Application of radiationless energy transfer for distance measurements across membranes. Transition Probabilities for radiationless energy transfer within several assemblies of donors and acceptors at stationary distances.

For several 2-or 3-dimensional configurations of stationary donors and acceptors on or near a spherical membrane shell the transition probabilities for radiationless energy transfer are calculated, using Förster's approximation obtained for Coulombic dipole-dipole interaction of the transition moments. It turns out that the difference in the refractive indices for membrane (lipid) and bulk phase (water) has only a small influence on the transition probabilities. Furthermore, the curvature of biological cell surfaces can be neglected, but affects the energy transfer across small vesicles. The ratio thickness/radius of small vesicles can be determined by measuring fluorescence quenching of excited donors by acceptors on the other side of the membrane.