Graded activation and free energy landscapes of a muscarinic G-protein–coupled receptor

Significance

G-protein–coupled receptors (GPCRs) represent primary targets of about one-third of currently marketed drugs. The structure, dynamics, and function of GPCRs result from complex free energy landscapes. In this work, we have applied Gaussian accelerated molecular dynamics (GaMD) to study the ligand-dependent behavior of the M₂ muscarinic GPCR. Extensive GaMD simulations have revealed distinct structural flexibility and free energy profiles that depict graded activation of the M₂ receptor. We have captured both dissociation and binding of an orthosteric ligand in a single all-atom GPCR simulation. GaMD is well poised to study large biomolecules and ligand recognition for drug discovery.

Abstract

G-protein–coupled receptors (GPCRs) recognize ligands of widely different efficacies, from inverse to partial and full agonists, which transduce cellular signals at differentiated levels. However, the mechanism of such graded activation remains unclear. Using the Gaussian accelerated molecular dynamics (GaMD) method that enables both unconstrained enhanced sampling and free energy calculation, we have performed extensive GaMD simulations (∼19 μs in total) to investigate structural dynamics of the M₂ muscarinic GPCR that is bound by the full agonist iperoxo (IXO), the partial agonist arecoline (ARC), and the inverse agonist 3-quinuclidinyl-benzilate (QNB), in the presence or absence of the G-protein mimetic nanobody. In the receptor–nanobody complex, IXO binding leads to higher fluctuations in the protein-coupling interface than ARC, especially in the receptor transmembrane helix 5 (TM5), TM6, and TM7 intracellular domains that are essential elements for GPCR activation, but less flexibility in the receptor extracellular region due to stronger binding compared with ARC. Two different binding poses are revealed for ARC in the orthosteric pocket. Removal of the nanobody leads to GPCR deactivation that is characterized by inward movement of the TM6 intracellular end. Distinct low-energy intermediate conformational states are identified for the IXO- and ARC-bound M₂ receptor. Both dissociation and binding of an orthosteric ligand are observed in a single all-atom GPCR simulation in the case of partial agonist ARC binding to the M₂ receptor. This study demonstrates the applicability of GaMD for exploring free energy landscapes of large biomolecules and the simulations provide important insights into the GPCR functional mechanism.

G-protein–coupled receptors (GPCRs) are primary targets of about one-third of currently marketed drugs. They recognize ligands of widely different efficacies, from inverse to partial and full agonists, which transduce cellular signals at differentiated levels. Increasing experimental and computational evidence suggests that GPCRs exist in an ensemble of different conformations that interconvert dynamically during activation and ligand recognition (1–3). The structure, dynamics, and function of GPCRs result from underlying free energy landscapes (4). However, quantitative characterization of the GPCR activation and ligand-dependent free energy profiles has proved challenging (4–12).

The M₂ muscarinic GPCR is widely distributed in mammalian tissues. It plays a key role in regulating the human heart rate and heart contraction forces. The M₂ receptor has been crystallized in both an inactive state bound by the inverse agonist 3-quinuclidinyl-benzilate (QNB) (13) and an active state bound by the full agonist iperoxo (IXO) and a G-protein mimetic nanobody (14). The receptor activation is characterized by rearrangements of the transmembrane (TM) helices 5, 6, and 7, particularly closing of the ligand-binding pocket, outward tilting of the TM6 cytoplasmic end, and close interaction of Tyr206^5.58 and Tyr440^7.53 in the G-protein–coupling site (14). The residue superscripts denote the Ballesteros–Weinstein (BW) numbering of GPCRs (15).

In addition to binding inverse and full agonists, the M₂ receptor recognizes partial agonists that often possess lower affinities and elicit submaximal activity (16). Coupling of the receptor with the G protein or mimetic nanobody typically increases agonist binding affinities (17). However, structural information of partial agonist binding is scarce, except for few other GPCRs (18). How can one GPCR accommodate chemically diverse ligands? What are the structural signatures underlying the binding of different ligands? Why do some partial agonists exhibit lower binding affinities than full agonists? Is it easier for partial agonists to dissociate from the receptor? What are the pathways of ligand dissociation and binding? Because the partial agonists elicit only submaximal activity of GPCRs, do they stabilize different receptor conformations? It is important to address these questions to elucidate the GPCR functional mechanism.

Using Gaussian accelerated molecular dynamics (GaMD) simulations that enable both unconstrained enhanced sampling and free energy calculation (19), here we investigate structural dynamics of the M₂ receptor that is bound by the full agonist IXO, the partial agonist arecoline (ARC), and the inverse agonist QNB, in the presence or absence of the G-protein mimetic nanobody Nb9-8 (Table S1). Upon binding of different ligands, the receptor exhibits distinct flexibility and free energy profiles in the orthosteric pocket, the extracellular vestibule, and the intracellular G-protein–coupling site, for which the sizes are characterized by the perimeter of triangle formed by the C_α atoms of Tyr104^3.33−Tyr403^6.51−Tyr426^7.39 or “tyrosine lid” (14), the distance between the C_α atoms of Tyr177 in extracellular loop 2 (ECL2) and Asn410^6.58, and the C_α atom distance between Arg121^3.50 and Thr386^6.34, respectively. The receptor orthosteric pocket samples distinct closed and open conformations, and the G-protein–coupling site interconverts between the inactive, intermediate, and fully active states. We have observed both dissociation and binding of an orthosteric ligand in a GPCR all-atom simulation. Therefore, we are able to obtain a detailed picture of GPCR graded activation.

Table S1.

List of present GaMD simulations performed on the M₂ muscarinic receptor that is bound by the full agonist IXO, partial agonist ARC, and inverse agonist QNB, in the presence or absence of the G-protein mimetic nanobody Nb9-8

System	Natoms	Dimension, Å3	GaMD production simulations, ns
M2-Nb–IXO	75,278	88 × 88 × 113	500, 500, 400
M2-Nb–ARC	75,272	88 × 88 × 113	400, 400, 400
M2-QNB	52,698	88 × 85 × 88	400, 400, 400
M2-ARC	55,262	88 × 88 × 86	2,030, 1,520, 1,190, 650, 650, 650, 620, 600, 600, 540
M2-IXO	55,268	88 × 88 × 86	1,050, 1,000, 940, 500, 500, 500, 500, 480, 450, 410

Results

Agonist-Dependent Flexibility and Free Energy Profiles of the Nanobody-Coupled Receptor.

