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

Abstract

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)].

Markov processes in single molecule fluorescence

“…In a clever experimental design to obtain an FPT distribution, the fast dynamics of a polymer were examined by looking at the fluorescence lifetime distribution that measured the contact time of the dye with a contact quencher [36,37]. Normally, however, the FPT distribution must be obtained from reconstructed state trajectories.…”

Theoretical analysis and computer simulation of fluorescence lifetime measurements. I. Kinetic regimes and experimental time scales

“…3,5 A more detailed discussion of the WF approximation and its validity regime are presented in paper II of this series. 22 The WF approximation for the quadratic reaction-rate process considered in Eq. ͑3͒ yields…”

“…3,5 A more detailed discussion of the generalized WF approximation and its applicability criteria are addressed in paper II of this series. 22 In Appendix B, we discuss the relation between the experimental time scale and the apparent distribution of the measured quantity obtained by single-molecule experiments.…”

Excitation Energy Transfer between Non-Spherical Metal Nanoparticles: Effects of Shape and Orientation on Distance Dependence of Transfer Rate

“…[1][2][3][4] Because of its popularity, this resonance energy transfer (FRET) method is referred to as "spectroscopic ruler", or "optical ruler". 5 The rate of excitation energy transfer for conventional resonance energy transfer systems (both donor (D) and acceptor (A) are dye molecules) is given by the well-known Förster expression 6 where the distance exponent, σ, is 6, k rad is the radiative rate of the donor dye molecule in absence of the acceptor molecule, r is the center-to-center distance between the donor and the acceptor and r 0 is the Förster radius.…”