Revisiting the hexane-water interface via molecular dynamics simulations using nonadditive alkane-water potentials

Predicting Partition Coefficients of Neutral and Charged Solutes in the Mixed SLES-Fatty Acid Micellar System

Sodium laureth sulfate (SLES) and fatty acids are common ingredients in many cosmetic products. Understanding how neutral and charged fatty acid compounds partition between micellar and water phases is crucial to achieve the optimal design of the product formulation. In this paper, we first study the formation of mixed SLES and fatty acid micelles using molecular dynamics (MD) simulations. Micelle/water partition coefficients of neutral and charged fatty acids are then calculated using COSMOmic as well as a MD approach based on the potential of mean force (PMF) calculations performed using umbrella sampling (US). The combined US/PMF approach was performed with both the additive, non-polarizable CHARMM general force field (CGenFF) and the classical Drude polarizable force field. The partition coefficients for the neutral solutes are shown to be accurately calculated with the COSMOmic and additive CGenFF US/PMF approaches, while only the US/PMF approach with the Drude polarizable force field accurately calculated the experimental partition coefficient of the charged solute. These results indicate the utility of the Drude polarizable force field as a tool for the rational development of mixed micelles.

Surfactant-enhanced heterogeneity of the aqueous interface drives water extraction into organic solvents

Liquid/liquid extraction (LLE) is one of the most industrially relevant separations methods. Adsorbed surfactant is demonstrated to enhance interfacial heterogeneity and lead to water protrusions that form the basis for transport into the organic phase.

Molecular Gibbs Surface Excess and CO2-Hydrate Density Determine the Strong Temperature- and Pressure-Dependent Supercritical CO2-Brine Interfacial Tension

In CO₂ geological storage, the interfacial tension (IFT) between supercritical CO₂ and brine is critical for the storage capacitance design to prevent CO₂ leakage. IFT relies not only on the interfacial molecule properties but also on the environmental conditions at different storage sites. In this paper, supercritical CO₂-NaCl solution systems are modeled at 343-373 K and 6-35 MPa under the salinity of 1.89 mol/L using molecular dynamics simulations. After computing and comparing the molecular density profile across the interface, the atomic radial distribution function, the molecular orientation distribution, the molecular Gibbs surface excess (derived from the molecular density profile), and the CO₂-hydrate number density under the above environmental conditions, we confirm that only the molecular Gibbs surface excess of CO₂ molecules and the CO₂-hydrate number density correlate strongly with the temperature- and pressure-dependent IFTs. We also compute the populations of two distinct CO₂-hydrate structures (T-type and H-type) and attribute the observed dependence of IFTs to the dominance of the more stable, surfactant-like T-type CO₂-hydrates at the interface. On the basis of these new molecular mechanisms behind IFT variations, this study could guide the rational design of suitable injecting environmental pressure and temperature conditions. We believe that the above two molecular-level metrics (Gibbs surface excess and hydrate number density) are of great fundamental importance for understanding the supercritical CO₂-water interface and engineering applications in geological CO₂ storage.

Ionic Effects on Supercritical CO2-Brine Interfacial Tensions: Molecular Dynamics Simulations and a Universal Correlation with Ionic Strength, Temperature, and Pressure

For geological CO2 storage in deep saline aquifers, the interfacial tension (IFT) between supercritical CO2 and brine is critical for the storage security and design of the storage capacitance. However, currently, no predictive model exists to determine the IFT of supercritical CO2 against complex electrolyte solutions involving various mixed salt species at different concentrations and compositions. In this paper, we use molecular dynamics (MD) simulations to investigate the effect of salt ions on the incremental IFT at the supercritical CO2-brine interface with respect to that at the reference supercritical CO2-water interface. Supercritical CO2-NaCl solution, CO2-CaCl2 solution and CO2-(NaCl+CaCl2) mixed solution systems are simulated at 343 K and 20 MPa under different salinities and salt compositions. We find that the valence of the cations is the primary contributor to the variation in IFT, while the Lennard-Jones potentials for the cations pose a smaller impact on the IFT. Interestingly, the incremental IFT exhibits a general linear correlation with the ionic strength in the above three electrolyte systems, and the slopes are almost identical and independent of the solution types. Based on this finding, a universal predictive formula for IFTs of CO2-complex electrolyte solution systems is established, as a function of ionic strength, temperature, and pressure. The predicted IFTs using the established formula agree perfectly (with a high statistical confidence level of ∼96%) with a wide range of experimental data for CO2 interfacing with different electrolyte solutions, such as those involving MgCl2 and Na2SO4. This work provides an efficient and accurate route to directly predict IFTs in supercritical CO2-complex electrolyte solution systems for practical engineering applications, such as geological CO2 sequestration in deep saline aquifers and other interfacial systems involving complex electrolyte solutions.

