OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials.

Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models can be added to a simulation and used to compute forces and energy. A higher-level interface allows users to easily model their molecules of interest with general purpose, pretrained potential functions. A collection of optimized CUDA kernels and custom PyTorch operations greatly improves the speed of simulations. We demonstrate these features in simulations of cyclin-dependent kinase 8 (CDK8) and the green fluorescent protein chromophore in water. Taken together, these features make it practical to use machine learning to improve the accuracy of simulations with only a modest increase in cost.

OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials.

Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models can be added to a simulation and used to compute forces and energy. A higher-level interface allows users to easily model their molecules of interest with general purpose, pretrained potential functions. A collection of optimized CUDA kernels and custom PyTorch operations greatly improves the speed of simulations. We demonstrate these features on simulations of cyclin-dependent kinase 8 (CDK8) and the green fluorescent protein (GFP) chromophore in water. Taken together, these features make it practical to use machine learning to improve the accuracy of simulations at only a modest increase in cost.

AmberTools.

AmberTools is a free and open-source collection of programs used to set up, run, and analyze molecular simulations. The newer features contained within AmberTools23 are briefly described in this Application note.

Improved chemistry restraints for crystallographic refinement by integrating the Amber force field into Phenix.

The refinement of biomolecular crystallographic models relies on geometric restraints to help to address the paucity of experimental data typical in these experiments. Limitations in these restraints can degrade the quality of the resulting atomic models. Here, an integration of the full all-atom Amber molecular-dynamics force field into Phenix crystallographic refinement is presented, which enables more complete modeling of biomolecular chemistry. The advantages of the force field include a carefully derived set of torsion-angle potentials, an extensive and flexible set of atom types, Lennard-Jones treatment of nonbonded interactions and a full treatment of crystalline electrostatics. The new combined method was tested against conventional geometry restraints for over 22 000 protein structures. Structures refined with the new method show substantially improved model quality. On average, Ramachandran and rotamer scores are somewhat better, clashscores and MolProbity scores are significantly improved, and the modeling of electrostatics leads to structures that exhibit more, and more correct, hydrogen bonds than those refined using traditional geometry restraints. In general it is found that model improvements are greatest at lower resolutions, prompting plans to add the Amber target function to real-space refinement for use in electron cryo-microscopy. This work opens the door to the future development of more advanced applications such as Amber-based ensemble refinement, quantum-mechanical representation of active sites and improved geometric restraints for simulated annealing.

A Coupled Ionization-Conformational Equilibrium Is Required To Understand the Properties of Ionizable Residues in the Hydrophobic Interior of Staphylococcal Nuclease.

Ionizable residues in the interior of proteins play essential roles, especially in biological energy transduction, but are relatively rare and seem incompatible with the complex and polar environment. We perform a comprehensive study of the internal ionizable residues on 21 variants of staphylococcal nuclease with internal Lys, Glu, or Asp residues. Using pH replica exchange molecular dynamics simulations, we find that, in most cases, the pKa values of these internal ionizable residues are shifted significantly from their values in solution. Our calculated results are in excellent agreement with the experimental observations of the Garcia-Moreno group. We show that the interpretation of the experimental pKa values requires the study of not only protonation changes but also conformational changes. The coupling between the protonation and conformational equilibria suggests a mechanism for efficient pH-sensing and regulation in proteins. This study provides new physical insights into how internal ionizable residues behave in the hydrophobic interior of proteins.

Improved Accuracy for Constant pH-REMD Simulations through Modification of Carboxylate Effective Radii.

The accuracy of computational models for simulating biomolecules under specific solution pH conditions is critical for properly representing the effect of pH in biological processes. Constant pH (CpH) simulations involving implicit solvent using the AMBER software often incorrectly estimate pKa values of aspartate and glutamate residues due to large effective radii stemming from the presence of dummy protons. These inaccuracies stem from problems in the sampled ensembles of titratable residues that can influence other observable pH-dependent behavior, such as conformational change. We investigate new radii assignments for atoms in titratable residues with carboxylate groups to mitigate the systematic overestimation in the current method. We find that decreased carboxylate radii correspond with increased agreement with experimentally derived pKa values for residues in hen egg-white lysozyme and Δ+PHS variants of staphylococcal nuclease (SNase) and improved conformation state sampling compared to experimentally described expectations of native-like structure. Our CpH simulations suggest that decreasing the effective radii of these carboxylate groups is essential for eliminating a significant source of systematic error that hurts the accuracy of both conformational and protonation state sampling with implicit solvent.

OpenMM 7: Rapid development of high performance algorithms for molecular dynamics.

