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Shape optimization in lipid nanotube networks

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Abstract.

Starting from a high surface free-energy state, lipid nanotube networks are capable to self-organize into tree-like structures with particular geometrical features. In this work we analyze the process of self-organization in such networks, and report a strong similarity to the Euclidian Steiner Tree Problem (ESTP). ESTP is a well-known NP-hard optimization problem of finding a network connecting a given set of terminal points on a plane, allowing addition of auxiliary points, with the overall objective to minimize the total network length. The present study shows that aggregate lipid structures self-organize into geometries that correspond to locally optimal solutions to such problems.

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References

  1. A. Roux, G. Cappello, J. Cartaud, J. Prost, B. Goud, P. Bassereau, Proc. Natl. Acad. Sci. U.S.A. 99, 5394 (2002).

    Article  ADS  Google Scholar 

  2. A.S. Cans, N. Wittenberg, R. Karlsson, L. Sombers, M. Karlsson, O. Orwar, A. Ewing, Proc. Natl. Acad. Sci. U.S.A. 100, 400 (2003).

    Article  ADS  Google Scholar 

  3. A. Karlsson, R. Karlsson, M. Karlsson, A.S. Cans, A. Stromberg, F. Ryttsen, O. Orwar, Nature 409, 150 (2001)

    Article  ADS  Google Scholar 

  4. P.Y. Bolinger, D. Stamou, H. Vogel, J. Am. Chem. Soc. 126, 8594 (2004).

    Article  Google Scholar 

  5. A. Jesorka, M. Markstrom, O. Orwar, Langmuir 21, 1230 (2005).

    Article  Google Scholar 

  6. A. Karlsson, K. Sott, M. Markstrom, M. Davidson, Z. Konkoli, O. Orwar, J. Phys. Chem. B 109, 1609 (2005)

    Article  Google Scholar 

  7. T. Nakagaki, R. Kobayashi, Y. Nishiura, T. Ueda, Proc. R. Soc. London, Ser. B-Biol. Sci. 271, 2305 (2004).

    Article  Google Scholar 

  8. L. Dreier, T.A. Rapoport, J. Cell Biol. 148, 883 (2000)

    Article  Google Scholar 

  9. M. Karlsson, M. Davidson, R. Karlsson, A. Karlsson, J. Bergenholtz, Z. Konkoli, A. Jesorka, T. Lobovkina, J. Hurtig, M. Voinova, O. Orwar, Ann. Rev. Phys. Chem. 55, 613 (2004)

    Article  Google Scholar 

  10. M. Criado, B.U. Keller, FEBS Lett. 224, 172 (1987).

    Article  Google Scholar 

  11. M. Karlsson, K. Nolkrantz, M.J. Davidson, A. Stromberg, F. Ryttsen, B. Akerman, O. Orwar, Anal. Chem. 72, 5857 (2000).

    Article  Google Scholar 

  12. M. Karlsson, K. Sott, A.S. Cans, A. Karlsson, R. Karlsson, O. Orwar, Langmuir 17, 6754 (2001).

    Article  Google Scholar 

  13. M. Karlsson, K. Sott, M. Davidson, A.S. Cans, P. Linderholm, D. Chiu, O. Orwar, Proc. Natl. Acad. Sci. U.S.A. 99, 11573 (2002).

    Article  ADS  Google Scholar 

  14. T. Lobovkina, P. Dommersnes, J. Hurtig, J.F. Joanny, O. Orwar, Phys. Rev. Lett. 97, 188105/1 (2006).

    Article  ADS  Google Scholar 

  15. I. Derenyi, F. Julicher, J. Prost, Phys. Rev. Lett. 88, 238101/1 (2002).

    Article  ADS  Google Scholar 

  16. G. Aloupis, S. Langerman, M. Soss, G. Toussaint, Comput. Geom. Theory Appl. 26, 69 (2003).

    MATH  MathSciNet  Google Scholar 

  17. D. Cuvelier, I. Derenyi, P. Bassereau, P. Nassoy, Biophys. J. 88, 2714 (2005).

    Article  Google Scholar 

  18. E. Evans, A. Yeung, Chem. Phys. Lipids 73, 39 (1994)

    Article  Google Scholar 

  19. D. Weaire, S. Hutzler, Physics of Foams (Oxford University Press, Oxford, 2000).

  20. T. Lobovkina, P. Dommersnes, J.F. Joanny, P. Bassereau, M. Karlsson, O. Orwar, Proc. Natl. Acad. Sci. U.S.A. 101, 7949 (2004).

    Article  ADS  Google Scholar 

  21. K. Sott, M. Karlsson, J. Pihl, J. Hurtig, T. Lobovkina, O. Orwar, Langmuir 19, 3904 (2003).

    Article  Google Scholar 

  22. M.R. Garey, R.L. Graham, D.S. Johnson, SIAM J. Appl. Math. 32, 835 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  23. J. Hurtig, O. Orwar, Biophys. J. 88, 6a (2005).

    ADS  Google Scholar 

  24. J.H. Rubinstein, D.A. Thomas, J. Weng, Geom. Dedic. 93, 57 (2002).

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Chemistry and Bioscience, Microtechnology Centre, Chalmers University of Technology, SE-412 96, Göteborg, Sweden

    T. Lobovkina & O. Orwar

  2. MSC, Université Paris Diderot, 10, rue Alice Domon et Léonie Duquet, F-75205, Paris, France

    P. G. Dommersnes

  3. Odinsgatan 9, Jeppesen Systems AB, 41103, Göteborg, Sweden

    S. Tiourine

  4. UMR 168, Institut Curie, 26 rue d'Ulm, F-75248, Paris, France

    J. -F. Joanny

Authors
  1. T. Lobovkina
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  2. P. G. Dommersnes
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  3. S. Tiourine
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  4. J. -F. Joanny
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  5. O. Orwar
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Corresponding author

Correspondence to O. Orwar.

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Lobovkina, T., Dommersnes, P.G., Tiourine, S. et al. Shape optimization in lipid nanotube networks. Eur. Phys. J. E 26, 295–300 (2008). https://doi.org/10.1140/epje/i2007-10325-x

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  • DOI: https://doi.org/10.1140/epje/i2007-10325-x

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