Molecular dynamics simulations of pressure effects on hydrophobic interactions

Potential of Mean Force of Hydrophobic Association: Dependence on Solute Size

The potentials of mean force (PMFs) were determined for systems involving formation of nonpolar dimers composed of methane, ethane, propane, isobutane, and neopentane, respectively, in water, using the TIP3P water model, and in vacuo. A series of umbrella-sampling molecular dynamics simulations with the AMBER force field was carried out for each pair in either water or in vacuo. The PMFs were calculated by using the weighted histogram analysis method (WHAM). The shape of the PMFs for dimers of all five nonpolar molecules is characteristic of hydrophobic interactions with contact and solvent-separated minima and desolvation maxima. The positions of all these minima and maxima change with the size of the nonpolar molecule, that is, for larger molecules they shift toward larger distances. The PMF of the neopentane dimer is similar to those of other small nonpolar molecules studied in this work, and hence the neopentane dimer is too small to be treated as a nanoscale hydrophobic object. The solvent contribution to the PMF was also computed by subtracting the PMF determined in vacuo from the PMF in explicit solvent. The molecular surface area model correctly describes the solvent contribution to the PMF together with the changes of the height and positions of the desolvation barrier for all dimers investigated. The water molecules in the first solvation sphere of the dimer are more ordered compared to bulk water, with their dipole moments pointing away from the surface of the dimer. The average number of hydrogen bonds per water molecule in this first hydration shell is smaller compared to that in bulk water, which can be explained by coordination of water molecules to the hydrocarbon surface. In the second hydration shell, the average number of hydrogen bonds is greater compared to bulk water, which can be explained by increased ordering of water from the first hydration shell; the net effect is more efficient hydrogen bonding between the water molecules in the first and second hydration shells.

Monte Carlo simulations of the hydrophobic effect in aqueous electrolyte solutions

The hydrophobic interaction between two methane molecules in salt-free and high salt-containing aqueous solutions and the structure in such solutions have been investigated using an atomistic model solved by Monte Carlo simulations. Monovalent salt representing NaCl and divalent salt with the same nonelectrostatic properties as the monovalent salt have been used to examine the influence of the valence of the salt species. In salt-free solution the effective interaction between the two methane molecules displayed a global minimum at close contact of the two methane molecules and a solvent-separated secondary minimum. In 3 and 5 M monovalent salt solution the potential of mean force became slightly more attractive, and in a 3 M divalent salt solution the attraction became considerably stronger. The structure of the aqueous solutions was determined by radial distribution functions and angular probability functions. The distortion of the native water structure increased with ion valence. The increase of the hydrophobic attraction was associated with (i) a breakdown of the tetrahedral structure formed by neighboring water molecules and of the hydrogen bonds between them and (i) the concomitant increase of the solution density.

On the salt-induced stabilization of pair and many-body hydrophobic interactions

Salting-out of hydrophobic solutes in aqueous salt solutions and their relevance to salt effects on biophysical phenomena are now well appreciated. Although salt effects on hydrophobic transfer have been well studied, to our knowledge, no quantitative molecular simulation study of salt-induced strengthening of hydrophobic interactions has yet been reported. Here we present quantitative characterization of salt-induced strengthening of hydrophobic interactions at the molecular and nanoscopic length scales through molecular dynamics simulations. Specifically, we quantify the effect of NaCl on the potential of mean force between molecular hydrophobic solutes (methanes) and on conformational equilibria of a 25-mer hydrophobic polymer that efficiently samples ensembles of compact and extended states in water. In both cases, we observe relative stabilization of compact conformations that is accompanied by a clear depletion of salt density (preferential exclusion) and a slight enhancement of water density (preferential hydration) in the solute vicinity. We show that the structural details of salt exclusion can be related to the salt-induced free energy changes using preferential interaction coefficients. We also test the applicability of surface-area-based models to describe the salt-induced free energy changes. These models provide a useful empirical description that can be used to predict the effects of salt on conformational equilibria of hydrophobic solutes. However, we find that the effective increase in the surface tension of the solute-aqueous solution interface depends on the type and concentration of salt as well as the length-scale (i.e., molecular vs nanoscopic) of the conformational change. These calculations underscore the utility of simulation studies to connect quantitatively structural details at the molecular level (described by preferential hydration/exclusion) to macroscopic solvation thermodynamics. The hydrophobic polymer also provides a useful model for studies of effect of thermodynamic variables (P, T, salt/additives) on many-body hydrophobic interactions at nanometer length scales.

