Electronic Continuum Correction Research Articles

Effect of counterions on the structure and dynamics of water near a negatively charged surfactant: a theoretical vibrational sum frequency generation study.

Charged aqueous interfaces are of paramount importance in electrochemical, biological and environmental sciences. The properties of aqueous interfaces with ionic surfactants can be influenced by the presence of counterions. Earlier experiments involving vibrational sum frequency generation (VSFG) spectroscopy of aqueous interfaces with negatively charged sodium dodecyl sulfate (Na+DS- or SDS) surfactants revealed that the hydrogen bonding strength of the interfacial water molecules follows a certain order when salts of monovalent and divalent cations are added. It is known that cations do not directly participate in hydrogen bonding with water molecules, rather they only influence the hydrogen bonded network through their electrostatic fields. In the current work, we have simulated the aqueous interfacial systems of sodium dodecyl sulfate in the presence of chloride salts of mono and divalent countercations. The electronic polarization effects on the ions are considered at a mean-field level within the electronic continuum correction model. Our calculations of the VSFG spectra show a blue shift in the presence of added countercations whose origin is traced to different relative contributions of water molecules from the solvation shells of the surfactant headgroups and the remaining water molecules in the presence of countercations. Furthermore, the cations shield the electric fields of the surfactant headgroups, which in turn influences the contributions of water molecules to the total VSFG spectrum. This shielding effect becomes more significant when divalent countercations are present. The dynamics of water molecules is found to be slower at the interface in comparison to the bulk. The interfacial depth dependence of various dynamical quantities shows that the interface is structurally and dynamically more heterogeneous at the microscopic level.

A molecular dynamics simulations study on the modification of aqueous solution structure and dynamics in presence of monovalent salts: An electronic continuum correction approach and effect of ion size

The hydrogen bonding structure and dynamics of water are investigated by varying the concentrations up to 6.18 m for full-charged and the electronic continuum correction with rescaling (ECCR) charged model for NaCl solutions using classical molecular dynamics simulations. We have also considered the seven different (MCl/NaX) salt solutions at 6.18 m with varying monovalent cations (M+) or anions (X-). The first and second solvation shells of water in both full- and ECCR models are affected by NaCl concentrations, and destruction of the tetrahedral network structure is observed. Probability of ion pair formation is higher in KCl and NaF solutions compared to other salts at 6.18 m. The self-diffusion coefficient values of water, Na+ in full-charged, and Cl− in ECCR models are in good agreement with the experimental results. The hydrogen bond lifetime of water does not significantly change with increasing NaCl salt concentrations, but Cl−-water lifetime is significantly lowered in the ECCR model.

Nonaqueous Ion Pairing Exemplifies the Case for Including Electronic Polarization in Molecular Dynamics Simulations.

The inclusion of electronic polarization is of crucial importance in molecular simulations of systems containing charged moieties. When neglected, as often done in force field simulations, charge-charge interactions in solution may become severely overestimated, leading to unrealistically strong bindings of ions to biomolecules. The electronic continuum correction introduces electronic polarization in a mean-field way via scaling of charges by the reciprocal of the square root of the high-frequency dielectric constant of the solvent environment. Here, we use ab initio molecular dynamics simulations to quantify the effect of electronic polarization on pairs of like-charged ions in a model nonaqueous environment where electronic polarization is the only dielectric response. Our findings confirm the conceptual validity of this approach, underlining its applicability to complex aqueous biomolecular systems. Simultaneously, the results presented here justify the potential employment of weaker charge scaling factors in force field development.

Influence of effective polarization on ion and water interactions within a biomimetic nanopore

Interactions between ions and water at hydrophobic interfaces within ion channels and nanopores are suggested to play a key role in the movement of ions across biological membranes. Previous molecular-dynamics simulations have shown that anion affinity for aqueous/hydrophobic interfaces can be markedly influenced by including polarization effects through an electronic continuum correction. Here, we designed a model biomimetic nanopore to imitate the polar pore openings and hydrophobic gating regions found in pentameric ligand-gated ion channels. Molecular-dynamics simulations were then performed using both a non-polarizable force field and the electronic-continuum-correction method to investigate the behavior of water, Na+, and Cl- ions confined within the hydrophobic region of the nanopore. Number-density distributions revealed preferential Cl- adsorption to the hydrophobic pore walls, with this interfacial layer largely devoid of Na+. Free-energy profiles for Na+ and Cl- permeating the pore also display an energy-barrier reduction associated with the localization of Cl- to this hydrophobic interface, and the hydration-number profiles reflect a corresponding reduction in the first hydration shell of Cl-. Crucially, these ion effects were only observed through inclusion of effective polarization, which therefore suggests that polarizability may be essential for an accurate description for the behavior of ions and water within hydrophobic nanoscale pores, especially those that conduct Cl-.