In the presence of the G-protein mimetic nanobody, the M₂ receptor exhibits varied structural flexibility when the ligand is changed from full agonist IXO to partial agonist ARC (Fig. 1A). Binding of ARC leads to significantly increased fluctuations in the ECL2 and orthosteric pocket. This is consistent with the fact that ARC possesses lower affinity than IXO (14, 16, 20). Thus, weaker interaction is formed between ARC and the receptor. Surprisingly, opposite flexibility change was observed in the receptor intracellular half. Binding of IXO leads to higher fluctuations in the G-protein–coupling interface, especially in the TM5, TM6, and TM7 intracellular domains, which have been shown as essential elements for activation of GPCRs (1). Therefore, increased flexibility of the receptor intracellular domains upon full agonist binding apparently contributes to GPCR activation.

Fig. 1.

Structural flexibility and free energy profiles of the M₂ receptor bound by the G-protein mimetic nanobody Nb9-8 and full agonist IXO or partial agonist ARC. (A) Schematic representation of the IXO-nanobody–bound M₂ receptor [Protein Data Bank (PDB) ID code 4MQS] that is colored by root-mean square fluctuation (RMSF) differences when the ligand is changed from IXO to ARC. A color scale of −0.5 Å (red) to 0.5 Å (blue) is used. The proteins are shown in ribbons and ligand in spheres. Important residues are represented by sticks and labeled with the BW numbers except Tyr177 in ECL2. (B and C) Two-dimensional PMF profiles of the M₂-nanobody–IXO system regarding (B) the Arg121^3.50−Thr386^6.34 and Tyr177^ECL2−Asn410^6.58 distances and (C) the Tyr104^3.33−Tyr403^6.51−Tyr426^7.39 triangle perimeter and the ligand−Asp103^3.32 distance. (D and E) The corresponding 2D PMF profiles of the M₂-nanobody–ARC system. (F and G) Two dominant binding poses of ARC in the orthosteric site: (F) ARC-P1 and (G) ARC-P1′. ARC is shown in thick sticks, the receptor in orange ribbons, and the interacting protein residues in thin sticks. The docking conformation of ARC in the 4MQS crystal structure is also shown in red for comparison.

Potential of mean force (PMF) calculations showed that the IXO-nanobody–bound M₂ receptor is confined in a local energy well centered at (14.5 Å, 13.5 Å) in the C_α atom distances between Arg121^3.50−Thr386^6.34 and Tyr177^ECL2−Asn410^6.58 (Fig. 1B and Fig. S1). The receptor maintains the active X-ray conformation through GaMD simulations. The distance between the ligand-charged N atom and the C_γ atom of Asp103^3.32 adopts a free energy minimum at 4.5 Å (same as the X-ray conformation) (Fig. 1C). The tyrosine lid exhibits an energy minimum at 30 Å, being similar to 29.7 Å in the closed X-ray conformation (Fig. 1C).

Fig. S1.

(A) Schematic representation of the IXO-nanobody–bound M₂ muscarinic receptor complex structure. (B–E) Time courses of important residue distances observed in the GaMD simulations: (B) the C_α atom distance between Arg121^3.50 and Thr386^6.34, (C) the C_α atom distance between Tyr177^ECL2 and Asn410^6.58, (D) the perimeter of triangle formed by the C_α atoms of Tyr104^3.33−Tyr403^6.51−Tyr426^7.39, and (E) the distance between the charged ligand N atom and the C_γ atom of Asp103^3.32.

In comparison, the ARC-nanobody–bound M₂ receptor exhibits a narrower energy well in the Arg121^3.50−Thr386^6.34 distance than the IXO-nanobody–bound form (Fig. 1D). This result is consistent with the above finding that changing the ligand from IXO to ARC leads to reduced flexibility in the receptor intracellular domains. On the other hand, the tyrosine lid explores a larger conformational space with weaker binding of ARC (Fig. 1E). ARC samples two low-energy conformations, “ARC-P1” (Fig. 1F) and “ARC-P1′” (Fig. 1G), for which the preferred distances between ARC and Asp103^3.32 are 3.5 Å and 5.5 Å, respectively (Fig. S2). The ARC-P1′ pose is closely similar to that obtained from Glide docking. ARC forms weaker interaction with the M₂ receptor than IXO and exhibits dynamic binding.

Fig. S2.

(A) Schematic representation of the ARC-nanobody–bound M₂ muscarinic receptor complex structure. (B–E) Time courses of important residue distances observed in the GaMD simulations: (B) the C_α atom distance between Arg121^3.50 and Thr386^6.34, (C) the C_α atom distance between Tyr177^ECL2 and Asn410^6.58, (D) the perimeter of triangle formed by the C_α atoms of Tyr104^3.33−Tyr403^6.51−Tyr426^7.39, and (E) the distance between the charged ligand N atom and the C_γ atom of Asp103^3.32.

Ligand-Dependent Dynamics of the Nanobody-Free Receptor.

Removal of the G-protein mimetic nanobody leads to deactivation of the M₂ receptor even with agonist binding. This is reflected by decreased distances between Arg121^3.50 and Thr386^6.34 in GaMD simulations of the M₂-ARC and M₂-IXO complexes (Figs. S3 and S4). The receptor in these two complexes is more flexible than in the QNB-bound form (Fig. 2 A–C and Fig. S5). The IXO-bound receptor exhibits lower flexibility in the extracellular vestibule, but higher fluctuations in the TM5, TM6, and TM7 intracellular domains than the ARC-bound form (Fig. S6), being similar to the nanobody-bound complexes (Fig. S7). Moreover, ARC undergoes significantly higher fluctuations than IXO (Fig. 2 B and C).

Fig. S3.

(A) Schematic representation of the ARC-bound M₂ muscarinic receptor complex structure. (B–E) Time courses of important residue distances observed in the GaMD simulations: (B) the C_α atom distance between Arg121^3.50 and Thr386^6.34, (C) the C_α atom distance between Tyr177^ECL2 and Asn410^6.58, (D) the perimeter of triangle formed by the C_α atoms of Tyr104^3.33−Tyr403^6.51−Tyr426^7.39, and (E) the distance between the charged ligand N atom and the C_γ atom of Asp103^3.32.

Fig. S4.

(A) Schematic representation of the IXO-bound M₂ muscarinic receptor complex structure. (B–E) Timecourses of important residue distances observed in the GaMD simulations: (B) the C_α atom distance between Arg121^3.50 and Thr386^6.34, (C) the C_α atom distance between Tyr177^ECL2 and Asn410^6.58, (D) the perimeter of triangle formed by the C_α atoms of Tyr104^3.33−Tyr403^6.51−Tyr426^7.39, and (E) the distance between the charged ligand N atom and the C_γ atom of Asp103^3.32.

