Budding and vesiculation induced by conical membrane inclusions

Abstract

Conical inclusions in a lipid bilayer generate an overall spontaneous curvature of the membrane that depends on concentration and geometry of the inclusions. Examples are integral and attached membrane proteins, viruses, and lipid domains. We propose an analytical model to study budding and vesiculation of the lipid bilayer membrane, which is based on the membrane bending energy and the translational entropy of the inclusions. If the inclusions are placed on a membrane with similar curvature radius, their repulsive membranemediated interaction is screened. Therefore, for high inclusion density the inclusions aggregate, induce bud formation, and finally vesiculation. Already with the bending energy alone our model allows the prediction of bud radii. However, in case the inclusions induce a single large vesicle to split into two smaller vesicles, bending energy alone predicts that the smaller vesicles have different sizes whereas the translational entropy favors the formation of equal-sized vesicles. Our results agree well with those of recent computer simulations.

Pointlike Inclusion Interactions in Tubular Membranes

“…Despite the presence of a repulsive pair potential between such inclusions in a flat membrane [12,13], because of the nonpairwise additive nature of many-body interactions, they collectively attract each other and form stable spatial patterns [14]. Numerous analytical investigations [15,16] and computer simulations [17,18] have been done to show that this nonadditivity drives vesiculation and budding in biological membranes. In contrast to flat membranes, membrane-mediated interactions between inclusions embedded in tubular membranes are not well understood.…”

Symmetry and Size of Membrane Protein Polyhedral Nanoparticles

“…1(b)]. The preferred MscS arrangement minimizing bilayer bending energy is expected [9][10][11] to be a uniform hexagonal lattice. Our simple mean-field model of MPPNs therefore considers, on the one hand, contri- butions to the MPPN energy arising from MscS-induced bilayer bending deformations for hexagonal protein arrangements [9][10][11]17].…”

“…The preferred MscS arrangement minimizing bilayer bending energy is expected [9][10][11] to be a uniform hexagonal lattice. Our simple mean-field model of MPPNs therefore considers, on the one hand, contri- butions to the MPPN energy arising from MscS-induced bilayer bending deformations for hexagonal protein arrangements [9][10][11]17]. On the other hand, the spherical shape of MPPNs necessitates defects in the preferred hexagonal packing of MscS which, in analogy to viral capsids [12,13], yields an energy penalty characteristic of the number of proteins per MPPN, n. Thus, we allow in the total MPPN energy E = E b + E d for contributions due to protein-induced bilayer bending, E b , and topological defects in protein packing, E d , respectively.…”

“…In this Letter we develop a physical description of MPPNs which establishes a quantitative link between the shape of MPPNs and key molecular properties of their constituents. We first describe a simple meanfield model of MPPNs inspired by previous work on membrane budding [9][10][11] and viral capsid self-assembly [12]. Our mean-field model of MPPNs accounts for the lipid bilayer bending deformations induced by MscS [3,5,6] and the MscS packing defects resulting from the spherical topology of MPPNs, and yields the MPPN energy as a function of the number of MscS per MPPN without any free parameters.…”

“…We estimate the MPPN bending energy E b using a formalism developed in the context of membrane budding [9][10][11], which we summarize here for completeness. The unit cell associated with uniform hexagonal protein arrangements can be approximated [9][10][11] by a circular membrane patch with the protein at its center and boundary conditions set by the spherical shape of MPPNs.…”