Hydration and conformational equilibria of simple hydrophobic and amphiphilic solutes

Effect of Conformational Equilibrium on Solvation Properties of 1,2-DCE in Water: A Solvation Thermodynamics and 3D-RISM Study

The contributions of the enthalpy and entropy of solvation for the study of chemical and biological systems are important in the prediction, interpretation, and manipulation of these processes. The relation between solvation Gibbs energies, enthalpies, and entropies of solvation, and their rigorous relation with the conformational equilibrium, are derived for the first time and applied with a computational method, in accordance with the Solvation Thermodynamics previous results, to 1,2-dichloroethane solvation in water. The rigid conformer calculations in solution were performed by using PC+/3D-RISM approach, with the conformational averaged results for enthalpy and solvation Gibbs energy reproducing the experimental results quite successfully. A qualitative agreement in the entropy of solvation predictions was also observed.

Reconciling the understanding of 'hydrophobicity' with physics-based models of proteins

The idea that a 'hydrophobic energy' drives protein folding, aggregation, and binding by favoring the sequestration of bulky residues from water into the protein interior is widespread. The solvation free energies (ΔGsolv) of small nonpolar solutes increase with surface area (A), and the free energies of creating macroscopic cavities in water increase linearly with A. These observations seem to imply that there is a hydrophobic component (ΔGhyd) of ΔGsolv that increases linearly with A, and this assumption is widely used in implicit solvent models. However, some explicit-solvent molecular dynamics studies appear to contradict these ideas. For example, one definition (ΔG(LJ)) of ΔGhyd is that it is the free energy of turning on the Lennard-Jones (LJ) interactions between the solute and solvent. However, ΔG(LJ) decreases with A for alanine and glycine peptides. Here we argue that these apparent contradictions can be reconciled by defining ΔGhyd to be a near hard core insertion energy (ΔGrep), as in the partitioning proposed by Weeks, Chandler, and Andersen. However, recent results have shown that ΔGrep is not a simple function of geometric properties of the molecule, such as A and the molecular volume, and that the free energy of turning on the attractive part of the LJ potential cannot be computed from first-order perturbation theory for proteins. The theories that have been developed from these assumptions to predict ΔGhyd are therefore inadequate for proteins.

Confinement induced conformational changes in n-alkanes sequestered within a narrow carbon nanotube

While alkanes in solution exhibit predominantly extended conformations, nanoscale confinement of these chains within protein binding sites and synthetic receptors can significantly alter the conformer distribution. As a simple model for the effect of confinement on the conformation, we report molecular simulations of n-alkanes absorbed from a bulk solvent into narrow carbon nanotubes. We observe that confinement of butane, hexane, and tetracosane induces a trans to gauche conformational redistribution. Moreover, confined hexane and tetracosane exhibit cooperative interactions between neighboring dihedral angles, which promote a helical gauche conformation for the portions of the chain within the nanotube. Hexane absorbed into the nanotube from water or benzene exhibits essentially the same conformation regardless of the bulk solvent. The PMF between the nanotube and hexane along the central nanotube axis finds that nanotube absorption is favorable from aqueous solution but neutral from benzene. The interaction between hexane and the nanotube in water is dominated by the direct interaction between the alkane and the nanotube and weakly opposed by indirect water-mediated forces. In benzene, however, the direct alkane/nanotube interaction is effectively balanced by the indirect benzene-mediated interaction. Our simulations in water stand in difference to standard interpretations of the hydrophobic effect, which posit that the attraction between non-polar species in water is driven by their mutual insolubility.

Ionization Equilibria and Conformational Transitions in Polyprotic Molecules and Polyelectrolytes

The coupling between proton binding and conformational degrees of freedom in polyprotic molecules and polyelectrolytes is studied theoretically. Our approach combines the classical rotational isomeric state (RIS) model developed by Flory and the site binding (SB) model used to treat proton binding equilibria. The properties of the resulting SBRIS model, which treats conformational degrees of freedom and proton binding on equal footing, are studied with statistical mechanical techniques. Quantities of interest, such as titration curves, conformational probabilities, or macroscopic binding constants, are expressed as thermal averages and are evaluated by direct enumeration of states or by transfer matrix techniques. We further demonstrate that in the SBRIS model conformational degrees of freedom can be averaged out, leading to the contracted description within the SB model. In most cases, this contraction leads to higher order interactions, which may not be present at the SBRIS level (e.g., triplet interactions). Several examples are discussed to illustrate the concepts developed. The case of succinic acid exemplifies the situation in its simplest form. The model can further rationalize the very different titration behavior of poly(acrylic acid) (PAA) and poly(methacrylic acid) (PMAA). In particular, the characteristic "jump" in the titration curve of PMAA is described quantitatively and is interpreted in terms of a conformational transition.

