Molecular simulation study of cooperativity in hydrophobic association: clusters of four hydrophobic particles

The multibody contribution to the potential of mean force (PMF) of hydrophobic association of four methane molecules in water was investigated by means of umbrella-sampling molecular dynamics. Two systems were considered: (i). a trigonal pyramid with three methane molecules at contact distance forming a fixed base, the fourth molecule being placed on the top with variable distance from the base; and (ii). a regular uniformly expanding tetrahedron. Methane-methane distances as far as 12.5 A, i.e. beyond the second solvent-separated minimum of the PMF, were considered to address the baseline problem. In contrast to the small effect in the three-body case studied previously (Protein Sci 9 (2000) 1235), the multibody contribution was found to amount to approximately 0.2 kcal/mol per methane-methane pair, or approximately 25% of the depth of the contact minimum in the PMF. The main effect of the multibody contribution to the PMF is a reduction of the height of the barrier between the contact and solvent separated minima and a narrowing of the region of its maximum, while the region of the contact minimum is affected only weakly. The reduction of the barrier is due to four-body contributions. The cooperative contributions to the PMF agree very well with those computed from the molecular surface of the systems under consideration, which further supports earlier observations that the molecular surface can be used with good accuracy to describe the energetics of hydrophobic association.     

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.     

Free energy landscapes of peptides by enhanced conformational sampling

The free energy landscapes of peptide conformations in water have been observed by the enhanced conformational sampling method, applying the selectively enhanced multicanonical molecular dynamics simulations. The conformations of the peptide dimers, -Gly-Gly-, -Gly-Ala-, -Gly-Ser-, -Ala-Gly-, -Asn-Gly-, -Pro-Gly-, -Pro-Ala-, and -Ala-Ala-, which were all blocked with N-terminal acetyl and C-terminal N-methyl groups, were individually sampled with the explicit TIP3P water molecules. From each simulation trajectory, we obtained the canonical ensemble at 300 K, from which the individual three-dimensional landscape was drawn by the potential of mean force using the three reaction coordinates: the backbone dihedral angle, psi, of the first amino acid, the backbone dihedral angle, phi, of the second amino acid, and the distance between the carbonyl oxygen of the N-terminal acetyl group and the C-terminal amide proton. The most stable state and several meta-stable states correspond to extended conformations and typical beta-turn conformations, and their free energy values were accounted for from the potentials of mean force at the states. In addition, the contributions from the intra-molecular energies of peptides and those from the hydration effects were analyzed. Consequently, the stable beta-turn conformations in the free energy landscape were consistent with the empirically preferred beta-turn types for each amino acid sequence. The thermodynamic values for the hydration effect were decomposed and they correlated well with the empirical values estimated from the solvent accessible surface area of each molecular conformation during the trajectories. The origin of the architecture of protein local fragments was analyzed from the viewpoint of the free energy and its decomposed factors.     

Simulation studies of the insolubility of cellulose

Molecular dynamics simulations have been used to calculate the potentials of mean force for separating short cellooligomers in aqueous solution as a means of estimating the contributions of hydrophobic stacking and hydrogen bonding to the insolubility of crystalline cellulose. A series of four potential of mean force (pmf) calculations for glucose, cellobiose, cellotriose, and cellotetraose in aqueous solution were performed for situations in which the molecules were initially placed with their hydrophobic faces stacked against one another, and another for the cases where the molecules were initially placed adjacent to one another in a co-planar, hydrogen-bonded arrangement, as they would be in cellulose Iβ. From these calculations, it was found that hydrophobic association does indeed favor a crystal-like structure over solution, as might be expected. Somewhat more surprisingly, hydrogen bonding also favored the crystal packing, possibly in part because of the high entropic cost for hydrating glucose hydroxyl groups, which significantly restricts the configurational freedom of the hydrogen-bonded waters. The crystal was also favored by the observation that there was no increase in chain configurational entropy upon dissolution, because the free chain adopts only one conformation, as previously observed, but against intuitive expectations, apparently due to the persistence of the intramolecular O3-O5 hydrogen bond.     

