The European Physical Journal E

, Volume 33, Issue 2, pp 165–173 | Cite as

Quantitative predictions on auxin-induced polar distribution of PIN proteins during vein formation in leaves

Regular Article


The dynamic patterning of the plant hormone auxin and its efflux facilitator the PIN protein are the key regulators for the spatial and temporal organization of plant development. In particular auxin induces the polar localization of its own efflux facilitator. Due to this positive feedback, auxin flow is directed and patterns of auxin and PIN arise. During the earliest stage of vein initiation in leaves auxin accumulates in a single cell in a rim of epidermal cells from which it flows into the ground meristem tissue of the leaf blade. There the localized auxin supply yields the successive polarization of PIN distribution along a strand of cells. We model the auxin and PIN dynamics within cells with a minimal canalization model. Solving the model analytically we uncover an excitable polarization front that triggers a polar distribution of PIN proteins in cells. As polarization fronts may extend to opposing directions from their initiation site, we suggest a possible resolution to the puzzling occurrence of bipolar cells, thus we offer an explanation for the development of closed, looped veins. Employing non-linear analysis, we identify the role of the contributing microscopic processes during polarization. Furthermore, we deduce quantitative predictions on polarization fronts establishing a route to determine the up to now largely unknown kinetic rates of auxin and PIN dynamics.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

