Evaluating force field accuracy with long-time simulations of a β-hairpin tryptophan zipper peptide

We have combined graphics processing unit-accelerated all-atom molecular dynamics with parallel tempering to explore the folding properties of small peptides in implicit solvent on the time scale of microseconds. We applied this methodology to the synthetic β-hairpin, trpzip2, and one of its sequence variants, W2W9. Each simulation consisted of over 8 μs of aggregated virtual time. Several measures of folding behavior showed good convergence, allowing comparison with experimental equilibrium properties. Our simulations suggest that the intramolecular interactions of tryptophan side chains are responsible for much of the stability of the native fold. We conclude that the ff99 force field combined with ff96 φ and ψ dihedral energies and an implicit solvent can reproduce plausible folding behavior in both trpzip2 and W2W9.     

Comparison of Secondary Structure Formation Using 10 Different Force Fields in Microsecond Molecular Dynamics Simulations

We have compared molecular dynamics (MD) simulations of a β-hairpin forming peptide derived from the protein Nrf2 with 10 biomolecular force fields using trajectories of at least 1 μs. The total simulation time was 37.2 μs. Previous studies have shown that different force fields, water models, simulation methods, and parameters can affect simulation outcomes. The MD simulations were done in explicit solvent with a 16-mer Nrf2 β-hairpin forming peptide using Amber ff99SB-ILDN, Amber ff99SB*-ILDN, Amber ff99SB, Amber ff99SB*, Amber ff03, Amber ff03*, GROMOS96 43a1p, GROMOS96 53a6, CHARMM27, and OPLS-AA/L force fields. The effects of charge-groups, terminal capping, and phosphorylation on the peptide folding were also examined. Despite using identical starting structures and simulation parameters, we observed clear differences among the various force fields and even between replicates using the same force field. Our simulations show that the uncapped peptide folds into a native-like β-hairpin structure at 310 K when Amber ff99SB-ILDN, Amber ff99SB*-ILDN, Amber ff99SB, Amber ff99SB*, Amber ff03, Amber ff03*, GROMOS96 43a1p, or GROMOS96 53a6 were used. The CHARMM27 simulations were able to form native hairpins in some of the elevated temperature simulations, while the OPLS-AA/L simulations did not yield native hairpin structures at any temperatures tested. Simulations that used charge-groups or peptide capping groups were not largely different from their uncapped counterparts with single atom charge-groups. On the other hand, phosphorylation of the threonine residue located at the β-turn significantly affected the hairpin formation. To our knowledge, this is the first study comparing such a large set of force fields with respect to β-hairpin folding. Such a comprehensive comparison will offer useful guidance to others conducting similar types of simulations.     

Free energies of hydration from thermodynamic integration: Comparison of molecular mechanics force fields and evaluation of calculation accuracy

Four commonly used molecular mechanics force fields, CHARMM22, OPLS, CVFF, and GROMOS87, are compared for their ability to reproduce experimental free energies of hydration (ΔG_hydr) from molecular dynamics (MD) simulations for a set of small nonpolar and polar organic molecules: propane, cyclopropane, dimethylether, and acetone. ΔG_hydr values were calculated by multiconfiguration thermodynamic integration for each of the different force fields with three different sets of partial atomic charges: full charges from an electrostatic potential fit (ESP), and ESP charges scaled by 0.8 and 0.6. All force fields, except for GROMOS87, give reasonable results for ΔG_hydr · if partial atomic charges of appropriate magnitude are assigned. For GROMOS87, the agreement with experiment for hydrocarbons (propane and ethane) was improved considerably by modifying the repulsive part of the carbon-water oxygen Lennard-Jones potential. The small molecules studied are related to the chemical moieties constituting camphor (C₁₀H_l6O). By invoking force-field transferability, we calculated the ΔG_hydr for camphor. With the modified GROMOS force field, a ΔG_hydr within 4 kJ/mol of the experimental value of −14.8 kJ/mol was obtained. Camphor is one of the largest molecules for which an absolute hydration free energy has been calculated by molecular simulation. The accuracy and reliability of the thermodynamic integration calculations were analyzed in detail and we found that, for ΔG_hydr calculations for the set of small molecules in aqueous solution, molecular dynamics simulations of 0.8–1.0 ns in length give an upper statistical error bound of 1.5 kJ/mol, whereas shorter simulations of 0.25 nm in length given an upper statistical error bound of 3.5 kJ/mol. © 1997 by John Wiley & Sons, Inc.     