Origin of Asymmetric Solvation Effects for Ions in Water and Organic Solvents Investigated Using Molecular Dynamics Simulations: The Swain Acity-Basity Scale Revisited

The asymmetric solvation of ions can be defined as the tendency of a solvent to preferentially solvate anions over cations or cations over anions, at identical ionic charge magnitudes and effective sizes. Taking water as a reference, these effects are quantified experimentally for many solvents by the relative acity (A) and basity (B) parameters of the Swain scale. The goal of the present study is to investigate the asymmetric solvation of ions using molecular dynamics simulations, and to connect the results to this empirical scale. To this purpose, the charging free energies of alkali and halide ions, and of their hypothetical oppositely charged counterparts, are calculated in a variety of solvents. In a first set of calculations, artificial solvent models are considered that present either a charge or a shape asymmetry at the molecular level. The solvation asymmetry, probed by the difference in charging free energy between the two oppositely charged ions, is found to encompass a term quadratic in the ion charge, related to the different solvation structures around the anion and cation, and a term linear in the ion charge, related to the solvation structure around the uncharged ion-sized cavity. For these simple solvent models, the two terms are systematically counteracting each other, and it is argued that only the quadratic term should be retained when comparing the results of simulations involving physical solvents to experimental data. In a second set of calculations, 16 physical solvents are considered. The theoretical estimates for the acity A are found to correlate very well with the Swain parameters, whereas the correlation for B is very poor. Based on this observation, the Swain scale is reformulated into a new scale involving an asymmetry parameter Σ, positive for acitic solvents and negative for basitic ones, and a polarity parameter Π. This revised scale has the same predictive power as the original scale, but it characterizes asymmetry in an absolute sense, the atomistic simulations playing the role of an extra-thermodynamic assumption, and is optimally compatible with the simulation results. Considering the 55 solvents in the Swain set, it is observed that a moderate basity (Σ between -0.9 and -0.3, related to electronic polarization) represents the baseline for most solvents, while a highly variable acity (Σ between 0.0 and 3.0, related to hydrogen-bond donor capacity modulated by inductive effects) represents a landmark of protic solvents.

Computer modelling of the surface tension of the gas–liquid and liquid–liquid interface

This review presents the state of the art in molecular simulations of interfacial systems and of the calculation of the surface tension from the underlying intermolecular potential.

Quantitative Predictions of the Interfacial Tensions of Liquid-Liquid Interfaces through Atomistic and Coarse Grained Models

We report molecular simulations of oil-water liquid-liquid interfaces by using atomistic and coarse grained (CG) MARTINI force fields. We also apply the electronic continuum (EC) model to the MARTINI force field for the calculation of the interfacial tension of oil/water-salt systems. In a first step, we propose to calculate the interfacial tensions using thermodynamic and mechanical definitions of hydrocarbon-water interfacial systems modified by the addition of salts and alcohol. We also establish here the order of magnitude of the long-range corrections to the interfacial tension in fluid-fluid interfaces. Whereas the atomistic models are able to reproduce quantitatively the interfacial tension and the coexisting densities of oil-water systems, the coarse-description shows some deviations in the prediction of the interfacial tensions. Nevertheless, the physical features of these liquid-liquid interfaces are well-captured by this CG description. The CG force field offers then a very challenging alternative that will require however a more developed calibration of the parameters on the basis of liquid-liquid properties.