10189_2010_9480_MOESM1_ESM.pdf (206 kb)
Supplementary material


  1. 1.
    J. Petrasek, J. Friml, Development 136, 2675 (2009)CrossRefGoogle Scholar
  2. 2.
    J. Friml, J. Wiśniewska, E. Benková, K. Mendgen, K. Palme, Nature 415, 806 (2002)ADSGoogle Scholar
  3. 3.
    A. Marchant, J. Kargul, S.T. May, P. Muller, A. Delbarre, C. Perrot-Rechenmann, M.J. Bennett, EMBO J. 18, 2066 (1999)CrossRefGoogle Scholar
  4. 4.
    D. Reinhardt, E.R. Pesce, P. Stieger, T. Mandel, K. Baltensperger, M. Bennett, J. Traas, J. Friml, C. Kuhlemeier, Nature 426, 255 (2003)CrossRefADSGoogle Scholar
  5. 5.
    L.E. Sieburth, Plant Physiol. 121, 1179 (1999)CrossRefGoogle Scholar
  6. 6.
    F.A.F.C. Went, Naturwiss. 21, 1 (1933)CrossRefADSGoogle Scholar
  7. 7.
    P.H. Rubery, A.R. Sheldrake, Nature New Biol. 244, 285 (1973)Google Scholar
  8. 8.
    M.H.M. Goldsmith, T.H. Goldsmith, M.H. Martin, Proc. Natl. Acad. Sci. U.S.A. 78, 976 (1981)CrossRefADSGoogle Scholar
  9. 9.
    G.J. Mitchison, Proc. R. Soc. London, Ser. B Bio. 209, 489 (1980)CrossRefADSGoogle Scholar
  10. 10.
    L. Gälweiler, C.H. Guan, A. Müller, E. Wisman, K. Mendgen, A. Yephremov, K. Palme, Science 282, 2226 (1998)CrossRefADSGoogle Scholar
  11. 11.
    K. Okada, J. Ueda, M.K. Komaki, C.J. Bell, Y. Shimura, Plant Cell 3, 677 (1991)CrossRefGoogle Scholar
  12. 12.
    E. Benková, M. Michniewicz, M. Sauer, T. Teichmann, D. Seifertová, G. Jürgens, J. Friml, Cell 115, 591 (2003)CrossRefGoogle Scholar
  13. 13.
    J. Friml, A. Vieten, M. Sauer, D. Weijers, H. Schwarz, T. Hamann, R. Offringa, G. Jürgens, Nature 426, 147 (2003)CrossRefADSGoogle Scholar
  14. 14.
    J. Petrášek, J. Mravec, R. Bouchard, J.J. Blakeslee, M. Abas, D. Seifertová, J. Wiśniewska, Z. Tadele, M. Kubeš, M. Čovanová et al., Science 312, 914 (2006)CrossRefADSGoogle Scholar
  15. 15.
    T. Sachs, Annu. Bot. London 33, 263 (1969)Google Scholar
  16. 16.
    G.J. Mitchison, Proc. R. Soc. London, Ser. B Bio. 207, 79 (1980)CrossRefADSGoogle Scholar
  17. 17.
    G.J. Mitchison, Philos. Trans. Roy. Soc. B 295, 461 (1981)CrossRefADSGoogle Scholar
  18. 18.
    M. Sauer, J. Balla, C. Luschnig, J. Wisniewska, V. Reinohl, J. Friml, E. Benkova, Genes Dev. 20, 2902 (2006)CrossRefGoogle Scholar
  19. 19.
    E. Scarpella, D. Marcos, J. Friml, T. Berleth, Genes Dev. 20, 1015 (2006)CrossRefGoogle Scholar
  20. 20.
    T. Paciorek, E. Zažimalová, N. Ruthardt, J. Petrášek, Y.D. Stierhof, J. Kleine-Vehn, D.A. Morris, N. Emans, G. Jürgens, N. Geldner et al., Nature 435, 1251 (2005)CrossRefADSGoogle Scholar
  21. 21.
    P. Dhonukshe, I. Grigoriev, R. Fischer, M. Tominaga, D.G. Robinson, J. Hasek, T. Paciorek, J. Petrásek, D. Seifertová, R. Tejos et al., Proc. Natl. Acad. Sci. U.S.A. 105, 4489 (2008)CrossRefADSGoogle Scholar
  22. 22.
    R. Benjamins, B. Scheres, Annu. Rev. Plant Biol. 59, 443 (2008)CrossRefGoogle Scholar
  23. 23.
    H. Jönsson, M.G. Heisler, B.E. Shapiro, E.M. Meyerowitz, E. Mjolsness, Proc. Natl. Acad. Sci. U.S.A. 103, 1633 (2006)CrossRefADSGoogle Scholar
  24. 24.
    F.G. Feugier, A. Mochizuki, Y. Iwasa, J. Theor. Biol. 236, 366 (2005)CrossRefGoogle Scholar
  25. 25.
    T. Berleth, E. Scarpella, P. Prusinkiewicz, Trends Plant Sci. 12, 151 (2007)CrossRefGoogle Scholar
  26. 26.
    R.S. Smith, E.M. Bayer, Plant Cell Environ. 32, 1258 (2009)CrossRefGoogle Scholar
  27. 27.
    C.L. Wenzel, M. Schuetz, Q. Yu, J. Mattsson, Plant J. 49, 387 (2007)CrossRefGoogle Scholar
  28. 28.
