Molecular Dynamics Simulations Of Biomolecules Research Articles

Transferable Implicit Solvation via Contrastive Learning of Graph Neural Networks.

Implicit solvent models are essential for molecular dynamics simulations of biomolecules, striking a balance between computational efficiency and biological realism. Efforts are underway to develop accurate and transferable implicit solvent models and coarse-grained (CG) force fields in general, guided by a bottom-up approach that matches the CG energy function with the potential of mean force (PMF) defined by the finer system. However, practical challenges arise due to the lack of analytical expressions for the PMF and algorithmic limitations in parameterizing CG force fields. To address these challenges, a machine learning-based approach is proposed, utilizing graph neural networks (GNNs) to represent the solvation free energy and potential contrasting for parameter optimization. We demonstrate the effectiveness of the approach by deriving a transferable GNN implicit solvent model using 600,000 atomistic configurations of six proteins obtained from explicit solvent simulations. The GNN model provides solvation free energy estimations much more accurately than state-of-the-art implicit solvent models, reproducing configurational distributions of explicit solvent simulations. We also demonstrate the reasonable transferability of the GNN model outside of the training data. Our study offers valuable insights for deriving systematically improvable implicit solvent models and CG force fields from a bottom-up perspective.

Accurate Simulations of Lipid Monolayers Require a Water Model with Correct Surface Tension.

Lipid monolayers provide our lungs and eyes their functionality and serve as proxy systems in biomembrane research. Therefore, lipid monolayers have been studied intensively including using molecular dynamics simulations, which are able to probe their lateral structure and interactions with, e.g., pharmaceuticals or nanoparticles. However, such simulations have struggled in describing the forces at the air–water interface. Particularly, the surface tension of water and long-range van der Waals interactions have been considered critical, but their importance in monolayer simulations has been evaluated only separately. Here, we combine the recent C36/LJ-PME lipid force field that includes long-range van der Waals forces with water models that reproduce experimental surface tensions to elucidate the importance of these contributions in monolayer simulations. Our results suggest that a water model with correct surface tension is necessary to reproduce experimental surface pressure–area isotherms and monolayer phase behavior. The latter includes the liquid expanded and liquid condensed phases, their coexistence, and the opening of pores at the correct area per lipid upon expansion. Despite these improvements of the C36/LJ-PME with certain water models, the standard cutoff-based CHARMM36 lipid model with the 4-point OPC water model still provides the best agreement with experiments. Our results emphasize the importance of using high-quality water models in applications and parameter development in molecular dynamics simulations of biomolecules.

Efficient formulation of polarizable Gaussian multipole electrostatics for biomolecular simulations.

Molecular dynamics simulations of biomolecules have been widely adopted in biomedical studies. As classical point-charge models continue to be used in routine biomolecular applications, there have been growing demands on developing polarizable force fields for handling more complicated biomolecular processes. Here, we focus on a recently proposed polarizable Gaussian Multipole (pGM) model for biomolecular simulations. A key benefit of pGM is its screening of all short-range electrostatic interactions in a physically consistent manner, which is critical for stable charge-fitting and is needed to reproduce molecular anisotropy. Another advantage of pGM is that each atom's multipoles are represented by a single Gaussian function or its derivatives, allowing for more efficient electrostatics than other Gaussian-based models. In this study, we present an efficient formulation for the pGM model defined with respect to a local frame formed with a set of covalent basis vectors. The covalent basis vectors are chosen to be along each atom's covalent bonding directions. The new local frame can better accommodate the fact that permanent dipoles are primarily aligned along covalent bonds due to the differences in electronegativity of bonded atoms. It also allows molecular flexibility during molecular simulations and facilitates an efficient formulation of analytical electrostatic forces without explicit torque computation. Subsequent numerical tests show that analytical atomic forces agree excellently with numerical finite-difference forces for the tested system. Finally, the new pGM electrostatics algorithm is interfaced with the particle mesh Ewald (PME) implementation in Amber for molecular simulations under the periodic boundary conditions. To validate the overall pGM/PME electrostatics, we conducted an NVE simulation for a small water box of 512 water molecules. Our results show that to achieve energy conservation in the polarizable model, it is important to ensure enough accuracy on both PME and induction iteration. It is hoped that the reformulated pGM model will facilitate the development of future force fields based on the pGM electrostatics for applications in biomolecular systems and processes where polarization plays crucial roles.

