Crawling motility through the analysis of model locomotors: Two case studies

Regular Article
Part of the following topical collections:
  1. Active Matter

Abstract

We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility.

Keywords

Regular Article - Topical issue: Active Matter 

References

  1. 1.
    R. Di Leonardo et al., Proc. Natl. Acad. Sci. U.S.A. 107, 9541 (2010).ADSCrossRefGoogle Scholar
  2. 2.
    L. Mahadevan et al., Proc. Natl. Acad. Sci. U.S.A. 101, 23 (2004).MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    B. Chan, N.L. Balmforth, A.E. Hosoi, Phys. Fluids 17, 113101 (2005).MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Z.V. Guo, L. Mahadevan, Proc. Natl. Acad. Sci. U.S.A. 105, 3179 (2008).ADSCrossRefGoogle Scholar
  5. 5.
    D.L. Hu et al., Proc. Natl. Acad. Sci. U.S.A. 106, 10081 (2009).ADSCrossRefGoogle Scholar
  6. 6.
    E.D. Tytell et al., Proc. Natl. Acad. Sci. U.S.A. 107, 19832 (2010).ADSCrossRefGoogle Scholar
  7. 7.
    E.M. Purcell, Am. J. Phys. 45, 3 (1977).ADSCrossRefGoogle Scholar
  8. 8.
    F. Alouges, A. DeSimone, L. Heltai, Math. Models Methods Appl. Sci. 21, 361 (2011).MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    F. Alouges, A. DeSimone, A. Lefebvre, J. Nonlinear Sci. 18, 277 (2008).MathSciNetADSMATHCrossRefGoogle Scholar
  10. 10.
    F. Alouges, A. DeSimone, A. Lefebvre, Eur. Phys. J. E 28, 279 (2009).CrossRefGoogle Scholar
  11. 11.
    L. Giomi, N. Hawley-Weld, L. Mahadevan Bristle-Bots: a model system for locomotion and swarming. Paper presented at the APS March Meeting, Boston 2012.CrossRefGoogle Scholar
  12. 12.
    G.I. Taylor, Proc. R. Soc. London, Ser. A. 209, 447 (1951).ADSMATHCrossRefGoogle Scholar
  13. 13.
    S. Childress Mechanics of Swimming and Flying, Cambridge Studies in Mathematical Biology, Vol. 2 (Cambridge University Press, Cambridge, 1981).CrossRefGoogle Scholar
  14. 14.
    G. Gray, G.J. Hancock, J. Exp. Biol. 32, 802 (1955).Google Scholar
  15. 15.
    Y. Tanaka, K. Ito, T. Nakagaki, R. Kobayashi, J. Roy. Soc. Interface 9, 222 (2012).CrossRefGoogle Scholar
  16. 16.
    F. Alouges, Optimally swimming stokesian robots, to be published in Discrete Contin. Dyn. Syst. B.Google Scholar
  17. 17.
    A. DeSimone in Natural Locomotion in Fluids and on Surfaces, edited by S. Childress, A. Hosoi, W.W. Schultz, Z.J. Wang, IMA Volumes in Mathematics and its Application (Springer-Verlag, 2012), pp. 177-185.CrossRefGoogle Scholar
  18. 18.
    G. Dal Maso, A. DeSimone, M. Morandotti, SIAM J. Math. Anal. 43, 1345 (2011).MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    A. Najafi, R. Golestanian, J. Phys.: Condens. Matter 17, S1203 (2005).ADSCrossRefGoogle Scholar
  20. 20.
    J.H. Lai, J.C. del Alamo, J. Rodriguez-Rodriguez, J.C. Lasheras, J. Exp. Biol. 213, 3920 (2010).CrossRefGoogle Scholar
  21. 21.
    M. Denny, Nature 285, 160 (1980).ADSCrossRefGoogle Scholar
  22. 22.
    E. Lauga, A.E. Hosoi, Phys. Fluids 18, 113102 (2006).ADSCrossRefGoogle Scholar
  23. 23.
    A. Tatone in Trends in Compuational Contact Mechanics, edited by G. Zavarise, P. Wriggers (Springer Verlag, 2011).CrossRefGoogle Scholar
  24. 24.
    P. Wriggers Computational Contact Mechanics (John Wiley & Sons, New York, 2006).CrossRefGoogle Scholar
  25. 25.
    B. Alberts Molecular Biology of the Cell, 4th edition (Garland Science, New York, 2002).CrossRefGoogle Scholar
  26. 26.
    L. Cardamone et al., Proc. Natl. Acad. Sci. U.S.A. 108, 13978 (2011).ADSCrossRefGoogle Scholar
  27. 27.
    T.D. Pollard, W.C. Earnshaw Cell Biology, 2nd edition (Saunders, Philadelphia, 2008).CrossRefGoogle Scholar
  28. 28.
    E.L. Barnhart et al., Biophys. J. 98, 933 (2010).ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.International School for Advanced StudiesSISSATriesteItaly
  2. 2.DICEAAUniversità dell’AquilaL’AquilaItaly

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