OpenMM is a molecular dynamics simulation toolkit with a unique focus on extensibility. It allows users to easily add new features, including forces with novel functional forms, new integration algorithms, and new simulation protocols. Those features automatically work on all supported hardware types (including both CPUs and GPUs) and perform well on all of them. In many cases they require minimal coding, just a mathematical description of the desired function. They also require no modification to OpenMM itself and can be distributed independently of OpenMM. This makes it an ideal tool for researchers developing new simulation methods, and also allows those new methods to be immediately available to the larger community.

Lessons learned from comparing molecular dynamics engines on the SAMPL5 dataset.

We describe our efforts to prepare common starting structures and models for the SAMPL5 blind prediction challenge. We generated the starting input files and single configuration potential energies for the host-guest in the SAMPL5 blind prediction challenge for the GROMACS, AMBER, LAMMPS, DESMOND and CHARMM molecular simulation programs. All conversions were fully automated from the originally prepared AMBER input files using a combination of the ParmEd and InterMol conversion programs. We find that the energy calculations for all molecular dynamics engines for this molecular set agree to better than 0.1 % relative absolute energy for all energy components, and in most cases an order of magnitude better, when reasonable choices are made for different cutoff parameters. However, there are some surprising sources of statistically significant differences. Most importantly, different choices of Coulomb's constant between programs are one of the largest sources of discrepancies in energies. We discuss the measures required to get good agreement in the energies for equivalent starting configurations between the simulation programs, and the energy differences that occur when simulations are run with program-specific default simulation parameter values. Finally, we discuss what was required to automate this conversion and comparison.

Advanced Potential Energy Surfaces for Molecular Simulation.

Advanced potential energy surfaces are defined as theoretical models that explicitly include many-body effects that transcend the standard fixed-charge, pairwise-additive paradigm typically used in molecular simulation. However, several factors relating to their software implementation have precluded their widespread use in condensed-phase simulations: the computational cost of the theoretical models, a paucity of approximate models and algorithmic improvements that can ameliorate their cost, underdeveloped interfaces and limited dissemination in computational code bases that are widely used in the computational chemistry community, and software implementations that have not kept pace with modern high-performance computing (HPC) architectures, such as multicore CPUs and modern graphics processing units (GPUs). In this Feature Article we review recent progress made in these areas, including well-defined polarization approximations and new multipole electrostatic formulations, novel methods for solving the mutual polarization equations and increasing the MD time step, combining linear-scaling electronic structure methods with new QM/MM methods that account for mutual polarization between the two regions, and the greatly improved software deployment of these models and methods onto GPU and CPU hardware platforms. We have now approached an era where multipole-based polarizable force fields can be routinely used to obtain computational results comparable to state-of-the-art density functional theory while reaching sampling statistics that are acceptable when compared to that obtained from simpler fixed partial charge force fields.

CHARMM-GUI Input Generator for NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM Simulations Using the CHARMM36 Additive Force Field.

Proper treatment of nonbonded interactions is essential for the accuracy of molecular dynamics (MD) simulations, especially in studies of lipid bilayers. The use of the CHARMM36 force field (C36 FF) in different MD simulation programs can result in disagreements with published simulations performed with CHARMM due to differences in the protocols used to treat the long-range and 1-4 nonbonded interactions. In this study, we systematically test the use of the C36 lipid FF in NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM. A wide range of Lennard-Jones (LJ) cutoff schemes and integrator algorithms were tested to find the optimal simulation protocol to best match bilayer properties of six lipids with varying acyl chain saturation and head groups. MD simulations of a 1,2-dipalmitoyl-sn-phosphatidylcholine (DPPC) bilayer were used to obtain the optimal protocol for each program. MD simulations with all programs were found to reasonably match the DPPC bilayer properties (surface area per lipid, chain order parameters, and area compressibility modulus) obtained using the standard protocol used in CHARMM as well as from experiments. The optimal simulation protocol was then applied to the other five lipid simulations and resulted in excellent agreement between results from most simulation programs as well as with experimental data. AMBER compared least favorably with the expected membrane properties, which appears to be due to its use of the hard-truncation in the LJ potential versus a force-based switching function used to smooth the LJ potential as it approaches the cutoff distance. The optimal simulation protocol for each program has been implemented in CHARMM-GUI. This protocol is expected to be applicable to the remainder of the additive C36 FF including the proteins, nucleic acids, carbohydrates, and small molecules.

MDTraj: A Modern Open Library for the Analysis of Molecular Dynamics Trajectories.

As molecular dynamics (MD) simulations continue to evolve into powerful computational tools for studying complex biomolecular systems, the necessity of flexible and easy-to-use software tools for the analysis of these simulations is growing. We have developed MDTraj, a modern, lightweight, and fast software package for analyzing MD simulations. MDTraj reads and writes trajectory data in a wide variety of commonly used formats. It provides a large number of trajectory analysis capabilities including minimal root-mean-square-deviation calculations, secondary structure assignment, and the extraction of common order parameters. The package has a strong focus on interoperability with the wider scientific Python ecosystem, bridging the gap between MD data and the rapidly growing collection of industry-standard statistical analysis and visualization tools in Python. MDTraj is a powerful and user-friendly software package that simplifies the analysis of MD data and connects these datasets with the modern interactive data science software ecosystem in Python.

