Temperature and length scale dependence of hydrophobic effects and their possible implications for protein folding

Dynamics of Water Trapped between Hydrophobic Solutes

We describe the model dynamical behavior of the solvent between two nanoscopic hydrophobic solutes. The dynamics of the vicinal water in various sized traps is found to be significantly different from bulk behavior. We consider the dynamics at normal temperature and pressure at three intersolute distances corresponding to the three solvent separated minima in the free energy profile between the solutes with attractions. These three states correspond to one, two, and three intervening layers of water molecules. Results are obtained from a molecular dynamics simulation at constant temperature and pressure (NPT) ensemble. Translational diffusion of water molecules trapped between the two solutes has been analyzed from the velocity correlation function as well as from the mean square displacement of the water molecules. The rotational behavior has been analyzed through the reorientational dynamics of the dipole moment vector of the water molecule by calculating both first and second rank dipole-dipole correlation functions. Both the translational and reorientational mobilities of water are found to be much slower at the smaller separation and increases as the separation between solutes becomes larger. The occupation time distribution functions calculated from the trajectories also show that the relaxation is much slower for the smallest intersolute separation as compared to other wider separations. The sublinear trend in mean square displacement and the stretched exponential decay of the relaxation of dipolar correlation and occupation distribution function indicate that the dynamical behavior of water in the confined region between two large hydrophobic solutes departs from usual Brownian behavior. This behavior is reminiscent of the behavior of water in the vicinity of protein surface clefts or trapped between two domains of a protein.

On the Mechanism of Hydrophobic Association of Nanoscopic Solutes

The hydration behavior of two planar nanoscopic hydrophobic solutes in liquid water at normal temperature and pressure is investigated by calculating the potential of mean force between them at constant pressure as a function of the solute-solvent interaction potential. The importance of the effect of weak attractive interactions between the solute atoms and the solvent on the hydration behavior is clearly demonstrated. We focus on the underlying mechanism behind the contrasting results obtained in various recent experimental and computational studies on water near hydrophobic solutes. The length scale where crossover from a solvent separated state to the contact pair state occurs is shown to depend on the solute sizes as well as on details of the solute-solvent interaction. We find the mechanism for attractive mean forces between the plates is very different depending on the nature of the solute-solvent interaction which has implications for the mechanism of the hydrophobic effect for biomolecules.

Water between Plates in the Presence of an Electric Field in an Open System

Molecular dynamics simulations of water at 298 K and 1 atm of pressure are used to investigate the electric-field dependence of the density and polarization density of water between two graphite-like plates of different sizes (9.8 x 9.2 and 17.7 x 17.2 A) in an open system for plate separations of 8.0, 9.5, and 16.4 A. The interactions with water were tuned to "hard-wall-like" and "normal" C-O hydrophobic potentials. Water between the larger plates at 16.4 A separation is layered but is metastable with respect to capillary evaporation at zero field (Bratko, D.; Curtis, R. A.; Blanch, H. W.; Prausnitz, J. M. J. Chem. Phys. 2001, 115, 3873). Applying a field decreases the density of the water between the plates, in apparent contradiction to thermodynamic and integral equation theories of bulk fluid electrostriction that ignore surface effects, rendering them inapplicable to finite-sized films of water between hydrophobic plates. This suggests that the free energy barrier for evaporation is lowered by the applied field. Water, between "hard-wall-like" plates at narrower separations of 9.5 A and less, shows a spontaneous but incomplete evaporation at zero field within the time scale of our simulation. Evaporation is further enhanced by an electric field. No such evaporation occurs, on these time scales, for the smaller plates with the "hard-wall-like" potential at a separation of 8.0 A at zero field, signaling a crossover in behavior as the plate dimension decreases, but the water density still diminishes with increasing field strength. These observations could have implications for the behavior of thin films of water between surfaces in real physical and biological systems.

Simple models for hydrophobic hydration

This tutorial review compares models that describe DeltaG(cavitation). Their qualitative agreement suggests the use of the simple, time-honored Pierotti equation. Its coefficients, fine-tuned with atomistic simulations, give a revised Pierotti approach, rPA. A discussion of the extension of the rPA model to non-spherical solutes is presented and the different roles of molecular volume and surface area of the solute are brought together. The tutorial review is aimed at experimentalists and theoreticians interested in the description of solvent effects.