Accurate Biomolecular Simulations Account for Electronic Polarization.

In this perspective, we discuss where and how accounting for electronic many-body polarization affects the accuracy of classical molecular dynamics simulations of biomolecules. While the effects of electronic polarization are highly pronounced for molecules with an opposite total charge, they are also non-negligible for interactions with overall neutral molecules. For instance, neglecting these effects in important biomolecules like amino acids and phospholipids affects the structure of proteins and membranes having a large impact on interpreting experimental data as well as building coarse grained models. With the combined advances in theory, algorithms and computational power it is currently realistic to perform simulations with explicit polarizable dipoles on systems with relevant sizes and complexity. Alternatively, the effects of electronic polarization can also be included at zero additional computational cost compared to standard fixed-charge force fields using the electronic continuum correction, as was recently demonstrated for several classes of biomolecules.

Computing the Free Energy without Collective Variables.

We introduce an approach for computing the free energy and the probability density in high-dimensional spaces, such as those explored in molecular dynamics simulations of biomolecules. The approach exploits the presence of correlations between the coordinates, induced, in molecular dynamics, by the chemical nature of the molecules. Due to these correlations, the data points lay on a manifold that can be highly curved and twisted, but whose dimension is normally small. We estimate the free energies by finding, with a statistical test, the largest neighborhood in which the free energy in the embedding manifold can be considered constant. Importantly, this procedure does not require defining explicitly the manifold and provides an estimate of the error that is approximately unbiased up to large dimensions. We test this approach on artificial and real data sets, demonstrating that the free energy estimates are reliable for data sets on manifolds of dimension up to ∼10, embedded in an arbitrarily large space. In practical applications our method permits the estimation of the free energy in a space of reduced dimensionality without specifying the collective variables defining this space.

細胞環境における生体分子ダイナミクスのシミュレーション

細胞環境における生体分子ダイナミクスのシミュレーション

Spotting the difference in molecular dynamics simulations of biomolecules

Comparing two trajectories from molecular simulations conducted under different conditions is not a trivial task. In this study, we apply a method called Linear Discriminant Analysis with ITERative procedure (LDA-ITER) to compare two molecular simulation results by finding the appropriate projection vectors. Because LDA-ITER attempts to determine a projection such that the projections of the two trajectories do not overlap, the comparison does not suffer from a strong anisotropy, which is an issue in protein dynamics. LDA-ITER is applied to two test cases: the T4 lysozyme protein simulation with or without a point mutation and the allosteric protein PDZ2 domain of hPTP1E with or without a ligand. The projection determined by the method agrees with the experimental data and previous simulations. The proposed procedure, which complements existing methods, is a versatile analytical method that is specialized to find the "difference" between two trajectories.

Early Experiences Porting the NAMD and VMD Molecular Simulation and Analysis Software to GPU-Accelerated OpenPOWER Platforms.

All-atom molecular dynamics simulations of biomolecules provide a powerful tool for exploring the structure and dynamics of large protein complexes within realistic cellular environments. Unfortunately, such simulations are extremely demanding in terms of their computational requirements, and they present many challenges in terms of preparation, simulation methodology, and analysis and visualization of results. We describe our early experiences porting the popular molecular dynamics simulation program NAMD and the simulation preparation, analysis, and visualization tool VMD to GPU-accelerated OpenPOWER hardware platforms. We report our experiences with compiler-provided autovectorization and compare with hand-coded vector intrinsics for the POWER8 CPU. We explore the performance benefits obtained from unique POWER8 architectural features such as 8-way SMT and its value for particular molecular modeling tasks. Finally, we evaluate the performance of several GPU-accelerated molecular modeling kernels and relate them to other hardware platforms.

