Hydrophobic Effects on a Molecular Scale

Relationship between cohesive energy density and hydrophobicity

It has been recently claimed that the large cohesive energy density of water is the ultimate cause of the poor solubility of nonpolar compounds in water. In order to test the validity of this idea, we analyze the difference in solubility between light water and heavy water of several nonpolar compounds. Even though the cohesive energy density of D(2)O is larger than that of H(2)O, nonpolar compounds are slightly more soluble in D(2)O than H(2)O. In such case experimental data do not support the correctness of the large cohesive energy density as the ultimate cause of hydrophobicity. We show that D(2)O is a slightly better solvent than H(2)O for nonpolar compounds because it is slightly less costly to create a cavity in the former liquid. This is because there is slightly more void volume in heavy water than in light water.

AGBNP: an analytic implicit solvent model suitable for molecular dynamics simulations and high-resolution modeling

We have developed an implicit solvent effective potential (AGBNP) that is suitable for molecular dynamics simulations and high-resolution modeling. It is based on a novel implementation of the pairwise descreening Generalized Born model for the electrostatic component and a new nonpolar hydration free energy estimator. The nonpolar term consists of an estimator for the solute-solvent van der Waals dispersion energy designed to mimic the continuum solvent solute-solvent van der Waals interaction energy, in addition to a surface area term corresponding to the work of cavity formation. AGBNP makes use of a new parameter-free algorithm to calculate the scaling coefficients used in the pairwise descreening scheme to take into account atomic overlaps. The same algorithm is also used to calculate atomic surface areas. We show that excellent agreement is achieved for the GB self-energies and surface areas in comparison to accurate, but much more expensive, numerical evaluations. The parameter-free approach used in AGBNP and the sensitivity of the AGBNP model with respect to large and small conformational changes makes the model suitable for high-resolution modeling of protein loops and receptor sites as well as high-resolution prediction of the structure and thermodynamics of protein-ligand complexes. We present illustrative results for these kinds of benchmarks. The model is fully analytical with first derivatives and is computationally efficient. It has been incorporated into the IMPACT molecular simulation program.

MHC–Peptide Binding is Assisted by Bound Water Molecules

Water plays an important role in determining the high affinity of epitopes to the class I MHC complex. To study the energy and dynamics of water interactions in the complex we performed molecular dynamics simulation of the class I MHC-HLA2 complex bound to the HIV reverse transcriptase epitope, ILKEPVHGV, and in the absence of the epitope. Each simulation was extended for 5ns. We studied the processes of water penetration in the interface between MHC and peptide, and identified 14 water molecules that stay bound for periods longer than 1ns in regions previously identified by crystallography. These water molecules in the interface perform definite "tasks" contributing to the binding energy: hydrogen bond bridges between MHC and peptide and filling empty spaces in the groove which enhance affinity without contributing to epitope specificity. We calculate the binding energy for interfacial water molecules and find that there is an overall gain in free energy resulting from the formation of water clusters at the epitope-MHC interface. Water molecules serving the task of filling empty spaces bind at the interface with a net gain in entropy, relative to their entropy in bulk. We conclude that water molecules at the interface play the role of active mediators in the MHC-peptide interaction, and might be responsible for the large binding affinity of the MHC complex to a large number of epitope sequences.

Molecular probes: what is the range of their interaction with the environment?

We performed pressure-tuning hole-burning experiments on a modified cytochrome c protein in a glycerol/buffer glass. The shift and the broadening of the holes were investigated for various frequencies within the inhomogeneous band. On the basis of a simple model, we were able to estimate the interaction range between chromophore and protein. It is approximately 4.5 A. The parameters that enter the model are the compressibility, the static mean-square displacement, the inhomogeneous width, and the average spectral shift per pressure. From this result and from our experiments on pressure-induced denaturing, we conclude that water molecules have to be brought very close to the chromophore during the denaturation process.

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.

