Hydrophobic hydration: a free energy perturbation study (original) (raw)
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International Journal of Quantum Chemistry, 2004
Free energies of hydration (FEH) have been computed for 13 neutral and nine ionic species as a difference of theoretically calculated Gibbs free energies in solution and in the gas phase. In-solution calculations have been performed using both SCIPCM and PCM polarizable continuum models at the density functional theory (DFT)/B3LYP and ab initio Hartree-Fock levels with two basis sets (6-31G* and 6-311ϩϩG**). Good linear correlation has been obtained for calculated and experimental gas-phase dipole moments, with an increase by ϳ30% upon solvation due to solute polarization. The geometry distortion in solution turns out to be small, whereas solute polarization energies are up to 3 kcal/mol for neutral molecules. Calculation of free energies of hydration with PCM provides a balanced set of values with 6-31G* and 6-311ϩϩG** basis sets for neutral molecules and ionic species, respectively. Explicit solvent calculations within Monte Carlo simulations applying free energy perturbation methods have been considered for 12 neutral molecules. Four different partial atomic charge sets have been studied, obtained by a fit to the gas-phase and in-solution molecular electrostatic potentials at in-solution optimized geometries. Calculated FEH values depend on the charge set and the atom model used. Results indicate a preference for the all-atom model and partial charges obtained by a fit to the molecular electrostatic potential of the solute computed at the SCIPCM/B3LYP/6-31G* level.
The Journal of Physical Chemistry, 1994
The absolute free energies of hydration of methane, methanol, and the ammonium ion have been determined from free energy perturbation (FEP) calculations, using two different sets of nonbonded van der Waals parameters, together with point charge models obtained from Mulliken population analysis and from ab initio 6-31G** molecular electrostatic potentials. The variation in absolute free energy found for methane with the two sets of charges suggests that, as expected, the role of the electrostatic term is minor in comparison with the sampling imperfections of the simulation. The case study of methanol illustrates the difficulties in deriving an unambiguously "correct" charge model that are often encountered when calculating the absolute free energy of hydration of flexible molecules. Fortuitously, it appears that, whether Mulliken or electrostatic potential derived charges are employed and whether the molecule is constrained to a rigid low-energy conformation or not, no major difference in free energy is observed. Concerning the ammonium ion, the generally overestimated magnitude of the electrostatic contribution to the total free energy of hydration when a Born-type correction is included confirms the limitations of a standard two-body additive model for simulating absolute solvation free energies of charged solutes.
Improved estimates for hydration free energy obtained by the reference interaction site model
Chemical Physics Letters, 2007
We propose to improve the existing free energy expressions obtained within the framework of the reference interaction site model (RISM) combined with the hypernetted closure. The proposed expression is based on the partial wave expression [S. Ten-no, J. Chem. Phys. 115 3724] but includes semiempirical corrections to account properly for excluded volume and hydrogen bonding effects. Testing several free energy expressions for various polar and hydrophobic solutes, we have found that such empirical parameterization of the partial wave expression can provide accurate estimates of hydration energies for different hydrophobic and polar solutes. The proposed correction allows one to reduce the discrepancy between the experimental and the calculated data down to 0.7 kcal/mol.
Toward a simple molecular theory of hydrophobic hydration
Journal of Molecular Liquids, 2014
A perturbation theory of water is extended to mixtures, and its application to aqueous solutions of noble gases is presented. The present approach is based on the thermodynamic perturbation theory of the primitive models of associating fluids, substituting the reference pseudo-hard-body term by a hard-sphere/pseudo-hard-body mixture term and introducing appropriate corrections. The primitive models are constructed in a rigorous way from realistic parents. The procedure yields equations of state allowing for the determination of all residual properties. The residual chemical potential is expressed and subsequently the Henry's law constants of noble gases, from He to Xe, are evaluated as functions of temperature showing qualitative agreement with experimental data. Throughout the procedure, no experimental data are used to adjust the parameters or to fine-tune the results.
Computation of hydration free energies of organic solutes with an implicit water model
Journal of Computational Chemistry, 2006
A new approach for computing hydration free energies ⌬G solv of organic solutes is formulated and parameterized. The method combines a conventional PCM (polarizable continuum model) computation for the electrostatic component ⌬G el of ⌬G solv and a specially detailed algorithm for treating the complementary nonelectrostatic contributions (⌬G nel ). The novel features include the following: (a) two different cavities are used for treating ⌬G el and ⌬G nel . For the latter case the cavity is larger and based on thermal atomic radii (i.e., slightly reduced van der Waals radii). (b) The cavitation component of ⌬G nel is taken to be proportional to the volume of the large cavity. (c) In the treatment of van der Waals interactions, all solute atoms are counted explicitly. The corresponding interaction energies are computed as integrals over the surface of the larger cavity; they are based on Lennard Jones (LJ) type potentials for individual solute atoms. The weighting coefficients of these LJ terms are considered as fitting parameters. Testing this method on a collection of 278 uncharged organic solutes gave satisfactory results. The average error (RMSD) between calculated and experimental free energy values varies between 0.15 and 0.5 kcal/mol for different classes of solutes. The larger deviations found for the case of oxygen compounds are probably due to a poor approximation of H-bonding in terms of LJ potentials. For the seven compounds with poorest fit to experiment, the error exceeds 1.5 kcal/mol; these outlier points were not included in the parameterization procedure. Several possible origins of these errors are discussed. Figure 3. (a) Calculated [⌬G nel (calc)] and experimental [⌬G nel (exp)] nonelectrostatic components of solvation free energies in kcal/mol for aromatic and nitrogen compounds. (b) Calculated [⌬G nel (calc)] and experimental [⌬G nel (exp)] nonelectrostatic components of solvation free energies in kcal/mol for aromatic and nitrogen compounds. ⌬G el calculated with DMol 3 . compounds: ethers and alcohols. (b) Calculated [⌬G nel (calc)] and experimental [⌬G nel (exp)] nonelectrostatic components of solvation free energies in kcal/mol for oxygen compounds: esters and carbonyl groups. (c) Calculated [⌬G nel (calc)] and experimental [⌬G nel (exp)] nonelectrostatic components of solvation free energies in kcal/mol for oxygen compounds: ethers and alcohols. ⌬G el calculated with DMol 3 .
