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

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Abstract
A detailed theory was derived to evaluate the efficiency of nonradiative transfer of electronic excitation energy between nonassociated membrane-bound chromophores. Two different approaches are presented and lead to identical numerical results. In the 1st of these, the efficiency of transfer is computed from the decay with time of the donor excited state. In the 2nd 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. 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 2 dimensionless parameters: an effective number of acceptors and a normalized distance of closest approach, which is a function of an excluded surface area and the depth in the membrane of a donor relative to that of an acceptor. Data analysis procedures are presented whereby the surface density of acceptors for a known geometry or distance of closest approach for known surface densities can be determined.