Fluctuating hydration structure around nanometer-size hydrophobic solutes. I. Caging and drying around C60 and C60H60 spheres

The hydration structure around nanometer-size hydrophobic solutes is studied with molecular dynamics simulation by taking aqueous solutions of C60 and C60H60 as examples. In the hydration shell around a single C60 or C60H60, dipoles of simulated water molecules tend to be aligned to form the vortexlike coherent pattern which lasts for 100 ps, while individual water molecules stay within the hydration shell for about 10 ps. This structural pattern organized by fluctuating and diffusively moving molecules should be called a "fluctuating cage". In the narrow region between a pair of C60 molecules or a pair of C60H60 molecules, water density strongly fluctuates and is correlated to the mean force between solutes. The fluctuating caging and drying between solutes affect the hydrophobic interaction and dynamical behaviors of solutes.     

Collective solvent flows around a protein investigated by molecular dynamics simulation

Translational motions of water molecules in various systems equilibrated at room temperature are thought to be diffusive and nondirectional. We performed molecular dynamics simulations of a protein system and showed that the water molecules collectively move around the protein. The motions of two water molecules, which were about 12 A away from each other, are correlated to each other. Such collective motions of water can be regarded as flows around the protein, and the flows exhibited various coherent patterns: fair currents, vortices, and divergent flows. The patterns were highly fluctuating: a set of patterns changed to a different set of patterns within a time scale of 10 ps. Thus, the water motions observed in a scale of length smaller than 12 A and a time scale shorter than 10 ps were nondiffusive, and the motions above these scales were diffusive, where the flows disappeared. The flows near the protein surface had an orientational propensity to be highly parallel to the protein surface, and this propensity gradually vanished with an increment of distance from the protein surface. The divergent patterns of flows, which frequently emerge during the fluctuations of flows, may temporarily cause solvent drying in the vicinity of solutes. The current simulation is supportive of a molecular interaction mechanism that the fluctuations of hydration structure induce attractive interactions between solutes.     

Benchmarking the thermodynamic analysis of water molecules around a model beta sheet

Water molecules play a vital role in biological and engineered systems by controlling intermolecular interactions in the aqueous phase. Inhomogeneous fluid solvation theory provides a method to quantify solvent thermodynamics from molecular dynamics or Monte Carlo simulations and provides an insight into intermolecular interactions. In this study, simulations of TIP4P‐2005 and TIP5P‐Ewald water molecules around a model beta sheet are used to investigate the orientational correlations and predicted thermodynamic properties of water molecules at a protein surface. This allows the method to be benchmarked and provides information about the effect of a protein on the thermodynamics of nearby water molecules. The results show that the enthalpy converges with relatively little sampling, but the entropy and thus the free energy require considerably more sampling to converge. The two water models yield a very similar pattern of hydration sites, and these hydration sites have very similar thermodynamic properties, despite notable differences in their orientational preferences. The results also predict that a protein surface affects the free energy of water molecules to a distance of approximately 4.0 Å, which is in line with previous work. In addition, all hydration sites have a favorable free energy with respect to bulk water, but only when the water–water entropy term is included. A new technique for calculating this term is presented and its use is expected to be very important in accurately calculating solvent thermodynamics for quantitative application. © 2012 Wiley Periodicals, Inc.     

Solute rotational dynamics at the water liquid/vapor interface

The rotational dynamics of a number of diatomic molecules adsorbed at different locations at the interface between water and its own vapors are studied using classical molecular dynamics computer simulations. Both equilibrium orientational and energy correlations and nonequilibrium orientational and energy relaxation correlations are calculated. By varying the dipole moment of the molecule and its location, and by comparing the results with those in bulk water, the effects of dielectric and mechanical frictions on reorientation dynamics and on rotational energy relaxation can be studied. It is shown that for nonpolar and weekly polar solutes, the equilibrium orientational relaxation is much slower in the bulk than at the interface. As the solute becomes more polar, the rotation slows down and the surface and bulk dynamics become similar. The energy relaxation (both equilibrium and nonequilibrium) has the opposite trend with the solute dipole (larger dipoles relax faster), but here again the bulk and surface results converge as the solute dipole is increased. It is shown that these behaviors correlate with the peak value of the solvent-solute radial distribution function, which demonstrates the importance of the first hydration shell structure in determining the rotational dynamics and dependence of these dynamics on the solute dipole and location.     

