Free Energy, Entropy and Heat Capacity of the Hydrophobic Interaction as a Function of Pressure

Solvation free energies of alcohols in water: temperature and pressure dependences

Solvation free energies μ* of amphiphilic species, methanol and 1,2-hexanediol, are obtained as a function of temperature or pressure based on molecular dynamics simulations combined with efficient free-energy calculation methods. In general, μ* of an amphiphile can be divided into and , the nonpolar and electrostatic contributions, and the former is further divided into and which are the work of cavity formation process and the free energy change due to weak, attractive interactions between the solute molecule and surrounding solvent molecules. We demonstrate that μ* of the two amphiphilic solutes can be obtained accurately using a perturbation combining method, which relies on the exact expressions for and and requires no simulations of intermediate systems between the solute with strong, repulsive interactions and the solute with the van der Waals and electrostatic interactions. The decomposition of μ* gives us several physical insights including that μ* is an increasing function of T due to , that the contributions of hydrophilic groups to the temperature dependence of μ* are additive, and that the contribution of the van der Waals attraction to the solvation volume is greater than that of the electrostatic interactions.

Role of cavities and hydration in the pressure unfolding of T4 lysozyme

It is well known that high hydrostatic pressures can induce the unfolding of proteins. The physical underpinnings of this phenomenon have been investigated extensively but remain controversial. Changes in solvation energetics have been commonly proposed as a driving force for pressure-induced unfolding. Recently, the elimination of void volumes in the native folded state has been argued to be the principal determinant. Here we use the cavity-containing L99A mutant of T4 lysozyme to examine the pressure-induced destabilization of this multidomain protein by using solution NMR spectroscopy. The cavity-containing C-terminal domain completely unfolds at moderate pressures, whereas the N-terminal domain remains largely structured to pressures as high as 2.5 kbar. The sensitivity to pressure is suppressed by the binding of benzene to the hydrophobic cavity. These results contrast to the pseudo-WT protein, which has a residual cavity volume very similar to that of the L99A-benzene complex but shows extensive subglobal reorganizations with pressure. Encapsulation of the L99A mutant in the aqueous nanoscale core of a reverse micelle is used to examine the hydration of the hydrophobic cavity. The confined space effect of encapsulation suppresses the pressure-induced unfolding transition and allows observation of the filling of the cavity with water at elevated pressures. This indicates that hydration of the hydrophobic cavity is more energetically unfavorable than global unfolding. Overall, these observations point to a range of cooperativity and energetics within the T4 lysozyme molecule and illuminate the fact that small changes in physical parameters can significantly alter the pressure sensitivity of proteins.

Simulation optimization of spherical non-polar guest recognition by deep-cavity cavitands

Biomimetic deep-cavity cavitand hosts possess unique recognition and encapsulation properties that make them capable of selectively binding a range of non-polar guests within their hydrophobic pocket. Adamantane based derivatives which snuggly fit within the pocket of octa-acid deep cavity cavitands exhibit some of the strongest host binding. Here we explore the roles of guest size and attractiveness on optimizing guest binding to form 1:1 complexes with octa-acid cavitands in water. Specifically we simulate the water-mediated interactions of the cavitand with adamantane and a range of simple Lennard-Jones guests of varying diameter and attractive well-depth. Initial simulations performed with methane indicate hydrated methanes preferentially reside within the host pocket, although these guests frequently trade places with water and other methanes in bulk solution. The interaction strength of hydrophobic guests increases with increasing size from sizes slightly smaller than methane to Lennard-Jones guests comparable in size to adamantane. Over this guest size range the preferential guest binding location migrates from the bottom of the host pocket upwards. For guests larger than adamantane, however, binding becomes less favorable as the minimum in the potential-of-mean force shifts to the cavitand face around the portal. For a fixed guest diameter, the Lennard-Jones well-depth is found to systematically shift the guest-host potential-of-mean force to lower free energies, however, the optimal guest size is found to be insensitive to increasing well-depth. Ultimately our simulations show that adamantane lies within the optimal range of guest sizes with significant attractive interactions to match the most tightly bound Lennard-Jones guests studied.

