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Mechanism of Vitamin D Receptor Ligand-Binding Domain Regulation Studied by gREST Simulations

  • Toru Ekimoto
    Toru Ekimoto
    Graduate School of Medical Life Science, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
    More by Toru Ekimoto
  • Takafumi Kudo
    Takafumi Kudo
    Graduate School of Medical Life Science, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
  • Tsutomu Yamane
    Tsutomu Yamane
    Center for Computational Science, RIKEN, 1-7-22 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
  • , and 
  • Mitsunori Ikeguchi*
    Mitsunori Ikeguchi
    Graduate School of Medical Life Science, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
    Center for Computational Science, RIKEN, 1-7-22 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
    *Email: [email protected]
Cite this: J. Chem. Inf. Model. 2021, 61, 7, 3625–3637
Publication Date (Web):June 30, 2021
https://doi.org/10.1021/acs.jcim.1c00534

Copyright © 2021 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

The vitamin D receptor ligand-binding domain (VDR-LBD) undergoes conformational changes upon ligand binding. In this nuclear receptor family, agonistic or antagonistic activities are controlled by the conformation of the helix (H)12. However, all crystal structures of VDR-LBD reported to date correspond to the active H12 conformation, regardless of agonist/antagonist binding. To understand the mechanism of VDR-LBD regulation structurally, conformational samplings of agonist- and antagonist-bound rat VDR-LBD were performed using the generalized replica exchange with solute tempering (gREST) method. The gREST simulations demonstrated different structural responses of rat VDR-LBD to agonist or antagonist binding, whereas in conventional molecular dynamics simulations, the conformation was the same as that of the crystal structures, regardless of agonist/antagonist binding. In the gREST simulations, a spontaneous conformational change of H12 was observed only for the antagonist complex. The different responses to agonist/antagonist binding were attributed to hydrophobic core formation at the ligand-binding pocket and cooperative rearrangements of H11. The gREST method can be applied to the examination of structure–activity relationships for multiple VDR-LBD ligands.

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Introduction

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The vitamin D receptor (VDR) is a member of the nuclear receptor (NR) family. (1−6) Depending on the binding of 1α,25-dihydroxyvitamin D3, VDR regulates the expression of genes related to calcium homeostasis, cell differentiation, proliferation, and immunomodulation. VDR and NRs are well-known drug targets. (7−9) For example, VDR and estrogen receptor (ER) agonists are therapeutic agents for osteoporosis, whereas ER antagonists are used to treat breast cancer. Depending on the disease being targeted, agonistic or antagonistic activity for the target NR is required. Therefore, understanding the mechanism of agonistic/antagonistic activity regulation is crucial from both biological and pharmaceutical perspectives.
According to experimental studies such as X-ray crystallography, NRs are commonly regulated by a local conformational change of the helix (H)12 of the ligand-binding domain (LBD). (1−6,8−11) In the apo state, H12 fluctuates freely (e.g., retinoid X receptor α, PDBID: 6HN6 (12)). Upon agonist binding, H10, H11, and, H12 undergo conformational changes, and H12 adopts an active conformation (e.g., ER/estradiol complex, PDBID: 1ERE; (13)Figure 1A). The active conformation generates the activation function 2 (AF-2) surface required for binding of the coactivator (e.g., ER/estradiol complex structure with a key-motif peptide of coactivator, PDBID: 4J24 (14)). Agonist binding to LBD, formation of the active conformation of H12, and coactivator recruitment occur at the beginning of a gene expression event. In contrast, upon antagonist binding, H12 does not adopt the active conformation and coactivator recruitment is inhibited (e.g., ER/tamoxifen complex, PDBID: 3ERT; (15)Figure 1B), resulting in the inhibition of gene expression.

Figure 1

Figure 1. Crystal structures and a solution model: (A,B) ER/agonist (PDBID: 1ERE (13)) or ER/antagonist (PDBID: 3ERT (15)) complexes, (C,D) VDR/agonist (PDBID: 2ZLC (33)) and VDR/antagonist (PDBID: 2ZXM (17)) complexes, and (E) solution model of the VDR/antagonist complex yielded by the MD-SAXS approach. (11) H11 and H12 are colored green and magenta, respectively.

