Crystal lattice properties fully determine short-range interaction parameters for alkali and halide ions

Accurate models of alkali and halide ions in aqueous solution are necessary for computer simulations of a broad variety of systems. Previous efforts to develop ion force fields have generally focused on reproducing experimental measurements of aqueous solution properties such as hydration free energies and ion-water distribution functions. This dependency limits transferability of the resulting parameters because of the variety and known limitations of water models. We present a solvent-independent approach to calibrating ion parameters based exclusively on crystal lattice properties. Our procedure relies on minimization of lattice sums to calculate lattice energies and interionic distances instead of equilibrium ensemble simulations of dense fluids. The gain in computational efficiency enables simultaneous optimization of all parameters for Li+, Na+, K+, Rb+, Cs+, F-, Cl-, Br-, and I- subject to constraints that enforce consistency with periodic table trends. We demonstrate the method by presenting lattice-derived parameters for the primitive model and the Lennard-Jones model with Lorentz-Berthelot mixing rules. The resulting parameters successfully reproduce the lattice properties used to derive them and are free from the influence of any water model. To assess the transferability of the Lennard-Jones parameters to aqueous systems, we used them to estimate hydration free energies and found that the results were in quantitative agreement with experimentally measured values. These lattice-derived parameters are applicable in simulations where coupling of ion parameters to a particular solvent model is undesirable. The simplicity and low computational demands of the calibration procedure make it suitable for parametrization of crystallizable ions in a variety of force fields.     

Comparison of structural,thermodynamic, kinetic and mass transport properties of Mg2+ ion models commonly used in biomolecular simulations

The prevalence of Mg²⁺ ions in biology and their essential role in nucleic acid structure and function has motivated the development of various Mg²⁺ ion models for use in molecular simulations. Currently, the most widely used models in biomolecular simulations represent a nonbonded metal ion as an ion‐centered point charge surrounded by a nonelectrostatic pairwise potential that takes into account dispersion interactions and exchange effects that give rise to the ion's excluded volume. One strategy toward developing improved models for biomolecular simulations is to first identify a Mg²⁺ model that is consistent with the simulation force fields that closely reproduces a range of properties in aqueous solution, and then, in a second step, balance the ion–water and ion–solute interactions by tuning parameters in a pairwise fashion where necessary. The present work addresses the first step in which we compare 17 different nonbonded single‐site Mg²⁺ ion models with respect to their ability to simultaneously reproduce structural, thermodynamic, kinetic and mass transport properties in aqueous solution. None of the models based on a 12‐6 nonelectrostatic nonbonded potential was able to reproduce the experimental radial distribution function, solvation free energy, exchange barrier and diffusion constant. The models based on a 12‐6‐4 potential offered improvement, and one model in particular, in conjunction with the SPC/E water model, performed exceptionally well for all properties. The results reported here establish useful benchmark calculations for Mg²⁺ ion models that provide insight into the origin of the behavior in aqueous solution, and may aid in the development of next‐generation models that target specific binding sites in biomolecules. © 2015 Wiley Periodicals, Inc.     

Solvation and ion-pairing properties of the aqueous sulfate anion: explicit versus effective electronic polarization

We assessed the relative merits of two approaches for including polarization effects in classical force fields for the sulfate anion. One of the approaches is the explicit shell model for atomic polarization and the other is an implicit dielectric continuum representation of the electronic polarization, wherein the polarizability density is spatially uniform. Both the solvation and ion association properties of sulfate were considered. We carried out an ab initio molecular dynamics simulation for a single sulfate anion in aqueous solution to obtain a benchmark for the solvation structure. For the ion-pairing properties, the models were compared to experimental thermodynamic data through Kirkwood-Buff theory, which relates the integrals of the pair correlation functions to measurable properties. While deficiencies were found for both of the approaches, the continuum polarization model was not systematically worse than the shell model. The shell model was found to give a more structured solution than the continuum polarization model, both with respect to solvation and ion pairing.     