How ions affect the structure of water

We model ion solvation in water. We use the MB model of water, a simple two-dimensional statistical mechanical model in which waters are represented as Lennard-Jones disks having Gaussian hydrogen-bonding arms. We introduce a charge dipole into MB waters. We perform (NPT) Monte Carlo simulations to explore how water molecules are organized around ions and around nonpolar solutes in salt solutions. The model gives good qualitative agreement with experiments, including Jones-Dole viscosity B coefficients, Samoilov and Hirata ion hydration activation energies, ion solvation thermodynamics, and Setschenow coefficients for Hofmeister series ions, which describe the salt concentration dependence of the solubilities of hydrophobic solutes. The two main ideas captured here are (1) that charge densities govern the interactions of ions with water, and (2) that a balance of forces determines water structure: electrostatics (water's dipole interacting with ions) and hydrogen bonding (water interacting with neighboring waters). Small ions (kosmotropes) have high charge densities so they cause strong electrostatic ordering of nearby waters, breaking hydrogen bonds. In contrast, large ions (chaotropes) have low charge densities, and surrounding water molecules are largely hydrogen bonded.     

Mechanism of OH radical hydration: a comparative computational study of liquid and supercritical solvent

Flexible models of the radical and water molecules including short-range interaction of hydrogen atoms have been employed in molecular dynamic simulation to understand mechanism of (●)OH hydration in aqueous systems of technological importance. A key role of H-bond connectivity patterns of water molecules has been identified. The behavior of (●)OH(aq) strongly depends on water density and correlates with topological changes in the hydrogen-bonded structure of water driven by thermodynamic conditions. Liquid and supercritical water above the critical density exhibit the radical localization in cavities existing in the solvent structure. A change of mechanism has been found at supercritical conditions below the critical density. Instead of cavity localization, we have identified accumulation of water molecules around (●)OH associated with the formation of a strong H-donor bond and diminution of non-homogeneity in the solvent structure. For all the systems investigated, the computed hydration number and the internal energy of hydration Δ(h)U showed approximately linear decrease with decreasing density of the solvent but a degree of radical-water hydrogen bonding exhibited non-monotonic dependence on density. The increase in the number of radical-water H-acceptor bonds is associated with diminution of extended nets of four-bonded water molecules in compressed solution at ~473 K. Up to 473 K, the isobaric heat of hydration in compressed liquid water remains constant and equal to -40 ± 1 kJ mol(-1).     

The importance of excluded solvent volume effects in computing hydration free energies

Continuum dielectric methods such as the Born equation have been widely used to compute the electrostatic component of the solvation free energy, DeltaG(solv)(elec), because they do not need to include solvent molecules explicitly and are thus far less costly compared to molecular simulations. All of these methods can be derived from Gauss Law of Maxwell's equations, which yields an analytical solution for the solvation free energy, DeltaG(Born), when the solute is spherical. However, in Maxwell's equations, the solvent is assumed to be a structureless continuum, whereas in reality, the near-solute solvent molecules are highly structured unlike far-solute bulk solvent. Since we have recently reformulated Gauss Law of Maxwell's equations to incorporate the near-solute solvent structure by considering excluded solvent volume effects, we have used it in this work to derive an analytical solution for the hydration free energy of an ion. In contrast to continuum solvent models, which assume that the normalized induced solvent electric dipole density P(n) is constant, P(n) mimics that observed from simulations. The analytical formula for the ionic hydration free energy shows that the Born radius, which has been used as an adjustable parameter to fit experimental hydration free energies, is no longer ill defined but is related to the radius and polarizability of the water molecule, the hydration number, and the first peak position of the solute-solvent radial distribution function. The resulting DeltaG(solv)(elec) values are shown to be close to the respective experimental numbers.     

