Simulating GTP:Mg and GDP:Mg with a simple force field: A structural and thermodynamic analysis

Di‐ and tri‐phosphate nucleotides are essential cofactors for many proteins, usually in an Mg²⁺‐bound form. Proteins like GTPases often detect the difference between NDP and NTP and respond by changing conformations. To study such complexes, simple, fixed charge force fields have been used, which allow long simulations and precise free energy calculations. The preference for NTP or NDP binding depends on many factors, including ligand structure and Mg²⁺ coordination and the changes they undergo upon binding. Here, we use a simple force field to examine two Mg²⁺ coordination modes for the unbound GDP and GTP: direct, or “Inner Sphere” (IS) coordination by one or more phosphate oxygens and indirect, “Outer Sphere” (OS) coordination involving one or more bridging waters. We compare GTP: and GDP:Mg binding with OS and IS coordination; combining the results with experimental data then indicates that GTP prefers the latter. We also examine different kinds of IS coordination and their sensitivity to a key force field parameter: the optimal Mg:oxygen van der Waals distance R_min. Increasing R_min improves the Mg:oxygen distances, the GTP: and GDP:Mg binding affinities, and the fraction of GTP:Mg with β + γ phosphate coordination, but does not improve or change the GTP/GDP affinity difference, which remains much larger than experiment. It has no effect on the free energy of GDP binding to a GTPase. © 2012 Wiley Periodicals, Inc.     

CHARMM fluctuating charge force field for proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model

A fluctuating charge (FQ) force field is applied to molecular dynamics simulations for six small proteins in explicit polarizable solvent represented by the TIP4P-FQ potential. The proteins include 1FSV, 1ENH, 1PGB, 1VII, 1H8K, and 1CRN, representing both helical and beta-sheet secondary structural elements. Constant pressure and temperature (NPT) molecular dynamics simulations are performed on time scales of several nanoseconds, the longest simulations yet reported using explicitly polarizable all-atom empirical potentials (for both solvent and protein) in the condensed phase. In terms of structure, the FQ force field allows deviations from native structure up to 2.5 A (with a range of 1.0 to 2.5 A). This is commensurate to the performance of the CHARMM22 nonpolarizable model and other currently existing polarizable models. Importantly, secondary structural elements maintain native structure in general to within 1 A (both helix and beta-strands), again in good agreement with the nonpolarizable case. In qualitative agreement with QM/MM ab initio dynamics on crambin (Liu et al. Proteins 2001, 44, 484), there is a sequence dependence of average condensed phase atomic charge for all proteins, a dependence one would anticipate considering the differing chemical environments around individual atoms; this is a subtle quantum mechanical feature captured in the FQ model but absent in current state-of-the-art nonpolarizable models. Furthermore, there is a mutual polarization of solvent and protein in the condensed phase. Solvent dipole moment distributions within the first and second solvation shells around the protein display a shift towards higher dipole moments (increases on the order of 0.2-0.3 Debye) relative to the bulk; protein polarization is manifested via the enhanced condensed phase charges of typical polar atoms such as backbone carbonyl oxygens, amide nitrogens, and amide hydrogens. Finally, to enlarge the sample set of proteins, gas-phase minimizations and 1 ps constant temperature simulations are performed on various-sized proteins to compare to earlier work by Kaminsky et al. (J Comp Chem 2002, 23, 1515). The present work establishes the feasibility of applying a fully polarizable force field for protein simulations and demonstrates the approach employed in extending the CHARMM force field to include these effects.     

A comparison of methods to compute the potential of mean force.

Most processes occurring in a system are determined by the relative free energy between two or more states because the free energy is a measure of the probability of finding the system in a given state. When the two states of interest are connected by a pathway, usually called reaction coordinate, along which the free-energy profile is determined, this profile or potential of mean force (PMF) will also yield the relative free energy of the two states. Twelve different methods to compute a PMF are reviewed and compared, with regard to their precision, for a system consisting of a pair of methane molecules in aqueous solution. We analyze all combinations of the type of sampling (unbiased, umbrella-biased or constraint-biased), how to compute free energies (from density of states or force averaging) and the type of coordinate system (internal or Cartesian) used for the PMF degree of freedom. The method of choice is constraint-bias simulation combined with force averaging for either an internal or a Cartesian PMF degree of freedom.     