A polarizable empirical force field for molecular dynamics simulation of liquid hydrocarbons

Electronic polarizability is usually treated implicitly in molecular simulations, which may lead to imprecise or even erroneous molecular behavior in spatially electronically inhomogeneous regions of systems such as proteins, membranes, interfaces between compounds, or mixtures of solvents. The majority of available molecular force fields and molecular dynamics simulation software packages does not account explicitly for electronic polarization. Even the simplest charge-on-spring (COS) models have only been developed for few types of molecules. In this work, we report a polarizable COS model for cyclohexane, as this molecule is a widely used solvent, and for linear alkanes, which are also used as solvents, and are the precursors of lipids, amino acid side chains, carbohydrates, or nucleic acid backbones. The model is an extension of a nonpolarizable united-atom model for alkanes that had been calibrated against experimental values of the density, the heat of vaporization and the Gibbs free energy of hydration for each alkane. The latter quantity was used to calibrate the parameters governing the interaction of the polarizable alkanes with water. Subsequently, the model was tested for other structural, thermodynamic, dielectric, and dynamic properties such as trans/gauche ratios, excess free energy, static dielectric permittivity, and self-diffusion. A good agreement with the experimental data for a large set of properties for each considered system was obtained, resulting in a transferable set of polarizable force-field parameters for CH2, CH3, and CH4 moieties.

Intermolecular network analysis of the liquid and vapor interfaces of pentane and water: microsolvation does not trend with interfacial properties

Mesoscopic interfacial properties are not correlated to the distribution of microsolvated species and mechanisms (above) for microsolvation at water:pentane interfaces.

QM/MM investigations of organic chemistry oriented questions

About 35 years after its first suggestion, QM/MM became the standard theoretical approach to investigate enzymatic structures and processes. The success is due to the ability of QM/MM to provide an accurate atomistic picture of enzymes and related processes. This picture can even be turned into a movie if nuclei-dynamics is taken into account to describe enzymatic processes. In the field of organic chemistry, QM/MM methods are used to a much lesser extent although almost all relevant processes happen in condensed matter or are influenced by complicated interactions between substrate and catalyst. There is less importance for theoretical organic chemistry since the influence of nonpolar solvents is rather weak and the effect of polar solvents can often be accurately described by continuum approaches. Catalytic processes (homogeneous and heterogeneous) can often be reduced to truncated model systems, which are so small that pure quantum-mechanical approaches can be employed. However, since QM/MM becomes more and more efficient due to the success in software and hardware developments, it is more and more used in theoretical organic chemistry to study effects which result from the molecular nature of the environment. It is shown by many examples discussed in this review that the influence can be tremendous, even for nonpolar reactions. The importance of environmental effects in theoretical spectroscopy was already known. Due to its benefits, QM/MM can be expected to experience ongoing growth for the next decade.In the present chapter we give an overview of QM/MM developments and their importance in theoretical organic chemistry, and review applications which give impressions of the possibilities and the importance of the relevant effects. Since there is already a bunch of excellent reviews dealing with QM/MM, we will discuss fundamental ingredients and developments of QM/MM very briefly with a focus on very recent progress. For the applications we follow a similar strategy.

Bubble bursting as an aerosol generation mechanism during an oil spill in the deep-sea environment: molecular dynamics simulations of oil alkanes and dispersants in atmospheric air/salt water interfaces

