Integral equations in the study of polar and ionic interaction site fluids

Conformation, hydration, and ligand exchange process of ruthenium nitrosyl complexes in aqueous solution: Free-energy calculations by a combination of molecular-orbital theories and different solvent models

Distribution of solvent molecules near transition-metal complex is key information to comprehend the functionality, reactivity, and so forth. However, polarizable continuum solvent models still are the standard and conventional partner of molecular-orbital (MO) calculations in the solution system including transition-metal complex. In this study, we investigate the conformation, hydration, and ligand substitution reaction between NO₂ ^- and H₂ O in aqueous solution for [Ru(NO)(OH)(NO₂ )₄ ]^2- (A), [Ru(NO)(OH)(NO₂ )₃ (ONO)]^2- (B), and [Ru(NO)(OH)(NO₂ )₃ (H₂ O)]^- (C) using a combination method of MO theories and a state-of-the-art molecular solvation technique (NI-MC-MOZ-SCF). A dominant species is found in the complex B conformers and, as expected, different between the solvent models, which reveals that molecular solvation beyond continuum media treatment are required for a reliable description of solvation near transition-metal complex. In the stability constant evaluation of ligand substitution reaction, an assumption that considers the direct association between the dissociated NO₂ ^- and complex C is useful to obtain a reliable stability constant.

Continuum Electrostatic Behavior of a 3D-RISM Theory

The electrostatic response underlying the 3D-RISM theory and its general relationship to models in which the solvent is represented in terms of a dielectric continuum are examined. It is found that the theory provides a coherent picture of solvation, although its behavior is not entirely consistent with the trends that are expected in the limit of a large solute. The electrostatic discrepancy is due to the nature of the isotropic pair additive site-site correlation function associated with the susceptibility response of the uniform fluid. The influence of the discrepancy in the magnitude of the solvation free energy is negligible for a solvent with a large dielectric constant.

Potential of Mean Force Calculations of Solute Permeation Across UT-B and AQP1: A Comparison between Molecular Dynamics and 3D-RISM

Membrane channels facilitate the efficient and selective flux of various solutes across biological membranes. A common approach to investigate the selectivity of a channel has been the calculation of potentials of mean force (PMFs) for solute permeation across the pore. PMFs have been frequently computed from molecular dynamics (MD) simulations, yet the three-dimensional reference interaction site model (3D-RISM) has been suggested as a computationally efficient alternative to MD. Whether the two methods yield comparable PMFs for solute permeation has remained unclear. In this study, we calculated potentials of mean force for water, ammonia, urea, molecular oxygen, and methanol across the urea transporter B (UT-B) and aquaporin-1 (AQP1), using 3D-RISM, as well as using MD simulations and umbrella sampling. To allow direct comparison between the PMFs from 3D-RISM and MD, we ensure that all PMFs refer to a well-defined reference area in the bulk or, equivalently, to a well-defined density of channels in the membrane. For PMFs of water permeation, we found reasonable agreement between the two methods, with differences of ≲3 kJ mol-1. In contrast, we found stark discrepancies for the PMFs for all other solutes. Additional calculations confirm that discrepancies between MD and 3D-RISM are not explained by the choice for the closure relation, the definition the reaction coordinate (center of mass-based versus atomic site-based), details of the molecule force field, or fluctuations of the protein. Comparison of the PMFs suggests that 3D-RISM may underestimate effects from hydrophobic solute-channel interactions, thereby, for instance, missing the urea binding sites in UT-B. Furthermore, we speculate that the orientational averages inherent to 3D-RISM might lead to discrepancies in the narrow channel lumen. These findings suggest that current 3D-RISM solvers provide reasonable estimates for the PMF for water permeation, but that they are not suitable to study the selectivity of membrane channels with respect to uncharged nonwater solutes.

Evidence for cooperative Na+ and Cl− binding by strongly hydrated l-proline

Strongly hydrated l-proline cooperatively binds Na⁺ and Cl⁻ ions in aqueous solution.