Parameterization of a reactive force field using a Monte Carlo algorithm

Parameterization of a molecular dynamics force field is essential in realistically modeling the physicochemical processes involved in a molecular system. This step is often challenging when the equations involved in describing the force field are complicated as well as when the parameters are mostly empirical. ReaxFF is one such reactive force field which uses hundreds of parameters to describe the interactions between atoms. The optimization of the parameters in ReaxFF is done such that the properties predicted by ReaxFF matches with a set of quantum chemical or experimental data. Usually, the optimization of the parameters is done by an inefficient single‐parameter parabolic‐search algorithm. In this study, we use a robust metropolis Monte‐Carlo algorithm with simulated annealing to search for the optimum parameters for the ReaxFF force field in a high‐dimensional parameter space. The optimization is done against a set of quantum chemical data for MgSO₄ hydrates. The optimized force field reproduced the chemical structures, the equations of state, and the water binding curves of MgSO₄ hydrates. The transferability test of the ReaxFF force field shows the extend of transferability for a particular molecular system. This study points out that the ReaxFF force field is not indefinitely transferable. © 2013 Wiley Periodicals, Inc.     

Are Protein Force Fields Getting Better? A Systematic Benchmark on 524 Diverse NMR Measurements

Recent hardware and software advances have enabled simulation studies of protein systems on biophysically-relevant timescales, often revealing the need for improved force fields. Although early force field development was limited by the lack of direct comparisons between simulation and experiment, recent work from several labs has demonstrated direct calculation of NMR observables from protein simulations. Here we quantitatively evaluate recent molecular dynamics force fields against a suite of 524 chemical shift and J coupling ((3)JH(N)H(α), (3)JH(N)C(β), (3)JH(α)C', (3)JH(N)C', and (3)JH(α)N) measurements on dipeptides, tripeptides, tetra-alanine, and ubiquitin. Of the force fields examined (ff96, ff99, ff03, ff03*, ff03w, ff99sb*, ff99sb-ildn, ff99sb-ildn-phi, ff99sb-ildn-nmr, CHARMM27, OPLS-AA), two force fields (ff99sb-ildn-phi, ff99sb-ildn-nmr) combining recent side chain and backbone torsion modifications achieve high accuracy in our benchmark. For the two optimal force fields, the calculation error is comparable to the uncertainty in the experimental comparison. This observation suggests that extracting additional force field improvements from NMR data may require increased accuracy in J coupling and chemical shift prediction. To further investigate the limitations of current force fields, we also consider conformational populations of dipeptides, which were recently estimated using vibrational spectroscopy.     

Peptide loop-closure kinetics from microsecond molecular dynamics simulations in explicit solvent

End-to-end contact formation rates of several peptides were recently measured by tryptophan triplet quenching (Lapidus et al. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 7220). Motivated by these experiments, we study loop-closure kinetics for two peptides of different lengths, Cys-(Ala-Gly-Gln)n-Trp (n = 1, 2), in multiple all-atom explicit-solvent molecular dynamics simulations with different initial conditions and force fields. In 150 simulations of approximately 20 ns each, we collect data covering 1.0 and 0.8 micros for the penta-peptide simulated with the AMBER and CHARMM force fields, respectively, and about 0.5 micros each with the two force fields for the octa-peptide. These extensive simulations allow us to analyze the dynamics of peptides in the unfolded state with atomic resolution, thus probing early events in protein folding, and to compare molecular dynamics simulations directly with experiment. The calculated lifetimes of the tryptophan triplet state are in the range of 50-100 ns, in agreement with experimental measurements. However, end-to-end contacts form more rapidly, with characteristic times less than 10 ns. The contact formation rates for the two force fields are similar despite differences in the respective ensembles of peptide conformations.     

Development of a polarizable force field for proteins via ab initio quantum chemistry: first generation model and gas phase tests

We present results of developing a methodology suitable for producing molecular mechanics force fields with explicit treatment of electrostatic polarization for proteins and other molecular system of biological interest. The technique allows simulation of realistic-size systems. Employing high-level ab initio data as a target for fitting allows us to avoid the problem of the lack of detailed experimental data. Using the fast and reliable quantum mechanical methods supplies robust fitting data for the resulting parameter sets. As a result, gas-phase many-body effects for dipeptides are captured within the average RMSD of 0.22 kcal/mol from their ab initio values, and conformational energies for the di- and tetrapeptides are reproduced within the average RMSD of 0.43 kcal/mol from their quantum mechanical counterparts. The latter is achieved in part because of application of a novel torsional fitting technique recently developed in our group, which has already been used to greatly improve accuracy of the peptide conformational equilibrium prediction with the OPLS-AA force field.1 Finally, we have employed the newly developed first-generation model in computing gas-phase conformations of real proteins, as well as in molecular dynamics studies of the systems. The results show that, although the overall accuracy is no better than what can be achieved with a fixed-charges model, the methodology produces robust results, permits reasonably low computational cost, and avoids other computational problems typical for polarizable force fields. It can be considered as a solid basis for building a more accurate and complete second-generation model.     

