Geometric pinning and antimixing in scaffolded lipid vesicles

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, two-dimensional fluids on curved substrates.


Synthesis and silica coating of colloidal particles with cubic shape
Hematite colloids with a cubic shape were synthesised following the sol-gel method of Sugimoto et al. [1]. Specifically, a sodium hydroxide (NaOH) solution was prepared by dissolving 20.14 g of NaOH in 100 mL water. This solution was added in 50 s to a 100 mL solution of 50.39 g iron (III) chloride (FeCl 3 ) dissolved in water while magnetically stirring at 300 rpm. Weighting of the FeCl 3 was done quickly because the salt is very hygroscopic. The mixture was stirred for another 10 minutes at 450 rpm and then transferred to a preheated oven at 100 • C, where it was left undisturbed for 10 days. The resulting cubic particles had a superball shape which can be described by the parameter m [2]: m = log 2 0.5 log 2 − log L D (1) where L and D are respectively the side and the corner-to-corner length of the cubic particle. The hematite cubes obtained from our synthesis had a m−value of 3.3 ± 0.6 and a corner-to-corner distance of 1.76 ± 0.08 µm. A TEM image of the particles is shown in Figure 1 A. The particles were washed and stored in ethanol.
To coat the particles with a silica layer, we followed a method described by Rossi et al. [3]. The reaction was preformed at 15 -20 • C in a 2L round bottom flask positioned in an ultrasonic bath (Elmasonic P300H, Elma). The reaction flask contained a uniform mixture of 920 mL ethanol, 62 mL of water, 42 mL of cube dispersion (3.8 %wt), 10 mL tetramethylammonium hydroxide (TMAH) dissolved in water (1% wt). To coat the particles with silica a mixture of 15 mL tetraethyl orthosilicate (TEOS) and 15 ml ethanol was added to the reaction flask under mechanic stirring at a rate of 230 µL/min using a syringe pump (Harvard apparatus). After addition, the reaction mixture was sonicated for 3h and stirred for another 16h to ensure that all TEOS had reacted (Supplementary Figure 1B).
These silica coated hematite cubes were then turned into hollow silica cubes by dissolving the hematite cores in 5M hydrochloric acid. The hollow silica cubes were washed three times and stored in ethanol (Supplementary Figure 1C).

Synthesis and silica coating of dumbbell and snowman-shaped particles
Colloidal dumbbell and snowman particles consisting of polystyrene (PS) and 3-(Trimethoxysilyl)propyl methacrylate (TPM) were synthesised using a modified version of the procedure described by Kim J. et. al. [4].
Linear polystyrene particles were synthesised by a dispersion polymerisation method and cross-linked by the addition of a swelling solution containing 90:10 styrene: TPM and divinylbenzene (DVB). After polymerisation initiated by azobisisobutyronitrile (AIBN) a second swelling step was performed to create a protrusion on the cross-linked spheres. Depending on the swelling ratio S, which is defined as the mass of the monomer/the mass of the polymer colloids, dumbbell particles (S = 3) or snowman shapes (S = 4) were obtained. The dumbbell particles have total length of 5.23 ± 0.05 µm and the ratio between the diameters of the two lobes is equal to 0.98 ± 0.04 (Supplementary Figure 2A). The snowman particles have total length of 4.01 ± 0.04 µm and the ratio between the diameters of the two lobes is equal to 0.57 ± 0.02 (Supplementary Figure 2B).
To achieve adsorption of the lipids to the surface of these particles, the dumbbell particles were coated with silica. We used a modified version of the protocol by Wang et al. to coat hematite particles [5]. Typically, 0.5 mL TEOS was added to an ultrasonicated mixture of 100 mL ethanol, 15 mL ammonia (28%-30%) and 5 mL of particle dispersion (0.5% wt) while mechanically stirring for 5h. The silica coated colloids were washed and stored in ethanol. A SEM image of the resulting dumbbell particles is shown in Supplementary Figure 5B).