    E.M. Bayer, R.S. Smith, T. Mandel, N. Nakayama, M. Sauer, P. Prusinkiewicz, C. Kuhlemeier, Genes Dev. 23, 373 (2009)CrossRefGoogle Scholar
  29. 29.
    D. Koenig, E. Bayer, J. Kang, C. Kuhlemeier, N. Sinha, Development 136, 2997 (2009)CrossRefGoogle Scholar
  30. 30.
    M.G. Sawchuk, P. Head, T.J. Donner, E. Scarpella, New Phytol. 176, 560 (2007)CrossRefGoogle Scholar
  31. 31.
    J.A. Raven, New Phytol. 74, 163 (1975)CrossRefGoogle Scholar
  32. 32.
    R. Swarup, E.M. Kramer, P. Perry, K. Knox, H.M.O. Leyser, J. Haseloff, G.T.S. Beemster, R. Bhalerao, M.J. Bennett, Nat. Cell. Biol. 7, 1057 (2005)CrossRefGoogle Scholar
  33. 33.
    A.S. Usenko, A.G. Zagorodny, Mol. Phys. 61, 1213 (1987)CrossRefADSGoogle Scholar
  34. 34.
    P. Larsen, Growth substances in higher plants, Vol. 3 of Modern Methods of Plant Physiology (Springer, Berlin, 1955)Google Scholar
  35. 35.
    E. Wangermann, G.J. Mitchison, Plant Cell Environ. 4, 141 (1981)CrossRefGoogle Scholar
  36. 36.
    E.M. Kramer, J. Exp. Bot. 59, 45 (2007)CrossRefGoogle Scholar
  37. 37.
    S. Pollmann, A. Müller, M. Piotrowski, E.W. Weiler, Planta 216, 155 (2002)CrossRefGoogle Scholar
  38. 38.
    A.G. Rolland-Lagan, P. Prusinkiewicz, Plant J. 44, 854 (2005)CrossRefGoogle Scholar
  39. 39.
    S. Stoma, M. Lucas, J. Chopard, M. Schaedel, J. Traas, C. Godin, PLoS Comput. Biol. 4, e1000207 (2008)CrossRefMathSciNetGoogle Scholar
  40. 40.
    E.M. Kramer, Trends Plant Sci. 14, 242 (2009)CrossRefGoogle Scholar
  41. 41.
    R.S. Smith, S. Guyomarc'h, T. Mandel, D. Reinhardt, C. Kuhlemeier, P. Prusinkiewicz, Proc. Natl. Acad. Sci. U.S.A. 103, 1301 (2006)CrossRefADSGoogle Scholar
  42. 42.
    R.M.H. Merks, Y.V. de Peer, D. Inzé, G.T.S. Beemster, Trends Plant Sci. 12, 384 (2007)CrossRefGoogle Scholar
  43. 43.
    M. Ibañes, N. Fàbregas, J. Chory, A. Caño-Delgado, Proc. Natl. Acad. Sci. U.S.A. 106, 13630 (2009)CrossRefADSGoogle Scholar
  44. 44.
    F. Rapparini, Y.Y. Tam, J.D. Cohen, J.P. Slovin, Plant Physiol. 128, 1410 (2002)CrossRefGoogle Scholar
  45. 45.
    A. Delbarre, P. Muller, V. Imhoff, J. Guern, Planta 198, 532 (1996)CrossRefGoogle Scholar
  46. 46.
    V.S. Zykov, A.T. Winfree, Simulation of Wave Processes in Excitable Media (Manchester University Press, Manchester, 1987)Google Scholar
  47. 47.
    A.S. Mikhailov, A.Y. Loskutov, Foundations of Synergetics I: Distributed Active Systems (Springer Verlag, New York, 1991)Google Scholar
  48. 48.
    C.L. Howe, W.C. Mobley, J. Neurobiol. 58, 207 (2004)CrossRefGoogle Scholar
  49. 49.
    P. Ortoleva, J. Ross, J. Chem. Phys. 63, 3398 (1975)CrossRefADSGoogle Scholar
  50. 50.
    R.G. Casten, H. Cohen, P.A. Lagerstrom, Q. Appl. Math. 32, 365 (1975)MATHMathSciNetGoogle Scholar
  51. 51.
    A. Newell, P. Shipman, Z. Sun, J. Theor. Biol. 251, 421 (2008)CrossRefGoogle Scholar
  52. 52.
    P. Sahlin, B. Söderberg, H. Jönsson, J. Theor. Biol. 258, 60 (2009)CrossRefGoogle Scholar
  53. 53.
    K. Ljung, A.K. Hull, J. Celenza, M. Yamada, M. Estelle, J. Normanly, G. Sandberg, Plant Cell 17, 1090 (2005)CrossRefGoogle Scholar
  54. 54.
    F. Feugier, Y. Iwasa, J. Theor. Biol. 243, 235 (2006)CrossRefMathSciNetGoogle Scholar
  55. 55.
    O. Hamant, M.G. Heisler, H. Jonsson, P. Krupinski, M. Uyttewaal, P. Bokov, F. Corson, P. Sahlin, A. Boudaoud, E.M. Meyerowitz et al., Science 322, 1650 (2008)CrossRefADSGoogle Scholar
  56. 56.
    P.A. Lawrence, G. Struhl, J. Casal, Nat. Rev. Genet. 8, 555 (2007)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScienceLudwig-Maximilians-UniversitätMünchenGermany

Personalised recommendations