Phase-field modelling of the dynamics of Z-ring formation in liposomes: Onset of constriction and coarsening

  • C. B. Picallo
  • R. A. Barrio
  • C. Varea
  • T. Alarcón
  • A. Hernandez-Machado
Open Access
Regular Article


We propose a model for the dynamics of the formation of rings of FtsZ on tubular liposomes which produce constriction on the corresponding membrane. Our phase-field model is based on a simple bending energy that captures the dynamics of the interplay between the protein and the membrane. The short-time regime is analyzed by a linear dispersion relation, with which we are able to predict the number of rings per unit length on a tubular liposome. We study numerically the long-time dynamics of the system in the non-linear regime where we observe coarsening of Z-rings on tubular liposomes. In particular, our numerical results show that, during the coarsening process, the number of Z-rings decreases as the radius of tubular liposome increases. This is consistent with the experimental observation that the separation between rings is proportional to the radius of the liposome. Our model predicts that the mechanism for the increased rate of coarsening in liposomes of larger radius is a consequence of the increased interface energy.

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Living systems: Biological Matter 


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • C. B. Picallo
    • 1
    • 2
  • R. A. Barrio
    • 3
  • C. Varea
    • 3
  • T. Alarcón
    • 4
    • 5
  • A. Hernandez-Machado
    • 1
    • 4
  1. 1.Departament ECM, Facultat de FísicaUniversitat de BarcelonaBarcelonaSpain
  2. 2.Institut Lumière MatièreUMR5306 Université Lyon 1-CNRS, Université de LyonVilleurbanne cedexFrance
  3. 3.Instituto de FísicaU.N.A.M.Mexico D.F.Mexico
  4. 4.Campus de BellaterraCentre de Recerca MatemàticaBarcelonaSpain
  5. 5.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBarcelonaSpain

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