A nucleation-based method to study hydrophobic interactions under confinement: enhanced hydrophobic association driven by energetic contributions

A novel simulation approach was developed and applied to the study of hydrophobic interactions for a small hydrophobic solute pair under confinement. In this method, the aggregation-volume-bias Monte Carlo algorithm, developed originally for nucleation studies, is used to evaluate the association free energy with water molecules for a methane pair through the gradual addition of water molecules into a nanometer-sized sphere. Through a thermodynamic cycle, this method allows for a convenient examination of the free energy difference between two different solvated configurations without sampling any of the configurations in between. The potential of mean force (PMF) for a methane pair under confinement obtained from this method reveals that the stability of the contact pair configuration can be enhanced compared to that in bulk water, which is in agreement with previous studies. Also, constraining the center of this methane pair at the center of this confined volume yields a PMF with a metastable solvent separated configuration, resembling more closely the PMF from the bulk-phase system compared to previous studies in which this solvent-separated minimum was found to be completely absent. A combination with histogram reweighting enables the study of this association behavior at different thermodynamic conditions without additional simulations. From a comprehensive thermodynamic analysis, it is evident that such hydrophobic association, known to be entropically driven in the bulk-phase system at ambient conditions, is entropically favorable only when a suitable range of solvent molecules is added to the confined system. More importantly, the energetic contributions are a favorable factor that explains the enhanced hydrophobic association toward the high number of solvent molecules.

Fluctuation theory of molecular association and conformational equilibria

General expressions relating the effects of pressure, temperature, and composition on solute association and conformational equilibria using the fluctuation theory of solutions are provided. The expressions are exact and can be used to interpret experimental or computer simulation data for any multicomponent mixture involving molecules of any size and character at any composition. The relationships involve particle-particle, particle-energy, and energy-energy correlations within local regions in the vicinity of each species involved in the equilibrium. In particular, it is demonstrated that the results can be used to study peptide and protein association or aggregation, protein denaturation, and protein-ligand binding. Exactly how the relevant fluctuating properties may be obtained from experimental or computer simulation data are also outlined. It is shown that the enthalpy, heat capacity, and compressibility differences associated with the equilibrium process can, in principle, be obtained from a single simulation. Fluctuation based expressions for partial molar heat capacities, thermal expansions, and isothermal compressibilities are also provided.

Structural rearrangement of ethanol-denatured soy proteins by high hydrostatic pressure treatment

The effects of high hydrostatic pressure (HHP) treatment (100-500 MPa) on solubility and structural properties of ethanol (EtOH)-denatured soy β-conglycinin and glycinin were investigated using differential scanning calorimetry, Fourier transform infrared and ultraviolet spectroscopy. HHP treatment above 200 MPa, especially at neutral and alkaline pH as well as low ionic strength, significantly improved the solubility of denatured soy proteins. Structural rearrangements of denatured β-conglycinin subjected to high pressure were confirmed, as evidenced by the increase in enthalpy value (ΔH) and the formation of the ordered supramolecular structure with stronger intramolecular hydrogen bond. HHP treatment (200-400 MPa) caused an increase in surface hydrophobicity (F(max)) of β-conglycinin, partially attributable to the exposure of the Tyr and Phe residues, whereas higher pressure (500 MPa) induced the decrease in F(max) due to hydrophobic rearrangements. The Trp residues in β-conglycinin gradually transferred into a hydrophobic environment, which might further support the finding of structural rearrangements. In contrast, increasing pressure induced the progressive unfolding of denatured glycinin, accompanied by the movement of the Tyr and Phe residues to the molecular surface of protein. These results suggested that EtOH-denatured β-conglycinin and glycinin were involved in different pathways of structural changes during HHP treatment.

Putting the squeeze on cavities in liquids: Quantifying pressure effects on solvation using simulations and scaled-particle theory

Extensive molecular simulations of the Lennard-Jones fluid are performed to examine the response of the excess chemical potential of cavitylike solutes to applied pressure. Solutes as large as ten times the solvent diameter are considered. The simulations are analyzed using the revised scaled-particle theory developed by Ashbaugh and Pratt to evaluate the thermodynamics of cavity solvation and curvature dependent interfacial properties well into the compressed liquid portion of the solvent phase diagram. The revised theory provides a quantitatively accurate description of the solvent-solute contact correlation function for all solutes and state points considered. The main structural effect of increasing pressure is to push the solvent molecules up against the solute surfaces, counteracting the dewetting that is observed at lower pressures along the solvent saturation curve. Decomposing the excess chemical potential of cavities into volume and surface-area contributions shows that pressure differentially affects the interfacial free energies of molecular versus macroscopic solutes. The interfacial free energy of surfaces of molecular dimension monotonically decreases with applied pressure, while that of surfaces larger than a small cluster of solvent molecules exhibit a maximum with increasing pressure, which may play a role in pressure-induced disaggregation of molecular assemblies. Moreover, since the pressure dependence of the interfacial free energy is thermodynamically linked to the excess adsorption of solvent on the solute surface, the former is potentially a measurable macroscopic indicator of microscopic wetting∕dewetting phenomena, implicated in hydrophobic interactions between macroscopic hydrophobic particles. Finally, some inferences about pressure-dependent solvation processes in water are made by using the revised theory to analyze previously published simulation data.