Collective properties of hydration: long range and specificity of hydrophobic interactions
Biophysical Journal, 1997
We report results of molecular dynamics (MD) simulations of composite model solutes in explicit molecular water solvent, eliciting novel aspects of the recently demonstrated, strong many-body character of hydration. Our solutes consist of identical apolar (hydrophobic) elements in fixed configurations. Results show that the many-body character of PMF is sufficiently strong to cause 1) a remarkable extension of the range of hydrophobic interactions between pairs of solute elements, up to distances large enough to rule out pairwise interactions of any type, and 2) a SIF that drives one of the hydrophobic solute elements toward the solvent rather than away from it. These findings complement recent data concerning SIFs on a protein at single-residue resolution and on model systems. They illustrate new important consequences of the collective character of hydration and of PMF and reveal new aspects of hydrophobic interactions and, in general, of SIFs. Their relevance to protein recognition, conformation, function, and folding and to the observed slight yet significant nonadditivity of functional effects of distant point mutations in proteins is discussed. These results point out the functional role of the configurational and dynamical states (and related statistical weights) corresponding to the complex configurational energy landscape of the two interacting systems: biomolecule + water.
The Journal of Physical Chemistry B, 2020
The occupancy distribution of water molecules in the first hydration shell around a solute is intimately connected with solvent density fluctuations and is of fundamental interest in understanding hydration. The free energies to evacuate the first hydration shell around a solute and a cavity defined by the first hydration shell depend on the system size, emphasizing that the solvent density fluctuations are themselves dependent on the system size. This observation interpreted within the quasichemical theory shows that both the hydrophilic and the hydrophobic contributions to hydration depend on the system size, decreasing with increasing system size. The net hydration free energy benefits somewhat from the compensation of hydrophilic and hydrophobic contributions; nevertheless a large system appears necessary to describe correctly the balance of these contributions in the hydration of the macromolecule.
Accuracy of free energies of hydration using CM1 and CM3 atomic charges
Journal of Computational Chemistry, 2004
Absolute free energies of hydration (⌬G hyd ) have been computed for 25 diverse organic molecules using partial atomic charges derived from AM1 and PM3 wave functions via the CM1 and CM3 procedures of Cramer, Truhlar, and coworkers. Comparisons are made with results using charges fit to the electrostatic potential surface (EPS) from ab initio 6-31G* wave functions and from the OPLS-AA force field. OPLS Lennard-Jones parameters for the organic molecules were used together with the TIP4P water model in Monte Carlo simulations with free energy perturbation theory. Absolute free energies of hydration were computed for OPLS united-atom and all-atom methane by annihilating the solutes in water and in the gas phase, and absolute ⌬G hyd values for all other molecules were computed via transformation to one of these references. Optimal charge scaling factors were determined by minimizing the unsigned average error between experimental and calculated hydration free energies. The PM3-based charge models do not lead to lower average errors than obtained with the EPS charges for the subset of 13 molecules in the original study. However, improvement is obtained by scaling the CM1A partial charges by 1.14 and the CM3A charges by 1.15, which leads to average errors of 1.0 and 1.1 kcal/mol for the full set of 25 molecules. The scaled CM1A charges also yield the best results for the hydration of amides including the E/Z free-energy difference for N-methylacetamide in water.
Theoretical Chemistry Accounts, 2008
Hartree-Fock (HF) and second-order Møller-Plesset (MP2) calculations were used to investigate the structures and thermochemistry of methylammonium-water clusters (Me 4−m NH m m=1-4, n=1-4). Water molecules were treated ab initio and with effective fragment potentials (EFP). In addition to a thorough phase-space search, the importance of basis set, electron correlation, and thermodynamic effects was systematically examined. Cluster structures resulted from hydrogen bond formation between the ammonium group and water molecules; upon saturation of the hydrogen bonding sites of the ammonium group, water molecules entered the second hydration shell. With only four water molecules, the experimental relative enthalpies of hydration were well reproduced at the HF level, while the MP2 relative free energies were in best agreement with experiment. Absolute energies of hydration were calculated using an empirical correction. These results strongly suggest that a HF-based microsolvation approach employing a small number of water molecules can be used to compute relative enthalpies of hydration.
Immobilized water in hydrophobic hydration
Springer Series in Chemical Physics, 2009
Although perfluorination is known to enhance hydrophobicity and change protein activity, its influence on hydration-shell structure and thermodynamics remains an open question. Here we address that question by combining experimental Raman multivariate curve resolution spectroscopy with theoretical classical simulations and quantum mechanical calculations. Perfluorination of the terminal methyl group of ethanol is found to enhance the disruption of its hydration-shell hydrogen bond network. Our results reveal that this disruption is not due to the associated volume change but rather to the electrostatic stabilization of the water dangling OH•••F interaction. Thus, the hydration shell structure of fluorinated methyl groups results from a delicate balance of solute−water interactions that is intrinsically different from that associated with a methyl group.