Search

The intramolecular ¹H NMR dipole–dipole relaxation of molecular fluids has traditionally been interpreted within the Bloembergen–Purcell–Pound (BPP) theory of NMR intramolecular relaxation. The BPP theory draws upon Debye’s theory for describing the rotational diffusion of the ¹H–¹H pair and predicts a monoexponential decay of the ¹H–¹H dipole–dipole autocorrelation function between distinct spin pairs. Using molecular dynamics (MD) simulations, we show that for both n-heptane and water this is not the case. In particular, the autocorrelation function of individual ¹H–¹H intramolecular pairs itself evinces a rich stretched-exponential behavior, implying a distribution in rotational correlation times. However, for the high-symmetry molecule neopentane, the individual ¹H–¹H intramolecular pairs do conform to the BPP description, suggesting an important role of molecular symmetry in aiding agreement with the BPP model. The intermolecular autocorrelation functions for n-heptane, water, and neopentane also do not admit a monoexponential behavior of individual ¹H–¹H intermolecular pairs at distinct initial separations. We suggest expanding the autocorrelation function in terms of modes, provisionally termed molecular modes, that do have an exponential relaxation behavior. With care, the resulting Fredholm integral equation of the first kind can be inverted to recover the probability distribution of the molecular modes. The advantages and limitations of this approach are noted.

Water molecules bind strongly to the polar calcite surface and form a surface-adsorbed layer that has properties akin to an apolar surface. This has important implications for understanding the thermodynamic driving forces underlying the adsorption of acid groups from crude oil, in particular, naphthenic acid, onto calcite. Free energy calculations show that naphthenic acid binds favorably to the water monolayer adsorbed on the calcite surface. However, to bond directly to calcite, a free energy barrier has to be overcome to expel the intervening layer of water. Further, naphthenic acids with longer alkyl chains bind with lower free energy to the calcite surface than those with shorter alkyl chains, and, for the same chain length, branching enhances adsorption. To better understand this behavior, for a specified alkyl chain length, we study adsorption at different temperatures. Consistent with experiments, we find that adsorption is enhanced at higher temperatures. Examination of the enthalpic and entropi...

Low salinity water flooding has shown great promise due to its cost-effectiveness and low environmental impact for improving and sustaining oil production. It is believed that injecting water with ionic strength lower than that of the reservoir changes the reservoir from less to more water-wet and enhances oil recovery. This alteration phenomenon is not well understood, due to complex interactions between oil, water, and rock. Here we use molecular simulations to characterize the wettability of the 10.4-face of calcite in a calcite/brine/oil system, and address how wettability is altered by changing ionic strength and salt type (NaCl vs. CaCl2). Using the test area method we calculate the superficial tension of the fluids against the solid and the surface tension between the two fluid phases. As the salinity is decreased, the wetting of calcite by brine is progressively less favored, contrary to what might be expected based on low salinity flooding. However, as salinity is decreased, forming the oil-brine interface is more favored. On balance, it is the latter effect that leads to the enhanced wetting of calcite by brine in the oil-brine-calcite system, and it is suggested as an important element in the physics underlying low-salinity flooding.

The role that van der Waals (vdW) attractive forces play in the hydration and association of atomic hydrophobic solutes such as argon (Ar) in water is reanalyzed using the local molecular field (LMF) theory of those interactions. In this problem, solute vdW attractive forces can reduce or mask hydrophobic interactions as measured by contact peak heights of the ArAr correlation function compared to reference results for purely repulsive core solutes. Nevertheless, both systems exhibit a characteristic hydrophobic inverse temperature behavior in which hydrophobic association becomes stronger with increasing temperature through a moderate temperature range. The new theoretical approximation obtained here is remarkably simple and faithful to the statistical mechanical LMF assessment of the necessary force balance. Our results extend and significantly revise approximations made in a recent application of the LMF approach to this problem and, unexpectedly, support a theory of nearly 40 years ago.

The stability of foam in the presence of oil is of fundamental interest in enhanced oil recovery processes using foam for mobility control. Experimentally, it is known that lauryl betaine (LB) increases foam stability of certain anionic surfactants, and LB is referred to as a foam booster. However, the molecular basis for this effect is not well understood. Using molecular dynamics simulations, here we study a system of LB and alpha olefin sulfonate (AOS-14), an anionic surfactant that is used as a foam stabilizer. We monitor the area per molecule, a quantity that correlates with the surface shear viscosity, and the surface dilatational modulus to infer the stability of the various mixtures. We find that the influence of LB is nonmonotonic: the area per molecule and surface dilatational modulus have a minimum and maximum, respectively, around 30% LB in the monolayer. We show that this net effect has its basis in two competing effects: the favorable interaction between LB and AOS-14 that tends to shrink th...

In honor of the 25th anniversary of the SAFT equation of state, this paper presents a brief review of successes in modeling fluid mixtures with associating, polyatomic, and polar components using the SAFT equation of state. Challenges for the association term to predict monomer and dimer fractions in comparison with spectroscopic data are described. To address these challenges and challenges in patchy colloids, extensions to the associating term are reviewed that incorporate multiple bonding at association sites and cooperative association. Approximations in these extensions are validated through comparisons with molecular simulation results. Further, application of the density functional form of the theory to form micelles is briefly reviewed.

The interfacial tension (IFT) between oil and water impacts many industrial operations. For example, in low salinity flooding, water with optimal salinity is injected into an oil reservoir, to change the oil/water interfacial tension and fluid/rock interfacial energy to mobilize trapped oil and enhance the displacement of oil. Theoretical and experimental studies have shown that different ions can enhance or inhibit the production. To develop a fundamental understanding of IFT in these systems, particularly in the context of salinity and the ion-type effect, molecular dynamics simulations were used to probe the change in IFT with the salt types and concentrations. In agreement with experimental measurements, our results show that the oil/water IFT increases with increasing salt concentration, with the increase dependent on the salt species. The results revealed that the presence of divalent anions at the interface increases the electrostatic interactions, which leads to a smaller increase in the IFT compared to other salts. Moreover, the analysis showed that the increase in IFT is due to ion depletion near the interface. The water orientations at the interface and the bulk explain why this depletion occurs.