The influence of cholesterol on interactions and dynamics of ibuprofen in a lipid bilayer

In this work, molecular dynamics (MD) simulations with atomistic details were performed to examine the influence of the cholesterol on the interactions and the partitioning of the hydrophobic drug ibuprofen in a fully hydrated 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) bilayer. Analysis of MD simulations indicated that ibuprofen molecules prefer to be located in the hydrophobic acyl chain region of DMPC/cholesterol bilayers. This distribution decreases the lateral motion of lipid molecules. The presence of ibuprofen molecules in the bilayers with 0 and 25 mol% cholesterol increases the ordering of hydrocarbon tails of lipids whereas for the bilayers with 50 mol% cholesterol, ibuprofen molecules perturb the flexible chains of DMPC lipids which leads to the reduction of the acyl chain order parameter. The potential of the mean force (PMF) method was used to calculate the free energy profile for the transferring of an ibuprofen molecule from the bulk water into the DMPC/cholesterol membranes. The PMF studies indicated that the presence of 50 mol% cholesterol in the bilayers increases the free energy barrier and slows down the permeation of the ibuprofen drug across the DMPC bilayer. This can be due to the condensing and ordering effects of the cholesterol on the bilayer.     

Use of a potential of mean force to analyze free energy contributions in protein folding.

A method for calculation of the free energy of residues as a function of residue burial is proposed. The method is based on the potential of mean force, with a reaction coordinate expressed by residue burial. Residue burials are calculated from high-resolution protein structures. The largest individual contributions to the free energy of a residue are found to be due to the hydrophobic interactions of the nonpolar atoms, interactions of the main chain polar atoms, and interactions of the charged groups of residues Arg and Lys. The contribution to the free energy of folding due to the uncharged side chain polar atoms is small. The contribution to the free energy of folding due to the main chain polar atoms is favorable for partially buried residues and less favorable or unfavorable for fully buried residues. Comparison of the accessible surface areas of proteins and model spheres shows that proteins deviate considerably from a spherical shape and that the deviations increase with the size of a protein. The implications of these results for protein folding are also discussed.     

Force-Induced Lysozyme—HyHEL5 Antibody Dissociation and Its Analysis by Means of a Cooperative Binding Model

Dynamic force spectroscopy probes the kinetic properties of molecules interacting with each other such as antibody-antigen, receptor-ligand, etc. In this article, a statistical model for the dissociation of such cooperative systems is presented. The partner molecules are assumed to be linked by a number of relatively weak bonds that can be grouped together into cooperative units. Single bonds are assumed to open and close statistically. Our model was used to analyze molecular recognition experiments of single receptor-ligand pairs in which the two molecules are brought into contact using an atomic force microscope, which leads to the formation of a strong and specific bond. Then a prescribed time-dependent force is applied to the complex and the statistical distribution of forces needed to pull the molecules completely apart is measured. This quantity is also calculated from our model. Furthermore, its dependence on the model parameters, such as binding free energy, number of bonds and groups, number of cooperative elementary bonds and degree of cooperativity within a group, influence of the force on the binding free energy, and the rate of change of the pulling force, is determined.     

Role of bound water in protein-ligand association processes

The role of water molecules on the protein-ligand interface during macromolecular association has been determined. The free energy of association of insulin has been calculated by the methods of molecular mechanics and continual electrostatics (Poisson-Boltzmann model). The previously developed scheme of the decomposition of association free energy onto contributions from individual interactions has been used to calculate intermolecular interactions, the solvation free energy, and the entropies of the process of macromolecular association. An analysis of the calculated oscillation spectra indicated that the presence of water molecules on the protein-protein interface promotes an increase in the contribution of vibration entropy to the free energy of association due to the enhancement of the flexibility of the complex. It was shown that water molecules involved in the formation of protein-water-ligand hydrogen bond network change the balance of forces in the system.     