Accelerating the weighted histogram analysis method by direct inversion in the iterative subspace

The weighted histogram analysis method (WHAM) for free energy calculations is a valuable tool to produce free energy differences with the minimal errors. Given multiple simulations, WHAM obtains from the distribution overlaps the optimal statistical estimator of the density of states, from which the free energy differences can be computed. The WHAM equations are often solved by an iterative procedure. In this work, we use a well-known linear algebra algorithm which allows for more rapid convergence to the solution. We find that the computational complexity of the iterative solution to WHAM and the closely-related multiple Bennett acceptance ratio (MBAR) method can be improved by using the method of direct inversion in the iterative subspace. We give examples from a lattice model, a simple liquid and an aqueous protein solution.

Hydration and Ion Binding of the Osmolyte Ectoine

Ectoine is a widespread osmolyte enabling halophilic bacteria to withstand high osmotic stress that has many potential applications ranging from cosmetics to its use as a therapeutic agent. In this contribution, combining experiment and theory, the hydration and ion-binding of this zwitterionic compound was studied to gain information on the functioning of ectoine in particular and of osmolytes in general. Dielectric relaxation spectroscopy was used to determine the effective hydration number of ectoine and its effective dipole moment in aqueous solutions with and without added NaCl. The obtained experimental data were compared with structural results from 1D-RISM and 3D-RISM calculations. It was found that ectoine is strongly hydrated, even in the presence of high salt concentrations. Upon addition of NaCl, ions are bound to ectoine but the formed complexes are not very stable. Interestingly, this osmolyte strongly rises the static relative permittivity of its solutions, shielding thus effectively long-range Coulomb interactions among ions in ectoine-containing solutions. We believe that via this effect, which should be common to all zwitterionic osmolytes, ectoine protects against excessive ions within the cell in addition to its strong osmotic activity protecting against ions outside.

A hybrid framework of first principles molecular orbital calculations and a three-dimensional integral equation theory for molecular liquids: multi-center molecular Ornstein-Zernike self-consistent field approach

In this study, we reported the development of a new quantum mechanics/molecular mechanics (QM/MM)-type framework to describe chemical processes in solution by combining standard molecular-orbital calculations with a three-dimensional formalism of integral equation theory for molecular liquids (multi-center molecular Ornstein-Zernike (MC-MOZ) method). The theoretical procedure is very similar to the 3D-reference interaction site model self-consistent field (RISM-SCF) approach. Since the MC-MOZ method is highly parallelized for computation, the present approach has the potential to be one of the most efficient procedures to treat chemical processes in solution. Benchmark tests to check the validity of this approach were performed for two solute (solute water and formaldehyde) systems and a simple SN2 reaction (Cl(-) + CH3Cl → ClCH3 + Cl(-)) in aqueous solution. The results for solute molecular properties and solvation structures obtained by the present approach were in reasonable agreement with those obtained by other hybrid frameworks and experiments. In particular, the results of the proposed approach are in excellent agreements with those of 3D-RISM-SCF.

Solvation and cavity occupation in biomolecules

BACKGROUND

Solvation density locations are important for protein dynamics and structure. Knowledge of the preferred hydration sites at biomolecular interfaces and those in the interior of cavities can enhance understanding of structure and function. While advanced X-ray diffraction methods can provide accurate atomic structures for proteins, that technique is challenged when it comes to providing accurate hydration structures, especially for interfacial and cavity bound solvent molecules.

METHODS

Advances in integral equation theories which include more accurate methods for calculating the long-ranged Coulomb interaction contributions to the three-dimensional distribution functions make it possible to calculate angle dependent average solvent structure, accurately, around and inside irregular molecular conformations. The proximal radial distribution method provides another approximate method to determine average solvent structures for biomolecular systems based on a proximal or near neighbor solvent distribution that can be constructed from previously collected solvent distributions. These two approximate methods, along with all-atom molecular dynamics simulations are used to determine the solvent density inside the myoglobin heme cavity.

DISCUSSION AND RESULTS

Myoglobin is a good test system for these methods because the cavities are many and one is large, tens of Å(3), but is shown to have only four hydration sites. These sites are not near neighbors which implies that the large cavity must have more than one way in and out.