AQUARIUS2: Knowledge-based modeling of solvent sites around proteins

The program AQUARIUS2 calculates probable positions for water molecules within the first hydration shell of any protein for which atomic coordinates are known. Like its predecessor, AQUARIUS, it uses a knowledge of water molecules sites from crystallographically determined protein structures. Energy calculations are not employed. It differs substantially from the original program in that a 3-D probability map (for solvent sites) is generated around the surface of the protein instead of the previously used discrete points. The accuracy of the program has been gauged by comparison with experimentally derived water molecule positions for proteins not used in the knowledge base of the program. It has also been tested by combining the probability density maps with crystallographically determined electron density maps for the protein porphobilinogen deaminase. This procedure filters the most likely solvent electron density peaks from the background noise and has been used in the determination of the solvent structure around the protein nerve growth factor. © John Wiley & Sons, Inc.     

Orientational dynamics for an amphiphilic-solvent solution

In this work, we performed Monte Carlo simulations on a lattice model for spontaneous amphiphilic aggregation, in order to study the orientational and hydrogen-bonding dynamics of water on different regions inside the micellar solution. We employed an associating lattice gas model that mimics the aqueous solvent, which presents a rich phase diagram with first- and second-order transition lines. Even though this is a simplified model, it makes possible to investigate the orientational dynamics of water in an equilibrium solution of amphiphiles, as well as the influence of the different phases of the solvent in the interfacial and bulk water dynamics. By means of extensive simulations, we showed that, at high temperatures, the behavior of the orientational relaxation and hydrogen bonding of water molecules in the bulk, first, and second hydration shells are considerable different. We observe the appearance of a very slow component for water molecules in the first hydration shell of micelles when the system reaches a high-density phase, consistent with previous theoretical and experimental studies concerning biological water. Also, at high temperatures, we find that water molecules in the second hydration shell of micelles have an orientational decay similar to that of bulk water, but with a generally slower dynamics. Otherwise, at low temperatures, we have two components for the orientational relaxation of bulk water in the low density liquid phase, and only a single component in the high density liquid (HDL) phase, which reflect the symmetry properties of the different phases of the solvent model. In the very dense region of water molecules in the first hydration shell of micelles at low temperatures, we find two components for the orientational relaxation on both liquid phases, one of them much slower than that in the single component of bulk water in the HDL phase. This happens even though our model does not present any hindrance to the water rotational freedom caused by the presence of the amphiphiles.     

Strategies to model the near-solute solvent molecular density/polarization

The solvent molecular distribution significantly affects the behavior of the solute molecules and is thus important in studying many biological phenomena. It can be described by the solvent molecular density distribution, g, and the solvent electric dipole distribution, p. The g and p can be computed directly by counting the number of solvent molecules/dipoles in a microscopic volume centered at r during a simulation or indirectly from the mean force F and electrostatic field E acting on the solvent molecule at r, respectively. However, it is not clear how the g and p derived from simulations depend on the solvent molecular center or the solute charge and if the g(F) and p(E) computed from the mean force and electric field acting on the solvent molecule, respectively, could reproduce the corresponding g and p obtained by direct counting. Hence, we have computed g, p, g(F), and p(E) using different water centers from simulations of a solute atom of varying charge solvated in TIP3P water. The results show that g(F) and p(E) can reproduce the g and p obtained using a given count center. This implies that rather than solving the coordinates of each water molecule by MD simulations, the distribution of water molecules could be indirectly obtained from analytical formulas for the mean force F and electrostatic field E acting on the solvent molecule at r. Furthermore, the dependence of the g and p distributions on the solute charge revealed provides an estimate of the change in g and p surrounding a biomolecule upon a change in its conformation.     

Solution structure of papain as studied by molecular mechanics and molecular dynamics techniques

In this paper, we report the molecular mechanics and molecular dynamics studies of the hydration of papain using the AMBER and CHARMm programs. We studied papain in an environment with minimal hydration involving only the X-ray waters and also in the hydrated environment by adding an extra 9 Å layer of water around the residues. The effect of nonbond cutoff was studied by performing minimizations with 8 Å and 15 Å nonbond cutoffs using the program AMBER. Two different solvent models—a constant dielectric and a distance-dependent dielectric—were considered. The AMBER-minimized structure and the average structure obtained from the CHARMm simulations for papain solvated with X-ray waters are presented and compared with the X-ray crystal structure results. Results of a similar comparison of the hydrated structures were also presented. The calculated root mean square deviation between the minimized structure and the X-ray structure is smaller for the hydrated system than for the system hydrated with only the X-ray waters. Results of the molecular mechanics and molecular dynamics simulations were presented for the various regions of papain. The hydration of the active site of papain and the effect of hydration on the torsional motion of the active site residues are presented. © 1996 by John Wiley & Sons, Inc.     