The role of internal motions and molecular geometry on $^1$H NMR relaxation times $T_{1,2}$ in hydrocarbons is investigated using MD (molecular dynamics) simulations of the autocorrelation functions for in{\it tra}molecular $G_R(t)$ and in{\it ter}molecular $G_T(t)$ $^1$H-$^1$H dipole-dipole interactions arising from rotational ($R$) and translational ($T$) diffusion, respectively. We show that molecules with increased molecular symmetry such as neopentane, benzene, and isooctane show better agreement with traditional hard-sphere models than their corresponding straight-chain $n$-alkane, and furthermore that spherically-symmetric neopentane agrees well with the Stokes-Einstein theory. The influence of internal motions on the dynamics and $T_{1,2}$ relaxation of $n$-alkanes are investigated by simulating rigid $n$-alkanes and comparing with flexible (i.e. non-rigid) $n$-alkanes. Internal motions cause the rotational and translational correlation-times $\tau_{R,T}$ to get significantly shorter and the relaxation times $T_{1,2}$ to get significantly longer, especially for longer-chain $n$-alkanes. Site-by-site simulations of $^1$H's along the chains indicate significant variations in $\tau_{R,T}$ and $T_{1,2}$ across the chain, especially for longer-chain $n$-alkanes. The extent of the stretched (i.e. multi-exponential) decay in the autocorrelation functions $G_{R,T}(t)$ are quantified using inverse Laplace transforms, for both rigid and flexible molecules, and on a site-by-site bases. Comparison of $T_{1,2}$ measurements with the site-by-site simulations indicate that cross-relaxation (partially) averages-out the variations in $\tau_{R,T}$ and $T_{1,2}$ across the chain of long-chain $n$-alkanes. This work also has implications on the role of nano-pore confinement on the NMR relaxation of fluids in the organic-matter pores of kerogen and bitumen.

The perturbed chain form of the polar statistical associating fluid theory (Polar PC-SAFT) was used to model lower 1-alcohol + n-alkane mixtures. The ability of the equation of state to predict accurate activity coefficients at infinite dilution was demonstrated as a function of temperature. Investigations show that the association term in SAFT plays an important role in capturing the right composition dependence of the activity coefficients in comparison with nonassociating models (UNIQUAC). Results also show that considering long-range polar interactions can significantly improve the fractions of free monomers predicted by PC-SAFT in comparison with spectroscopic data and molecular dynamic (MD) simulations carried out in this work. Furthermore, evidence of hydrogen-bonding cooperativity in 1-alcohol + n-alkane systems is discussed using spectroscopy, simulation, and theory. In general, results demonstrate the theory's predictive power, limitations of first-order perturbation theories, as well as the importance of considering long-range polar interactions for better hydrogen-bonding thermodynamics.

Experiments show that at 298~K and 1 atm pressure the transfer free energy, $\mu^{\rm ex}$, of water from its vapor to liquid normal alkanes $C_nH_{2n+2}$ ($n=5\ldots12$) is negative. Earlier it was found that with the united-atom TraPPe model for alkanes and the SPC/E model for water, one had to artificially enhance the attractive alkane-water cross interaction to capture this behavior. Here we revisit the calculation of $\mu^{\rm ex}$ using the polarizable AMOEBA and the non-polarizable Charmm General (CGenFF) forcefields. We test both the AMOEBA03 and AMOEBA14 water models; the former has been validated with the AMOEBA alkane model while the latter is a revision of AMOEBA03 to better describe liquid water. We calculate $\mu^{\rm ex}$ using the test particle method. With CGenFF, $\mu^{\rm ex}$ is positive and the error relative to experiments is about 1.5 $k_{\rm B}T$. With AMOEBA, $\mu^{\rm ex}$ is negative and deviations relative to experiments are between 0.25 $k_{\rm B}T$ (AMOEBA14) and 0.5 $k_{\rm B}T$ (AMOEBA03). Quantum chemical calculations in a continuum solvent suggest that zero point effects may account for some of the deviation. Forcefield limitations notwithstanding, electrostatic and induction effects, commonly ignored in considerations of water-alkane interactions, appear to be decisive in the solubility of water in alkanes., Comment: Fixed several small typos throughout the document. Added a discussion on coarse-graining, including new figure 5. This version is being submitted to JCP

Molecular dynamics (MD) simulations are used to investigate $^1$H nuclear magnetic resonance (NMR) relaxation and diffusion of bulk $n$-C$_5$H$_{12}$ to $n$-C$_{17}$H$_{36}$ hydrocarbons and bulk water. The MD simulations of the $^1$H NMR relaxation times $T_{1,2}$ in the fast motion regime where $T_1 = T_2$ agree with measured (de-oxygenated) $T_2$ data at ambient conditions, without any adjustable parameters in the interpretation of the simulation data. Likewise, the translational diffusion $D_T$ coefficients calculated using simulation configurations are well-correlated with measured diffusion data at ambient conditions. The agreement between the predicted and experimentally measured NMR relaxation times and diffusion coefficient also validate the forcefields used in the simulation. The molecular simulations naturally separate intramolecular from intermolecular dipole-dipole interactions helping bring new insight into the two NMR relaxation mechanisms as a function of molecular chain-length (i.e. carbon number). Comparison of the MD simulation results of the two relaxation mechanisms with traditional hard-sphere models used in interpreting NMR data reveals important limitations in the latter. With increasing chain length, there is substantial deviation in the molecular size inferred on the basis of the radius of gyration from simulation and the fitted hard-sphere radii required to rationalize the relaxation times. This deviation is characteristic of the local nature of the NMR measurement, one that is well-captured by molecular simulations., Revision: References 27 and 28 were updated. Formatting of last name in acknowledgement was corrected; Expressions for Larmor frequency in terms of magnetic field was included. Caption for figure 7 was corrected (table I should read table II)

