Dynamics of the Orientational Factor in Fluorescence Resonance Energy Transfer

A one-dimensional diffusion equation is derived for the time evolution of the orientational factor, κ², in the Förster energy transfer rate. The κ²-dependent diffusion coefficient is obtained in three different ways: (1) by requiring the κ² autocorrelation function, calculated using the κ² diffusion equation, to be single-exponential with the exact characteristic time; (2) by projecting the multidimensional diffusion equation for the transition dipoles onto κ² using the local equilibrium approximation; and (3) by requiring exact and approximate κ² trajectories to be as close as possible using a Bayesian approach. Within the framework of this simple theory, the distance dependence of the fluorescence resonance energy transfer (FRET) efficiency can be calculated for all values of the ratio of the rotational correlation time of the transition dipoles to the lifetime of the donor excited state. The theoretical predictions are compared to the exact values obtained from Brownian dynamics simulations of the reorientation of the donor and acceptor transition dipoles.