CONCLUSIONS

Our results show that main solvation sites are well reproduced by all three methods. The techniques also produce a clearly identifiable solvent pathway into the interior of the protein.

GENERAL SIGNIFICANCE

The agreement between molecular dynamics and less computationally demanding approximate methods is encouraging. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

A Cavity Corrected 3D-RISM Functional for Accurate Solvation Free Energies

We show that an Ng bridge function modified version of the three-dimensional reference interaction site model (3D-RISM-NgB) solvation free energy method can accurately predict the hydration free energy (HFE) of a set of 504 organic molecules. To achieve this, a single unique constant parameter was adjusted to the computed HFE of single atom Lennard-Jones solutes. It is shown that 3D-RISM is relatively accurate at predicting the electrostatic component of the HFE without correction but requires a modification of the nonpolar contribution that originates in the formation of the cavity created by the solute in water. We use a free energy functional with the Ng scaling of the direct correlation function [Ng, K. C. J. Chem. Phys.1974, 61, 2680]. This produces a rapid, reliable small molecule HFE calculation for applications in drug design.

Simple electrolyte solutions: comparison of DRISM and molecular dynamics results for alkali halide solutions

Using the dielectrically consistent reference interaction site model (DRISM) of molecular solvation, we have calculated structural and thermodynamic information of alkali-halide salts in aqueous solution, as a function of salt concentration. The impact of varying the closure relation used with DRISM is investigated using the partial series expansion of order-n (PSE-n) family of closures, which includes the commonly used hypernetted-chain equation (HNC) and Kovalenko-Hirata closures. Results are compared to explicit molecular dynamics (MD) simulations, using the same force fields, and to experiment. The mean activity coefficients of ions predicted by DRISM agree well with experimental values at concentrations below 0.5 m, especially when using the HNC closure. As individual ion activities (and the corresponding solvation free energies) are not known from experiment, only DRISM and MD results are directly compared and found to have reasonably good agreement. The activity of water directly estimated from DRISM is nearly consistent with values derived from the DRISM ion activities and the Gibbs-Duhem equation, but the changes in the computed pressure as a function of salt concentration dominate these comparisons. Good agreement with experiment is obtained if these pressure changes are ignored. Radial distribution functions of NaCl solution at three concentrations were compared between DRISM and MD simulations. DRISM shows comparable water distribution around the cation, but water structures around the anion deviate from the MD results; this may also be related to the high pressure of the system. Despite some problems, DRISM-PSE-n is an effective tool for investigating thermodynamic properties of simple electrolytes.

A modified repulsive bridge correction to accurate evaluation of solvation free energy in integral equation theory for molecular liquids

Integral equation theory for molecular liquids is one of the powerful frameworks to evaluate solvation free energy (SFE). Different from molecular simulation methods, the theory computes SFE in an analytical manner. In particular, the correction method proposed by Kovalenko and Hirata [Chem. Phys. Lett. 290, 237 (1998); and J. Chem. Phys. 113, 2793 (2000)] is quite efficient in the accurate evaluation of SFE. However, the application has been limited to aqueous solution systems. In the present study, an improved method is proposed that is applicable to a wide range of solution systems. The SFE of a variety of solute molecules in chloroform and benzene solvents is evaluated. A key is the adequate treatment of excluded volume in SFE calculation. By utilizing the information of chemical bonds in the solvent molecule, the accurate computation of SFE is achieved.

Integral Equation Theory of Biomolecules and Electrolytes

The so-called three-dimensional version (3D-RISM) can be used to describe the interactions of solvent components (here we treat water and ions) with a chemical or biomolecular solute of arbitrary size and shape. Here we give an overview of the current status of such models, describing some aspects of “pure” electrolytes (water plus simple ions) and of ionophores, proteins and nucleic acids in the presence of water and salts. Here we focus primarily on interactions with water and dissolved salts; as a practical matter, the discussion is mostly limited to monovalent ions, since studies of divalent ions present many difficult problems that have not yet been addressed. This is not a comprehensive review, but covers a few recent examples that illustrate current issues.