Effect of trifluoroethanol on the conformational stability of a hyperthermophilic esterase: a CD study

The conformational stability of the hyperthermophilic esterase AFEST from Archeoglobus fulgidus against the denaturing action of 2,2,2-trifluoroethanol (TFE) has been investigated by means of circular dichroism (CD) measurements. At room temperature far-UV and near-UV CD spectra point out the occurrence of a co-operative transition from the native structure to a denatured state characterized by a high content of alpha-helix. The TFE concentration at half-completion of the transition proves to be 3.5 M (25% v v(-1)), by recording the molar ellipticity at both 222 and 276 nm. Thermal transition curves of AFEST in the absence and in the presence of TFE indicate a significant stability decrease on increasing the TFE concentration. The denaturation temperature is 99 degrees C for native AFEST, but becomes 85 degrees C at 1.4 M TFE (10% v v(-1)), and 56 degrees C at 2.8 M TFE (20% v v(-1)). It is also shown that, even though AFEST is very resistant to temperature, its resistance towards the denaturing action of TFE is similar to that of mesophilic proteins, including an esterase from Escherichia coli, AES. The proposal of a general mechanism for the TFE action on globular proteins leads to a reliable rationale of experimental data.

Molecular dynamics simulations of peptides and proteins with a continuum electrostatic model based on screened Coulomb potentials

A continuum electrostatics approach for molecular dynamics (MD) simulations of macromolecules is presented and analyzed for its performance on a peptide and a globular protein. The approach incorporates the screened Coulomb potential (SCP) continuum model of electrostatics, which was reported earlier. The model was validated in a broad set of tests some of which were based on Monte Carlo simulations that included single amino acids, peptides, and proteins. The implementation for large-scale MD simulations presented in this article is based on a pairwise potential that makes the electrostatic model suitable for fast analytical calculation of forces. To assess the suitability of the approach, a preliminary validation is conducted, which consists of (i) a 3-ns MD simulation of the immunoglobulin-binding domain of streptococcal protein G, a 56-residue globular protein and (ii) a 3-ns simulation of Dynorphin, a biological peptide of 17 amino acids. In both cases, the results are compared with those obtained from MD simulations using explicit water (EW) molecules in an all-atom representation. The initial structure of Dynorphin was assumed to be an alpha-helix between residues 1 and 9 as suggested from NMR measurements in micelles. The results obtained in the MD simulations show that the helical structure collapses early in the simulation, a behavior observed in the EW simulation and consistent with spectroscopic data that suggest that the peptide may adopt mainly an extended conformation in water. The dynamics of protein G calculated with the SCP implicit solvent model (SCP-ISM) reveals a stable structure that conserves all the elements of secondary structure throughout the entire simulation time. The average structures calculated from the trajectories with the implicit and explicit solvent models had a cRMSD of 1.1 A, whereas each average structure had a cRMSD of about 0.8A with respect to the X-ray structure. The main conformational differences of the average structures with respect to the crystal structure occur in the loop involving residues 8-14. Despite the overall similarity of the simulated dynamics with EW and SCP models, fluctuations of side-chains are larger when the implicit solvent is used, especially in solvent exposed side-chains. The MD simulation of Dynorphin was extended to 40 ns to study its behavior in an aqueous environment. This long simulation showed that the peptide has a tendency to form an alpha-helical structure in water, but the stabilization free energy is too weak, resulting in frequent interconversions between random and helical conformations during the simulation time. The results reported here suggest that the SCP implicit solvent model is adequate to describe electrostatic effects in MD simulation of both peptides and proteins using the same set of parameters. It is suggested that the present approach could form the basis for the development of a reliable and general continuum approach for use in molecular biology, and directions are outlined for attaining this long-term goal.

