Direct and remote constriction of membrane necks

Bojan Božič, Jemal Guven, Pablo Vázquez-Montejo, and Saša Svetina

Phys. Rev. E 89, 052701 – Published 2 May 2014

Abstract

The physical properties of membrane necks are relevant in vesiculation, a process that plays an essential role in cellular physiology. Because the neck's radius is, in general, finite, membrane scission and the consequent pinching off of the vesicle can only occur if it is narrowed to permit the necessary membrane topological reformation. Here we examine, in a simple single phase lipid vesicle, how external forces can promote neck constriction not only by direct compression at the neck but also, counterintuitively, by dilation at remote locations. These results provide a new perspective on the role played by actin polymerization in the process of endocytosis.

Received 24 September 2013
Revised 16 April 2014

DOI:https://doi.org/10.1103/PhysRevE.89.052701

Authors & Affiliations

Bojan Božič^1,*, Jemal Guven², Pablo Vázquez-Montejo³, and Saša Svetina^1,4

¹Institute of Biophysics, Faculty of Medicine, University of Ljubljana, Vrazov trg 2, SI-1000 Ljubljana, Slovenia
²Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, México D.F., Mexico
³Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
⁴Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia

^*bojan.bozic@mf.uni-lj.si

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Vol. 89, Iss. 5 — May 2014

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Images

Figure 1
Shapes of unconstrained vesicle at the reduced volume 0.82, with the reduced spontaneous curvature ( $c_{0}$ ) equal to (a) 3, (b) 3.5, (c) $-$ 1.5, and (d) $-$ 2.1. The corresponding neck radii ( $R_{n}$ ) are (a) 0.0213 $R_{0}$ , (b, d) zero, and (c) 0.0164 $R_{0}$ .
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Figure 2
Neck constriction due to a diminishing ring at the neck radius (full lines) and an expanding ring at the equator of the bud (dashed lines) in the case of exovesiculation. The arrows denote the direction of the radial forces. (a) The dependence of the dimensionless radial force [ $f R_{0} / (8 π k_{c})$ ], (b) fraction of membrane area in the bud ( $A_{s} / A$ ), (c) relative volume of the bud ( $V_{s} / V_{0}$ ), (d) dimensionless radius of the equator of the bud ( $R_{s} / R_{0}$ ), (e) dimensionless multiplier $λ R_{0}^{2} / k_{c}$ , and (f) dimensionless pressure difference ( $μ R_{0}^{3} / k_{c}$ ) on the neck radius ( $R_{n} / R_{0}$ ). (g) The limiting shape that is composed of two spheres obtained by direct constriction of the neck. (h) The limiting shape obtained by the constriction of the neck by dilating the bud along its equator.
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Figure 3
Comparison of vesicle morphology in the neck region at $R_{n} = 0.001 R_{0}$ for direct and indirect radial forces. (a) The shape for direct (full line) and indirect (dashed line) constriction. (b) The corresponding dependence of the dimensionless arc-length derivative of the curvature along meridians ( $\ddot{ψ} R_{0}^{2}$ ) on dimensionless position along symmetry axis ( $Z / R_{0}$ ). (c) The distribution of membrane stress in the neighborhood of the neck normalized to ( $k_{c} / R_{0}^{3}$ ) for direct constriction: the meridional and azimuthal stresses ( $f_{⊥ ⊥}$ and $f_{∥ ∥}$ , defined in [16]), i.e., the tangential stresses on line elements of a parallel and meridian exerted by the regions across them, and the normal stress on the line element of a parallel ( $f_{⊥}$ ) exerted by the region to its left. Note that $f_{⊥}$ exhibits a discontinuity at the ring, whereas $f_{⊥ ⊥}$ and $f_{∥ ∥}$ exhibit kinks there. (d) The same dependencies as in (c) but for remote constriction.
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Figure 4
Neck constriction due to a diminishing ring at the neck radius (full lines) and an expanding ring at the equator of the endobud (dashed lines) in the process of endovesiculation. (a) The dependence of the radial force, (b) the membrane area of the endobud, (c) its volume (negative because it lies outside the vesicle), (d) radius of the equator of the endobud, (e) and multipliers fixing area, and (f) volume on the neck radius. The corresponding dimensionless parameters are defined in the caption of Fig. 2. (g) The limiting shape, consisting of two spheres obtained by direct constriction of the neck. (h) The limiting shape obtained by remote constriction of the neck by dilating of the endobud along its equator.
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Figure 5
Schematic presentation of an axisymmetric vesicle in cylindrical coordinates with a narrow neck. The arc length of the membrane contour ( $S$ ) is the independent variable. The slope of the curve is denoted by $ψ$ and the neck radius by $R_{n}$ . The radius of the ring boundaries ( $S_{L}$ and $S_{U}$ ) are denoted by $R_{L}$ and $R_{U}$ . The shape of the membrane is given by $R$ and $Z$ whose values are obtained by solving Eqs. (A1) to (A3) and the equation $d Z / d S = - sin ψ$ . The enlarged parts of the vesicle near the ring boundary for two possible locations of the ring are also shown.
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