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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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Comparison with all-atom simulation results.A. Time trace of the distance between  atoms of residues 21 and 256 from a 235 ns long conventional MD simulation of the fully solvated system. The simulation was started from a structure obtained from a targeted MD simulation originated from the OFc state. The system undergoes a spontaneous transition to the IFo state. B. Comparison of the ANMPathway method and all-atom MD in the space of two order parameters. The all-atom MD results are shown as a pseudo free energy landscape , where P is the 2D distribution. The color-scale goes from blue (low energy) to red (high energy). The pathway predicted by ANMPathway (white line) goes mostly through the low energy regions of the free energy landscape.
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pcbi-1003521-g004: Comparison with all-atom simulation results.A. Time trace of the distance between atoms of residues 21 and 256 from a 235 ns long conventional MD simulation of the fully solvated system. The simulation was started from a structure obtained from a targeted MD simulation originated from the OFc state. The system undergoes a spontaneous transition to the IFo state. B. Comparison of the ANMPathway method and all-atom MD in the space of two order parameters. The all-atom MD results are shown as a pseudo free energy landscape , where P is the 2D distribution. The color-scale goes from blue (low energy) to red (high energy). The pathway predicted by ANMPathway (white line) goes mostly through the low energy regions of the free energy landscape.

Mentions: To gain more insights and validate the analysis, we compared the pathway from ANMPathway to a 235 ns long all-atom MD trajectory using as initial structure an intermediate close to the OF occluded state [75]. The details of the simulation protocols are described in the text S1 of the Supplemental Material (SM). The time evolution of the structure during this transition was probed by monitoring a relevant order parameter, namely the distance between the binding-site residues N21 and S256 shown in Fig. (4A). Notably, a spontaneous transition to IF open state was observed in this conventional (unbiased) full atomistic MD simulation. The MD trajectory thus provides an important data-set for benchmarking the ANMPathway method. Fig. (4B) compares the projection from the ANMPathway (white curve) and the MD trajectory on the space of two order parameters, the N21-S256 distance and the RMSD from the OF occluded state. The MD data are represented as a crude free energy calculated by taking the logarithm of the two-dimensional histogram of the above mentioned two order parameters shown in Fig. (4B). The pathway predicted by ANMPathway is constructed on a smooth potential energy function and has no thermal fluctuations. As such, it is representative of an average pathway of the real system and it should go through the low energy regions of the free energy landscape obtained from the MD simulation of LeuT embedded in fully solvated membrane lipids at finite temperature. This is exactly the behavior we observe in Fig. (4B) for the most parts where all-atom MD data are available. This agreement is satisfactory, given the minimal computational cost required by ANMPathway compared to that (several orders of magnitude larger) required for the full scale all-atom MD simulation.


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)

Comparison with all-atom simulation results.A. Time trace of the distance between  atoms of residues 21 and 256 from a 235 ns long conventional MD simulation of the fully solvated system. The simulation was started from a structure obtained from a targeted MD simulation originated from the OFc state. The system undergoes a spontaneous transition to the IFo state. B. Comparison of the ANMPathway method and all-atom MD in the space of two order parameters. The all-atom MD results are shown as a pseudo free energy landscape , where P is the 2D distribution. The color-scale goes from blue (low energy) to red (high energy). The pathway predicted by ANMPathway (white line) goes mostly through the low energy regions of the free energy landscape.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1003521-g004: Comparison with all-atom simulation results.A. Time trace of the distance between atoms of residues 21 and 256 from a 235 ns long conventional MD simulation of the fully solvated system. The simulation was started from a structure obtained from a targeted MD simulation originated from the OFc state. The system undergoes a spontaneous transition to the IFo state. B. Comparison of the ANMPathway method and all-atom MD in the space of two order parameters. The all-atom MD results are shown as a pseudo free energy landscape , where P is the 2D distribution. The color-scale goes from blue (low energy) to red (high energy). The pathway predicted by ANMPathway (white line) goes mostly through the low energy regions of the free energy landscape.
Mentions: To gain more insights and validate the analysis, we compared the pathway from ANMPathway to a 235 ns long all-atom MD trajectory using as initial structure an intermediate close to the OF occluded state [75]. The details of the simulation protocols are described in the text S1 of the Supplemental Material (SM). The time evolution of the structure during this transition was probed by monitoring a relevant order parameter, namely the distance between the binding-site residues N21 and S256 shown in Fig. (4A). Notably, a spontaneous transition to IF open state was observed in this conventional (unbiased) full atomistic MD simulation. The MD trajectory thus provides an important data-set for benchmarking the ANMPathway method. Fig. (4B) compares the projection from the ANMPathway (white curve) and the MD trajectory on the space of two order parameters, the N21-S256 distance and the RMSD from the OF occluded state. The MD data are represented as a crude free energy calculated by taking the logarithm of the two-dimensional histogram of the above mentioned two order parameters shown in Fig. (4B). The pathway predicted by ANMPathway is constructed on a smooth potential energy function and has no thermal fluctuations. As such, it is representative of an average pathway of the real system and it should go through the low energy regions of the free energy landscape obtained from the MD simulation of LeuT embedded in fully solvated membrane lipids at finite temperature. This is exactly the behavior we observe in Fig. (4B) for the most parts where all-atom MD data are available. This agreement is satisfactory, given the minimal computational cost required by ANMPathway compared to that (several orders of magnitude larger) required for the full scale all-atom MD simulation.

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