However, in the case of VDR, the antagonistic activity cannot be explained structurally because X-ray crystal structures of LBD, except for the VDR-LBD/5b complex (PDBID: 5XPL (16)), are essentially identical to the active conformation, regardless of agonist/antagonist binding (Figure 1C,D). (1,4,6,11) The antagonists used were JB (PDBID: 2ZXM (17)), TEI9647 (PDBID: 3A2H (18)), ADTT (PDBID: 2ZMI (19)), ADMI4 (PDBID: 2ZMJ (19)), and 5b (PDBID: 5XPL (16)). Because these antagonists have different scaffolds, their structural mechanisms for exhibiting antagonist activities may differ; however, the antagonist-bound conformation around H12 is identical to the active conformation. Only the crystal structure of the rat VDR-LBD/5b complex (PDBID: 5XPL (16)) has provided structural insight into antagonism: the end of H11 shifts from the canonical position of the active conformation, and the region between H11 and H12 is disordered. However, the position of H12 is still identical to that in the active conformation, and therefore, agonistic or antagonistic activity cannot be distinguished solely by the crystal structures of the VDR-LBD/ligand complexes.
To obtain structural information about the mechanism of VDR-LBD regulation beyond the scope of X-ray crystallography, experimental and computational studies have been conducted to investigate solution structures. According to experimental studies using small-angle X-ray scattering (SAXS), (20) hydrogen/deuterium exchange coupled with mass spectrometry, (21,22) and nuclear magnetic resonance, (23) natural hormone (agonist)-bound VDR adopts an active conformation even in solution, (20) whereas structural fluctuations in the H11-H12 region were observed in the apo state. (21,22) In contrast, in the antagonist-bound state, the H11-H12 region is disordered, (23) suggesting that the flexibility around H12 prevents the active conformation of H12. Molecular dynamics (MD) simulations have been applied to study the structural fluctuation of H12 in agonist- and/or antagonist-bound VDR-LBD, (24−26) VDR-LBD with coactivator, (27) drug design, (28) conformational changes in the apo state, (29) and pathway analysis of ligand dissociation from VDR-LBD (30) and NRs. (31) During simulations of several tens of nanoseconds, (24−26) the VDR-LBD/antagonist complex fluctuated around the crystal structure (i.e., the active conformation), and a large conformational change around H12 was not observed. Even in microsecond-scale all-atom or coarse-grained MD simulations of VDR-LBD without ligand, (29) the position of H12 was not significantly different from that in the active conformation. Ligand-unbound pathway analyses of VDR-LBD (30,31) revealed five ligand-dissociation pathways, including dissociation through a space opened between H12 and the C-terminal part of H11. However, conformational changes of H12 in response to antagonist binding and the explicit conformation of the VDR-LBD/antagonist complex remain unclear.
In contrast to these studies using MD simulations alone, a combined approach of SAXS and MD simulations, termed the MD-SAXS approach, (11) yielded a reasonable model of the VDR-LBD/antagonist complex explaining the antagonistic activity (Figure 1E). In this approach, SAXS experiments and MD simulations were performed independently. From several initial models prepared by homology modeling of H12, short 100 ns MD simulations were performed. By comparing the theoretical scattering intensity of each snapshot with the experimental intensity, the solution model most consistent with the experimental data was selected. In the rat VDR-LBD/antagonist model, H12 was partially unraveled in a position different from that in the active conformation at the coactivator binding region (Figure 1E). As the conformation around H12 prohibited AF-2 surface generation and coactivator recruitment, the model explained antagonism structurally. In addition, the model showed characteristic features: the kink between H10 and H11 had disappeared, and the region from the end of H11 to H12 (Loop11-12) was disordered. The participation of H11 in the formation/deformation of the active/inactive conformations of H12 was a key finding, with a disordered conformation of Loop11-12 observed in the crystal structure of the rat VDR-LBD/5b complex (PDBID: 5XPL (16)).
Although the MD-SAXS approach (11) yielded a reasonable model of the VDR-LBD/antagonist complex, the initial-model dependence remains an issue in structural sampling. Experimental SAXS data were required to select a reasonable model from the sampled structures starting from multiple initial models. Because of the dependency on initial models, the structural details of the regulatory mechanism, that is, the structural origin of conformational changes induced by ligand binding and relationships among the conformational changes, remain unclear. Therefore, to more extensively examine the regulatory mechanism, a computational protocol is required to capture spontaneous conformational changes from the active conformation in response to the two ligand types.
In this study, we examined the structural difference between agonist- and antagonist-bound rat VDR-LBD and the regulatory mechanism of spontaneous conformational changes sampled by the generalized replica exchange with solute tempering (gREST) method. (32) The gREST method enhances structural sampling of a specific protein region by scaling specific energy terms. According to data from the MD-SAXS approach, (11) conformational changes of H11 near the kink and the Loop11-12 region are key to obtaining structures that are consistent with the experimental SAXS data. Thus, H11 and H12 were set to the solute-tempering region (where the enhanced sampling was performed) in the gREST simulations. The natural hormones 1α,25-(OH)2D3 and JB (17) were selected as the agonist and the antagonist, respectively (Figure S1). These two ligands share the same scaffold at the A-ring, seco-B, and CD ring, differing only at the side chain. JB has a bifurcated side chain of a butyl group at C-22 and does not have two methyl groups at the edge of the hydroxy group. Despite their different activities, their crystal structures (PDBID: 2ZLC, (33)2ZXM (17)) are essentially identical, that is, the active conformation (Figure 1C,D). Using the active conformation as an initial structure, we demonstrate different structural responses of VDR-LBD to agonist and antagonist binding. Hereafter, the rat VDR-LBD/hormone complex and rat VDR-LBD/antagonist JB complex are denoted as the agonist complex and antagonist complex, respectively.

Methods

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Initial Model Setup

Initial structures of agonist- and antagonist-bound rat VDR-LBD for simulations were prepared from the rat VDR-LBD/agonist 1 complex (PDBID: 2ZLC (33)) and rat VDR-LBD/antagonist JB (PDBID: 2ZXM (17)) crystal structures, respectively. The missing regions of residues 160–217 (Δ165–211) in helix 3 (H3) and residues 421–423 in the C-terminus were transplanted from the modeled structure used in our previous simulations. (11) The protonation states of the ligands were determined by the Epik module in Maestro. (34)
Solution systems were prepared using Solution Builder (35,36) implemented in CHARMM-GUI. (37) In the building process, missing hydrogen atoms were added: the Nδ atom in histidine was protonated (see Supporting Information), and the N- and C-termini at residues 123 and 423 were set to NH3+ and COO, respectively. In MD simulations, we used a rectangular unit cell filled with water molecules (TIP3 water model (38)) after placing the initial model in the center of the cell. In addition, sodium and chloride ions were added so that the ion density, including counterions, was 150 mM.

Conventional MD Simulations

For comparison with the gREST simulations, conventional MD simulations were performed using the program package GROMACS ver. 2016.3 (39−41) under periodic boundary conditions. The CHARMM36 force field (42−44) and CHARMM Generalized Force Field (CGenFF) (45) were used for proteins and ligands, respectively. After energy minimization (steepest descent method) and a 25 ps equilibration run, a 1 μs production run was performed. The electrostatic interaction was handled by the smooth particle mesh Ewald (PME) method, (46) and the van der Waals interaction was truncated by the switching function in the range of 10–12 Å. The lengths of bonds containing hydrogen atoms were constrained using the P-LINKS algorithm. (47) The canonical (NVT) ensemble and isothermal–isobaric (NPT) ensemble were adopted in the equilibration and production runs, respectively. The temperature and pressure were set to 300 K and 1 atm, respectively. A Nosé-Hoover thermostat (48,49) and isotropic Parrinello–Rahman barostat (50,51) were used. The time step was set to 1 fs in the equilibration run and to 2 fs in the production run. In the energy minimization and equilibration runs, harmonic positional restraints were imposed on the protein backbone (0.96 kcal mol–1 Å–2), the protein side chain (0.096 kcal mol–1 Å–2), and the heavy atoms of the ligand (0.96 kcal mol–1 Å–2).