Free energetics of rigid body association of ubiquitin binding domains: A biochemical model for binding mediated by hydrophobic interaction

Weak intermolecular interactions, such as hydrophobic associations, underlie numerous biomolecular recognition processes. Ubiquitin is a small protein that represents a biochemical model for exploring thermodynamic signatures of hydrophobic association as it is widely held that a major component of ubiquitin's binding to numerous partners is mediated by hydrophobic regions on both partners. Here, we use atomistic molecular dynamics simulations in conjunction with the Adaptive Biasing Force sampling method to compute potentials of mean force (the reversible work, or free energy, associated with the binding process) to investigate the thermodynamic signature of complexation in this well‐studied biochemical model of hydrophobic association. We observe that much like in the case of a purely hydrophobic solute (i.e., graphene, carbon nanotubes), association is favored by entropic contributions from release of water from the interprotein regions. Moreover, association is disfavored by loss of enthalpic interactions, but unlike in the case of purely hydrophobic solutes, in this case protein‐water interactions are lost and not compensated for by additional water‐water interactions generated upon release of interprotein and moreso, hydration, water. We further find that relative orientations of the proteins that mutually present hydrophobic regions of each protein to its partner are favored over those that do not. In fact, the free energy minimum as predicted by a force field based method recapitulates the experimental NMR solution structure of the complex. Proteins 2014; 82:1453–1468. © 2014 Wiley Periodicals, Inc.     

Adhesive and conformational behaviour of mycolic acid monolayers

We have studied the pH-dependent interaction between mycolic acid (MA) monolayers and hydrophobic and hydrophilic surfaces using molecular (colloidal probe) force spectroscopy. In both cases, hydrophobic and hydrophilic monolayers (prepared by Langmuir-Blodgett and Langmuir-Schaefer deposition on silicon or hydrophobized silicon substrates, respectively) were studied. The force spectroscopy data, fitted with classical DLVO (Derjaguin, Landau, Verwey, and Overbeek) theory to examine the contribution of electrostatic and van der Waals forces, revealed that electrostatic forces are the dominant contribution to the repulsive force between the approaching colloidal probe and MA monolayers. The good agreement between data and the DLVO model suggest that beyond a few nm away from the surface, hydrophobic, hydration, and specific chemical bonding are unlikely to contribute to any significant extent to the interaction energy between the probe and the surface. The pH-dependent conformation of MA molecules in the monolayer at the solid-liquid interface was studied by ellipsometry, neutron reflectometry, and with a quartz crystal microbalance. Monolayers prepared by the Langmuir-Blodgett method demonstrated a distinct pH-responsive behaviour, while monolayers prepared by the Langmuir-Schaefer method were less sensitive to pH variation. It was found that the attachment of water molecules plays a vital role in determining the conformation of the MA monolayers.     

Hydrophobe-water interactions: methane as a model

Recent molecular-dynamics simulations have demonstrated that the use of an empirical hydrophobic potential displaying two minima, i.e., one for hydrophobes in close contact and one for hydrophobes separated by a hydration layer, leads to a marked improvement in protein structure prediction. This potential is supported by experimental data and simulations, but its physical origin and mathematical formulation have not been derived as yet. Here we show that water-mediated attraction (the “wetting regime”) between two hydrophobic molecules originates in the interaction between the dipoles induced at the surface of the hydrophobes by the surrounding structured water. As an example, we derive the effective hydrophobic potential that describes the interaction between two methane molecules, a classical model of a double-well energy function. We found an excellent agreement with published results from all-atom, explicit solvent molecular-dynamics simulations of this interaction. The approach presented here provides the theoretical basis for implementing an adequate representation of the wetting regime of the hydrophobic interactions in force fields used for structure prediction. The results are useful for modeling both protein folding and binding.     

Salting-in of neopentane in the aqueous solutions of urea and glycine-betaine

The effects of urea and glycine-betaine (GB) osmolytes on the hydrophobic interactions of neopentane in water have been studied using molecular dynamics simulations. From the study of the potentials of mean force, it is observed that both urea and GB decrease the association and solvation of neopentane. The calculated equilibrium constants show that urea and GB decrease the population of solvent-separated minima of neopentane. The hydrophobic association as well as solvation of neopentane molecules are stabilised by entropy and enthalpy in the mixtures. The radial distribution functions (RDFs) and running coordination numbers of water, urea and GB molecules show that neopentane shows salting-in behaviour in aqueous-GB, aqueous-urea and aqueous-urea-GB mixtures. Neopentane is preferentially solvated by GB in aqueous-GB and preferentially solvated by urea in aqueous-urea-GB solutions. The preferential solvation of neopentane by GB suggests that GB decreases the interaction between neopentane molecules i.e. salting-in of neopentane. The calculated solvation free energies and radial density profiles of neopentane also support the salting-in behaviour of neopentane in the mixtures of these osmolytes.     