Fig. 2.

Structural flexibility and free energy profiles of the M₂ receptor bound by the inverse agonist QNB, partial agonist ARC, and full agonist IXO, in the absence of the G-protein mimetic nanobody. (A–C) Schematic representations of the (A) M₂-QNB, (B) M₂-ARC, and (C) M₂-IXO complex structures colored by the protein/ligand RMSFs with a scale of 0 Å (blue) to 3 Å (red). The protein is shown in ribbons and ligands in spheres. (D–F) Two-dimensional PMF profiles of the Arg121^3.50−Thr386^6.34 and Tyr177^ECL2−Asn410^6.58 distances for the (D) M₂-QNB, (E) M₂-ARC, and (F) M₂-IXO systems. Distinct conformational states of the M₂ receptor identified in the low-energy wells, including the inactive and intermediates I1 and I2, are labeled and shown in Fig. 3. (G–I) Two-dimensional PMF profiles of the Tyr104^3.33−Tyr403^6.51−Tyr426^7.39 triangle perimeter and ligand–Asp103^3.32 distance for the (G) M₂-QNB, (H) M₂-ARC, and (I) M₂-IXO systems. Different binding poses of the ligands identified in the low-energy wells are labeled, particularly ARC-P1, ARC-P1′, and ARC-P2 (corresponding to cluster C2 in Fig. 4 that is located in the receptor extracellular vestibule).

Fig. S5.

(A) Schematic representation of the QNB-bound M₂ muscarinic receptor complex structure. (B–E) Time courses of important residue distances observed in the GaMD simulations: (B) the C_α atom distance between Arg121^3.50 and Thr386^6.34, (C) the C_α atom distance between Tyr177^ECL2 and Asn410^6.58, (D) the perimeter of triangle formed by the C_α atoms of Tyr104^3.33−Tyr403^6.51−Tyr426^7.39, and (E) the distance between the charged ligand N atom and the C_γ atom of Asp103^3.32.

Fig. S6.

Schematic representation of the IXO-bound M₂ receptor complex structure that is colored by differences in the protein/ligand RMSFs when the ligand is changed from IXO to ARC. A color scale of −0.5 Å (red) to 0.5 Å (blue) is used. The proteins are shown in ribbons and ligands in spheres. The original protein/ligand RMSFs of the M₂-ARC and M₂-IXO complex systems are shown in Fig. 2 B and C, respectively.

Fig. S7.

Schematic representations of the (A) M₂-nanobody–IXO and (B) M₂-nanobody–ARC complex structures colored by the protein/ligand RMSFs with a scale of 0 Å (blue) to 3 Å (red). The protein is shown in ribbons and ligands are shown in spheres. The differences in the protein/ligand RMSF between the M₂-nanobody–IXO and M₂-nanobody–ARC complex systems are depicted in Fig. 1A.

In the QNB-bound receptor, the Tyr177^ECL2−Asn410^6.58 distance exhibits a free energy minimum at 14.5 Å, similar to 15.9 Å in the X-ray structure (13). Binding of the smaller agonists ARC and IXO shrinks the extracellular vestibule to an energy minimum distance of 12.5 Å between Tyr177^ECL2 and Asn410^6.58, although with fluctuations (Fig. 2 E and F). On the intracellular side, the global energy minimum is identified for the nanobody-free receptor in the inactive state with ∼6–7 Å distance between Arg121^3.50−Thr386^6.34. Additional low-energy states are also observed with outward movement of the TM6 cytoplasmic end at differentiated magnitudes. Upon binding IXO, the receptor samples two intermediate states with the Arg121^3.50−Thr386^6.34 distance centered at 10.0 Å (“I1”) and 12.0 Å (“I2”), respectively (Fig. 2F). In comparison, only the intermediate I1 appears in PMF of the ARC-bound receptor in addition to the inactive state (Fig. 2E). Although agonists alone could not open the intracellular pocket up to the fully active state, IXO binding leads to greater movement of the TM6 cytoplasmic end than ARC.

Upon binding QNB, the receptor tyrosine lid is confined to the X-ray conformation (Fig. 2G). QNB remains tightly bound to the orthosteric site through the GaMD simulations. In contrast, the full and partial agonists allow the receptor to sample a significantly larger conformational space in the tyrosine lid (Fig. 2 H and I). IXO is able to escape out of the orthosteric pocket in one of the GaMD simulations, visiting the extracellular vestibule with 12.5 Å distance between ligand and Asp103^3.32 (Fig. 2I and Fig. S8). In the case of ARC, not only does it escape out of the orthosteric pocket, but also it dissociates completely and rebinds repeatedly to the receptor (described in more detail below). The distance between ARC and Asp103^3.32 samples different low-energy states at 3.5 Å (ARC-P1), 5.5 Å (ARC-P1′), and ∼10 Å (ARC-P2) (Fig. 2H). This finding presumably results from weaker binding of ARC compared with IXO and QNB (14, 16, 20).

Fig. S8.

The pathways of dissociation and binding observed for full agonist IXO in GaMD simulation. (A) The distance between the charged N atom in IXO and the C_γ atom of D103^3.32 is plotted as a function of time during a 500-ns GaMD simulation of the M₂-IXO complex system (Sim5 in Fig. S4). (B and C) Schematic representations of the ligand pathways during (B) dissociation D1 and (C) binding B1. The receptor is represented by blue ribbons and the ligand by sticks colored by the position along z axis (the lipid membrane normal). (D) Five binding poses of IXO with the lowest free energies that are located in the receptor orthosteric pocket and extracellular vestibule. The ligand-binding poses are depicted as centroids of structural clusters obtained from the DBSCAN structural clustering of diffusing IXO by combining all GaMD trajectories of the M₂-IXO system. The PMF values were computed through energetic reweighting of the IXO structural clusters. The IXO clusters (binding poses) are labeled and colored in a GWR scale according to the free energies.

Low-Energy Conformational States of the M₂ Receptor.