Development of molecular simulation methods to accurately represent protein-surface interactions: The effect of pressure and its determination for a system with constrained atoms

When performing molecular dynamics simulations for a system with constrained (fixed) atoms, traditional isobaric algorithms (e.g., NPT simulation) often cannot be used. In addition, the calculation of the internal pressure of a system with fixed atoms may be highly inaccurate due to the nonphysical nature of the atomic constraints and difficulties in accurately defining the volume occupied by the unconstrained atoms in the system. The inability to properly set and control pressure can result in substantial problems for the accurate simulation of condensed-phase systems if the behavior of the system (e.g., peptide/protein adsorption) is sensitive to pressure. To address this issue, the authors have developed an approach to accurately determine the internal pressure for a system with constrained atoms. As the first step in this method, a periodically extendable portion of the mobile phase of the constrained system (e.g., the solvent atoms) is used to create a separate unconstrained system for which the pressure can be accurately calculated. This model system is then used to create a pressure calibration plot for an intensive local effective virial parameter for a small volume cross section or "slab" of the system. Using this calibration plot, the pressure of the constrained system can then be determined by calculating the virial parameter for a similarly sized slab of mobile atoms. In this article, the authors present the development of this method and demonstrate its application using the CHARMM molecular simulation program to characterize the adsorption behavior of a peptide in explicit water on a hydrophobic surface whose lattice spacing is maintained with atomic constraints. The free energy of adsorption for this system is shown to be dramatically influenced by pressure, thus emphasizing the importance of properly maintaining the pressure of the system for the accurate simulation of protein-surface interactions.

Studying pressure denaturation of a protein by molecular dynamics simulations

Many globular proteins unfold when subjected to several kilobars of hydrostatic pressure. This "unfolding-up-on-squeezing" is counter-intuitive in that one expects mechanical compression of proteins with increasing pressure. Molecular simulations have the potential to provide fundamental understanding of pressure effects on proteins. However, the slow kinetics of unfolding, especially at high pressures, eliminates the possibility of its direct observation by molecular dynamics (MD) simulations. Motivated by experimental results-that pressure denatured states are water-swollen, and theoretical results-that water transfer into hydrophobic contacts becomes favorable with increasing pressure, we employ a water insertion method to generate unfolded states of the protein Staphylococcal Nuclease (Snase). Structural characteristics of these unfolded states-their water-swollen nature, retention of secondary structure, and overall compactness-mimic those observed in experiments. Using conformations of folded and unfolded states, we calculate their partial molar volumes in MD simulations and estimate the pressure-dependent free energy of unfolding. The volume of unfolding of Snase is negative (approximately -60 mL/mol at 1 bar) and is relatively insensitive to pressure, leading to its unfolding in the pressure range of 1500-2000 bars. Interestingly, once the protein is sufficiently water swollen, the partial molar volume of the protein appears to be insensitive to further conformational expansion or unfolding. Specifically, water-swollen structures with relatively low radii of gyration have partial molar volume that are similar to that of significantly more unfolded states. We find that the compressibility change on unfolding is negligible, consistent with experiments. We also analyze hydration shell fluctuations to comment on the hydration contributions to protein compressibility. Our study demonstrates the utility of molecular simulations in estimating volumetric properties and pressure stability of proteins, and can be potentially extended for applications to protein complexes and assemblies.