Signatures of hydrophobic collapse in extended proteins captured with force spectroscopy

We unfold and extend single proteins at a high force and then linearly relax the force to probe their collapse mechanisms. We observe a large variability in the extent of their recoil. Although chain entropy makes a small contribution, we show that the observed variability results from hydrophobic interactions with randomly varying magnitude from protein to protein. This collapse mechanism is common to highly extended proteins, including nonfolding elastomeric proteins like PEVK from titin. Our observations explain the puzzling differences between the folding behavior of highly extended proteins, from those folding after chemical or thermal denaturation. Probing the collapse of highly extended proteins with force spectroscopy allows separation of the different driving forces in protein folding.

Integral equation study of hydrophobic interaction: A comparison between the simple point charge model for water and a Lennard-Jones model for solvent

The hydrophobic interaction that is characterized by a potential of mean force (PMF) between spherical apolar solutes immersed in the simple point charge (SPCE) model for water was studied using an interaction site model integral equation based on a density-functional theory for molecular fluids. For comparison with the PMFs for various size solutes in the SPCE model, the PMFs in a Lennard-Jones (LJ) model for a solvent whose diameter is same as the SPCE model were also studied using a hypernetted chain integral equation. It is noted in the LJ model that the hydrogen bond and its network structure are completely ignored, but the translational entropy is taken into account. Both PMFs obtained from the SPCE model and from the LJ model have a large first minimum at a contact distance of solutes. In the case that the solute size is about three times larger than water, these PMFs also have a large maximum at a longer distance than the contact position. The strong attraction is attributed to the translational entropy of the solvent, and that the large activation barrier is arising from the weak attraction between the solute and the solvent. The comparison between the SPCE model and the LJ solvent model suggests that the qualitative description of the hydrophobic interaction is possible by using the LJ solvent model. On the other hand, the dewetting tendency on the surface of the apolar solute in a room condition is observed only on the SPCE model. These results indicate that the characteristics of water such as the hydrogen bond affect rather the hydrophobic hydration than the hydrophobic interaction.

Analytical model for studying how environmental factors influence protein conformational stability in solution

We introduce an analytical modeling strategy for probing the conformational stability of globular proteins in aqueous solution. In this approach, the intrinsic (i.e., infinite dilution) thermodynamic stability and coarse structural properties of the proteins, as well as the effective protein-protein interactions, derive from a heteropolymer collapse theory that incorporates predicted temperature- and pressure-dependent hydrophobic interactions. Protein concentration effects are estimated by integrating this information into a molecular thermodynamic model, which is an ad hoc generalization of the exact equilibrium theory of a one-dimensional binary mixture of square-well particles that interconvert through an isomerization (i.e., folding) reaction. The end result is an analytical multiscale modeling approach which, although still schematic, can predict that folded proteins exhibit a closed-loop region of stability in the pressure-temperature plane and that protein concentration has a nonmonotonic effect on protein stability, results consistent with qualitative trends observed in both experiments of protein solutions and simulations of coarse-grained protein models.

Heteropolymer collapse theory for protein folding in the pressure-temperature plane

We revisit a heteropolymer collapse theory originally introduced to explore how the balance between hydrophobic interactions and configurational entropy determines the thermal stability of globular proteins at ambient pressure. We generalize the theory by introducing a basic statistical mechanical treatment for how pressure impacts the solvent-mediated interactions between hydrophobic amino-acid residues. In particular, we estimate the strength of the hydrophobic interactions using a molecular thermodynamic model for the interfacial free energy between liquid water and a curved hydrophobic solute. The model, which also reproduces many of the distinctive thermodynamic properties of aqueous solutions in bulk and interfacial environments, predicts that the water-solute interfacial free energy is significantly reduced by the application of high hydrostatic pressures. This allows water to penetrate into folded heteropolymers at high pressure and break apart their hydrophobic cores, a scenario suggested earlier by information theory calculations. As a result, folded heteropolymers are predicted to display the kind of closed region of stability in the pressure-temperature plane exhibited by native proteins. We compare predictions of the collapse theory with experimental data for several proteins.

Protein unfolding, amyloid fibril formation and configurational energy landscapes under high pressure conditions

High hydrostatic pressure induces conformational changes in proteins ranging from compression of the molecules to loss of native structure. In this tutorial review we describe how the interplay between the volume change and the compressibility leads to pressure-induced unfolding of proteins and dissociation of amyloid fibrils. We also discuss the effect of pressure on protein folding and free energy landscapes. From a molecular viewpoint, pressure effects can be rationalised in terms of packing and hydration of proteins.

