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 dyelabeled, 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 s, >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.A detailed description and understanding of mechanisms of protein folding has been one of the great challenges to biophysical science. The simplest system to study, and the one that has produced the most insights, is a protein exhibiting 2-state behavior (1-7). A 2-state protein has only 2-populations of molecules in equilibrium and at all times in kinetic experiments-folded and unfolded. In ensemble folding experiments kinetics are studied by rapidly changing solution conditions, e.g., the temperature or denaturant concentration, and monitoring the relaxation of the 2 populations to their new equilibrium ratio with probes such as fluorescence, circular dichroism or infrared spectroscopy. Single molecule kinetics, however, can be studied at equilibrium. As can be seen from the schematic of a trajectory in Fig. 1, the dynamical nature of equilibrium is dramatically demonstrated when observing Förster resonance energy transfer (FRET) in a single-molecule fluorescence experiment. There are fluctuations due to shot noise about a mean value in each state, interrupted by what appear to be instantaneous jumps in FRET efficiency signaling folding or unfolding. The residence or waiting times in each state are exponentially distributed, with the mean time in the unfolded and folded segments of the trajectories corresponding to the inverse of the folding and ...

Protein folding kinetics and thermodynamics from atomistic simulation

“…The transition path time is the time it takes the molecule to transition between the folded and unfolded basin, and can be substantially shorter than the mean waiting times between such folding and unfolding events (39,40). The mean value of the transition path time is of considerable interest as it contains useful information regarding the properties of the free-energy barrier.…”

“…The mean value of the transition path time is of considerable interest as it contains useful information regarding the properties of the free-energy barrier. It also determines the time resolution needed in experiments in order to resolve individual folding events in single-molecule studies (39,40). For each folding and unfolding event we determined the transition path time as the time required to transition fully between the RMSD cutoffs used to define these two states.…”

Is there an en route folding intermediate for cold shock proteins?

“…As the structures in TSE have relatively high free energies and very short lifetimes, 22 it is difficult to study them directly in experiments. The dependence of rate constants of refolding and unfolding on denaturant concentration suggests that the transition state (TS) of Csp should be very compact.…”

Denaturant-dependent folding of GFP

“…Indeed, it can be justly stated that simulations of structure-based models are remarkably successful in predicting the folding mechanisms in the presence (20)(21)(22) and absence of denaturants (23)(24)(25). More refined questions, such as the relationship between pathway diversity and the symmetry of the underlying native structures (26), transition path times for crossing free energy barriers (27), the nature of the transition state ensemble (28)(29)(30)(31) have also been addressed using theory and experiments. In contrast, much less is known about how large proteins with number, N, of amino acids exceeding ≈200 with complex β-sheet fold.…”