Extensive all-atom Monte Carlo sampling and QM/MM corrections in the SAMPL4 hydration free energy challenge

We present our predictions for the SAMPL4 hydration free energy challenge. Extensive all-atom Monte Carlo simulations were employed to sample the compounds in explicit solvent. While the focus of our study was to demonstrate well-converged and reproducible free energies, we attempted to address the deficiencies in the general Amber force field force field with a simple QM/MM correction. We show that by using multiple independent simulations, including different starting configurations, and enhanced sampling with parallel tempering, we can obtain well converged hydration free energies. Additional analysis using dihedral angle distributions, torsion-root mean square deviation plots and thermodynamic cycles support this assertion. We obtain a mean absolute deviation of 1.7 kcal mol^?1 and a Kendall’s τ of 0.65 compared with experiment.     

In silico prediction of drug solubility: 4. Will simple potentials suffice?

In view of the extreme importance of reliable computational prediction of aqueous drug solubility, we have established a Monte Carlo simulation procedure which appears, in principle, to yield reliable solubilities even for complex drug molecules. A theory based on judicious application of linear response and mean field approximations has been found to reproduce the computationally demanding free energy determinations by simulation while at the same time offering mechanistic insight. The focus here is on the suitability of the model of both drug and solvent, i.e., the force fields. The optimized potentials for liquid simulations all atom (OPLS‐AA) force field, either intact or combined with partial charges determined either by semiempirical AM1/CM1A calculations or taken from the condensed‐phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field has been used. The results illustrate the crucial role of the force field in determining drug solubilities. The errors in interaction energies obtained by the simple force fields tested here are still found to be too large for our purpose but if a component of this error is systematic and readily removed by empirical adjustment the results are significantly improved. In fact, consistent use of the OPLS‐AA Lennard‐Jones force field parameters with partial charges from the COMPASS force field will in this way produce good predictions of amorphous drug solubility within 1 day on a standard desktop PC. This is shown here by the results of extensive new simulations for a total of 47 drug molecules which were also improved by increasing the water box in the hydration simulations from 500 to 2000 water molecules. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

Predicting hydrophobic solvation by molecular simulation: 1. Testing united‐atom alkane models

We present a systematic test of the performance of three popular united‐atom force fields—OPLS‐UA, GROMOS and TraPPE—at predicting hydrophobic solvation, more precisely at describing the solvation of alkanes in alkanes. Gibbs free energies of solvation were calculated for 52 solute/solvent pairs from Molecular Dynamics simulations and thermodynamic integration making use of the IBERCIVIS volunteer computing platform. Our results show that all force fields yield good predictions when both solute and solvent are small linear or branched alkanes (up to pentane). However, as the size of the alkanes increases, all models tend to increasingly deviate from experimental data in a systematic fashion. Furthermore, our results confirm that specific interaction parameters for cyclic alkanes in the united‐atom representation are required to account for the additional excluded volume within the ring. Overall, the TraPPE model performs best for all alkanes, but systematically underpredicts the magnitude of solvation free energies by about 6% (RMSD of 1.2 kJ/mol). Conversely, both GROMOS and OPLS‐UA systematically overpredict solvation free energies (by ∼13% and 15%, respectively). The systematic trends suggest that all models can be improved by a slight adjustment of their Lennard‐Jones parameters. © 2016 Wiley Periodicals, Inc.     

Implicit solvent models: Combining an analytical formulation of continuum electrostatics with simple models of the hydrophobic effect

The recent development of approximate analytical formulations of continuum electrostatics opens the possibility of efficient and accurate implicit solvent models for biomolecular simulations. One such formulation (ACE, Schaefer & Karplus, J. Phys. Chem., 1996, 100:1578) is used to compute the electrostatic contribution to solvation and conformational free energies of a set of small solutes and three proteins. Results are compared to finite-difference solutions of the Poisson equation (FDPB) and explicit solvent simulations and experimental data where available. Small molecule solvation free energies agree with FDPB within 1–1.5 kcal/mol, which is comparable to differences in FDPB due to different surface treatments or different force field parameterizations. Side chain conformation free energies of aspartate and asparagine are in qualitative agreement with explicit solvent simulations, while 74 conformations of a surface loop in the protein Ras are accurately ranked compared to FDPB. Preliminary results for solvation free energies of small alkane and polar solutes suggest that a recent Gaussian model could be used in combination with analytical continuum electrostatics to treat nonpolar interactions. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 322–335, 1999     

