Hydration Mimicry by Membrane Ion Channels.

Ions transiting biomembranes might pass readily from water through ion-specific membrane proteins if these protein channels provide environments similar to the aqueous solution hydration environment. Indeed, bulk aqueous solution is an important reference condition for the ion permeation process. Assessment of this hydration mimicry concept depends on understanding the hydration structure and free energies of metal ions in water in order to provide a comparison for the membrane channel environment. To refine these considerations, we review local hydration structures of ions in bulk water and the molecular quasi-chemical theory that provides hydration free energies. In doing so, we note some current views of ion binding to membrane channels and suggest new physical chemical calculations and experiments that might further clarify the hydration mimicry concept.

Quasi-Chemical Theory with Cluster Sampling from Ab Initio Molecular Dynamics: Fluoride (F-) Anion Hydration.

Accurate predictions of the hydration free energy for anions typically has been more challenging than that for cations. Hydrogen bond donation to the anion in hydrated clusters such as F(H2O) n - can lead to delicate structures. Consequently, the energy landscape contains many local minima, even for small clusters, and these minima present a challenge for computational optimization. Utilization of cluster experimental results for the free energies of gas-phase clusters shows that even though anharmonic effects are interesting they need not be of troublesome magnitudes for careful applications of quasi-chemical theory to ion hydration. Energy-optimized cluster structures for anions can leave the central ion highly exposed, and application of implicit solvation models to these structures can incur more serious errors than those for metal cations. Utilizing cluster structures sampled from ab initio molecular dynamics simulations substantially fixes those issues.

Comparison of single-ion molecular dynamics in common solvents.

Laying a basis for molecularly specific theory for the mobilities of ions in solutions of practical interest, we report a broad survey of velocity autocorrelation functions (VACFs) of Li+ and PF6- ions in water, ethylene carbonate, propylene carbonate, and acetonitrile solutions. We extract the memory function, γ(t), which characterizes the random forces governing the mobilities of ions. We provide comparisons controlling for the effects of electrolyte concentration and ion-pairing, van der Waals attractive interactions, and solvent molecular characteristics. For the heavier ion (PF6-), velocity relaxations are all similar: negative tail relaxations for the VACF and a clear second relaxation for γt, observed previously also for other molecular ions and with n-pentanol as the solvent. For the light Li+ ion, short time-scale oscillatory behavior masks simple, longer time-scale relaxation of γt. But the corresponding analysis of the solventberg Li+H2O4 does conform to the standard picture set by all the PF6- results.

Concentration dependence of the Flory-Huggins interaction parameter in aqueous solutions of capped PEO chains.

The dependence on volume fraction φ of the Flory-Huggins interaction parameter χwp(φ) describing the free energy of mixing of polymers in water is obtained by exploiting the connection of χwp(φ) to the chemical potential of the water, for which quasi-chemical theory is satisfactory. We test this theoretical approach with simulation data for aqueous solutions of capped PEO (polyethylene oxide) oligomers. For CH3(CH2-O-CH2)mCH3 (m = 11), χwp(φ) depends strongly on φ, consistent with experiment. These results identify coexisting water-rich and water-poor solutions at T = 300 K and p = 1 atm. Direct observation of the coexistence of these two solutions on simulation time scales supports that prediction for the system studied. This approach directly provides the osmotic pressures. The osmotic second virial coefficient for these chains is positive, reflecting repulsive interactions between the chains in the water, a good solvent for these chains.

Pairing of 1-hexyl-3-methylimidazolium and tetrafluoroborate ions in n-pentanol.

Molecular dynamics simulations are obtained and analyzed to study pairing of 1-hexyl-3-methylimidazolium and tetrafluoroborate ions in n-pentanol, in particular by evaluating the potential-of-mean-force between counter ions. The present molecular model and simulation accurately predicts the dissociation constant K(d) in comparison to experiment, and thus the behavior and magnitudes for the ion-pair potential-of-mean-force at molecular distances, even though the dielectric constant of the simulated solvent differs from the experimental value by about 30%. A naive dielectric model does not capture molecule structural effects such as multiple conformations and binding geometries of the Hmim(+) and BF(4)(-) ion-pairs. Mobilities identify multiple time-scale effects in the autocorrelation of the random forces on the ions, and specifically a slow, exponential time-decay of those long-ranged forces associated here with dielectric friction effects.