Through this study, distinct low-energy states are identified from free energy profiles of the M₂ receptor upon binding of different ligands. The orthosteric pocket exhibits both closed and open conformations (Fig. 3A), for which the tyrosine lid samples free energy minima at ∼30 Å and ∼33 Å, respectively (Fig. 3C). In the presence of the G-protein mimetic nanobody, IXO shifts the receptor conformational equilibrium to the closed state. In contrast, ARC allows the orthosteric pocket to sample both the closed and open states. Without the nanobody, QNB confines the receptor orthosteric pocket in the open state. ARC and IXO, however, yield a significantly broader energy well covering both the open and closed states although the open state is favored.

Fig. 3.

Distinct low-energy states sampled by the M₂ receptor in the orthosteric ligand-binding and intracellular G-protein–coupling sites. (A) The orthosteric site exhibits closed (red, 4MQS X-ray) and open (green, 3UON X-ray) conformations. (B) The G-protein–coupling site samples inactive (green, 3UON X-ray), intermediates I1 (orange) and I2 (purple), and active (red, 4MQS X-ray) conformational states. (C and D) The 1D PMF profiles of (C) the Tyr104^3.33−Tyr403^6.51−Tyr426^7.39 triangle perimeter and (D) the Arg121^3.50−Thr386^6.34 distance calculated for the M₂-QNB, M₂-ARC, M₂-IXO, M₂-nanobody–ARC, and M₂-nanobody–IXO complex systems.

The G-protein–coupling site samples the inactive, intermediates I1 and I2, and active conformational states (Fig. 3B), for which low-energy minima are found for the Arg121^3.50−Thr386^6.34 distance at 6.0–7.0 Å, ∼10 Å, ∼12 Å, and ∼15 Å, respectively (Fig. 3D). QNB confines the receptor in the inactive state, whereas binding of IXO and ARC, along with the nanobody, shifts the receptor to the fully active state. In contrast, the full/partial agonist alone allows the receptor to sample more than one low-energy state. The M₂-ARC complex samples the inactive and intermediate I1 states with similar free energies. In addition, IXO shifts the conformational equilibrium further and allows the receptor to visit the intermediate I2 state.

Pathways of Ligand Dissociation and Binding.

During the 2,030-ns GaMD simulation of the M₂-ARC system (Table S1), ARC was observed to dissociate completely and rebind to the receptor multiple times as indicated by the time course of the ligand–Asp103^3.32 distance (Fig. 4A and Movie S1). Four dissociation (denoted “D1,” “D2,” “D3,” and “D4”) and three binding (denoted “B1,” “B2,” and “B3”) events took place. ARC exited the receptor via three extracellular openings, one formed between ECL2 and ECL3 (D1, Fig. 4B), the second between ECL2 and TM2 and TM7 (D2, Fig. 4F), and the third between ECL2 and TM7 (D3 and D4, Fig. 4 G and H). ARC rebound to the receptor through two of the three openings, i.e., ECL2/ECL3 (B1, Fig. 4C) and ECL2/TM7 (B2 and B3, Fig. 4 E and G).

Fig. 4.

Pathways of partial agonist dissociation and binding observed in GaMD simulation. (A) Time course of the ARC−Asp103^3.32 distance during 2,030-ns simulation. Four dissociation and three binding events are labeled. (B–H) Schematic representations of the ligand pathways during (B) D1, (C) B1, (D) B2, (E) B3, (F) D2, (G) D3, and (H) D4. The receptor is represented by blue ribbons and the ligand by sticks colored by the position along the membrane normal. (I) Ten lowest-energy structural clusters of ARC that are labeled and colored in a Green–White–Red (GWR) scale according to the PMF values.

To obtain a quantitative picture of the ligand-binding pathways, the density-based spatial clustering of applications with noise (DBSCAN) algorithm (21) was applied to cluster trajectory snapshots of the ligand by combining all 10 GaMD simulations of M₂-ARC (total 9,100 ns). Energetic reweighting (19, 22) was then performed on each of the ligand clusters to recover the original free energy (details in SI Methods). Ten ligand clusters with the lowest free energies are shown in Fig. 4I. A global energy minimum (0 kcal/mol) is found for cluster “C1” in the orthosteric pocket. The second-lowest energy is identified for cluster “C2” (1.34 kcal/mol) at the center of the extracellular vestibule between ECL2 and TM7. Two clusters of higher energies, “C3” with 2.01 kcal/mol and “C4” with 2.29 kcal/mol, appear to connect C1 in the orthosteric pocket and C2 in the extracellular vestibule. A cavity formed by the extracellular domains of TM3/TM2/TM7 is filled with two clusters, “C5” (2.33 kcal/mol) and “C8” (2.69 kcal/mol). Similarly, another cavity formed by the TM4/TM5/TM6 extracellular domains is filled with clusters “C7” and “C9” with 2.49 kcal/mol and 3.15 kcal/mol free energies, respectively. In the extracellular vestibule, although ARC was observed to exit between ECL2 and TM2 and TM7 in one of the dissociation events, this location does not appear among the 10 lowest-energy clusters. In contrast, two energetically favored clusters are found in the opening between ECL2 and ECL3, i.e., “C6” (2.36 kcal/mol) and “C10” (3.22 kcal/mol). Therefore, clusters C1 ↔ C3 ↔ C4 ↔ C2 ↔ C10 ↔ C6 appear to represent an energetically preferred pathway for ARC dissociation and binding. IXO also follows a similar pathway during dissociation from the orthosteric site to the ECL2/ECL3 opening and rebinding to the center of the extracellular vestibule (Fig. S8 and Movie S2).

SI Methods

GaMD.

GaMD enhances the conformational sampling of biomolecules by adding a harmonic boost potential to the system when the system potential $V\left(r\right)$ is lower than a reference energy E,

$$\begin{array}{c}\mathit{V}*\left(\stackrel{\rightharpoonup }{r}\right)=\mathit{V}\left(\stackrel{\rightharpoonup }{r}\right)+\mathrm{\Delta }\mathit{V}\left(\stackrel{\rightharpoonup }{r}\right)\\ \mathrm{\Delta }\mathit{V}\left(\stackrel{\rightharpoonup }{r}\right)=\{\begin{array}{ll}\frac{1}{2}k{\left(E-V\left(\stackrel{\rightharpoonup }{r}\right)\right)}^2,\hfill & V\left(\stackrel{\rightharpoonup }{r}\right)<\mathit{E}\hfill \\ 0,\hfill & V\left(\stackrel{\rightharpoonup }{r}\right)\ge \mathit{E},\hfill \end{array}\end{array}$$ [S1]