Folding of a highly conserved diverging turn motif from the SH3 domain

Recent NMR structural characterization studies showed that a seven-residue segment (FKKGERL) from the src SH3 domain adopts the nativelike diverging type II beta-turn in aqueous solution in support of the prediction based on the I-sites library of sequence structural motifs. We study the conformational variability and folding/unfolding thermodynamics of this peptide in explicit solvent using replica-exchange molecular dynamics simulations, which greatly enhances the sampling of the conformational space. This peptide samples three main free energy basins (nativelike, intermediate, and unfolded) separated by small barriers. The nativelike basin is fractionally populated (DeltaG(300K) = 0.4 kcal/mol) with structures that satisfy a subset of the NMR-derived constraints. The intrinsic stability of the diverging turn is examined in relationship to the nature of three specific contacts: a turn-hydrogen bond, a mainchain-to-sidechain hydrogen bond, and an end-to-end hydrophobic contact. We have carried out simulations of mutants at the highly conserved GE positions in the sequence. The mutation E5D destabilizes the isolated diverging turn motif, contrary to the observation that this mutation stabilizes the fyn SH3 domain. The G4T mutation also destabilizes the isolated diverging turn; however, the extent of destabilization is smaller than that of the reverse mutation in the drk SH3.

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.

Origins of protein denatured state compactness and hydrophobic clustering in aqueous urea: inferences from nonpolar potentials of mean force

Free energies of pairwise hydrophobic association are simulated in aqueous solutions of urea at concentrations ranging from 0-8 M. Consistent with the expectation that hydrophobic interactions are weakened by urea, the association of relatively large nonpolar solutes is destabilized by urea. However, the association of two small methane-sized nonpolar solutes in water has the opposite tendency of being slightly strengthened by the addition of urea. Such size effects and the dependence of urea-induced stability changes on the configuration of nonpolar solutes are not predicted by solvent accessible surface area approaches based on energetic parameters derived from bulk-phase solubilities of model compounds. Thus, to understand hydrophobic interactions in proteins, it is not sufficient to rely solely on transfer experiment data that effectively characterize a single nonpolar solute in an aqueous environment but not the solvent-mediated interactions among two or more nonpolar solutes. We find that the m-values for the rate of change of two-methane association free energy with respect to urea concentration is a dramatically nonmonotonic function of the spatial separation between the two methanes, with a distance-dependent profile similar to the corresponding two-methane heat capacity of association in pure water. Our results rationalize the persistence of residual hydrophobic contacts in some proteins at high urea concentrations and explain why the heat capacity signature (DeltaC(P)) of a compact denatured state can be similar to DeltaC(P) values calculated by assuming an open random-coil-like unfolded state.

Connecting local structure to interface formation: a molecular scale van der Waals theory of nonuniform liquids

This article reviews a new and general theory of nonuniform fluids that naturally incorporates molecular scale information into the classical van der Waals theory of slowly varying interfaces. The method optimally combines two standard approximations, molecular (mean) field theory to describe interface formation and linear response (or Gaussian fluctuation) theory to describe local structure. Accurate results have been found in many different applications in nonuniform simple fluids and these ideas may have important implications for the theory of hydrophobic interactions in water.

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.

Relating interactions between neurofilaments to the structure of axonal neurofilament distributions through polymer brush models

Neurofilaments (NFs) have been proposed to interact with one another through mutual steric exclusion of their unstructured C-terminal "sidearm" domains, producing order in axonal NF distributions and conferring mechanical strength to the axon. Here we apply theory developed for polymer brushes to examine the relationship between the brush properties of the sidearms and NF organization in axons. We first measure NF-NF radial distribution functions and occupancy probability distributions for adult mice. Interpreting the probability distributions using information theory, we show that the NF distributions may be represented by a single pair potential of mean force. Then, to explore the relationship between model parameters and NF architecture, we conduct two-dimensional Monte Carlo simulations of NF cross-sectional distributions. We impose purely repulsive interaction potentials in which the sidearms are represented as neutral and polyelectrolyte chains. By treating the NFs as telechelic polymer brushes, we also incorporate cross-bridging interactions. Both repulsive potentials are capable of reproducing NF cross-sectional densities and their pair correlations. We find that NF structure is sensitive to changes in brush thickness mediated by chain charge, consistent with the experimental observation that sidearm phosphorylation regulates interfilament spacing. The presence of attractive cross-bridging interactions contributes only modestly to structure for moderate degrees of cross-bridging and leads to NF aggregation for extensive cross-bridging.