AFNMR: automated fragmentation quantum mechanical calculation of NMR chemical shifts for biomolecules.

We evaluate the performance of the automated fragmentation quantum mechanics/molecular mechanics approach (AF-QM/MM) on the calculation of protein and nucleic acid NMR chemical shifts. The AF-QM/MM approach models solvent effects implicitly through a set of surface charges computed using the Poisson-Boltzmann equation, and it can also be combined with an explicit solvent model through the placement of water molecules in the first solvation shell around the solute; the latter substantially improves the accuracy of chemical shift prediction of protons involved in hydrogen bonding with solvent. We also compare the performance of AF-QM/MM on proteins and nucleic acids with two leading empirical chemical shift prediction programs SHIFTS and SHIFTX2. Although the empirical programs outperform AF-QM/MM in predicting chemical shifts, the differences are in some cases small, and the latter can be applied to chemical shifts on biomolecules which are outside the training set employed by the empirical programs, such as structures containing ligands, metal centers, and non-standard residues. The AF-QM/MM described here is implemented in version 5 of the SHIFTS software, and is fully automated, so that only a structure in PDB format is required as input.

Interpretation of pH-activity profiles for acid-base catalysis from molecular simulations.

The measurement of reaction rate as a function of pH provides essential information about mechanism. These rates are sensitive to the pK(a) values of amino acids directly involved in catalysis that are often shifted by the enzyme active site environment. Experimentally observed pH-rate profiles are usually interpreted using simple kinetic models that allow estimation of "apparent pK(a)" values of presumed general acid and base catalysts. One of the underlying assumptions in these models is that the protonation states are uncorrelated. In this work, we introduce the use of constant pH molecular dynamics simulations in explicit solvent (CpHMD) with replica exchange in the pH-dimension (pH-REMD) as a tool to aid in the interpretation of pH-activity data of enzymes and to test the validity of different kinetic models. We apply the methods to RNase A, a prototype acid-base catalyst, to predict the macroscopic and microscopic pK(a) values, as well as the shape of the pH-rate profile. Results for apo and cCMP-bound RNase A agree well with available experimental data and suggest that deprotonation of the general acid and protonation of the general base are not strongly coupled in transphosphorylation and hydrolysis steps. Stronger coupling, however, is predicted for the Lys41 and His119 protonation states in apo RNase A, leading to the requirement for a microscopic kinetic model. This type of analysis may be important for other catalytic systems where the active forms of the implicated general acid and base are oppositely charged and more highly correlated. These results suggest a new way for CpHMD/pH-REMD simulations to bridge the gap with experiments to provide a molecular-level interpretation of pH-activity data in studies of enzyme mechanisms.

Constant pH Replica Exchange Molecular Dynamics in Explicit Solvent Using Discrete Protonation States: Implementation, Testing, and Validation.

By utilizing Graphics Processing Units, we show that constant pH molecular dynamics simulations (CpHMD) run in Generalized Born (GB) implicit solvent for long time scales can yield poor pKa predictions as a result of sampling unrealistic conformations. To address this shortcoming, we present a method for performing constant pH molecular dynamics simulations (CpHMD) in explicit solvent using a discrete protonation state model. The method involves standard molecular dynamics (MD) being propagated in explicit solvent followed by protonation state changes being attempted in GB implicit solvent at fixed intervals. Replica exchange along the pH-dimension (pH-REMD) helps to obtain acceptable titration behavior with the proposed method. We analyzed the effects of various parameters and settings on the titration behavior of CpHMD and pH-REMD in explicit solvent, including the size of the simulation unit cell and the length of the relaxation dynamics following protonation state changes. We tested the method with the amino acid model compounds, a small pentapeptide with two titratable sites, and hen egg white lysozyme (HEWL). The proposed method yields superior predicted pKa values for HEWL over hundreds of nanoseconds of simulation relative to corresponding predicted values from simulations run in implicit solvent.

Multidimensional Replica Exchange Molecular Dynamics Yields a Converged Ensemble of an RNA Tetranucleotide.

