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Experimental Mechanics

, Volume 50, Issue 9, pp 1303–1311 | Cite as

The Effects of Fluid Viscosity on the Kinematics and Material Properties of C. elegans Swimming at Low Reynolds Number

  • J. Sznitman
  • X. Shen
  • P. K. Purohit
  • P. E. Arratia
Article

Abstract

The effects of fluid viscosity on the kinematics of a small swimmer at low Reynolds numbers are investigated in both experiments and in a simple model. The swimmer is the nematode Caenorhabditis elegans, which is an undulating roundworm approximately 1 mm long. Experiments show that the nematode maintains a highly periodic swimming behavior as the fluid viscosity is varied from 1.0 to 12 mPa s. Surprisingly, the nematode’s swimming speed (~0.35 mm/s) is nearly insensitive to the range of fluid viscosities investigated here. However, the nematode’s beating frequency decreases to an asymptotic value (~1.7 Hz) with increasing fluid viscosity. A simple model is used to estimate the nematode’s Young’s modulus and tissue viscosity. Both material properties increase with increasing fluid viscosity. It is proposed that the increase in Young’s modulus may be associated with muscle contraction in response to larger mechanical loading while the increase in effective tissue viscosity may be associated with the energy necessary to overcome increased fluid drag forces.

Keywords

Swimming Low Reynolds number Material properties Kinematics Caenorhabditis elegans 

Notes

Acknowledgements

The authors would like to thank T. Lamitina for helpful discussions. Some nematode strains used in this work were provided by the Caenorhabditis Genetics Center, which is funded by the NIH National Center for Research Resources (NCRR).