A new set of atomic radii for accurate estimation of solvation free energy by Poisson–Boltzmann solvent model

The Poisson–Boltzmann implicit solvent (PB) is widely used to estimate the solvation free energies of biomolecules in molecular simulations. An optimized set of atomic radii (PB radii) is an important parameter for PB calculations, which determines the distribution of dielectric constants around the solute. We here present new PB radii for the AMBER protein force field to accurately reproduce the solvation free energies obtained from explicit solvent simulations. The presented PB radii were optimized using results from explicit solvent simulations of the large systems. In addition, we discriminated PB radii for N‐ and C‐terminal residues from those for nonterminal residues. The performances using our PB radii showed high accuracy for the estimation of solvation free energies at the level of the molecular fragment. The obtained PB radii are effective for the detailed analysis of the solvation effects of biomolecules. © 2014 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Testing the semi-explicit assembly model of aqueous solvation in the SAMPL4 challenge

Here, we test a method, called semi-explicit assembly (SEA), that computes the solvation free energies of molecules in water in the SAMPL4 blind test challenge. SEA was developed with the intention of being as accurate as explicit-solvent models, but much faster to compute. It is accurate because it uses pre-simulations of simple spheres in explicit solvent to obtain structural and thermodynamic quantities, and it is fast because it parses solute free energies into regionally additive quantities. SAMPL4 provided us the opportunity to make new tests of SEA. Our tests here lead us to the following conclusions: (1) The newest version, called Field-SEA, which gives improved predictions for highly charged ions, is shown here to perform as well as the earlier versions (dipolar and quadrupolar SEA) on this broad blind SAMPL4 test set. (2) We find that both the past and present SEA models give solvation free energies that are as accurate as TIP3P. (3) Using a new approach for force field parameter optimization, we developed improved hydroxyl parameters that ensure consistency with neat-solvent dielectric constants, and found that they led to improved solvation free energies for hydroxyl-containing compounds in SAMPL4. We also learned that these hydroxyl parameters are not just fixing solvent exposed oxygens in a general sense, and therefore do not improve predictions for carbonyl or carboxylic-acid groups. Other such functional groups will need their own independent optimizations for potential improvements. Overall, these tests in SAMPL4 indicate that SEA is an accurate, general and fast new approach to computing solvation free energies.     

Effects of all-atom force fields on amyloid oligomerization: replica exchange molecular dynamics simulations of the Aβ(16-22) dimer and trimer

The aim of this work is to investigate the effects of molecular mechanics force fields on amyloid peptide assembly. To this end, we performed extensive replica exchange molecular dynamics (REMD) simulations on the monomer, dimer and trimer of the seven-residue fragment of the Alzheimer's amyloid-β peptide, Aβ(16-22), using the AMBER99, GROMOS96 and OPLS force fields. We compared the force fields by analysing the resulting global and local structures as well as the free energy landscapes at 300 K. We show that AMBER99 strongly favors helical structures for the monomer and does not predict any β-sheet structure for the dimer and trimer. In contrast, the dimer and trimer modeled by GROMOS96 form antiparallel β-sheet structures, while OPLS predicts diverse structures. Overall, the free energy landscapes obtained by three force fields are very different, and we also note a weak structural dependence of our results on temperature. The implications of this computational study on amyloid oligomerization, fibril growth and inhibition are also discussed.     

Developing multisite empirical force field models for Pt(II) and cisplatin

We have developed empirical force field parameters for Pt(II) and cisplatin. Two force field frameworks were used—modified OPLS‐AA and our second‐order polarizable POSSIM. A seven‐site model was used for the Pt(II) ion. The goal was to create transferable parameter sets compatible with the force field models for proteins and general organic compounds. A number of properties of the Pt(II) ion and its coordination compounds have been considered, including geometries and energies of the complexes, hydration free energy, and radial distribution functions in water. Comparison has been made with experimental and quantum mechanical results. We have demonstrated that both versions are generally capable of reproducing key properties of the system, but the second‐order polarizable POSSIM formalism permits more accurate quantitative results to be obtained. For example, the energy of formation of cisplatin as calculated with the modified OPLS‐AA exhibited an error of 9.9%, while the POSSIM error for the same quantity was 6.2%. The produced parameter sets are transferable and suitable to be used in protein‐metal binding simulations in which position or even coordination of the ion does not have to be constrained using preexisting knowledge. © 2016 Wiley Periodicals, Inc.     

Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model alpha-helical systems

The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper, was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala(10) polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala(10) polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain-side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time.     

Adapting the semi-explicit assembly solvation model for estimating water-cyclohexane partitioning with the SAMPL5 molecules

We describe here some tests we made in the SAMPL5 communal event of ‘Semi-Explicit Assembly’ (SEA), a recent method for computing solvation free energies. We combined the prospective tests of SAMPL5 with followup retrospective calculations, to improve two technical aspects of the field variant of SEA. First, SEA uses an approximate analytical surface around the solute on which a water potential is computed. We have improved and simplified the mathematical model of that surface. Second, some of the solutes in SAMPL5 were large enough to need a way to treat solvating waters interacting with ‘buried atoms’, i.e. interior atoms of the solute. We improved SEA with a buried-atom correction. We also compare SEA to Thermodynamic Integration molecular dynamics simulations, so that we can sort out force field errors.     

Evaluation of DNA Force Fields in Implicit Solvation

DNA structural deformations and dynamics are crucial to its interactions in the cell. Theoretical simulations are essential tools to explore the structure, dynamics, and thermodynamics of biomolecules in a systematic way. Molecular mechanics force fields for DNA have benefited from constant improvements during the last decades. Several studies have evaluated and compared available force fields when the solvent is modeled by explicit molecules. On the other hand, few systematic studies have assessed the quality of duplex DNA models when implicit solvation is employed. The interest of an implicit modeling of the solvent consists in the important gain in the simulation performance and conformational sampling speed. In this study, respective influences of the force field and the implicit solvation model choice on DNA simulation quality are evaluated. To this end, extensive implicit solvent duplex DNA simulations are performed, attempting to reach both conformational and sequence diversity convergence. Structural parameters are extracted from simulations and statistically compared to available experimental and explicit solvation simulation data. Our results quantitatively expose the respective strengths and weaknesses of the different DNA force fields and implicit solvation models studied. This work can lead to the suggestion of improvements to current DNA theoretical models.     

Parameterization of the Hamiltonian Dielectric Solvent (HADES) Reaction‐Field Method for the Solvation Free Energies of Amino Acid Side‐Chain Analogs

Optimization of the Hamiltonian dielectric solvent (HADES) method for biomolecular simulations in a dielectric continuum is presented with the goal of calculating accurate absolute solvation free energies while retaining the model’s accuracy in predicting conformational free‐energy differences. The solvation free energies of neutral and polar amino acid side‐chain analogs calculated by using HADES, which may optionally include nonpolar contributions, were optimized against experimental data to reach a chemical accuracy of about 0.5 kcal mol^?1. The new parameters were evaluated for charged side‐chain analogs. The HADES results were compared with explicit‐solvent, generalized Born, Poisson–Boltzmann, and QM‐based methods. The potentials of mean force (PMFs) between pairs of side‐chain analogs obtained by using HADES and explicit‐solvent simulations were used to evaluate the effects of the improved parameters optimized for solvation free energies on intermolecular potentials.     

Benchmarking implicit solvent folding simulations of the amyloid beta(10-35) fragment

A pathogenetic feature of Alzhemier disease is the aggregation of monomeric beta-amyloid proteins (Abeta) to form oligomers. Usually these oligomers of long peptides aggregate on time scales of microseconds or longer, making computational studies using atomistic molecular dynamics models prohibitively expensive and making it essential to develop computational models that are cheaper and at the same time faithful to physical features of the process. We benchmark the ability of our implicit solvent model to describe equilibrium and dynamic properties of monomeric Abeta(10-35) using all-atom Langevin dynamics (LD) simulations, since Alphabeta(10-35) is the only fragment whose monomeric properties have been measured. The accuracy of the implicit solvent model is tested by comparing its predictions with experiment and with those from a new explicit water MD simulation, (performed using CHARMM and the TIP3P water model) which is approximately 200 times slower than the implicit water simulations. The dependence on force field is investigated by running multiple trajectories for Alphabeta(10-35) using the CHARMM, OPLS-aal, and GS-AMBER94 force fields, whereas the convergence to equilibrium is tested for each force field by beginning separate trajectories from the native NMR structure, a completely stretched structure, and from unfolded initial structures. The NMR order parameter, S2, is computed for each trajectory and is compared with experimental data to assess the best choice for treating aggregates of Alphabeta. The computed order parameters vary significantly with force field. Explicit and implicit solvent simulations using the CHARMM force fields display excellent agreement with each other and once again support the accuracy of the implicit solvent model. Alphabeta(10-35) exhibits great flexibility, consistent with experiment data for the monomer in solution, while maintaining a general strand-loop-strand motif with a solvent-exposed hydrophobic patch that is believed to be important for aggregation. Finally, equilibration of the peptide structure requires an implicit solvent LD simulation as long as 30 ns.     

