Enthalpy−Entropy and Cavity Decomposition of Alkane Hydration Free Energies: Numerical Results and Implications for Theories of Hydrophobic Solvation

A new angle on heat capacity changes in hydrophobic solvation

The differential solubility of polar and apolar groups in water is important for the self-assembly of globular proteins, lipid membranes, nucleic acids, and other specific biological structures through hydrophobic and hydrophilic effects. The increase in water's heat capacity upon hydration of apolar compounds is one signature of the hydrophobic effect and differentiates it from the hydration of polar compounds, which cause a decrease in heat capacity. Water structuring around apolar and polar groups is an important factor in their differential solubility and heat capacity effects. Here, it is shown that joint radial/angular distribution functions of water obtained from simulations reveal quite different hydration structures around polar and apolar groups: polar and apolar groups have a deficit or excess, respectively, of "low angle hydrogen bonds". Low angle hydrogen bonds have a larger energy fluctuation than high angle bonds, and analysis of these differences provides a physical reason for the opposite changes in heat capacity and new insight into water structure around solutes and the hydrophobic effect.

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.

On the cavity size distribution in water and n-hexane

The cavity size distribution functions in water and n-hexane were determined by Pohorille and Pratt, in a series of important works, from molecular dynamics simulations. These functions are considered as experimental data. In the present investigation the ability of scaled particle theory in reproducing such distributions is tested. In the case of water the scaled particle theory results compare favorably with the experimental distribution if a proper choice of the size to be assigned to water molecules is performed. Specifically, a slight size increase from 2.70 to 2.80 A is necessary to reach agreement for the largest cavities detected by Pohorille and Pratt. In the case of n-hexane the scaled particle theory results do not agree with the experimental distribution especially in the region of small cavities. This deficiency is because a n-hexane molecule cannot be realistically treated as a single spherical exclusion volume. The implications of such findings are analyzed and discussed in depth.

Molecular dynamics simulations of end-to-end contact formation in hydrocarbon chains in water and aqueous urea solution

We probe the urea-denaturation mechanism using molecular dynamics simulations of an elementary "folding" event, namely, the formation of end-to-end contact in the linear hydrocarbon chain (HC) CH(3)(CH(2))(18)CH(3). Electrostatic effects are examined using a model HC in which one end of the chain is positively charged (+0.2e) and the other contains a negative charge (-0.2e). For these systems multiple transitions between "folded" (conformations in which the chain ends are in contact) and "unfolded" (end-to-end contact is broken) can be observed during 4 ns molecular dynamics simulations. In water and 6 M aqueous urea solution HC and the charged HC fluctuate between collapsed globular conformations and a set of expanded structures. The collapsed conformation adopted by the HC in water is slightly destablized in 6 M urea. In contrast, the end-to-end contact is disrupted in the charged HC only in aqueous urea solution. Despite the presence of a large hydrophobic patch, on length scales on the order of approximately 8-10 A "denaturation" (transition to the expanded unfolded state) occurs by a direct interaction of urea with charges on the chain ends. The contiguous patch of hydrophobic moieties leads to "mild dewetting", which becomes more pronounced in the charged HC in 6 M aqueous urea solution. Our simulations establish that the urea denaturation mechanism is most likely electrostatic in origin.

Converging free energy estimates: MM-PB(GB)SA studies on the protein-protein complex Ras-Raf

Estimating protein-protein interaction energies is a very challenging task for current simulation protocols. Here, absolute binding free energies are reported for the complex H-Ras/C-Raf1 using the MM-PB(GB)SA approach, testing the internal consistency and model dependence of the results. Averaging gas-phase energies (MM), solvation free energies as determined by Generalized Born models (GB/SA), and entropic contributions calculated by normal mode analysis for snapshots obtained from 10 ns explicit-solvent molecular dynamics in general results in an overestimation of the binding affinity when a solvent-accessible surface area-dependent model is used to estimate the nonpolar solvation contribution. Applying the sum of a cavity solvation free energy and explicitly modeled solute-solvent van der Waals interaction energies instead provides less negative estimates for the nonpolar solvation contribution. When the polar contribution to the solvation free energy is determined by solving the Poisson-Boltzmann equation (PB) instead, the calculated binding affinity strongly depends on the atomic radii set chosen. For three GB models investigated, different absolute deviations from PB energies were found for the unbound proteins and the complex. As an alternative to normal-mode calculations, quasiharmonic analyses have been performed to estimate entropic contributions due to changes of solute flexibility upon binding. However, such entropy estimates do not converge after 10 ns of simulation time, indicating that sampling issues may limit the applicability of this approach. Finally, binding free energies estimated from snapshots of the unbound proteins extracted from the complex trajectory result in an underestimate of binding affinity. This points to the need to exercise caution in applying the computationally cheaper "one-trajectory-alternative" to systems where there may be significant changes in flexibility and structure due to binding. The best estimate for the binding free energy of Ras-Raf obtained in this study of -8.3 kcal mol(-1) is in good agreement with the experimental result of -9.6 kcal mol(-1), however, further probing the transferability of the applied protocol that led to this result is necessary.

