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. We determined 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 two-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 following 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. Acquisition of single molecule spectra enabled a clear distinction between jumps in the FRET efficiency due to folding or unfolding transitions of the polypeptide and those correspond-ing to a previously unknown photophysical change of the com-monly-used donor dye, Alexa 488. 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 less than 200 microsec, more than 10,000 times shorter than the mean waiting time in the unfolded state (the inverse of the folding rate coefficient). A. Szabos theory for diffusive transition paths shows that the upper bound for the transition path time is consistent with previous estimates of the Kramers pre-exponential factor for the rate coefficient. The theory also predicts that for smooth free energy barriers the transition path time is remarkably insensitive to the folding rate, with only a 2-fold difference for rate coefficients that differ by 100,000-fold. FRET efficiency distributions in single molecule experiments contain both structural and dynamical information. Extraction of this information from these distributions requires a careful analysis of contributions from dye photophysics. To investigate how mechanisms other than FRET affect the distributions obtained by counting donor and acceptor photons, we have measured single molecule fluorescence trajectories of a small alpha/beta protein, protein GB1, undergoing two-state, folding/unfolding transitions. Alexa 488 donor and and Alexa 594 acceptor dyes were attached to cysteines at positions 10 and 57 to yield 2 isomers donor10/accepor57 and donor57/acceptor 10 which were not separated by purification. The protein was immobilized via binding of a histidine tag added to a linker sequence at the N-terminus to cupric ions embedded in a polyethyleneglycol-coated glass surface. The distribution of FRET efficiencies assembled from the trajectories is complex with widths for the individual peaks in large excess of that caused by shot noise. Most of this complexity can be explained by two interfering photophysical effects a photo-induced red shift of the donor dye and differences in the quantum yield of the acceptor dye for the two isomers resulting from differences in quenching rate by the cupric ion. Measurements of steady state polarization, calculation of the donor-acceptor cross-correlation function from photon-by-photon trajectories, and comparison of the single molecule and ensemble kinetics all indicate that conformational distributions and dynamics do not contribute to the complexity. Recently developed statistical methods by Gopich and Szabo were used to extract folding and unfolding rate coefficients from single-molecule Forster resonance energy transfer (FRET) data for proteins with kinetics too fast to measure waiting time distributions. Two types of experiments and two different analyses were performed. In one experiment bursts of photons were collected from donor and acceptor fluorophores attached to a 73-residue protein, alpha3D, freely diffusing through the illuminated volume of a confocal microscope system. In the second, the protein was immobilized by linkage to a surface, and photons were collected until one of the fluorophores bleached. Folding and unfolding rate coefficients and mean FRET efficiencies for the folded and unfolded subpopulations were obtained from a photon by photon analysis of the trajectories using a maximum likelihood method. The ability of the method to describe the data in terms of a two-state model was checked by recoloring the photon trajectories with the extracted parameters and comparing the calculated FRET efficiency histograms with the measured histograms. The sum of the rate coefficients for the two-state model agreed to within 30% with the relaxation rate obtained from the decay of the donor-acceptor cross correlation function, confirming the high accuracy of the method. Interestingly, apparently reliable rate coefficients could be extracted using the maximum likelihood method, even at low (<10%) population of the minor component where the cross-correlation function was too noisy to obtain any useful information. The rate coefficients and mean FRET efficiencies were also obtained in an approximate procedure by simply fitting the FRET efficiency histograms, calculated by binning the donor and acceptor photons, with a sum of three-Gaussian functions. The kinetics are exposed in these histograms by the growth of a FRET efficiency peak at values intermediate between the folded and unfolded peaks as the bin size increases, a phenomenon with similarities to NMR exchange broadening. When comparable populations of folded and unfolded molecules are present, this method yields rate coefficients in very good agreement with those obtained with the maximum likelihood method. As a first step toward characterizing transition paths, the Viterbi algorithm was used to locate the most probable transition points in the photon trajectories.
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