Atomic Point Charges Research Articles

Developing and Validating a Set of All-Atom Potential Models for Sodium Dodecyl Sulfate.

We present a set of novel all-atom potential models for sodium dodecyl sulfate (SDS), developed within the framework of the widely used OPLS-AA and General AMBER force fields. The choice of the parameters for the models is made by rigorously following the methodology of the used force fields to ensure full compatibility with the models for other compounds. For the GAFF model, extensive quantum-chemical computations are performed to obtain reliable Boltzmann-averaged atomic point charges, and the latter are compared with the single-conformation charges. For representation of the hydrocarbon tail, we use recently published improved parameters that correctly reproduce the properties of lipids and long alkanes. The models are validated on the basis of correct reproduction of the main properties of micelles (size, degree of counterion binding) as well as diffusion coefficient of the SDS monomer. As an extended test, a simulation of a micelle with a high aggregation number (382) and unnatural initial shape is performed, and a restructuring to the correct shape is observed. This proves the suitability of the developed models for simulations of concentrated SDS solutions containing large micelles and also emphasizes importance of hydrocarbon tail parameters for the micelle properties. Finally, the developed DS- models are tested in combination with several common Na+ and water models. Their effect on the properties of SDS micelles is discussed, and suitable combinations are determined.

Revisiting Partition in Hydrated Bilayer Systems.

We discuss potential-of-mean force convergence issues involving the methods for generating starting structures of umbrella sampling simulations for the study of the water-bilayer permeation of drug-like compounds. We provide a proof of concept of the benefits of potential-energy modification methods, in particular the flooding technique, to enhance the sampling and improve the convergence of the potential-of-mean force. In addition, we also discuss how these potential modifiers could introduce the necessary bias to induce the correct description of other relevant internal degrees of freedom for the compounds, thus providing a more accurate description of the permeation process. Effective methodological approximations are taken into consideration, more specifically the inclusion of atomic polarization, and experimental data are used in the validation of computed values whenever possible. The parametrization of the atomic point charges is always a relevant issue in biomolecular simulations. We discuss the influence of a molecule's conformation-dependent atomic point charges and their impact on the predicted potential-of-mean force.

Fine-tuning of atomic point charges: Classical simulations of pyridine in different environments

A correct description of electrostatic contributions in force fields for classical simulations is mandatory for an accurate modeling of molecular interactions in pure liquids or solutions. Here, we propose a new protocol for point charge fitting, aimed to take into the proper account different polarization effects due to the environment employing virtual sites and tuning the point charge within the polarizable continuum model framework. The protocol has been validated by means of molecular dynamics simulations on pure pyridine liquid and on pyridine aqueous solution, reproducing a series of experimental observables and providing the information for their correct interpretation at atomic level.

Towards a dissociative SPC-like water model - probing the impact of intramolecular Coulombic contributions.

The dissociative water potential introduced by Garofalini et al. proved to be a simple and effective description to account for proton transfer in aqueous media, enabling for instance the execution of simulation studies at different pH values. In this model the charge of each particle is represented by a point-charge surrounded by a Gaussian charge-cloud of opposite sign, thus four Coulombic terms (point-charge-point-charge, point-charge-charge-cloud, charge-cloud-point-charge and charge-cloud-charge-cloud) are required per atom pair. In this work it is demonstrated that the Gaussian charge distributions can be removed from the model after a minor modification of the overall atomic point-charges. Despite this substantial modification of the model, structural properties obtained via pair- and angle distributions remain largely unaffected and the change in dynamical properties (vibrational frequencies, proton transfer properties) was found to be minor. As an additional improvement an adjustment of the bending mode vibration was carried out by carefully evaluating the parametrization of the three-body interaction potential, thereby retaining the good agreement of the transfer properties of the aqueous excess proton reported in an earlier study. The proposed simple point-charge (SPC) type parametrization of the Coulombic interactions not only leads to a notable decrease in computational demand but generalizes the dissociative model by improving its transferability to established third-party simulation software and enabling the application of different theoretical approaches such as Ewald summation techniques not considered in the original parametrization. The outlined optimization strategy demonstrates that despite the complex and challenging formulation of the force field, various dynamical properties can be selectively adjusted without influencing other critical parameters of the simulated systems.