FFParam: Standalone package for CHARMM additive and Drude polarizable force field parametrization of small molecules

Accurate force-field (FF) parameters are key to reliable prediction of properties obtained from molecular modeling (MM) and molecular dynamics (MD) simulations. With ever-widening applicability of MD simulations, robust parameters need to be generated for a wider range of chemical species. The CHARMM General Force Field program (CGenFF, https://cgenff.umaryland.edu/ ) is a tool for obtaining initial parameters for a given small molecule based on analogy with the available CGenFF parameters. However, improvement of these parameters is often required and performing their optimization remains tedious and time consuming. In addition, tools for optimization of small molecule parameters in the context of the Drude polarizable FF are not yet available. To overcome these issues, the FFParam package has been designed to facilitate the parametrization process. The package includes a graphical user interface (GUI) created using Qt libraries. FFParam supports Gaussian and Psi4 for performing quantum mechanical calculations and CHARMM and OpenMM for MM calculations. A Monte Carlo simulated annealing (MCSA) algorithm has been implemented for automated fitting of partial atomic charge, atomic polarizabilities and Thole scale parameters. The LSFITPAR program is called for automated fitting of bonded parameters. Accordingly, FFParam provides all the features required for generation and analysis of CHARMM and Drude FF parameters for small molecules. FFParam-GUI includes a text editor, graph plotter, molecular visualization, and text to table converter to meet various requirements of the parametrization process. It is anticipated that FFParam will facilitate wider use of CGenFF as well as promote future use of the Drude polarizable FF.     

Evaluation of solvation free energies for small molecules with the AMOEBA polarizable force field

The effects of electronic polarization in biomolecular interactions will differ depending on the local dielectric constant of the environment, such as in solvent, DNA, proteins, and membranes. Here the performance of the AMOEBA polarizable force field is evaluated under nonaqueous conditions by calculating the solvation free energies of small molecules in four common organic solvents. Results are compared with experimental data and equivalent simulations performed with the GAFF pairwise‐additive force field. Although AMOEBA results give mean errors close to “chemical accuracy,” GAFF performs surprisingly well, with statistically significantly more accurate results than AMOEBA in some solvents. However, for both models, free energies calculated in chloroform show worst agreement to experiment and individual solutes are consistently poor performers, suggesting non‐potential‐specific errors also contribute to inaccuracy. Scope for the improvement of both potentials remains limited by the lack of high quality experimental data across multiple solvents, particularly those of high dielectric constant. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Assessment of performance of the general purpose polarizable force field QMPFF3 in condensed phase

The recently introduced force field (FF) QMPFF3 is thoroughly validated in gas, liquid, and solid phases. For the first time, it is demonstrated that a physically well-grounded general purpose FF fitted exclusively to a comprehensive set of high level vacuum quantum mechanical data applied as it is to simulation of condensed phase provides high transferability for a wide range of chemical compounds. QMPFF3 demonstrates accuracy comparable with that of the FFs explicitly fitted to condensed phase data, but due to high transferability it is expected to be successful in simulating large molecular complexes.     

Columnar Aggregates of Azobenzene Stars: Exploring Intermolecular Interactions,Structure, and Stability in Atomistic Simulations

