91. Müller UK, van den Heuvel BLE, Stamhuis EJ, Videler JJ. 1997. Fish foot prints: morphology and energetics of the wake behind a continuously swimming mullet (Chelon labrosus Risso). J. Exp. Biol. 200:2893–906 [Google Scholar]
  92. Niedermayer T, Eckhardt B, Lenz P. 2008. Synchronization, phase locking, and metachronal wave formation in ciliary chains. Chaos 18:037128 [Google Scholar]
  93. Orme BAA, Blake JR, Otto SR. 2003. Modelling the motion of particles around choanoflagellates. J. Fluid Mech. 475:333–55 [Google Scholar]
  94. Pazour GJ, Agrin N, Leszyk J, Witman GB. 2005. Proteomic analysis of a eukaryotic cilium. J. Cell. Biol. 170:103–13 [Google Scholar]
  95. Pedley TJ, Kessler JO. 1992. Hydrodynamic phenomena in suspensions of swimming microorganisms. Annu. Rev. Fluid Mech. 24:313–58 [Google Scholar]
  96. Pepper RE, Roper M, Ryu S, Matsudaira P, Stone HA. 2010. Nearby boundaries create eddies near microscopic filter feeders. J. R. Soc. Interface 7:851–62 [Google Scholar]
  97. Pettitt ME, Orme BAA, Blake JR, Leadbeater BSC. 2002. The hydrodynamics of filter feeding in choanoflagellates. Eur. J. Protistol. 38:313–32 [Google Scholar]
  98. Polin M, Tuval I, Drescher K, Gollub JP, Goldstein RE. 2009. Chlamydomonas swims with two “gears” in a eukaryotic version of run-and-tumble locomotion. Science 325:487–90 [Google Scholar]
  99. Prochnik SE, Umen J, Nedelcu AM, Hallmann A, Miller SM. et al. 2010. Genomic analysis of organismal complexity in the multicellular green alga Volvox carteri. Science 329:223–26 [Google Scholar]
  100. Pushking DO, Shum H, Yeomans JM. 2013. Fluid transport by individual microswimmers. J. Fluid Mech. 726:5–25 [Google Scholar]
  101. Rafai S, Jibuti L, Peyla P. 2010. Effective viscosity of microswimmer suspensions. Phys. Rev. Lett. 104:098102 [Google Scholar]
  102. Ratcliff WC, Denison RF, Borrello M, Travisano M. 2012. Experimental evolution of multicellularity. Proc. Natl. Acad. Sci. USA 109:1595–600 [Google Scholar]
  103. Ratcliff WC, Herron MD, Howell K, Pentz JT, Rosenzweig F, Travisano M. 2013. Experimental evolution of an alternating uni- and multicellular life cycle in Chlamydomonas reinhardtii. Nat. Commun. 4:2742 [Google Scholar]
  104. Riedel-Kruse IH, Hilfinger A, Howard J, Jülicher F. 2007. How molecular motors shape the flagellar beat. HFSP J. 1:192–208 [Google Scholar]
  105. Roper M, Dayel MJ, Pepper RE, Koehl MAR. 2013. Cooperatively generated stresslet flows supply fresh fluid to multicellular choanoflagellate colonies. Phys. Rev. Lett. 110:228104 [Google Scholar]
  106. Rothschild L. 1949. Measurement of sperm activity before artificial insemination. Nature 163:358–59 [Google Scholar]
  107. Rüffer U, Nultsch W. 1985. High-speed cinematographic analysis of the movement of Chlamydomonas. Cell Motil. Cytoskelet. 5:251–63 [Google Scholar]
  108. Rüffer U, Nultsch W. 1987. Comparison of the beating of cis- and trans-flagella of Chlamydomonas cells held on micropipettes. Cell Motil. Cytoskelet. 7:87–93 [Google Scholar]
  109. Rüffer U, Nultsch W. 1997a. Flagellar coordination in Chlamydomonas cells held on micropipettes. Cell Motil. Cytoskelet. 41:297–307 [Google Scholar]
  110. Rüffer U, Nultsch W. 1997b. Flagellar photoresponses of ptx1, a nonphototactic mutant of Chlamydomonas. Cell Motil. Cytoskelet. 37:111–19 [Google Scholar]
  111. Rushkin I, Kantsler V, Goldstein R. 2010. Fluid velocity fluctuations in a suspension of swimming protists. Phys. Rev. Lett. 105:188101 [Google Scholar]
  112. Schaller K, David R, Uhl R. 1997. How Chlamydomonas keeps track of the light once it has reached the right phototactic orientation. Biophys. J. 73:1562–72 [Google Scholar]
  113. Schmidt JA, Eckert R. 1976. Calcium couples flagellar reversal to photostimulation in Chlamydonas reinhardtii. Nature 262:713–15 [Google Scholar]
  114. Short MB, Solari CA, Ganguly S, Powers TR, Kessler JO, Goldstein RE. 2006. Flows driven by flagella of multicellular organisms enhance long-range molecular transport. Proc. Natl. Acad. Sci. USA 103:8315–19 [Google Scholar]
