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Vesicle shape, molecular tilt, and the suppression of necks

Hongyuan Jiang1, Greg Huber2, Robert A. Pelcovits3, and Thomas R. Powers1

  • 1Division of Engineering, Box D, Brown University, Providence, Rhode Island 02912, USA
  • 2Center for Cell Analysis & Modeling, and Department of Cell Biology, University of Connecticut Health Center, Farmington, Connecticut 06030, USA and Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269, USA
  • 3Department of Physics, Brown University, Providence, Rhode Island 02912, USA

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Phys. Rev. E 76, 031908 – Published 11 September, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.031908

Abstract

Can the presence of molecular-tilt order significantly affect the shapes of lipid bilayer membranes, particularly membrane shapes with narrow necks? Motivated by the propensity for tilt order and the common occurrence of narrow necks in the intermediate stages of biological processes such as endocytosis and vesicle trafficking, we examine how tilt order inhibits the formation of necks in the equilibrium shapes of vesicles. For vesicles with a spherical topology, point defects in the molecular order with a total strength of +2 are required. We study axisymmetric shapes and suppose that there is a unit-strength defect at each pole of the vesicle. The model is further simplified by the assumption of tilt isotropy: invariance of the energy with respect to rotations of the molecules about the local membrane normal. This isotropy condition leads to a minimal coupling of tilt order and curvature, giving a high energetic cost to regions with Gaussian curvature and tilt order. Minimizing the elastic free energy with constraints of fixed area and fixed enclosed volume determines the allowed shapes. Using numerical calculations, we find several branches of solutions and identify them with the branches previously known for fluid membranes. We find that tilt order changes the relative energy of the branches, suppressing thin necks by making them costly, leading to elongated prolate vesicles as a generic family of tilt-ordered membrane shapes.

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Phys. Rev. E 76, 031908– Published 11 September, 2007
  • Received 5 July 2007

© 2007 American Physical Society

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