where k is the harmonic force constant. The two adjustable parameters E and k are automatically determined by applying the following three criteria. First, for any two arbitrary potential values $V_1\left(\stackrel{\rightharpoonup }{r}\right)$ and $V_2\left(\stackrel{\rightharpoonup }{r}\right)$ found on the original energy surface, if $V_1\left(\stackrel{\rightharpoonup }{r}\right)<V_2\left(\stackrel{\rightharpoonup }{r}\right),$ $\mathrm{\Delta }V$ should be a monotonic function that does not change the relative order of the biased potential values; i.e., $V_1^{*}\left(\stackrel{\rightharpoonup }{r}\right)<V_2^{*}\left(\stackrel{\rightharpoonup }{r}\right).$ Second, if $V_1\left(\stackrel{\rightharpoonup }{r}\right)<V_2\left(\stackrel{\rightharpoonup }{r}\right),$ the potential difference observed on the smoothened energy surface should be smaller than that of the original; i.e., $V_2^{*}\left(\stackrel{\rightharpoonup }{r}\right)-V_1^{*}\left(\stackrel{\rightharpoonup }{r}\right)<V_2\left(\stackrel{\rightharpoonup }{r}\right)-V_1\left(\stackrel{\rightharpoonup }{r}\right).$ By combining the first two criteria and plugging in the formula of $V^{\ast }\left(\stackrel{\rightharpoonup }{r}\right)$ and $\mathrm{\Delta }V,$ we obtain

$$V_{\max }\le E\le V_{\min }+\frac{1}{k},$$ [S2]

where $V_{\min }$ and $V_{\max }$ are the system minimum and maximum potential energies. To ensure that Eq. S2 is valid, $k$ has to satisfy $k\le 1/\left(V_{\max }-V_{\min }\right).$ Let us define $k=k_0\mathrm{•}1/\left(V_{\max }-V_{\min }\right);$ then $0<k_0\le 1.$ Third, the standard deviation (SD) of $\mathrm{\Delta }V$ needs to be small enough (i.e., narrow distribution) to ensure accurate reweighting using cumulant expansion to the second order (22): ${\sigma }_{\mathrm{\Delta }V}=k\left(E-V_{\text{avg}}\right){\sigma }_V\le {\sigma }_0,$ where $V_{\text{avg}}$ and ${\sigma }_V$ are the average and SD of the system potential energies, and ${\sigma }_{\mathrm{\Delta }V}$ is the SD of $\mathrm{\Delta }V$ with ${\sigma }_0$ as a user-specified upper limit (e.g., 10 k_BT) for accurate reweighting. When E is set to the lower bound $E=V_{\max }$ according to Eq. S2, $k_0$ can be calculated as

$$k_0=\min \left(1.0,{k\prime }_0\right)\left(1.0,\frac{{\sigma }_0}{{\sigma }_V}•\frac{V_{\max }-V_{\min }}{V_{\max }-V_{\text{avg}}}\right).$$ [S3]

Alternatively, when the threshold energy E is set to its upper bound $E=V_{\min }+1/k,$ $k_0$ is set to

$$k_0={k^{″}}_0\equiv \left(1-\frac{{\sigma }_0}{{\sigma }_V}\right)•\frac{V_{\max }-V_{\min }}{V_{\text{avg}}-V_{\min }},$$ [S4]

if ${k^{″}}_0$ is calculated between 0 and 1. Otherwise, $k_0$ is calculated using Eq. S3.

Energetic Reweighting of GaMD Simulations.

For simulations of a biomolecular system, the probability distribution along a selected reaction coordinate $A\left(\mathit{r}\right)$ is written as $p\ast \left(A\right),$ where $\mathit{r}$ denotes the atomic positions $\left\{{\mathit{r}}_1,\mathrm{\cdots },{\mathit{r}}_{\mathit{N}}\right\}.$ Given the boost potential $\mathrm{\Delta }V\left(\mathit{r}\right)$ of each frame, $p\ast \left(A\right)$ can be reweighted to recover the canonical ensemble distribution, $p\left(A\right),$ as

$$p\left(A_j\right)=p\ast \left(A_j\right)\frac{{\langle e^{\beta \mathrm{\Delta }V\left(\mathit{r}\right)}\rangle }_j}{{\displaystyle {\sum }_{j=1}^M{\langle e^{\beta \mathrm{\Delta }V\left(\mathit{r}\right)}\rangle }_j}},\hspace{1em}j=1,\cdots ,M,$$ [S5]

where M is the number of bins, $\beta =k_{B}T,$ and ${\langle e^{\beta \mathrm{\Delta }V\left(\mathit{r}\right)}\rangle }_j$ is the ensemble-averaged Boltzmann factor of $\mathrm{\Delta }V\left(\mathit{r}\right)$ for simulation frames found in the jth bin. To reduce the energetic noise, the ensemble-averaged reweighting factor can be approximated using cumulant expansion,

$$\langle e^{\beta \mathrm{\Delta }V}\rangle =\exp \left\{{\displaystyle \sum _{k=\mathit{1}}^{\infty }\frac{{\beta }^k}{k\mathrm{!}}{C}_k}\right\},$$ [S6]

where the first three cumulants are given by

$$\begin{array}{l}{C}_1=\langle \mathrm{\Delta }V\rangle ,\\ C_2=\langle \mathrm{\Delta }{V}^2\rangle -{\langle \mathrm{\Delta }V\rangle }^2={\sigma }_{\mathrm{\Delta }V}^2,\\ C_3=\langle \mathrm{\Delta }{V}^3\rangle -3\langle \mathrm{\Delta }{V}^2\rangle \langle \mathrm{\Delta }V\rangle +2{\langle \mathrm{\Delta }V\rangle }^3.\end{array}$$ [S7]

As shown earlier, when the boost potential follows near-Gaussian distribution, cumulant expansion to the second order provides the more accurate reweighting compared with the exponential average and Maclaurin series expansion methods (22). Finally, the reweighted free energy is calculated as $F\left(A_j\right)=-\left(1/\beta \right)\ln p\left(A_j\right).$

System Setup.