Ion and water interactions with a biomimetic nanopore: molecular dynamics with effective polarization

Interactions of ions and water at hydrophobic interfaces are suggested to play a key role in biological anion transport. Molecular dynamics (MD) have revealed the surface affinity for polarizable anions to aqueous/hydrophobic interfaces through the inclusion of polarization. Classical force fields neglect electronic polarizability which in turn dismisses the effects of electronic shielding and overestimates the strength of interactions between interacting charges. The electronic continuum correction (ECC) is a mean-field approach used to achieve an approximation to polarization effects in non-polarizable (NP) force fields by rescaling ionic charge and, more recently, the ionic van der Waals parameters (ECCR).

Prosecco: polarization reintroduced by optimal scaling of electronic continuum correction origin in MD simulations

Molecular dynamics (MD) is a powerful microscope that allows studying molecular processes in silico at atomistic resolution. The accessible timescales (sub-millisecond) and size scales (sub-micrometer) are hardly accessible by most experimental techniques. Still, its primary focus of concern is the accuracy given by the models they rely on. Faulty models result in wrong results. MD models have improved significantly in the last decade. Despite their impressive performance, classical nonpolarizable MD possess intrinsic limitations.

Lithium-ion distribution and motion in two-dimensional covalent organic frameworks: the example of TAPB-PDA COF

Efficient molecular dynamics simulations with electronic continuum correction show that ion clusters form inside covalent organic frameworks, resulting in noncontinuous pathways detrimental to Li+ transport.

Influence of Hydrophobicity on Anion Selectivity

Hydrophobic interfaces play a central role in biological anion transport. Crystal structures of ion channels and transporter proteins have recently suggested that chloride ions may form favourable interactions with hydrophobic pore-lining sidechains. Molecular dynamics (MD) have revealed the surface affinity of polarizable anions to hydrophobic/water interfaces through the inclusion of polarisation. Classical force fields neglect electronic polarisability which in turn dismisses the effects of electronic shielding and overestimates the strength of interactions between interacting charges. The electronic continuum correction (ECC) is a mean-field approach for approximating polarisation effects and is achieved by simply rescaling ionic charges in non-polarisable force fields. Here, we used MD simulations to investigate the behavior of water, sodium and chloride ions in a model hydrophobic nanopore by constructing a modified carbon nanotube (CNT). The distributions of ions and water relative to the nanopore walls were analysed and compared for simulations with and without the use of ECC. Radial density profiles revealed an internal layer-by-layer structure of ions and water, with chloride ions showing a preference for the hydrophobic pore walls. A similar yet stronger effect is seen with ECC. Our findings provide insight into the localisation of chloride ions to hydrophobic surfaces in nanopore geometries which contributes to our understanding of anion permeation and selectivity in biological ion channels.

A practical guide to biologically relevant molecular simulations with charge scaling for electronic polarization.

Molecular simulations can elucidate atomistic-level mechanisms of key biological processes, which are often hardly accessible to experiment. However, the results of the simulations can only be as trustworthy as the underlying simulation model. In many of these processes, interactions between charged moieties play a critical role. Current empirical force fields tend to overestimate such interactions, often in a dramatic way, when polyvalent ions are involved. The source of this shortcoming is the missing electronic polarization in these models. Given the importance of such biomolecular systems, there is great interest in fixing this deficiency in a computationally inexpensive way without employing explicitly polarizable force fields. Here, we review the electronic continuum correction approach, which accounts for electronic polarization in a mean-field way, focusing on its charge scaling variant. We show that by pragmatically scaling only the charged molecular groups, we qualitatively improve the charge-charge interactions without extra computational costs and benefit from decades of force field development on biomolecular force fields.

Pressure in Molecular Simulations with Scaled Charges. 1. Ionic Systems.

