The Importance of Excluded Solvent Volume Effects in Computing Hydration Free Energies

Why oppositely charged ions of equal radii have different heats of hydration?

Looking for the answer to the title question a number of oversimplifications of the Born model of ion hydration are discussed. They involved: ionic radius, dielectric saturation, structure of water molecules around ions and the nature of ion-water interactions. On the basis of recent literature the last factor-pure electrostatic interactions of alkali metal cations with water molecules but hydrogen bonding of halide anions-has been found to decide on the minimum energy of interactions, the charge transferred between interacting species in equilibrium and the distance between them. Thus, different nature of interactions for cations and anions explains difference in their hydration heats as well as the observation that solvent-solvent interactions in hydrogen bond donor solvents give the important contribution to solvation heats only for anions.

Incorporating excluded solvent volume and physical dipoles for computing solvation free energy

The solvation free energy described using the Born equation depends on the solute charge, solute radius, and solvent dielectric constant. However, the dielectric polarization derived from Gauss's law used in the Born equation differs from that obtained from molecular dynamics simulations. Therefore, the adjustment of Born radii is insufficient for fitting the solvation free energy to various solute conformations. In order to mimic the dielectric polarization surrounding a solute in molecular dynamics simulations, the water molecule in the first coordination shell is modeled as a physical dipole in a van der Waals sphere, and the intermediate water is treated as a bulk solvent. The electric dipole of the first-shell water is modeled as positive and negative surface charge layers with fixed charge magnitudes, but with variable separation distance as derived from the distributions of hydrogen and oxygen atoms of water dictated by their orientational distribution functions. An equation that describes the solvation free energy of ions using this solvent scheme with a TIP3P water model is derived, and the values of the solvation free energies of ions estimated from this derived equation are found to be similar to those obtained from the experimental data.

Incorporating the excluded solvent volume and surface charges for computing solvation free energy

Gauss's law or Poisson's equation is conventionally used to calculate solvation free energy. However, the near-solute dielectric polarization from Gauss's law or Poisson's equation differs from that obtained from molecular dynamics (MD) simulations. To mimic the near-solute dielectric polarization from MD simulations, the first-shell water was treated as two layers of surface charges, the densities of which are proportional to the electric field at the solvent molecule that is modeled as a hard sphere. The intermediate water was treated as a bulk solvent. An equation describing the solvation free energy of ions using this solvent scheme was derived using the TIP3P water model.

Strategy using three layers of surface charge for computing solvation free energy of ions

Continuum solvent model is the common used strategy for computing the solvation free energy. However, the dielectric polarization from Gauss's law differs from that obtained from molecular dynamics simulations. To mimic the dielectric polarization surrounding a solute in molecular dynamics simulations, the first-shell water molecule was modeled using a charge distribution of TIP4P molecule in a hard sphere. The dielectric polarization of the first-shell water was modeled as a pair of surface charge layers with a fixed distance between them, but with variable, equal, and opposite charge magnitudes that respond to the electric field on the first-shell water. The water outside the first shell water is treated as a bulk solvent, and the electric effect of the bulk solvent can be modeled as a surface charge. Based on this strategy, the analytical solution describing the solvation free energy of ions was derived, and the values of computed solvation free energy were compared to the values of experiments.

Dependence of interaction free energy between solutes on an external electrostatic field

To explore the athermal effect of an external electrostatic field on the stabilities of protein conformations and the binding affinities of protein-protein/ligand interactions, the dependences of the polar and hydrophobic interactions on the external electrostatic field, -Eext, were studied using molecular dynamics (MD) simulations. By decomposing Eext into, along, and perpendicular to the direction formed by the two solutes, the effect of Eext on the interactions between these two solutes can be estimated based on the effects from these two components. Eext was applied along the direction of the electric dipole formed by two solutes with opposite charges. The attractive interaction free energy between these two solutes decreased for solutes treated as point charges. In contrast, the attractive interaction free energy between these two solutes increased, as observed by MD simulations, for Eext = 40 or 60 MV/cm. Eext was applied perpendicular to the direction of the electric dipole formed by these two solutes. The attractive interaction free energy was increased for Eext = 100 MV/cm as a result of dielectric saturation. The force on the solutes along the direction of Eext computed from MD simulations was greater than that estimated from a continuum solvent in which the solutes were treated as point charges. To explore the hydrophobic interactions, Eext was applied to a water cluster containing two neutral solutes. The repulsive force between these solutes was decreased/increased for Eext along/perpendicular to the direction of the electric dipole formed by these two solutes.

Solution-phase electronegativity scale: insight into the chemical behaviors of metal ions in solution

By incorporating the solvent effect into the Born effective radius, we have proposed an electronegativity scale of metal ions in aqueous solution with the most common oxidation states and hydration coordination numbers in terms of the effective ionic electrostatic potential. It is found that the metal ions in aqueous solution are poorer electron acceptors compared to those in the gas phase. This solution-phase electronegativity scale shows its efficiency in predicting some important properties of metal ions in aqueous solution such as the aqueous acidities of the metal ions, the stability constants of metal complexes, and the solubility product constants of the metal hydroxides. We have elaborated that the standard reduction potential and the solution-phase electronegativity are two different quantities for describing the processes of metal ions in aqueous solution to soak up electrons with different final states. This work provides a new insight into the chemical behaviors of the metal ions in aqueous solution, indicating a potential application of this electronegativity scale to the design of solution reactions.