Role of electrostatics in modulating hydrophobic interactions and barriers to hydrophobic assembly

Hydrophobic effects continue to be an active area of research due to implications for a wide range of physicochemical phenomena. Molecular dynamics simulations have been used extensively in the study of such effects using various water potential models, with few studies addressing the differences between models. In particular, studies considering the explicit treatment of water polarizability are underrepresented in the literature. We present results from molecular dynamics simulations that systematically compare the dependence of large-scale hydrophobic effects on the water model. We consider three common nonpolarizable models (SPC/E, TIP3P, and TIP4P) and two common polarizable models (TIP4P-FQ and SWM4-NDP). Results highlight the similarities and differences of the different water models in the vicinity of two large hydrophobic plates. In particular, profiles of average density, density fluctuations, orientation, and hydrogen bonding show only minor differences among the water models studied. However, the potential of mean force for the hydrophobe dimerization is significantly reduced in the polarizable water systems. TIP4P-FQ shows the deepest minimum of approximately -54(+/-3) kcal/mol compared to -40(+/-3), -40(+/-2), -42(+/-3), and -45(+/-5) kcal/mol for TIP4P, TIP3P, SPC/E, and SWM4-NDP (all relative to the dissociated state). We discuss the relationship between hydrophobic association and the strength of water-water interactions in the liquid phase. Results suggest that models treating polarizability (both implicitly and explicitly) influence a stronger driving force toward hydrophobic assembly. Implications of these results, as well as prospectives on future work, are discussed.

Enthalpy-entropy contributions to the potential of mean force of nanoscopic hydrophobic solutes

Entropic and enthalpic contributions to the hydrophobic interaction between nanoscopic hydrophobic solutes, modeled as graphene plates in water, have been calculated using molecular dynamics simulations in the isothermal-isobaric (NPT) ensemble with free energy perturbation methodology. We find the stabilizing contribution to the free energy of association (contact pair formation) to be the favorable entropic part, the enthalpic contribution being highly unfavorable. The desolvation barrier is dominated by the unfavorable enthalpic contribution, despite a fairly large favorable entropic compensation. The enthalpic contributions, incorporating the Lennard-Jones solute-solvent terms, largely determine the stability of the solvent separated configuration. We decompose the enthalpy into a direct solute-solute term, the solute-solvent interactions, and the remainder that contains pressure-volume work as well as contributions due to solvent reorganization. The enthalpic contribution due to changes in water-water interactions arising from solvent reorganization around the solute molecules is shown to have major contribution in the solvent induced enthalpy change.

Pressure and temperature dependence of hydrophobic hydration: Volumetric, compressibility, and thermodynamic signatures

The combined effect of pressure and temperature on hydrophobic hydration of a nonpolar methanelike solute is investigated by extensive simulations in the TIP4P model of water. Using test-particle insertion techniques, free energies of hydration under a range of pressures from 1 to 3000 atm are computed at eight temperatures ranging from 278.15 to 368.15 K. Corresponding enthalpy, entropy, and heat capacity accompanying the hydration process are estimated from the temperature dependence of the free energies. Partial molar and excess volumes calculated using pressure derivatives of the simulated free energies are consistent with those determined by direct volume simulations; but direct volume determination offers more reliable estimates for compressibility. At 298.15 K, partial molar and excess isothermal compressibilities of methane are negative at 1 atm. Partial molar and excess adiabatic (isentropic) compressibilities are estimated to be also negative under the same conditions. But partial molar and excess isothermal compressibilities are positive at high pressures, with a crossover from negative to positive compressibility at approximately 100-1000 atm. This trend is consistent with experiments on aliphatic amino acids and pressure-unfolded states of proteins. For the range of pressures simulated, hydration heat capacity exhibits little pressure dependence, also in apparent agreement with experiment. When pressure is raised at constant room temperature, hydration free energy increases while its entropic component remains essentially constant. Thus, the increasing unfavorability of hydration under raised pressure is seen as largely an enthalpic effect. Ramifications of the findings of the authors for biopolymer conformational transitions are discussed.

Low-temperature and high-pressure induced swelling of a hydrophobic polymer-chain in aqueous solution

We report molecular dynamics simulations of a hydrophobic polymer-chain in aqueous solution between 260 K and 420 K at pressures of 1 bar, 3000 bar, and 4500 bar. The simulations reveal a hydrophobically collapsed structure at low pressures and high temperatures. At 3000 bar and about 260 K and at 4500 bar and about 260 K, however, an abrupt transition to a swelled state is observed. The transition is driven by a smaller volume and a remarkably strong lower enthalpy of the swelled state, indicating a steep positive slope of the corresponding transition line. The swelling is strongly stabilized by the energetically favorable state of water in the polymer's hydrophobic first hydration shell at low temperatures. This finding is consistent with the observation of a positive heat capacity of hydrophobic solvation. Moreover, the slope and location of the estimated swelling transition line for the collapsed hydrophobic chain coincides remarkably well with the cold denaturation transition of proteins.

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.