  115. Smith JM, Szathmáry E. 1995. The Major Transitions in Evolution San Francisco: Freeman [Google Scholar]
  116. Solari CA, Drescher K, Ganguly S, Kessler JO, Michod RE, Goldstein RE. 2011. Flagellar phenotypic plasticity of volvocalean algae correlates with Péclet number. J. R. Soc. Interface 8:1409–17 [Google Scholar]
  117. Solari CA, Ganguly S, Kessler JO, Michod RE, Goldstein RE. 2006a. Multicellularity and the functional interdependence of motility and molecular transport. Proc. Natl. Acad. Sci. USA 103:1353–58 [Google Scholar]
  118. Solari CA, Kessler JO, Goldstein RE. 2007. Motility, mixing, and multicellularity. Genet. Prog. Evol. Mach. 8:115–29 [Google Scholar]
  119. Solari CA, Kessler JO, Michod RE. 2006b. A hydrodynamics approach to the evolution of multicellularity: flagellar motility and germ-soma differentiation in volvocalean green algae. Am. Nat. 167:537–54 [Google Scholar]
  120. Squires TM. 2001. Effective pseudo-potentials of hydrodynamic origin. J. Fluid Mech. 443:403–12 [Google Scholar]
  121. Squires TM, Brenner MP. 2000. Like-charge attraction and hydrodynamic interaction. Phys. Rev. Lett. 85:4976–79 [Google Scholar]
  122. Stone HA, Samuel ADT. 1996. Propulsion of microorganisms by surface distortions. Phys. Rev. Lett. 77:4102–4 [Google Scholar]
  123. Szathmáry E, Smith JM. 1995. The major evolutionary transitions. Nature 374:227–32 [Google Scholar]
  124. Tam D, Hosoi AE. 2011. Optimal feeding and swimming gaits of biflagellated organisms. Proc. Natl. Acad. Sci. USA 108:1001–6 [Google Scholar]
  125. Taylor GI. 1951. Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209:447–61 [Google Scholar]
  126. Toner J, Tu Y. 1995. Long-range order in a two-dimensional dynamical XY model: how birds fly together. Phys. Rev. Lett. 75:4326–29 [Google Scholar]
  127. Turner L, Ryu WS, Berg HC. 2000. Real-time imaging of fluorescent flagellar filaments. J. Bacteriol. 182:2793–801 [Google Scholar]
  128. Uchida N, Golestanian R. 2011. Generic conditions for hydrodynamic synchronization. Phys. Rev. Lett. 106:058104 [Google Scholar]
  129. Uchida N, Golestanian R. 2012. Hydrodynamic synchronization between objects with cyclic rigid trajectories. Eur. Phys. J. E 35:135 [Google Scholar]
  130. Ueki N, Matsunaga S, Inouye I, Hallmann A. 2010. How 5000 independent rowers coordinate their strokes in order to row into the sunlight: phototaxis in the multicellular green alga Volvox. BMC Biol. 8:103 [Google Scholar]
  131. van Leeuwenhoek A. 1700. IV. Part of a letter from Mr. Antony van Leeuwenhoek, concerning the worms in sheeps livers, gnats, and animalcula in the excrements of frogs. Philos. Trans. R. Soc. 22:509–18 [Google Scholar]
  132. Vicsek T, Czirok A, Jacob EB, Cohen I, Shochet O. 1995. Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75:1226–29 [Google Scholar]
  133. Vilfan A, Jülicher F. 2006. Hydrodynamic flow patterns and synchronization of beating cilia. Phys. Rev. Lett. 96:058102 [Google Scholar]
  134. Wan KY, Leptos KC, Goldstein RE. 2014. Lag, lock, sync, slip: the many ‘phases’ of coupled flagella. J. R. Soc. Interface 11:20131160 [Google Scholar]
  135. Wang B, Anthony SM, Bae SC, Granik S. 2009. Anomalous yet Brownian. Proc. Natl. Acad. Sci. USA 106:15160–64 [Google Scholar]
  136. Weismann A. 1892. Essays on Heredity and Kindred Biological Problems Oxford: Clarendon [Google Scholar]
  137. Wu XL, Libchaber A. 2000. Particle diffusion in a quasi-two-dimensional bacterial bath. Phys. Rev. Lett. 84:3017–20 [Google Scholar]
  138. Yoshimura K, Kamiya R. 2001. The sensitivity of Chlamydomonas photoreceptor is optimized for the frequency of cell body rotation. Plant Cell Physiol. 42:665–72 [Google Scholar]
  139. Zaid IM, Dunkel J, Yeomans JM. 2011. Lévy fluctuations and mixing in dilute suspensions of algae and bacteria. J. R. Soc. Interface 8:1314–31 [Google Scholar]
/content/journals/10.1146/annurev-fluid-010313-141426
Loading
/content/journals/10.1146/annurev-fluid-010313-141426
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error