Protein folding transition states can have zero lifetime
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The retrieved evidence discusses transition states and measures non-zero transition path times for proteins in the microsecond range, but does not establish whether transition states can have a zero lifetime.
Understanding the folding mechanisms of biomolecules, such as proteins and nucleic acids, requires probing time-dependent changes of conformations, including secondary and tertiary structure formation. All these mechanism-relevant structural transitions, typically seen as coarse-grained descriptions in molecular dynamics simulations, occur in the tiny fraction of a molecular trajectory called the transition path (TP). However, TPs have been inaccessible for most proteins due to the limited time resolution of single-molecule techniques. Here, we measure the TP times of eight two-state single-domain proteins in aqueous solution using nanophotonics-enhanced single-molecule fluorescence spectroscopy. We found that the TP times are extremely short, ranging from 0.7 to 4 μs, and insensitive to most protein properties. Surprisingly, however, the extracted diffusion coefficient at the free energy barrier on the number of native contacts coordinate increases with protein length. This facilitation of diffusion in larger proteins is explained by increased cooperative native contact formation during folding, which reduces the roughness of the energy landscape. Our results reveal that evolutionary optimization of the energy landscape is much more efficient for protein folding than for other biomolecular processes.
This facilitation of diffusion in larger proteins is explained by increased cooperative native contact formation during folding, which reduces the roughness of the energy landscape. Our results reveal that evolutionary optimization of the energy landscape is much more efficient for protein folding than for other biomolecular processes. The transition path (TP) is part of a molecular trajectory connecting stable conformational states, such as folded and unfolded states for a two-state protein ( Fig. 1(a) ) [ 1 – 3 ]. Therefore, the TP encodes the dynamics of crossing a free energy barrier between these states.
A few TP times close to 10 μ s have been measured by slowing down the dynamics using viscogen [ 12 ] or for a designed protein [ 13 , 14 ], in which a large number of non-native salt-bridges lengthens the TP. Fig. 1. Single-molecule FRET with zero-mode waveguides to measure folding transition paths. Open in a new tab (a) Schematic illustration of the transition paths on a one-dimensional free energy profile (top), idealized (noise-free) FRET efficiency traces (middle), and photon trajectory (bottom). Yellow shaded regions indicate the transition path region.
(b) Schematic illustration of the free-diffusion experiment, in which a donor (green circle) and acceptor (orange circle)-labeled protein can diffuse in and out (red trajectory) of a zero-mode waveguide. (Bottom) Scanning electron microscope image of a single zero-mode waveguide. (c) Fluorescence enhancement from the waveguide (0.1 ms bin time). (d) Representative trajectories at high-illumination intensity to measure transition paths (0.1 ms bin time). (e) Representative binned fluorescence trajectories, binned FRET traces, and photon trajectories of a folding transition (left) and an unfolding transition (right). Bin time: 10 μ s .
Red dashed lines indicate the transition time point determined from the Viterbi algorithm. Yellow shaded regions indicate the transition path region predicted by the maximum likelihood method. In this work, we use a zero-mode waveguide [ 15 ] ( Fig. 1(b) ) that enhances fluorescence emission [ 16 , 17 ] to improve the time resolution by a factor of ~10 and measure transition path times for protein folding in aqueous solution. We studied eight two-state single-domain proteins (see Supplemental Material [ 18 ], Fig. S1 ) with different secondary structures (all α , all β , and α / β ), sequence lengths, and folding kinetics to investigate how various properties of proteins affect the TP times.
Maximum likelihood analysis to determine folding transition path (TP) times. Open in a new tab (a) (Left) One-intermediate model with acceptor blinking (six-state model). U: unfolded state, S: virtual intermediate state representing the TP highlighted in yellow, F: folded state. The lifetime ( τ S ) and FRET efficiency of the intermediate state correspond to the TP time ( t TP ) and the FRET efficiency, respectively. Subscripted d: acceptor dark state, subscripted b: acceptor bright state. (Right) Double-TP model (eight-state model). S1 and S2 represent the true and fake TP, respectively. (b) (Left) Structures of proteins and their relaxation rates and TP times.
To determine the parameters accurately, we fitted the data with free parameters of the double-TP model and obtained the TP times of these proteins from the value of the fast TP (S1) (see Supplemental Material [ 18 ], Table S5 ). These times are 0.8 μ s for both protein G and Csp Tm ( Figs. 2(b) and 5 ). The parameters of the double-TP model for the six fast-folding proteins converge to those of the single-TP model (six-state), indicating that the effect of fake transitions is negligible in the data analysis of these proteins. Fig. 5. Maximum likelihood analysis to determine folding transition path (TP) times.
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Small single-domain proteins often exhibit only a single free-energybarrier, or transition state, between the denatured and the native state.The folding kinetics of these proteins is usually explored via mutationalanalysis. A central question is which structural information on thetransition state can be derived from the mutational data. To interpret thesedata, we have developed models that are based (a) on the substructuralcooperativity of helices and hairpins, and (b) on splitting upmutation-induced stability changes of a protein into components for itssubstructures. We obtain a consistent st
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