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Minimum free energy path of ligand-induced transition in adenylate kinase.

Matsunaga Y, Fujisaki H, Terada T, Furuta T, Moritsugu K, Kidera A - PLoS Comput. Biol. (2012)

Bottom Line: It was found that the LID domain was able to partially close without the ligand, while the closure of the AMPbd domain required the ligand binding.It was also found that complete closure of the LID domain required the dehydration of solvents around the P-loop.These findings suggest that the interplay of the two different types of domain motion is an essential feature in the conformational transition of the enzyme.

View Article: PubMed Central - PubMed

Affiliation: Computational Science Research Program, RIKEN, Wako, Japan. ymatsunaga@riken.jp

ABSTRACT
Large-scale conformational changes in proteins involve barrier-crossing transitions on the complex free energy surfaces of high-dimensional space. Such rare events cannot be efficiently captured by conventional molecular dynamics simulations. Here we show that, by combining the on-the-fly string method and the multi-state Bennett acceptance ratio (MBAR) method, the free energy profile of a conformational transition pathway in Escherichia coli adenylate kinase can be characterized in a high-dimensional space. The minimum free energy paths of the conformational transitions in adenylate kinase were explored by the on-the-fly string method in 20-dimensional space spanned by the 20 largest-amplitude principal modes, and the free energy and various kinds of average physical quantities along the pathways were successfully evaluated by the MBAR method. The influence of ligand binding on the pathways was characterized in terms of rigid-body motions of the lid-shaped ATP-binding domain (LID) and the AMP-binding (AMPbd) domains. It was found that the LID domain was able to partially close without the ligand, while the closure of the AMPbd domain required the ligand binding. The transition state ensemble of the ligand bound form was identified as those structures characterized by highly specific binding of the ligand to the AMPbd domain, and was validated by unrestrained MD simulations. It was also found that complete closure of the LID domain required the dehydration of solvents around the P-loop. These findings suggest that the interplay of the two different types of domain motion is an essential feature in the conformational transition of the enzyme.

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PMF along the strings and the corresponding domain motions.(Top) PMFs along the snapshots of the strings for (A) apo and (B) holo-AK at t = 0 (initial path), 2, 4, 6, 8, 10, 12 (MFEP) ns. The indices of string images are numbered from the open (PDBid: 4ake) to closed crystal structures (PDBid: 1ake). Partially-closed state of apo-AK and a substantial PMF barrier of holo-AK are encircled. (Bottom) Projections of MFEP onto the space defined by the distances of  mass centers between the LID-CORE and AMPbd-CORE domains, for (C) apo and (D) holo-AK. The black curves indicate the initial paths (t = 0), and the red curves are the MFEPs (t = 12 ns). The PMF is visualized by the colored contour lines (delineating regions of low energy (blue) to regions of high energy (red)).
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pcbi-1002555-g002: PMF along the strings and the corresponding domain motions.(Top) PMFs along the snapshots of the strings for (A) apo and (B) holo-AK at t = 0 (initial path), 2, 4, 6, 8, 10, 12 (MFEP) ns. The indices of string images are numbered from the open (PDBid: 4ake) to closed crystal structures (PDBid: 1ake). Partially-closed state of apo-AK and a substantial PMF barrier of holo-AK are encircled. (Bottom) Projections of MFEP onto the space defined by the distances of mass centers between the LID-CORE and AMPbd-CORE domains, for (C) apo and (D) holo-AK. The black curves indicate the initial paths (t = 0), and the red curves are the MFEPs (t = 12 ns). The PMF is visualized by the colored contour lines (delineating regions of low energy (blue) to regions of high energy (red)).

Mentions: The MFEPs for apo and holo-AKs, and their PMFs, were obtained from the string method and the MBAR method, respectively (see Videos S1 and S2). The MFEPs were calculated using the same 20 principal components selected for the collective variables. The holo-AK calculations were undertaken with the bisubstrate analog inhibitor (Ap5A) as the bound ligand without imposing any restraint on the ligand. Figures 2A and 2B show the MBAR estimates of the PMFs along the images of the MFEP (the converged string at 12 ns in Figures 2A and 2B) for apo and holo-AK, respectively. Here, the images on the string are numbered from the open (; PDBid: 4ake [28]) to the closed conformation (; PDBid: 1ake [29]). These terminal images were fixed during the simulations to enable sampling of the conformations around the crystal structures. In the figures, the convergence of the PMF in the string method process is clearly seen in both systems. Convergence was also confirmed by the error estimates (Figure S1), and by the root-mean-square displacement (RMSD) of the string from its initial path (Figure S2). The PMF along the MFEP reveals a broad potential well on the open-side conformations of apo-AK, suggesting that the open form of AK is highly flexible [20]. This broad well is divided into two regions, the fully open () and partially closed states (, encircled) by a small PMF barrier. In holo-AK (Figure 2B), the MFEP exhibits a single substantial free energy barrier () between the open and closed states, which does not appear in the initial path. This barrier will be identified as the transition state below. It is shown in the PMF along the MFEP that the closed form (tightly binding the ligand) is much more stable than the open form with loose binding to the ligand (large fluctuations of the ligand will be shown later).


