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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.


Three-well landscape with an off-pathway state: The potential for the driving force.General notations are as in Fig. 2. In panel c the Φ(r) = const and Ψ(r) = const isolines are shown with interval of . Characteristic values of Ψ(r) in the reaction channel: in region 1 Ψ(r) ≈ −1 × 10−5, and in region 2 Ψ(r) ≈ 2 × 10−5.
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pone.0121640.g006: Three-well landscape with an off-pathway state: The potential for the driving force.General notations are as in Fig. 2. In panel c the Φ(r) = const and Ψ(r) = const isolines are shown with interval of . Characteristic values of Ψ(r) in the reaction channel: in region 1 Ψ(r) ≈ −1 × 10−5, and in region 2 Ψ(r) ≈ 2 × 10−5.

Mentions: Another typical complication of the basic folding scenario described previously is the presence of off-pathway intermediates, which lead to a deviation from two-state kinetics [11]. When comparable with the native state in the life-time, such intermediates can play a role of “latent” states [44]. Table 3 gives the parameters of the potential energy function we used to construct the model PES in this case, and Fig. 5a depicts the PES. The simulations were performed at T = 1.25. The native state was associated with the point xn = 0.75, yn = 0.15, and the MD trajectories were initiated in the vicinity of the point xu = 0.25, yu = 0.8. The off-pathway intermediate is presented by a basin centered at x = 0.75, y = 0.65. The MFPT is . The simulation results are shown in Figs. 5b-5f and 6a-6c.


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)

Three-well landscape with an off-pathway state: The potential for the driving force.General notations are as in Fig. 2. In panel c the Φ(r) = const and Ψ(r) = const isolines are shown with interval of . Characteristic values of Ψ(r) in the reaction channel: in region 1 Ψ(r) ≈ −1 × 10−5, and in region 2 Ψ(r) ≈ 2 × 10−5.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0121640.g006: Three-well landscape with an off-pathway state: The potential for the driving force.General notations are as in Fig. 2. In panel c the Φ(r) = const and Ψ(r) = const isolines are shown with interval of . Characteristic values of Ψ(r) in the reaction channel: in region 1 Ψ(r) ≈ −1 × 10−5, and in region 2 Ψ(r) ≈ 2 × 10−5.
Mentions: Another typical complication of the basic folding scenario described previously is the presence of off-pathway intermediates, which lead to a deviation from two-state kinetics [11]. When comparable with the native state in the life-time, such intermediates can play a role of “latent” states [44]. Table 3 gives the parameters of the potential energy function we used to construct the model PES in this case, and Fig. 5a depicts the PES. The simulations were performed at T = 1.25. The native state was associated with the point xn = 0.75, yn = 0.15, and the MD trajectories were initiated in the vicinity of the point xu = 0.25, yu = 0.8. The off-pathway intermediate is presented by a basin centered at x = 0.75, y = 0.65. The MFPT is . The simulation results are shown in Figs. 5b-5f and 6a-6c.

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.