The origins of stability of spontaneous vesicles

Abstract

Equilibrium unilamellar vesicles are stabilized by one of two distinct mechanisms depending on the value of the bending constant. Helfrich undulations ensure that the interbilayer potential is always repulsive when the bending constant, K, is of order k(B)T. When K k(B)T, unilamellar vesicles are stabilized by the spontaneous curvature that picks out a particular vesicle radius; other radii are disfavored energetically. We present measurements of the bilayer elastic constant and the spontaneous curvature, R(o), for three different systems of equilibrium vesicles by an analysis of the vesicle size distribution determined by cryo-transmission electron microscopy and small-angle neutron scattering. For cetyltrimethylammonium bromide (CTAB)/sodium octyl sulfonate catanionic vesicles, K =.7 k(B)T, suggesting that the unilamellar vesicles are stabilized by Helfrich-undulation repulsions. However, for CTAB and sodium perfluorooctanoate (FC(7)) vesicles, K = 6 k(B)T, suggesting stabilization by the energetic costs of deviations from the spontaneous curvature. Adding electrolyte to the sodium perfluorooctanoate/CTAB vesicles leads to vesicles with two bilayers; the attractive interactions between the bilayers can overcome the cost of small deviations from the spontaneous curvature to form two-layer vesicles, but larger deviations to form three and more layer vesicles are prohibited. Vesicles with a discrete numbers of bilayers at equilibrium are possible only for bilayers with a large bending modulus coupled with a spontaneous curvature.

Figure 1

(A) Cryo-TEM image of CTAB/SOS/water (2 wt % total surfactant, CTAB/SOS ratio of 3:7 by weight) system showing unilamellar vesicles with a broad size distribution. The vesicles are polydisperse, with the average radius of 37 nm and a standard deviation of 10 nm. (B) Vesicle size distribution histogram determined from measurements of about 3,000 vesicles from many different samples and cryo-TEM images. There are a few much larger vesicles (100–500 nm) in this mixture, but the fraction is so small that they were not plotted in the histogram. The solid line is a fit to Eq. 6 with R_o = 37 nm and K = 0.7 ± 0.2 k_BT.

Figure 2

(A) Cryo-TEM image of CTAB/FC₇ (2 wt % total surfactant, CTAB/FC₇ ratio of 2:8 by weight) vesicle system with a significantly more narrow size distribution than the CTAB/SOS vesicles in Fig. 1. All of the vesicles were unilamellar under these conditions. The vesicle phase exists on the FC₇- (and FC₅-) rich side at concentrations between ≈2 and 4 wt % surfactant and for mixing ratios greater than 80% FC₇ (and FC₅). (B) Vesicle size distribution histogram determined from the cryo-TEM images; the solid line is a fit to Eq. 6 with R_o = 23 nm and K = 6 ± 2 k_BT.

Figure 3

SANS spectra (open circles) for CTAB/FC₇ vesicles (2 wt % total surfactant, CTAB/FC₇ ratio of 2:8 by weight; see Fig. 2). The expected q⁻² dependence for hollow spheres is observed for q > 0.04 Å⁻¹. A distinct minimum is present over the range 0.01 < q < 0.02 Å⁻¹. The solid lines through the data represent the best fit of a simple hollow-sphere model with three adjustable parameters: the average inner-vesicle radius, the bilayer thickness, and the polydispersity. The model results yield outer-vesicle radii between 23 and 24 nm, a bilayer thickness of 2.8 nm, and a polydispersity of 17%. These results are in remarkable agreement with the size distribution measured by TEM (Fig. 2), which also shows a monodisperse population with an average radius of 23 nm. This data is to be compared with the neutron scattering from CTAB/SOS vesicles (solid circles, ×10) that only show the expected q⁻² dependence with no characteristic minimum (Fig. 1). This result indicates a more polydisperse sample also in good agreement with the TEM data. Neutron-scattering experiments were performed by using the NG-7 spectrometer at the National Institute of Standards and Technology (NIST) in Gaithersburg, MD. Neutrons with wavelength of 6 Å (with a spread of Δλ/λ = 0.10) and 3 sample-to-detector distance (1.0, 4.5, and 13.0 m) were used with the detector on axis for the long distance and offset 25 cm for the two shorter distances. These configurations produced a scattering vector range of 0.005 to 0.50 Å⁻¹. Samples were transferred into quartz scattering cells (0.2-cm path length) and equilibrated in a temperature-controlled heating block before measurement. The scattered intensity was corrected for background scattering as well as detector efficiency and placed on absolute scale by using standards provided by the NIST.

Figure 4

Cryo-TEM image of CTAB/FC₇ (2 wt % total surfactant, CTAB/FC₇ ratio of 2:8 by weight) in 1 wt % NaBr. Two-layer vesicles are distinguished from one-layer vesicles (Figs. 1 and 2) by the darker rim on the inside edge of the vesicle membrane (arrows). This dark inside rim is caused by the increased projection of the electron beam through both the interior and exterior vesicle bilayers; the single-bilayer vesicles in Figs. 1 and 2 have membranes with a uniform intensity and do not show the interior dark rim. From examining many images, about 90% of the vesicles with added salt have two bilayers, and the rest appear to have one bilayer. There were essentially no vesicles with three layers or more. The vesicles in the 1% NaBr sample also had a greater tendency to adhere both to each other and the polymer-coated electron microscope grid (23) and flatten, consistent with the enhanced attraction between the vesicle bilayers (41). Some of the vesicles are clustered and appear polygonal; the vesicles can come into closer proximity because of the screening of the residual electrostatic forces, indicative of the net attractive forces between the bilayers. Although the vesicles cluster, they maintain a discrete number of bilayers.