Hydration entropy change from the hard sphere model

The gas to liquid transfer entropy change for a pure non-polar liquid can be calculated quite accurately using a hard sphere model that obeys the Carnahan-Starling equation of state. The same procedure fails to produce a reasonable value for hydrogen bonding liquids such as water, methanol and ethanol. However, the size of the molecules increases when the hydrogen bonds are turned off to produce the hard sphere system and the volume packing density rises. We show here that the hard sphere system that has this increased packing density reproduces the experimental transfer entropy values rather well. The gas to water transfer entropy values for small non-polar hydrocarbons is also not reproduced by a hard sphere model, whether one uses the normal (2.8 A diameter) or the increased (3.2 A) size for water. At least part of the reason that the hard sphere model with 2.8 A size water produces too small entropy change is that the size of water is too small for a system without hydrogen bonds. The reason that the 3.2 A model also produces too small entropy values is that this is an overly crowded system and that the free volume introduced in the system by the addition of a solute molecule produces too much of a relief to this crowding. A hard sphere model, in which the free volume increase is limited by requiring that the average surface-to-surface distance between the solute and water molecules is the same as that between the increased-size water molecules, does approximately reproduce the experimental hydration entropy values.

A revised quantum chemistry-based potential for poly(ethylene oxide) and its oligomers in aqueous solution

We have conducted a high-level quantum chemistry study of the interactions of 1,2-dimethoxyethane (DME) with water for complexes representing both hydrophilic and hydrophobic hydration. It was found that our previous quantum chemistry-based force field for poly(ethylene oxide) (PEO) and its oligomers in aqueous solution did a poor job in describing the hydrophobic binding of water to the ether, consistent with our recent calculations of the excess free energy and entropy of hydration of DME. Our original force field was revised to more accurately reproduce the interaction of water with the carboneous portions of DME. Molecular dynamics simulations of aqueous DME solutions using the revised quantum chemistry-based potential yielded good agreement with experiment for excess free energy, enthalpy, and volume as well as excess solution viscosity and the self-diffusion of water. Comparison with our original potential revealed that the relatively hydrophobic ether-water interactions in the new potential strongly reduced the favorable excess free energy and enthalpy but have relatively little influence on the excess entropy for dilute DME solutions. Other properties of DME and PEO solutions including conformational populations and dynamics, solution viscosity, hydrogen bonding, water translational and rotational diffusion and neutron structure factor as a function of solution composition were found to be largely unchanged from those obtained using the original potential.

Using extrathermodynamic relationships to model the temperature dependence of Henry's law constants of 209 PCB congeners

Our previous measurements of the temperature dependencies of Henry's law constants of 26 polychlorinated biphenyls (PCBs) showed a well-defined linear relationship between the enthalpy and the entropy of phase change. Within a homologue group, the Henry's law constants converged to a common value at a specific isoequilibrium temperature. We use this relationship to model the temperature dependencies of the Henry's law constants of the remaining PCB congeners. By using experimentally measured Henry's law constants at 11 degrees C for 61 PCB congeners described in this paper combined with the isoequilibrium temperatures from our previous measurements of Henry's law constants of 26 PCB congeners, we have derived an empirical relationship between the enthalpies and the entropies of phase change for these additional PCB congeners. A systematic variation in the enthalpies and entropies of phase change was found to be partially dependent on the chlorine number and substitution patterns on the biphenyl rings, allowing further estimation of the temperature dependence of Henry's law constants for the remaining 122 PCB congeners. The enthalpies of phase change for all 209 PCB congeners ranged between 10 and 169 kJ mol(-1), where the enthalpies of phase change decreased as the number of ortho chlorine substitutions on the biphenyl rings increased within homologue groups. These data are used to predict the temperature dependence of Henry's law constants for all 209 PCB congeners.

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.