X-ray crystal structures of the IXO-nanobody–bound M₂ receptor (PDB ID code 4MQS; Fig. S1A) (14) and the QNB-bound M₂ receptor (PDB ID code 3UON; Fig. S5A) (13) were used for simulations of the M₂-nanobody–IXO and M₂-QNB complex systems, respectively. Preparation of the M₂-QNB complex system followed the same protocol presented earlier (12) and a summary is provided here. The T4 lysozyme that was fused into the receptor to replace intracellular loop 3 (ICL3) for crystallizing the complex structure was omitted, based on previous findings that removal of the bulk of ICL3 does not appear to affect GPCR function and ICL3 is highly flexible (6). All chain termini were capped with neutral groups (acetyl- and methylamide). Two disulphide bonds that were resolved in the crystal structure, i.e., Cys96^3.25-Cys176^ECL2 and Cys413^6.61-Cys416^7.29, were maintained in the simulations. Using the psfgen plugin in VMD (35), protein residues were set to the standard CHARMM protonation states at neutral pH, with the exception of Asp69^2.50, which is buried in the hydrophobic core and thus protonated (5). For the IXO-nanobody–bound M₂ receptor complex system, the receptor was prepared similarly to the M₂-QNB complex except that the T4 lysozyme was absent. The G-protein mimetic nanobody Nb9-8 was kept for simulation.

For the M₂-nanobody–ARC complex system, the IXO ligand was removed from the 4MQS X-ray structure and ARC was docked to the orthosteric site with Glide standard precision (SP) (36) as the simulation starting structure (Fig. S2A). The M₂-ARC (Fig. S3A) and M₂-IXO (Fig. S4A) systems were prepared by removing the G-protein mimetic nanobody Nb9-8 from the M₂-nanobody–ARC and M₂-nanobody–IXO complex structures, respectively.

For each of the complex systems, the M₂ receptor was inserted into a palmitoyl-oleoyl-phosphatidyl-choline (POPC) bilayer with all overlapping lipid molecules removed using the Membrane plugin in VMD (35). The system charges were then neutralized at 0.15 M NaCl, using the Solvate plugin in VMD (35). The M₂-nanobody–IXO complex system was solvated in a box of 88 × 88 × 113 ų and contained 154 lipid molecules and 45 Na⁺, 45 Cl⁻, and 16,082 water molecules, for a total of ∼75,300 atoms. The M₂-nanobody–IXO complex system has a similar size. The M₂-QNB complex system initially measured 88 × 85 × 88 ų and contained 154 lipid molecules and 28 Na⁺, 39 Cl⁻, and 9,949 water molecules, for a total of ∼52,700 atoms. The M₂-IXO complex system measured 88 × 88 × 86 ų and contained 136 lipid molecules and 28 Na⁺, 39 Cl⁻, and 10,010 water molecules, for a total of ∼55,300 atoms, similar to the M₂-ARC complex system (Table S1). Periodic boundary conditions were applied on all simulation systems.

Simulation Protocol.

The CHARMM36 parameter set (33) was used for the M₂ receptor, G-protein mimetic nanobody, and POPC lipids. Force-field parameters of QNB were obtained from the CHARMM ParamChem web server and QNB was simulated in the protonated state as described previously (5). For full agonist IXO and partial agonist ARC, the force-field parameters were computed using the general automated atomic model parameterization (GAAMP) tool (37). With ab initio quantum mechanical calculations, GAAMP (37) generates force-field parameters that are compatible with CHARMM as used for protein and lipids (11).

For each of the M₂ receptor complex systems, initial energy minimization, thermalization, and 100-ns cMD equilibration were performed using NAMD2.10 (32). A cutoff distance of 12 Å was used for the van der Waals and short-range electrostatic interactions and the long-range electrostatic interactions were computed with the particle-mesh Ewald summation method, using a grid point density of 1/Å. A 2-fs integration time step was used for all MD simulations and a multiple-time–stepping algorithm was used with bonded and short-range nonbonded interactions computed every time step and long-range electrostatic interactions every two time steps. The SHAKE algorithm was applied to all hydrogen-containing bonds. The NAMD simulation started with equilibration of the lipid tails. With all other atoms fixed, the lipid tails were energy minimized for 1,000 steps using the conjugate gradient algorithm and melted with a constant number, volume, and temperature (NVT) run for 0.5 ns at 310 K. The two systems were further equilibrated using a constant number, pressure, and temperature (NPT) run at 1 atm and 310 K for 10 ns with 5 kcal/(mol⋅Ų) harmonic position restraints applied to the crystallographically identified atoms in the protein and ligand. The system volume was found to decrease with a flexible unit cell applied and level off within a 10-ns NPT run, suggesting that solvent and lipid molecules in the system were well equilibrated. Final equilibration of each system was performed using an NPT run at 1 atm and 310 K for 0.5 ns with all atoms unrestrained. After energy minimization and system equilibration, cMD simulation was performed on each system for 100 ns at 1 atm pressure and 310 K with a constant ratio constraint applied on the lipid bilayer in the X-Y plane.

With the NAMD output structure, along with the system topology and CHARM36 force-field files, the ParmEd tool in the AMBER package was used to convert the simulation files into the AMBER format (34). The GaMD module implemented in the GPU version of AMBER14 (19, 34) was then applied to perform the GaMD simulation, which included a 10-ns short cMD simulation used to collect the potential statistics for calculating GaMD acceleration parameters, a 50-ns equilibration after adding the boost potential, and finally multiple independent GaMD production simulations with randomized initial atomic velocities. All GaMD simulations were run at the “dual-boost” level by setting the reference energy to the lower bound; i.e., $E=V_{\max }$ (19). One boost potential is applied to the dihedral energetic term and another to the total potential energetic term. The average and SD of the system potential energies were calculated every 200,000 steps (400 ps) and every 250,000 steps (500 ps) for the nanobody-free and nanobody-bound complex systems, respectively. The upper limit of the boost potential SD, ${\sigma }_0$ was set to 6.0 kcal/mol for both the dihedral and the total potential energetic terms. Similar temperature and pressure parameters were used as in the NAMD simulations. A list of GaMD production simulations on the different M₂ receptor complex systems at 400-ns to 2,030-ns lengths (total ∼19 μs) is provided in Table S1.

Simulation Analysis.

CPPTRAJ (38) and VMD (35) were used to analyze the GaMD simulation trajectories. Particularly, distances were calculated between the C_α atom of Arg121^3.50−Thr386^6.34 and Tyr177^ECL2−Asn410^6.58, the ligand-charged N atom and the C_γ atom of Asp103^3.32, and similarly for the perimeter of triangle formed by the C_α atoms of Tyr104^3.33−Tyr403^6.51−Tyr426^7.39. RMSFs were calculated for the protein residues and ligand, averaged over multiple independent GaMD simulations and color coded for schematic representation of each complex system (e.g., Figs. 1A and 2 A–C).

