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

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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.

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References

  1. R. Di Leonardo et al., Proc. Natl. Acad. Sci. U.S.A. 107, 9541 (2010).

    Article  ADS  Google Scholar 

  2. L. Mahadevan et al., Proc. Natl. Acad. Sci. U.S.A. 101, 23 (2004).

    Article  MathSciNet  ADS  Google Scholar 

  3. B. Chan, N.L. Balmforth, A.E. Hosoi, Phys. Fluids 17, 113101 (2005).

    Article  MathSciNet  ADS  Google Scholar 

  4. Z.V. Guo, L. Mahadevan, Proc. Natl. Acad. Sci. U.S.A. 105, 3179 (2008).

    Article  ADS  Google Scholar 

  5. D.L. Hu et al., Proc. Natl. Acad. Sci. U.S.A. 106, 10081 (2009).

    Article  ADS  Google Scholar 

  6. E.D. Tytell et al., Proc. Natl. Acad. Sci. U.S.A. 107, 19832 (2010).

    Article  ADS  Google Scholar 

  7. E.M. Purcell, Am. J. Phys. 45, 3 (1977).

    Article  ADS  Google Scholar 

  8. F. Alouges, A. DeSimone, L. Heltai, Math. Models Methods Appl. Sci. 21, 361 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  9. F. Alouges, A. DeSimone, A. Lefebvre, J. Nonlinear Sci. 18, 277 (2008).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. F. Alouges, A. DeSimone, A. Lefebvre, Eur. Phys. J. E 28, 279 (2009).

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  12. G.I. Taylor, Proc. R. Soc. London, Ser. A. 209, 447 (1951).

    Article  ADS  MATH  Google Scholar 

  13. S. Childress Mechanics of Swimming and Flying, Cambridge Studies in Mathematical Biology, Vol. 2 (Cambridge University Press, Cambridge, 1981).

    Article  Google Scholar 

  14. G. Gray, G.J. Hancock, J. Exp. Biol. 32, 802 (1955).

    Google Scholar 

  15. Y. Tanaka, K. Ito, T. Nakagaki, R. Kobayashi, J. Roy. Soc. Interface 9, 222 (2012).

    Article  Google Scholar 

  16. F. Alouges, Optimally swimming stokesian robots, to be published in Discrete Contin. Dyn. Syst. B.

  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.

    Article  Google Scholar 

  18. G. Dal Maso, A. DeSimone, M. Morandotti, SIAM J. Math. Anal. 43, 1345 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  19. A. Najafi, R. Golestanian, J. Phys.: Condens. Matter 17, S1203 (2005).

    Article  ADS  Google Scholar 

  20. J.H. Lai, J.C. del Alamo, J. Rodriguez-Rodriguez, J.C. Lasheras, J. Exp. Biol. 213, 3920 (2010).

    Article  Google Scholar 

  21. M. Denny, Nature 285, 160 (1980).

    Article  ADS  Google Scholar 

  22. E. Lauga, A.E. Hosoi, Phys. Fluids 18, 113102 (2006).

    Article  ADS  Google Scholar 

  23. A. Tatone in Trends in Compuational Contact Mechanics, edited by G. Zavarise, P. Wriggers (Springer Verlag, 2011).

    Article  Google Scholar 

  24. P. Wriggers Computational Contact Mechanics (John Wiley & Sons, New York, 2006).

    Article  Google Scholar 

  25. B. Alberts Molecular Biology of the Cell, 4th edition (Garland Science, New York, 2002).

    Article  Google Scholar 

  26. L. Cardamone et al., Proc. Natl. Acad. Sci. U.S.A. 108, 13978 (2011).

    Article  ADS  Google Scholar 

  27. T.D. Pollard, W.C. Earnshaw Cell Biology, 2nd edition (Saunders, Philadelphia, 2008).

    Article  Google Scholar 

  28. E.L. Barnhart et al., Biophys. J. 98, 933 (2010).

    Article  ADS  Google Scholar 

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DeSimone, A., Tatone, A. Crawling motility through the analysis of model locomotors: Two case studies. Eur. Phys. J. E 35, 85 (2012). https://doi.org/10.1140/epje/i2012-12085-x

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  • DOI: https://doi.org/10.1140/epje/i2012-12085-x

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