Dipolar ordering in the ripple phases of molecular-scale models of lipid membranes

Symmetric and asymmetric ripple phases have been observed to form in molecular dynamics simulations of a simple molecular-scale lipid model. The lipid model consists of an dipolar head group and an ellipsoidal tail. Within the limits of this model, an explanation for generalized membrane curvature is a simple mismatch in the size of the heads with the width of the molecular bodies. The persistence of a bilayer structure requires strong attractive forces between the head groups. One feature of this model is that an energetically favorable orientational ordering of the dipoles can be achieved by out-of-plane membrane corrugation. The corrugation of the surface stabilizes the long range orientational ordering for the dipoles in the head groups which then adopt a bulk anti-ferroelectric state. We observe a common feature of the corrugated dipolar membranes: the wave vectors for the surface ripples are always found to be perpendicular to the dipole director axis.     

Reformulation of Maxwell's equations to incorporate near-solute solvent structure

Maxwell's equations, which treat electromagnetic interactions between macroscopic charged objects in materials, have explained many phenomena and contributed to many applications in our lives. Derived in 1861 when no methods were available to determine the atomic structure of macromolecules, Maxwell's equations assume the solvent to be a structureless continuum. However, near-solute solvent molecules are highly structured, unlike far-solute bulk solvent molecules. Current methods cannot treat both the near-solute solvent structure and time-dependent electromagnetic interactions in a macroscopic system. Here, we derive "microscopic" electrodynamics equations that can treat macroscopic time-dependent electromagnetic field problems like Maxwell's equations and reproduce the solvent molecular and dipole density distributions observed in molecular dynamics simulations. These equations greatly reduce computational expense by not having to include explicit solvent molecules, yet they treat the solvent electrostatic and van der Waals effects more accurately than continuum models. They provide a foundation to study electromagnetic interactions between molecules in a macroscopic system that are ubiquitous in biology, bioelectromagnetism, and nanotechnology. The general strategy presented herein to incorporate the near-solute solvent structure would enable studies on how complex cellular protein-ligand interactions are affected by electromagnetic radiation, which could help to prevent harmful electromagnetic spectra or find potential therapeutic applications.     

Effect of molecular structure of a dichroic dye and the ordering of a liquid crystal on the dichroism of the dye-liquid crystal binary mixtures

The orientational ordering of dyes doped into liquid crystals has been investigated. The experimental results show that the ordering of the dyes can be expressed as a function of the order parameter of the liquid crystal host and the molecular structure of the dye. In addition a theory of the ordering of molecules in a binary mixture system has been derived by extending Kimura's theory. The validity of the theory has been confirmed by comparison with the experimental results using various combination of azo dyes and liquid crystals.     

Two-particle entropy and structural ordering in liquid water

Entropies of simple point charge (SPC) water were calculated over the temperature range 278-363 K using the two-particle correlation function approximation. Then, the total two-particle contribution to the entropy of the system was divided into three parts, which we call translational, configurational, and orientational. The configurational term describes the contribution to entropy, which originates from spatial distribution of surrounding water molecules (treated as points, represented by the center of mass) around the central one. It has been shown that this term can serve as the metric of the overall orientational ordering in liquid water. Analyzing each of these three terms as a function of intermolecular distance, r, we also find a rational definition of the hydration shell around the water molecule; the estimated radii of the first and second hydration shells are 0.35 nm and 0.58 nm, respectively. We find, moreover, that the first hydration shell around the water molecule participates roughly in 70% of the total orientational entropy of water, and this rate is roughly temperature independent.     