Constraint methods that accelerate free-energy simulations of biomolecules.

Atomistic molecular dynamics simulations of biomolecules are critical for generating narratives about biological mechanisms. The power of atomistic simulations is that these are physics-based methods that satisfy Boltzmann's law, so they can be used to compute populations, dynamics, and mechanisms. But physical simulations are computationally intensive and do not scale well to the sizes of many important biomolecules. One way to speed up physical simulations is by coarse-graining the potential function. Another way is to harness structural knowledge, often by imposing spring-like restraints. But harnessing external knowledge in physical simulations is problematic because knowledge, data, or hunches have errors, noise, and combinatoric uncertainties. Here, we review recent principled methods for imposing restraints to speed up physics-based molecular simulations that promise to scale to larger biomolecules and motions.

Significance of Molecular Dynamics Simulations for Life Sciences

AbstractThis article illustrates by examples the limited acceptance by biologists of predictions made with molecular dynamics simulations of biomolecules. Its purpose is to increase the awareness of biologists of the contribution that simulations can make to our understanding of biomolecule function.

Coarse-grained molecular dynamics simulations of biomolecules

Coarse-grained molecular dynamics (CGMD) simulations are increasingly being used to analyze the behaviors of biological systems. When appropriately used, CGMD can simulate the behaviors of molecular systems several hundred times faster than elaborate all-atom molecular dynamics simulations with similar accuracy. CGMD parameters for lipids, proteins, nucleic acids, and some artificial substances such as carbon nanotubes have been suggested. Here we briefly discuss a method for CGMD system configuration and the types of analysis and perturbations that can be performed with CGMD simulations. We also describe specific examples to show how CGMD simulations have been applied to various situations, and then describe experimental results that were used to validate the simulation results. CGMD simulations are applicable to resolving problems for various biological systems.

Mixing coarse-grained and fine-grained water in molecular dynamics simulations of a single system

The use of a supra-molecular coarse-grained (CG) model for liquid water as solvent in molecular dynamics simulations of biomolecules represented at the fine-grained (FG) atomic level of modelling may reduce the computational effort by one or two orders of magnitude. However, even if the pure FG model and the pure CG model represent the properties of the particular substance of interest rather well, their application in a hybrid FG/CG system containing varying ratios of FG versus CG particles is highly non-trivial, because it requires an appropriate balance between FG-FG, FG-CG, and CG-CG energies, and FG and CG entropies. Here, the properties of liquid water are used to calibrate the FG-CG interactions for the simple-point-charge water model at the FG level and a recently proposed supra-molecular water model at the CG level that represents five water molecules by one CG bead containing two interaction sites. Only two parameters are needed to reproduce different thermodynamic and dielectric properties of liquid water at physiological temperature and pressure for various mole fractions of CG water in FG water. The parametrisation strategy for the FG-CG interactions is simple and can be easily transferred to interactions between atomistic biomolecules and CG water.

Optimizing Solute–Water van der Waals Interactions To Reproduce Solvation Free Energies

An accurate representation of solute-water interactions is necessary for molecular dynamics simulations of biomolecules that reside in aqueous environments. Modern force fields and advanced water models describe solute-solute and water-water interactions reasonably accurately but have known shortcomings in describing solute-water interactions, demonstrated by the large differences between calculated and experimental solvation free energies across a range of peptide and drug chemistries. In this work, we introduce a method for optimizing solute-water van der Waals interactions to reproduce experimental solvation free energy data and apply it to the optimization of a fixed charge force field (AMBER ff99SB/GAFF) and advanced water model (TIP4P-Ew). We show that, with these optimizations, the combination of AMBER ff99SB/GAFF and TIP4P-Ew is able to reproduce the solvation free energies of a variety of biologically relevant small molecules to within 1.0 k(B)T. We further validate these optimizations by examining the aggregation propensities of dipeptide-water solutions, the conformational preferences of short disordered peptides, and the native state stability and dynamics of a folded protein.