We present a simulation study of supramolecular aggregates formed by three-arm azobenzene (Azo) stars with a benzene-1,3,5-tricarboxamide (BTA) core in water. Previous experimental works by other research groups demonstrate that such Azo stars assemble into needle-like structures with light-responsive properties. Disregarding the response to light, we intend to characterize the equilibrium state of this system on the molecular scale. In particular, we aim to develop a thorough understanding of the binding mechanism between the molecules and analyze the structural properties of columnar stacks of Azo stars. Our study employs fully atomistic molecular dynamics (MD) simulations to model pre-assembled aggregates with various sizes and arrangements in water. In our detailed approach, we decompose the binding energies of the aggregates into the contributions due to the different types of non-covalent interactions and the contributions of the functional groups in the Azo stars. Initially, we investigate the origin and strength of the non-covalent interactions within a stacked dimer. Based on these findings, three arrangements of longer columnar stacks are prepared and equilibrated. We confirm that the binding energies of the stacks are mainly composed of π–π interactions between the conjugated parts of the molecules and hydrogen bonds formed between the stacked BTA cores. Our study quantifies the strength of these interactions and shows that the π–π interactions, especially between the Azo moieties, dominate the binding energies. We clarify that hydrogen bonds, which are predominant in BTA stacks, have only secondary energetic contributions in stacks of Azo stars but remain necessary stabilizers. Both types of interactions, π–π stacking and H-bonds, are required to maintain the columnar arrangement of the aggregates.     

CHARMM fluctuating charge force field for proteins: I parameterization and application to bulk organic liquid simulations

A first-generation fluctuating charge (FQ) force field to be ultimately applied for protein simulations is presented. The electrostatic model parameters, the atomic hardnesses, and electronegativities, are parameterized by fitting to DFT-based charge responses of small molecules perturbed by a dipolar probe mimicking a water dipole. The nonbonded parameters for atoms based on the CHARMM atom-typing scheme are determined via simultaneously optimizing vacuum water-solute geometries and energies (for a set of small organic molecules) and condensed phase properties (densities and vaporization enthalpies) for pure bulk liquids. Vacuum solute-water geometries, specifically hydrogen bond distances, are fit to 0.19 A r.m.s. error, while dimerization energies are fit to 0.98 kcal/mol r.m.s. error. Properties of the liquids studied include bulk liquid structure and polarization. The FQ model does indeed show a condensed phase effect in the shifting of molecular dipole moments to higher values relative to the gas phase. The FQ liquids also appear to be more strongly associated, in the case of hydrogen bonding liquids, due to the enhanced dipolar interactions as evidenced by shifts toward lower energies in pair energy distributions. We present results from a short simulation of NMA in bulk TIP4P-FQ water as a step towards simulating solvated peptide/protein systems. As expected, there is a nontrivial dipole moment enhancement of the NMA (although the quantitative accuracy is difficult to assess). Furthermore, the distribution of dipole moments of water molecules in the vicinity of the solutes is shifted towards larger values by 0.1-0.2 Debye in keeping with previously reported work.     

Multipole electrostatics in hydration free energy calculations

Hydration free energy (HFE) is generally used for evaluating molecular solubility, which is an important property for pharmaceutical and chemical engineering processes. Accurately predicting HFE is also recognized as one fundamental capability of molecular mechanics force field. Here, we present a systematic investigation on HFE calculations with AMOEBA polarizable force field at various parameterization and simulation conditions. The HFEs of seven small organic molecules have been obtained alchemically using the Bennett Acceptance Ratio method. We have compared two approaches to derive the atomic multipoles from quantum mechanical calculations: one directly from the new distributed multipole analysis and the other involving fitting to the electrostatic potential around the molecules. Wave functions solved at the MP2 level with four basis sets (6-311G*, 6-311++G(2d,2p), cc-pVTZ, and aug-cc-pVTZ) are used to derive the atomic multipoles. HFEs from all four basis sets show a reasonable agreement with experimental data (root mean square error 0.63 kcal/mol for aug-cc-pVTZ). We conclude that aug-cc-pVTZ gives the best performance when used with AMOEBA, and 6-311++G(2d,2p) is comparable but more efficient for larger systems. The results suggest that the inclusion of diffuse basis functions is important for capturing intermolecular interactions. The effect of long-range correction to van der Waals interaction on the hydration free energies is about 0.1 kcal/mol when the cutoff is 12?, and increases linearly with the number of atoms in the solute/ligand. In addition, we also discussed the results from a hybrid approach that combines polarizable solute with fixed-charge water in the HFE calculation.     