Effect of molecular structure of a dichroic dye and the ordering of a liquid crystal on the dichroism of the dye-liquid crystal binary mixtures

The orientational ordering of dyes doped into liquid crystals has been investigated. The experimental results show that the ordering of the dyes can be expressed as a function of the order parameter of the liquid crystal host and the molecular structure of the dye. In addition a theory of the ordering of molecules in a binary mixture system has been derived by extending Kimura's theory. The validity of the theory has been confirmed by comparison with the experimental results using various combination of azo dyes and liquid crystals.     

Hydration of sodium, potassium, and chloride ions in solution and the concept of structure maker/breaker

Neutron diffraction data with hydrogen isotope substitution on aqueous solutions of NaCl and KCl at concentrations ranging from high dilution to near-saturation are analyzed using the Empirical Potential Structure Refinement technique. Information on both the ion hydration shells and the microscopic structure of the solvent is extracted. Apart from obvious effects due to the different radii of the three ions investigated, it is found that water molecules in the hydration shell of K+ are orientationally more disordered than those hydrating a Na+ ion and are inclined to orient their dipole moments tangentially to the hydration sphere. Cl- ions form instead hydrogen-bonded bridges with water molecules and are readily accommodated into the H-bond network of water. The results are used to show that concepts such as structure maker/breaker, largely based on thermodynamic data, are not helpful in understanding how these ions interact with water at the molecular level.     

When is a molecule properly solvated by a continuum model or in a cluster ansatz? A first-principles simulation of alanine hydration

In order to test the validity of the cluster ansatz approach as well as of the continuum model approach and to learn about the solvation shell, we carried out first-principles molecular dynamics simulations of the alanine hydration. Our calculations contained one alanine molecule dissolved in 60 water molecules. Dipole moments of individual molecules were derived by means of maximally localized Wannier functions. We observed an average dipole moment of about 16.0 D for alanine and of about 3.3 D for water. In particular, the average water dipole moment in proximity of alanine's COO(-) group decayed continously with increasing distance, while, surprisingly, close to the CH3 and NH3+ group, the dipole moment first rose before its value dropped. In a cluster ansatz approach, we considered snapshots of alanine surrounded by different water molecule shells. The dipole moments from the cluster approaches utilizing both maximally localized Wannier functions as well as natural population analysis served to approximate the dipole moments of the total trajectory. Sufficient convergence of the cluster ansatz approach is found for either of the two solvent shells around the polar groups and one solvent shell around the apolar groups or two solvent shells around the polar groups surrounded by a dieletric continuum.     

Structure, energetics, and dynamics of water adsorbed on the muscovite (001) surface: a molecular dynamics simulation

Molecular dynamics (MD) computer simulations of liquid water adsorbed on the muscovite (001) surface provide a greatly increased, atomistically detailed understanding of surface-related effects on the spatial variation in the structural and orientational ordering, hydrogen bond (H-bond) organization, and local density of H2O molecules at this important model phyllosilicate surface. MD simulations at constant temperature and volume (statistical NVT ensemble) were performed for a series of model systems consisting of a two-layer muscovite slab (representing 8 crystallographic surface unit cells of the substrate) and 0 to 319 adsorbed H2O molecules, probing the atomistic structure and dynamics of surface aqueous films up to 3 nm in thickness. The results do not demonstrate a completely liquid-like behavior, as otherwise suggested from the interpretation of X-ray reflectivity measurements and earlier Monte Carlo simulations. Instead, a more structurally and orientationally restricted behavior of surface H2O molecules is observed, and this structural ordering extends to larger distances from the surface than previously expected. Even at the largest surface water coverage studied, over 20% of H2O molecules are associated with specific adsorption sites, and another 50% maintain strongly preferred orientations relative to the surface. This partially ordered structure is also different from the well-ordered 2-dimensional ice-like structure predicted by ab initio MD simulations for a system with a complete monolayer water coverage. However, consistent with these ab initio results, our simulations do predict that a full molecular monolayer surface water coverage represents a relatively stable surface structure in terms of the lowest diffusional mobility of H2O molecules along the surface. Calculated energies of water adsorption are in good agreement with available experimental data.