Crystal polymorphs of glucose isomerase were examined to characterize the properties and to quantify the energetics of protein crystal growth. Transitions of polymorph stability were measured in poly(ethylene glycol)/NaCl solutions, and one transition point was singled out for more detailed quantitative analysis. Single crystal x-ray diffraction was used to confirm space groups and identify complementary crystal structures. Crystal polymorph stability was found to depend on the NaCl concentration, with stability transitions requiring > 1 M NaCl combined with a low concentration of PEG. Both salting-in and salting-out behavior was observed and was found to differ for the two polymorphs. For NaCl concentrations above the observed polymorph transition, the increase in solubility of the less stable polymorph together with an increase in the osmotic second virial coefficient suggests that changes in protein hydration upon addition of salt may explain the experimental trends. A combination of atomistic and continuum models was employed to dissect this behavior. Molecular dynamics simulations of the solvent environment were interpreted using quasi-chemical theory to understand changes in protein hydration as a function of NaCl concentration. The results suggest that protein surface hydration and Na+ binding may introduce steric barriers to contact formation, resulting in polymorph selection.

The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.

By introducing an external field to temper short-range protein water interactions, we regularize the statistical problem of calculating the hydration free energy, μ(ex), of the protein cytochrome C using the potential distribution theorem. Using this approach, we calculate the nonelectrostatic (dispersion) and electrostatic contributions to μ(ex). The nonelectrostatic contribution interpreted within an accessible surface area approach leads to a surface energy parameter that is about twice the value based on the hydration of small alkanes: at the size scale of the protein, hydrophobic hydration is more stronger relative to small alkanes. The electrostatic contribution does not obey linear response behavior. Further, depending on the choice of the protein dielectric constant, continuum dielectric calculations of the electrostatic contribution differ from the all-atom result by between 6%-12% (in a net value of about -2000 kcal/mol). We conclude by indicating potential applications of the present physically transparent approach toward illuminating the role of water, ions, and osmolytes in protein solution thermodynamics, including in protein folding and aggregation.

Cosolvent hydrophobic preferential interactions with methane in aqueous methanol solutions are evaluated on the basis of the solute excess chemical potential derived from molecular simulations using the quasi-chemical (QC) theory generalization of the potential distribution theorem (PDT). We find that the methane-methanol preferential interaction parameter derived from QC theory quantitatively captures the favorable solvation of methane in methanol solutions in terms of important local solute-solvent (water and methanol) intermolecular interactions within a defined inner shell around the solute, and nonlocal solute interactions with solvent molecules outside this inner shell. Moreover, a unique inner shell can be defined such that the preferential interaction parameter is derived exclusively from the free energy of cavity formation in the aqueous cosolvent solution without the solute, where this cavity corresponds to the specified inner shell, and the mean interaction or binding energy of the solute with solvent molecules outside this inner shell. This inner-shell definition leads to a description of solute-cosolvent preferential interactions in which the molecular details of those interactions are derived from the effect of cosolvent on cavity statistics in the aqueous cosolvent solution alone. The finding suggests that solution thermodynamic behavior beyond steric exclusion (macromolecular crowding) contribute to the molecular mechanisms by which cosolvent preferential interactions influence protein stability and activity.

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.

For a model deca-alanine peptide the cavity (ideal hydrophobic) contribution to hydration favors the helix state over extended states and the paired helix bundle in the assembly of two helices. The energetic contributions of attractive protein-solvent interactions are separated into quasi-chemical components consisting of a short-range part arising from interactions with solvent in the first hydration shell and the remaining long-range part that is well described by a Gaussian. In the helix-coil transition, short-range attractive protein-solvent interactions outweigh hydrophobic hydration and favor the extended coil states. Analysis of enthalpic effects shows that it is the favorable hydration of the peptide backbone that favors the unfolded state. Protein intramolecular interactions favor the helix state and are decisive in favoring folding. In the pairing of two helices, the cavity contribution outweighs the short-range attractive protein-water interactions. However, long-range, protein-solvent attractive interactions can either enhance or reverse this trend depending on the mutual orientation of the helices. In helix-helix assembly, change in enthalpy arising from change in attractive protein-solvent interactions favors disassembly. In helix pairing as well, favorable protein intramolecular interactions are found to be as important as hydration effects. Overall, hydrophilic protein-solvent interactions and protein intramolecular interactions are found to play a significant role in the thermodynamics of folding and assembly in the system studied.

We study two designed and one natural zinc finger peptide each with the Cys(2)His(2) (CCHH) type of metal binding motif. In the approach we have developed, we describe the role of the protein and solvent outside the Zn(II)-CCHH metal-residue cluster by a molecular field represented by generalized harmonic restraints. The strength of the field is adjusted to reproduce the binding energy distribution of the metal with the cluster obtained in a reference all-atom simulation with empirical potentials. The quadratic field allows us to investigate analytically the protein restraints on the binding site in terms of its eigenmodes. Examining these eigenmodes suggests, consistent with experimental observations, the importance of the first histidine (H) in the CCHH cluster in metal binding. Further, the eigenvalues corresponding to these modes also indicate that the designed proteins form a tighter complex with the metal. We find that the bulk protein and solvent response tends to destabilize metal binding, emphasizing that the favorable energetics of metal-residue interaction is necessary to drive folding in this system. The representation of the bulk protein and solvent response by a local field allows us to perform Monte Carlo simulations of the metal-residue cluster using quantum-chemical approaches, here using a semiempirical Hamiltonian. For configurations sampled from this simulation, we study the free energy of replacing Zn(2+) with Fe(2+), Co(2+), and Ni(2+) using density functional theory. The calculated selectivities are in fair agreement with experimental results.

