GENESIS 1.1: A hybrid-parallel molecular dynamics simulator with enhanced sampling algorithms on multiple computational platforms

Anharmonic Vibrational Analysis of Biomolecules and Solvated Molecules Using Hybrid QM/MM Computations

Quantum mechanics/molecular mechanics (QM/MM) calculations are applied for anharmonic vibrational analyses of biomolecules and solvated molecules. The QM/MM method is implemented into a molecular dynamics (MD) program, GENESIS, by interfacing with external electronic structure programs. Following the geometry optimization and the harmonic normal-mode analysis based on a partial Hessian, the anharmonic potential energy surface (PES) is generated from QM/MM energies and gradients calculated at grid points. The PES is used for vibrational self-consistent field (VSCF) and post-VSCF calculations to compute the vibrational spectrum. The method is first applied to a phosphate ion in solution. With both the ion and neighboring water molecules taken as a QM region, IR spectra of representative hydration structures are calculated by the second-order vibrational quasi-degenerate perturbation theory (VQDPT2) at the level of B3LYP/cc-pVTZ and TIP3P force field. A weight-average of IR spectra over the structures reproduces the experimental spectrum with a mean absolute deviation of 16 cm^–1. Then, the method is applied to an enzyme, P450 nitric oxide reductase (P450nor), with the NO molecule bound to a ferric (Fe^III) heme. Starting from snapshot structures obtained from MD simulations of P450nor in solution, QM/MM calculations have been carried out at the level of B3LYP-D3/def2-SVP(D). The spin state of Fe^III(NO) is likely a closed-shell singlet state based on a ratio of N–O and Fe–NO stretching frequencies (ν_N–O and ν_Fe–NO) calculated for closed- and open-shell singlet states. The calculated ν_N–O and ν_Fe–NO overestimate the experimental ones by 120 and 75 cm^–1, respectively. The electronic structure and solvation of Fe^III(NO) affect the structure around the heme of P450nor leading to an increase in ν_N–O and ν_Fe–NO.

Replica-Exchange Methods for Biomolecular Simulations

In this study, a replica-exchange method was developed to overcome conformational sampling difficulties in computer simulations of spin glass or other systems with rugged free-energy landscapes. This method was then applied to the protein-folding problem in combination with molecular dynamics (MD) simulation. Owing to its simplicity and sampling efficiency, the replica-exchange method has been applied to many other biological problems and has been continuously improved. The method has often been combined with other sampling techniques, such as umbrella sampling, free-energy perturbation, metadynamics, and Gaussian accelerated MD (GaMD). In this chapter, we first summarize the original replica-exchange molecular dynamics (REMD) method and discuss how new algorithms related to the original method are implemented to add new features. Heterogeneous and flexible structures of an N-glycan in a solution are simulated as an example of applications by REMD, replica exchange with solute tempering, and GaMD. The sampling efficiency of these methods on the N-glycan system and the convergence of the free-energy changes are compared. REMD simulation protocols and trajectory analysis using the GENESIS software are provided to facilitate the practical use of advanced simulation methods.

Optimal Temperature Evaluation in Molecular Dynamics Simulations with a Large Time Step

In molecular dynamics (MD) simulations, an accurate evaluation of temperature is essential for controlling temperature as well as pressure in the isothermal-isobaric conditions. According to the Tolman's equipartition theorem, all motions of all particles should share a single temperature. However, conventional temperature estimation from kinetic energy does not include Hessian terms properly, and thereby, the equipartition theorem is not satisfied with a large time step. In this paper, we show how to evaluate temperature the most accurately without increasing computational cost. We define two kinds of kinetic energies, evaluated at full- and half-time steps that underestimate or overestimate temperature, respectively. A combination of these two kinetic energies provides an optimal instantaneous temperature up to the third order of the time step. The method is tested for a one-dimensional harmonic oscillator, pure water molecules, a Bovine pancreatic trypsin inhibitor (BPTI) protein in water molecules, and a hydrated 1,2-dispalmitoyl- sn-phosphatidylcholine (DPPC) lipid bilayer in water molecules. In all tests, the optimal temperature estimator fulfills the equipartition theorem better than existing methods and reproduces well the usual physical properties for time steps up to and including 5 fs.

Population Shift Mechanism for Partial Agonism of AMPA Receptor

α-amino-3-hydroxy-5-methyl-4-isoaxazolepropionic acid (AMPA) ionotropic glutamate receptors mediate fast excitatory neurotransmission in the central nervous system, and their dysfunction is associated with neurological diseases. Glutamate binding to ligand-binding domains (LBDs) of AMPA receptors induces channel opening in the transmembrane domains of the receptors. The T686A mutation reduces glutamate efficacy so that the glutamate behaves as a partial agonist. The crystal structures of wild-type and mutant LBDs are very similar and cannot account for the observed behavior. To elucidate the molecular mechanism inducing partial agonism of the T686A mutant, we computed the free-energy landscapes governing GluA2 LBD closure using replica-exchange umbrella sampling simulations. A semiclosed state, not observed in crystal structures, appears in the mutant during simulation. In this state, the LBD cleft opens slightly because of breaking of interlobe hydrogen bonds, reducing the efficiency of channel opening. The energy difference between the LBD closed and semiclosed states is small, and transitions between the two states would occur by thermal fluctuations. Evidently, glutamate binding to the T686A mutant induces a population shift from a closed to a semiclosed state, explaining the partial agonism in the AMPA receptor.