gREST Simulations

Simulations were performed using the program package GENESIS ver. 1.3.0 (52) under periodic boundary conditions. The force fields used for proteins and ligands were the same as those used in the MD simulations. Before the replica simulations, energy minimization, two 10 ps equilibration runs (NVT and NPT ensembles) with 1 kcal mol–1 Å–2 positional restraints for heavy atoms, and a 10 ps equilibration run (NPT ensemble) without restraints were performed. The temperature and pressure were set to 300 K and 1 atm, respectively, with Langevin dynamics (53) used for temperature and pressure control. Electrostatic and van der Waals interactions were handled by the PME method (54) and the switching function in the range of 10–12 Å, respectively. The time step was 2 fs. All bonds involving hydrogen atoms were fixed using SHAKE, (55) and water molecules were kept rigid using SETTLE. (56) After the above equilibration runs, six replicas were prepared at six different solute temperatures (300, 340, 390, 450, 520, and 600 K). The solute region was defined as the C-terminal region below the kink, which included H11 and H12, that is, residues 396–423. The dihedral angle, the energy correction maps (CMAP), and Lennard-Jones energy terms were used in solute tempering. Each replica at a different temperature was equilibrated by a 100 ps equilibration run (NPT ensemble) without exchange. After equilibration of the six replicas without exchange, a 1 μs gREST simulation (NPT ensemble) was performed with an exchange period of 2 ps. The total sampling time was 6 μs per ligand.
To assess the reproducibility of the conformational changes induced by the bindings of other ligands, gREST simulations for the antagonist 5b complex and the partial-agonist complex also were performed. Their initial structures were prepared from the crystal structures of the rat VDR-LBD/antagonist 5b complex (PDBID: 5XPL (16)) and rat VDR-LBD/partial-agonist 5 complex (PDBID: 5AWJ (57)), respectively. Missing residues and protonation states were modeled using the same procedures used for the agonist/antagonist complexes described above. For the alternative coordinates of the residues in the PDB data, coordinate A was selected. In the partial agonist complex, the conformer A of the partial agonist was used. Here, the Nε atoms of His301 and His393 were protonated in the case of the antagonist 5b complex because the positions of these residues were different from those in the other crystal structures (see Supporting Information). Solution system setups and gREST simulations were carried out as the same procedures in the agonist/antagonist complexes.

Trajectory Analyses

To examine the convergence behavior of conventional MD simulations, the root mean square deviation (rmsd) was calculated using Cα atoms. To eliminate the influence of the flexible parts of the N- and C-termini, calculations were performed for residues 125–420. The reference structure was the initial structure of the antagonist complex, and structural alignment of the VDR was performed using backbone heavy atoms in residues 125–395.
The structural distributions of the sampled structures by conventional MD and gREST simulations were analyzed by principal component analysis (PCA). After a 1 μs gREST simulation, snapshots at 300 K were extracted (10,000 snapshots per ligand). Using the snapshots for both the agonist and the antagonist complexes (20,000 total), principal axes were determined, and the reference structure was set to an averaged structure of residues 123–418 based on structural alignments of residues 125–395. After the determination of the principal component (PC) axes, the snapshots sampled by the MD simulations (10,000 per ligand) were projected onto the PC axes. Then, the free-energy landscapes were obtained by −ln(P), where P is the existence probability calculated on the basis of the normalized histogram of 1 Å × 1 Å pixels on the PC space. The representative structure was selected by clustering the structures at 1 pixel corresponding to the free-energy minimum region. We used hierarchical clustering implemented in the MMTSB tool, (58) using Cα atoms of the region (residues 123–157 and 222–418) without H3 and the C-terminus of H12. The cluster with the most members was adopted, with the central structure used as the representative structure.
To measure the effects of structural changes observed in the gREST simulations on coactivator binding, we performed conventional MD simulations for the VDR-LBD and coactivator peptide (CoA) complexes. The initial structures of the simulations were the representative structures of the agonist and antagonist complex at free-energy minima in the free-energy landscape using the rmsds of Glu416 and H12 described in Results and Discussion. The bound CoA in the initial structures was prepared by the superimposition of the crystal structure of the rat VDR-LBD/CoA complex (PDBID: 2ZLC (33)). The structures were aligned using the backbone atoms of residues 123–159 and 218–420, and the CoA was structurally incorporated into the representative structures. For comparison, MD simulation starting from the crystal structure of the VDR-LBD/CoA complex was also carried out. The solution system setups, energy minimization, equilibration runs, and production runs were executed using the same procedures as used in the conventional MD simulations of the agonist/antagonist complexes described above. The relative rmsd of the CoA (residues 628–635) from H12 was calculated using Cα atoms, and the best fit was executed using residues 411–418.
In the antagonist complex and the apo structure, theoretical SAXS profiles were calculated from snapshots sampled by the gREST simulations using CRYSOL. (59) The length of the rat VDR-LBD in this study was different from that used in the previous MD-SAXS approach; (11) therefore, the N-terminal tail (residues 106–122) was structurally incorporated into the snapshot from the MD-SAXS model because the theoretical intensity depends on the length of the protein used in the SAXS profile calculations. Specifically, the MD-SAXS model was aligned to the snapshot using the backbone atoms of residues 125–140, and the residues 106–125 of the aligned MD-SAXS model were replaced with those in the snapshot. The discrepancy between theoretical and experimental profiles χ and the radius of gyration Rg were estimated using CRYSOL. (59)

Results and Discussion

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Convergence of Conventional MD and gREST Simulations

A 1 μs conventional MD simulation was performed for each agonist and antagonist complex. The simulated structures were stable at the initial structure, that is, the active conformation. The rmsd from the initial antagonist complex was constant at ∼2.5 Å in both simulations (Figure S2).
A 1 μs gREST simulation was performed for each complex. Exchange events among all the replicas were observed during the gREST simulations (Figures S3 and S4). Exchange probabilities for each replica were 6–9% for the agonist complex and 5.6–7% for the antagonist complex. The energy distributions at each temperature overlapped (Figure S5). To examine the convergence behavior of the structural distribution of the sampled structures, free-energy landscapes calculated from trajectories in simulations of various durations were compared on a PC space (Figure S6). After the 800 ns gREST simulation, the free-energy landscape converged for both the agonist and antagonist complexes. Then, the gREST simulations were converged at 1 μs. Hereafter, we analyzed the free-energy landscapes obtained from the 1 μs gREST simulation because it was sufficient for assessing the differences between the agonist/antagonist complexes.

Free-Energy Landscapes of Agonist/Antagonist Complexes

In MD simulations, the structures of both complexes were trapped at free-energy minima (Figure 2A,C), corresponding to the active conformations, which were close to the crystal structures. In contrast, in the gREST simulations, we observed spontaneous conformational changes of the antagonist complex and thus, clearly different free-energy landscapes between the agonist and antagonist complexes (Figure 2B,D). The agonist complex exhibited one dominant free-energy minimum corresponding to the active conformation in both the gREST and MD simulations (Figure 2B). In contrast, the antagonist complex showed two free-energy minima (denoted as a and b in Figure 2D) in the gREST simulations, both of which were different from the minimum observed in the simulations of the agonist complex.