We study the solvation free energy of two different conformations (helix and extended) of two different peptides (deca-alanine and deca-glycine) in two different solvents (water and aqueous guanidinium chloride, GdmCl). The free energies are obtained using the quasichemical organization of the potential distribution theorem, an approach that naturally provides the repulsive (solvophobic or cavity) and attractive (solvophilic) contributions to solvation. The solvophilic contribution is further parsed into a chemistry contribution arising from solute interaction with the solvent in the first solvation shell and a long-range contribution arising from non-specific interactions between the solute and the solvent beyond the first solvation shell. The cavity contribution is obtained for two different envelopes, ΣSE, which theory helps identify as the solvent excluded volume, and ΣG, a larger envelope beyond which solute-solvent interactions are Gaussian. The ΣSE envelope is independent of the solvent, as expected on the basis of the insensitivity to the solvent type of the distance of closest approach between protein heavy atoms and solvent heavy atoms, but contrary to the intuition based on treating solvent constituents as spheres of some effective radii. For both envelopes, the cavity contribution in water is proportional to the surface area of the envelope. The same does not hold for GdmCl(aq), revealing the limitation of using molecular area to assess solvation energetics. The ΣG-cavity contribution predicts that GdmCl(aq) should favor the more compact state, contrary to the role of GdmCl in unfolding proteins. The chemistry contribution attenuates this effect, but still the net local (chemistry plus ΣG-packing) contribution is inadequate in capturing the role of GdmCl. With the inclusion of the long-range contribution, which is dominated by van der Waals interaction, aqueous GdmCl favors the extended conformation over the compact conformation. Our finding emphasizes the importance of weak, but attractive, long-range dispersion interactions in protein solution thermodynamics.

To understand the thermodynamic exclusion of Na + relative to K + from the S 2 site of the selectivity filter, the distribution P X ( ɛ ) (X = K + or Na + ) of the binding energy ( ɛ ) of the ion with the channel is analyzed using the potential distribution theorem. By expressing the excess chemical potential of the ion as a sum of mean-field 〈 ɛ 〉 and fluctuation μ ex flux,X contributions, we find that selectivity arises from a higher value of μ flux , Na + ex relative to μ flux , K + ex . To understand the role of site-site interactions on μ ex flux,X , we decompose P X ( ɛ ) into n -dependent distributions, where n is the number of ion-coordinating ligands within a distance λ from the ion. For λ comparable to typical ion-oxygen bond distances, investigations building on this multistate model reveal an inverse correlation between favorable ion-site and site-site interactions: the ion-coordination states that most influence the thermodynamics of the ion are also those for which the binding site is energetically less strained and vice versa. This correlation motivates understanding entropic effects in ion binding to the site and leads to the finding that μ ex flux,X is directly proportional to the average site-site interaction energy, a quantity that is sensitive to the chemical type of the ligand coordinating the ion. Increasing the coordination number around Na + only partially accounts for the observed magnitude of selectivity; acknowledging the chemical type of the ion-coordinating ligand is essential.

We model the hydration contribution to short-range electrostatic/dispersion protein interactions embodied in the osmotic second virial coefficient, B(2), by adopting a quasi-chemical description in which water molecules associated with the protein are identified through explicit molecular dynamics simulations. These water molecules reduce the surface complementarity of highly favorable short-range interactions, and therefore can play an important role in mediating protein-protein interactions. Here we examine this quasi-chemical view of hydration by predicting the interaction part of B(2) and comparing our results with those derived from light-scattering measurements of B(2) for staphylococcal nuclease, lysozyme, and chymotrypsinogen at 25 degrees C as a function of solution pH and ionic strength. We find that short-range protein interactions are influenced by water molecules strongly associated with a relatively small fraction of the protein surface. However, the effect of these strongly associated water molecules on the surface complementarity of short-range protein interactions is significant, and must be taken into account for an accurate description of B(2). We also observe remarkably similar hydration behavior for these proteins despite substantial differences in their three-dimensional structures and spatial charge distributions, suggesting a general characterization of protein hydration.

The excess proton in water, H + (aq), plays a fundamental role in aqueous solution chemistry. Its solution thermodynamic properties are essential to molecular descriptions of that chemistry and for validation of dynamical calculations. Within the quasichemical theory of solutions those thermodynamic properties are conditional on recognizing underlying solution structures. The quasichemical treatment identifies H 3 O + and H 2 O 5 + as natural inner-shell complexes, corresponding to the cases of n = 1, 2 water molecule ligands, respectively, of a distinguished H + ion. A quantum-mechanical treatment of the inner-shell complex with both a dielectric continuum and a classical molecular dynamics treatment of the outer-shell contribution identifies the latter case (the Zundel complex) as the more numerous species. Ab initio molecular dynamics simulations, with two different electron density functionals, suggest a preponderance of Zundel-like structures, but a symmetrical ideal Zundel cation is not observed.

The usual rate-determining step in the catalytic mechanism of the low molecular weight tyrosine phosphatases involves the hydrolysis of a phosphocysteine intermediate. To explain this hydrolysis, general base-catalyzed attack of water by the anion of a conserved aspartic acid has sometimes been invoked. However, experimental measurements of solvent deuterium kinetic isotope effects for this enzyme do not reveal a rate-limiting proton transfer accompanying dephosphorylation. Moreover, base activation of water is difficult to reconcile with the known gas-phase proton affinities and solution phase pK(a)'s of aspartic acid and water. Alternatively, hydrolysis could proceed by a direct nucleophilic attack by a water molecule. To understand the hydrolysis mechanism, we have used high-level density functional methods of quantum chemistry combined with continuum electrostatics models of the protein and the solvent. Our calculations do not support a catalytic activation of water by the aspartate. Instead, they indicate that the water oxygen directly attacks the phosphorus, with the aspartate residue acting as a H-bond acceptor. In the transition state, the water protons are still bound to the oxygen. Beyond the transition state, the barrier to proton transfer to the base is greatly diminished; the aspartate can abstract a proton only after the transition state, a result consistent with experimental solvent isotope effects for this enzyme and with established precedents for phosphomonoester hydrolysis.