Prediction of polymer-solvent miscibility properties using the force field based quasi-chemical method PAC-MAC

We present a modification to the recently developed Pair Configuration to Molecular Activity Coefficient (PAC-MAC) method in order to obtain miscibility properties of multicomponent mixtures containing polymers. PAC-MAC is a force field based quasi-chemical method originally used for rapid calculation of binary phase diagrams of small molecules. A comparison with an experimental database, containing 779 Flory Huggins χ-interaction parameters of polymer solutions, results in a correlation coefficient of 0.837 and a total root mean squared error (RMSE) of 0.593. The highest accuracy is obtained for solutions containing polystyrenes (RMSE = 0.212) or polyacrylates (RMSE = 0.308). PAC-MAC and the competitive COSMO-RS model show comparable accuracy in the prediction of solvent activities, even though PAC-MAC only uses atomic point charges instead of a quantum mechanically calculated charge distribution. PAC-MAC is a quick method for obtaining a rough indication of the mixing free energy.

Simple combined explicit/implicit water model

A simple combined water model (SCW model) for the calculation of the hydration free energy is presented. In the frame of the model a solute is placed in the centre of the spherical cavity with explicit water molecules, which are considered at the atomistic level. Rigid wall potential at the boundary of the cavity restricts the moving of the explicit water molecules. Water outside the sphere is considered as the conducting continuum (implicit part of the model). Simulation is performed in the frame of the NVT ensemble (constant number of particles, volume and temperature), density of water is fixed and equal to experimental value 1 g/cm3. The energy of electrostatic interaction of atomic point charges of the explicit water molecules with conducting continuum is calculated analytically by means of the image charges method. It provides high computational efficiency of the SCW model. For the averaging of the calculated thermodynamic and structural values over microstates of the system the thermodynamic integration method is used. The possible using of SCW for the docking problem is discussed.

A Comprehensive Set of High-Quality Point Charges for Simulations of Metal–Organic Frameworks

Most classical simulations of metal–organic frameworks model electrostatic interactions using point charges on each atom in the structure. We report atomic point charges derived from periodic density functional theory (DFT) electronic structure calculations for more than 2000 unique experimentally synthesized metal–organic frameworks (MOFs). These charges are publicly available as a supplement to the Computation-Ready Experimental MOF database. These DFT-derived atomic point charges are compared to semiempirical group contribution and charge equilibration methods for assigning charges. As an example of using these charges, we examined each MOF for usefulness in the adsorptive removal of tert-butyl mercaptan (TBM) from natural gas. Monte Carlo simulations revealed many candidate MOF structures with high selectivity for TBM over CH4 and high TBM capacity. We anticipate that this public data set of atomic point charges for MOFs will facilitate high-throughput screening for a wide variety of applications in w...

Evaluation of the OPLS-AA force field for the study of structural and energetic aspects of molecular organic crystals.

Motivated by the need for reliable experimental data for the assessment of theoretical predictions, this work proposes a data set of enthalpies of sublimation determined for specific crystalline structures, for the validation of molecular force fields (FF). The selected data were used to explore the ability of the OPLS-AA parametrization to investigate the properties of solid materials in molecular dynamics simulations. Furthermore, several approaches to improve this parametrization were also considered. These modifications consisted in replacing the original FF atomic point charges (APC), by values calculated using quantum chemical methods, and by the implementation of a polarizable FF. The obtained results indicated that, in general, the best agreement between theoretical and experimental data is found when the OPLS-AA force field is used with the original APC or when these are replaced by ChelpG charges, computed at the MP2/aug-cc-pVDZ level of theory, for isolated molecules in the gaseous phase. If a good description of the energetic relations between the polymorphs of a compound is required then either the use of polarizable FF or the use of charges determined taking into account the vicinity of the molecules in the crystal (combining the ChelpG and MP2/cc-pVDZ methods) is recommended. Finally, it was concluded that density functional theory methods, like B3LYP or B3PW91, are not advisable for the evaluation of APC of organic compounds for molecular dynamic simulations. Instead, the MP2 method should be considered.

Genetic algorithm optimization of point charges in force field development: challenges and insights.

Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields.

Virtual fragment preparation for computational fragment-based drug design.

