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Protein folding as a complex reaction: a two-component potential for the driving force of folding and its variation with folding scenario.

Chekmarev SF - PLoS ONE (2015)

Bottom Line: Chem.The Ψ-component is more complex and reveals characteristic features of the process of folding.The present approach is potentially applicable to other complex reactions, for which the transition from the reactant to the product can be described in a space of two (collective) variables.

View Article: PubMed Central - PubMed

Affiliation: Institute of Thermophysics, 630090 Novosibirsk, Russia and Department of Physics, Novosibirsk State University, 630090 Novosibirsk, Russia.

ABSTRACT
The Helmholtz decomposition of the vector field of probability fluxes in a two-dimensional space of collective variables makes it possible to introduce a potential for the driving force of protein folding [Chekmarev, J. Chem. Phys. 139 (2013) 145103]. The potential has two components: one component (Φ) is responsible for the source and sink of the folding flow, which represent, respectively, the unfolded and native state of the protein, and the other (Ψ) accounts for the flow vorticity inherently generated at the periphery of the flow field and provides the canalization of the flow between the source and sink. Both components obey Poisson's equations with the corresponding source/sink terms. In the present paper, we consider how the shape of the potential changes depending on the scenario of protein folding. To mimic protein folding dynamics projected onto a two-dimensional space of collective variables, the two-dimensional Müller and Brown potential is employed. Three characteristic scenarios are considered: a single pathway from the unfolded to the native state without intermediates, two parallel pathways without intermediates, and a single pathway with an off-pathway intermediate. To determine the probability fluxes, the hydrodynamic description of the folding reaction is used, in which the first-passage folding is viewed as a steady flow of the representative points of the protein from the unfolded to the native state. We show that despite the possible complexity of the folding process, the Φ-component is simple and universal in shape. The Ψ-component is more complex and reveals characteristic features of the process of folding. The present approach is potentially applicable to other complex reactions, for which the transition from the reactant to the product can be described in a space of two (collective) variables.

No MeSH data available.


Two-well landscape with a single pathway: General characterization.(a) the potential energy surface, (b) the free energy surface, (c) the first-passage time distribution, (d) the vector flow field, (e) the distribution of the divergence, and (f) the vorticity distribution.
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pone.0121640.g001: Two-well landscape with a single pathway: General characterization.(a) the potential energy surface, (b) the free energy surface, (c) the first-passage time distribution, (d) the vector flow field, (e) the distribution of the divergence, and (f) the vorticity distribution.

Mentions: This case corresponds to the simplest, two-state kinetics of protein folding, which are characteristic of small proteins [38]. Table 1 gives the values of the parameters determining the potential energy function, Equation (1), and Fig. 1a shows the corresponding PES. The simulations were performed at T = 3.0. The native state was associated with the point xn = 0.75, yn = 0.2. The MD trajectories were initiated in the vicinity of the point xu = 0.25, yu = 0.78 with a uniform random scattering of the points within ∣Δux∣ = ∣Δuy∣ = 0.1; these points were intended to mimic the completely unfolded (extended) protein states. The native state was considered to be reached if the deviation from the native state was not larger than ∣Δnx∣ = ∣Δny∣ = 0.01. The same conditions to choose the initial points (the scattering of the points) and to terminate the trajectories in the native state were used for the other systems.


Protein folding as a complex reaction: a two-component potential for the driving force of folding and its variation with folding scenario.

Chekmarev SF - PLoS ONE (2015)

Two-well landscape with a single pathway: General characterization.(a) the potential energy surface, (b) the free energy surface, (c) the first-passage time distribution, (d) the vector flow field, (e) the distribution of the divergence, and (f) the vorticity distribution.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4388825&req=5

pone.0121640.g001: Two-well landscape with a single pathway: General characterization.(a) the potential energy surface, (b) the free energy surface, (c) the first-passage time distribution, (d) the vector flow field, (e) the distribution of the divergence, and (f) the vorticity distribution.
Mentions: This case corresponds to the simplest, two-state kinetics of protein folding, which are characteristic of small proteins [38]. Table 1 gives the values of the parameters determining the potential energy function, Equation (1), and Fig. 1a shows the corresponding PES. The simulations were performed at T = 3.0. The native state was associated with the point xn = 0.75, yn = 0.2. The MD trajectories were initiated in the vicinity of the point xu = 0.25, yu = 0.78 with a uniform random scattering of the points within ∣Δux∣ = ∣Δuy∣ = 0.1; these points were intended to mimic the completely unfolded (extended) protein states. The native state was considered to be reached if the deviation from the native state was not larger than ∣Δnx∣ = ∣Δny∣ = 0.01. The same conditions to choose the initial points (the scattering of the points) and to terminate the trajectories in the native state were used for the other systems.

Bottom Line: Chem.The Ψ-component is more complex and reveals characteristic features of the process of folding.The present approach is potentially applicable to other complex reactions, for which the transition from the reactant to the product can be described in a space of two (collective) variables.

View Article: PubMed Central - PubMed

Affiliation: Institute of Thermophysics, 630090 Novosibirsk, Russia and Department of Physics, Novosibirsk State University, 630090 Novosibirsk, Russia.

ABSTRACT
The Helmholtz decomposition of the vector field of probability fluxes in a two-dimensional space of collective variables makes it possible to introduce a potential for the driving force of protein folding [Chekmarev, J. Chem. Phys. 139 (2013) 145103]. The potential has two components: one component (Φ) is responsible for the source and sink of the folding flow, which represent, respectively, the unfolded and native state of the protein, and the other (Ψ) accounts for the flow vorticity inherently generated at the periphery of the flow field and provides the canalization of the flow between the source and sink. Both components obey Poisson's equations with the corresponding source/sink terms. In the present paper, we consider how the shape of the potential changes depending on the scenario of protein folding. To mimic protein folding dynamics projected onto a two-dimensional space of collective variables, the two-dimensional Müller and Brown potential is employed. Three characteristic scenarios are considered: a single pathway from the unfolded to the native state without intermediates, two parallel pathways without intermediates, and a single pathway with an off-pathway intermediate. To determine the probability fluxes, the hydrodynamic description of the folding reaction is used, in which the first-passage folding is viewed as a steady flow of the representative points of the protein from the unfolded to the native state. We show that despite the possible complexity of the folding process, the Φ-component is simple and universal in shape. The Ψ-component is more complex and reveals characteristic features of the process of folding. The present approach is potentially applicable to other complex reactions, for which the transition from the reactant to the product can be described in a space of two (collective) variables.

No MeSH data available.