The hydration of some of the alkaline earth divalent metal cations and first row transition metal cations is considered within the quasi-chemical theory of solutions. Quantum chemical calculations provide information on the chemically important interactions between the ion and its first-shell water molecules. A dielectric continuum model supplies the outer-shell contribution. The theory then provides the framework to mesh these quantities together. The agreement between the calculated and experimental quantities is good. For the transition metal cations, it is seen that the ligand field contributions play an important role in the physics of hydration. Removing these bonding contributions from the computed hydration free energy results in a linear decrease in the hydration free energy along the period. It is precisely such effects that molecular mechanics force fields have not captured. The implications and extensions of this study to metal atoms in proteins are suggested.

The K+(aq) ion is an integral component of many cellular processes, amongst which the most important, perhaps, is its role in transmitting electrical impulses along the nerve. Understanding its hydration structure and thermodynamics is crucial in dissecting its role in such processes. Here we address these questions using both the statistical mechanical quasi-chemical theory of solutions and ab initio molecular dynamics simulations. Simulations predict an interesting hydration structure for K+(aq): the population of about six (6) water molecules within the initial minimum of the observed gKO(r) at infinite dilution involves four (4) innermost molecules that the quasi-chemical theory suggests should be taken as the theoretical inner shell. The contribution of the fifth and sixth closest water molecules is observable as a distinct shoulder on the principal maximum of the gKO(r). The quasi-chemical estimate of solvation free energy for the neutral pair KOH is also in good agreement with experiments.

Quasi-chemical theory and electronic structure results on inner-sphere H(H2O)n+ clusters are used to discuss the absolute hydration free energy of H+(aq). It is noted that this quantity is not thermodynamically measurable, and this leads to some relative misalignment of available tables of absolute hydration free energies of ions in water. The simplest quasi-chemical model produces a reasonable quantitative result in the range of −256 to −251 kcal/mol. The primitive concepts on which the model is based naturally identify the Zundel cation H5O2+ as the principal chemical structure contributing to this hydration free energy. The specific participation of an Eigen cation H9O4+ is not required in this model because the definition of that structure depends on outer-sphere arrangements, and a crude dielectric continuum model is here used for outer-sphere contributions.

The hydration thermodynamics of the amino acid X relative to the reference G (glycine) or the hydration thermodynamics of a small-molecule analog of the side chain of X is often used to model the contribution of X to protein stability and solution thermodynamics. We consider the reasons for successes and limitations of this approach by calculating and comparing the conditional excess free energy, enthalpy, and entropy of hydration of the isoleucine side chain in zwitterionic isoleucine, in extended penta-peptides, and in helical deca-peptides. Butane in gauche conformation serves as a small-molecule analog for the isoleucine side chain. Parsing the hydrophobic and hydrophilic contributions to hydration for the side chain shows that both of these aspects of hydration are context-sensitive. Furthermore, analyzing the solute–solvent interaction contribution to the conditional excess enthalpy of the side chain shows that what is nominally considered a property of the side chain includes entirely nonobvious contributions of the background. The context-sensitivity of hydrophobic and hydrophilic hydration and the conflation of background contributions with energetics attributed to the side chain limit the ability of a single scaling factor, such as the fractional solvent exposure of the group in the protein, to map the component energetic contributions of the model-compound data to their value in the protein. But ignoring the origin of cancellations in the underlying components the group-transfer model may appear to provide a reasonable estimate of the free energy for a given error tolerance.

The accurate calculation of the energetics of electrostatically driven binding of amino acid residues to other amino acids (salt bridges) or to synthetic molecules is critical in numerous physiological and technological processes. Commonly used continuum methods are unable to capture differences in interaction energies resulting from specific chemical changes, such as the stronger retention of basic proteins on sulfated (strong) than on carboxylated (weak) cation exchangers. The inadequacies of continuum models in describing hydration effects, specifically local solvent structure and associated polarization effects, are especially apparent in such systems. These shortcomings have been addressed by modeling the protein−cation exchanger interaction as that of methylammonium, a model for a protonated lysine residue, with the methylated analogues of the ion-exchange functionalities, namely methyl sulfate and acetate ion, respectively. A hybrid quantum-continuum treatment of the solvent is able to capture the ...

An orthorhombic crystal form of subtilisin BPN’ variant s88 exhibits a systematic variation in growth rates of its three unique faces, resulting in pronounced variations in crystal morphology as a function of the ionic strength (Gallagher et al., J. Crystal Growth 193 (1998) 665). We have sought to explain these observations by performing energetics calculations using the full structural details of the protein. The approach of correlating growth rates with the strength of interactions of molecular pairs in the crystal proved unsatisfactory. The attachment of protein molecules to growing crystal faces is a stochastic process: a protein molecule samples numerous configurational (orientational and translational) states before attaching to the crystal in a configuration consistent with the crystal symmetry. This search-and-bind process determines the rate of crystal growth. We present a simplified approach that mimics this dynamical process: we perform docking of a protein molecule with another protein molecule or a cluster of molecules. An analysis of the bound configurations reveals the presence of orientations that are incommensurate with the crystal symmetry but in which a protein molecule can also bind strongly to the crystal face. Such improperly oriented molecules can be thought of as competitive inhibitors, and their presence is shown to affect the growth rate. Thus procedures aimed at decreasing the effect of such competitive inhibition, or conversely increasing the specificity of protein–protein interactions forming the crystal, are expected to offer better control of crystal growth rates.