Fragment-based drug design (FBDD) has become an important component of the drug discovery process. The use of fragments can accelerate both the search for a hit molecule and the development of that hit into a lead molecule for clinical testing. In addition to experimental methodologies for FBDD such as NMR and X-ray Crystallography screens, computational techniques are playing an increasingly important role. The success of the computational simulations is due in large part to how the database of virtual fragments is prepared. In order to prepare the fragments appropriately it is necessary to understand how FBDD differs from other approaches and the issues inherent in building up molecules from smaller fragment pieces. The ultimate goal of these calculations is to link two or more simulated fragments into a molecule that has an experimental binding affinity consistent with the additive predicted binding affinities of the virtual fragments. Computationally predicting binding affinities is a complex process, with many opportunities for introducing error. Therefore, care should be taken with the fragment preparation procedure to avoid introducing additional inaccuracies.This chapter is focused on the preparation process used to create a virtual fragment database. Several key issues of fragment preparation which affect the accuracy of binding affinity predictions are discussed. The first issue is the selection of the two-dimensional atomic structure of the virtual fragment. Although the particular usage of the fragment can affect this choice (i.e., whether the fragment will be used for calibration, binding site characterization, hit identification, or lead optimization), general factors such as synthetic accessibility, size, and flexibility are major considerations in selecting the 2D structure. Other aspects of preparing the virtual fragments for simulation are the generation of three-dimensional conformations and the assignment of the associated atomic point charges.

Ion Transport in Electrolytes for Dye-Sensitized Solar Cells: A Combined Experimental and Theoretical Study

The ion transport properties of electrolytes based on room temperature ionic liquids (RTILs) used in dye-sensitized solar cells (DSCs) have been studied by electrochemical voltammetry experiments and molecular dynamics (MD) simulations. Fully atomistic models based on the Lennard-Jones potential with atomic point charges have been developed for imidazolium and pyrrolidinium imides (Tf2N). MD simulations with the proposed force fields reproduce accurately the density and the self-diffusion coefficient of the anion and cation of the RTIL, as well as their temperature dependence and the effect of the length of the alkyl chain. The diffusion coefficients of iodide/tri-iodide redox mediator in mixture of RTIL and acetonitrile have been studied by voltammetry and MD. Both experiment and simulation show a 2 orders of magnitude decrease of the diffusion coefficient of the redox mediator between pure acetonitrile and pure RTIL. However, the variation of the diffusion coefficient with the RTIL/acetonitrile mixing ratio shows that a small amount of acetonitrile is sufficient to induce an improvement of the ion transport properties of the electrolyte, which can be very beneficial to design efficient and stable electrolytes for DSCs.

Advancement of polarizable force field and its use for molecular modeling and design.

The most important requirement of biomolecular modeling is to deal with electrostatic energies. The electrostatic polarizability is an important part of electrostatic interaction for simulation systems. However, AMBER, CHARMM, OPLS, GROMOS, MMFF force fields etc. used in the past mostly apply fixed atomic center point charge to describe electrostatic energies, and are not sufficient for considering the influence of the electrostatic polarization. The emergence of polarizable force fields has solved this problem. In recent years, quickly developed polarizable force fields have involved a lot of fields. The chapter relating to polarizable force fields spread over several aspects. Firstly, we reviewed the history of the classical force fields and compared with polarizable force fields to elucidate the advancements of polarizable force fields. Secondly, it is introduced that the application of polarizable force fields to small molecules and biological macromolecules simulation, including molecular design. Finally, a brief development trend and perspective is given on rapidly growing polarizable force fields.

Charge Anisotropy: Where Atomic Multipoles Matter Most.

Specific intermolecular interactions are largely guided by electrostatics. However, the most common model for electrostatic interactions-atomic point charges-fails to reproduce anisotropic charge distributions, such as lone pairs and sigma holes. Although this has long been known, point charges are still widely used in chemical modeling and reasoning. In this contribution, we analyze the deficiency of atomic point charges in reproducing the electrostatic potential (ESP) around molecules and find that multipole moments up to quadrupoles can, with a much lower error than point charges, reproduce the relevant ESP for all cases. Mapping the surface to the closest atom allows to compare ESP errors between atom types and to identify cases with the most urgent need for atomic multipoles. Our analysis shows that almost all heteroatoms require multipoles to correctly describe their charge distribution, with the most serious cases being nitrogen, sulfur, and halogens. Comparison with small molecule crystallography data studies supports our findings and emphasizes the need for incorporating anisotropic charge descriptions in chemical models. The scheme introduced here can be used to identify anisotropic binding preferences for atom types where there is too little coverage in crystal structure databases.

