Theoretical analysis and computer simulation of fluorescence lifetime measurements. II. Contour length dependence of...

Fluorescence lifetime measurements in a polymer chain are modeled using a memory function expansion, computer simulations, and simple scaling arguments. Unless the quenching rate is localized and infinitely fast, the fluorescence lifetime is generally not equivalent to the first passage time. The fluorescence lifetime distribution is decomposed into memory functions that can be measured separately in single-molecule experiments. The leading order of the expansion gives the Wilemski-Fixman (WF) approximation, and the convergence of higher order terms determines its validity. Simulations of the fluorescence quenching on a Rouse chain verify the accuracy of the WF approximation at small contact radii, short contour lengths, and small quenching rates. Detailed investigation of the average fluorescence lifetime reveals two competing mechanisms: the independent motion of end-to-end vector, which dominates at small contact radius, and the slowest relaxation of polymer, which dominates at large contact radius. The Wilemski-Fixman rate is used in combination with scaling arguments to predict the dependence of fluorescence lifetime on the contour length. Our predictions for the scaling of the average lifetime with the contour length are in good agreement with both simulations and recent experiments by Eaton and his group [L. J. Lapidus, W. A. Eaton, and J. Hofrichter, Proc. Natl. Acad. Sci. U.S.A. 97, 7220 (2000)].