Repulsive solvent-induced interaction between C60 fullerenes in water

The role of water-fullerene interactions in the behavior of C60 in aqueous solution was investigated utilizing realistic Lennard-Jones (LJ) and repulsive Weeks-Chandler-Anderson (WCA) potentials. Strong water-fullerene dispersion interactions in the LJ potential dramatically influence the hydration of the fullerene promoting the formation of a high-density hydration shell of water. In contrast to the WCA potential, the water liquid phase between fullerenes remains stable with decreasing fullerene separation, resulting in a repulsive solvent-induced contribution to the fullerene potential of mean force.

Nanoscale hydrophobic interaction and nanobubble nucleation

We report large-scale atomistic simulation of midrange nanoscale hydrophobic interaction, manifested by the nucleation of nanobubble between nanometer-sized hydrophobes at constrained equilibrium. When the length scale of the hydrophobes is greater than 2 nm, the nanobubble formation shows hysteresis behavior resembling the first-order transition. Calculation of the potential of mean force versus interhydrophobe distance provides a quantitative measure of the strength of the nanoscale hydrophobic interaction.

Hydrophobic collapse in multidomain protein folding

We performed molecular dynamics simulations of the collapse of a two-domain protein, the BphC enzyme, into a globular structure to examine how water molecules mediate hydrophobic collapse of proteins. In the interdomain region, liquid water persists with a density 10 to 15% lower than in the bulk, even at small domain separations. Water depletion and hydrophobic collapse occur on a nanosecond time scale, which is two orders of magnitude slower than that found in the collapse of idealized paraffin-like plates. When the electrostatic protein-water forces are turned off, a dewetting transition occurs in the interdomain region and the collapse speeds up by more than an order of magnitude. When attractive van der Waals forces are turned off as well, the dewetting in the interdomain region is more profound, and the collapse is even faster.

Ultrafast hydration dynamics in protein unfolding: human serum albumin

We report studies of unfolding and ultrafast hydration dynamics of the protein human serum albumin. Unique in this study is our ability to examine different domains of the same protein and the intermediate on the way to the unfolded state. With femtosecond resolution and site-selective labeling, we isolate the dynamics of domains I and II of the native protein, domain I of the intermediate at 2 M guanidine hydrochloride, and the unfolded state at 6 M of the denaturant. For studies of unfolding, we used the fluorophores, acrylodan (covalently bound to Cys-34 in domain I) and the intrinsic tryptophan (domain II), whereas for hydration dynamics, we probed acrylodan and prodan; the latter is bound to domain II. From the time-dependent spectra and the correlation functions, we obtained the time scale of dynamically ordered water: 57 ps for the more stable domain I and 32 ps for the less stable domain II, in contrast to approximately 0.8 ps for labile, bulk-type water. This trend suggests an increased hydrophilic residues-water interaction of domain I, contrary to some packing models. In the intermediate state, which is characterized by essentially intact domain I and unfolded domain II, the dynamics of ordered water around domain I is nearly the same (61 ps) as that of native state (57 ps), whereas that in the unfolded protein is much shorter (13 ps). We discuss the role of this fluidity in the correlation between stability and function of the protein.

Efficient approximate all-atom solvent accessible surface area method parameterized for folded and denatured protein conformations

Continuing advances in computer hardware and software are permitting atomic-resolution molecular simulations for longer time scales and on larger systems. Despite these advances, routinely performing atomistic simulations with explicit water for even small proteins, which reach the folding time of such proteins, remains intractable for the foreseeable future. An implicit approximation of the solvent environment using a solvent accessible surface area (SASA) term in a molecular mechanics potential function allows exclusion of the explicit water molecules in protein simulations. This reduces the number of particles by approximately an order of magnitude. We present a fast and acceptably accurate approximate all-atom SASA method parameterized using a set of folded and heat-denatured conformations of globular proteins. The parameters are shown to be transferable to folded and heat-denatured conformations for another set of proteins. Calculation of the approximate SASA and the associated derivatives with respect to atomic positions for a 4644 atom protein requires only 1/11th the CPU time required for calculation of the nonbonded interactions for this system. On a per atom basis, this algorithm is three times faster than the fastest previously published approximate SASA method and achieves the same level of accuracy.

Entropy convergence in hydrophobic hydration: a scaled particle theory analysis

The occurrence of entropy convergence in hydrophobic hydration is verified from available experimental thermodynamic data for both noble gases and hydrocarbons. The entropy convergence phenomenon can be reproduced by means of the scaled particle theory, provided that a temperature-dependent hard sphere diameter is used for water molecules. The calculated work of cavity creation shows a non-monotonic temperature dependence with a flat maximum slightly above 100 degrees C, irrespective of the cavity size. The corresponding cavity entropy changes converge approximately 100 degrees C, in qualitative agreement with the experimental finding.