A generalized Born formalism for heterogeneous dielectric environments: application to the implicit modeling of biological membranes

Reliable computer simulations of complex biological environments such as integral membrane proteins with explicit water and lipid molecules remain a challenging task. We propose a modification of the standard generalized Born theory of homogeneous solvent for modeling the heterogeneous dielectric environments such as lipid/water interfaces. Our model allows the representation of biological membranes in the form of multiple layered dielectric regions with dielectric constants that are different from the solute cavity. The proposed new formalism is shown to predict the electrostatic component of solvation free energy with a relative error of 0.17% compared to exact finite-difference solutions of the Poisson equation for a transmembrane helix test system. Molecular dynamics simulations of melittin and bacteriorhodopsin are carried out and performed over 10 ns and 7 ns of simulation time, respectively. The center of melittin along the membrane normal in these stable simulations is in excellent agreement with the relevant experimental data. Simulations of bacteriorhodopsin started from the experimental structure remained stable and in close agreement with experiment. We also examined the free energy profiles of water and amino acid side chain analogs upon membrane insertion. The results with our implicit membrane model agree well with the experimental transfer free energy data from cyclohexane to water as well as explicit solvent simulations of water and selected side chain analogs.     

Predicting hydration free energies using all-atom molecular dynamics simulations and multiple starting conformations

Molecular dynamics simulations in explicit solvent were applied to predict the hydration free energies for 23 small organic molecules in blind SAMPL2 test. We found good agreement with experimental results, with an RMS error of 2.82 kcal/mol over the whole set and 1.86 kcal/mol over all the molecules except several hydroxyl-rich compounds where we find evidence for a systematic error in the force field. We tested two different solvent models, TIP3P and TIP4P-Ew, and obtained very similar hydration free energies for these two models; the RMS difference was 0.64 kcal/mol. We found that preferred conformation of the carboxylic acids in water differs from that in vacuum. Surprisingly, this conformational change is not adequately sampled on simulation timescales, so we apply an umbrella sampling technique to include free energies associated with the conformational change. Overall, the results of this test reveal that the force field parameters for some groups of molecules (such as hydroxyl-rich compounds) still need to be improved, but for most compounds, accuracy was consistent with that seen in our previous tests.     

Comparison of two simulation methods to compute solvation free energies and partition coefficients

The thermodynamic integration (TI) and expanded ensemble (EE) methods are used here to calculate the hydration free energy in water, the solvation free energy in 1‐octanol, and the octanol‐water partition coefficient for a six compounds of varying functionality using the optimized potentials for liquid simulations (OPLS) all‐atom (AA) force field parameters and atomic charges. Both methods use the molecular dynamics algorithm as a primary component of the simulation protocol, and both have found wide applications in fields such as the calculation of activity coefficients, phase behavior, and partition coefficients. Both methods result in solvation free energies and 1‐octanol/water partition coefficients with average absolute deviations (AAD) from experimental data to within 4 kJ/mol and 0.5 log units, respectively. Here, we find that in simulations the OPLS‐AA force field parameters (with fixed charges) can reproduce solvation free energies of solutes in 1‐octanol with AAD of about half that for the solute hydration free energies using a extended simple point charge (SPC/E) model of water. The computational efficiency of the two simulation methods are compared based on the time (in nanoseconds) required to obtain similar standard deviations in the solvation free energies and 1‐octanol/water partition coefficients. By this analysis, the EE method is found to be a factor of nine more efficient than the TI algorithm. For both methods, solvation free energy calculations in 1‐octanol consume roughly an order of magnitude more CPU hours than the hydration free energy calculations. © 2012 Wiley Periodicals, Inc.     

