Normal-mode analysis of lateral diffusion on a bounded membrane surface.

The normal-mode analysis of fluorescence redistribution after photobleaching, introduced for the characterization of lateral diffusion on spherical membrane surfaces, has been generalized and extended to other surface geometries. Theoretical expressions are derived for the characteristic values and orthogonal characteristic functions of the diffusion equations for cylindrical surfaces, ellipsoids of revolution and dimpled discoidal surfaces. On the basis of these results, a simple analytical function is proposed as an empirical solution for the analysis of photobleaching data on a variety of discoidal surfaces. Special experimental and computational methods for determining the surface-diffusion coefficient are described, and demonstrated with data for lipid diffusion in erythrocyte membranes.