Intramembrane positions of membrane-bound chromophores determined by excitation energy transfer

A detailed theory has been derived to evaluate the efficiency of nonradiative transfer of electronic excitation energy between nonassociated membrane-bound chromophores. Two different approaches are presented and shown to lead to identical numerical results. In the first of these the efficiency of transfer is computed from the decay with time of the donor excited state. In the second approach, the efficiency is calculated directly, demonstrating that to a high degree of accuracy the array of acceptors can be represented as consisting of a single nearest acceptor plus a continuum of secondary acceptors. A general expression is derived for the dipole-dipole orientation factor as a function of the position of an acceptor. It is shown that, by invoking the range of orientations that must be present at the very least in a particular case, the expected values of transfer efficiency may be limited to a relatively narrow band of uncertainty about those predicted for total randomization. In the limit of total randomization, the theory reduces to functions of but two dimensionless parameters: an effective number of acceptors and a normalized distance of closest approach, a parameter which in turn is a function of an excluded surface area and the depth in the membrane of a donor relative to that of an acceptor. Finally, data analysis procedures are presented whereby one can determine the surface density of acceptors for a known geometry or, alternatively, determine the distance of closest approach for known surface densities.