Temperature dependence of the hydrophobic hydration and interaction of simple solutes: An examination of five popular water models

We examine five different popular rigid water models (SPC, SPCE, TIP3P, TIP4P, and TIP5P) using molecular dynamics simulations in order to investigate the hydrophobic hydration and interaction of apolar Lennard-Jones solutes as a function of temperature in the range between 275 and 375 K along the 0.1 MPa isobar. For all investigated models and state points we calculate the excess chemical potential for the noble gases and methane employing the Widom particle insertion technique. All water models exhibit too small hydration entropies, but show a clear hierarchy. TIP3P shows poorest agreement with experiment, whereas TIP5P is closest to the experimental data at lower temperatures and SPCE is closest at higher temperatures. As a first approximation, this behavior can be rationalized as a temperature shift with respect to the solvation behavior found in real water. A rescaling procedure inspired by the information theory model of Hummer et al. [Chem. Phys. 258, 349 (2000)] suggests that the different solubility curves for the different models and real water can be largely explained on the basis of the different density curves at constant pressure. In addition, the models that give a good representation of the water structure at ambient conditions (TIP5P, SPCE, and TIP4P) show considerably better agreement with the experimental data than the ones which exhibit less structured O-O correlation functions (SPC and TIP3P). In the second part of the paper we calculate the hydrophobic interaction between xenon particles directly from a series of 60 ns simulation runs. We find that the temperature dependence of the association is to a large extent related to the strength of the solvation entropy. Nevertheless, differences between the models seem to require a more detailed molecular picture. The TIP5P model shows by far the strongest temperature dependence. The suggested density rescaling is also applied to the chemical potential in the xenon-xenon contact-pair configuration, indicating the presence of a temperature where the hydrophobic interaction turns into purely repulsive. The predicted association for xenon in real water suggests the presence of a strong variation with temperature, comparable to the behavior found for TIP5P water. Comparing different water models and experimental data we conclude that a proper description of density effects is an important requirement for a water model to account correctly for the correct description of the hydrophobic effects. A water model exhibiting a density maximum at the correct temperature is desirable.

Dewetting-induced collapse of hydrophobic particles

A molecular dynamics study of the depletion of water (drying) around a single and between two hydrophobic nanoscale oblate plates in explicit water as a function of the distance of separation between them, their size, and the strength of the attraction between the plates and the water molecules is presented. A simple macroscopic thermodynamic model based on Young's law successfully predicts drying between the stacked plates and accounts for the free-energy barriers to this drying. However, because drying around a single plate is not macroscopic, a molecular theory is required to describe it. The data are consistent with the rate-determining step in the hydrophobic collapse of the two plates being a large-scale drying fluctuation, characterized by a free-energy barrier that grows with particle size.

Anti-cooperativity and cooperativity in hydrophobic interactions: Three-body free energy landscapes and comparison with implicit-solvent potential functions for proteins

Potentials of mean force (PMFs) of three-body hydrophobic association are investigated to gain insight into similar processes in protein folding. Free energy landscapes obtained from explicit simulations of three methanes in water are compared with that predicted by popular implicit-solvent effective potentials for the study of proteins. Explicit-water simulations show that for an extended range of three-methane configurations, hydrophobic association at 25 degrees C under atmospheric pressure is mostly anti-cooperative, that is, less favorable than if the interaction free energies were pairwise additive. Effects of free energy nonadditivity on the kinetic path of association and the temperature dependence of additivity are explored by using a three-methane system and simplified chain models. The prevalence of anti-cooperativity under ambient conditions suggests that driving forces other than hydrophobicity also play critical roles in protein thermodynamic cooperativity. We evaluate the effectiveness of several implicit-solvent potentials in mimicking explicit water simulated three-body PMFs. The favorability of the contact free energy minimum is found to be drastically overestimated by solvent accessible surface area (SASA). Both the SASA and a volume-based Gaussian solvent exclusion model fail to predict the desolvation barrier. However, this barrier is qualitatively captured by the molecular surface area model and a recent "hydrophobic force field." None of the implicit-solvent models tested are accurate for the entire range of three-methane configurations and several other thermodynamic signatures considered.

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.