Silica dumbbells fabricated by destabilization of silica spheres
To investigate how different silica surfaces affect the phase separation of the bilayer, we prepared silica particles with a dumbbell shape and with a size comparable to the silica-coated PS-TPM particles through an alternative route. Colloidal dumbbell and snowman shaped particles of silica were obtained by destabilisation of chargestabilised silica spheres. Destabilisation was achieved by mixing a solution of 200 µL potassium chloride (KCl) with 100 µL dispersion of silica particles (2.06 ± 0.05 µm and 7.00 ± 0.29 µm) in water (5 %wt). The mixture was tumbled end-over-end for 20 minutes before being quenched with 20 mL water. The resulting aggregates consisted of varying numbers of spheres were washed six times with water to remove the KCl and re-stabilise the particles. An example of an obtained dumbbell particle is reported in Supplementary Figure 5A. We coated an aliquot of the dispersion with a lipid bilayer and then only inspected phase separation on aggregates consisting of two spheres.

Fluorescence Recovery After Photobleaching
A fundamental property of the lipid bilayer that allows phase separation is its fluidity, that is the lateral diffusion of the lipids. To check the fluidity of the bilayer we used the Fluorescence recovery after photobleaching (FRAP) technique. FRAP is a method that consists of bleaching a fluorescent area of the sample and observing the fluorescence recovery. In this work we used FRAP to check the mobility of the bilayer in the following way: a circular area of the membrane containing fluorescent DOPE-Rhodamine lipids is bleached and the subsequent recovery of the intensity of this region is measured. We observed that the recovery of the signal is exponential (see Supplementary Figure 4) and therefore fitted the data using the following fit function: where I norm (t) = I(t)/[I(t = 0)I(t) ref ] is the measured intensity I(t) normalised with respect to the intensity just before bleaching I(t = 0) and corrected for bleaching through measurement of the intensity of a non-bleached reference area, I(t) ref .
A is the extent of the recovery, t − t 0 is the time elapsed since the beginning of the recovery process and τ the recovery time. We report in the following table the values of the parameters obtained from the fit in Supplementary Figure 4: 0.75 ± 0.02 0.35 ± 0.04 3.9 ± 0.2 Cube 0.74 ± 0.05 0.07 ± 0.02 1 ± 1 Snowman 0.68 ± 0.02 0.08 ± 0.01 5 ± 1

Lipid composition
In supported lipid bilayers the substrate can affect the physical properties of phase separation, such as the temperature at which phase separation occurs [6]. Therefore, we varied the lipid composition on spherical supports to identify the conditions under which phase separation occurs. We found that phase separation can be obtained with the following mixtures of porcine brain sphingomyelin (BSM), 1-palmitoyl-2-  Table 1.
No phase separation was observed for 0 to 10% of cholesterol on spherical SLVs. We used the mixture 2:1:1 BSM:POPC:chol. This ratio has also been shown to phase separate in free-standing bilayers both at 23 • C and 37 • C, albeit with a different type of sphingomyelin, the palmitoylsphingomyelin PSM [7]. We confirmed that also for our mixture phase separation occurs in free standing bilayers (giant unilamellar vesicles) made via electro-swelling (see Supplementary Figure 5).

Comparison of probability of phase separation and number of domains on dumbbell particles with different surfaces
In order to exclude that surface properties of the supporting colloidal particles, such as the roughness or the type of silica, affect the phase separation landscape, we compared dumbbell shaped SLVs made on two different types of dumbbell-shaped substrates: silica dumbbells made via destabilisation of colloidal silica spheres and silica-coated dumbbells made from polystyrene 3-(Trimethoxysilyl)propyl methacrylate Silica coated (PS-TPM-Si) particles particles. We studied the likelihood of phase separation and of the number of domain (Figure 7). We observed that these quantities are similar for the two types of particles, indicating that the properties of the surfaces of the supports that we use do not significantly influence phase separation properties.   Figure 11: A Phase-separated lipid bilayer on colloid made with SUVs kept at room temperature. The two phases are localized in random patches on the surface of the colloids and the membrane appeared to have varying thickness, pointing to incomplete fusion of the SUVs on the surface, which prohibits attainment of an equilibrium state. B Fluorescence recovery after photobleaching experiment of a colloid made with SUVs kept at room temperature. The dye bleached is the DOPE-Rhodamine. On the top, fluorescence images are taken before the bleaching, after the bleaching, and at the end of the experiment. On the bottom, the normalized intensity corrected for bleaching is plotted with time.