Theoretical Chemistry—Quo Vadis?

Theoretical concepts permeate chemistry more thoroughly than we often think. Chemists are intuitively familiar with different types of chemical bonding; with the structure, spectroscopy, and dynamics of molecules; and with the variety of different possible chemical reactions. They use theory-based concepts, for example from quantum mechanics or statistical mechanics, to describe and analyze chemical phenomena. The primary task of theoretical chemistry has always been to provide the conceptual and terminological framework that is necessary to understand chemistry.

Stereochemical errors and their implications for molecular dynamics simulations

BackgroundBiological molecules are often asymmetric with respect to stereochemistry, and correct stereochemistry is essential to their function. Molecular dynamics simulations of biomolecules have increasingly become an integral part of biophysical research. However, stereochemical errors in biomolecular structures can have a dramatic impact on the results of simulations.ResultsHere we illustrate the effects that chirality and peptide bond configuration flips may have on the secondary structure of proteins throughout a simulation. We also analyze the most common sources of stereochemical errors in biomolecular structures and present software tools to identify, correct, and prevent stereochemical errors in molecular dynamics simulations of biomolecules.ConclusionsUse of the tools presented here should become a standard step in the preparation of biomolecular simulations and in the generation of predicted structural models for proteins and nucleic acids.

Characterizing rare-event property distributions via replicate molecular dynamics simulations of proteins

As computational resources increase, molecular dynamics simulations of biomolecules are becoming an increasingly informative complement to experimental studies. In particular, it has now become feasible to use multiple initial molecular configurations to generate an ensemble of replicate production-run simulations that allows for more complete characterization of rare events such as ligand-receptor unbinding. However, there are currently no explicit guidelines for selecting an ensemble of initial configurations for replicate simulations. Here, we use clustering analysis and steered molecular dynamics simulations to demonstrate that the configurational changes accessible in molecular dynamics simulations of biomolecules do not necessarily correlate with observed rare-event properties. This informs selection of a representative set of initial configurations. We also employ statistical analysis to identify the minimum number of replicate simulations required to sufficiently sample a given biomolecular property distribution. Together, these results suggest a general procedure for generating an ensemble of replicate simulations that will maximize accurate characterization of rare-event property distributions in biomolecules.

Simulations of a Protein Crystal: Explicit Treatment of Crystallization Conditions Links Theory and Experiment in the Streptavidin−Biotin Complex

A 250 ns molecular dynamics simulation of the biotin-liganded streptavidin crystal lattice, including cryoprotectant molecules and crystallization salts, is compared to a 250 ns simulation of the lattice solvated with pure water. The simulation using detailed crystallization conditions preserves the initial X-ray structure better than the simulation using pure water, even though the protein molecules display comparable mobility in either simulation. Atomic fluctuations computed from the simulation with crystallization conditions closely reproduce fluctuations derived from experimental temperature factors (correlation coefficient of 0.88, omitting two N-terminal residues with very high experimental B-factors). In contrast, fluctuations calculated from the simulation with pure water were less accurate, particularly for two of the streptavidin loops exposed to solvent in the crystal lattice. Finally, we obtain good agreement between the water and cryoprotectant densities obtained from the simulated crystallization conditions and the electron density due to solvent molecules in the X-ray structure. Our results suggest that detailed lattice simulations with realistic crystallization conditions can be used to assess potential function parameters, validate simulation protocols, and obtain valuable insights that solution-phase simulations do not easily provide. We anticipate that this will prove to be a powerful strategy for molecular dynamics simulations of biomolecules.