Determination of alkali and halide monovalent ion parameters for use in explicitly solvated biomolecular simulations

Alkali (Li(+), Na(+), K(+), Rb(+), and Cs(+)) and halide (F(-), Cl(-), Br(-), and I(-)) ions play an important role in many biological phenomena, roles that range from stabilization of biomolecular structure, to influence on biomolecular dynamics, to key physiological influence on homeostasis and signaling. To properly model ionic interaction and stability in atomistic simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model or representation of the monovalent ions is critically necessary. A good model needs to simultaneously reproduce many properties of ions, including their structure, dynamics, solvation, and moreover both the interactions of these ions with each other in the crystal and in solution and the interactions of ions with other molecules. At present, the best force fields for biomolecules employ a simple additive, nonpolarizable, and pairwise potential for atomic interaction. In this work, we describe our efforts to build better models of the monovalent ions within the pairwise Coulombic and 6-12 Lennard-Jones framework, where the models are tuned to balance crystal and solution properties in Ewald simulations with specific choices of well-known water models. Although it has been clearly demonstrated that truly accurate treatments of ions will require inclusion of nonadditivity and polarizability (particularly with the anions) and ultimately even a quantum mechanical treatment, our goal was to simply push the limits of the additive treatments to see if a balanced model could be created. The applied methodology is general and can be extended to other ions and to polarizable force-field models. Our starting point centered on observations from long simulations of biomolecules in salt solution with the AMBER force fields where salt crystals formed well below their solubility limit. The likely cause of the artifact in the AMBER parameters relates to the naive mixing of the Smith and Dang chloride parameters with AMBER-adapted Aqvist cation parameters. To provide a more appropriate balance, we reoptimized the parameters of the Lennard-Jones potential for the ions and specific choices of water models. To validate and optimize the parameters, we calculated hydration free energies of the solvated ions and also lattice energies (LE) and lattice constants (LC) of alkali halide salt crystals. This is the first effort that systematically scans across the Lennard-Jones space (well depth and radius) while balancing ion properties like LE and LC across all pair combinations of the alkali ions and halide ions. The optimization across the entire monovalent series avoids systematic deviations. The ion parameters developed, optimized, and characterized were targeted for use with some of the most commonly used rigid and nonpolarizable water models, specifically TIP3P, TIP4P EW, and SPC/E. In addition to well reproducing the solution and crystal properties, the new ion parameters well reproduce binding energies of the ions to water and the radii of the first hydration shells.     

Hydration free energies of monovalent ions in transferable intermolecular potential four point fluctuating charge water: an assessment of simulation methodology and force field performance and transferability

Hydration free energies of nonpolarizable monovalent atomic ions in transferable intermolecular potential four point fluctuating charge (TIP4P-FQ) are computed using several commonly employed ion-water force fields including two complete model sets recently developed for use with the simple water model with four sites and Drude polarizability and TIP4P water models. A simulation methodology is presented which incorporates a number of finite-system free energy corrections within the context of constant pressure molecular dynamics simulations employing the Ewald method and periodic boundary conditions. The agreement of the computed free energies and solvation structures with previously reported results for these models in finite droplet systems indicates good transferability of ion force fields from these water models to TIP4Q-FQ even when ion polarizability is neglected. To assess the performance of the ion models in TIP4P-FQ, we compare with consensus values for single-ion hydration free energies arising from recently improved cluster-pair estimates and a reevaluation of commonly cited, experimentally derived single-ion hydration free energies; we couple the observed consistency of these energies with a justification of the cluster-pair approximation in assigning single-ion hydration free energies to advocate the use of these consensus energies as a benchmark set in the parametrization of future ion force fields.     

Choice of Force Fields and Water Models for Sampling Solution Conformations of Bacteriophage T4 Lysozyme

A protein may exist as an ensemble of different conformations in solution, which cannot be represented by a single static structure. Molecular dynamics (MD) simulation has become a useful tool for sampling protein conformations in solution, but force fields and water models are important issues. This work presents a case study of the bacteriophage T4 lysozyme (T4L). We have found that MD simulations using a classic AMBER99SB force field and TIP4P water model cannot well describe hinge-bending domain motion of the wild-type T4L at the timescale of one microsecond. Other combinations, such as a residue-specific force field called RSFF2+ and a dispersion-corrected water model TIP4P-D, are able to sample reasonable solution conformations of T4L, which are in good agreement with experimental data. This primary study may provide candidates of force fields and water models for further investigating conformational transition of T4L.     

