Continuous fluorescence microphotolysis to observe lateral diffusion in membranes. Theoretical methods and applications

On the basis of solutions to two-dimensional diffusion-reaction equations the fluorescence signal for photobleaching experiments with arbitrary time-dependent and time-independent irradiation profiles is evaluated. The solutions involve spatial discretization and spectral expansion, spatial and temporal discretization employing the Crank-Nicholson integration scheme, generalized moment expansion, and an approximation yielding an analytical expression. The algorithms developed can be installed on small computers to determine lateral diffusion coefficients from observed fluorescence signals. The theory developed is applied to photobleaching with constant irradiation profiles and the resulting diffusion coefficients, in the range 0.001 to μm² s^-1 for the systems investigated, are compared to the results of conventional photobleaching experiments. Applications of the theory compare further the signals resulting from Gaussian and rectangular irradiation profiles, the influence of the membrane geometry, i.e., planar or spherical, on the fluorescence signal, and the effect of finite diffusion spaces.