Charge scaling, rationalized as MDEC (molecular dynamics in electronic continuum) or ECC (electronic continuum correction), has become a widely used simple approach to how to avoid self-consistent induced dipoles yet approximately take into account the effects of electronic polarizability. It has been assumed that the continuum permittivity does not depend on density; in turn, pressure is calculated by standard formulas. In this work, we elaborate a complementary approximation of density-independent molecular polarizability and derive formulas for pressure corrections within the MDEC framework; real behavior lies between these two extremes. The pressure corrections for test ionic systems are huge and negative, leading to sizable densities in constant-pressure MDEC simulations. A comparison of MDEC results with equivalent polarizable systems gives a good pressure match for a crystal but very low MDEC pressures for ionic liquids. These results witness about the importance of a correct density dependence not only of continuum permittivity in MDEC simulations but also of polarizability in polarizable simulations.

Molecular modeling of aqueous electrolytes at interfaces: Effects of long-range dispersion forces and of ionic charge rescaling.

Molecular dynamics simulations of aqueous electrolytes generally rely on empirical force fields, combining dispersion interactions-described by a truncated Lennard-Jones (LJ) potential-and electrostatic interactions-described by a Coulomb potential computed with a long-range solver. Recently, force fields using rescaled ionic charges [electronic continuum correction (ECC)], possibly complemented with rescaling of LJ parameters [ECC rescaled (ECCR)], have shown promising results in bulk, but their performance at interfaces has been less explored. Here, we started by exploring the impact of the LJ potential truncation on the surface tension of a sodium chloride aqueous solution. We show a discrepancy between the numerical predictions for truncated LJ interactions with a large cutoff and for untruncated LJ interactions computed with a long-range solver, which can bias comparison of force field predictions with experiments. Using a long-range solver for LJ interactions, we then show that an ionic charge rescaling factor chosen to correct long-range electrostatic interactions in bulk accurately describes image charge repulsion at the liquid-vapor interface, and the rescaling of LJ parameters in ECCR models-aimed at capturing local ion-ion and ion-water interactions in bulk- describes well the formation of an ionic double layer at the liquid-vapor interface. Overall, these results suggest that the molecular modeling of aqueous electrolytes at interfaces would benefit from using long-range solvers for dispersion forces and from using ECCR models, where the charge rescaling factor should be chosen to correct long-range electrostatic interactions.

Electronic continuum correction without scaled charges

In recent years the “Pandora's box” of charges used in classical simulations of nonpolarizable molecular models, especially for aqueous solutions and ionic liquids, has been opened. Particularly we refer to the Electronic continuum correction (ECC) model that suggests applying scaled down charges of ions and tearing down the ‘dogma’ of identical charges used to describe the potential energy surfaces (PES) and dipole moment surface (DMS). We elaborate on both ideas and integrate them into a consistent description of ‘real’ atomic charges of water and ions, which does not necessarily need to violate the ‘dogma’. We promote ECCε approach directly incorporating the electronic polarizability into screening of electrostatic interactions, avoiding the use of scaled charges, which perplex the comparison with experiment, ab initio or polarizable models and are cumbersome for interactions with external electric or magnetic fields. We conclude that none of the existing nonpolarizable water models is fully consistent with the continuum electronic polarizability and stimulate a quest for a better model implementing ECCε ideas.

Benefits of the Electronic Continuum Correction in Bio-Force Fields

The interplay between charged groups in biosystems is ubiquitous. They are crucial when considering ions, but also for many other biomolecules. Interestingly, the amount of evidence suggesting an overestimation of the interaction between charged groups in classical molecular dynamics (MD) simulations for biosystems keeps increasing. Notorious examples are lipid membranes, proteins rich in charged amino acids, and even charged sugar biopolymers when interacting with other charged species. Furthermore, the overestimation is especially dramatic when interacting with divalent ions like Ca2+. MD force fields have started to introduce empirical corrections (NBFIX). These corrections artificially increase the interatomic distance between charged atoms, effectively reducing overbinding. There is, however, a reason behind the overbinding. MD simulations can correctly capture the nuclear part of the molecular polarization, which wants to orient any molecule to the local electric field. However, they miss the electronic polarizability, which ultimately shields interacting charges. The electronic continuum correction (ECC) can recover this missing contribution. This mean-field approach provides a cheap while physically sound fix that mostly consists of scaling down the partial charges within a charged group. In this work, we present the ECC correction for the widely used CHARMM36 force field. We provide five lipid families (PI, PC, PE, PS, and PG), charged amino acids, and few sugar moieties (Glucuronic, iduronic and sialic acids). We show that the ECC correction dramatically improves their interaction with other charged groups when comparing to osmotic coefficients or NMR data. We also show that the resulting molecular structure is not worsened as compared to the original force field. Occasionally, the structure is even improved when benchmarked against experimental Raman/NMR spectra of the moieties in solution. Overall, our results show how CHARMM36 can benefit from the adoption of the ECC approach for future improvements.

