Effect of Diffusion on Resonance Energy Transfer Rate Distributions: Implications for Distance Measurements

Intrinsically disordered protein regions and many other biopolymers lack the three-dimensional structure that could be determined by X-ray crystallography or NMR, which encourages the application of alternative experimental methods. Time-resolved resonance energy transfer data are often used to measure distances between two fluorophores attached to a flexible biopolymer. This is complicated by the rotational and translational diffusion of the fluorophores and by nonmonoexponential donor decay in the absence of the acceptor. Equation <i>I</i>_DA(<i>t</i>) = <i>I</i>_D(<i>t</i>)·<i>F</i>(<i>t</i>) is derived here, which is applicable regardless of whether <i>I</i>_D(<i>t</i>) is monoexponential. <i>I</i>_D(<i>t</i>) and <i>I</i>_DA(<i>t</i>) are the δ-excitation donor emission decays in the absence and in the presence of the acceptor; <i>F</i>(<i>t</i>) contains information about energy transfer, donor–acceptor distance distribution, and diffusion dynamics. It is shown that in the absence of rotational and translational diffusion, <i>F</i>(<i>t</i>) is a continuous distribution of exponentials, whereas in the presence of rotational and translational diffusion, <i>F</i>(<i>t</i>) is a sum of discrete exponentials. For each case it is shown how <i>F</i>(<i>t</i>) is related to the distance distribution. Experimental data obtained with a flexible tetradecapeptide in aqueous solution clearly demonstrate that <i>F</i>(<i>t</i>) is a sum of discrete exponential terms. A partial differential equation describing resonance energy transfer in the presence of both rotational and translational diffusion of the donor and acceptor tethered to the ends of a semiflexible chain is solved in this work using a combination of analytical and numerical methods; the solution is used to fit time-resolved emission of the donor, which makes it possible to determine the model parameters: contour length, persistence length, and the end-to-end translational diffusion coefficient