Hydration thermodynamic properties of amino acid analogues: a systematic comparison of biomolecular force fields and water models

We present an extensive study on hydration thermodynamic properties of analogues of 13 amino acid side chains at 298 K and 1 atm. The hydration free energies DeltaG, entropies DeltaS, enthalpies DeltaH, and heat capacities Deltac(P)() were determined for 10 combinations of force fields and water models. The statistical sampling was extended such that precisions of 0.3, 0.8, 0.8 kJ/mol and 25 J/(mol K) were reached for DeltaG, TDeltaS, DeltaH, and Deltac(P)(), respectively. The three force fields used in this study are AMBER99, GROMOS 53A6, and OPLS-AA; the five water models are SPC, SPC/E, TIP3P, TIP4P, and TIP4P-Ew. We found that the choice of water model strongly influences the accuracy of the calculated hydration entropies, enthalpies, and heat capacities, while differences in accuracy between the force fields are small. On the basis of an analysis of the hydrophobic analogues of the amino acid side chains, we discuss what properties of the water models are responsible for the observed discrepancies between computed and experimental values. The SPC/E water model performs best with all three biomolecular force fields.     

Effective force fields for condensed phase systems from ab initio molecular dynamics simulation: a new method for force-matching

A novel least-squares fitting approach is presented to obtain classical force fields from trajectory and force databases produced by ab initio (e.g., Car-Parrinello) molecular dynamics (MD) simulations. The method was applied to derive effective nonpolarizable three-site force fields for liquid water at ambient conditions from Car-Parrinello MD simulations in the Becke-Lee-Yang-Parr approximation to the electronic density functional theory. The force-matching procedure includes a fit of short-ranged nonbonded forces, bonded forces, and atomic partial charges. The various parameterizations of the water force field differ by an enforced smooth cut-off applied to the short-ranged interaction term. These were obtained by fitting to the trajectory and force data produced by Car-Parrinello MD simulations of systems of 32 and 64 H(2)O molecules. The new water force fields were developed assuming both flexible or rigid molecular geometry. The simulated structural and self-diffusion properties of liquid water using the fitted force fields are in close agreement with those observed in the underlying Car-Parrinello MD simulations. The resulting empirical models compare to experiment much better than many conventional simple point charge (SPC) models. The fitted potential is also shown to combine well with more sophisticated intramolecular potentials. Importantly, the computational cost of the new models is comparable to that for SPC-like potentials.     

Molecular modeling and dynamics studies with explicit inclusion of electronic polarizability: theory and applications

A current emphasis in empirical force fields is on the development of potential functions that explicitly treat electronic polarizability. In the present article, the commonly used methodologies for modeling electronic polarization are presented along with an overview of selected application studies. Models presented include induced point-dipoles, classical Drude oscillators, and fluctuating charge methods. The theoretical background of each method is followed by an introduction to extended Lagrangian integrators required for computationally tractable molecular dynamics simulations using polarizable force fields. The remainder of the review focuses on application studies using these methods. Emphasis is placed on water models, for which numerous examples exist, with a more thorough discussion presented on the recently published models associated with the Drude-based CHARMM and the AMOEBA force fields. The utility of polarizable models for the study of ion solvation is then presented followed by an overview of studies of small molecules (e.g., CCl₄, alkanes, etc.) and macromolecule (proteins, nucleic acids and lipid bilayers) application studies. The review is written with the goal of providing a general overview of the current status of the field and to facilitate future application and developments.     

Assessment of biomolecular force fields for molecular dynamics simulations in a protein crystal

Different biomolecular force fields (OPLS‐AA, AMBER03, and GROMOS96) in conjunction with SPC, SPC/E and TIP3P water models are assessed for molecular dynamics simulations in a tetragonal lysozyme crystal. The root mean square deviations for the C_a atoms of lysozymes are about 0.1 to 0.2 nm from OPLS‐AA and AMBER03, smaller than 0.4 nm from GROMOS96. All force fields exhibit similar pattern in B‐factors, whereas OPLS‐AA and AMBER03 accurately reproduce experimental measurements. Despite slight variations, the primary secondary structures are well conserved using different force fields. Water diffusion in the crystal is approximately ten‐fold slower than in bulk phase. The directional and average water diffusivities from OPLS‐AA and AMBER03 along with SPC/E model match fairly well with experimental data. Compared to GROMOS96, OPLS‐AA and AMBER03 predict larger hydrophilic solvent‐accessible surface area of lysozyme, more hydrogen bonds between lysozyme and water, and higher percentage of water in hydration shell. SPC, SPC/E and TIP3P water models have similar performance in most energetic and structural properties, but SPC/E outperforms in water diffusion. While all force fields overestimate the mobility and electrical conductivity of NaCl, a combination of OPLS‐AA for lysozyme and the Kirkwood‐Buff model for ions is superior to others. As attributed to the steric restraints and surface interactions, the mobility and conductivity in the crystal are reduced by one to two orders of magnitude from aqueous solution. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Effect of Protein Dimerization on Ion Conductivity of Gramicidin A Channel Studied Using Polarizable Force Field