Exploring the parameter space of the coarse‐grained UNRES force field by random search: Selecting a transferable medium‐resolution force field

We explored the energy‐parameter space of our coarse‐grained UNRES force field for large‐scale ab initio simulations of protein folding, to obtain good initial approximations for hierarchical optimization of the force field with new virtual‐bond‐angle bending and side‐chain‐rotamer potentials which we recently introduced to replace the statistical potentials. 100 sets of energy‐term weights were generated randomly, and good sets were selected by carrying out replica‐exchange molecular dynamics simulations of two peptides with a minimal α‐helical and a minimal β‐hairpin fold, respectively: the tryptophan cage (PDB code: 1L2Y) and tryptophan zipper (PDB code: 1LE1). Eight sets of parameters produced native‐like structures of these two peptides. These eight sets were tested on two larger proteins: the engrailed homeodomain (PDB code: 1ENH) and FBP WW domain (PDB code: 1E0L); two sets were found to produce native‐like conformations of these proteins. These two sets were tested further on a larger set of nine proteins with α or α + β structure and found to locate native‐like structures of most of them. These results demonstrate that, in addition to finding reasonable initial starting points for optimization, an extensive search of parameter space is a powerful method to produce a transferable force field. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

The influence of electrostatic forces on the structure and dynamics of molecular ionic liquids

The vast majority of molecular dynamics simulations are based on nonpolarizable force fields with fixed partial charges for all atoms. The traditional way to obtain these charges are quantum-mechanical calculations performed prior to simulation. Unfortunately, the set of the partial charges heavily relies on the method and the basis set used. Therefore, investigations of the influence of charge variation on simulation data are necessary in order to validate various charge sets. This paper elucidates the consequences of different charge sets on the structure and dynamics of the ionic liquid: 1-ethyl-3-methyl-imidazolium dicyanoamide. The structural features seem to be more or less independent of the partial charge set pointing to a dominance of shape force as modeled by Lennard-Jones parameters. This can be seen in the radial distribution and orientational correlation functions. The role of electrostatic forces comes in when studying dynamical properties. Here, significant deviations between different charge sets can be observed. Overall, dynamics seems to be governed by viscosity. In fact, all dynamical parameters presented in this work can be converted from one charge set to another by viscosity scaling.     

How sensitive are nanosecond molecular dynamics simulations of proteins to changes in the force field?

The sensitivity of molecular dynamics simulations to variations in the force field has been examined in relation to a set of 36 structures corresponding to 31 proteins simulated by using different versions of the GROMOS force field. The three parameter sets used (43a1, 53a5, and 53a6) differ significantly in regard to the nonbonded parameters for polar functional groups and their ability to reproduce the correct solvation and partitioning behavior of small molecular analogues of the amino acid side chains. Despite the differences in the force field parameters no major differences could be detected in a wide range of structural properties such as the root-mean-square deviation from the experimental structure, radii of gyration, solvent accessible surface, secondary structure, or hydrogen bond propensities on a 5 to 10 ns time scale. The small differences that were observed correlated primarily with the presence of charged residues as opposed to residues that differed most between the parameter sets. The work highlights the variation that can be observed in nanosecond simulations of protein systems and implications of this for force field validation, as well as for the analysis of protein simulations in general.     

Molecular force field for ionic liquids III: imidazolium, pyridinium, and phosphonium cations; chloride, bromide, and dicyanamide anions

This is the third set of parameters of a force field for the molecular simulation of ionic liquids, developed within the spirit of the OPLS-AA model and thus oriented toward the calculation of equilibrium thermodynamic and structural properties. The parameter sets reported here concern the cations alkylimidazolium, tetra-alkylphosphonium, and N-alkylpyridinium, and the anions chloride, bromide, and dicyanamide. The force field is built in a stepwise manner that allows the construction of models for an entire family of cations, with alkyl side chains of different length, for example. Due to the transferability of the present force field, the ions studied here can be combined with those reported in our two previous publications to create a large variety of ionic liquids that can be studied by molecular simulation. The parameters reported were obtained through different series of ab initio calculations concerning the geometry, force constants, torsion energy profiles, and electrostatic charge distributions of the ions under study. Validation of the force field consisted of comparison with experimental crystal structure and liquid density data.     

