Thermal undulations of quasi-spherical vesicles stabilized by gravity.

The classical treatment of quasi-spherical vesicle undulations has, in the present work, been reviewed and extended to systems, which are affected by a gravitational field caused by a density difference across the membrane. The effects have been studied by the use of perturbation theory leading to corrections to the mean shape and the fluctuation correlation matrix. These corrections have been included in an analytical expression for the flicker spectrum to probe how the experimentally accessible spectrum changes with gravity. The results are represented in terms of the gravitational parameter, g(0) = Delta(rho)g R(4)/kappa. The contributions from gravity are in most experimental situations small and thus negligible, but for values of g(0) above a certain limit, the perturbational corrections must be included. Expressions for the relative error on the flicker spectrum have been worked out, so that it is possible to define the regime where gravity is negligible. An upper limit of g(0) has also been identified, where the error in all modes of the flicker spectrum is significant due to distortion of the mean shape.