End-to-End Distance Distributions of Flexible Molecules: Frequency-Domain Fluorescence Energy Transfer Measurements and Rotational Isomeric State Model Calculations.

We used frequency-domain measurements of fluorescence energy transfer to determine the end-to-end distance distribution of donor-acceptor (D-A) pairs linked by flexible alkyl chains. The length of the linker was varied from 11 to 28 atoms, and two different D-A pairs were used. In each case the D-A distributions were recovered from global analysis of measurements with different values for the Förster distance, which were obtained by collisional quenching of the donors. In all cases essentially the same distance distribution was recovered from the frequency-domain data for each value of the Förster distance. Additionally, these recovered distributions were also in agreement with those recovered from steady-state measurements of the energy-transfer efficiency for various Förster distances. We compared the experimentally recovered distance distributions with those calculated from the rotational isomeric state (RIS) model of Flory. The experimentally recovered distance distributions for the largest chain molecules were in agreement with the predictions of the RIS model. However, the experimental and RIS distributions were distinct for the shorter D-A pairs. The experimental distance distributions were not in agreement with the predictions of two simpler models, the freely jointed and the freely rotating chain models. Overall, these results demonstrate that the current resolution of distance distributions is adequate for comparison with the results of conformational modeling, which in turn should allow refinement of these models.