Potential of mean force (PMF) calculations and molecular dynamics (MD) simulations were performed to investigate the properties of oil n-alkanes [i.e., n-pentadecane (C15), n-icosane (C20) and n-triacontane (C30)], as well as several surfactant species [i.e., the standard anionic surfactant sodium dodecyl sulfate (SDS), and three model dispersants similar to the Tween and Span species present in Corexit 9500A] at air/salt water interfaces. This study was motivated by the 2010 Deepwater Horizon (DWH) oil spill, and our simulation results show that, from the thermodynamic point of view, the n-alkanes and the model dispersants have a strong preference to remain at the air/salt water interface, as indicated by the presence of deep free energy minima at these interfaces. The free energy minimum of these n-alkanes becomes deeper as their chain length increases, and as the concentration of surfactant species at the interface increases. The n-alkanes tend to adopt a flat orientation and form aggregates at the bare air/salt water interface. When this interface is coated with surfactants, the n-alkanes tend to adopt more tilted orientations with respect to the vector normal to the interface. These simulation results are consistent with the experimental findings reported in the accompanying paper [Ehrenhauser et al., Environ. Sci.: Processes Impacts 2013, in press, (DOI: 10.1039/c3em00390f)]. The fact that these long-chain n-alkanes show a strong thermodynamic preference to remain at the air/salt water interfaces, especially if these interfaces are coated with surfactants, makes these species very likely to adsorb at the surface of bubbles or droplets and be ejected to the atmosphere by sea surface processes such as whitecaps (breaking waves) and bubble bursting. Finally, the experimental finding that more oil hydrocarbons are ejected when Corexit 9500A is present in the system is consistent with the deeper free energy minima observed for the n-alkanes at the air/salt water interface at increasing concentrations of surfactant species.

Advanced potential energy surfaces for condensed phase simulation

Computational modeling at the atomistic and mesoscopic levels has undergone dramatic development in the past 10 years to meet the challenge of adequately accounting for the many-body nature of intermolecular interactions. At the heart of this challenge is the ability to identify the strengths and specific limitations of pairwise-additive interactions, to improve classical models to explicitly account for many-body effects, and consequently to enhance their ability to describe a wider range of reference data and build confidence in their predictive capacity. However, the corresponding computational cost of these advanced classical models increases significantly enough that statistical convergence of condensed phase observables becomes more difficult to achieve. Here we review a hierarchy of potential energy surface models used in molecular simulations for systems with many degrees of freedom that best meet the trade-off between accuracy and computational speed in order to define a sweet spot for a given scientific problem of interest.

Charge equilibration force fields for molecular dynamics simulations of lipids, bilayers, and integral membrane protein systems

With the continuing advances in computational hardware and novel force fields constructed using quantum mechanics, the outlook for non-additive force fields is promising. Our work in the past several years has demonstrated the utility of polarizable force fields, those based on the charge equilibration formalism, for a broad range of physical and biophysical systems. We have constructed and applied polarizable force fields for lipids and lipid bilayers. In this review of our recent work, we discuss the formalism we have adopted for implementing the charge equilibration (CHEQ) method for lipid molecules. We discuss the methodology, related issues, and briefly discuss results from recent applications of such force fields. Application areas include DPPC-water monolayers, potassium ion permeation free energetics in the gramicidin A bacterial channel, and free energetics of permeation of charged amino acid analogs across the water-bilayer interface. This article is part of a Special Issue entitled: Membrane protein structure and function.

Computation of methodology-independent single-ion solvation properties from molecular simulations. III. Correction terms for the solvation free energies, enthalpies, entropies, heat capacities, volumes, compressibilities, and expansivities of solvated ions

The raw single-ion solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions (finite or periodic system, system or box size) and treatment of electrostatic interactions (Coulombic, lattice-sum, or cutoff-based) used during these simulations. However, as shown by Kastenholz and Hünenberger [J. Chem. Phys. 124, 224501 (2006)], correction terms can be derived for the effects of: (A) an incorrect solvent polarization around the ion and an incomplete or/and inexact interaction of the ion with the polarized solvent due to the use of an approximate (not strictly Coulombic) electrostatic scheme; (B) the finite-size or artificial periodicity of the simulated system; (C) an improper summation scheme to evaluate the potential at the ion site, and the possible presence of a polarized air-liquid interface or of a constraint of vanishing average electrostatic potential in the simulated system; and (D) an inaccurate dielectric permittivity of the employed solvent model. Comparison with standard experimental data also requires the inclusion of appropriate cavity-formation and standard-state correction terms. In the present study, this correction scheme is extended by: (i) providing simple approximate analytical expressions (empirically-fitted) for the correction terms that were evaluated numerically in the above scheme (continuum-electrostatics calculations); (ii) providing correction terms for derivative thermodynamic single-ion solvation properties (and corresponding partial molar variables in solution), namely, the enthalpy, entropy, isobaric heat capacity, volume, isothermal compressibility, and isobaric expansivity (including appropriate standard-state correction terms). The ability of the correction scheme to produce methodology-independent single-ion solvation free energies based on atomistic simulations is tested in the case of Na(+) hydration, and the nature and magnitude of the correction terms for derivative thermodynamic properties is assessed numerically.