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.

Pressure effects on intra- and intermolecular interactions within proteins

The effects of pressure on protein structure and function can vary dramatically depending on the magnitude of the pressure, the reaction mechanism (in the case of enzymes), and the overall balance of forces responsible for maintaining the protein's structure. Interactions between the protein and solvent are also critical in determining the response of a protein to pressure. Pressure has long been recognized as a potential denaturant of proteins, often promoting the disruption of multimeric proteins, but recently examples of pressure-induced stabilization have also been reported. These global effects can be explained in terms of pressure effects on individual molecular interactions within proteins, including hydrophobic, electrostatic, and van der Waals interactions, which can now be studied in greater detail than ever before. However, many uncertainties remain, and thorough descriptions of how proteins respond to pressure remain elusive. This review summarizes basic concepts and new findings related to pressure effects on intra- and intermolecular interactions within proteins and protein complexes, and discusses their implications for protein structure-function relationships under pressure.

Stability diagram and unfolding of a modified cytochrome c: what happens in the transformation regime?

We determined the stability diagram of a modified cytochrome c protein in a glycerol water mixture by measuring the first and the second moment of the fluorescence from the chromophore as a function of temperature and pressure. Temperature and pressure were varied between 273 and 363 K and 0.0001 and 1 GPa, respectively. The shift of the fluorescence maximum showed a characteristic sigmoid-like pattern from which information on the microscopic processes during unfolding is obtained: as the transformation regime is entered, the fluorescence shows a significant blue shift. The conclusion is that water molecules get into contact with the chromophore. They lead to strong electrostatic contributions in the solvent shift, which counteract the red shifting dispersion interactions. Assuming that there are just two relevant states that determine the stability diagram, the complete set of thermodynamic parameters can be determined from the data. However, under certain pressure-temperature conditions the fluorescence pattern is more complicated, pointing toward reentrant transitions and, possibly, to consecutive steps in the unfolding process.

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.

Thermodynamics and kinetics of actin filament nucleation

We have performed computer simulations and free energy calculations to determine the thermodynamics and kinetics of actin nucleation and thus identify a probable nucleation pathway and critical nucleus size. The binding free energies of structures along the nucleation pathway are found through a combination of electrostatic calculations and estimates of the entropic and surface area contributions. The association kinetics for the formation of each structure are determined through a series of Brownian dynamics simulations. The combination of the binding free energies and the association rate constants determines the dissociation rate constants, allowing for a complete characterization of the nucleation and polymerization kinetics. The results indicate that the trimer is the size of the critical nucleus, and the rate constants produce polymerization plots that agree very well with experimental results over a range of actin monomer concentrations.

Water at hydrophobic surfaces: weak hydrogen bonding and strong orientation effects

Vibrational studies that selectively probe molecular structure at CCl4/H2O and hydrocarbon/H2O interfaces show that the hydrogen bonding between adjacent water molecules at these interfaces is weak, in contrast to generally accepted models of water next to fluid hydrophobic surfaces that suggest strong hydrogen bonding. However, interactions between these water molecules and the organic phase result in substantial orientation of these weakly hydrogen-bonded water molecules in the interfacial region. The results have important implications for understanding water adjacent to hydrophobic surfaces and the penetration of water into hydrophobic phases.

Structure and bonding of molecules at aqueous surfaces

Significant advances toward understanding the structure of aqueous surfaces on a molecular level have been made in recent years. This review focuses on the recent contributions of surface vibrational sum frequency spectroscopy (VSFS) to this field of study. An overview of recent VSFS studies of the molecular structure and orientation of molecules at the vapor-water interface and the interface between water and an immiscible organic liquid is presented, with particular emphasis on studies that compare the molecular properties and adsorbate behavior at these two different but related interfaces. This discussion is preceded by a general introduction to VSFS studies at aqueous surfaces and a description of the fundamental principles underlying the technique.