Title:

Thermodynamics and stability of vesicle growth

The stability of growing unilamellar vesicles is investigated using the formalism of nonequilibrium thermodynamics. The vesicles, which are assumed to be in an otherwise aqueous solution, are growing due to the accretion of lipids to the bilayer which forms the vesicle membrane. The thermodynamic description is based on the hydrodynamics of a waterlipid mixture together with a model of the vesicle as a discontinuous system in the sense of linear nonequilibrium thermodynamics. The approach assumes that the energy of the bilayer membrane is given by the spontaneous curvature model attributed to Helfrich. Furthermore, the rate at which lipids incorporate into the membrane is taken to be proportional to the surface area of the membrane. In this way, the relevant forces and fluxes of the system are identified in the context of a stability analysis. The resulting constitutive equation for the flux of water across the membrane is used to analyse the stability of spherical vesicles that are subject to different perturbations. First, a simplified approach is presented which restricts perturbations to axisymmetric ellipsoids. In that case, the analysis is carried out using an explicit Cartesian parametrisation. A perturbation theory which describes more general deformations is then developed and applied to the case of arbitrary axisymmetric perturbations. It is found that there are generically two critical radii at which changes of stability occur. For the case where the perturbation takes the form of a single zonal harmonic, only one of these radii is physical and is given by the ratio $2L_p / L_\gamma$, where $L_p$ is the hydraulic conductivity and $L_\gamma$ is the Onsager coefficient related to changes in membrane area due to lipid accretion. The stability of such perturbations is related to the value of l corresponding to the particular zonal harmonic: those with lower l are more unstable than those with higher l. The conditions under which general axisymmetric perturbations reduce to explicit ellipsoidal calculations are also found. A heuristic explanation for the results is proposed whilst possible extensions of the current work and the need for experimental input are also discussed.
