Equilibrium shapes of tubular lipid membranes

Abstract

Tubular vesicles represent abundant structural motifs which are observed both in experiments and in nature. We analyse them within the theory of bending elasticity and determine the equilibrium solutions at fixed volume, surface area, and segment length without imposing any specific symmetry or periodicity. We identify four different non-periodic equilibrium shapes. Depending on the precise value of the constraints or the corresponding Lagrange multipliers, these four shapes include: (i) snake-like and (ii) helical structures, (iii) tubes with a spherical body, and (iv) tubes with a discoidal body. However different in the details, all of the shapes have the same general cylindrical morphology which is either globally modulated or is a superposition of an additional structural motif and the cylinder. These results point to a great significance of the circular cylindrical shape and offer a comprehensive and general analysis of the shape of tubular vesicles.

Inception Mechanisms of Tunneling Nanotubes

“…A feature common to most TNT formations is the presence of membrane continuity [14]. Tubular membrane structures are structurally robust and are common in most cellular environments with a large surface-to-volume ratio [42]. However, continuity is difficult to assess if there is no evidence of cargo trafficking between neighboring cells.…”

Rayleigh–Plateau instability of anisotropic interfaces. Part 2. Limited instability of elastic interfaces

“…1973) as well as neo-Hookean laws (Barthès-Biesel, Diaz & Dhenin 2002; Barthès-Biesel 2016; Jaensson & Vermant 2018) have been established. The elasticity is not only important for the regulation of vesicle or cell shape (Fischer 2004; Barthès-Biesel 2016; Jelerčič 2017), it is further known to drive wrinkling on the vesicle surface (Finken & Seifert 2006; Li & Sarkar 2008; Finken, Kessler & Seifert 2011; Dupont et al. 2015; Narsimhan et al.…”

“…For bending, the Helfrich Hamiltonian (Helfrich 1973;Guckenberger & Gekle 2017) is the most widely used description, while for shear and area dilatation the Skalak (Skalak et al 1973) as well as neo-Hookean laws (Barthès-Biesel, Diaz & Dhenin 2002;Barthès-Biesel 2016;Jaensson & Vermant 2018) have been established. The elasticity is not only important for the regulation of vesicle or cell shape (Fischer 2004;Barthès-Biesel 2016;Jelerčič 2017), it is further known to drive wrinkling on the vesicle surface (Finken & Seifert 2006;Li & Sarkar 2008;Finken, Kessler & Seifert 2011;Dupont et al 2015;Narsimhan et al 2015) and can lead to budding of vesicles (Seifert, Berndl & Lipowsky 1991;Seifert & Lipowsky 1995).…”