Acceleration of cryo-EM Flexible Fitting for Large Biomolecular Systems by Efficient Space Partitioning

Flexible fitting is a powerful technique to build the 3D structures of biomolecules from cryoelectron microscopy (cryo-EM) density maps. One popular method is a cross-correlation coefficient-based approach, where the molecular dynamics (MD) simulation is carried out with the biasing potential that includes the cross-correlation coefficient between the experimental and simulated density maps. Here, we propose efficient parallelization schemes for the calculation of the cross-correlation coefficient to accelerate flexible fitting. Our schemes are tested for small, medium, and large biomolecules using CPU and hybrid CPU + GPU architectures. The scheme for the atomic decomposition MD is suitable for small proteins such as Ca²⁺-ATPase with the all-atom Go model, while that for the domain decomposition MD is better for larger systems such as ribosome with the all-atom Go or the all-atom explicit solvent models. Our methods allow flexible fitting for various biomolecules with reasonable computational cost. This approach also connects high-resolution structure refinements with investigation of protein structure-function relationship.

Exploring Configuration Space and Path Space of Biomolecules Using Enhanced Sampling Techniques-Searching for Mechanism and Kinetics of Biomolecular Functions

To understand functions of biomolecules such as proteins, not only structures but their conformational change and kinetics need to be characterized, but its atomistic details are hard to obtain both experimentally and computationally. Here, we review our recent computational studies using novel enhanced sampling techniques for conformational sampling of biomolecules and calculations of their kinetics. For efficiently characterizing the free energy landscape of a biomolecule, we introduce the multiscale enhanced sampling method, which uses a combined system of atomistic and coarse-grained models. Based on the idea of Hamiltonian replica exchange, we can recover the statistical properties of the atomistic model without any biases. We next introduce the string method as a path search method to calculate the minimum free energy pathways along a multidimensional curve in high dimensional space. Finally we introduce novel methods to calculate kinetics of biomolecules based on the ideas of path sampling: one is the Onsager⁻Machlup action method, and the other is the weighted ensemble method. Some applications of the above methods to biomolecular systems are also discussed and illustrated.

Flexible selection of the solute region in replica exchange with solute tempering: Application to protein-folding simulations

Replica-exchange molecular dynamics (REMD) and their variants have been widely used in simulations of the biomolecular structure and dynamics. Replica exchange with solute tempering (REST) is one of the methods where temperature of a pre-defined solute molecule is exchanged between replicas, while solvent temperatures in all the replicas are kept constant. REST greatly reduces the number of replicas compared to the temperature REMD, while replicas at low temperatures are often trapped under their conditions, interfering with the conformational sampling. Here, we introduce a new scheme of REST, referred to as generalized REST (gREST), where the solute region is defined as a part of a molecule or a part of the potential energy terms, such as the dihedral-angle energy term or Lennard-Jones energy term. We applied this new method to folding simulations of a β-hairpin (16 residues) and a Trp-cage (20 residues) in explicit water. The protein dihedral-angle energy term is chosen as the solute region in the simulations. gREST reduces the number of replicas necessary for good random walks in the solute-temperature space and covers a wider conformational space compared to the conventional REST2. Considering the general applicability, gREST should become a promising tool for the simulations of protein folding, conformational dynamics, and an in silico drug design.

Linking time-series of single-molecule experiments with molecular dynamics simulations by machine learning

Single-molecule experiments and molecular dynamics (MD) simulations are indispensable tools for investigating protein conformational dynamics. The former provide time-series data, such as donor-acceptor distances, whereas the latter give atomistic information, although this information is often biased by model parameters. Here, we devise a machine-learning method to combine the complementary information from the two approaches and construct a consistent model of conformational dynamics. It is applied to the folding dynamics of the formin-binding protein WW domain. MD simulations over 400 μs led to an initial Markov state model (MSM), which was then "refined" using single-molecule Förster resonance energy transfer (FRET) data through hidden Markov modeling. The refined or data-assimilated MSM reproduces the FRET data and features hairpin one in the transition-state ensemble, consistent with mutation experiments. The folding pathway in the data-assimilated MSM suggests interplay between hydrophobic contacts and turn formation. Our method provides a general framework for investigating conformational transitions in other proteins.