The SGB/NP hydration free energy model based on the surface generalized born solvent reaction field and novel nonpolar hydration free energy estimators

The development and parameterization of a solvent potential of mean force designed to reproduce the hydration thermodynamics of small molecules and macromolecules aimed toward applications in conformation prediction and ligand binding free energy prediction is presented. The model, named SGB/NP, is based on a parameterization of the Surface Generalized Born continuum dielectric electrostatic model using explicit solvent free energy perturbation calculations and a newly developed nonpolar hydration free energy estimator motivated by the results of explicit solvent simulations of the thermodynamics of hydration of hydrocarbons. The nonpolar model contains, in addition to the more commonly used solvent accessible surface area term, a component corresponding to the attractive solute-solvent interactions. This term is found to be important to improve the accuracy of the model, particularly for cyclic and hydrogen bonding compounds. The model is parameterized against the experimental hydration free energies of a set of small organic molecules. The model reproduces the experimental hydration free energies of small organic molecules with an accuracy comparable or superior to similar models employing more computationally demanding estimators and/or a more extensive set of parameters.

Size and temperature dependence of hydrocarbon solubility in concentrated aqueous solutions of urea and guanidine hydrochloride

At 25°C, methane and ethane are more soluble in water than in 7 M aqueous urea or 4.9 M aqueous guanidine hydrochloride (GuHCl); the reverse is true for larger hydrocarbons. In addition, the hydrocarbon solubility in 7 M aqueous urea or 4.9 M aqueous GuHCl increases compared with that in water on raising the temperature in the range of 5–45°C. These experimental data have not yet been rationalized. Using a well-founded theory of hydrophobic hydration, the present analysis indicates that the transfer of hydrocarbons from water to 7 M aqueous urea or to 4.9 M aqueous GuHCl is favored by the difference in the solute–solvent van der Waals interaction energy, and contrasted by the difference in the work of cavity creation. At room temperature, on increasing the hydrocarbon size, the first contribution rises in magnitude more rapidly than the second contribution, accounting for the threshold size occurrence. Moreover, the second contribution decreases in magnitude with an increase in temperature, becoming less unfavorable, while the first contribution is practically constant in the range of 5–45°C. The different temperature dependence of the work of cavity creation in such solvent systems is due to the fact that the density of 7 M aqueous urea and 4.9 M aqueous GuHCl decreases more rapidly than that of water when raising the temperature. The relationship between the density of a liquid and the work to create a cavity in it is discussed in detail.Key words: work of cavity creation, solute-solvent van der Waals interaction energy, H-bond reorganization.

Solvent size vs cohesive energy as the origin of hydrophobicity

Two main physical explanations of hydrophobicity seem to be currently competing. The classical, intuitive view attributes it to the fact that interactions between water molecules are much stronger than those between water and nonpolar groups. The second, "heretical" view attributes it to the small size of the water molecule which increases the entropic cost of opening up a cavity to accommodate the solute. Here we examine the solvation of methane in water and in model liquids that lack one or more of water's properties and report a detailed decomposition of the solvation free energy, enthalpy, entropy, and heat capacity in these solvents. The results fully support the classical view. It is found that fluids with strong intermolecular interactions favor expulsion of methane to its pure phase or to CCl(4), whereas fluids with weak intermolecular interactions do not. However, the specific thermodynamic signature of the hydrophobic effect (entropy driven at room temperature with a large heat capacity change) is a result of the hydrogen-bonding structure of water.

An analysis of the hydration thermodynamics of the CONH group

The hydration thermodynamics of the CONH group play a fundamental role for the stability of the native conformation of globular proteins, but cannot be measured in a direct manner. The values of the thermodynamic functions have to be extracted from experimental measurements on model compounds using group additivity approaches. The estimates determined by Makhatadze and Privalov in the temperature range 5–100°C are used in the present study in view of their qualitative reliability. They are analyzed by means of a suitable approach that couples scaled particle theory calculations with the application of the modified Muller's model. It results that the negative entropy change is caused by the excluded volume effect for cavity creation, exaggerated in liquid water by the small size of water molecules themselves; the negative enthalpy change is determined by the H-bond energetics, formation of CONH–water H-bonds, and reorganization of water–water H-bonds. The negative heat capacity change, a striking feature of CONH hydration thermodynamics, is because the H-bonds in the hydration shell of the CONH group are less broken than those in bulk water in the temperature range examined.Key words: peptide group, hydration, excluded volume effect, H-bonds, two-state model, negative heat capacity change.