Osmolyte trimethylamine-N-oxide does not affect the strength of hydrophobic interactions: origin of osmolyte compatibility

Osmolytes are small organic solutes accumulated at high concentrations by cells/tissues in response to osmotic stress. Osmolytes increase thermodynamic stability of folded proteins and provide protection against denaturing stresses. The mechanism of osmolyte compatibility and osmolyte-induced stability has, therefore, attracted considerable attention in recent years. However, to our knowledge, no quantitative study of osmolyte effects on the strength of hydrophobic interactions has been reported. Here, we present a detailed molecular dynamics simulation study of the effect of the osmolyte trimethylamine-N-oxide (TMAO) on hydrophobic phenomena at molecular and nanoscopic length scales. Specifically, we investigate the effects of TMAO on the thermodynamics of hydrophobic hydration and interactions of small solutes as well as on the folding-unfolding conformational equilibrium of a hydrophobic polymer in water. The major conclusion of our study is that TMAO has almost no effect either on the thermodynamics of hydration of small nonpolar solutes or on the hydrophobic interactions at the pair and many-body level. We propose that this neutrality of TMAO toward hydrophobic interactions-one of the primary driving forces in protein folding-is at least partially responsible for making TMAO a "compatible" osmolyte. That is, TMAO can be tolerated at high concentrations in organisms without affecting nonspecific hydrophobic effects. Our study implies that protein stabilization by TMAO occurs through other mechanisms, such as unfavorable water-mediated interaction of TMAO with the protein backbone, as suggested by recent experimental studies. We complement the above calculations with analysis of TMAO hydration and changes in water structure in the presence of TMAO molecules. TMAO is an amphiphilic molecule containing both hydrophobic and hydrophilic parts. The precise balance of the effects of hydrophobic and hydrophilic segments of the molecule appears to explain the virtual noneffect of TMAO on the strength of hydrophobic interactions.

Simulations of the pressure and temperature unfolding of an alpha-helical peptide

We study by molecular simulations the reversible folding/unfolding equilibrium as a function of density and temperature of a solvated alpha-helical peptide. We use an extension of the replica exchange molecular dynamics method that allows for density and temperature Monte Carlo exchange moves. We studied 360 thermodynamic states, covering a density range from 0.96 to 1.14 g.cm(-3) and a temperature range from 300 to 547.6 K. We simulated 10 ns per replica for a total simulation time of 3.6 micros. We characterize the structural, thermodynamic, and hydration changes as a function of temperature and pressure. We also calculate the compressibility and expansivity of unfolding. We find that pressure does not affect the helix-coil equilibrium significantly and that the volume change upon pressure unfolding is small and negative (-2.3 ml/mol). However, we find significant changes in the coordination of water molecules to the backbone carbonyls. This finding predicts that changes in the chemical shifts and IR spectra with pressure can be due to changes in coordination and not only changes in the helical content. A simulation of the IR spectrum shows that water coordination effects on frequency shifts are larger than changes due to elastic structural changes in the peptide.

Hydrophobic effect in the pressure-temperature plane

The free energy of the hydrophobic hydration and the strength of the solvent-mediated attraction between hydrophobic solute molecules are calculated in the pressure-temperature plane. This is done in the framework of an exactly soluble model that is an extension of the lattice model proposed by Kolomeisky and Widom. The model takes into account both the mechanism of the hydrophobic effect dominant at low temperatures and the opposite mechanism of solvation appearing at high temperatures and has the pressure as a second thermodynamic variable. With this model, two boundaries are identified in the pressure-temperature plane: the first one within which the solubility, or the Ostwald absorption coefficient, decreases with increasing temperature at fixed pressure and the second one within which the strength of solvent-mediated attraction increases with increasing temperature. The two are nearly linear and parallel to each other, and the second boundary lies in the low-temperature and low-pressure side of the first boundary. It is found that a single, near-linear relation between the hydration free energy and the strength of the hydrophobic attraction holds over the entire area within the second boundary in the pressure-temperature plane.

Heat capacity effects associated with the hydrophobic hydration and interaction of simple solutes: A detailed structural and energetical analysis based on molecular dynamics simulations

