The role of solvent polarity in the free energy of transfer of amino acid side chains from water to organic solvents

The transfer free energies of amino acid side chains from water to N-methylacetamide have been determined and compared with those obtained from other model systems. Although the process of transfer from water to N-methylacetamide represents transfer from a lower dielectric phase to a higher dielectric phase, the transfer free energies of most of the amino acid side chains are nearly the same as those obtained from the water to ethanol system. Among the apolar side chains studied, only the transfer free energies of methionine and the aromatic side chains are apparently influenced to some extent by the polarity of the organic solvent phase. The transfer free energies of the neutral polar side chains also exhibit significant dependence on solvent polarity. The van't Hoff plots for most of the apolar side chains exhibit nonlinear curves, indicating that the enthalpy of transfer from water to N-methylacetamide is temperature-dependent. It is suggested that to assess the contribution of the hydrophobic free energy to the stability of globular proteins, it is probably not necessary to account for variation in the internal environment of the protein.     

The apolar surface area of amino acids and its empirical correlation with hydrophobic free energy

A linear equation is presented which accounts quantitatively for the free energy of transfer of amino acids from water to apolar solvent as a function of accessible surface area and partial charges of the constituents of amino acids. Starting from these parameters the apolar surface area is defined and correlated with the measured free transfer energy. The resulting linear correlation makes it possible to calculate more precisely the "hydrophobic" contribution of both apolar and polar groups including uncharged side chains of arginine, lysine, glutamic and aspartic acids, and histidine, respectively, to protein stabilization.     

The thermodynamics of protein-ligand interaction and solvation: insights for ligand design

Isothermal titration calorimetry is able to provide accurate information on the thermodynamic contributions of enthalpy and entropy changes to free energies of binding. The Structure/Calorimetry of Reported Protein Interactions Online database of published isothermal titration calorimetry studies and structural information on the interactions between proteins and small-molecule ligands is used here to reveal general thermodynamic properties of protein-ligand interactions and to investigate correlations with changes in solvation. The overwhelming majority of interactions are found to be enthalpically favoured. Synthetic inhibitors and biological ligands form two distinct subpopulations in the data, with the former having greater average affinity due to more favourable entropy changes on binding. The greatest correlation is found between the binding free energy and apolar surface burial upon complex formation. However, the free-energy contribution per unit area buried is only 30-50% of that expected from earlier studies of transfer free energies of small molecules. A simple probability-based estimator for the maximal affinity of a binding site in terms of its apolar surface area is proposed. Polar surface area burial also contributes substantially to affinity but is difficult to express in terms of unit area due to the small variation in the amount of polar surface buried and a tendency for cancellation of its enthalpic and entropic contributions. Conventionally, the contribution of apolar desolvation to affinity is attributed to gain of entropy due to solvent release. Although data presented here are supportive of this notion, because the correlation of entropy change with apolar surface burial is relatively weak, it cannot, on present evidence, be confidently considered to be correct. Further, thermodynamic changes arising from small differences between ligands binding to individual proteins are relatively large and, in general, uncorrelated with changes in solvation, suggesting that trends identified across widely differing proteins are of limited use in explaining or predicting the effects of ligand modifications.     

Solvophobic forces and molecular surface area changes in drug-biomolecule associations as with actinomycin-deoxyguanosine in a wide range of methanol/water mixtures

A method is given to predict the unitary free energies of complexation between drug-like and nucleoside-like biomolecules in a range of mixed solvent compositions. A stability maximum for the actinomycin (A)-deoxyguanosine (D) complex at 8% MeOH (v/v) in methanol/water mixtures is correctly predicted by the theory in agreement with existing experimental data. The molecular surface areas of A and D exposed to the solvent are found to diminish by 36.4 A(2) upon association. The 'microthermodynamic differential surface tension' of the solvophobic theory obtained for nucleoside-like and organic molecules in contact with MeOH/H2O can be used to predict the solvent effect free energies in other such molecular or biopolymeric associations in solution.     

Optimization of linear disorder predictors yields tight association between crystallographic disorder and hydrophobicity

X-ray crystallographic protein structures often contain disordered regions that are observed as missing electron density. Diffraction data may give little or no direct evidence as to the specific nature of disordered regions. We have developed a weighted window-based disorder predictor optimized using crystallographic data. Performance of a predictor is strongly influenced by chain termini. Optimized score adjustment values for amino- and carboxy-terminal positions demonstrate a simple, monotonic relationship between disorder and residue distance from termini. This optimized disorder predictor performs similarly to DISOPRED2 on crystallographically disordered regions. Data-optimized residue disorder propensities show strong linear correlation with experimentally determined amino acid transfer energies between water and hydrogen-bonding organic solvents, which primarily reflect residue hydrophobicity (exemplified by the Nozaki-Tanford hydrophobicity scale). Disorder propensities do not correlate as well with transfer energies between water and apolar solvents, which primarily reflect a different hydropathic property: residue hydrophilicity (also reflected by the Kyte-Doolittle hydropathy scale). Our results suggest that while hydrophobic side-chain interactions are primarily involved in determining stability of the folded conformation, hydrogen bonding, and similar polar interactions are primarily involved in conformational and interaction specificity.     

Molecular basis of co-operativity in protein folding. III. Structural identification of cooperative folding units and folding intermediates.