Derivation of class II force fields: V. Quantum force field for amides,peptides, and related compounds

As the field of biomolecular structure advances, there is an ever-growing need for accurate modeling of molecular energy surfaces to simulate and predict the properties of these important systems. To address this need, a second generation amide force field for use in simulations of small organics as well as proteins and peptides has been derived. The critical question of what accuracy can be expected from calculations in general, and with this class II force field in particular, is addressed for structural, dynamic, and energetic properties. The force field is derived from a recent methodology we have developed that involves the systematic use of quantum mechanical observables. Systematic ab initio calculations were carried out for numerous configurations of 17 amide and related compounds. Relative energies and first and second derivatives of the energy of 638 structures of these compounds resulted in 140,970 ab initio quantum mechanical observables. The class II peptide quantum mechanical force field (QMFF), containing 732 force constants and reference values, was parameterized against these observables. A major objective of this work is to help establish the role of anharmonicity and coupling in improving the accuracy of molecular force fields, as these terms have not yet become an agreed upon standard in the ever more extensive simulations being used to probe biomolecular properties. This has been addressed by deriving a class I harmonic diagonal force field (HDFF), which was fit to the same energy surface as the QMFF, thus providing an opportunity to quantify the effects of these coupling and anharmonic contributions. Both force field representations are assessed in terms of their ability to fit the observables. They have also been tested by calculating the properties of 11 stationary states of these amide molecules. Optimized structures, vibrational frequencies, and conformational energies obtained from the quantum calculations and from both the QMFF and the HDFF are compared. Several strained and derivatized compounds including urea, formylformamide, and butyrolactam are included in these tests to assess the range of applicability (transferability) of the force fields. It was found that the class II coupled anharmonic force field reproduced the structures, energies, and vibrational frequencies significantly more faithfully than the class I harmonic diagonal force field. An important measure, rms energy deviation, was found to be 1.06 kcal/mol with the class II force field, and 2.30 kcal/mol with the harmonic diagonal force field. These deviations represent the error in relative configurational energy differences for strained and distorted structures calculated with the force fields compared with quantum mechanics. This provides a measure of the accuracy that might be expected in applications where strain may be important such as calculating the energy of a system as it approaches a (rotational) barrier, in ligand binding to a protein, or effects of introducing substituents into a molecule that may induce strain. Similar results were found for structural properties. Protein dynamics is becoming of ever-increasing interest, and, to simulate dynamic properties accurately, the dynamic behavior of model compounds needs to be well accounted for. To this end, the ability of the class I and class II force fields to reproduce the vibrational frequencies obtained from the quantum energy surface was assessed. An rms deviation of 43 cm⁻¹ was achieved with the coupled anharmonic force field, as compared to 105 cm⁻¹ with the harmonic diagonal force field. Thus, the analysis presented here of the class II force field for the amide functional group demonstrates that the incorporation of anharmonicity and coupling terms in the force field significantly improves the accuracy and transferability with regard to the simulation of structural, energetic, and dynamic properties of amides. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 430–458, 1998     

NMR solvent shifts of acetonitrile from frozen density embedding calculations

We present a density functional theory (DFT) study of solvent effects on nuclear magnetic shielding parameters. As a test example we have focused on the sensitive nitrogen shift of acetonitrile immersed in a selected set of solvents, namely water, chloroform, and cyclohexane. To include the effect of the solvent environment in an accurate and efficient manner, we employed the frozen-density embedding (FDE) scheme. We have included up to 500 solvent molecules in the NMR computations and obtained the cluster geometries from a large set of conformations generated with molecular dynamics. For small solute-solvent clusters comparison of the FDE results with conventional supermolecular DFT calculations shows close agreement. For the large solute-solvent clusters the solvent shift values are compared with experimental data and with values obtained using continuum solvent models. For the water --> cyclohexane shift the obtained value is in very good agreement with experiments. For the water --> chloroform NMR solvent shift the classical force field used in the molecular dynamics simulations is found to introduce an error. This error can be largely avoided by using geometries taken from Car-Parrinello molecular dynamics simulations.     