A necessary step to properly assess and validate the performance of force fields for biomolecules is to exhaustively sample the accessible conformational space, which is challenging for large RNA structures. Given questions regarding the reliability of modeling RNA structure and dynamics with current methods, we have begun to use RNA tetranucleotides to evaluate force fields. These systems, though small, display considerable conformational variability and complete sampling with standard simulation methods remains challenging. Here we compare and discuss the performance of known variations of replica exchange molecular dynamics (REMD) methods, specifically temperature REMD (T-REMD), Hamiltonian REMD (H-REMD), and multidimensional REMD (M-REMD) methods, which have been implemented in Amber's accelerated GPU code. Using two independent simulations, we show that M-REMD not only makes very efficient use of emerging large-scale GPU clusters, like Blue Waters at the University of Illinois, but also is critically important in generating the converged ensemble more efficiently than either T-REMD or H-REMD. With 57.6 µs aggregate sampling of a conformational ensemble with M-REMD methods, the populations can be compared to NMR data to evaluate force field reliability and further understand how putative changes to the force field may alter populations to be in more consistent agreement with experiment.

SPAM: A Simple Approach for Profiling Bound Water Molecules.

A method that identifies the hydration shell structure of proteins and estimates the relative free energies of water molecules within that hydration shell is described. The method, which we call "SPAM" (maps spelled in reverse), utilizes explicit solvent molecular dynamics (MD) simulations to capture discrete hydration sites at the water-protein interface and computes a local free energy measure from the distribution of interaction energies between water and the environment at a specific site. SPAM is able to provide a qualitative estimate of the thermodynamic profile of bound water molecules that correlates nicely with well-studied structure-activity relationships and observed binding "hot spots". This is demonstrated in retrospective analyses of HIV1 protease and hen egg white lysozyme, where the effects of water displacement and solvent binding have been studied extensively. The simplicity and effectiveness of SPAM allow for prospective application during the drug discovery process.

Enhancing Conformation and Protonation State Sampling of Hen Egg White Lysozyme Using pH Replica Exchange Molecular Dynamics.

We evaluate the efficiency of the pH replica exchange molecular dynamics (pH-REMD) method proposed by Itoh et al. (Proteins2011, 79, 3420-3436) by using it to predict the pKa values of the titratable residues in hen egg white lysozyme (HEWL). pKa values predicted using pH-REMD converge significantly faster than those calculated using constant pH molecular dynamics (CpHMD). Furthermore, increasing the frequency between exchange attempts in pH-REMD simulations improves protonation and conformational state sampling. By enabling the simulation to sample both conformational and protonation states more rapidly, pH-REMD simulations provide valuable insight into the pH-dependence of HEWL that the CpHMD simulations failed to capture. We present an efficient and highly scalable implementation of pH-REMD as an attractive enhancement to traditional CpHMD methods.

MMPBSA.py: An Efficient Program for End-State Free Energy Calculations.

MM-PBSA is a post-processing end-state method to calculate free energies of molecules in solution. MMPBSA.py is a program written in Python for streamlining end-state free energy calculations using ensembles derived from molecular dynamics (MD) or Monte Carlo (MC) simulations. Several implicit solvation models are available with MMPBSA.py, including the Poisson-Boltzmann Model, the Generalized Born Model, and the Reference Interaction Site Model. Vibrational frequencies may be calculated using normal mode or quasi-harmonic analysis to approximate the solute entropy. Specific interactions can also be dissected using free energy decomposition or alanine scanning. A parallel implementation significantly speeds up the calculation by dividing frames evenly across available processors. MMPBSA.py is an efficient, user-friendly program with the flexibility to accommodate the needs of users performing end-state free energy calculations. The source code can be downloaded at http://ambermd.org/ with AmberTools, released under the GNU General Public License.

pH-dependent mechanism of nitric oxide release in nitrophorins 2 and 4.

Nitrophorins are NO carrier proteins that transport and release NO through a pH-dependent conformational change. They bind NO tightly in a low pH environment and release it in a higher pH environment. Experimental evidence shows that the increase in the NO dissociation equilibrium constant, K(d), is due mainly to an increase in the NO release rate. Structural and kinetic data strongly suggest that NPs control NO escape by modulating its migration from the active site to the solvent through a pH-dependent conformational change. NP2 and NP4 are two representative proteins of the family displaying a 39% overall sequence identity, and interestingly, NP2 releases NO slower than NP4. The proposal that NPs' NO release relies mainly on the NO escape rate makes NPs a very peculiar case among typical heme proteins. The connection between the pH-dependent conformational change and ligand release mechanism is not fully understood and the structural basis for the pH induced structural transition and the different NO release patterns in NPs are unresolved, yet interesting issues. In this work, we have used state of the art molecular dynamics simulations to study the NO escape process in NP2 and NP4 in both the low and high pH states. Our results show that both NPs modulate NO release by switching between a "closed" conformation in a low pH environment and an "open" conformation at higher pH. In both proteins, the change is caused by the differential protonation of a common residue Asp30 in NP4 and Asp29 in NP2, and the NO escape route is conserved. Finally, our results show that, in NP2, the conformational change to the "open" conformation is smaller than that for NP4 which results in a higher barrier for NO release.