Figure 2

Figure 2. Free-energy landscapes of VDR-LBD structures. In panels (A) and (B), free-energy landscapes of the agonist complex are compared between (A) conventional and (B) gREST simulations. In panels (C,D), free-energy landscapes of the antagonist complex are compared between (C) conventional and (D) gREST simulations. The unit is kBT. Representative structures at minima are shown as cyan squares; crystal structures for the agonist (PDBID: 2ZLC (33)) and antagonist (PDBID: 2ZXM (17)) are shown as gray squares. H11 and Loop11-12 (residues 396–410) are colored green and H12 (residues 411–423) is colored magenta.

Representative structures of the antagonist complex sampled by gREST differed from the active conformation. In particular, the region from the end of H11 to the beginning of H12 showed conformational flexibility. The position of H11 was different from that in the active conformation, the region from the end of H11 to the beginning of H12 (residues 400–410) was disordered, and the position of H12 deviated from its canonical position in the active conformation. Comparing the two representative structures at the free-energy minima a and b, the difference was that H11 (residues 400–402) at minimum a was one turn shorter than that at minimum b.
The gREST representative structures (Figure S7A,B) are compared with the MD-SAXS model and crystal structure in Figure S7C. The major characteristics of the gREST structures at minima a and b, that is, the disappearance of the H10/11 kink, extended H11, flexible Loop11–12 and H12 displacement, were shared with those in the MD-SAXS model. However, the structural details were slightly different between the gREST and MD-SAXS models. First, the displacement of H12 in the gREST models was smaller than that in the MD-SAXS model (Figure S8). Second, the partial unfolding of the beginning of H12 at Pro412 and Leu413 in the MD-SAXS model (Figure S9A,B) was not observed in the gREST models (Figure S9C,D). Third, at the end of H11, a helix from Arg398 to Phe402 was broken in the MD-SAXS model (Figure S9A,B). This helix break was also observed in the gREST model at minimum a (Figure S9C) but not in the minimum b model (Figure S9D). The theoretical SAXS profiles of the gREST representative models were compared with the experimental profile. The profiles of both gREST models at minima a and b are fitted better to the experimental profile (χ = 0.33 and 0.31 for minima a and b, respectively) than to the crystal structure (the initial model of the simulations) (χ = 0.38) (Figure S10). In the middle-angle region at Q ∼ 0.2, the profiles of the gREST models were close to the experimental profile, which was affected by the flexible Loop11-12. (11)
As crystal structures were used as initial structures for both agonist and antagonist complexes, the gREST simulations succeeded in capturing spontaneous structural responses to agonist and antagonist binding. The free-energy landscapes of the agonist and antagonist complexes in the gREST simulations were clearly different; therefore, the agonist and antagonist activities could be structurally distinguished using gREST simulations.

Correlation between Helix 12 and Activity

To examine the conformations sampled by the gREST simulations in terms of agonist and antagonist activities, the conformation around H12 was analyzed. For agonist activity, AF-2 surface creation and coactivator recruitment are important. The coactivator has the LXXLL sequence and is bound to the AF-2 surface so that the LXXLL region is sandwiched between H12 and H3 through three hydrogen bonds, termed the charge clamp (Figure S11A): (1,2,60) the backbone amido groups of Met629 and Leu630 in the CoA interact with the sidechain of Glu416 in H12, and the backbone carbonyl oxygen of Leu633 in CoA interacts with the sidechain of Lys242 in H3 (Figure S11B). The mutation studies (61−64) of human VDR have shown that the binding between VDR and the coactivator is reduced by the mutations altering the charge clamp; activity is also reduced in Lys246Ala, (61) Glu420Gln, (61−63) or Glu420Ala. (64) Notably, the Glu420Lys substitution has been shown to cause hereditary vitamin D-resistant rickets. (65) Here, Lys246 and Glu420 of human VDR correspond to Lys242 and Glu416 of rat VDR, respectively. In the gREST simulations, no structural changes in H3, including Lys242, were observed. Therefore, in terms of the position of Glu416 located at H12, charge-clamp formation in the gREST simulations was examined.
The position of Glu416 changed with the movement of H12 (Figure 3A,C). In the agonist complex, most structures exhibited an rmsd of ∼2 Å from the crystal structure at H12. In the representative structure with minimum free energy (Figure 3A, cyan dot), the position of H12 and the side chain of Glu416 were in good agreement with those of the active conformation in the crystal structure (Figures 3B and S12A). In these structures, the side chain of Glu416 is capable of forming interactions with the coactivator, and H12 in the agonist complex could form a charge clamp. In contrast to the agonist complex, the rmsd values for H12 were greater than 2 Å in the antagonist complex (Figure 3C). In the representative minimum free-energy structure (Figure 3C, cyan dot), H12 deviated from its canonical position in the active conformation of the crystal structure, and Glu416 was displaced away from the coactivator (Figures 3D and S12B). This displacement of Glu416 possibly reduces coactivator binding. To confirm the destabilization of coactivator binding by the movement of H12 sampled by gREST simulations, 1 μs conventional MD simulations for the representative structures of agonist/antagonist complexes with the bound CoA were performed. During a 1 μs conventional MD simulation, the CoA was not dissociated completely from the binding surface, regardless of the agonist/antagonist complexes. However, the relative position of CoA with respect to H12 was unstable in the antagonist complex (Figure S13A), whereas the CoA relative position was stable in the simulations starting from the agonist complex and the crystal structure. In the snapshot at 1 μs, CoA was far from H12 in the simulation of the antagonist complex (Figure S13B); in contrast, CoA and H12 were close to each other in the simulations from the agonist complex and the crystal structure (Figure S13C,D). The distances between Glu416 of H12 and Met629 or Leu630 of the CoA, corresponding to the charge clamp, were larger in the antagonist complex than in the agonist complex (Figure S13E,F). The distances in the agonist complex were the same as those sampled by the simulation of the crystal structure of the VDR-LBD/CoA complex (PDBID: 2ZLC (33)). These results suggested that coactivator binding was reduced in the antagonist complex, possibly due to the displacement of H12. These characteristic features of the agonist/antagonist complexes are consistent with experimental data suggesting that both agonist and antagonist activities are regulated by coactivator recruitment. (1,2,17)

Figure 3

Figure 3. Correlations between rmsds of H12 and Glu416 for (A) agonist and (C) antagonist complexes in the free-energy landscape. The free-energy minimum is represented by the cyan dot. Structural alignment of the representative structure for (B) agonist or (D) antagonist complex and crystal structure (PDBID: 2ZLC (33)) using residues 125–395. The crystal structures of VDR and the coactivator are colored yellow and orange, respectively. In the representative structure (gray), H11 and H12 are colored green and magenta, respectively.