Accurate Biomolecular Simulations Account for Electronic Polarization.

In this perspective, we discuss where and how accounting for electronic many-body polarization affects the accuracy of classical molecular dynamics simulations of biomolecules. While the effects of electronic polarization are highly pronounced for molecules with an opposite total charge, they are also non-negligible for interactions with overall neutral molecules. For instance, neglecting these effects in important biomolecules like amino acids and phospholipids affects the structure of proteins and membranes having a large impact on interpreting experimental data as well as building coarse grained models. With the combined advances in theory, algorithms and computational power it is currently realistic to perform simulations with explicit polarizable dipoles on systems with relevant sizes and complexity. Alternatively, the effects of electronic polarization can also be included at zero additional computational cost compared to standard fixed-charge force fields using the electronic continuum correction, as was recently demonstrated for several classes of biomolecules.

Improved Cation Binding to Lipid Bilayers with Negatively Charged POPS by Effective Inclusion of Electronic Polarization.

Phosphatidylserine (PS) lipids are important signaling molecules and the most common negatively charged lipids in eukaryotic membranes. The signaling can be often regulated by calcium, but its interactions with PS headgroups are not fully understood. Classical molecular dynamics (MD) simulations can potentially give detailed description of lipid-ion interactions, but the results strongly depend on the used force field. Here, we apply the electronic continuum correction (ECC) to the Amber Lipid17 parameters of 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-l-serine (POPS) lipid to improve its interactions with K+, Na+, and Ca2+ ions. The partial charges of the headgroup, glycerol backbone, and carbonyls of POPS, bearing a unit negative charge, were scaled with a factor of 0.75, derived for monovalent ions, and the Lennard-Jones σ parameters of the same segments were scaled with a factor of 0.89. The resulting ECC-POPS model gives more realistic interactions with Na+ and Ca2+ cations than the original Amber Lipid17 parameters when validated using headgroup order parameters and the "electrometer concept". In ECC-lipids simulations, populations of complexes of Ca2+ cations with more than two PS lipids are negligible, and interactions of Ca2+ cations with only carboxylate groups are twice more likely than with only phosphate groups, while interactions with carbonyls almost entirely involve other groups as well. Our results pave the way for more realistic MD simulations of biomolecular systems with anionic membranes, allowing signaling processes involving PS and Ca2+ to be elucidated.

Overbinding and Qualitative and Quantitative Changes Caused by Simple Na+ and K+ Ions in Polyelectrolyte Simulations: Comparison of Force Fields with and without NBFIX and ECC Corrections.

Overbinding of ions is a common and well-known problem in classical molecular dynamics simulations. One of its main causes is the absence of electronic polarizability in the force fields. The current approaches for minimizing overbinding typically either retain the original charges and use an ad hoc readjustment of the Lennard-Jones parameters as done in the nonbonded fix (NBFIX) approach or rescale the charges using a theoretical framework. The goal in the latter is to include shielding produced by the missing electronic polarizability as done in the electronic continuum correction (ECC) approach. NBFIX and ECC are the most common corrections, and we compare their performance to the default parameterizations provided by five different commonly used biomolecular force fields, OPLS-AA/L, CHARMM27, CHARMM36m, CHARMM22*, and AMBER99SB-ILDN. As test systems, we use poly-α,l-glutamic and poly-α,l-aspartic amino acid molecules in explicit water together with Na+ and K+ counterions. We demonstrate that the different force fields yield results that are not only quantitatively but also qualitatively different. The resulting structures of the macroions depend strongly on the model for ions. NBFIX corrections alleviate the problem of overbinding, resulting in extended peptides. The ECC corrections depend nontrivially on the original underlying model, and despite being based on a theoretical framework, they cannot always solve the problem.

Development of Nonbonded Models for Metal Cations Using the Electronic Continuum Correction

The parametrization of classical nonbonded models of metal ions has been widely addressed in the recent years. Despite the continuous development of novel and more physically inspired functional forms, the 12-6 Lennard-Jones plus Coulomb potential is still the most adopted force field in molecular dynamics (MD) codes, owing to its simple form and easy implementation. However, due to the integer formal charge, unpolarizable force fields of ions may suffer from overestimated interatomic electrostatic interactions, leading to nonphysical clustering or repulsion between such full charges. The electronic continuum correction (ECC) can fix this problem through a simple inclusion of solvent polarization effects via ionic charge rescaling. In this work, the development of novel nonbonded models for mono, divalent, and highly charged metal ions is presented. For each metal species, the ionic charge has been scaled, according to the ECC. Lennard-Jones parameters have been optimized using experimental structural and thermodynamic properties as target quantities. Performances of the proposed models are discussed and compared with the literature data, while transferability attitudes among different and well-known water models are evaluated. © 2019 Wiley Periodicals, Inc.