A molecular basis is presented for characterizing the osmotic second virial coefficient, B 22 , of dilute protein solutions, which provides a measure of the nature of protein–protein interactions and has been shown to be correlated with crystallization behavior. Experimental measurements of the second virial coefficient of lysozyme and bovine α -chymotrypsinogen A were performed by static light scattering, as a function of pH and electrolyte concentration. Although some of the trends can be explained qualitatively by simple colloidal models of protein interactions, a more realistic interpretation based on protein crystallographic structures suggests a different explanation of experimental trends. The interactions accounted for are solute–solute excluded volume (steric), electrostatic and short-range (mainly van der Waals) interactions. The interactions depend strongly on orientation, and this profoundly affects calculated second virial coefficients. We find that molecular configurations in which complementary surfaces are apposed contribute disproportionately to the second virial coefficient, mainly through short-range interactions; electrostatic interactions play a secondary role in many of these configurations. Thus molecular recognition events can play a role in determining the solution thermodynamic properties of proteins, and this provides a plausible basis for explaining the observed relationship with crystallization behavior.

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.

In studying ion-selectivity in biomaterials, it is common to study ion-protein interactions within a local neighborhood around the ion. This local system analysis for the S 2 site of KcsA, its semisynthetic analog, and valinomycin yields the free energy change in exchanging K + with Na + in quantitative agreement with the value obtained by considering ion-interactions with the entire system. But the energetics of ion binding in the local system and in the entire system differ significantly and lead to different conclusions regarding the physical basis of ion selectivity. For configurations sampled from an all-atom simulation, we show that the selectivity free energy can be decomposed into a contribution arising from interactions of the ion with its local neighborhood, Δ W local , and a term arising from the field imposed on the ion and the binding site by the rest of the medium, Δ W ϕ . The local contribution Δ W local is numerically close to the actual free energy difference because the field contribution is small. The field contribution is small because of cancellation of inversely related ion-medium and site-medium interactions. Our analysis presents a rigorous foundation for the numerical success of the local system analysis and shows that its implications do not always hold for the entire protein.

We study the selective binding of the softer K+ ion over the harder Na+ and Mg++ ions to the 58 nucleotide ribosomal RNA fragment and the S2 site of the KcsA K+ channel using all atom MD simulations. The ribosomal RNA is interesting in that it binds the K+ over the harder Mg++ ion. We calculate the free energy of exchanging K+ with Mg++ in the binding site relative to the change in the aqueous solution. In order to explain the selectivity, we find that it is necessary to consider the change in the internal energy of the ion binding site. Interestingly, similar physics is observed in the KcsA S2 site. There we elucidate the role of coordination number fluctuations, ion-site binding energetics, and site-site interaction energetics in determining the selectivity of the S2 site for K+: once again, the reduced strain in the site in the presence of K+ (relative to Na+) explains selectivity. Thus, despite the uncommon origin and completely different chemical composition of the binding site, in both the cases the binding site is constricted in the presence of the harder ion and causes an increase in the unfavorable electrostatic strain. This strain is what leads to the observed selectivity for the softer K+ ion.

The hydration free energy of an ion is separated into a chemical term, arising due to the interaction of the ion with water molecules within the defined coordination sphere (the inner shell), a packing contribution, accounting for forming an ion-free coordination sphere (the observation volume) in the solvent, and a long range correction, accounting for the interaction of the ion with the solvent outside the coordination sphere. The chemical term is recast as a sum over coordination states, with the nth term depending on the probability of observing n water molecules in the observation volume and the free energy of assembling the n water molecules around the ion in the presence of the outer-shell solvent. Each stepwise increment in the coordination number more fully accounts for the chemical contribution, and this molecular aufbau approach is used to interrogate the thermodynamic importance of various hydration structures X[H(2)O](n) of X(aq) (X = Na(+), K(+), F(-)) within a classical molecular mechanics framework. States with n less than (and at best equal to) the most probable coordination state ñ account for all of the chemical term and evince the role of the ion in drawing water molecules into the coordination sphere. For states with nñ, the influence of the ion is tempered and changes in coordination states due to density fluctuations in water also appear important. Thus the influence of the ion on the solvent matrix is local, and only a subset of water molecules (nor = ñ) contributes dominantly to the hydration thermodynamics. The n = 4 state of Na(+) (ñ = 5) and K(+) (ñ = 7) and the n = 6 state of F(-) (ñ = 6) are thermodynamically dominant; adding a water molecule to the dominant state additionally contributes only about 2-3 k(B)T toward the chemical term, but removing a water molecule is very unfavorable.

Motivated by a quasi-chemical view of protein hydration, we define specific hydration sites on the surface of globular proteins in terms of the local water density at each site relative to bulk water density. The corresponding kinetic definition invokes the average residence time for a water molecule at each site and the average time that site remains unoccupied. Bound waters are identified by high site occupancies using either definition. In agreement with previous molecular dynamics simulation studies, we find only a weak correlation between local water densities and water residence times for hydration sites on the surface of two globular proteins, lysozyme and staphylococcal nuclease. However, a strong correlation is obtained when both the average residence and vacancy times are appropriately taken into account. In addition, two distinct kinetic regimes are observed for hydration sites with high occupancies: long residence times relative to vacancy times for a single water molecule, and short residence times with high turnover involving multiple water molecules. We also correlate water dynamics, characterized by average occupancy and vacancy times, with local heterogeneities in surface charge and surface roughness, and show that both features are necessary to obtain sites corresponding to kinetically bound waters.

A quasi-chemical theory implemented on the basis of molecular simulation is derived and tested for the hydrophobic hydration of CF4(aq). The theory formulated here subsumes a van der Waals treatment of solvation and identifies contributions to the hydration free energy of CF4(aq) that naturally arise from chemical contributions defined by quasi-chemical theory and fluctuation contributions analogous to Debye-Huckel or random phase approximations. The resulting Gaussian statistical thermodynamic model avoids consideration of hypothetical drying-then-rewetting problems and is physically reliable in these applications as judged by the size of the fluctuation contribution. The specific results here confirm that unfavorable tails of binding energy distributions reflect few-body close solute-solvent encounters. The solvent near-neighbors are pushed by the medium into unfavorable interactions with the solute, in contrast to the alternative view that a preformed interface is pulled by the solute-solvent attractive interactions into contact with the solute. The polyatomic model of CF4(aq) studied gives a satisfactory description of the experimental solubilities including the temperature dependence. The proximal distributions evaluated here for polyatomic solutes accurately reconstruct the observed distributions of water near these molecules which are nonspherical. These results suggest that drying is not an essential consideration for the hydrophobic solubilities of CF4, or of C(CH3)4 which is more soluble.