Structural Mechanism of the Conformational Change of H12

To better understand the mechanism underlying the deviation of H12 from its canonical position in the antagonist complex, cooperative rearrangement motions of H11 and H12 were analyzed. The deviation of H12 from the active conformation was correlated with structural deviations of H11 and Loop11-12 (residues 396–410) from their canonical positions (Figure 4). In the agonist complex, the conformations of the H11 and Loop11-12 structures at minimum free energy were similar to those in the canonical form (rmsds of H11 and Loop11-12 were ∼2 Å) (Figure 4A, minimum a). In contrast, in the antagonist complex, H11 and Loop11-12 underwent conformational changes: the rmsds of H11 and Loop11-12 from the canonical structure were >4 Å (Figure 4B). In representative structures of the two basins, minima b and c, the conformations of H11 differed from the active conformation. H11 at minimum b was partially unraveled and had one turn less than that at minimum c. In particular, the region of Loop11-12 was disordered in both structures, and the flexible structure of Loop11-12 pulled H12, resulting in a positional shift of H12.

Figure 4

Figure 4. Correlations between the rmsd of H12 and that of H11 and Loop11-12 for (A) agonist and (B) antagonist complexes in the free-energy landscape. Local minima are represented by the cyan dots. In the representative structures for minima a, b, and c, H11 and Loop11-12 are colored green and H12 is colored magenta.

The flexibility of H11 and Loop11-12 was related to the disappearance of the kink at H10/11. To maintain the active conformation of H12, H11 should bend inward from the kink, as is the case in the crystal structure. We evaluated the correlation between the bending feature of H10/11 at the kink and the position of H12 (Figure 5A,B), using the definition of the bend angles of M379, D390, and Y397 (Figure 5C). In the agonist complex, H10/11 bent at ∼158.5° at the kink, where the position of H12 was close to its canonical position (Figure 5A). The bend angle was close to that of the crystal structure (156.6° for PDBID: 2ZLC, (33) 157.6° for PDBID: 2ZXM (17)). In contrast, the bend angle was ∼169.5° in the antagonist complex (Figure 5B). The kink disappeared, and H10/11 tended to form an extended helix, where the position of H12 deviated from the canonical position. As the bent structure was relaxed, the end of H11 became flexible, and H11 and Loop11-12 did not maintain the active conformation. The position of H12 was modulated by the conformational change in Loop11-12. Here, the angle of the antagonist complex was similar to that of the crystal structure, in which the region between H11 and H12 was disordered (171.7° for PDBID: 5XPL (16)). The structure of H10/11 in the crystal structure was the same as that in the model; however, the dynamic effect of the extended H11 and the disorder near H12 were identified by the spontaneous conformational change in the gREST simulation.

Figure 5

Figure 5. Correlations between the rmsd of H12 and the angle of the kink for the (A) agonist and (B) antagonist complexes in the free-energy landscape. Local minima are represented by the cyan dots. In the representative structures, H11 and Loop11-12 are colored green and H12 is colored magenta. (C) Definition of the angle at the kink.

The structural mechanism underlying the conformational change of H12 discussed above is consistent with the folding-door model, (11) rather than the mouse-trap model. (10) The deviation of H12 from its canonical position was accompanied by a cooperatively rearranging deviation of H11. The flexibility of H11 was caused by the disappearance of the kink, and the disordered conformation of Loop11-12 pulled the N-terminus of H12, leading to its displacement. These structural features are in good agreement with key findings using the folding-door model, (11) and the relationships among these features can be clarified by gREST simulations.

Agonist and Antagonist Regulation Mechanisms

To understand the mechanism of VDR regulation by the agonist and antagonist, the difference in stability of the active conformation in interaction with both was examined. Because the ligands have different sidechain structures (Figure S1), the residues in contact with the ligands were different (Figure 6A). In particular, the H10, H11, and H12 areas showed significantly different patterns between the agonist and antagonist complexes. The antagonist showed a few loose contacts with residues of H11 and H12, whereas the agonist had tight contacts with the same residues. The edge of the side chain of the agonist (near the dimethyl group, Figure S1) interacted with the hydrophobic residues Tyr397, Leu400, Leu410, and Val414. These residues and the agonist formed a hydrophobic core in the H11-H12 region (Figure 6B).

Figure 6

Figure 6. (A) Residues in contact with the agonist and antagonist. Contact is defined by a 5 Å distance between heavy atoms. Ligand contact residues in residues 301–423 for (B) agonist and (C) antagonist complexes are illustrated. Contact residues for the agonist and antagonist complexes are colored orange and cyan, respectively.

