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Stochastic emergence of multiple intermediates detected by single-molecule quasi-static mechanical unfolding of protein

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ABSTRACT

Experimental probing of a protein-folding energy landscape can be challenging, and energy landscapes comprising multiple intermediates have not yet been defined. Here, we quasi-statically unfolded single molecules of staphylococcal nuclease by constant-rate mechanical stretching with a feedback positioning system. Multiple discrete transition states were detected as force peaks, and only some of the multiple transition states emerged stochastically in each trial. This finding was confirmed by molecular dynamics simulations, and agreed with another result of the simulations which showed that individual trajectories took highly heterogeneous pathways. The presence of Ca2+ did not change the location of the transition states, but changed the frequency of the emergence. Transition states emerged more frequently in stabilized domains. The simulations also confirmed this feature, and showed that the stabilized domains had rugged energy surfaces. The mean energy required per residue to disrupt secondary structures was a few times the thermal energy (1–3 kBT), which agreed with the stochastic feature. Thus, single-molecule quasi-static measurement has achieved notable success in detecting stochastic features of a huge number of possible conformations of a protein.

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Trajectory density map and 2D ‘topographic’ energy landscape by MD simulations. (a and b) Trajectory density maps in the absence (a) and presence (b) of Ca2+ in αβ number coordinates (see Methods). Three representative trajectories are shown as lines. Trajectories start from the upper right area (N′: 34.6±2.4, 29.5±3.2) in the absence of Ca2+, (N′: 34.5±2.1, 31.6±1.9) in the presence of Ca2+, and end at the coordinate origin (U: 0, 0). (c and d) 2D energy landscapes in the absence (a) and presence (b) of Ca2+. Deviation of the energy landscape from the fitted plane is depicted (see Supplementary Information, Fig. S5). Red curve represents the boundary distance of 25 nm (see Fig. 6f).
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f7-5_25: Trajectory density map and 2D ‘topographic’ energy landscape by MD simulations. (a and b) Trajectory density maps in the absence (a) and presence (b) of Ca2+ in αβ number coordinates (see Methods). Three representative trajectories are shown as lines. Trajectories start from the upper right area (N′: 34.6±2.4, 29.5±3.2) in the absence of Ca2+, (N′: 34.5±2.1, 31.6±1.9) in the presence of Ca2+, and end at the coordinate origin (U: 0, 0). (c and d) 2D energy landscapes in the absence (a) and presence (b) of Ca2+. Deviation of the energy landscape from the fitted plane is depicted (see Supplementary Information, Fig. S5). Red curve represents the boundary distance of 25 nm (see Fig. 6f).

Mentions: These findings were confirmed by MD simulations, which showed multiple transition states and heterogeneous pathways with stochastic appearance (Figs. 4 and 7; see Supplementary Information, Movies S1 to S3 and Supplementary Discussion). Individual trajectories underwent vigorous fluctuations, and the 2D trajectory density map clearly showed that individual trajectories were not uniquely determined and took highly heterogeneous pathways (Fig. 7). Meanwhile, kinetic studies analyzed folding processes using schemes with multiple intermediates and parallel pathways24–27, which differed in number depending on each kinetic study. This characteristic might be comparable to the present finding that individual trajectories stochastically take heterogeneous pathways through multiple intermediates in a complicated energy landscape.


Stochastic emergence of multiple intermediates detected by single-molecule quasi-static mechanical unfolding of protein
Trajectory density map and 2D ‘topographic’ energy landscape by MD simulations. (a and b) Trajectory density maps in the absence (a) and presence (b) of Ca2+ in αβ number coordinates (see Methods). Three representative trajectories are shown as lines. Trajectories start from the upper right area (N′: 34.6±2.4, 29.5±3.2) in the absence of Ca2+, (N′: 34.5±2.1, 31.6±1.9) in the presence of Ca2+, and end at the coordinate origin (U: 0, 0). (c and d) 2D energy landscapes in the absence (a) and presence (b) of Ca2+. Deviation of the energy landscape from the fitted plane is depicted (see Supplementary Information, Fig. S5). Red curve represents the boundary distance of 25 nm (see Fig. 6f).
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Related In: Results  -  Collection

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f7-5_25: Trajectory density map and 2D ‘topographic’ energy landscape by MD simulations. (a and b) Trajectory density maps in the absence (a) and presence (b) of Ca2+ in αβ number coordinates (see Methods). Three representative trajectories are shown as lines. Trajectories start from the upper right area (N′: 34.6±2.4, 29.5±3.2) in the absence of Ca2+, (N′: 34.5±2.1, 31.6±1.9) in the presence of Ca2+, and end at the coordinate origin (U: 0, 0). (c and d) 2D energy landscapes in the absence (a) and presence (b) of Ca2+. Deviation of the energy landscape from the fitted plane is depicted (see Supplementary Information, Fig. S5). Red curve represents the boundary distance of 25 nm (see Fig. 6f).
Mentions: These findings were confirmed by MD simulations, which showed multiple transition states and heterogeneous pathways with stochastic appearance (Figs. 4 and 7; see Supplementary Information, Movies S1 to S3 and Supplementary Discussion). Individual trajectories underwent vigorous fluctuations, and the 2D trajectory density map clearly showed that individual trajectories were not uniquely determined and took highly heterogeneous pathways (Fig. 7). Meanwhile, kinetic studies analyzed folding processes using schemes with multiple intermediates and parallel pathways24–27, which differed in number depending on each kinetic study. This characteristic might be comparable to the present finding that individual trajectories stochastically take heterogeneous pathways through multiple intermediates in a complicated energy landscape.

View Article: PubMed Central - PubMed

ABSTRACT

Experimental probing of a protein-folding energy landscape can be challenging, and energy landscapes comprising multiple intermediates have not yet been defined. Here, we quasi-statically unfolded single molecules of staphylococcal nuclease by constant-rate mechanical stretching with a feedback positioning system. Multiple discrete transition states were detected as force peaks, and only some of the multiple transition states emerged stochastically in each trial. This finding was confirmed by molecular dynamics simulations, and agreed with another result of the simulations which showed that individual trajectories took highly heterogeneous pathways. The presence of Ca2+ did not change the location of the transition states, but changed the frequency of the emergence. Transition states emerged more frequently in stabilized domains. The simulations also confirmed this feature, and showed that the stabilized domains had rugged energy surfaces. The mean energy required per residue to disrupt secondary structures was a few times the thermal energy (1–3 kBT), which agreed with the stochastic feature. Thus, single-molecule quasi-static measurement has achieved notable success in detecting stochastic features of a huge number of possible conformations of a protein.

No MeSH data available.


Related in: MedlinePlus