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The stability of solitons in biomembranes and nerves

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Abstract

We examine the stability of a class of solitons, obtained from a generalization of the Boussinesq equation, which have been proposed to be relevant for pulse propagation in biomembranes and nerves. These solitons are found to be stable with respect to small-amplitude fluctuations. They emerge naturally from non-solitonic initial excitations and are robust in the presence of dissipation. Solitary waves pass through each other with only minor dissipation when their amplitude is small. Large-amplitude solitons fall apart into several pulses and small-amplitude noise upon collision when the maximum density of the membrane is limited by the density of the solid phase membrane.

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References

  1. A.L. Hodgkin, A.F. Huxley, J. Physiol. 117, 500 (1952).

    Google Scholar 

  2. T. Heimburg, A.D. Jackson, Proc. Natl. Acad. Sci. U.S.A. 102, 9790 (2005).

    Article  ADS  Google Scholar 

  3. T. Heimburg, A.D. Jackson, Biophys. Rev. Lett. 2, 57 (2007).

    Article  Google Scholar 

  4. T. Heimburg, A.D. Jackson, in Structure and Dynamics of Membranous Interfaces, edited by K. Nag (Wiley, 2008) pp. 317--339

  5. S.S.L. Andersen, A.D. Jackson, T. Heimburg, Progr. Neurobiol. 88, 104 (2009).

    Article  Google Scholar 

  6. E. Villagran Vargas, A. Ludu, R. Hustert, P. Gumrich, A.D. Jackson, T. Heimburg, Biophys. Chem. 153, 159 (2011).

    Article  Google Scholar 

  7. B.C. Abbott, A.V. Hill, J.V. Howarth, Proc. R. Soc. London, Ser. B 148, 149 (1958).

    Article  ADS  Google Scholar 

  8. J.V. Howarth, R. Keynes, J.M. Ritchie, J. Physiol. 194, 745 (1968).

    Google Scholar 

  9. J.M. Ritchie, R.D. Keynes, Q. Rev. Biophys. 392, 451 (1985).

    Article  Google Scholar 

  10. Y. Kobatake, I. Tasaki, A. Watanabe, Adv. Biophys. 208, 1 (1971).

    Google Scholar 

  11. A. Blicher, K. Wodzinska, M. Fidorra, M. Winterhalter, T. Heimburg, Biophys. J. 96, 4581 (2009).

    Article  ADS  Google Scholar 

  12. B. Wunderlich, C. Leirer, A. Idzko, U.F. Keyser, V. Myles, T. Heimburg, M. Schneider, Biophys. J. 96, 4592 (2009).

    Article  ADS  Google Scholar 

  13. K. Wodzinska, A. Blicher, T. Heimburg, Soft Matter 5, 3319 (2009).

    Article  ADS  Google Scholar 

  14. T. Heimburg, Biophys. Chem. 150, 2 (2010).

    Article  Google Scholar 

  15. J. Gallaher, K. Wodzinska, T. Heimburg, M. Bier, Phys. Rev. E 81, 061925 (2010).

    Article  ADS  Google Scholar 

  16. T. Heimburg, A.D. Jackson, Biophys. J. 92, 3159 (2007).

    Article  ADS  Google Scholar 

  17. J. Boussinesq, J. Math. Pures. Appl. 7, 55 (1872).

    Google Scholar 

  18. P.G. Drazin, R.S. Johnson, Solitons: An Introduction (Cambridge University Press, 1989).

  19. N.J. Zabusky, M.D. Kruskal, Phys. Rev. Lett. 15, 240 (1965).

    Article  ADS  MATH  Google Scholar 

  20. R.V. Mishmash, L.D. Carr, Phys. Rev. Lett. 103, 140403 (2009).

    Article  ADS  Google Scholar 

  21. H.-B. Braun, J. Kulda, B. Roessli, D. Visser, K.W. Krämer, H.-U. Güdel, P. Böni, Nature Phys. 1, 159 (2005).

    Article  ADS  Google Scholar 

  22. R. Meppelink, S.B. Koller, J.M. Vogels, P.P. van der Straten, E.D. van Ooijen, N.R. Heckenberg, H. Rubinsztein-Dunlop, S.A. Haine, M.J. Davis, Phys. Rev. A 80, 043606 (2009).

    Article  ADS  Google Scholar 

  23. B. Damski, W.H. Zurek, Phys. Rev. Lett. 104, 160404 (2010).

    Article  ADS  Google Scholar 

  24. J.E. Bjorkholm, A. Ashkin, Phys. Rev. Lett. 32, 129 (1974).

    Article  ADS  Google Scholar 

  25. C.-J. Chen, P.K.A. Wai, C.R. Menyuk, Opt. Lett. 17, 417 (1992).

    Article  ADS  Google Scholar 

  26. C. Conti, G. Ruocco, S. Trillo, Phys. Rev. Lett. 95, 183902 (2005).

    Article  ADS  Google Scholar 

  27. S. Yomosa, Phys. Rev. A 27, 2120 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  28. C.T. Zhang, Phys. Rev. A 35, 886 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  29. J.H. Ipsen, G. Karlström, O.G. Mouritsen, H. Wennerström, M.J. Zuckermann, Biochim. Biophys. Acta 905, 162 (1987).

    Article  Google Scholar 

  30. T. Heimburg, Biochim. Biophys. Acta 1415, 147 (1998).

    Article  Google Scholar 

  31. S. Halstenberg, T. Heimburg, T. Hianik, U. Kaatze, R. Krivanek, Biophys. J. 75, 264 (1998).

    Article  ADS  Google Scholar 

  32. W. Schrader, H. Ebel, P. Grabitz, E. Hanke, T. Heimburg, M. Hoeckel, M. Kahle, F. Wente, U. Kaatze, J. Phys. Chem. B 106, 6581 (2002).

    Article  Google Scholar 

  33. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C, second edition (Cambridge University Press, 1997) Chapt. Random Numbers, pp. 274--283

  34. I. Tasaki, Biochim. Biophys. Acta 3, 494 (1949).

    Article  Google Scholar 

  35. R. FitzHugh, Biophys. J. 1, 445 (1961).

    Article  ADS  Google Scholar 

  36. J. Nagumo, S. Arimoto, S. Yoshizawa, Proc. IRE 50, 2061 (1962).

    Article  Google Scholar 

  37. M. Argentina, P. Coullet, V. Krinsky, J. Theor. Biol. 205, 47 (2000).

    Article  Google Scholar 

  38. K. Iwasa, I. Tasaki, R.C. Gibbons, Science 210, 338 (1980).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark

    B. Lautrup, R. Appali, A. D. Jackson & T. Heimburg

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  1. B. Lautrup
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  2. R. Appali
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  3. A. D. Jackson
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  4. T. Heimburg
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Correspondence to B. Lautrup or T. Heimburg.

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Lautrup, B., Appali, R., Jackson, A.D. et al. The stability of solitons in biomembranes and nerves. Eur. Phys. J. E 34, 57 (2011). https://doi.org/10.1140/epje/i2011-11057-0

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  • DOI: https://doi.org/10.1140/epje/i2011-11057-0

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