Effect of PEG end-group hydrophobicity on lysozyme interactions in solution characterized by light scattering.

We compare protein-protein and protein-polymer osmotic virial coefficients measured by static light scattering for aqueous solutions of lysozyme with low-molecular-weight, hydroxy-terminated (hPEG) and methyl-terminated (mPEG) poly(ethylene glycol) at two solution conditions: pH 7.0 and 0.01 M ionic strength, and pH 6.2 and 0.8 M ionic strength. We find that adding PEG to aqueous lysozyme solutions makes a net repulsive contribution to lysozyme-lysozyme interactions, independent of ionic strength and PEG end-group hydrophobicity. PEG end-group hydrophobicity has a profound effect on the magnitude of this contribution, however, at low ionic strength where mPEG-lysozyme attractive interactions become significant. The enhanced attractions promote mPEG-lysozyme preferential interactions at the expense of lysozyme self-interactions, which leads to lysozyme-lysozyme interactions that are more repulsive in the presence of mPEG. These preferential interactions also lead to the preferential exclusion of diffusable ions locally around the protein, which results in a pronounced ionic strength dependence of mPEG-mediated lysozyme-lysozyme interactions.

Generalizations of the Fuoss approximation for ion pairing.

An elementary statistical observation identifies generalizations of the Fuoss approximation for the probability distribution function that describes ion clustering in electrolyte solutions. The simplest generalization, equivalent to a Poisson distribution model for inner-shell occupancy, exploits measurable interionic correlation functions, and is correct at the closest pair distances whether primitive electrolyte solutions models or molecularly detailed models are considered, and for low electrolyte concentrations in all cases. With detailed models, these generalizations include nonionic interactions and solvation effects. These generalizations are relevant for computational analysis of bimolecular reactive processes in solution. Comparisons with direct numerical simulation results show that the simplest generalization is accurate for a slightly supersaturated solution of tetraethylammonium tetrafluoroborate in propylene carbonate ([tea][BF(4)]/PC), and also for a primitive model associated with the [tea][BF(4)]/PC results. For [tea][BF(4)]/PC, the atomically detailed results identify solvent-separated nearest-neighbor ion-pairs. This generalization is examined also for the ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF(4)]) where the simplest implementation is less accurate. In this more challenging situation an augmented maximum entropy procedure is satisfactory, and explains the more varied near-neighbor distributions observed in that case.

Shapes of Nonsymmetric Capillary Bridges.

Here we study the shapes of droplets captured between chemically distinct parallel plates. This work is a preliminary step toward characterizing the influence of second-phase bridging between biomolecular surfaces on their solution contacts, i.e., capillary attraction or repulsion. We obtain a simple, variable-separated quadrature formula for the bridge shape. The technical complication of double-ended boundary conditions on the shapes of nonsymmetric bridges is addressed by studying waists in the bridge shape, i.e., points where the bridge silhouette has zero derivative. Waists are generally expected with symmetric bridges, but waist points can serve to characterize shape segments in general cases. We study how waist possibilities depend on the physical input to these problems, noting that these formulas change with the sign of the inside-outside pressure difference of the bridge. These results permit a variety of different interesting shapes, and the development below is accompanied by several examples.

Ion selectivity from local configurations of ligands in solutions and ion channels.

Probabilities of numbers of ligands proximal to an ion lead to simple, general formulae for the free energy of ion selectivity between different media. That free energy does not depend on the definition of an inner shell for ligand-counting, but other quantities of mechanistic interest do. If analysis is restricted to a specific coordination number, then two distinct probabilities are required to obtain the free energy in addition. The normalizations of those distributions produce partition function formulae for the free energy. Quasi-chemical theory introduces concepts of chemical equilibrium, then seeks the probability that is simplest to estimate, that of the most probable coordination number. Quasi-chemical theory establishes the utility of distributions of ligand-number, and sharpens our understanding of quasi-chemical calculations based on electronic structure methods. This development identifies contributions with clear physical interpretations, and shows that evaluation of those contributions can establish a mechanistic understanding of the selectivity in ion channels.