The hydrophobic core around H12 determined the stability of the active conformation. The antagonist had two side chains, with the one closer to H12 shorter than the side chain of the agonist, as it lacks the dimethyl group at the edge of the hydroxy group (Figure S1). As indicated by the loose contacts, the antagonist was unable to form a hydrophobic core on the H12 side (Figure 6C). Instead, the butyl group of the antagonist had tight contacts in the region of H7 and H10 near Leu389 and Asn390 (Figure 6A) and formed a hydrophobic core on the H7/10 side (Figure 6C). Because of the lack of the hydrophobic core around H12, the weak interactions with the antagonist were insufficient to maintain the conformation around H12 in the active conformation; therefore, the inner bending of H11 disappeared and the position of H12 shifted due to the disordered Loop11-12 as discussed in the previous subsection. The residues involved in hydrophobic-core formation in H12 (Leu400, Leu410, and Val414) are known to be important for agonist activity. (66) The hydrophobic core in H7/H10 of the antagonist complex may be involved in maintaining antagonist-binding affinity rather than in regulating activity.
The crystal structure of the antagonist complex, that is, the active form, corresponds to one of the multiple metastable states. In fact, in the conventional MD simulation for the antagonist complex, the active form of the antagonist complex was stable for at least 1 μs. However, the previous SAXS experiment (11) indicated that the major solution structure of the antagonist complex is different from the crystal structure. Under crystal conditions, for example, crystal packing, a metastable structure (active form) is likely crystalized. Correspondingly, compared with the agonist complex, the hydrophobic interactions between the antagonist and the H11-H12 region are weak, leading to the destabilization of the active form. Therefore, in the antagonist complex, the active form is less populated in solution. In the free-energy landscape sampled by the gREST simulation, the frequency of structures close to the active form was low (Figure 2D).
Given the high sequence identity (91%) between rat and human VDR-LBD, the regulatory mechanism described above may be conserved in human VDR-LBD. The important residues for activation determined by experimental alanine scanning of the human VDR-LBD (66) are completely conserved. The differing residues in helices 11 and 12, the focus of this study, were only two: Ser399 at the end of H11 and Asn406 at the H11-12 loop in the rat VDR-LBD were mutated as cysteine residues in the human VDR-LBD. The side chain of Ser399 was exposed to the solution, and no specific interactions with surrounding residues were observed (Figure S14). Although the side chain of Asn406 was close to Leu223 and Leu400 in the agonist complex, Asn406 was located at the outside of the hydrophobic core, so that it had no contact with the ligand (Figure S14C). Therefore, the Ser399Cys and Asn406Cys substitutions between rat and human would not affect the results. Notably, all residues with clearly different contact frequencies between the agonist and antagonist complexes in this study are conserved between the rat and human orthologs.

Conformational Changes Induced by the Binding of Other Ligands

To determine whether the conformational changes induced by antagonist binding extended to other ligands, gREST simulations were performed for the antagonist 5b (16) and the partial agonist 5, (57) hereafter denoted as the “partial agonist” (Figure S15). Both ligands have a bifurcated side chain at C-22, and their scaffolds around C-22 are the same chirality as the antagonist JB. Comparing the antagonists JB and 5b (Figure S1), 5b has the same butyl group but has a p-hydroxyphenyl group at the H12 side instead of the hydroxy group. The partial agonist has the same hydroxy group but the butyl group changes to the hexyl group. In addition, the A-ring of both the antagonist 5b and the partial agonist is different from that of the agonist and the antagonist JB. However, this modification of the A-ring did not change the agonist/antagonist activities. (11)
In the crystal structure of the rat VDR-LBD/antagonist 5b complex (PDBID: 5XPL (16)), the end of H11 (Phe402 and Gln403) was disordered (Figure S16A) and had an extended structure compared to the active conformation (Figure S16B). However, the position of H12 was identical to that in the active form (Figure S16B). In the free-energy landscape, the crystal structure of the antagonist 5b was close to the crystal structure of the agonist complex corresponding to the active conformation (Figure S17A).
In the gREST simulation, the antagonist 5b complex showed a different free-energy landscape from the agonist complex (Figure S17A). A free-energy minimum was observed at the different regions from the active form and the crystal structures of the antagonist 5b complex and was close to the minimum a of the antagonist complex. In the representative structure at the free-energy minimum, a different position of H11 from the active form and the disordered Loop11-12 were observed (Figure S17B,C). The Loop11-12 maintained a disordered conformation as was so for the crystal structure of the antagonist 5b complex. H12 was displaced from its original canonical position in the crystal structure. The gREST representative structure of the antagonist 5b complex shares structural features with the antagonist JB complex. However, minor differences from the antagonist JB complex (Figure S18) were also observed. The C-terminal part of H11 maintained through Arg398 was the same as the structure at the minimum a (Figure S18A) but shorter than the structure at the minimum b (Figure S18B). The kink disappeared; however, the orientation of the end of H11 was different between them. Furthermore, although H12 was displaced from its original canonical position in both complexes, the final positions of H12 after the displacement were different. Despite these minor structural differences, the major structural features remained consistent with those in the antagonist complex. These results suggested that the conformational changes induced by antagonist binding were captured structurally by the gREST simulations.
In the crystal structure of the rat VDR-LBD/partial-agonist complex (PDBID: 5AWJ (57)), the structure of the VDR-LBD was essentially identical to other crystal structures; however, a mixed population of the partial-agonist conformer is present. There are three conformers of the partial-agonist (called major, minor-B, and minor-C), with populations 40, 20, and 20%, respectively (Figure S19). The difference among them is the orientation of the side chains: the hydroxyl group is oriented toward H12 in the major conformer (Figure S19A) and is oriented toward the region of H7 and H10/11 in the minor conformers (Figure S19B,C). We had expected that the major and minor conformers would induce inactive and active conformations of rat VDR-LBD, respectively, and that the mixed population of inactive and active conformations would be responsible for the partial-agonist activity. (57) However, the mechanism of regulation was not explained structurally because the position of H12 was essentially unchanged from that in the active form, regardless of the major and minor conformers of the ligand.
To explore the structural response of the rat VDR-LBD to partial-agonist binding, the gREST simulation starting from the major conformer was performed. The gREST simulation for the partial-agonist complex showed four free-energy minima (denoted as a, b, c, and d in Figure S20): The minimum a was close to the minimum observed for the agonist complex, and the remaining three minima were located at different regions. The region of H11 and H12 in the representative structure at the minimum a was essentially identical to that of the active form (Figure S21A). In contrast, the region for the representative structures at the remaining three minima exhibited different conformations from those in the active form: H11 and Loop11-12 showed flexible conformations, and the position of H12 deviated from the canonical position, as it did in the antagonist complex (Figure S21B–D). Although the region around H12 adopted the same conformation in the representative structure at the minimum a, the difference from the active form was on the H7 side (Figure S22A); due to the hexyl group of the partial agonist, H7 and H10 were separated, which was the same as in other representative structures. These results suggested that both active and inactive conformations around H12 might appear in the partial-agonist bound rat VDR-LBD, and in the mixed population state, the frequency of the active conformation might be decreased, producing the partial-agonist activity.
On the basis of the free-energy landscapes of the antagonist 5b and the partial agonist described above, the conformational changes of H12 induced by antagonist binding were reproducible. In all of the initial structures prepared from the crystal structures, the position of H12 was essentially identical to that of the active form. However, the free-energy landscapes of the antagonist 5b and the partial agonist produced by the gREST simulations were clearly different from that of the agonist complex, with the conformations around H12 also different among them. These different characteristics of the hydrophobic-core formation between the agonist and antagonist complexes were also consistent: the antagonist 5b and the partial agonist exhibited tight contacts on the H7/H10 side, with few contacts on the H12 side (Figure S23). In the representative structures, the residues contributing to hydrophobic core formation in H12 (Tyr397, Leu400, Leu410, Val414, Phe418) did not form contacts with the ligand except for in the agonist complex and the partial-agonist complex at the minimum a (Figure S24). Here, because the manner of interaction on the H12 side differed depending on the different side chains of the ligands (Figure S24), the detailed mechanism for inhibition of the hydrophobic core formation on the H12 side would be different.
For completeness of the structural samplings for all known states, apo, holo-agonist, and holo-antagonist, gREST simulation of the apo structure was performed. Because the crystal structure of the apo VDR-LBD has not been solved to date, the crystal structure in which the antagonist was removed from the antagonist complex (PDBID: 2ZXM (17)) was used as an initial structure. The free energy was distributed over a wide area from the structure of the agonist complex (denoted as a in Figure S25) to the structure of the antagonist complex (denoted as b in Figure S25). In both representative structures at the points a and b, the position of H12 was deviated from its canonical position; moreover, the end of H11 and Loop11-12 had a flexible structure, suggesting that the apo structure sampled by the gREST simulation adopted different conformations from the active form. However, the gREST representative structures were slightly inconsistent with the experimental SAXS data (Figure S26); in particular, their theoretical SAXS profiles deviated from the experimental profile at the middle-angle region Q ∼ 0.2. In this region, according to the MD-SAXS study, (11) a wide entrance to the ligand-binding pocket generated by the outward-bending motion of H11, centered on the kink, was required to fit the experimental profile. Compared with the MD-SAXS model, H11 was located inside in the gREST representative structures. The large movement of H11 observed in the MD-SAXS model might require a large positional change of H12, so that the orientation of H12 changed significantly. Because the orientation of H12 in the representative structures was opposite to that of the MD-SAXS model (Figure S27), further samplings were necessary so that the position and conformation of H12 changed more flexibly. Although these results were within a 1 μs gREST simulation, we found that the structural distribution was widened in the apo state, with the active structure not dominating without agonist binding.
This study had some limitations that should be addressed in the future. First, upon comparing the antagonist complexes yielded by gREST simulation with those of the MD-SAXS approach, (11) the displacement of H12 was smaller in the former than in the latter. In the current study, displacement of H12 was sufficient to distinguish the active conformation; however, the H12 conformation may fluctuate in solution, as revealed by the MD-SAXS approach. (11) Thus, further enhanced sampling of H12 may be required. Second, it is still challenging to predict structure–activity relationships in a mixed population of active and inactive conformations (e.g., the partial agonist 5 (57) described above and the partial agonist 8a (67)). Accurate evaluation of the free-energy differences in the active and inactive conformations is warranted. Within the present gREST simulations, we did not observe that the bifurcated sidechain of the ligand interacting with the H7/H10 side and the H12 side were interchanged. Therefore, we must develop a method to evaluate the free energy for the mixed conformations. Third, we cannot discount the possibility of other regulatory mechanisms that mediate antagonism. The shift of H12 from its canonical position is thought to be a common mechanism; however, the structural origin of this shift may differ depending on the scaffold of the antagonist. Fourth, the present procedure cannot handle ligands whose binding affinity is determined by the kinetic features of the ligand binding/dissociation processes. For example, ligands binding to ER exhibit different rate constants for binding and dissociation, (68,69) and the dissociation rates of ligands binding to the mineralocorticoid receptor vary depending on the type of ligand or mutants. (70,71) To deal with such ligands, it will be necessary to incorporate methods for simulating the binding/dissociation processes (72−74) or kinetic methods, such as the Markov state model. (75)