Fast estimation of solvation free energies for diverse chemical species

The free energy of solvation can play an important or even dominant role in the accurate prediction of binding affinities and various other molecular-scale interaction phenomena critical to the study of biochemical processes. Many research applications for solvation modeling, such as fragment-based drug design, require algorithms that are both accurate and computationally inexpensive. We have developed a calculation of solvation free energy which runs fast enough for interactive applications, functions for a wide range of chemical species relevant to simulating molecules for biological and pharmaceutical applications, and is readily extended when data for new species becomes available. We have also demonstrated that the incorporation of ab initio data provides necessary access to sufficient reference data for a broad range of chemical features. Our empirical model, including an electrostatic term and a different set of atom types, demonstrates improvements over a previous, solvent-accessible surface area-only model by Wang et al. when fit to identical training sets (mean absolute error of 0.513 kcal/mol versus the 0.538 kcal/mol reported by Wang). The incorporation of ab initio solvation free energies provides a significant increase in the breadth of chemical features for which the model can be applied by introducing classes of compounds for which little or no experimental data is available. The increased breadth and the speed of this solvation model allow for conformational minimization, conformational search, and ligand binding free energy calculations that economically account for the complex interplay of bonded, nonbonded, and solvation free energies as conformations with varying solvent-accessible surfaces are sampled.

The Born Formula Describes Enthalpy of Ions Solvation

The process of ion solvation has been studied in the reversible system using the Van't Hoff equilibrium box. It is shown that the Born formula for solvation energy describes a change in enthalpy rather than in Gibbs energy.

Discrepancy in the near-solute electric dipole moment calculated from the electric field

The electric dipole moment p(r) was computed as the integral of the permanent dipole moment of the solvent molecule μ(r) weighted by the orientational probability distribution Ω(r;O) over all orientations, where O is the orientation of the solvent molecule at r. The relationship between Ω(r;O) and the potential of the mean torque was derived; p(r) is proportional to the electric field E(r) under the following assumptions: (1) the van der Waals (vdW) interaction is independent of the orientation of the solvent molecule at r; (2) the solvent molecule and its electrical effect are modeled as a point dipole moment; (3) the solvent molecule at r is in a region far from the solute; and (4) μE(r) ≪ k(B) T, where k(B) is Boltzmann's constant and T is absolute temperature. The errors caused by calculating near-solute Ω(r) and p(r) from E(r) are unclear. The results show that Ω(r) is inconsistent with the value calculated from E(r) for water molecules in the first and second shells of solute with charge state Q = ±1 e, and a large variation in solvent molecular polarizability γ(mol) (r), which appeared in the first valley of 4πr(2) E(r) for |Q| < 1 e. Nonetheless, p(r) is consistent with the values calculated from E(r) for |Q| ≤ 1 e. The implication is that the assumptions for calculating p(r) can be ignored in the calculation of the solvation free energy of biomolecules, as they pertain to protein folding and protein-protein/ligand interactions.

Quasichemical and structural analysis of polarizable anion hydration

Quasichemical theory is utilized to analyze the relative roles of solute polarization and size in determining the structure and thermodynamics of bulk anion hydration for the Hofmeister series Cl(-), Br(-), and I(-). Excellent agreement with experiment is obtained for whole salt hydration free energies using the polarizable AMOEBA force field. The total hydration free energies display a stronger dependence on ion size than on polarizability. The quasichemical approach exactly partitions the solvation free energy into inner-shell, outer-shell packing, and outer-shell long-ranged contributions by means of a hard-sphere condition. The inner-shell contribution becomes slightly more favorable with increasing ion polarizability, indicating electrostriction of the nearby waters. Small conditioning radii, even well inside the first maximum of the ion-water(oxygen) radial distribution function, result in Gaussian behavior for the long-ranged contribution that dominates the ion hydration free energy. This in turn allows for a mean-field treatment of the long-ranged contribution, leading to a natural division into first-order electrostatic, induction, and van der Waals terms. The induction piece exhibits the strongest ion polarizability dependence, while the larger-magnitude first-order electrostatic piece yields an opposing but weaker polarizability dependence. The van der Waals piece is small and positive, and it displays a small ion specificity. The sum of the inner-shell, packing, and long-ranged van der Waals contributions exhibits little variation along the anion series for the chosen conditioning radii, targeting electrostatic effects (influenced by ion size) as the largest determinant of specificity. In addition, a structural analysis is performed to examine the solvation anisotropy around the anions. As opposed to the hydration free energies, the solvation anisotropy depends more on ion polarizability than on ion size: increased polarizability leads to increased anisotropy. The water dipole moments near the ion are similar in magnitude to bulk water, while the ion dipole moments are found to be significantly larger than those observed in quantum mechanical studies. Possible impacts of the observed over-polarization of the ions on simulated anion surface segregation are discussed.