A molecular dynamics simulation study decodes the Zika virus NS5 methyltransferase bound to SAH and RNA analogue

Since 2015, widespread Zika virus outbreaks in Central and South America have caused increases in microcephaly cases, and this acute problem requires urgent attention. We employed molecular dynamics and Gaussian accelerated molecular dynamics techniques to investigate the structure of Zika NS5 protein with S-adenosyl-L-homocysteine (SAH) and an RNA analogue, namely 7-methylguanosine 5'-triphosphate (m7GTP). For the binding motif of Zika virus NS5 protein and SAH, we suggest that the four Zika NS5 substructures (residue orders: 101-112, 54-86, 127-136 and 146-161) and the residues (Ser56, Gly81, Arg84, Trp87, Thr104, Gly106, Gly107, His110, Asp146, Ile147, and Gly148) might be responsible for the selectivity of the new Zika virus drugs. For the binding motif of Zika NS5 protein and m7GTP, we suggest that the three Zika NS5 substructures (residue orders: 11-31, 146-161 and 207-218) and the residues (Asn17, Phe24, Lys28, Lys29, Ser150, Arg213, and Ser215) might be responsible for the selectivity of the new Zika virus drugs.

Tinker-HP: a massively parallel molecular dynamics package for multiscale simulations of large complex systems with advanced point dipole polarizable force fields

We present Tinker-HP, a massively MPI parallel package dedicated to classical molecular dynamics (MD) and to multiscale simulations, using advanced polarizable force fields (PFF) encompassing distributed multipoles electrostatics. Tinker-HP is an evolution of the popular Tinker package code that conserves its simplicity of use and its reference double precision implementation for CPUs. Grounded on interdisciplinary efforts with applied mathematics, Tinker-HP allows for long polarizable MD simulations on large systems up to millions of atoms. We detail in the paper the newly developed extension of massively parallel 3D spatial decomposition to point dipole polarizable models as well as their coupling to efficient Krylov iterative and non-iterative polarization solvers. The design of the code allows the use of various computer systems ranging from laboratory workstations to modern petascale supercomputers with thousands of cores. Tinker-HP proposes therefore the first high-performance scalable CPU computing environment for the development of next generation point dipole PFFs and for production simulations. Strategies linking Tinker-HP to Quantum Mechanics (QM) in the framework of multiscale polarizable self-consistent QM/MD simulations are also provided. The possibilities, performances and scalability of the software are demonstrated via benchmarks calculations using the polarizable AMOEBA force field on systems ranging from large water boxes of increasing size and ionic liquids to (very) large biosystems encompassing several proteins as well as the complete satellite tobacco mosaic virus and ribosome structures. For small systems, Tinker-HP appears to be competitive with the Tinker-OpenMM GPU implementation of Tinker. As the system size grows, Tinker-HP remains operational thanks to its access to distributed memory and takes advantage of its new algorithmic enabling for stable long timescale polarizable simulations. Overall, a several thousand-fold acceleration over a single-core computation is observed for the largest systems. The extension of the present CPU implementation of Tinker-HP to other computational platforms is discussed.

Hybrid Methods for Modeling Protein Structures Using Molecular Dynamics Simulations and Small-Angle X-Ray Scattering Data

Small-angle X-ray scattering (SAXS) is an efficient experimental tool to measure the overall shape of macromolecular structures in solution. However, due to the low resolution of SAXS data, high-resolution data obtained from X-ray crystallography or NMR and computational methods such as molecular dynamics (MD) simulations are complementary to SAXS data for understanding protein functions based on their structures at atomic resolution. Because MD simulations provide a physicochemically proper structural ensemble for flexible proteins in solution and a precise description of solvent effects, the hybrid analysis of SAXS and MD simulations is a promising method to estimate reasonable solution structures and structural ensembles in solution. Here, we review typical and useful in silico methods for modeling three dimensional protein structures, calculating theoretical SAXS profiles, and analyzing ensemble structures consistent with experimental SAXS profiles. We also review two examples of the hybrid analysis, termed MD-SAXS method in which MD simulations are carried out without any knowledge of experimental SAXS data, and the experimental SAXS data are used only to assess the consistency of the solution model from MD simulations with those observed in experiments. One example is an investigation of the intrinsic dynamics of EcoO109I using the computational method to obtain a theoretical profile from the trajectory of an MD simulation. The other example is a structural investigation of the vitamin D receptor ligand-binding domain using snapshots generated by MD simulations and assessment of the snapshots by experimental SAXS data.

Multiscale molecular dynamics simulations of rotary motor proteins

Protein functions require specific structures frequently coupled with conformational changes. The scale of the structural dynamics of proteins spans from the atomic to the molecular level. Theoretically, all-atom molecular dynamics (MD) simulation is a powerful tool to investigate protein dynamics because the MD simulation is capable of capturing conformational changes obeying the intrinsically structural features. However, to study long-timescale dynamics, efficient sampling techniques and coarse-grained (CG) approaches coupled with all-atom MD simulations, termed multiscale MD simulations, are required to overcome the timescale limitation in all-atom MD simulations. Here, we review two examples of rotary motor proteins examined using free energy landscape (FEL) analysis and CG-MD simulations. In the FEL analysis, FEL is calculated as a function of reaction coordinates, and the long-timescale dynamics corresponding to conformational changes is described as transitions on the FEL surface. Another approach is the utilization of the CG model, in which the CG parameters are tuned using the fluctuation matching methodology with all-atom MD simulations. The long-timespan dynamics is then elucidated straightforwardly by using CG-MD simulations.