The DBSCAN algorithm (21) implemented in CPPTRAJ was applied to cluster trajectory frames of the diffusing ARC and IXO by combining all of the GaMD production simulations of the M₂-ARC and M₂-IXO systems, respectively. A total length of ∼9,100 ns GaMD simulation (∼91 million frames) was obtained for ARC clustering. Because of the large dataset, the frames were sieved at a stride of 2,000 for clustering. A distance cutoff of 1.6 Å and a minimum number of 80 sieved frames were set for forming a cluster. The remaining frames were assigned to the closest cluster afterward. Similar parameters were used to cluster the M₂-IXO simulation (total ∼6,300 ns), except that a minimum number of 10 sieved frames were set for forming a cluster.

The PyReweighting (22) toolkit was used to reweight the atom distances, perimeter of the tyrosine triangle, and ligand structural clusters to compute the PMF profiles. A bin size of 0.5 Å was used for the atom distances and perimeter of the tyrosine triangle. The cutoff was set to 5,000 frames for 1D PMF and to 500 frames for 2D PMF calculations. The 2D PMF profiles were obtained for each complex system regarding the Arg121^3.50−Thr386^6.34 and Tyr177^ECL2−Asn410^6.58 distances and the Tyr104^3.33−Tyr403^6.51−Tyr426^7.39 triangle perimeter and ligand−Asp103^3.32 distances (Figs. 1 and 2). One-dimensional PMF profiles were calculated for all receptor complex systems on the Arg121^3.50−Thr386^6.34 distance and the Tyr104^3.33−Tyr403^6.51−Tyr426^7.39 triangle perimeter and plotted in Fig. 3. PMF values were also computed for top-ranked structural clusters of partial agonist ARC (Fig. 4I) and full agonist IXO (Fig. S8D), using combined GaMD simulations of the M₂-ARC and M₂-IXO systems, respectively.

Discussion

In this study, detailed ligand-dependent dynamics and free energy profiles of the M₂ muscarinic GPCR have been obtained through extensive GaMD simulations (∼19 us in total). The energy minimum states identified from GaMD simulations of the QNB-bound and the IXO-nanobody–bound receptor are the same as the inactive and fully active receptor X-ray structures (13, 14), respectively. The simulations also revealed new low-energy states in the IXO/ARC-bound receptor upon removal the nanobody. Whereas the inverse agonist QNB with high binding affinity (∼0.06 nM) (14) remains tightly bound to the orthosteric site, the full and partial agonists with lower affinities, ∼5 μM for ARC (16, 20) and ∼0.01 μM for IXO (14), exhibit significantly higher fluctuations. We have captured both dissociation and binding of an orthosteric ligand in a single all-atom GPCR simulation in the case of ARC binding to the M₂ receptor. These results are consistent with the recent experimental finding that the G-protein mimetic nanobody stabilizes a closed receptor conformation and dramatically affects the association and dissociation of GPCR ligands (17). Notably, Dror et al. (23) successfully observed both binding and dissociation of allosteric modulators at the M₂ receptor through long-timescale conventional MD (cMD) simulations. However, the allosteric site is located in the receptor extracellular vestibule, ∼15Å above the deeply buried orthosteric site. It is also important to note that a direct link between the binding affinity of individual GPCR ligands and their efficacy is still lacking (16, 20, 24). Whereas ARC exhibits lower affinity than IXO or QNB as investigated in the present study, certain partial agonists are not necessarily weaker binders compared with full or inverse agonists (16, 24). Nevertheless, there appears to be a correlation between efficacy and the breadth of the dispersion of affinities for agonists of the M₂ receptor (16, 20, 25). The GaMD simulations provided important insights into the binding mechanism of three studied ligands and GPCR graded activation.

Overall, the M₂ receptor samples a large conformational space (Fig. 5). In the presence of the G-protein mimetic nanobody, the receptor is stabilized in the fully active state with the most open intracellular pocket and the narrowest extracellular vestibule. In the orthosteric pocket, IXO stabilizes the receptor in the closed state, whereas ARC binding allows the receptor to change between the closed and open states with two alternative poses (ARC-P1 and ARC-P1′). Such dynamic binding of the partial agonist, along with multiple associated receptor conformations, has previously been observed in NMR experiments of the peroxisome proliferator-activated receptor γ (26).

Fig. 5.

Mechanism of graded activation of the M₂ muscarinic GPCR. The M₂ receptor (ribbons) samples a large conformational space with significant structural rearrangements, especially for the TM6 helix. Binding of the inverse agonist QNB (green spheres) confines the receptor in the inactive state. Without the G protein or mimetic nanobody, the partial agonist ARC (yellow spheres) biases the M₂ receptor to visit an intermediate state I1 (orange ribbons). ARC is able to dissociate completely to the bulk solvent via the extracellular vestibule and rebinds to the receptor repeatedly during a 2,030-ns GaMD simulation. In comparison, the full agonist IXO (red spheres) biases the receptor further, sampling both intermediate I1 (orange ribbons) and I2 (purple ribbons). IXO escapes out of the orthosteric pocket and visits the extracellular vestibule in one of the GaMD simulations. By adding the G-protein mimetic nanobody (purple surface), the M₂ receptor is stabilized in the fully active state (red ribbons) as bound by IXO or ARC, although ARC adopts two alternative conformations in the orthosteric pocket, ARC-P1 (yellow spheres) and ARC-P1′ (cyan spheres).

Removal of the nanobody leads to deactivation of the M₂ receptor with inward displacement of the TM6 cytoplasmic end. This is consistent with extensive experimental and computational studies of GPCRs, especially on the β₂-adrenergic receptor (β₂AR) (6). Binding of QNB confines the receptor in the inactive state with the shortest distance between Arg121^3.50 and Thr386^6.34 (∼6–7 Å). Without the G-protein or mimetic nanobody, ARC biases the receptor to visit an intermediate state I1 that exhibits increased distance between Arg121^3.50 and Thr386^6.34 (∼10 Å). In comparison, IXO is able to bias the receptor further, sampling both intermediates I1 and I2 with ∼10 Å and ∼12 Å distances between Arg121^3.50 and Thr386^6.34, respectively. Note that our earlier accelerated MD (aMD) simulations captured a similar conformational change during activation of the apo M₂ receptor that exhibits basal activity (12). Even without agonist binding, the apo receptor undergoes transient outward movement of the TM6 cytoplasmic end up to ∼12 Å. To a certain extent, the intermediate I2 in the present study can be considered an “active-like” state, which has been used to define the agonist-bound adenosine A_2A receptor (A_2AAR) (27). In summary, graded activation of the M₂ receptor is characterized by outward movement of the TM6 cytoplasmic end at increasing magnitudes when the ligand changes from inverse to partial and full agonists.