References

  1. 1.
    Brennen C, Winet H (1977) Fluid mechanics of propulsion by cilia and flagella. Annu Rev Fluid Mech 9:339CrossRefGoogle Scholar
  2. 2.
    Childress S (1981) Mechanics of swimming and flying. Cambridge University Press, CambridgeMATHCrossRefGoogle Scholar
  3. 3.
    Vogel S (1994) Life in moving fluids. Princeton University Press, PrincetonGoogle Scholar
  4. 4.
    Qian B, Powers TR, Breuer KS (2008) Shape transition and propulsive force of an elastic rod rotating in a viscous fluid. Phys Rev Let 100:078101CrossRefGoogle Scholar
  5. 5.
    Yu TS, Lauga E, Hosoi AE (2006) Experimental investigations of elastic tail propulsion at low Reynolds number. Phys Fluids 18:091701CrossRefGoogle Scholar
  6. 6.
    Purcell EM (1977) Life at low reynolds number. Am J Phys 45:3CrossRefGoogle Scholar
  7. 7.
    Taylor GI (1951) Analysis of the swimming of microscopic organisms. Proc R Soc A 209:447MATHCrossRefGoogle Scholar
  8. 8.
    Brenner S (1974) The genetics of Caenorhabditis elegans. Genetics 77:71Google Scholar
  9. 9.
    C. elegans Seqeuncing Consoritum (1998) Genome sequence of the nematode C. elegans: a platform for investigating biology. Science 282:2012CrossRefGoogle Scholar
  10. 10.
    White JG, Southgate E, Thomson JN, Brenner S (1976) The structure of the ventral nerve cord of Caenorhabditis elegans. Philos Trans R Soc Lond B Biol Sci 275:327CrossRefGoogle Scholar
  11. 11.
    White JG, Southgate E, Thomson JN, Brenner S (1986) The structure of the nervous system of the nematode C. elegans. Philos Trans R Soc Lond B Biol Sci 314:1CrossRefGoogle Scholar
  12. 12.
    Liu Q, Chen B, Gaier E, Joshi J, Wang ZW (2006) Low conductance gap junctions mediate specific electrical coupling in body-wall muscle cells of Caenorhabditis elegans. J Biol Chem 281:7881CrossRefGoogle Scholar
  13. 13.
    Boyle JH, Cohen N (2008) C. elegans body wall muscles are simple actuators. BioSystems 94:170CrossRefGoogle Scholar
  14. 14.
    Korta J, Clark DA, Gabel CV, Mahadevan L, Samuel ADT (2007) Mechanosensation and mechanical load modulate the locomotory gait of swimming C. elegans. J Exp Biol 210:2383CrossRefGoogle Scholar
  15. 15.
    Pierce-Shimomura JT, Chen BL, Mun JJ, Ho R, Sarkis R, McIntire SL (2008) Genetic analysis of crawling and swimming locomotory patterns in C. elegans. Proc Natl Acad Sci USA 105:20982–20987CrossRefGoogle Scholar
  16. 16.
    Gaugler R, Bilgrami AL (2004) Nematode behaviour. CABI, WallingfordCrossRefGoogle Scholar
  17. 17.
    Karbowski J, Cronin CJ, Seah A, Mendel JE, Cleary D, Sternberg PW (2006) Conservation rules, their breakdown, and optimalityu in Caenorhabditis sinusoidal locomotion. J Theor Biol 242:652CrossRefMathSciNetGoogle Scholar
  18. 18.
    Guo ZV, Mahadevan L (2008) Limbless undulatory propulsion on land. Proc Natl Acad Sci USA 105:3179CrossRefGoogle Scholar
  19. 19.
    Fung YC (1993) A first course in continuum mechanics. Prentice-Hall, Englewood CliffsGoogle Scholar
  20. 20.
    Cronin CJ, Mendel JE, Mukhtar S, Kim Y-M, Stirb RC, Bruck J, Sternberg PW (2005) An automated system for measuring parameters of nematode sinusoidal movement. BMC Genet 6:5CrossRefGoogle Scholar
  21. 21.
    Feng Z, Cronin CJ, Wittig JH, Sternberg PW, Schafer WR (2004) An imaging system for standardized quantitative analysis of C. elegans behavior. BMC Bioinformatics 5:115CrossRefGoogle Scholar
  22. 22.
    Ramot D, Johnson BE, Berry TL, Carnell L, Goodman MB (2008) The parallel worm tracker: a platform for measuring average speed and drug-induced paralysis in nematodes. PLOS One 3:e2208CrossRefGoogle Scholar
  23. 23.
    Park S-J, Goodman MB, Pruitt BL (2007) Analysis of nematode mechanics by piezoresistive displacement clamp. Proc Natl Acad Sci USA 104:17376CrossRefGoogle Scholar
  24. 24.
    Sznitman J, Purohit PK, Krajacic P, Lamitina T, Arratia PE (2010) Material properties of Caenorhabditis elegans swimming at low Reynolds number. Biophys J 98, arXiv:0911.1731v1
  25. 25.
    Engler AJ, Sen S, Sweener HL, Discher DE (2006) Matrix elasticity directs stem cell lineage specification. Cell 126:677CrossRefGoogle Scholar
  26. 26.
    Yamada S, Wirtz D, Kuo SC (2000) Mechanics of living cells measured by laser tracking microrheology. Biophys J 78:1736CrossRefGoogle Scholar
  27. 27.
    Arratia PE, Shinbrot T, Alvarez M, Muzzio FJ (2005) Mixing of non-Newtonian fluids in steadily forced flows. Phys Rev Lett 94:084501CrossRefGoogle Scholar
  28. 28.
    Arratia PE, Voth GA, Gollub JP (2005) Stretching and mixing of non-newtonian fluids in time-periodic flows. Phys Fluids 17:053102CrossRefMathSciNetGoogle Scholar
  29. 29.
    Gray J, Hancock G (1955) The propulsion of sea-urchin spermatozoa. J Exp Biol 32:802Google Scholar
  30. 30.
    Katz DF, Blake JR, Paveri-Fontana SL (1975) On the movement of slender bodies near plane boundaries at low reynolds number. J Fluid Mech 72:529MATHCrossRefGoogle Scholar
  31. 31.
    Harris JE, Crofton HD (1957) Structure and function in the nematodes: Internal pressure and cuticular structure in ascaris. J Exp Biol 34:116Google Scholar
  32. 32.
    Thomas N, Thornhill R (1998) The physics of biological molecular motors. J Phys D, Appl Phys 31:253CrossRefGoogle Scholar
  33. 33.
    Zelenskaya A, de Monvel JB, Pesen D, Radmacher M, Hoh JH, Ulfendahl M (2005) Evidence for a highly elastic shell-core organization of cochlear outer hair cells by local membrane indentation. Biophys J 88:2982CrossRefGoogle Scholar
  34. 34.
    Thoumine O, Ott A (1997) Time scale dependent viscoelastic and contractile regimes in fibroblasts probed by microplate manipulation. J Cell Sci 110:2109Google Scholar
  35. 35.
    Tawada A, Kawai M (1990) Covalent cross-linking of single fibers from rabbit psoas increases oscillatory power. Biophys J 57:643CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2010

Authors and Affiliations

  • J. Sznitman
    • 1
  • X. Shen
    • 1
  • P. K. Purohit
    • 1
  • P. E. Arratia
    • 1
  1. 1.Department of Mechanical Engineering & Applied MechanicsUniversity of PennsylvaniaPhiladelphiaUSA

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