Assessing the efficiency of free energy calculation methods

The efficiencies of two recently developed methods for calculating free energy changes along a generalized coordinate in a system are discussed in the context of other, related approaches. One method is based on Jarzynski's identity [Phys. Rev. Lett. 78, 2690 (1997)]. The second method relies on thermodynamic integration of the average force and is called the adaptive biasing force method [Darve and Pohorille, J. Chem. Phys. 115, 9169 (2001)]. Both methods are designed such that the system evolves along the chosen coordinate(s) without experiencing free energy barriers and they require calculating the instantaneous, unconstrained force acting on this coordinate using the formula derived by Darve and Pohorille. Efficiencies are analyzed by comparing analytical estimates of statistical errors and by considering two numerical examples-internal rotation of hydrated 1,2-dichloroethane and transfer of fluoromethane across a water-hexane interface. The efficiencies of both methods are approximately equal in the first but not in the second case. During transfer of fluoromethane the system is easily driven away from equilibrium and, therefore, the performance of the method based on Jarzynski's identity is poor.

Quasiequilibrium unfolding thermodynamics of a small protein studied by molecular dynamics simulation with an explicit water model

The 124 independent molecular dynamics simulations are completed with total time of 196.8 ns. The calculated unfolding quasiequilibrium thermodynamics of G-IgG-binding domain B1 (GB1) shows the experimentally observed protein transitions: a coil to disordered globule transition, a disordered globule to molten globule transition, a molten globule to nativelike transition, and a nativelike to solidlike state transition. The first protein unfolding phase diagram has been constructed from molecular dynamics simulations with an explicit water model. The calculated melting temperature of GB1 agrees with early experiment. The results also agree with the recent experiment result in which GB1 has more than one intermediate.

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 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.

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.

High pressure refolding of recombinant human growth hormone from insoluble aggregates. Structural transformations, kinetic barriers, and energetics

Two different types of insoluble, non-native aggregates of recombinant human growth hormone were formed by agitation in buffer or buffer containing 0.75 m guanidine HCl (GdnHCl) and characterized by infrared and second derivative UV spectroscopies. The degree of secondary structural perturbation was greater in the aggregates formed in 0.75 m GdnHCl. Both aggregate types were dissolved and refolded using high hydrostatic pressures in combination with either elevated temperature or non-denaturing levels of guanidine HCl or urea. The effects of a range of temperature, pressure, and chaotrope concentrations were tested and led to optimal conditions that approached 100% yield of native protein. The aggregates formed in 0.75 m GdnHCl required higher concentrations of urea or GdnHCl, or higher temperature or pressure for a yield equivalent to that for aggregates formed in buffer alone. Investigation of the effects of pressure, temperature, and chaotrope on unfolding of rhGH documented that under conditions used for optimal high pressure disaggregation and refolding, the native state is greatly favored thermodynamically (e.g. 25 kJ/mol at 2000 bar and 0.75 m GdnHCl). Dissolution of aggregates under pressure is a kinetically limited process. Comparison of refolding yields in GdnHCl and urea solutions suggest that pressure effects on electrostatic interactions do not dominate pressure effects on disaggregation. We suggest that non-native hydrogen bonds between protein molecules within aggregates of recombinant human growth hormone are responsible for the rate-limiting kinetic barrier in pressure-induced disaggregation.

Molecular dynamics simulations of pressure effects on hydrophobic interactions

We report results on the pressure effects on hydrophobic interactions obtained from molecular dynamics simulations of aqueous solutions of methanes in water. A wide range of pressures that is relevant to pressure denaturation of proteins is investigated. The characteristic features of water-mediated interactions between hydrophobic solutes are found to be pressure-dependent. In particular, with increasing pressure we find that (1) the solvent-separated configurations in the solute-solute potential of mean force (PMF) are stabilized with respect to the contact configurations; (2) the desolvation barrier increases monotonically with respect to both contact and solvent-separated configurations; (3) the locations of the minima and the barrier move toward shorter separations; and (4) pressure effects are considerably amplified for larger hydrophobic solutes. Together, these observations lend strong support to the picture of the pressure denaturation process proposed previously by Hummer et al. (Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 1552): with increasing pressure, the transfer of water into protein interior becomes key to the pressure denaturation process, leading to the dissociation of close hydrophobic contacts and subsequent swelling of the hydrophobic protein interior through insertions of water molecules. The pressure dependence of the PMF between larger hydrophobic solutes shows that pressure effects on the interaction between hydrophobic amino acids may be considerably amplified compared to those on the methane-methane PMF.