Solvation effects in phase transitions in soft matter

Phase transitions in polar binary mixtures can be drastically altered by even a small amount of salt. This is because the preferential solvation strongly depends on the ambient composition. Together with a summary of our research on this problem, we present some detailed results on the role of antagonistic salt composed of hydrophilic and hydrophobic ions. These ions tend to segregate at liquid-liquid interfaces and selectively couple to water-rich and oil-rich composition fluctuations, leading to mesophase formation. In our two-dimensional simulation, the coarsening of the domain structures can be stopped or slowed down, depending on the interaction parameter (or the temperature) and the salt density. We realize stripe patterns at the critical composition and droplet patterns at off-critical compositions. In the latter case, charged droplets emerge with considerable size dispersity in a percolated region. We also give the structure factors among the ions, accounting for the Coulomb interaction and the solvation interaction mediated by the composition fluctuations.

Phase-transfer energetics of small-molecule alcohols across the water-hexane interface: molecular dynamics simulations using charge equilibration models

We study the water-hexane interface using molecular dynamics (MD) and polarizable charge equilibration (CHEQ) force fields. Bulk densities for TIP4P-FQ water and hexane, 1.0086±0.0002 and 0.6378±0.0001 g/cm(3), demonstrate excellent agreement with experiment. Interfacial width and interfacial tension are consistent with previously reported values. The in-plane component of the dielectric permittivity (ɛ(||)) for water is shown to decrease from 81.7±0.04 to unity, transitioning longitudinally from bulk water to bulk hexane. ɛ(||) for hexane reaches a maximum in the interface, but this term represents only a small contribution to the total dielectric constant (as expected for a non-polar species). Structurally, net orientations of the molecules arise in the interfacial region such that hexane lies slightly parallel to the interface and water reorients to maximize hydrogen bonding. Interfacial potentials due to contributions of the water and hexane are calculated to be -567.9±0.13 and 198.7±0.01 mV, respectively, giving rise to a total potential in agreement with the range of values reported from previous simulations of similar systems. Potentials of mean force (PMF) calculated for methanol, ethanol, and 1-propanol for the transfer from water to hexane indicate an interfacial free energy minimum, corresponding to the amphiphilic nature of the molecules. The magnitudes of transfer free energies were further characterized from the solvation free energies of alcohols in water and hexane using thermodynamic integration. This analysis shows that solvation free energies for alcohols in hexane are 0.2-0.3 kcal/mol too unfavorable, whereas solvation of alcohols in water is approximately 1 kcal/mol too favorable. For the pure hexane-water interfacial simulations, we observe a monotonic decrease of the water dipole moment to near-vacuum values. This suggests that the electrostatic component of the desolvation free energy is not as severe for polarizable models than for fixed-charge force fields. The implications of such behavior pertain to the modeling of polar and charged solutes in lipidic environments.

Revised Charge Equilibration Parameters for More Accurate Hydration Free Energies of Alkanes

We present a refined alkane charge equilibration (CHEQ) force field, improving our previously reported CHEQ alkane force field[1] to better reproduce experimental hydration free energies. Experimental hydration free energies of ethane, propane, butane, pentane, hexane, and heptane are reproduced to within 3.6% on average. We demonstrate that explicit polarization results in a shift in molecular dipole moment for water molecules associated with the alkane molecule. We also show that our new parameters do not have a significant effect on the alkane-water interactions as measured by the radial distribution function (RDF).

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 modelling 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 Langrangian 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. CCl(4), 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.