Molecular dynamics simulation, ab initio calculation, and size-selected anion photoelectron spectroscopy study of initial hydration processes of calcium chloride.

To understand the initial hydration processes of CaCl2, we performed molecular simulations employing the force field based on the theory of electronic continuum correction with rescaling. Integrated tempering sampling molecular dynamics were combined with ab initio calculations to overcome the sampling challenge in cluster structure search and refinement. The calculated vertical detachment energies of CaCl2(H2O)n- (n = 0-8) were compared with the values obtained from photoelectron spectra, and consistency was found between the experiment and computation. Separation of the Cl-Ca ion pair is investigated in CaCl2(H2O)n- anions, where the first Ca-Cl ionic bond required 4 water molecules, and both Ca-Cl bonds are broken when the number of water molecules is larger than 7. For neutral CaCl2(H2O)n clusters, breaking of the first Ca-Cl bond starts at n = 5, and 8 water molecules are not enough to separate the two ion pairs. Comparing with the observations on magnesium chloride, it shows that separating one ion pair in CaCl2(H2O)n requires fewer water molecules than those for MgCl2(H2O)n. Coincidentally, the solubility of calcium chloride is higher than that of magnesium chloride in bulk solutions.

Accurate Binding of Sodium and Calcium to a POPC Bilayer by Effective Inclusion of Electronic Polarization.

Binding affinities and stoichiometries of Na+ and Ca2+ ions to phospholipid bilayers are of paramount significance in the properties and functionality of cellular membranes. Current estimates of binding affinities and stoichiometries of cations are, however, inconsistent due to limitations in the available experimental and computational methods. In this work, we improve the description of the binding details of Na+ and Ca2+ ions to a 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) bilayer by implicitly including electronic polarization as a mean field correction, known as the electronic continuum correction (ECC). This is applied by scaling the partial charges of a selected state-of-the-art POPC lipid model for molecular dynamics simulations. Our improved ECC-POPC model reproduces not only the experimentally measured structural parameters for the ion-free membrane, but also the response of lipid headgroup to a strongly bound cationic amphiphile, as well as the binding affinities of Na+ and Ca2+ ions. With our new model, we observe on the one side negligible binding of Na+ ions to POPC bilayer, while on the other side stronger interactions of Ca2+ primarily with phosphate oxygens, which is in agreement with the previous interpretations of the experimental spectroscopic data. The present model results in Ca2+ ions forming complexes with one to three POPC molecules with almost equal probabilities, suggesting more complex binding stoichiometries than those from simple models used to interpret the NMR data previously. The results of this work pave the way to quantitative molecular simulations with realistic electrostatic interactions of complex biochemical systems at cellular membranes.

Does an electronic continuum correction improve effective short-range ion-ion interactions in aqueous solution?

Non-polarizable force fields for hydrated ions not always accurately describe short-range ion-ion interactions, frequently leading to artificial ion clustering in bulk aqueous solutions. This can be avoided by adjusting the nonbonded anion-cation or cation-water Lennard-Jones parameters. This approach has been successfully applied to different systems, but the parameterization is demanding owing to the necessity of separate investigations of each ion pair. Alternatively, polarization effects may effectively be accounted for using the electronic continuum correction (ECC) of Leontyev et al. [J. Chem. Phys. 119, 8024 (2003)], which involves scaling the ionic charges with the inverse square-root of the water high-frequency dielectric permittivity. ECC has proven to perform well for monovalent salts as well as for divalent salts in water. Its performance, however, for multivalent salts with higher valency remains unexplored. The present work illustrates the applicability of the ECC model to trivalent K3PO4 and divalent K2HPO4 in water. We demonstrate that the ECC models, without additional tuning of force field parameters, provide an accurate description of water-mediated interactions between salt ions. This results in predictions of the osmotic coefficients of aqueous K3PO4 and K2HPO4 solutions in good agreement with experimental data. Analysis of ion pairing thermodynamics in terms of contact ion pair (CIP), solvent-separated ion pair, and double solvent-separated ion pair contributions shows that potassium-phosphate CIP formation is stronger with trivalent than with divalent phosphate ions.