Increased protein backbone conformational entropy upon hydrophobic ligand binding

For complexes between proteins and very small hydrophobic ligands, hydrophobic effects alone may be insufficient to outweigh the unfavorable entropic terms resulting from bimolecular association. NMR relaxation experiments indicate that the backbone flexibility of mouse major urinary protein increases upon binding the hydrophobic mouse pheromone 2-sec-butyl-4,5-dihydrothiazole. The associated increase in backbone conformational entropy of the protein appears to make a substantial contribution toward stabilization of the protein-pheromone complex. This term is likely comparable in magnitude to other important free energy contributions to binding and may represent a general mechanism to promote binding of very small ligands to macromolecules.     

End-to-end attraction of duplex DNA

Recent experiments [Nakata, M. et al., End-to-end stacking and liquid crystal condensation of 6 to 20 basepair DNA duplexes. Science 2007; 318:1276-1279] have demonstrated spontaneous end-to-end association of short duplex DNA fragments into long rod-like structures. By means of extensive all-atom molecular dynamic simulations, we characterized end-to-end interactions of duplex DNA, quantitatively describing the forces, free energy and kinetics of the end-to-end association process. We found short DNA duplexes to spontaneously aggregate end-to-end when axially aligned in a small volume of monovalent electrolyte. It was observed that electrostatic repulsion of 5'-phosphoryl groups promoted the formation of aggregates in a conformation similar to the B-form DNA double helix. Application of an external force revealed that rupture of the end-to-end assembly occurs by the shearing of the terminal base pairs. The standard binding free energy and the kinetic rates of end-to-end association and dissociation processes were estimated using two complementary methods: umbrella sampling simulations of two DNA fragments and direct observation of the aggregation process in a system containing 458 DNA fragments. We found the end-to-end force to be short range, attractive, hydrophobic and only weakly dependent on the ion concentration. The relation between the stacking free energy and end-to-end attraction is discussed as well as possible roles of the end-to-end interaction in biological and nanotechnological systems.     

Posttransition state desolvation of the hydrophobic core of the src-SH3 protein domain

The folding thermodynamics of the src-SH3 protein domain were characterized under refolding conditions through biased fully atomic molecular dynamics simulations with explicit solvent. The calculated free energy surfaces along several reaction coordinates revealed two barriers. The first, larger barrier was identified as the transition state barrier for folding, associated with the formation of the first hydrophobic sheet of the protein. phi values calculated from structures residing at the transition state barrier agree well with experimental phi values. The microscopic information obtained from our simulations allowed us to unambiguously assign intermediate phi values as the result of multiple folding pathways. The second, smaller barrier occurs later in the folding process and is associated with the cooperative expulsion of water molecules between the hydrophobic sheets of the protein. This posttransition state desolvation barrier cannot be observed through traditional folding experiments, but is found to be critical to the correct packing of the hydrophobic core in the final stages of folding. Hydrogen exchange and NMR experiments are suggested to probe this barrier.     

Water-membrane partition thermodynamics of an amphiphilic lipopeptide: an enthalpy-driven hydrophobic effect

To shed light on the driving force for the hydrophobic effect that partitions amphiphilic lipoproteins between water and membrane, we carried out an atomically detailed thermodynamic analysis of a triply lipid modified H-ras heptapeptide anchor (ANCH) in water and in a DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) bilayer. Combining molecular mechanical and continuum solvent approaches with an improved technique for solute entropy calculation, we obtained an overall transfer free energy of ~−13 kcal mol⁻¹. This value is in qualitative agreement with free energy changes derived from a potential of mean force calculation and indirect experimental observations. Changes in free energies of solvation and ANCH conformational reorganization are unfavorable, whereas ANCH-DMPC interactions—especially van der Waals—favor insertion. These results are consistent with an enthalpy-driven hydrophobic effect, in accord with earlier calorimetric data on the membrane partition of other amphiphiles. Furthermore, structural and entropic analysis of molecular dynamics-generated ensembles suggests that conformational selection may play a hitherto unappreciated role in membrane insertion of lipid-modified peptides and proteins.     