Molecular-Scale Description of SPAN80 Desorption from a Squalane-Water Interface.

Extensive all-atom molecular dynamics calculations on the water-squalane interface for nine different loadings with sorbitan monooleate (SPAN80), at T = 300 K, are analyzed for the surface tension equation of state, desorption free-energy profiles as they depend on loading, and to evaluate escape times for adsorbed SPAN80 into the bulk phases. These results suggest that loading only weakly affects accommodation of a SPAN80 molecule by this squalane-water interface. Specifically, the surface tension equation of state is simple through the range of high tension to high loading studied, and the desorption free-energy profiles are weakly dependent on loading here. The perpendicular motion of the centroid of the SPAN80 headgroup ring is well-described by a diffusional model near the minimum of the desorption free-energy profile. Lateral diffusional motion is weakly dependent on loading. Escape times evaluated on the basis of a diffusional model and the desorption free energies are 7 × 10-2 s (into the squalane) and 3 × 102 h (into the water). The latter value is consistent with desorption times of related lab-scale experimental work.

Molecular Theory and the Effects of Solute Attractive Forces on Hydrophobic Interactions.

The role of solute attractive forces on hydrophobic interactions is studied by coordinated development of theory and simulation results for Ar atoms in water. We present a concise derivation of the local molecular field (LMF) theory for the effects of solute attractive forces on hydrophobic interactions, a derivation that clarifies the close relation of LMF theory to the EXP approximation applied to this problem long ago. The simulation results show that change from purely repulsive atomic solute interactions to include realistic attractive interactions diminishes the strength of hydrophobic bonds. For the Ar-Ar rdfs considered pointwise, the numerical results for the effects of solute attractive forces on hydrophobic interactions are opposite in sign and larger in magnitude than predicted by LMF theory. That comparison is discussed from the point of view of quasichemical theory, and it is suggested that the first reason for this difference is the incomplete evaluation within LMF theory of the hydration energy of the Ar pair. With a recent suggestion for the system-size extrapolation of the required correlation function integrals, the Ar-Ar rdfs permit evaluation of osmotic second virial coefficients B2. Those B2's also show that incorporation of attractive interactions leads to more positive (repulsive) values. With attractive interactions in play, B2 can change from positive to negative values with increasing temperatures. This is consistent with the puzzling suggestions of decades ago that B2 ≈ 0 for intermediate cases of temperature or solute size. In all cases here, B2 becomes more attractive with increasing temperature.

Loop-Closure and Gaussian Models of Collective Structural Characteristics of Capped PEO Oligomers in Water.

Parallel-tempering MD results for a CH3(CH2-O-CH2)mCH3 chain in water are exploited as a database for analysis of collective structural characteristics of the PEO globule with a goal of defining models permitting statistical thermodynamic analysis of dispersants of Corexit type. The chain structure factor, relevant to neutron scattering from a deuterated chain in null water, is considered specifically. The traditional continuum-Gaussian structure factor is inconsistent with the simple k → ∞ behavior, but we consider a discrete-Gaussian model that does achieve that consistency. Shifting and scaling the discrete-Gaussian model helps to identify the low-k to high-k transition near k ≈ 2π/0.6 nm when an empirically matched number of Gaussian links is about one-third of the total number of effective atom sites. This short distance-scale boundary of 0.6 nm is directly verified with the r space distributions, and this distance is thus identified with a natural size for coarsened monomers. The probability distribution of Rg(2) is compared with the classic predictions for both the Gaussian model and freely jointed chains. ⟨Rg(2)(j)⟩, the contribution of the jth chain segment to ⟨Rg(2)⟩, depends on the contour index about as expected for Gaussian chains despite significant quantitative discrepancies that express the swelling of these chains in water. Monomers central to the chain contour occupy the center of the chain globule. The density profiles of chain segments relative to their center of mass can show distinctive density structuring for smaller chains due to the close proximity of central elements to the globule center. However, that density structuring washes out for longer chains where many chain elements additively contribute to the density profiles. Gaussian chain models thus become more satisfactory for the density profiles for longer chains.