3D Hydrophobic Moment Vectors as a Tool to Characterize the Surface Polarity of Amphiphilic Peptides

The interaction of membranes with peptides and proteins is largely determined by their amphiphilic character. Hydrophobic moments of helical segments are commonly derived from their two-dimensional helical wheel projections, and the same is true for β-sheets. However, to the best of our knowledge, there exists no method to describe structures in three dimensions or molecules with irregular shape. Here, we define the hydrophobic moment of a molecule as a vector in three dimensions by evaluating the surface distribution of all hydrophilic and lipophilic regions over any given shape. The electrostatic potential on the molecular surface is calculated based on the atomic point charges. The resulting hydrophobic moment vector is specific for the instantaneous conformation, and it takes into account all structural characteristics of the molecule, e.g., partial unfolding, bending, and side-chain torsion angles. Extended all-atom molecular dynamics simulations are then used to calculate the equilibrium hydrophobic moments for two antimicrobial peptides, gramicidin S and PGLa, under different conditions. We show that their effective hydrophobic moment vectors reflect the distribution of polar and nonpolar patches on the molecular surface and the calculated electrostatic surface potential. A comparison of simulations in solution and in lipid membranes shows how the peptides undergo internal conformational rearrangement upon binding to the bilayer surface. A good correlation with solid-state NMR data indicates that the hydrophobic moment vector can be used to predict the membrane binding geometry of peptides. This method is available as a web application on http://www.ibg.kit.edu/HM/.

QM quality atomic charges for proteins

The concept of atomic point charges is well established in theoretical chemistry. Atomic point charges have played an important role in understanding and modeling chemical behavior by allowing to extract and quantify information stored in the molecular electron distribution of chemical compounds. Thus, atomic point charges have been used to estimate reactivity indices, dissociation constants, partition coefficients, the electrostatic contribution in molecular dynamics or docking studies. It is therefore desirable to have knowledge of the values of atomic charges in proteins (see, e.g., [1]). Unfortunately, accurate and universally applicable approaches for atomic charge calculation based on quantum mechanics (QM) are very time consuming and thus cannot be employed for large biomolecules like proteins. An alternative is to use empirical charge calculation methods, such as the electronegativity equalization method (EEM) [2], which is very fast and has accuracy comparable to QM. The challenge is to calibrate (i.e., parametrize) this method for proteins. This parameterization can be done using atomic charges calculated by different types of QM approaches. EEM can be as accurate as the QM approach for which EEM was calibrated. In our work, we present the workflow of the EEM calibration process. Afterwards, we calibrate and validate EEM models for 12 types of QM charges, including the newest approaches like iterative Hirshfeld [3]. The accuracy of the obtained EEM models is evaluated on insulin and ubiquitin. We also show two case studies demonstrating the applicability of atomic charges computed via EEM: a small docking study, and the calculation of electrostatic potential based on the EEM charges [4].

Multipolar electrostatics.

Atomistic simulation of chemical systems is currently limited by the elementary description of electrostatics that atomic point-charges offer. Unfortunately, a model of one point-charge for each atom fails to capture the anisotropic nature of electronic features such as lone pairs or π-systems. Higher order electrostatic terms, such as those offered by a multipole moment expansion, naturally recover these important electronic features. The question remains as to why such a description has not yet been widely adopted by popular molecular mechanics force fields. There are two widely-held misconceptions about the more rigorous formalism of multipolar electrostatics: (1) Accuracy: the implementation of multipole moments, compared to point-charges, offers little to no advantage in terms of an accurate representation of a system's energetics, structure and dynamics. (2) Efficiency: atomistic simulation using multipole moments is computationally prohibitive compared to simulation using point-charges. Whilst the second of these may have found some basis when computational power was a limiting factor, the first has no theoretical grounding. In the current work, we disprove the two statements above and systematically demonstrate that multipole moments are not discredited by either. We hope that this perspective will help in catalysing the transition to more realistic electrostatic modelling, to be adopted by popular molecular simulation software.

Electrostatic forces in the Poisson-Boltzmann systems.