Protein folding and association: insights from the interfacial and thermodynamic properties of hydrocarbons.

We demonstrate in this work that the surface tension, water-organic solvent, transfer-free energies and the thermodynamics of melting of linear alkanes provide fundamental insights into the nonpolar driving forces for protein folding and protein binding reactions. We first develop a model for the curvature dependence of the hydrophobic effect and find that the macroscopic concept of interfacial free energy is applicable at the molecular level. Application of a well-known relationship involving surface tension and adhesion energies reveals that dispersion forces play little or no net role in hydrophobic interactions; rather, the standard model of disruption of water structure (entropically driven at 25 degrees C) is correct. The hydrophobic interaction is found, in agreement with the classical picture, to provide a major driving force for protein folding. Analysis of the melting behavior of hydrocarbons reveals that close packing of the protein interior makes only a small free energy contribution to folding because the enthalpic gain resulting from increased dispersion interactions (relative to the liquid) is countered by the freezing of side chain motion. The identical effect should occur in association reactions, which may provide an enormous simplification in the evaluation of binding energies. Protein binding reactions, even between nearly planar or concave/convex interfaces, are found to have effective hydrophobicities considerably smaller than the prediction based on macroscopic surface tension. This is due to the formation of a concave collar region that usually accompanies complex formation. This effect may preclude the formation of complexes between convex surfaces.     

The nature of cation-pi binding: interactions between tetramethylammonium ion and benzene in aqueous solution.

A combined quantum mechanical and molecular mechanical Monte Carlo simulation method was used to determine the free energy of binding between tetramethylammonium ion (TMA+) and benzene in water. The computed free energy as a function of distance (the potential of mean force) has two minima that represent contact and solvent-separated complexes. These species are separated by a broad barrier of about 3 kJ/mol. The results are in good accord with experimental data and suggest that TMA+ binds to benzene more favorably than to chloride ion, with an association constant of about 0.8 M-1.     

Many-body energies during proton transfer in an aqueous system

The energetics of the mechanism of proton transfer from a hydronium ion to one of the water molecules in its first solvation shell are studied using density functional theory and the Møller–Plesset perturbation (MP2) method. The potential energy surface of the proton transfer mechanism is obtained at the B3LYP and MP2 levels with the 6-311++G** basis set. Many-body analysis is applied to the proton transfer mechanism to obtain the change in relaxation energy, two-body, three-body and four-body energies when proton transfer occurs from the hydronium ion to one of the water molecules in its first solvation shell. It is observed that the binding energy (BE) of the complex decreases during the proton transfer process at both levels of theory. During the proton transfer process, the % contribution of the total two-body energy to the binding energy of the complex increases from 62.9 to 68.09% (39.9 to 45.95%), and that of the total three-body increases from 25.9 to 27.09% (24.16 to 26.17%) at the B3LYP/6-311++G** (MP2/ 6-311++G**) level. There is almost no change in the water–water–water three-body interaction energy during the proton transfer process at both levels of theory. The contribution of the relaxation energy and the total four-body energy to the binding energy of the complex is greater at the MP2 level than at the B3LYP level. Significant differences are found between the relaxation energies, the hydronium–water interaction energies and the four-body interaction energies at the B3LYP and MP2 levels.     

Decomposition analysis of free energy profile for Hsp90-ADP association

The functional cycle of heat shock protein 90 (Hsp90) is driven and inhibited by the association/dissociation of ligand molecules. In order to understand the molecular mechanism of the association of N-terminal domain of Hsp90 (N-Hsp90) and its ligand molecule, it is necessary to investigate which part in the target system promotes or inhibits the association of N-Hsp90 and its ligand molecule. We apply the decomposition analysis for the association free energy of N-Hsp90 and ADP. The mean force calculated by thermodynamic integration method combined with molecular dynamic simulations is divided into the contributions from molecules in the target system. Van der Waals interaction of the solvent water molecules strongly stabilises the association. Three lysine residues on the surface of the N-Hsp90 pull ADP toward the binding pocket of N-Hsp90. This study elucidates the association process of ADP from the bulk region to the binding pocket of the N-terminal domain Hsp90. This approach is applicable to elucidate the association process of biomolecules.