Protein-protein binding is key in cellular signaling processes. Molecular dynamics (MD) simulations of protein-protein binding, however, are challenging due to limited timescales. In particular, binding of the medically important G-protein-coupled receptors (GPCRs) with intracellular signaling proteins has not been simulated with MD to date. Here, we report a successful simulation of the binding of a G-protein mimetic nanobody to the M₂ muscarinic GPCR using the robust Gaussian accelerated MD (GaMD) method. Through long-timescale GaMD simulations over 4,500 ns, the nanobody was observed to bind the receptor intracellular G-protein-coupling site, with a minimum rmsd of 2.48 Å in the nanobody core domain compared with the X-ray structure. Binding of the nanobody allosterically closed the orthosteric ligand-binding pocket, being consistent with the recent experimental finding. In the absence of nanobody binding, the receptor orthosteric pocket sampled open and fully open conformations. The GaMD simulations revealed two low-energy intermediate states during nanobody binding to the M₂ receptor. The flexible receptor intracellular loops contribute remarkable electrostatic, polar, and hydrophobic residue interactions in recognition and binding of the nanobody. These simulations provided important insights into the mechanism of GPCR-nanobody binding and demonstrated the applicability of GaMD in modeling dynamic protein-protein interactions.

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.

Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations.

A novel Gaussian Accelerated Molecular Dynamics (GaMD) method has been developed for simultaneous unconstrained enhanced sampling and free energy calculation of biomolecules. Without the need to set predefined reaction coordinates, GaMD enables unconstrained enhanced sampling of the biomolecules. Furthermore, by constructing a boost potential that follows a Gaussian distribution, accurate reweighting of GaMD simulations is achieved via cumulant expansion to the second order. The free energy profiles obtained from GaMD simulations allow us to identify distinct low energy states of the biomolecules and characterize biomolecular structural dynamics quantitatively. In this chapter, we present the theory of GaMD, its implementation in the widely used molecular dynamics software packages (AMBER and NAMD), and applications to the alanine dipeptide biomolecular model system, protein folding, biomolecular large-scale conformational transitions and biomolecular recognition.

G-protein coupled receptors (GPCRs), the largest family of human membrane proteins, mediate cellular signaling and represent primary targets of about one third of currently marketed drugs. GPCRs undergo highly dynamic structural transitions during signal transduction, from binding of extracellular ligands to coupling with intracellular effector proteins. Molecular dynamics (MD) simulations have been utilized to investigate GPCR signaling mechanisms (such as pathways of ligand binding and receptor activation/deactivation) and to design novel small-molecule drug candidates. Future research directions point towards modeling cooperative binding of multiple orthosteric and allosteric ligands to GPCRs, GPCR oligomerization and interactions of GPCRs with different intracellular signaling proteins. Through methodological and supercomputing advances, MD simulations will continue to provide important insights into GPCR signaling mechanisms and further facilitate structure-based drug design.

Elucidating the detailed process of ligand binding to a receptor is pharmaceutically important for identifying druggable binding sites. With the ability to provide atomistic detail, computational methods are well poised to study these processes. Here, accelerated molecular dynamics (aMD) is proposed to simulate processes of ligand binding to a G-protein-coupled receptor (GPCR), in this case the M3 muscarinic receptor, which is a target for treating many human diseases, including cancer, diabetes and obesity. Long-timescale aMD simulations were performed to observe the binding of three chemically diverse ligand molecules: antagonist tiotropium (TTP), partial agonist arecoline (ARc) and full agonist acetylcholine (ACh). In comparison with earlier microsecond-timescale conventional MD simulations, aMD greatly accelerated the binding of ACh to the receptor orthosteric ligand-binding site and the binding of TTP to an extracellular vestibule. Further aMD simulations also captured binding of ARc to the receptor orthosteric site. Additionally, all three ligands were observed to bind in the extracellular vestibule during their binding pathways, suggesting that it is a metastable binding site. This study demonstrates the applicability of aMD to protein-ligand binding, especially the drug recognition of GPCRs.

A Gaussian accelerated molecular dynamics (GaMD) approach for simultaneous enhanced sampling and free energy calculation of biomolecules is presented. By constructing a boost potential that follows Gaussian distribution, accurate reweighting of the GaMD simulations is achieved using cumulant expansion to the second order. Here, GaMD is demonstrated on three biomolecular model systems: alanine dipeptide, chignolin folding, and ligand binding to the T4-lysozyme. Without the need to set predefined reaction coordinates, GaMD enables unconstrained enhanced sampling of these biomolecules. Furthermore, the free energy profiles obtained from reweighting of the GaMD simulations allow us to identify distinct low-energy states of the biomolecules and characterize the protein-folding and ligand-binding pathways quantitatively.

The A_2A adenosine receptor (A_2A AR) is a G protein-coupled receptor that is pharmacologically targeted for the treatment of inflammation, sepsis, cancer, neurodegeneration, and Parkinson's disease. Recently, we applied long-timescale molecular dynamics simulations on two ligand-free receptor conformations, starting from the agonist-bound (PDB ID: 3QAK) and antagonist-bound (PDB ID: 3EML) X-ray structures. This analysis revealed four distinct conformers of the A_2A AR: the active, intermediate 1, intermediate 2, and inactive. In this study, we apply the fragment-based mapping algorithm, FTMap, on these receptor conformations to uncover five non-orthosteric sites on the A_2A AR. Two sites that are identified in the active conformation are located in the intracellular region of the transmembrane helices (TM) 3/TM4 and the G protein-binding site in the intracellular region between TM2/TM3/TM6/TM7. Three sites are identified in the intermediate 1 and intermediate 2 conformations, annexing a site in the lipid interface of TM5/TM6. Five sites are identified in the inactive conformation, comprising a site in the intracellular region of TM1/TM7 and in the extracellular region of TM3/TM4 of the A_2A AR. We postulate that these sites on the A_2A AR be screened for allosteric modulators for the treatment of inflammatory and neurological diseases.

Gaussian accelerated molecular dynamics (GaMD) is a recently developed enhanced sampling technique that provides efficient free energy calculations of biomolecules. Like the previous accelerated molecular dynamics (aMD), GaMD allows for "unconstrained" enhanced sampling without the need to set predefined collective variables and so is useful for studying complex biomolecular conformational changes such as protein folding and ligand binding. Furthermore, because the boost potential is constructed using a harmonic function that follows Gaussian distribution in GaMD, cumulant expansion to the second order can be applied to recover the original free energy profiles of proteins and other large biomolecules, which solves a long-standing energetic reweighting problem of the previous aMD method. Taken together, GaMD offers major advantages for both unconstrained enhanced sampling and free energy calculations of large biomolecules. Here, we have implemented GaMD in the NAMD package on top of the existing aMD feature and validated it on three model systems: alanine dipeptide, the chignolin fast-folding protein, and the M₃ muscarinic G protein-coupled receptor (GPCR). For alanine dipeptide, while conventional molecular dynamics (cMD) simulations performed for 30 ns are poorly converged, GaMD simulations of the same length yield free energy profiles that agree quantitatively with those of 1000 ns cMD simulation. Further GaMD simulations have captured folding of the chignolin and binding of the acetylcholine (ACh) endogenous agonist to the M₃ muscarinic receptor. The reweighted free energy profiles are used to characterize the protein folding and ligand binding pathways quantitatively. GaMD implemented in the scalable NAMD is widely applicable to enhanced sampling and free energy calculations of large biomolecules.