Plateaus in water adsorption isotherms on hydroxylated BeO surfaces suggest significant differences between the hydroxylated (100) and (001) surface structures and reactivities. Density functional theory structures and energies clarify these differences. Using relaxed surface energies, a Wulff construction yields a prism crystal shape exposing long (100) sides and much smaller (001) faces. This is consistent with the BeO prisms observed when beryllium metal is oxidized. A water oxygen atom binds to a single surface beryllium ion in the preferred adsorption geometry on either surface. The water oxygen/beryllium bonding is stronger on the surface with greater beryllium atom exposure, namely the less-stable (001) surface. Water/beryllium coordination facilitates water dissociation. On the (001) surface, the dissociation products are a hydroxide bridging two beryllium ions and a metal coordinated hydride with some surface charge depletion. On the (100) surface, water dissociates into a hydroxide ligating a Be atom and a proton coordinated to a surface oxygen but the lowest energy water state on the (100) surface is the undissociated metal-coordinated water. The (100) fully hydroxylated surface structure has a hydrogen bonding network which facilitates rapid proton shuffling within the network. The corresponding (001) hydroxylated surface is fairly open and lacks internal hydrogen bonding. This supports previous experimental interpretations of the step in water adsorption isotherms. Further, when the (100) surface is heated to 1000 K, hydroxides and protons associate and water desorbs. The more open (001) hydroxylated surface is stable at 1000 K. This is consistent with the experimental disappearance of the isotherm step when heating to 973 K., 21 pages, 2 table, 5 figures

The hydroxide anion plays an essential role in many chemical and biochemical reactions. But a molecular-scale description of its hydration state, and hence also its transport, in water is currently controversial. The statistical mechanical quasichemical theory of solutions suggests that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{HO}}{\cdot}[{\mathrm{H}}_{2}{\mathrm{O}}]_{3}^{-}\end{equation*}\end{document} is the predominant species in the aqueous phase under standard conditions. This result agrees with recent spectroscopic studies on hydroxide water clusters and with the available thermodynamic hydration free energies. In contrast, a recent ab initio molecular dynamics simulation has suggested that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{HO}}{\cdot}[{\mathrm{H}}_{2}{\mathrm{O}}]_{4}^{-}\end{equation*}\end{document} is the only dominant aqueous solution species. We apply adiabatic ab initio molecular dynamics simulations and find good agreement with both the quasichemical theoretical predictions and experimental results. The present results suggest a picture that is simpler, more traditional, but with additional subtlety. These coordination structures are labile but the tricoordinate species is the prominent case. This conclusion is unaltered with changes in the electronic density functional. No evidence is found for rate-determining activated interconversion of a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{HO}}{\cdot}[{\mathrm{H}}_{2}{\mathrm{O}}]_{4}^{-}\end{equation*}\end{document} trap structure to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{HO}}{\cdot}[{\mathrm{H}}_{2}{\mathrm{O}}]_{3}^{-}\end{equation*}\end{document} mediating hydroxide transport. The view of HO - diffusion as the hopping of a proton hole has substantial validity, the rate depending largely on the dynamic disorder of the water hydrogen-bond network.

The HO$^-$(aq) ion participates in myriad aqueous phase chemical processes of biological and chemical interest. A molecularly valid description of its hydration state, currently poorly understood, is a natural prerequisite to modeling chemical transformations involving HO$^-$(aq). Here it is shown that the statistical mechanical quasi-chemical theory of solutions predicts that $\mathrm{HO\cdot[H_2O]_3{}^-}$ is the dominant inner shell coordination structure for HO$^-$(aq) under standard conditions. Experimental observations and other theoretical calculations are adduced to support this conclusion. Hydration free energies of neutral combinations of simple cations with HO$^-$(aq) are evaluated and agree well with experimental values., 10 pages, 1 figure

AIMD results on a liquid krypton-water system are compared to recent XAFS results for the radial hydration structure for a Kr atom in liquid water solution. The comparisons with the liquid solution results are satisfactory and significantly different from the radial distributions extracted from the data on the solid clathrate hydrate phase. The calculations also produce the coordination number distribution that can be examined for metastable coordination structures suggesting possibilities for clathrate-like organization; none are seen in these results. Clathrate pictures of hydrophobic hydration are discussed, as is the quasi-chemical theory that should provide a basis for clathrate pictures. Outer shell contributions are discussed and accurately estimated; they are positive and larger than the positive experimental hydration free energy of Kr(aq), implying that inner shell contributions must be negative. Clathrate-like inner shell coordination structures extracted from the simulation of the liquid, and then subjected to quantum chemical optimization, always decomposed. Interactions with the outer shell material are decisive in stabilizing coordination structures observed in liquid solution and in clathrate phases. The ``what are we to tell students'' question about hydrophobic hydration, often answered with structural models such as clathrate pictures, is then considered; we propose an alternative answer that is consistent with successful molecular theories of hydrophobic effects and based upon distinctive observable properties of liquid water. Considerations of parsimony, for instance Ockham's razor, then suggest that additional structural hypotheses in response to ``what are we to tell students'' aren't required at this stage, 33 pages, 6 figures

Continuum and atomistic descriptions of the partitioning of ions into a self-assembled (D,L)-octapeptide nanotube, cyclo[-(L-Ala-D-Ala)(4)-], are presented. Perturbation free energy calculations, including Ewald electrostatics, are used to estimate the electrostatic component of the excess free energy of charging Li(+), Na(+), Rb(+), and Cl(minus sign) ions inside the nanotube. The radial density and orientational distribution of water around the ion is calculated for the ion at two different positions inside the tube; it is seen that the calculated distributions are sensitive to the location of the ions. Two different continuum electrostatic models are formulated to describe the ion solvation inside the nanotube. When enhanced orientational structuring of water dipoles is evidenced, explicitly including the first solvation shell as part of the low dielectric nanotube environment provides good agreement with molecular dynamics simulations. When water orientational structuring is as in the reference bulk solvent, we find that treating the first shell water explicitly or as a high dielectric continuum leads to similar results. These results are discussed, and their importance for continuum electrostatic modeling of ion channels are highlighted.

