Theory for establishing proximity relations in biological membranes by excitation energy transfer measurements

In a previous publication (Shaklai et al., 1977a) the present author developed a theory for evaluating proximity relations and surface densities sigma in biological membranes by measurements of excitation energy transfer from a donor attached to a specific site of a membrane protein and an acceptor attached to a specific carbon on a membrane lipid. It was assumed that the protein and lipid are randomly distributed in the plane of the membrane and that the donor and acceptor groups are confined to different planes in the membrane separated by a distance Rp. In this article several aspects of the theory presented in the previous paper are clarified, especially noting that the previous theoretical expressions for the time-dependent and steady state fluorescence intensities assumed that the labeled protein molecule is cylindrically symmetric with the symmetry axis perpendicular to the plane of the membrane and that the donor is positioned on the symmetry axis of the protein. This assumption is also implicitly or explicitly made in subsequent formulations by other investigators. In this article we generalize the theory to include the case where the donor is not on the symmetry axis of the labeled protein. Equations for calculating the time-dependent and steady state fluorescence intensities for this more general case are presented, and methods for applying these theoretical expressions to the analysis of steady state fluorescence intensity data and evaluation of proximity parameters are discussed. It is also shown in this article that the linear relation l/lo = 1 + Kq sigma previously derived for simple analysis of excitation transfer data for the condition rc/Ro 1 can be modified to apply to almost all practical ranges of rc/Ro without much affecting its simplicity in the analysis of experimental data