Two Different Models to Predict Ionic‐Liquid Diffraction Patterns: Fixed‐Charge versus Polarizable Potentials

This study reports the performance of classical molecular dynamics (MD) in predicting the X‐ray diffraction patterns of butylammonium nitrate (BAN) and two derivatives, 4‐hydroxybutan‐1‐ammonium nitrate (4‐HOBAN) and 4‐methoxybutan‐1‐ammonium nitrate (4‐MeOBAN). The structure functions and radial distribution functions obtained from energy‐dispersive X‐ray diffraction spectra, recorded newly for BAN and for the first time for 4‐MeOBAN and 4‐HOBAN, are compared with the corresponding quantities calculated from MD trajectories, to access information on the morphology of these liquids. The different behavior of two force fields, a polarizable multipole force field and a fixed‐charge one supplemented by an explicit three‐body term, is shown. The three‐body force field proves to be superior in reproducing the intermediate q range, for which the polarizable force field gives the wrong peak position and intensities. In addition, both models can correctly account for the presence or absence of a low q peak in the scattering patterns.     

Importance of explicit smeared lone‐pairs in anisotropic polarizable molecular mechanics. Torture track angular tests for exchange‐repulsion and charge transfer contributions

A correct representation of the short‐range contributions such as exchange‐repulsion (E _rep) and charge‐transfer (E _ct) is essential for the soundness of separable, anisotropic polarizable molecular mechanics potentials. Within the context of the SIBFA procedure, this is aimed at by explicit representations of lone pairs in their expressions. It is necessary to account for their anisotropic behaviors upon performing not only in‐plane, but also out‐of‐plane, variations of a probe molecule or cation interacting with a target molecule or molecular fragment. Thus, E _rep and E _ct have to reproduce satisfactorily the corresponding anisotropies of their quantum chemical (QC) counterparts. A significant improvement of the out‐of‐plane dependencies was enabled when the sp² and sp localized lone‐pairs are, even though to a limited extent, delocalized on both sides of the plane, above and below the atom bearer but at the closely similar angles as the in‐plane lone pair. We report calibration and validation tests on a series of monoligated complexes of a probe Zn(II) cation with several biochemically relevant ligands. Validations are then performed on several polyligated Zn(II) complexes found in the recognition sites of Zn‐metalloproteins. Such calibrations and validations are extended to representative monoligated and polyligated complexes of Mg(II) and Ca(II). It is emphasized that the calibration of all three cations was for each ΔE contribution done on a small training set bearing on a limited number of representative N , O , and S monoligated complexes. Owing to the separable nature of ΔE , a secure transferability is enabled to a diversity of polyligated complexes. For these the relative errors with respect to the target ΔE (QC) values are generally < 3%. Overall, the article proposes a full set of benchmarks that could be useful for force field developers. © 2017 Wiley Periodicals, Inc.     

Atomistic insight into chondroitin‐6‐sulfate glycosaminoglycan chain through quantum mechanics calculations and molecular dynamics simulation

Chondroitin‐6‐sulfate (C6S) is a glycosaminoglycan (GAG) constituent in the extracellular matrix, which participates actively in crucial biological processes, as well as in various pathological conditions, such as atherosclerosis and cancer. Molecular interactions involving the C6S chain are therefore of considerable interest. A computational model for atomistic simulation was built. This work describes the design and validation of a force field for a C6S dodecasaccharide chain. The results of an extensive molecular dynamics simulation performed with the new force field provide a novel insight into the structure and dynamics of the C6S chain. The intramolecular H‐bonds in the disaccharide linkage region are suggested to play a major role in determining the chain structural dynamics. Moreover, the unravelling of an additional H‐bond involving the sulfate groups in C6S is interesting as changes in sulfation have been claimed to be an important factor in several diseases. The force field will prove useful for future studies of crucial interactions between C6S and various nanoassemblies. It can also be used as a basis for modeling of other GAGs. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

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.     