Size dependence of the solubility of nonpolar compounds in different solvents

At 25°C, plots of the standard Gibbs energy change associated with the solvation of noble gases and aliphatic hydrocarbons vs. the size of the solutes prove to be approximately linear with a negative slope for common organic solvents but not for water. In the latter case, the plot has a characteristic V-shape. The slope is negative for noble gases, methane, and ethane, but is positive for larger alkanes. This means that the solubility of nonpolar solutes increases with solute size in every solvent except water. The solvation thermodynamics of noble gases and aliphatic hydrocarbons in five solvents (water, ethanol, benzene, c-hexane, and n-hexane) are analyzed in detail by a general theory, which is rederived to avoid risky misunderstandings. The calculations are performed in the same manner for all solvents, using simple formulas where the physical reliability is well established and the results are consistent. The work of cavity creation increases with solute size in every solvent, but to a far greater extent in water. Additionally, the work to turn on the solute–solvent attractive interactions increases in magnitude with solute size in every solvent, but to a lesser extent in water. By combining these two factors a satisfactory explanation for experimental data obtained emerges. The microscopic origins of the difference between water and common organic solvents are discussed.Key words: solvation, excluded-volume effect, solute–solvent interactions, enthalpy–entropy compensation, molecular size.

Hydrophobicity at a Janus interface

Water confined between adjoining hydrophobic and hydrophilic surfaces (a Janus interface) is found to form stable films of nanometer thickness whose responses to shear deformations are extraordinarily noisy. The power spectrum of this noise is quantified. In addition, the frequency dependence of the complex shear modulus is a power law with slope one-half, indicating a distribution of relaxation processes rather than any dominant one. The physical picture emerges that whereas surface energetics encourage water to dewet the hydrophobic side of the interface, the hydrophilic side constrains water to be present, resulting in a flickering, fluctuating complex.

Model of a fluid at small and large length scales and the hydrophobic effect

We present a statistical field theory to describe large length scale effects induced by solutes in a cold and otherwise placid liquid. The theory divides space into a cubic grid of cells. The side length of each cell is of the order of the bulk correlation length of the bulk liquid. Large length scale states of the cells are specified with an Ising variable. Finer length scale effects are described with a Gaussian field, with mean and variance affected by both the large length scale field and by the constraints imposed by solutes. In the absence of solutes and corresponding constraints, integration over the Gaussian field yields an effective lattice-gas Hamiltonian for the large length scale field. In the presence of solutes, the integration adds additional terms to this Hamiltonian. We identify these terms analytically. They can provoke large length scale effects, such as the formation of interfaces and depletion layers. We apply our theory to compute the reversible work to form a bubble in liquid water, as a function of the bubble radius. Comparison with molecular simulation results for the same function indicates that the theory is reasonably accurate. Importantly, simulating the large length scale field involves binary arithmetic only. It thus provides a computationally convenient scheme to incorporate explicit solvent dynamics and structure in simulation studies of large molecular assemblies.

Effect of solute size and solute-water attractive interactions on hydration water structure around hydrophobic solutes

Using Monte Carlo simulations, we investigated the influence of solute size and solute-water attractive interactions on hydration water structure around spherical clusters of 1, 13, 57, 135, and 305 hexagonally close-packed methanes and the single hard-sphere (HS) solute analogues of these clusters. We obtain quantitative results on the density of water molecules in contact with the HS solutes as a function of solute size for HS radii between 3.25 and 16.45 A. Analysis of these results based on scaled-particle theory yields a hydration free energy/surface area coefficient equal to 139 cal/(mol A2), independent of solute size, when this coefficient is defined with respect to the van der Waals surface of the solute. The same coefficient defined with respect to the solvent-accessible surface decreases with decreasing solute size for HS radii less than approximately 10 A. We also find that solute-water attractive interactions play an important role in the hydration of the methane clusters. Water densities in the first hydration shell of the three largest clusters are greater than bulk water density and are insensitive to the cluster size. In contrast, contact water densities for the HS analogues of these clusters decrease with solute size, falling below the bulk density of water for the two largest solutes. Thus, the large HS solutes dewet, while methane clusters of the same size do not.

Macromolecular electrostatics: continuum models and their growing pains

Theoretical understanding of macromolecular electrostatics has advanced substantially over the past year. Continuum models have given promising results for calculating protein-ligand binding free energy differences, as well as pK(a)s and redox properties, particularly with explicit treatment of multiple conformers. Generalized Born and other techniques have led to the first molecular dynamics simulations of proteins and RNA with continuum solvent. Continuum and microscopic descriptions of dielectric relaxation have been critically compared.