In studies of ion channel systems, due to the huge computational cost of polarizable force fields, classical force fields remain the most widely used for a long time. In this work, we used the AMOEBA polarizable atomic multipole force field in enhanced sampling simulations of single-channel gramicidin A (gA) and double-channel gA systems and investigated its reliability in characterizing ion-transport properties of the gA ion channel under dimerization. The influence of gA dimerization on the permeation of potassium and sodium ions through the channel was described in terms of conductance, diffusion coefficient, and free energy profile. Results from the polarizable force field simulations show that the conductance of potassium and sodium ions passing through the single- and double-channel agrees well with experimental values. Further data analysis reveals that the molecular mechanism of protein dimerization affects the ion-transport properties of gA channels, i.e., protein dimerization accelerates the permeation of potassium and sodium ions passing through the double-channel by adjusting the environment around gA protein (the distribution of phospholipid head groups, ions outside the channel, and bulk water), rather than directly adjusting the conformation of gA protein.     

A macroion electrokinetics algorithm

A numerical algorithm is presented for the standard model of macroion electrokinetics and certain generalizations of it. The macroion consists of a cylindrical section with identical, hemispheroidal endcaps, each piece having arbitrary length. The system of one macroion and adjoining salt solution is subjected to an arbitrary sequence of pulsed electrical fields and pulsed translational and rotational velocities. Numerical solutions are obtained for the time dependent electrostatic and mobile ion concentration fields and the solvent velocity. From these fields the dielectric response, force, and torque are calculated. Generalizations of the standard model include the diffusive motion of macroion surface charges, partial slip of solvent motion at the macroion surface, and a simple model for the reactive exchange of surface charge with solution ions. The primary illustrative application is to recent measurements of electric birefringence versus applied field frequency for poly-(tetrafluorothylene) colloidal particles, but a few results are presented for the dielectric response of DNA fragments and of spherical colloidal particles. The source code and additional details are provided as supplementary documentation.     

Vibrational spectra and normal coordinate analysis of two isotopomers of the thiosulfate ion

The Raman spectra of ¹⁸O-thiosulfate ion (S₁O⁻²₃) in H₁¹⁸O solution and the IR spectrum of ¹⁸O-sodium thiosulfate in the solid have been obtained. Normal Coordinate calculations fitting all the fundamental wavenumbers of both ¹⁶O and ¹⁸O isotopomers have been carried out transferring the GVFF of the sulfate ion as the starting point and employing a symmetry force field for the least-squares adjustment procedure. A comparison of the results is made with the known force fields for several sulfur compounds.     

Ions interacting in solution: Moving from intrinsic to collective properties

A crucial determinant of Hofmeister effects is the direct interaction of ions in solution with the charged groups on the surface of larger particles. Understanding ion–ion interactions in solution is therefore a necessary first step to explaining Hofmeister effects. Here, we advocate an approach to modeling these types of properties where state of the art Ab Initio Molecular Dynamics (AIMD) simulation of ions in solution is used to establish benchmark values for the intrinsic properties of ions in solution such as solvation structures and ion–ion Potentials of Mean Force (PMFs). This information can then be combined with, or used to parametrize and improve, reduced models, which use approximations such as the continuum solvent model (CSM). These reduced models can then be used to calculate collective and concentration dependent properties of electrolyte solution and so make accurate predictions about complex systems of relevance for direct applications. We provide an example of this approach using AIMD calculations of the sodium chloride PMF to calculate osmotic coefficients of all 20 alkali halide electrolytes.     

Further insights in the ability of classical nonadditive potentials to model actinide ion–water interactions

Pursuing our efforts on the development of accurate classical models to simulate radionuclides in complex environments (Réal et al., J. Phys. Chem. A 2010, 114, 15913; Trumm et al. J. Chem. Phys. 2012, 136, 044509), this article places a large emphasis on the discussion of the influence of models/parameters uncertainties on the computed structural, dynamical, and temporal properties. Two actinide test cases, trivalent curium and tetravalent thorium, have been studied with three different potential energy functions, which allow us to account for the polarization and charge‐transfer effects occurring in hydrated actinide ion systems. The first type of models considers only an additive energy term for modeling ion/water charge‐transfer effects, whereas the other two treat cooperative charge‐transfer interactions with two different analytical expressions. Model parameters are assigned to reproduce high‐level ab initio data concerning only hydrated ion species in gas phase. For the two types of cooperative charge‐transfer models, we define two sets of parameters allowing or not to cancel out possible errors inherent to the force field used to model water/water interactions at the ion vicinity. We define thus five different models to characterize the solvation of each ion. For both ions, our cooperative charge‐transfer models lead to close results in terms of structure in solution: the coordination number is included within 8 and 9, and the mean ion/water oxygen distances are 2.45 and 2.49 Å, respectively, for Th(IV) and Cm(III). © 2012 Wiley Periodicals, Inc.     

