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

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)].

[1]  M. Fixman,et al.  Diffusion‐controlled intrachain reactions of polymers. I Theory , 1974 .

[2]  Robert Zwanzig,et al.  Rate processes with dynamical disorder , 1990 .

[3]  James Witkoskie,et al.  Single-molecule dynamics of semiflexible Gaussian chains , 2002 .

[4]  J. Bechhoefer,et al.  Diffusion-limited loop formation of semiflexible polymers: Kramers theory and the intertwined time scales of chain relaxation and closing , 2003, cond-mat/0306546.

[5]  George H. Weiss,et al.  A perturbation analysis of the Wilemski–Fixman approximation for diffusion‐controlled reactions , 1984 .

[6]  X. Zhuang,et al.  Correlating Structural Dynamics and Function in Single Ribozyme Molecules , 2002, Science.

[7]  Thomas Basché,et al.  Single-molecule optical detection, imaging and spectroscopy , 1997 .

[8]  B. Zimm.  Dynamics of Polymer Molecules in Dilute Solution: Viscoelasticity, Flow Birefringence and Dielectric Loss , 1956 .

[9]  Lisa J. Lapidus,et al.  Dynamics of Intramolecular Contact Formation in Polypeptides , 2001 .

[10]  R. Hochstrasser,et al.  Dynamics and folding of single two-stranded coiled-coil peptides studied by fluorescent energy transfer confocal microscopy. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Lisa J. Lapidus,et al.  Effects of chain stiffness on the dynamics of loop formation in polypeptides. Appendix: Testing a 1-dimensional diffusion model for peptide dynamics , 2002 .

[12]  Jianshu Cao,et al.  Two-Event Echos in Single-Molecule Kinetics: A Signature of Conformational Fluctuations† , 2001 .

[13]  Klaus Schulten,et al.  First passage time approach to diffusion controlled reactions , 1980 .

[14]  Robert Zwanzig,et al.  Dynamical disorder: Passage through a fluctuating bottleneck , 1992 .

[15]  Robert Zwanzig,et al.  Diffusion limited first contact of the ends of a polymer: Comparison of theory with simulation , 1996 .

[16]  J. Hopfield,et al.  Transient kinetics of chemical reactions with bounded diffusion perpendicular to the reaction coordinate: Intramolecular processes with slow conformational changes , 1983 .

[17]  Jianshu Cao,et al.  Theoretical analysis and computer simulation of fluorescence lifetime measurements. I. Kinetic regimes and experimental time scales. , 2004, The Journal of chemical physics.

[18]  X. Xie,et al.  Optical studies of single molecules at room temperature. , 1998, Annual review of physical chemistry.

[19]  S. Edwards,et al.  The Theory of Polymer Dynamics , 1986 .

[20]  Jianshu Cao.  Event-averaged measurements of single-molecule kinetics , 2000 .

[21]  Sangyoub Lee,et al.  Intrachain fluorescence quenching in a flexible polymer: A theory for frequency-domain fluorometric experiments , 2001 .

[22]  T. Kiefhaber,et al.  The speed limit for protein folding measured by triplet-triplet energy transfer. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[23]  D. Ermak,et al.  Brownian dynamics with hydrodynamic interactions , 1978 .

[24]  D. Makarov,et al.  Rate of intramolecular contact formation in peptides: The loop length dependence , 2002 .

[25]  Lisa J. Lapidus,et al.  Measuring the rate of intramolecular contact formation in polypeptides. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Andrew B. Martin,et al.  Single-molecule protein folding: diffusion fluorescence resonance energy transfer studies of the denaturation of chymotrypsin inhibitor 2. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[27]  M. Fixman,et al.  Diffusion‐controlled intrachain reactions of polymers. II Results for a pair of terminal reactive groups , 1974 .

[28]  Lisa J. Lapidus,et al.  Dynamics of intramolecular contact formation in polypeptides: distance dependence of quenching rates in a room-temperature glass. , 2001, Physical review letters.

[29]  P. Wolynes,et al.  Passage through fluctuating geometrical bottlenecks. The general Gaussian fluctuating case , 1993 .