Combining the polarizable Drude force field with a continuum electrostatic Poisson–Boltzmann implicit solvation model

In this work, we have combined the polarizable force field based on the classical Drude oscillator with a continuum Poisson–Boltzmann/solvent‐accessible surface area (PB/SASA) model. In practice, the positions of the Drude particles experiencing the solvent reaction field arising from the fixed charges and induced polarization of the solute must be optimized in a self‐consistent manner. Here, we parameterized the model to reproduce experimental solvation free energies of a set of small molecules. The model reproduces well‐experimental solvation free energies of 70 molecules, yielding a root mean square difference of 0.8 kcal/mol versus 2.5 kcal/mol for the CHARMM36 additive force field. The polarization work associated with the solute transfer from the gas‐phase to the polar solvent, a term neglected in the framework of additive force fields, was found to make a large contribution to the total solvation free energy, comparable to the polar solute–solvent solvation contribution. The Drude PB/SASA also reproduces well the electronic polarization from the explicit solvent simulations of a small protein, BPTI. Model validation was based on comparisons with the experimental relative binding free energies of 371 single alanine mutations. With the Drude PB/SASA model the root mean square deviation between the predicted and experimental relative binding free energies is 3.35 kcal/mol, lower than 5.11 kcal/mol computed with the CHARMM36 additive force field. Overall, the results indicate that the main limitation of the Drude PB/SASA model is the inability of the SASA term to accurately capture non‐polar solvation effects. © 2018 Wiley Periodicals, Inc.     

Absolute Protein Binding Free Energy Simulations for Ligands with Multiple Poses,a Thermodynamic Path That Avoids Exhaustive Enumeration of the Poses

We propose a free energy calculation method for receptor–ligand binding, which have multiple binding poses that avoids exhaustive enumeration of the poses. For systems with multiple binding poses, the standard procedure is to enumerate orientations of the binding poses, restrain the ligand to each orientation, and then, calculate the binding free energies for each binding pose. In this study, we modify a part of the thermodynamic cycle in order to sample a broader conformational space of the ligand in the binding site. This modification leads to more accurate free energy calculation without performing separate free energy simulations for each binding pose. We applied our modification to simple model host–guest systems as a test, which have only two binding poses, by using a single decoupling method (SDM) in implicit solvent. The results showed that the binding free energies obtained from our method without knowing the two binding poses were in good agreement with the benchmark results obtained by explicit enumeration of the binding poses. Our method is applicable to other alchemical binding free energy calculation methods such as the double decoupling method (DDM) in explicit solvent. We performed a calculation for a protein–ligand system with explicit solvent using our modified thermodynamic path. The results of the free energy simulation along our modified path were in good agreement with the results of conventional DDM, which requires a separate binding free energy calculation for each of the binding poses of the example of phenol binding to T4 lysozyme in explicit solvent. © 2019 Wiley Periodicals, Inc.     

Molecular dynamics simulations of structure and dynamics of organic molecular crystals

A set of model compounds covering a range of polarity and flexibility have been simulated using GAFF, CHARMM22, OPLS and MM3 force fields to examine how well classical molecular dynamics simulations can reproduce structural and dynamic aspects of organic molecular crystals. Molecular structure, crystal structure and thermal motion, including molecular reorientations and internal rotations, found from the simulations have been compared between force fields and with experimental data. The MM3 force field does not perform well in condensed phase simulations, while GAFF, CHARMM and OPLS perform very similarly. Generally molecular and crystal structure are reproduced well, with a few exceptions. The atomic displacement parameters (ADPs) are mostly underestimated in the simulations with a relative error of up to 70%. Examples of molecular reorientation and internal rotation, observed in the simulations, include in-plane reorientations of benzene, methyl rotations in alanine, decane, isopropylcyclohexane, pyramidal inversion of nitrogen in amino group and rotation of the whole group around the C-N bond. Frequencies of such dynamic processes were calculated, as well as thermodynamic properties for reorientations in benzene and alanine. We conclude that MD simulations can be used for qualitative analysis, while quantitative results should be taken with caution. It is important to compare the outcomes from simulations with as many experimental quantities as available before using them to study or quantify crystal properties not available from experiment.