Coupling hydrophobicity, dispersion, and electrostatics in continuum solvent models

An implicit solvent model is presented that couples hydrophobic, dispersion, and electrostatic solvation energies by minimizing the system Gibbs free energy with respect to the solvent volume exclusion function. The solvent accessible surface is the output of the theory. The method is illustrated with the solvation of simple solutes on different length scales and captures the sensitivity of hydration to the particular form of the solute-solvent interactions in agreement with recent computer simulations.

Coupling nonpolar and polar solvation free energies in implicit solvent models

Recent studies on the solvation of atomistic and nanoscale solutes indicate that a strong coupling exists between the hydrophobic, dispersion, and electrostatic contributions to the solvation free energy, a facet not considered in current implicit solvent models. We suggest a theoretical formalism which accounts for coupling by minimizing the Gibbs free energy of the solvent with respect to a solvent volume exclusion function. The resulting differential equation is similar to the Laplace-Young equation for the geometrical description of capillary interfaces but is extended to microscopic scales by explicitly considering curvature corrections as well as dispersion and electrostatic contributions. Unlike existing implicit solvent approaches, the solvent accessible surface is an output of our model. The presented formalism is illustrated on spherically or cylindrically symmetrical systems of neutral or charged solutes on different length scales. The results are in agreement with computer simulations and, most importantly, demonstrate that our method captures the strong sensitivity of solvent expulsion and dewetting to the particular form of the solvent-solute interactions.

Computation of hydration free energies of organic solutes with an implicit water model

A new approach for computing hydration free energies DeltaG(solv) of organic solutes is formulated and parameterized. The method combines a conventional PCM (polarizable continuum model) computation for the electrostatic component DeltaG(el) of DeltaG(solv) and a specially detailed algorithm for treating the complementary nonelectrostatic contributions (DeltaG(nel)). The novel features include the following: (a) two different cavities are used for treating DeltaG(el) and DeltaG(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 DeltaG(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.

The non-polar solvent potential of mean force for the dimerization of alanine dipeptide: the role of solute-solvent van der Waals interactions

The non-polar component of the potential of mean force of dimerization of alanine dipeptide has been calculated in explicit solvent by free energy perturbation. We observe that the calculated PMF is inconsistent with a non-polar hydration free energy model based solely on the solute surface area. The non-linear behavior of the solute-solvent van der Waals energy is primarily responsible for the non-linear dependence of the potential of mean force with respect to the surface area. The calculated potential of mean force is reproduced by an implicit solvent model based on a solvent continuum model for the solute-solvent van der Waals interaction energy and the surface area for the work of forming the solute cavity.

On the nonpolar hydration free energy of proteins: surface area and continuum solvent models for the solute-solvent interaction energy

Implicit solvent hydration free energy models are an important component of most modern computational methods aimed at protein structure prediction, binding affinity prediction, and modeling of conformational equilibria. The nonpolar component of the hydration free energy, consisting of a repulsive cavity term and an attractive van der Waals solute-solvent interaction term, is often modeled using estimators based on the solvent exposed solute surface area. In this paper, we analyze the accuracy of linear surface area models for predicting the van der Waals solute-solvent interaction energies of native and non-native protein conformations, peptides and small molecules, and the desolvation penalty of protein-protein and protein-ligand binding complexes. The target values are obtained from explicit solvent simulations and from a continuum solvent van der Waals interaction energy model. The results indicate that the standard surface area model, while useful on a coarse-grained scale, may not be accurate or transferable enough for high resolution modeling studies of protein folding and binding. The continuum model constructed in the course of this study provides one path for the development of a computationally efficient implicit solvent nonpolar hydration free energy estimator suitable for high-resolution structural and thermodynamic modeling of biological macromolecules.

Molecular theory of hydrophobic effects: "She is too mean to have her name repeated."

This paper reviews the molecular theory of hydrophobic effects relevant to biomolecular structure and assembly in aqueous solution. Recent progress has resulted in simple, validated molecular statistical thermodynamic theories and clarification of confusing theories of decades ago. Current work is resolving effects of wider variations of thermodynamic state, e.g., pressure denaturation of soluble proteins, and more exotic questions such as effects of surface chemistry in treating stability of macromolecular structures in aqueous solution.

Conformational equilibria of alkanes in aqueous solution: relationship to water structure near hydrophobic solutes

Conformational free energies of butane, pentane, and hexane in water are calculated from molecular simulations with explicit waters and from a simple molecular theory in which the local hydration structure is estimated based on a proximity approximation. This proximity approximation uses only the two nearest carbon atoms on the alkane to predict the local water density at a given point in space. Conformational free energies of hydration are subsequently calculated using a free energy perturbation method. Quantitative agreement is found between the free energies obtained from simulations and theory. Moreover, free energy calculations using this proximity approximation are approximately four orders of magnitude faster than those based on explicit water simulations. Our results demonstrate the accuracy and utility of the proximity approximation for predicting water structure as the basis for a quantitative description of n-alkane conformational equilibria in water. In addition, the proximity approximation provides a molecular foundation for extending predictions of water structure and hydration thermodynamic properties of simple hydrophobic solutes to larger clusters or assemblies of hydrophobic solutes.