Morphology and growth of polarized tissues

Regular Article

Abstract

We study and classify the time-dependent morphologies of polarized tissues subject to anisotropic but spatially homogeneous growth. Extending previous studies, we model the tissue as a fluid, and discuss the interplay of the active stresses generated by the anisotropic cell division and three types of passive mechanical forces: viscous stresses, friction with the environment and tension at the tissue boundary. The morphology dynamics is formulated as a free-boundary problem, and conformal mapping techniques are used to solve the evolution numerically. We combine analytical and numerical results to elucidate how the different passive forces compete with the active stresses to shape the tissue in different temporal regimes and derive the corresponding scaling laws. We show that in general the aspect ratio of elongated tissues is non-monotonic in time, eventually recovering isotropic shapes in the presence of friction forces, which are asymptotically dominant.

Graphical abstract

Keywords

Living systems: Multicellular Systems 

References

  1. 1.
    L. LeGoff, H. Rouault, T. Lecuit, Development 140, 4051 (2013).CrossRefGoogle Scholar
  2. 2.
    P. Campinho, M. Behrndt, J. Ranft, T. Risler, N. Minc, C.P. Heisenberg, Nat. Cell Biol. 15, 1405 (2013).CrossRefGoogle Scholar
  3. 3.
    T. Lecuit, L. Le Goff, Nature 450, 189 (2007).CrossRefADSGoogle Scholar
  4. 4.
    D.M. Bryant, K.E. Mostov, Nat. Rev. Mol. Cell Biol. 9, 887 (2008).CrossRefGoogle Scholar
  5. 5.
    S. Tlili, C. Gay, F. Graner, P. Marcq, F. Molino, P. Saramito, arXiv:1309.7432 (2013).
  6. 6.
    Y.K. Murugesan, D. Pasini, A.D. Rey, Soft Matter 7, 7078 (2011).CrossRefADSGoogle Scholar
  7. 7.
    F. Corson, O. Hamant, S. Bohn, J. Traas, A. Boudaoud, Y. Couder, Proc. Natl. Acad. Sci. U.S.A. 106, 8453 (2009).CrossRefADSGoogle Scholar
  8. 8.
    S.H. Tindemans, R.J. Hawkins, B.M. Mulder, Phys. Rev. Lett. 104, 058103 (2010).CrossRefADSGoogle Scholar
  9. 9.
    T. Bittig, O. Wartlick, M. González-Gaitán, F. Jülicher, Eur. Phys. J. E 30, 93 (2009).CrossRefGoogle Scholar
  10. 10.
    J. Ranft, M. Basan, J. Elgeti, J.F. Joanny, J. Prost, F. Jülicher, Proc. Natl. Acad. Sci. U.S.A. 107, 20863 (2010).CrossRefADSGoogle Scholar
  11. 11.
    E.K. Rodriguez, A. Hoger, A. D. McCulloch, J. Biomech. 27, 455 (1994).CrossRefGoogle Scholar
  12. 12.
    M. Ben Amar, A. Goriely, J. Mech. Phys. Solids 53, 2284 (2005).MATHMathSciNetCrossRefADSGoogle Scholar
  13. 13.
    M.H. Köpf, L.M. Pismen, Soft Matter 9, 3727 (2013).CrossRefADSGoogle Scholar
  14. 14.
    T. Bittig, O. Wartlick, A. Kicheva, M. González-Gaitán, F. Jülicher, New J. Phys. 10, 063001 (2008).CrossRefADSGoogle Scholar
  15. 15.
    P. Kollmannsberger, C.M. Bidan, J.W.C. Dunlop, P. Fratzl, Soft Matter 7, 9549 (2011).CrossRefADSGoogle Scholar
  16. 16.
    F. Jülicher, K. Kruse, J. Prost, J.F. Joanny, Phys. Rep. 449, 3 (2007).MathSciNetCrossRefADSGoogle Scholar
  17. 17.
    M.C. Marchetti, J.F. Joanny, S. Ramaswamy, T.B. Liverpool, J. Prost, M. Rao, R.A. Simha, Rev. Mod. Phys. 85, 1143 (2013).CrossRefADSGoogle Scholar
  18. 18.
    J. Ranft, J. Prost, F. Jülicher, J.F. Joanny, Eur. Phys. J. E 35, 1 (2012).CrossRefGoogle Scholar
  19. 19.
    R.A. Foty, G. Forgacs, C.M. Pfleger, M.S. Steinberg, Phys. Rev. Lett. 72, 2298 (1994).CrossRefADSGoogle Scholar
  20. 20.
    C. Blanch-Mercader, J. Casademunt, Phys. Rev. Lett. 110, 078102 (2013).CrossRefADSGoogle Scholar
  21. 21.
    M. Basan, J.F. Joanny, J. Prost, T. Risler, Phys. Rev. Lett. 106, 158101 (2011).CrossRefADSGoogle Scholar
  22. 22.
    P. Lee, C.W. Wolgemuth, PLoS Comput. Biol. 7, e1002007 (2011).CrossRefADSGoogle Scholar
  23. 23.
    F. Montel, M. Delarue, J. Elgeti, L. Malaquin, M. Basan, T. Risler, B. Cabane, D. Vignjevic, J. Prost, G. Cappello, J.F. Joanny, Phys. Rev. Lett. 107, 188102 (2011).CrossRefADSGoogle Scholar
  24. 24.
    C. Godrèche, Solids far from Equilibrium, Vol. 1 (Cambridge University Press, 1991).Google Scholar
  25. 25.
    M.L. Manning, R.A. Foty, M.S. Steinberg, E.M. Schoetz, Proc. Natl. Acad. Sci. U.S.A. 107, 12517 (2010).CrossRefADSGoogle Scholar
  26. 26.
    B. Aigouy, R. Farhadifar, D.B. Staple, A. Sagner, J.C. Röper, F. Jülicher, S. Eaton, Cell 142, 773 (2010).CrossRefGoogle Scholar
  27. 27.
    L.J. Cummings, S.D. Howison, J.R. King, Eur. J. Appl. Math. 10, 635 (1999).MATHMathSciNetCrossRefGoogle Scholar
  28. 28.
    M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Vol. 55 (Dover Publications, 1964).Google Scholar
  29. 29.
    D. Bensimon, L.P. Kadanoff, S. Liang, B.I. Shraiman, C. Tang, Rev. Mod. Phys. 58, 977 (1986).CrossRefADSGoogle Scholar
  30. 30.
    J. Casademunt, Chaos 14, 809 (2004).MATHMathSciNetCrossRefADSGoogle Scholar
  31. 31.
    E. Álvarez-Lacalle, J. Ortín, J. Casademunt, Phys. Rev. Lett. 92, 054501 (2004).CrossRefADSGoogle Scholar
  32. 32.
    S.A. Lira, J.A. Miranda, R.M. Oliveira, Phys. Rev. E 82, 036318 (2010).CrossRefADSGoogle Scholar
  33. 33.
    L.J. Cummings, S.D. Howison, J.R. King, Phys. Fluids 9, 477 (1997).MATHMathSciNetCrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • C. Blanch-Mercader
    • 1
    • 2
  • J. Casademunt
    • 1
  • J. F. Joanny
    • 2
  1. 1.Departament d’ECMUniversitat de BarcelonaBarcelonaSpain
  2. 2.UMR 168Institut CurieParisFrance

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