Polarization effects in molecular mechanical force fields

The focus here is on incorporating electronic polarization into classical molecular mechanical force fields used for macromolecular simulations. First, we briefly examine currently used molecular mechanical force fields and the current status of intermolecular forces as viewed by quantum mechanical approaches. Next, we demonstrate how some components of quantum mechanical energy are effectively incorporated into classical molecular mechanical force fields. Finally, we assess the modeling methods of one such energy component-polarization energy-and present an overview of polarizable force fields and their current applications. Incorporating polarization effects into current force fields paves the way to developing potentially more accurate, though more complex, parameterizations that can be used for more realistic molecular simulations.

CHARMM: the biomolecular simulation program

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

Charge equilibration force fields for lipid environments: applications to fully hydrated DPPC bilayers and DMPC-embedded gramicidin A

Polarizable force fields for lipid and solvent environments are used for molecular dynamics simulations of a fully hydrated dipalmitoylphosphatidylcholine (DPPC) bilayer and gramicidin A (gA) dimer embedded in a dimyristoylphosphatidylcholine (DMPC) bilayer. The lipid bilayer is modeled using the CHARMM charge equilibration (CHEQ) polarizable force field for lipids and the TIP4P-FQ force field to represent solvent. For the DPPC bilayer system, results are compared to the same system simulated using the nonpolarizable CHARMM27r (C27r) force field and TIP3P water. Calculated atomic and electron density profiles, head group orientations as measured by the phosphorus-nitrogen vector orientation, and deuterium order parameters are found to be consistent with previous simulations and with experiment. The CHEQ model exhibits greater water penetration into the bilayer interior, as demonstrated by the potential of mean force calculated from the water density profile. This is a result of the variation of the water molecular dipole from 2.55 D in the bulk to 1.88 D in the interior. We discuss this finding in the context of previous studies (both simulation and experiment) that have investigated the extent of penetration of water into DPPC bilayers. We also discuss the effects of including explicit polarization on the water dipole moment variation as a function of distance from the bilayer. We show distributions of atomic charges over the course of the simulation since the CHEQ model allows the charges to fluctuate. We have calculated the interfacial dipole potential, which the CHEQ model predicts to be 0.95 V compared to 0.86 V as predicted by the C27r model. We also discuss dielectric permittivity profiles and the differences arising between the two models. We obtain bulk values of 72.77 for the CHEQ model (TIP4P-FQ water) and 91.22 for C27r (TIP3P), and values approaching unity in the membrane interior. Finally, we present results of simulations of gA embedded in a DMPC bilayer using the CHEQ model and discuss structural properties.

Molecular dynamics simulations of a DMPC bilayer using nonadditive interaction models

We present a polarizable force field based on the charge-equilibration formalism for molecular dynamics simulations of phospholipid bilayers. We discuss refinement of headgroup dihedral potential parameters to reproduce ab initio conformational energies of dimethylphosphate calculated at the MP2/cc-pVTZ level of theory. We also address the refinement of electrostatic and Lennard-Jones (van der Waals) parameters to reproduce ab initio polarizabilities and water interaction energies of dimethylphosphate and tetramethylammonium. We present results of molecular dynamics simulations of a solvated dimyristoylphosphatidylcholine bilayer using this polarizable force field as well as the nonpolarizable, fixed-charge CHARMM27 and CHARMM27r force fields for comparison. Calculated atomic and electron-density profiles, deuterium order parameters, and headgroup orientations are found to be consistent with previous simulations and with experiment. Polarizable interaction models for solvent and lipid exhibit greater water penetration into the lipid interior; this is due to the variation of water molecular dipole moment from a bulk value of 2.6 Debye to a value of 1.9 Debye in the membrane interior. The reduction in the electrostatic component of the desolvation free-energy penalty allows for greater water density. The surface dipole potential predicted by the polarizable model is 0.95 V compared to the value of 0.8 V based on nonpolarizable force-field calculations. Effects of inclusion of explicit polarization are discussed in relation to water dipole moment and varying charge distributions. Dielectric permittivity profiles for polarizable and nonpolarizable interactions exhibit subtle differences arising from the nature of the individual component parameterizations; for the polarizable force field, we obtain a bulk dielectric permittivity of 79, whereas the nonpolarizable force field plateaus at 97 (the value for pure TIP3P water). In the membrane interior, both models predict unit permittivities, with the polarizable models contributing from one to two more units due to the optical dielectric (high-frequency dipole fluctuations). This contribution is a step toward the continuing development of a CHARMM (Chemistry at Harvard Molecular Mechanics) polarizable force field for simulations of biomacromolecular systems.

