Phospholipid vesicles are conveniently prepared lipid constructs that mimic biological membranes. In particular, spherical unilamellar vesicles, containing a single phospholipid bilayer (as opposed to multilamellar liposomes) are widely used in biochemical assays.
In our work with the tocopherol transfer protein (TTP) we observed that ligand transfer was faster to vesicles of smaller diameter that, we argue, have a more highly curved surface. To claim that it was curvature alone that enhanced protein binding it would be necessary to show that the available surface area of the vesicles in assays did not vary substantially.
Pidgeon and Hunt[1] have investigated such variables as entrapped volume, lipid volume, and surface area of complex mixed systems of multilamellar liposomes of varying sizes. Unilamellar vesicles of low size dispersion (i.e. that are all close to the same diameter) present a much simpler situation, since if one assumes a pure preparation of unilamellar vesicles of fixed diameter then it is straightforward to calculate the total surface area of bilayer lipids that can be prepared from a known and fixed concentration of phospholipids.
A similar calculation has been described by Cullis and Hope[3]) as well as Encapsula Nano Sciences (ENS) (
The assumptions for these calculations are as follows:
• Vesicles are of uniform size and unilamellar
• The membrane thickness is 5 nm
• The area per phospholipid (here assumed to be DOPC) is 67.4 nm2[2]
A calculation such as this is surely simplistic as it ignores variables such as packing density, hydration, and curvature stresses. Still, it approximates the structure of the vesicles sufficiently well for the case in hand.
The total number of lipid molecules in a unilamellar lipsosome can be calculated by calculating the surface area of both the outer and inner leaflet and dividing by the area occupied per phospholipid. This is accomplished using the following equation:
where Ntot is the total number of lipid molecules, d is the diameter of the vesicle (nm), h is the thickness of the bilayer (nm), and ais the area occupied per lipid molecule (nm2).
From Ntot we can calculate the number of vesicles, Nvesicles, of any diameter in a hypothetical sample of 1 ml and a total concentration of phospholipids of 100 M.
The total outer surface area, Atot, (since it is only the outer surface area that is accessible to a protein) of this number of vesicles is given by
Calculated values for Ntot, Nvesicles, and Atot, the relative amount of outer leaflet surface area, and the inherent curvature for vesicles of size 20 – 200 nm are shown in Table 1.
Vesicle diameter / Ntot / Nvesicles / Atot (nm2) / Relative outer surface area / Curvature, K=1/R (nm-1)(nm)
200 / 351581 / 1.71 x 1011 / 2.15 x 1016 / 1 / 0.005
100 / 83622 / 7.20 x 1011 / 2.26 x 1016 / 1.05 / 0.010
50 / 18942 / 3.18 x 1012 / 2.50 x 1016 / 1.16 / 0.020
30 / 6006 / 1.00 x 1013 / 2.83 x 1016 / 1.32 / 0.033
20 / 2310 / 2.61 x 1013 / 3.27 x 1016 / 1.52 / 0.050
Table 1. Variation in the total number of phospholipids molecules per vesicle (Ntot), the total number of vesicles (Nvesicles), and the total outer surface area (Atot) , as well as the relative amount of outer leaflet surface area for vesicles of size 20 – 200 nm. Bilayer thickness is assumed to 5 nm and area per phospholipids molecule to be 67.4 nm2.[2]
Thus, for a constant concentration of total lipid, the area available on the outer leaflet, Atot,increases by only 1.5 times when vesicle size is reduced from 200 nm to 20 nm. This ratio increases to only 1.75 fold if we assume that the membrane is 7 nm rather than 5 nm thick. However, the curvature, K, has increased by ten-fold as the vesicle size is reduced from 200 to 20 nm.
If the rate of ligand deposition was determined solely by the available surface area, we should have seen no more than an ~ 1.5 fold increase in transfer rate as vesicle size was varied from the larger 200 nm LUVs to smaller SUVs. However, we repeatedly saw transfer rate increases of ~ 12-fold on moving from extruded LUVs, to SUVs prepared by either extrusion or sonication, substantiating that TTP prefers to bind to SUV membranes of higher curvature.
1.Pidgeon, C., and Hunt, C. A. (1981) Calculating number and surface area of liposomes in any suspension, J Pharm Sci70: 173-176.
2.Kucerka, N., Nagle, J. F., Sachs, J. N., Feller, S. E., Pencer, J., Jackson, A., and Katsaras, J. (2008) Lipid bilayer structure determined by the simultaneous analysis of neutron and X-ray scattering data, Biophys J95: 2356-2367.
3.Cullis, P. R., and Hope, M. J. (1991) Physcial properties and functional roles of lipids in membranes, in Biochemistry of Lipids, Lipoproteins and Membranes (Vance, D. E., and Vance, J., Eds.), pp 1-41, Elsevier, Amsterdam.