Geometric pinning and antimixing in scaffolded lipid vesicles

Abstract

Previous studies on the phase behaviour of multicomponent lipid bilayers found an intricate interplay between membrane geometry and its composition, but a fundamental understanding of curvature-induced effects remains elusive. Thanks to a combination of experiments on lipid vesicles supported by colloidal scaffolds and theoretical work, we demonstrate that the local geometry and global chemical composition of the bilayer determine both the spatial arrangement and the amount of mixing of the lipids. In the mixed phase, a strong geometrical anisotropy can give rise to an antimixed state, where the lipids are mixed, but their relative concentration varies across the membrane. After phase separation, the bilayer organizes in multiple lipid domains, whose location is pinned in specific regions, depending on the substrate curvature and the bending rigidity of the lipid domains. Our results provide critical insights into the phase separation of cellular membranes and, more generally, twodimensional fluids on curved substrates.

Measuring Gaussian Rigidity Using Curved Substrates

“…The striking difference between Eqs. 7and (9) is that in the latter case the m ¼ 1 mode has a nonzero energy cost, implying that hjϵ 1 j 2 i is a nondiverging quantity. This mode does not correspond to pure translations anymore, but rather involves a "tilt" in which the center of the domain misaligns with the catenoid's axis [see Figs.…”

“…In vitro such a transition is often controlled by decreasing the temperature below some critical value. In the present work we analyze two-phase membranes supported on preengineered substrate surfaces, such as have recently been developed [9,10].…”

“…While there are several techniques to measure the bending rigidity and surface tension of membranes (see, e.g., Refs. [16][17][18]), the Gaussian rigidity is much more elusive and very few estimates exist, either from simulations [19] or experiment [9,[20][21][22]. The essential difficulty is that the integral R KdA is a topological invariant for any closed surface meaning that the Gaussian rigidity does not affect the total free energy of a membrane unless it is subject to topology-changing deformations, such as fission and fusion.…”

“…While the energy equation (1) can describe the shape of phase-separated freestanding membranes, such as multicomponent vesicles [20,23], it also applies to the case of curved supported lipid bilayers, where the membrane lies on a rigid substrate of nontrivial curvature, while preserving its liquid nature [24][25][26]. These experimental techniques have been recently extended to a wide variety of shapes with both open and closed surfaces in [9,10]. Thus, supporting a membrane using a preengineered surface with arbitrary shape is therefore now a realistic proposal [27].…”

“…This differs from the planar case. It has two additional terms in the denominator: the first is due to the nontrivial intrinsic geometry of the substrate and the second to the coupling with the Gaussian rigidity, expressed in terms of the length scale L¯k ¼ −Δk=σ > 0 (typically of the order of a few hundred nanometers [9,20,21]). Notice that the temperature-dependent prefactor also has dimensions of a length, which we write as L σ ¼ k B T=4πσ.…”