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Exploring the conformational transitions of biomolecular systems using a simple two-state anisotropic network model.

Das A, Gur M, Cheng MH, Jo S, Bahar I, Roux B - PLoS Comput. Biol. (2014)

Bottom Line: Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach.Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied.An open-access web server has been created to deliver ANMPathway results.

View Article: PubMed Central - PubMed

Affiliation: Department of Biochemistry and Molecular Biology, Gordon Center for Integrative Science, University of Chicago, Chicago, Illinois, United States of America.

ABSTRACT
Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results.

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Effect of smoothing of the two-state potential on the adenylate kinase transition pathway.A. Energy of the system along the pathway for several pathways obtained by refining the original pathway by zero temperature string method calculation on the smoothed potential defined in Eq. (9). B. RMSD of the refined pathways from the pathway produced by ANMPathway.
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pcbi-1003521-g011: Effect of smoothing of the two-state potential on the adenylate kinase transition pathway.A. Energy of the system along the pathway for several pathways obtained by refining the original pathway by zero temperature string method calculation on the smoothed potential defined in Eq. (9). B. RMSD of the refined pathways from the pathway produced by ANMPathway.

Mentions: The effect of the cusp hypersurface on the potential energy surface was further examined by refining the pathway on a smoothed surface based on the following potential function [54], [57],(9)where and are ANM potentials defined in Eq. (1). The parameter determines the amount of mixing and the height of the barrier. In the limit , the potential defined above becomes the two-state potential with a cusp hypersurface defined previously in Eq. (4) i. e. . Therefore, if we refine the pathway after smoothing the potential using Eq. (9) with a high value of , the resulting pathway should not be very different. We tested this hypothesis by performing zero temperature string method [92] calculation on the smoothed energy surface starting from the final path produced by the ANMPathway method. The results for AK are shown in Fig. (11). It is noteworthy that, for , the RMSDs between corresponding images along the two pathways are extremely small (compared to the the resolution of the structures) and the position of the transition state is almost unchanged (the projections of the pathways on the space spanned by the two order parameters described in Fig. (2) are shown in the SM Fig. S4). As the value of is decreased the RMSDs increase and the position of the transition state moves slowly to the right. These observations demonstrate that the algorithm used in ANMPathway has the ability to find a proper transition state on the two-state surface with the cusp hypersurface and also illustrate that presence of cusp hypersurface does not have a significant impact on the over all features of the two-state potential.


Exploring the conformational transitions of biomolecular systems using a simple two-state anisotropic network model.

Das A, Gur M, Cheng MH, Jo S, Bahar I, Roux B - PLoS Comput. Biol. (2014)

Effect of smoothing of the two-state potential on the adenylate kinase transition pathway.A. Energy of the system along the pathway for several pathways obtained by refining the original pathway by zero temperature string method calculation on the smoothed potential defined in Eq. (9). B. RMSD of the refined pathways from the pathway produced by ANMPathway.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3974643&req=5

pcbi-1003521-g011: Effect of smoothing of the two-state potential on the adenylate kinase transition pathway.A. Energy of the system along the pathway for several pathways obtained by refining the original pathway by zero temperature string method calculation on the smoothed potential defined in Eq. (9). B. RMSD of the refined pathways from the pathway produced by ANMPathway.
Mentions: The effect of the cusp hypersurface on the potential energy surface was further examined by refining the pathway on a smoothed surface based on the following potential function [54], [57],(9)where and are ANM potentials defined in Eq. (1). The parameter determines the amount of mixing and the height of the barrier. In the limit , the potential defined above becomes the two-state potential with a cusp hypersurface defined previously in Eq. (4) i. e. . Therefore, if we refine the pathway after smoothing the potential using Eq. (9) with a high value of , the resulting pathway should not be very different. We tested this hypothesis by performing zero temperature string method [92] calculation on the smoothed energy surface starting from the final path produced by the ANMPathway method. The results for AK are shown in Fig. (11). It is noteworthy that, for , the RMSDs between corresponding images along the two pathways are extremely small (compared to the the resolution of the structures) and the position of the transition state is almost unchanged (the projections of the pathways on the space spanned by the two order parameters described in Fig. (2) are shown in the SM Fig. S4). As the value of is decreased the RMSDs increase and the position of the transition state moves slowly to the right. These observations demonstrate that the algorithm used in ANMPathway has the ability to find a proper transition state on the two-state surface with the cusp hypersurface and also illustrate that presence of cusp hypersurface does not have a significant impact on the over all features of the two-state potential.

Bottom Line: Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach.Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied.An open-access web server has been created to deliver ANMPathway results.

View Article: PubMed Central - PubMed

Affiliation: Department of Biochemistry and Molecular Biology, Gordon Center for Integrative Science, University of Chicago, Chicago, Illinois, United States of America.

ABSTRACT
Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results.

Show MeSH