Validation of Molecular Dynamics Simulations of Biomolecules Using NMR Spin Relaxation as Benchmarks: Application to the AMBER99SB Force Field.

Biological function of biomolecules is accompanied by a wide range of motional behavior. Accurate modeling of dynamics by molecular dynamics (MD) computer simulations is therefore a useful approach toward the understanding of biomolecular function. NMR spin relaxation measurements provide rigorous benchmarks for assessing important aspects of MD simulations, such as the amount and time scales of conformational space sampling, which are intimately related to the underlying molecular mechanics force field. Until recently, most simulations produced trajectories that exhibited too much dynamics particularly in flexible loop regions. Recent modifications made to the backbone φ and ψ torsion angle potentials of the AMBER and CHARMM force fields indicate that these changes produce more realistic molecular dynamics behavior. To assess the consequences of these changes, we performed a series of 5-20 ns molecular dynamics trajectories of human ubiquitin using the AMBER99 and AMBER99SB force fields for different conditions and water models and compare the results with NMR experimental backbone N-H S(2) order parameters. A quantitative analysis of the trajectories shows significantly improved agreement with experimental NMR data for the AMBER99SB force field as compared to AMBER99. Because NMR spin relaxation data (T1, T2, NOE) reflect the combined effects of spatial and temporal fluctuations of bond vectors, it is found that comparison of experimental and back-calculated NMR spin-relaxation data provides a more objective way of assessing the quality of the trajectory than order parameters alone. Analysis of a key mobile β-hairpin in ubiquitin demonstrates that the dynamics of mobile sites are not only reduced by the modified force field, but the extent of motional correlations between amino acids is also markedly diminished.

Error and timing analysis of multiple time-step integration methods for molecular dynamics

Molecular dynamics simulations of biomolecules performed using multiple time-step integration methods are hampered by resonance instabilities. We analyze the properties of a simple 1D linear system integrated with the symplectic reference system propagator MTS (r-RESPA) technique following earlier work by others. A closed form expression for the time step dependent Hamiltonian which corresponds to r-RESPA integration of the model is derived. This permits us to present an analytic formula for the dependence of the integration accuracy on short-range force cutoff range. A detailed analysis of the force decomposition for the standard Ewald summation method is then given as the Ewald method is a good candidate to achieve high scaling on modern massively parallel machines. We test the new analysis on a realistic system, a protein in water. Under Langevin dynamics with a weak friction coefficient ( ζ = 1 ps −1 ) to maintain temperature control and using the SHAKE algorithm to freeze out high frequency vibrations, we show that the 5 fs resonance barrier present when all degrees of freedom are unconstrained is postponed to ≈ 12 fs . An iso-error boundary with respect to the short-range cutoff range and multiple time step size agrees well with the analytical results which are valid due to dominance of the high frequency modes in determining integrator accuracy. Using r-RESPA to treat the long range interactions results in a 6× increase in efficiency for the decomposition described in the text.

Quality Assurance for Biomolecular Simulations.

Contemporary structural biology has an increased emphasis on high-throughput methods. Biomolecular simulations can add value to structural biology via the provision of dynamic information. However, at present there are no agreed measures for the quality of biomolecular simulation data. In this Letter, we suggest suitable measures for the quality assurance of molecular dynamics simulations of biomolecules. These measures are designed to be simple, fast, and general. Reporting of these measures in simulation papers should become an expected practice, analogous to the reporting of comparable quality measures in protein crystallography. We wish to solicit views and suggestions from the simulation community on methods to obtain reliability measures from molecular-dynamics trajectories. In a database which provides access to previously obtained simulations [Formula: see text] for example BioSimGrid ( http://www.biosimgrid.org/ ) [Formula: see text] the user needs to be confident that the simulation trajectory is suitable for further investigation. This can be provided by the simulation quality measures which a user would examine prior to more extensive analyses.