Conclusions

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Using the gREST method, we demonstrated that agonist and antagonist complexes exhibited different structural responses in accordance with their activities. Although their initial structures were the active crystal structures, the antagonist complex exhibited spontaneous conformational changes, with the position of H12 deviating from its canonical position. In contrast, in the agonist complex, the active conformation was stable. In the case of the deviated position of H12 in the antagonist complex, the H12 residue involved in coactivator binding was positioned far from its canonical position, required to maintain the charge clamp between H12 and the coactivator, consistent with experimental data suggesting that agonist/antagonist activities are regulated by coactivator recruitment. Thus, we conclude that gREST simulations can capture reasonable conformations for explaining agonism and antagonism.
The regulatory mechanism is understood by the stability of the active conformation, which depends on hydrophobic core formation. The agonist and hydrophobic residues at H11, Loop11-12, and H12 exhibited tight contacts and formed a hydrophobic core, maintaining the active conformation. In contrast, due to the weak interactions between the antagonist and the same residues, this hydrophobic core could not be formed in the antagonist complex. Consequently, the region around H12 adopted a flexible conformation; the kink at H10/11 disappeared, and the inward bend of H11 was dissolved, leading to a disorder of Loop11-12. Owing to the flexibility of Loop11-12, H12 was pulled, resulting in a positional shift of H12 from that in the active conformation.
Even when only the active structure in the complex with compounds is experimentally solved, gREST simulations demonstrated that complex stability can be assessed by observing spontaneous conformational changes. During these simulations, conformational changes around H12 occurred due to physicochemical alterations, involving different protein–ligand interactions. Therefore, the present procedure can be applied for examining structure–activity relationships for multiple ligands.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jcim.1c00534.

  • Ligand scaffolds, time dependence of the rmsd in conventional MD simulations, temperature exchange in replica systems, temperatures assigned to each replica, energy histogram, free-energy landscape as a function of simulation duration, structural alignments of the antagonist complex and of representative and MD-SAXS structures of the antagonist complex, backbone conformations, SAXS profiles for the antagonist complex, crystal structure of rat VDR-LBD with a coactivator peptide, structural alignment of representative and crystal structures, simulations for the representative structure with coactivator peptide, representative structures from gREST simulations, ligand scaffolds of the antagonist 5b and the partial agonist, crystal structure of the antagonist 5b and rat VDR-LBD complex, free-energy landscape of the antagonist 5b complex and the partial-agonist complex, structural alignment of antagonist 5b and antagonist complexes, partial-agonist and agonist complexes, and partial agonist and the agonist complexes from H7 side, initial structures of the rat VDR-LBD/partial-agonist complex , residues contacting the antagonist 5b, partial agonist, and agonist, representative structures for the agonist, antagonist, antagonist 5b, and partial agonist, free-energy landscape of the apo structure, SAXS profiles for the apo structure, MD-SAXS model and representative structure at the point a, and protonation states of histidine residues (PDF)