Minimum free energy path of ligand-induced transition in adenylate kinase.

Matsunaga Y, Fujisaki H, Terada T, Furuta T, Moritsugu K, Kidera A - PLoS Comput. Biol. (2012)

PMF along the strings and the corresponding domain motions.(Top) PMFs along the snapshots of the strings for (A) apo and (B) holo-AK at t = 0 (initial path), 2, 4, 6, 8, 10, 12 (MFEP) ns. The indices of string images are numbered from the open (PDBid: 4ake) to closed crystal structures (PDBid: 1ake). Partially-closed state of apo-AK and a substantial PMF barrier of holo-AK are encircled. (Bottom) Projections of MFEP onto the space defined by the distances of  mass centers between the LID-CORE and AMPbd-CORE domains, for (C) apo and (D) holo-AK. The black curves indicate the initial paths (t = 0), and the red curves are the MFEPs (t = 12 ns). The PMF is visualized by the colored contour lines (delineating regions of low energy (blue) to regions of high energy (red)).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3369945&req=5

pcbi-1002555-g002: PMF along the strings and the corresponding domain motions.(Top) PMFs along the snapshots of the strings for (A) apo and (B) holo-AK at t = 0 (initial path), 2, 4, 6, 8, 10, 12 (MFEP) ns. The indices of string images are numbered from the open (PDBid: 4ake) to closed crystal structures (PDBid: 1ake). Partially-closed state of apo-AK and a substantial PMF barrier of holo-AK are encircled. (Bottom) Projections of MFEP onto the space defined by the distances of mass centers between the LID-CORE and AMPbd-CORE domains, for (C) apo and (D) holo-AK. The black curves indicate the initial paths (t = 0), and the red curves are the MFEPs (t = 12 ns). The PMF is visualized by the colored contour lines (delineating regions of low energy (blue) to regions of high energy (red)).
Mentions: The MFEPs for apo and holo-AKs, and their PMFs, were obtained from the string method and the MBAR method, respectively (see Videos S1 and S2). The MFEPs were calculated using the same 20 principal components selected for the collective variables. The holo-AK calculations were undertaken with the bisubstrate analog inhibitor (Ap5A) as the bound ligand without imposing any restraint on the ligand. Figures 2A and 2B show the MBAR estimates of the PMFs along the images of the MFEP (the converged string at 12 ns in Figures 2A and 2B) for apo and holo-AK, respectively. Here, the images on the string are numbered from the open (; PDBid: 4ake [28]) to the closed conformation (; PDBid: 1ake [29]). These terminal images were fixed during the simulations to enable sampling of the conformations around the crystal structures. In the figures, the convergence of the PMF in the string method process is clearly seen in both systems. Convergence was also confirmed by the error estimates (Figure S1), and by the root-mean-square displacement (RMSD) of the string from its initial path (Figure S2). The PMF along the MFEP reveals a broad potential well on the open-side conformations of apo-AK, suggesting that the open form of AK is highly flexible [20]. This broad well is divided into two regions, the fully open () and partially closed states (, encircled) by a small PMF barrier. In holo-AK (Figure 2B), the MFEP exhibits a single substantial free energy barrier () between the open and closed states, which does not appear in the initial path. This barrier will be identified as the transition state below. It is shown in the PMF along the MFEP that the closed form (tightly binding the ligand) is much more stable than the open form with loose binding to the ligand (large fluctuations of the ligand will be shown later).

Bottom Line: It was found that the LID domain was able to partially close without the ligand, while the closure of the AMPbd domain required the ligand binding.It was also found that complete closure of the LID domain required the dehydration of solvents around the P-loop.These findings suggest that the interplay of the two different types of domain motion is an essential feature in the conformational transition of the enzyme.

View Article: PubMed Central - PubMed

Affiliation: Computational Science Research Program, RIKEN, Wako, Japan. ymatsunaga@riken.jp

ABSTRACT
Large-scale conformational changes in proteins involve barrier-crossing transitions on the complex free energy surfaces of high-dimensional space. Such rare events cannot be efficiently captured by conventional molecular dynamics simulations. Here we show that, by combining the on-the-fly string method and the multi-state Bennett acceptance ratio (MBAR) method, the free energy profile of a conformational transition pathway in Escherichia coli adenylate kinase can be characterized in a high-dimensional space. The minimum free energy paths of the conformational transitions in adenylate kinase were explored by the on-the-fly string method in 20-dimensional space spanned by the 20 largest-amplitude principal modes, and the free energy and various kinds of average physical quantities along the pathways were successfully evaluated by the MBAR method. The influence of ligand binding on the pathways was characterized in terms of rigid-body motions of the lid-shaped ATP-binding domain (LID) and the AMP-binding (AMPbd) domains. It was found that the LID domain was able to partially close without the ligand, while the closure of the AMPbd domain required the ligand binding. The transition state ensemble of the ligand bound form was identified as those structures characterized by highly specific binding of the ligand to the AMPbd domain, and was validated by unrestrained MD simulations. It was also found that complete closure of the LID domain required the dehydration of solvents around the P-loop. These findings suggest that the interplay of the two different types of domain motion is an essential feature in the conformational transition of the enzyme.

Show MeSH
Related in: MedlinePlus