On the origin of the electrostatic potential difference at a liquid-vacuum interface

The microscopic origin of the interface potential calculated from computer simulations is elucidated by considering a simple model of molecules near an interface. The model posits that molecules are isotropically oriented and their charge density is Gaussian distributed. Molecules that have a charge density that is more negative toward their interior tend to give rise to a negative interface potential relative to the gaseous phase, while charge densities more positive toward their interior give rise to a positive interface potential. The interface potential for the model is compared to the interface potential computed from molecular dynamics simulations of the nonpolar vacuum-methane system and the polar vacuum-water interface system. The computed vacuum-methane interface potential from a molecular dynamics simulation (-220 mV) is captured with quantitative precision by the model. For the vacuum-water interface system, the model predicts a potential of -400 mV compared to -510 mV, calculated from a molecular dynamics simulation. The physical implications of this isotropic contribution to the interface potential is examined using the example of ion solvation in liquid methane.

Incorporating Phase-Dependent Polarizability in Non-Additive Electrostatic Models for Molecular Dynamics Simulations of the Aqueous Liquid-Vapor Interface

We discuss a new classical water force field that explicitly accounts for differences in polarizability between liquid and vapor phases. The TIP4P-QDP (4-point transferable intermolecular potential with charge dependent-polarizability) force field is a modification of the original TIP4P-FQ fluctuating charge water force field of Rick et al.(1) that self-consistently adjusts its atomic hardness parameters via a scaling function dependent on the M-site charge. The electronegativity (χ) parameters are also scaled in order to reproduce condensed-phase dipole moments of comparable magnitude to TIP4P-FQ. TIP4P-QDP is parameterized to reproduce experimental gas-phase and select condensed-phase properties. The TIP4P-QDP water model possesses a gas phase polarizability of 1.40 Å(3) and gas-phase dipole moment of 1.85 Debye, in excellent agreement with experiment and high-level ab initio predictions. The liquid density of TIP4P-QDP is 0.9954(±0.0002) g/cm(3) at 298 K and 1 atmosphere, and the enthalpy of vaporization is 10.55(±0.12) kcal/mol. Other condensed-phase properties such as the isobaric heat capacity, isothermal compressibility, and diffusion constant are also calculated within reasonable accuracy of experiment and consistent with predictions of other current state-of-the-art water force fields. The average molecular dipole moment of TIP4P-QDP in the condensed phase is 2.641(±0.001) Debye, approximately 0.02 Debye higher than TIP4P-FQ and within the range of values currently surmised for the bulk liquid. The dielectric constant, ε = 85.8 ± 1.0, is 10% higher than experiment. This is reasoned to be due to the increase in the condensed phase dipole moment over TIP4P-FQ, which estimates ε remarkably well. Radial distribution functions for TIP4P-QDP and TIP4P-FQ show similar features, with TIP4P-QDP showing slightly reduced peak heights and subtle shifts towards larger distance interactions. Since the greatest effects of the phase-dependent polarizability are anticipated in regions with both liquid and vapor character, interfacial simulations of TIP4P-QDP were performed and compared to TIP4P-FQ, a static polarizability analog. Despite similar features in density profiles such as the position of the GDS and interfacial width, enhanced dipole moments are observed for the TIP4P-QDP interface and onset of the vapor phase. Water orientational profiles show an increased preference (over TIP4P-FQ) in the orientation of the permanent dipole vector of the molecule within the interface; an enhanced z-induced dipole moment directly results from this preference. Hydrogen bond formation is lower, on average, in the bulk for TIP4P-QDP than TIP4P-FQ. However, the average number of hydrogen bonds formed by TIP4P-QDP in the interface exceeds that of TIP4P-FQ, and observed hydrogen bond networks extend further into the gaseous region. The TIP4P-QDP interfacial potential, calculated to be -11.98(±0.08) kcal/mol, is less favorable than that for TIP4P-FQ by approximately 2% as a result of a diminished quadrupole contribution. Surface tension is calculated within a 1.3% reduction from the experimental value. Results reported demonstrate TIP4P-QDP as a model comparable to the popular TIP4P-FQ while accounting for a physical effect previously neglected by other water models. Further refinements to this model, as well as future applications are discussed.