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Author Information

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  • Corresponding Author
    • Mitsunori Ikeguchi - Graduate School of Medical Life Science, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, JapanCenter for Computational Science, RIKEN, 1-7-22 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, JapanOrcidhttps://orcid.org/0000-0003-3199-6931 Email: [email protected]
  • Authors
    • Toru Ekimoto - Graduate School of Medical Life Science, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
    • Takafumi Kudo - Graduate School of Medical Life Science, Yokohama City University, 1-7-29 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
    • Tsutomu Yamane - Center for Computational Science, RIKEN, 1-7-22 Suehiro-cho, Tsurumi-ku, Yokohama 230-0045, Japan
  • Funding

    This work was financially supported by “Priority Issue on Post-K computer” (Building Innovative Drug Discovery Infrastructure through Functional Control of Biomolecular Systems) (project ID: hp150269, hp160223, hp170255, hp180191, and hp190171) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT); by “Program for Promoting Researches on the Supercomputer Fugaku” (MD-driven Precision Medicine) (project ID: hp200129 and hp210172) from MEXT; by the Basis for Supporting Innovative Drug Discovery and Life Science Research (BINDS) (project ID: JP21am0101109) from the Japan Agency for Medical Research and Development (AMED); by a Grant-in-Aid for Scientific Research on Innovative Areas “Molecular Engine” (grant no: 18H05426) from MEXT, and by the RIKEN Dynamic Structural Biology Project.

  • Notes
    The authors declare no competing financial interest.

    Input, data, and script files for conventional MD and gREST simulations are freely available at https://github.com/IkeguchiLab/VDR-gREST. Simulations were performed using open-source software GROMACS version 2016.3 and GENESIS version 1.3.0.

Acknowledgments

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We would like to acknowledge the computational resources of supercomputers Fugaku and K provided by the RIKEN Center for Computational Science.

Abbreviations

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VDR-LBD

vitamin D receptor ligand-binding domain

NR

nuclear receptor

ER

estrogen receptor

LBD

ligand-binding domain

MD

molecular dynamics

SAXS

small-angle X-ray scattering

gREST

generalized replica exchange with solute tempering

CGenFF

CHARMM Generalized Force Field

PME

particle mesh Ewald

NVT

canonical ensemble

NPT

isothermal–isobaric ensemble

CMAP

energy correction maps

rmsd

root mean square deviation

PCA

principal component analysis

References

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  • Abstract

    Figure 1

    Figure 1. Crystal structures and a solution model: (A,B) ER/agonist (PDBID: 1ERE (13)) or ER/antagonist (PDBID: 3ERT (15)) complexes, (C,D) VDR/agonist (PDBID: 2ZLC (33)) and VDR/antagonist (PDBID: 2ZXM (17)) complexes, and (E) solution model of the VDR/antagonist complex yielded by the MD-SAXS approach. (11) H11 and H12 are colored green and magenta, respectively.

    Figure 2

    Figure 2. Free-energy landscapes of VDR-LBD structures. In panels (A) and (B), free-energy landscapes of the agonist complex are compared between (A) conventional and (B) gREST simulations. In panels (C,D), free-energy landscapes of the antagonist complex are compared between (C) conventional and (D) gREST simulations. The unit is kBT. Representative structures at minima are shown as cyan squares; crystal structures for the agonist (PDBID: 2ZLC (33)) and antagonist (PDBID: 2ZXM (17)) are shown as gray squares. H11 and Loop11-12 (residues 396–410) are colored green and H12 (residues 411–423) is colored magenta.

    Figure 3

    Figure 3. Correlations between rmsds of H12 and Glu416 for (A) agonist and (C) antagonist complexes in the free-energy landscape. The free-energy minimum is represented by the cyan dot. Structural alignment of the representative structure for (B) agonist or (D) antagonist complex and crystal structure (PDBID: 2ZLC (33)) using residues 125–395. The crystal structures of VDR and the coactivator are colored yellow and orange, respectively. In the representative structure (gray), H11 and H12 are colored green and magenta, respectively.

    Figure 4

    Figure 4. Correlations between the rmsd of H12 and that of H11 and Loop11-12 for (A) agonist and (B) antagonist complexes in the free-energy landscape. Local minima are represented by the cyan dots. In the representative structures for minima a, b, and c, H11 and Loop11-12 are colored green and H12 is colored magenta.

    Figure 5

    Figure 5. Correlations between the rmsd of H12 and the angle of the kink for the (A) agonist and (B) antagonist complexes in the free-energy landscape. Local minima are represented by the cyan dots. In the representative structures, H11 and Loop11-12 are colored green and H12 is colored magenta. (C) Definition of the angle at the kink.

    Figure 6

    Figure 6. (A) Residues in contact with the agonist and antagonist. Contact is defined by a 5 Å distance between heavy atoms. Ligand contact residues in residues 301–423 for (B) agonist and (C) antagonist complexes are illustrated. Contact residues for the agonist and antagonist complexes are colored orange and cyan, respectively.

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    • Ligand scaffolds, time dependence of the rmsd in conventional MD simulations, temperature exchange in replica systems, temperatures assigned to each replica, energy histogram, free-energy landscape as a function of simulation duration, structural alignments of the antagonist complex and of representative and MD-SAXS structures of the antagonist complex, backbone conformations, SAXS profiles for the antagonist complex, crystal structure of rat VDR-LBD with a coactivator peptide, structural alignment of representative and crystal structures, simulations for the representative structure with coactivator peptide, representative structures from gREST simulations, ligand scaffolds of the antagonist 5b and the partial agonist, crystal structure of the antagonist 5b and rat VDR-LBD complex, free-energy landscape of the antagonist 5b complex and the partial-agonist complex, structural alignment of antagonist 5b and antagonist complexes, partial-agonist and agonist complexes, and partial agonist and the agonist complexes from H7 side, initial structures of the rat VDR-LBD/partial-agonist complex , residues contacting the antagonist 5b, partial agonist, and agonist, representative structures for the agonist, antagonist, antagonist 5b, and partial agonist, free-energy landscape of the apo structure, SAXS profiles for the apo structure, MD-SAXS model and representative structure at the point a, and protonation states of histidine residues (PDF)


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