Lipid vesicle

A lipid vesicle is a closed lipid bilayer enclosing fluid. Its shape and thermal membrane undulations depend on membrane tension, membrane bending modulus, and constraints such as fixed enclosed volume.

A liposome is a closed artificial lipid vesicle enclosing an aqueous compartment. It may contain one lipid bilayer or several concentric bilayers. A single-bilayer spherical model distinguishes the inner aqueous radius, the boundary between opposing tail regions, and the outer head-group radius; finite molecular packing constrains all three.

A proteoliposome is a liposome containing one or more reconstituted membrane proteins in its lipid bilayer. It combines a controlled membrane boundary with a chosen molecular machine. A solution containing detergent-solubilized protein is not automatically a proteoliposome: a closed vesicle and a membrane-incorporated protein must actually be formed.

The artificial compartment is useful because material can be placed on one side of a lipid bilayer and transport measured across it. In an originating experiment on the NhaA sodium/proton antiporter, purified protein was reconstituted into sodium-loaded proteoliposomes. Parallel sodium and proton flux measurements, together with an independent membrane-potential equilibrium method, supported a stoichiometry of two protons per sodium ion over the tested pH range 7.2–8.1.^[ref]

For a bookkeeping example,100 sodium ions moved outward through a perfectly coupled $2{\mathrm{H}}^{+}/\mathrm{N}{\mathrm{a}}^{+}$ exchanger would accompany 200 protons moving inward. The net movement is 100 positive elementary charges inward, which explains the word electrogenic. These invented counts illustrate coupling, not a measured single-vesicle trace.

Interpreting a proteoliposome assay still requires knowing which way the membrane protein faces, whether the vesicles leak, and how much protein is incorporated. An otherwise matched empty liposome helps estimate membrane background. Reconstitution simplifies a biological system; it does not automatically eliminate every alternative source of the measured flux.

For a tension-dominated cylindrical lipid vesicle of fixed length $L$ and volume, a real axisymmetric sine amplitude $u_q$ has stiffness $K_q=\pi \sigma L[(q{R}_0{)}^2-1]/R_0$. Fixed volume requires a mean-radius shift $-u_q^2/(4R_0)$. Stable modes have $⟨u_q^2⟩=k_{B}T/K_q$ by the equipartition theorem. Modes with $q{R}_0<1$ have the Rayleigh–Plateau instability, rather than a negative equilibrium variance. Bending modifies very short wavelengths and near-marginal modes.

An axisymmetric cylindrical membrane deformation is invariant under rotations about the cylinder axis, so its radius depends only on the axial coordinate. Its surface area is $2\pi \int R\sqrt{1+R_z^2}dz$, and its enclosed volume is $\pi \int R^{2}dz$. These scalar shape constraints are the basis of the fixed-volume capillary spectrum of a cylindrical membrane.