The orthosteric pocket samples two distinct conformations, being open in the QNB-bound M₂ receptor (13) and closed in the IXO-nanobody–bound form (14). It interconverts dynamically between the closed and open states when the ligand is changed from IXO to ARC in the nanobody-coupled receptor (Fig. 3C), although the extracellular vestibule remains to adopt the narrowest opening (Fig. S9B). It also exhibits a broad energy well covering both the closed and open states in the M₂-IXO and M₂-ARC complexes. Given such plasticity, the orthosteric pocket of the M₂ receptor is able to accommodate different ligands of various sizes (14, 16). In addition, the extracellular vestibule in the IXO- and ARC-bound receptor samples both the narrow and wide opening conformations, for which the distances between Tyr177^ECL2 and Asn410^6.58 are 12.5 Å and ∼16 Å, respectively(Fig. 2 and Fig. S9). Overall, the extracellular vestibule appears highly flexible. Binding of allosteric modulators may stabilize it in specific conformations and alter the orthosteric ligand-mediated responses (14, 23).

Fig. S9.

(A–E) Two-dimensional PMF profiles of the Tyr177^ECL2−Asn410^6.58 distance and Tyr104^3.33−Tyr403^6.51−Tyr426^7.39 triangle perimeter in the (A) M₂-nanobody–IXO, (B) M₂-nanobody–ARC, (C) M₂- IXO, (D) M₂-ARC, and (E) M₂-QNB systems.

In earlier computational studies, ligand-dependent dynamics of GPCRs were investigated using the cMD (7, 10), metadynamics (8, 9), and aMD (11) methods. Whereas cMD simulations revealed distinct conformational changes in several known GPCR activation elements (7), these simulations lasting several hundred nanoseconds were not long enough to capture the entire GPCR activation/deactivation processes. For the β₂AR, cMD simulations were combined with coarse-grained modeling to sample the receptor ensemble conformations (10). Moreover, metadynamics were used to characterize free energy landscapes of the β₂AR (8) and A_2AAR (9). However, metadynamics require predefined collective variables and may constrain the dynamic GPCR activation or deactivation pathways. Recently, we applied aMD to simulate binding of different ligands to the M₃ muscarinic receptor (11). Although the aMD simulations successfully captured binding of the partial and full agonists without constraints, the boost potential suffered from large energetic noise and precluded accurate reweighting to recover the original free energy landscapes. By constructing boost potential that follows a Gaussian distribution, GaMD enabled simultaneous unconstrained enhanced sampling and free energy calculations. It allows for detailed characterization of the ligand-dependent dynamics of the M₂ receptor.

During one of the GaMD simulations, IXO with ∼0.01 μM affinity escapes out of the orthosteric pocket and visits the extracellular vestibule (Fig. S8 and Movie S2). For ARC with 5.0 μM binding affinity, not only does it escape out of the orthosteric pocket, but also it dissociates completely and rebinds to the receptor repeatedly during a 2,030-ns GaMD simulation (Fig. 4 and Movie S1). A pathway connecting the orthosteric site, the center of the extracellular vestibule, and the ECL2/ECL3 opening appears to be energetically favorable for ligand dissociation and binding (Fig. 4I). This route has also been identified as the dominant pathway for drug binding to the β₂AR (28). Therefore, it may be a common pathway adopted by class A GPCRs for ligand recognition, although this may also depend on structural arrangement of the receptor extracellular domains and ligand size and chemical properties. For the M₂ receptor, it is worth investigating the binding of more ligands and associated receptor dynamics in the future, e.g., the N-methylscopolamine and atropine inverse agonists (16), the pilocarpine and McN-A343 partial agonists that elicit more consistent partial response of the M₂ receptor (16, 20), etc. In this context, although ligand dissociation from β₂AR was simulated in a previous random acceleration MD (RAMD) study (29), it was difficult to capture rebinding of the ligand. The ligand was observed to exit with similar probability via the ECL2/ECL3 and ECL2/TM2/TM7 openings, but the RAMD simulations could not differentiate the two pathways energetically. Another steered MD study on ligand dissociation from the β-ARs also suggested the two routes “may serve indistinguishably for ligand entry and exit” (ref. 30, p. 6). Although free energy profiles were obtained from the steered MD simulations, the ligand was constrained to predetermined CAVER channels, which may not reflect the real pathways as observed in cMD simulations (28). In comparison, GaMD provides unconstrained enhanced sampling and allows for free ligand diffusion. The simulation-derived free energy profiles can be used to characterize the ligand pathways quantitatively. Notably, the orthosteric pocket and extracellular vestibule were calculated as two low-energy binding sites of ARC. This finding is consistent with previous binding assay experiments, suggesting that several partial agonists have two or more binding sites in the M₂ receptor (16, 31). Earlier computational studies also identified the extracellular vestibule as a metastable site during binding of orthosteric ligands to the M₂ and M₃ muscarinic receptors (5, 11). Therefore, GaMD is well suited for investigating ligand binding and dissociation of GPCRs and other large biomolecules. With continuing computing advances and method development, sufficient sampling of biomolecular conformations and ligand pathways may become increasingly useful for drug discovery.

Methods

GaMD simulations were performed on the M₂ muscarinic receptor that is bound by the full agonist IXO, the partial agonist ARC, and the inverse agonist QNB, in the presence or absence of the G-protein mimetic nanobody Nb9-8. For each of the receptor complexes, initial energy minimization, thermalization, and 100-ns cMD equilibration were performed using NAMD2.10 (32). Using the NAMD output structure, along with the system topology and CHARMM36 (33) force-field files, ParmEd was used to convert the simulation files into the AMBER format (34). The GaMD module implemented in the graphics processing unit (GPU) version of AMBER14 (19, 34) was then applied to perform GaMD simulation, which included 10-ns short cMD simulation used to collect potential statistics for calculating the GaMD acceleration parameters, 50-ns equilibration after adding the boost potential, and finally multiple independent GaMD production runs with randomized initial atomic velocities. The simulation frames were saved every 0.1 ps for analysis. The GaMD production simulations performed on the different M₂ receptor systems at 400-ns to 2,030-ns lengths (total ∼19 μs) are listed in Table S1. Details of the GaMD simulations, energetic reweighting, system setup, and simulation analysis are provided in SI Methods.