Temperature dependence of the solubility of non-polar gases in water.

An explanation is provided for the experimentally observed temperature dependence of the solubility and the solubility minimum of non-polar gases in water. The influence of solute size and solute-water attractive interactions on the solubility minimum temperature is investigated. The transfer of a non-polar solute from the ideal gas into water is divided into two steps: formation of a cavity in water with the size and shape of the solute and insertion of the solute in this cavity which is equivalent to 'turning on' solute-water attractive interactions. This two step process divides the excess chemical potential of the non-polar solute in water into repulsive and attractive contributions, respectively. The reversible work for cavity formation is modeled using an information theory model of hydrophobic hydration. Attractive contributions are calculated by modeling the water structure in the vicinity of non-polar solutes. These models make a direct connection between microscopic quantities and macroscopic observables. Moreover, they provide an understanding of the peculiar temperature dependences of the hydration thermodynamics from properties of pure water; specifically, bulk water density and the water oxygen-oxygen radial distribution function.

Solution influence on biomolecular equilibria: nucleic acid base associations.

This paper consists of two parts. In the first part, the general problem of biomolecular equilibria in solution is considered, stressing that molecular interactions ultimately determine the answer to this problem. It is discussed how computer simulation techniques can reliably treat the problem and several pitfalls of computer simulation to be avoided are pointed out. Other approaches based on modeling and conceptual simplifications such as perturbative methods, long-range interaction approximations, surface thermodynamic approaches, and hydration shell models are discussed. In the second part, the results of Monte Carlo calculations on the associations of nucleic acid bases in water and carbon tetrachloride are presented. Stacked self-associations are found to be preferred in water and hydrogen-bonded complexes are favored in nonpolar solutions, in agreement with experimental data. The influence of the solvent on base associations is explained in terms of solute-solvent and solvent-solvent contributions to the total energy. No enthalpic stabilization of the complexes by the solvent was found. The results are used to examine the validity of various approximations discussed in the first part of the paper.

Interaction of a sodium ion with the water liquid-vapor interface.

Molecular dynamics results are presented for the density profile of a sodium ion near the water liquid-vapor interface at 320 K. These results are compared with the predictions of a simple dielectric model for the interaction of a monovalent ion with this interface. The interfacial region described by the model profile is too narrow and the profile decreases too abruptly near the solution interface. Thus, the simple model does not provide a satisfactory description of the molecular dynamics results for ion positions within two molecular diameters from the solution interface where appreciable ion concentrations are observed. These results suggest that surfaces associated with dielectric models of ionic processes at aqueous solution interfaces should be located at least two molecular diameters inside the liquid phase. A free energy expense of about 2 kcal/mol is required to move the ion within two molecular layers of the free water liquid-vapor interface.

Multiscale theory in the molecular simulation of electrolyte solutions.

To define a role for AIMD simulation on the limited time and space scales accessible to those demanding methods, this paper organizes McMillan-Mayer theory, the potential distribution approach, and quasi-chemical theory to provide theory for the thermodynamic effects associated with long-length scales. The theory treats composition fluctuations that would be accessed by larger-scale calculations, and also longer-ranged interactions that are of special interest for electrolyte solutions. The quasi-chemical organization breaks-up governing free energies into physically distinct contributions: packing, outer-shell, and chemical contributions. Here we study specifically the outer-shell contributions that express electrolyte screening. For that purpose we adopt a primitive model suggested by observation of ion-pairing in tetraethylammonium tetrafluoroborate dissolved in propylene carbonate. Gaussian statistical models are shown to be effective physical models for outer-shell contributions, and they are conclusive for the free energies within the quasi-chemical formulation. With the present data set the Gaussian physical approximation obtains more accurate mean activity coefficients than does the Bennett direct evaluation of that free energy.