We examine the SPCE [H. J. C. Berendsen et al., J. Chem. Phys. 91, 6269 (1987)] and TIP5P [M. W. Mahoney and W. L. Jorgensen, J. Chem. Phys 112, 8910 (2000)] water models using a temperature series of molecular-dynamics simulations in order to study heat-capacity effects associated with the hydrophobic hydration and interaction of xenon particles. The temperature interval between 275 and 375 K along the 0.1-MPa isobar is studied. For all investigated models and state points we calculate the excess chemical potential for xenon employing the Widom particle insertion technique. The solvation enthalpy and excess heat capacity is obtained from the temperature dependence of the chemical potentials and, alternatively, directly by Ewald summation, as well as a reaction field based method. All three methods provide consistent results. In addition, the reaction field technique allows a separation of the solvation enthalpy into solute/solvent and solvent/solvent parts. We find that the solvent/solvent contribution to the excess heat capacity is dominating, being about one order of magnitude larger than the solute/solvent part. This observation is attributed to the enlarged heat capacity of the water molecules in the hydration shell. A detailed spatial analysis of the heat capacity of the water molecules around a pair of xenon particles at different separations reveals that even more enhanced heat capacity of the water located in the bisector plane between two adjacent xenon atoms is responsible for the maximum of the heat capacity found for the desolvation barrier distance, recently reported by Shimizu and Chan [J. Am. Chem. Soc. 123, 2083 (2001)]. The about 60% enlarged heat capacity of water in the concave part of the joint xenon-xenon hydration shell is the result of a counterplay of strengthened hydrogen bonds and an enhanced breaking of hydrogen bonds with increasing temperature. Differences between the two models with respect to the heat capacity in the xenon-xenon contact state are attributed to the different water model bulk heat capacities, and to the different spatial extension of the structure effect introduced by the hydrophobic particles. Similarities between the different states of water in the joint xenon-xenon hydration shell and the properties of stretched water are discussed.

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.

Characterization of the pressure-induced intermediate and unfolded state of red-shifted green fluorescent protein--a static and kinetic FTIR, UV/VIS and fluorescence spectroscopy study

The green fluorescence proteins (GFP) are widely used as reporters in molecular and cell biology. For their use it in high-pressure microbiology and biotechnology studies, their structural properties, thermodynamic parameters and stability diagrams have to be known. We investigated the pressure stability of the red-shifted green fluorescent protein (rsGFP) using Fourier-transform infrared spectroscopy, fluorescence and UV/Vis spectroscopy. We found that rsGFP does not unfold up to approximately 9kbar at room temperature. Its unique three-dimensional structure is held responsible for the high-pressure stability. At higher temperatures, its secondary structure collapses below 9kbar (e.g. the denaturation pressure at 58 degrees C is 7.8kbar). The analysis of the IR data shows that the pressure-denatured state contains more disordered structures at the expense of a decrease of intramolecular beta-sheets. As indicated by the large volume change of DeltaV degrees (u) approximately -250(+/-50)mlmol(-1) at 58 degrees C, this highly cooperative transition can be interpreted as a collapse of the beta-can structure of rsGFP. For comparison, the temperature-induced unfolding of rsGFP has also been studied. At high temperature (T(m)=78 degrees C), the unfolding resulted in the formation of an aggregated state. Contrary to the pressure-induced unfolding, the temperature-induced unfolding and aggregation of GFP is irreversible. From the FT-IR data, a tentative p,T-stability diagram for the secondary structure collapse of GFP has been obtained. Furthermore, changes in fluorescence and absorptivity were found which are not correlated to the secondary structural changes. The fluorescence and UV/Vis data indicate smaller conformational changes in the chromophore region at much lower pressures ( approximately 4kbar) which are probably accompanied by the penetration of water into the beta-can structure. In order to investigate also the kinetics of this initial step, pressure-jump relaxation experiments were carried out. The partial activation volumes observed indicate that the conformational changes in the chromophore region when passing the transition state are indeed rather small, thus leading to a comparably small volume change of -20 ml mol(-1) only. The use of the chromophore absorption and fluorescence band of rsGFP in using GFP as reporter for gene expression and other microbiological studies under high pressure conditions is thus limited to pressures of about 4kbar, which still exceeds the pressure range relevant for studies in vivo in micro-organisms, including piezophilic bacteria from deep-sea environments.

Potential of mean force between two hydrophobic solutes in water

We study the potential of mean force between two nonpolar solutes in the Mercedes Benz model of water. Using NPT Monte Carlo simulations, we find that the solute size determines the relative preference of two solute molecules to come into contact ('contact minimum') or to be separated by a single layer of water ('solvent-separated minimum'). Larger solutes more strongly prefer the contacting state, while smaller solutes have more tendency to become solvent-separated, particularly in cold water. The thermal driving forces oscillate with solute separation. Contacts are stabilized by entropy, whereas solvent-separated solute pairing is stabilized by enthalpy. The free energy of interaction for small solutes is well-approximated by scaled-particle theory.

Molecular dynamics simulations

Molecular dynamics simulations have become a standard tool for the investigation of biomolecules. Simulations are performed of ever bigger systems using more realistic boundary conditions and better sampling due to longer sampling times. Recently, realistic simulations of systems as complex as transmembrane channels have become feasible. Simulations aid our understanding of biochemical processes and give a dynamic dimension to structural data; for example, the transformation of harmless prion protein into the disease-causing agent has been modeled.