Comparing Dimerization Free Energies and Binding Modes of Small Aromatic Molecules with Different Force Fields

Dimerization free energies are fundamental quantities that describe the strength of interaction of different molecules. Obtaining accurate experimental values for small molecules and disentangling the conformations that contribute most to the binding can be extremely difficult, due to the size of the systems and the small energy differences. In many cases, one has to resort to computational methods to calculate such properties. In this work, we used molecular dynamics simulations in conjunction with metadynamics to calculate the free energy of dimerization of small aromatic rings, and compared three models from popular online servers for atomistic force fields, namely G54a7, CHARMM36 and OPLS. We show that, regardless of the force field, the profiles for the dimerization free energy of these compounds are very similar. However, significant care needs to be taken when studying larger molecules, since the deviations from the trends increase with the size of the molecules, resulting in force field dependent preferred stacking modes; for example, in the cases of pyrene and tetracene. Our results provide a useful background study for using topology builders to model systems which rely on stacking of aromatic moieties, and are relevant in areas ranging from drug design to supramolecular assembly.     

Force field evaluation for biomolecular simulation: free enthalpies of solvation of polar and apolar compounds in various solvents.

Recently, the GROMOS biomolecular force field parameter set 53A6--which has been parametrized to reproduce experimentally determined free enthalpies of hydration and solvation in cyclohexane of amino acid side-chain analogs--was presented. To investigate the transferability of the new parameter set, we calculated free enthalpies of solvation of a range of polar and apolar compounds in different solvents (methanol, dimethyl sulfoxide (DMSO), acetonitrile, and acetone) from molecular dynamics simulations using the GROMOS 53A6 force field. For methanol and DMSO, parameters were used that are available in the 53A6 parameter set. For acetonitrile, a recently developed model was taken and for acetone, two models available in literature were used. We found that trends in and values for the solvation free enthalpies are in satisfactory agreement with experiment, except for the solvation in acetone for which deviations from experiment can be explained in terms of the properties of the models used.     

乙醇醛的分子动态结构

以量子化学计算作为起点, 为最简单的糖类分子——乙醇醛开发了两套分子力学力场参数: 基于肽类的力场和基于醛类的力场. 分子动力学模拟结果表明, 所开发的类醛力场参数能够较好地描述乙醇醛分子在水中的结构以及水分子在其周围的分布. 通过瞬时简正模式分析, 得到了3N-6个模式的瞬时振动频率和振动跃迁偶极矩等振动光谱参数的统计分布及其相关性. 结合量子化学计算和分子动力学模拟对生物分子体系的多元振动光谱参数进行预测和评估, 为从化学键水平出发模拟宽带飞秒二维红外相关光谱提供了一个新方法.     

Practical considerations for building GROMOS-compatible small-molecule topologies

Molecular dynamics simulations are being applied to increasingly complex systems, including those involving small endogenous compounds and drug molecules. In order to obtain meaningful and accurate data from these simulations, high-quality topologies for small molecules must be generated in a manner that is consistent with the derivation of the force field applied to the system. Often, force fields are designed for use with macromolecules such as proteins, making their transferability to other species challenging. Investigators are increasingly attracted to automated topology generation programs, although the quality of the resulting topologies remains unknown. Here we assess the applicability of the popular PRODRG server that generates small-molecule topologies for use with the GROMOS family of force fields. We find that PRODRG does not reproduce topologies for even the most well-characterized species in the force field due to inconsistent charges and charge groups. We assessed the effects of PRODRG-derived charges on several systems: pure liquids, amino acids at a hydrophobic-hydrophilic interface, and an enzyme-cofactor complex. We found that partial atomic charges generated by PRODRG are largely incompatible with GROMOS force fields, and the behavior of these systems deviates substantially from that of simulations using GROMOS parameters. We conclude by proposing several points as "best practices" for parametrization of small molecules under the GROMOS force fields.     

Peptide free‐energy profile is strongly dependent on the force field: Comparison of C96 and AMBER95

The C96 and AMBER95 force fields were compared with small model peptides Ac‐(Ala)_n‐NMe (Ac = CH₃CO, NMe = NHCH₃, n=2 and 3) in vacuo and in TIP3P water by computing the free‐energy profiles using multicanonical molecular dynamics method. The C96 force field is a modified version of the AMBER95 force field, which was adjusted to reproduce the energy difference between extended β‐ and constrained α‐helical energies for the alanine tetrapeptide, obtained by the high level ab initio MO method. The slight modification resulted in a large difference in the free energy profiles. The C96 force field prefers relatively extended conformers, whereas the AMBER95 force field favors turn conformations. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 748–762, 2000