Continuum modeling of electrostatic interactions based upon numerical solutions of the Poisson-Boltzmann equation has been widely used in structural and functional analyses of biomolecules. A limitation of the numerical strategies is that it is conceptually difficult to incorporate these types of models into molecular mechanics simulations, mainly because of the issue in assigning atomic forces. In this theoretical study, we first derived the Maxwell stress tensor for molecular systems obeying the full nonlinear Poisson-Boltzmann equation. We further derived formulations of analytical electrostatic forces given the Maxwell stress tensor and discussed the relations of the formulations with those published in the literature. We showed that the formulations derived from the Maxwell stress tensor require a weaker condition for its validity, applicable to nonlinear Poisson-Boltzmann systems with a finite number of singularities such as atomic point charges and the existence of discontinuous dielectric as in the widely used classical piece-wise constant dielectric models.

Parameterization of the prosthetic redox centers of the bacterial cytochrome bc 1 complex for atomistic molecular dynamics simulations

Cytochrome (cyt) bc 1 is a multi-subunit membrane protein complex that is a vital component of the respiratory and photosynthetic electron transfer chains both in bacteria and eukaryotes. Although the complex’s dimer structure has been solved using X-ray crystallography, it has not yet been studied in large-scale classical molecular dynamics (MD) simulations. In part, this is due to lack of suitable force field parameters, centered atomic point charges in particular, for the complex’s prosthetic redox centers. Accurate redox center charges are needed to depict realistically the inter-molecular interactions at different redox stages of the cyt bc 1 complex. Accordingly, here we present high-precision atomic point charges for the metal centers of the cyt bc 1 complex of Rhodobacter capsulatus derived from extensive density functional theory calculations, fitted using the restrained electrostatic potential methodology and combined with the CHARMM force field parameters. We also provide the Hartree–Fock charges for all substrate forms (quinol, quinone, and semiquinone) and the inhibitors antimycin and stigmatellin of the bacterial bc 1 complex. The accuracy of the parameterization scheme was verified by running a 200-ns MD simulation encompassing the entire cyt bc 1 complex embedded in a lipid bilayer and solvated with explicit water. The results indicate that these meticulously derived parameters are ready for running extensive MD simulations encompassing all biologically relevant stages of the cyt bc 1 complex reaction cycle.

QM/MM Modeling of Environmental Effects on Electronic Transitions of the FMO Complex

The Fenna-Matthews-Oslon (FMO) light harvesting pigment-protein complex in green sulfur bacteria transfers the excitation energy from absorbed sunlight to the reaction center with almost 100% quantum efficiency. The protein-pigment coupling (part of the environmental effects) is believed to play an important role in determining excitation energy transfer pathways. To study the effect of environment on the electronic transitions in the FMO complex, especially by taking into account the newly discovered eighth extra pigment, we have employed hybrid quantum-mechanics/molecular-mechanics (QM/MM) methods in combination with molecular dynamics (MD) simulations. The averaged site energies of individual pigments are calculated using the semiempirical ZINDO/S-CIS method considering the protein residues as atomic point charges along the MD trajectories. The exciton energies are calculated from the site energies and excitonic couplings based on MD simulations. The new eighth pigment displays the largest site energy and contributes mainly to the highest exciton level, which may facilitate transfer of excitation energies from the baseplate to the reaction center. Further, the multimode Brownian oscillator (MBO) model is used to fit the linear absorption spectra of the FMO complex, validating the exciton energies obtained from the QM/MM calculations. Our results indicate that the QM/MM method combined with MD simulations is a powerful tool to model the environmental effects on electronic transitions of light harvesting antenna complexes.

Atomistic Simulations of the ZnO(12̅10)/Water Interface: A Comparison between First-Principles, Tight-Binding, and Empirical Methods.

We investigate the adsorption behavior of water over the zinc oxide (12̅10) surface starting from single molecules up to bulk liquid by means of atomistic molecular dynamics simulations. We compare results obtained with density-functional theory, density-functional tight binding, and a recently developed reactive force field. The methods perform comparably up to the level of a single monolayer of adsorbed water, predicting only small differences in adsorption energies and, as a consequence, adsorption geometries. These lie within the error bars of typical quantum mechanical calculations performed with different exchange-correlation functionals. However, the discrepancies among the methods have a dramatic effect on the dissociation equilibria and the structuring of liquid water layers in contact with the surface. Especially the different treatment of electrostatic interactions via self-consistent atomic point charges appears to heavily influence the simulation outcomes. Critical comparisons with experimental studies and possibly ad hoc reparametrizations of the semiempirical functionals may thus be necessary to study phenomena such as dissolution or biomolecular adsorption at ZnO surfaces within statistically relevant time and size scales.