Experimental determination of upper bound for transition path times in protein folding from single-molecule photon-by-photon trajectories

Abstract

Transition paths are a uniquely single-molecule property not yet observed for any molecular process in solution. The duration of transition paths is the tiny fraction of the time in an equilibrium single-molecule trajectory when the process actually happens. Here, we report the determination of an upper bound for the transition path time for protein folding from photon-by-photon trajectories. FRET trajectories were measured on single molecules of the dye-labeled, 56-residue 2-state protein GB1, immobilized on a glass surface via a biotin-streptavidin-biotin linkage. Characterization of individual emitted photons by their wavelength, polarization, and absolute and relative time of arrival after picosecond excitation allowed the determination of distributions of FRET efficiencies, donor and acceptor lifetimes, steady state polarizations, and waiting times in the folded and unfolded states. Comparison with the results for freely diffusing molecules showed that immobilization has no detectable effect on the structure or dynamics of the unfolded protein and only a small effect on the folding/unfolding kinetics. Analysis of the photon-by-photon trajectories yields a transition path time <200 micros, >10,000 times shorter than the mean waiting time in the unfolded state (the inverse of the folding rate coefficient). Szabo's theory for diffusive transition paths shows that this upper bound for the transition path time is consistent with previous estimates of the Kramers preexponential factor for the rate coefficient, and predicts that the transition path time is remarkably insensitive to the folding rate, with only a 2-fold difference for rate coefficients that differ by 10(5)-fold.