Macromolecular association is an integral component of numerous cellular and technologically relevant processes. Most molecular theories of such association neglect the explicit solvent structure and rely on continuum concepts such as surface energies for calculating short-range interactions. We present a new such method for calculating the non-electrostatic component of the interaction-free energy, based on formalisms for calculating dispersion interactions between macromolecules. The interactions are separated into a short-ranged component that is treated atomistically, and a longer range component that is treated within the continuum Lifshitz–Hamaker approach. This description avoids the singularities inherent in the continuum dispersion formulation, and its effectiveness in characterizing the shape complementarity between interacting surfaces is shown to be comparable to that of surface area-based methods of similar parametric complexity. An advantage of the new method is that it allows facile calculation of the interaction free energy as a function of intermolecular separation, including steric effects; this makes it suitable for use in simulations of protein solutions.

Coordination state probabilities for the [Zn(H(2)O)(n)(CH(3)OH)(m)](2+) complex in aqueous methanol solutions are calculated as a function of the bulk solution concentration, and the number of methanol ligands, m = 0, 1, ..., 6 with n+m = 6. Zinc ion solvation free energies, which serve to normalize these probabilities, also reproduce the methanol concentration dependence of the experimentally derived free energy of zinc ion transfer from water to aqueous methanol solutions. Coordination state probabilities, p(n, m), are derived by extending quasi-chemical theory of ion hydration to solvent mixtures and mixed ligands. Free energy contributions to p(n, m) include the free energy of forming the mixed-ligand complex in the ideal gas, obtained by quantum chemical calculations, and the solvation free energy of the complex, approximated by a dielectric continuum model. We find that replacing water ligands with methanol ligands preferentially stabilizes methanol-rich complexes in the ideal gas. Conversely, water-rich complexes are stabilized by the solvation free energy contribution, such that the [Zn(H(2)O)(6)](2+) complex is the dominant species in solution for all methanol concentrations considered. Stabilization of the methanol-rich complexes is a consequence of the local coordination chemistry, dominated by the delocalization of charge on the zinc ion, while the stabilization of water-rich complexes is a consequence of favorable ion-solvent electrostatic interactions and smaller dielectric cavities for the water-rich complexes at fixed total charge in the dielectric continuum model. Our analysis also highlights an entropic contribution associated with the reversible work required to remove n water and m methanol molecules from bulk solution to form the [Zn(H(2)O)(n)(CH(3)OH)(m)](2+) complex, which captures the methanol concentration dependence of the solvation free energy of the zinc ion.

To gain analytical insights into metal binding to proteins, we express the effective Hamiltonian of an ion binding site in a protein as a combination of the restraints from the protein and the instrinsic vacuum Hamiltonian of the ion bound site. The protein restraints are described by the elastic network mode and the vacuum Hamiltonian of the ion bound site is a generalized Hessian. The resultant of the addition of the two quadratic forms is recast as a pure quadratic form. The free energy of the ion bound protein is analytical. We apply our model to the zinc finger peptide. The model quantitatively captures thermodynamics of Zn2+ preference over its competitors Fe2+, Co2+, Ni2+, and Cd2+ in the protein binding site. We predict that a binding site with minimal protein restraints will select for Zn2+ better than a zinc finger peptide over Fe2+ and Ni2+ while the preference for Zn2+ over Cd2+ and Co2+ will be diminished. We show that the inspecting the interplay between the instrinsic modes of vibrations of the the ion-site cluster and the restraints from the proteins provides a platform for completely analytical and rigorously thermodynamic design principles for metalloproteins.

In a zinc-finger protein, we treat a defined metal-residue cluster at atomic detail and the role of the remaining protein and solvent is described by a molecular field. The structure of this field is obtained by treating the protein outside the cluster as an elastic medium. The strength of the field is adjusted self-consistently to reproduce the binding energy distribution of the metal with the cluster in a reference all-atom simulation. Comparison of the binding energy distribution of the metal with the cluster in vacuum and with the molecular field shows that the protein destabilizes the binding site, revealing the role of favorable metal-site interactions in driving peptide folding. We extensively sample configurations of the cluster (with the field) using a semi-empirical Hamiltonian. For configurations from this sample, we study the free energy of replacing Zn2+ with Fe2+, Co2+, and Ni2+ using density functional theory with a large basis set. The calculated selectivities are found to be in good agreement with experimental results. Advantages and limitations of the method are discussed.

To understand the basis of ion-specific effects in biology, it is necessary to first understand the hydration structure and thermodynamics of ions. Based on a multi-state organization of the potential distribution theorem, we present new insights on the role of ion-water interactions and water density fluctuations at the size-scale of the ion in determining the ion-hydration structure and thermodynamics. We find that the hydration free energy of the ion depends on three quantities: 1) the hydration free energy of the ion in a specified n-coordinate state, where in the n-coordinate state n water molecules are present within the coordination volume of the ion; 2) the probability, xn, of observing that n-coordinate state around the ion; and 3) the probability, pn, of observing n water molecules in the coordination volume in the absence of the ion. Based on this development we find that only a small subset of water molecules in the first hydration shell of the ion sense the chemical type of the ion. Further, these core-water molecules tend to attenuate the interaction of the ion with the rest of the medium, and thus the higher coordination states of the ion more sensitively reflect density fluctuations of the solvent medium at the size scale of the observation volume. The relevance of this development in understanding ion-pairing and the selective binding of ions to biological molecules is discussed.