Revised charge equilibration potential for liquid alkanes

We present a revised liquid alkane force field based on the charge equilibration formalism for incorporating electrostatic nonadditive effects arising from local polarization. The model is a revision of earlier work by Patel and Brooks, specifically addressing deficiencies in the dihedral potential, electrostatic, and Lennard-Jones (van der Waals) parameters of the force field. We discuss refinement of the alkane backbone torsion potential to match high-level ab initio relative conformational energetics for pentane, hexane, and heptane. We further discuss refinement of the electrostatic and Lennard-Jones (van der Waals) parameters to reproduce the experimental polarizability, liquid density, and vaporization enthalpy of hexane. Finally, we calculate bulk liquid properties including densities, vaporization enthalpies, self-diffusion constants, isothermal compressibilities, constant pressure heat capacities, and NMR T 1 relaxation times for a series of linear alkanes ranging from hexane to pentadecane based on the current revised model. We also compute free energies of hydration for pentane, hexane, and heptane. The revised force field offers a significantly improved overall description of these properties relative to the original parametrization. The current alkane force field represents a platform for ongoing development of a CHARMM (Chemistry at Harvard Molecular Mechanics) polarizable force field for lipids and integral membrane proteins.

Quantitative computer simulations of biomolecules: A snapshot

A recent workshop titled "Quantitative Computational Biophysics" at Florida State University provided an overview of the state of the art in quantitative modeling of biomolecular systems. The presentations covered a wide range of interrelated topics, including the development and validation of force fields, the modeling of protein-protein interactions, the sampling of conformational space, and the assessment of equilibration and statistical errors. Substantial progress in all these areas was reported.

Long-range Lennard-Jones and electrostatic interactions in interfaces: application of the isotropic periodic sum method

Molecular dynamics (MD) simulations of heptane/vapor, hexadecane/vapor, water/vapor, hexadecane/water, and dipalmitoylphosphatidylcholine (DPPC) bilayers and monolayers are analyzed to determine the accuracy of treating long-range interactions in interfaces with the isotropic periodic sum (IPS) method. The method and cutoff (rc) dependences of surface tensions, density profiles, water dipole orientation, and electrostatic potential profiles are used as metrics. The water/vapor, heptane/vapor, and hexadecane/vapor interfaces are accurately and efficiently calculated with 2D IPS (rc=10 A). It is demonstrated that 3D IPS is not practical for any of the interfacial systems studied. However, the hybrid method PME/IPS [Particle Mesh Ewald for electrostatics and 3D IPS for Lennard-Jones (LJ) interactions] provides an efficient way to include both types of long-range forces in simulations of large liquid/vacuum and all liquid/liquid interfaces, including lipid monolayers and bilayers. A previously published pressure-based long-range LJ correction yields results similar to those of PME/IPS for liquid/liquid interfaces. The contributions to surface tension of LJ terms arising from interactions beyond 10 A range from 13 dyn/cm for the hexadecane/vapor interface to approximately 3 dyn/cm for hexadecane/water and DPPC bilayers and monolayers. Surface tensions of alkane/vapor, hexadecane/water, and DPPC monolayers based on the CHARMM lipid force fields agree very well with experiment, whereas surface tensions of the TIP3P and TIP4P-Ew water models underestimate experiment by 16 and 11 dyn/cm, respectively. Dipole potential drops (DeltaPsi) are less sensitive to long-range LJ interactions than surface tensions. However, DeltaPsi for the DPPC bilayer (845+/-3 mV proceeding from water to lipid) and water (547+/-2 mV for TIP4P-Ew and 521+/-3 mV for TIP3P) overestimate experiment by factors of 3 and 5, respectively, and represent expected deficiencies in nonpolarizable force fields.