Folding and unfolding rates for the ultrafast folding villin subdomain were determined from a photon-by-photon analysis of fluorescence trajectories in single molecule FRET experiments. One of the obstacles to measuring fast kinetics in single molecule fluorescence experiments is blinking of the fluorophores on a timescale that is not well separated from the process of interest. By incorporating acceptor blinking into a two-state kinetics model, we show that it is possible to extract accurate rate coefficients on the microsecond time scale for folding and unfolding using the maximum likelihood method of I.V. Gopich and A. Szabo. This method yields the most likely parameters of a given model that can reproduce the observed photon trajectories. The extracted parameters agree with both the decay rate of the donor-acceptor cross correlation function and the results of ensemble equilibrium and kinetic experiments using nanosecond laser temperature jump. Kramers developed the theory on how chemical reaction rates are influenced by the viscosity of the medium. At the viscosity of water, the kinetics of unimolecular reactions are described by diffusion of a Brownian particle over a free-energy barrier separating reactants and products. For reactions in solution this famous theory extended Eyring's transition state theory, and is widely applied in physics, chemistry, and biology, including reactions as complex as protein folding3,4. Because the diffusion coefficient of Kramers theory is determined by the dynamics in the sparsely-populated region of the barrier top, its properties have not been directly measured for any molecular system. Here we show that the Kramers diffusion coefficient and free energy barrier can be characterized by measuring the temperature- and viscosity-dependence of the transition path time for protein folding. The transition path is the small fraction of an equilibrium trajectory for a single molecule when the free-energy barrier separating two states is actually crossed (Fig. 1a). Its duration, the transition path time, can now be determined from photon trajectories for single protein molecules undergoing folding/unfolding transitions5. Our finding of a long transition path time with an unusually small solvent viscosity-dependence suggests that internal friction as well as solvent friction determine the Kramers diffusion coefficient for alpha-helical proteins, as opposed to a breakdown of his theory that occurs for many small-molecule reactions2. It is noteworthy that the new and fundamental information concerning Kramers theory and the dynamics of barrier crossings obtained here come from experiments on a protein rather than a much simpler chemical or physical system.
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