The tetracycline: Mg2+ complex: a molecular mechanics force field

Tetracycline (Tc) is an important antibiotic, which binds specifically to the ribosome and several proteins, in the form of a Tc-:Mg2+ complex. To model Tc:protein and Tc:RNA interactions, we have developed a molecular mechanics force field model of Tc, which is consistent with the CHARMM force field for proteins and nucleic acids. We used structures from the Cambridge Crystallographic Data Base to identify the main Tc conformations that are likely to be present in solution and in biomolecular complexes. A conformational search was also done, using the MM3 force field to perform simulated annealing of Tc. Several resulting, low-energy structures were optimized with an ab initio model and used in developing the new Tc force field. Atomic charges and Lennard-Jones parameters were derived from a supermolecule ab initio approach. We considered the ab initio energies and geometries of a probe water molecule interacting with Tc at 36 different positions. We considered both a neutral and a zwitterionic Tc form, with and without bound Mg2+. The final rms deviation between the ab initio and force field energies, averaged over all forms, was just 0.35 kcal/mol. The model also reproduces the ab initio geometry and flexibility of Tc. As further tests, we did simulations of a Tc crystal, of Tc:Mg2+ and Tc:Ca2+ complexes in aqueous solution, and of a solvated complex between Tc:Mg2+ and the Tet repressor protein (TetR). With slight, ad hoc adjustments, the model can reproduce the experimental, relative, Tc binding affinities of Mg2+ and Ca2+. It performs well for the structure and fluctuations of the Tc:Mg2+:TetR complex. The model should therefore be suitable to investigate the interactions of Tc with proteins and RNA. It provides a starting point to parameterize other compounds in the large Tc family.     

On the Relative Merits of Equilibrium and Non‐Equilibrium Simulations for the Estimation of Free‐Energy Differences

The possibility of estimating equilibrium free‐energy profiles from multiple non‐equilibrium simulations using the fluctuation–dissipation theory or the relation proposed by Jarzynski has attracted much attention. Although the Jarzynski estimator has poor convergence properties for simulations far from equilibrium, corrections have been derived for cases in which the work is Gaussian distributed. Here, we examine the utility of corrections proposed by Gore and collaborators using a simple dissipative system as a test case. The system consists of a single methane‐like particle in explicit water. The Jarzynski equality is used to estimate the change in free energy associated with pulling the methane particle a distance of 3.9 nm at rates ranging from ～0.1 to 100 m s^?1. It is shown that although the corrections proposed by Gore and collaborators have excellent numerical performance, the profiles still converge slowly. Even when the corrections are applied in an ideal case where the work distribution is necessarily Gaussian, performing simulations under quasi‐equilibrium conditions is still most efficient. Furthermore, it is shown that even for a single methane molecule in water, pulling rates as low as 1 m s^?1 can be problematic. The implications of this finding for studies in which small molecules or even large biomolecules are pulled through inhomogeneous environments at similar pulling rates are discussed.     

QuanPol: A full spectrum and seamless QM/MM program

The quantum chemistry polarizable force field program (QuanPol) is implemented to perform combined quantum mechanical and molecular mechanical (QM/MM) calculations with induced dipole polarizable force fields and induced surface charge continuum solvation models. The QM methods include Hartree–Fock method, density functional theory method (DFT), generalized valence bond theory method, multiconfiguration self‐consistent field method, Møller–Plesset perturbation theory method, and time‐dependent DFT method. The induced dipoles of the MM atoms and the induced surface charges of the continuum solvation model are self‐consistently and variationally determined together with the QM wavefunction. The MM force field methods can be user specified, or a standard force field such as MMFF94, Chemistry at Harvard Molecular Mechanics (CHARMM), Assisted Model Building with Energy Refinement (AMBER), and Optimized Potentials for Liquid Simulations‐All Atom (OPLS‐AA). Analytic gradients for all of these methods are implemented so geometry optimization and molecular dynamics (MD) simulation can be performed. MD free energy perturbation and umbrella sampling methods are also implemented. © 2013 Wiley Periodicals, Inc.