Assessing the accuracy of improved force‐matched water models derived from Ab initio molecular dynamics simulations

The accuracy of water models derived from ab initio molecular dynamics simulations by means on an improved force‐matching scheme is assessed for various thermodynamic, transport, and structural properties. It is found that although the resulting force‐matched water models are typically less accurate than fully empirical force fields in predicting thermodynamic properties, they are nevertheless much more accurate than generally appreciated in reproducing the structure of liquid water and in fact superseding most of the commonly used empirical water models. This development demonstrates the feasibility to routinely parametrize computationally efficient yet predictive potential energy functions based on accurate ab initio molecular dynamics simulations for a large variety of different systems. © 2016 Wiley Periodicals, Inc.     

ABEEM浮动电荷分子力场在含离子体系中的发展和应用

离子水合及生物分子体系内离子选择性的微观作用机制是人们长期探索的重要课题,其难点在于如何合理精确地描述上述体系内的离子-水、离子-生物分子等各种相互作用.本文主要总结近年来原子-键电负性均衡浮动电荷分子力场（ABEEM/MM）在含离子体系中的发展和应用,包括离子水溶液、金属蛋白、离子-核酸碱基体系的研究.我们优选相关参数,构建上述体系的势能函数,并对气相水合离子团簇、离子水溶液、金属蛋白、离子-核酸碱基体系进行研究,模拟其结构、活性、热力学和动力学等性质.研究和比较结果表明,我们的ABEEM浮动电荷力场总体上优于其它力场方法,其精度可达到或接近高水平从头计算MP2方法.这为进一步探讨生物分子体系内的离子选择性、金属酶及其它含离子体系的结构和性质奠定了基础.     

Development and applications of the ABEEM fluctuating charge molecular force field in the ion-containing systems

The microscopic mechanisms of ion hydration and ion selectivity in biomolecular systems are long-standing research topics,in which the difficulty is how to reasonably and accurately describe the ion-water and ion-biomolecule interactions.This paper summarizes the development and applications of the atom-bond electronegativity equalization fluctuating charge force field model,ABEEM/MM,in the investigations of ion hydration,metalloproteins and ion-DNA bases systems.Based on high-level quantum chemistry calculations,the parameters were optimized and the molecular potential functions were constructed and applied to studies of structures,activities,energetics,and thermodynamic and kinetic properties of these ion-containing systems.The results show that the performance of ABEEM/MM is generally better than that of the common force fields,and its accuracy can reach or approach that of the high-level ab initio MP2 method.These studies provide a solid basis for further investigations of ion selectivity in biomolecular systems,the structures and properties of metalloproteins and other related ion-containing systems.     

A theoretical study of aqueous solvation of K comparing ab initio, polarizable, and fixed-charge models

The hydration of K(+) is studied using a hierarchy of theoretical approaches, including ab initio Born-Oppenheimer molecular dynamics and Car-Parrinello molecular dynamics, a polarizable force field model based on classical Drude oscillators, and a nonpolarizable fixed-charge potential based on the TIP3P water model. While models based more directly on quantum mechanics offer the possibility to account for complex electronic effects, polarizable and fixed-charges force fields allow for simulations of large systems and the calculation of thermodynamic observables with relatively modest computational costs. A particular emphasis is placed on investigating the sensitivity of the polarizable model to reproduce key aspects of aqueous K(+), such as the coordination structure, the bulk hydration free energy, and the self diffusion of K(+). It is generally found that, while the simple functional form of the polarizable Drude model imposes some restrictions on the range of properties that can simultaneously be fitted, the resulting hydration structure for aqueous K(+) agrees well with experiment and with more sophisticated computational models. A counterintuitive result, seen in Car-Parrinello molecular dynamics and in simulations with the Drude polarizable force field, is that the average induced molecular dipole of the water molecules within the first hydration shell around K(+) is slightly smaller than the corresponding value in the bulk. In final analysis, the perspective of K(+) hydration emerging from the various computational models is broadly consistent with experimental data, though at a finer level there remain a number of issues that should be resolved to further our ability in modeling ion hydration accurately.