The hierarchical partition function formalism for protein folding developed earlier has been extended through the use of three-dimensional polar and apolar contact plots. For each amino acid residue in the protein, these plots indicate the apolar and polar surfaces that are buried from the solvent, the identity of all amino acid residues that contribute to this shielding, and the magnitude of their contributions. These contact plots are then used to examine the distribution of the free energy of stabilization throughout the protein molecule. Analysis of these data allows identification of co-operative folding units and their hierarchical levels, and the identification of partially folded intermediates with a significant probability of being populated. The overall folding/unfolding thermodynamics of 12 globular proteins, for which crystallographic and experimental thermodynamics are available, is predicted within error. An energetic classification of partially folded intermediates is presented and the results compared to those cases for which structural and thermodynamic experimental information is available. Four different types of partially folded states and their structural energies are considered. (1) Local intermediates, in which only a local region of the protein loses secondary and tertiary interactions, while the rest of the protein remains intact. (2) Global intermediates, corresponding to the standard molten globule definition, in which significant secondary structure is maintained but native-like tertiary structure contacts are disrupted. (3) Extended intermediates characterized by the existence of secondary structure elements (e.g. alpha-helices) exposed to solvent. (4) Folding intermediates in proteins with two structural domains. The structure and energetics of folding intermediates of apo-myoglobin, alpha-lactalbumin, phosphoglycerate kinase and arabinose-binding protein are considered in detail.     

Hydration and conformational equilibria of simple hydrophobic and amphiphilic solutes.

We consider whether the continuum model of hydration optimized to reproduce vacuum-to-water transfer free energies simultaneously describes the hydration free energy contributions to conformational equilibria of the same solutes in water. To this end, transfer and conformational free energies of idealized hydrophobic and amphiphilic solutes in water are calculated from explicit water simulations and compared to continuum model predictions. As benchmark hydrophobic solutes, we examine the hydration of linear alkanes from methane through hexane. Amphiphilic solutes were created by adding a charge of +/-1e to a terminal methyl group of butane. We find that phenomenological continuum parameters fit to transfer free energies are significantly different from those fit to conformational free energies of our model solutes. This difference is attributed to continuum model parameters that depend on solute conformation in water, and leads to effective values for the free energy/surface area coefficient and Born radii that best describe conformational equilibrium. In light of these results, we believe that continuum models of hydration optimized to fit transfer free energies do not accurately capture the balance between hydrophobic and electrostatic contributions that determines the solute conformational state in aqueous solution.     

Solvation Free Energy of the Peptide Group: Its Model Dependence and Implications for the Additive-Transfer Free-Energy Model of Protein Stability

The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)_n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)_n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.     

Solvation Free Energy of the Peptide Group: Its Model Dependence and Implications for the Additive-Transfer Free-Energy Model of Protein Stability

The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)_n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)_n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.     

A model binding site for testing scoring functions in molecular docking

Prediction of interaction energies between ligands and their receptors remains a major challenge for structure-based inhibitor discovery. Much effort has been devoted to developing scoring schemes that can successfully rank the affinities of a diverse set of possible ligands to a binding site for which the structure is known. To test these scoring functions, well-characterized experimental systems can be very useful. Here, mutation-created binding sites in T4 lysozyme were used to investigate how the quality of atomic charges and solvation energies affects molecular docking. Atomic charges and solvation energies were calculated for 172,118 molecules in the Available Chemicals Directory using a semi-empirical quantum mechanical approach by the program AMSOL. The database was first screened against the apolar cavity site created by the mutation Leu99Ala (L99A). Compared to the electronegativity-based charges that are widely used, the new charges and desolvation energies improved ranking of known apolar ligands, and better distinguished them from more polar isosteres that are not observed to bind. To investigate whether the new charges had predictive value, the non-polar residue Met102, which forms part of the binding site, was changed to the polar residue glutamine. The structure of the resulting Leu99Ala and Met102Gln double mutant of T4 lysozyme (L99A/M102Q) was determined and the docking calculation was repeated for the new site. Seven representative polar molecules that preferentially docked to the polar versus the apolar binding site were tested experimentally. All seven bind to the polar cavity (L99A/M102Q) but do not detectably bind to the apolar cavity (L99A). Five ligand-bound structures of L99A/M102Q were determined by X-ray crystallography. Docking predictions corresponded to the crystallographic results to within 0.4A RMSD. Improved treatment of partial atomic charges and desolvation energies in database docking appears feasible and leads to better distinction of true ligands. Simple model binding sites, such as L99A and its more polar variants, may find broad use in the development and testing of docking algorithms.     

Hydrophobicity regained.

A widespread practice is to use free energies of transfer between organic solvents and water (delta G0transfer to define hydrophobicity scales for the amino acid side chains. A comparison of four delta G0transfer scales reveals that the values for hydrogen-bonding side chains are highly dependent on the non-aqueous environment. This property of polar side chains violates the assumptions underlying the paradigm of equating delta G0transfer with hydrophobicity or even with a generic solvation energy that is directly relevant to protein stability and ligand binding energetics. This simple regaining of the original concept of hydrophobicity reveals a flaw in approaches that use delta G0transfer values to derive generic estimates of the energetics of the burial of polar groups, and allows the introduction of a "pure" hydrophobicity scale for the amino acid residues.     

Macromolecular solvation energies derived from small molecule crystal morphology.

The morphology of small molecule crystals provides a model for evaluating surface solvation energies in a system with similar packing density to that observed for amino acid residues in proteins. The solvation energies associated with the transfer of methylene and carboxyl groups between vacuum and aqueous phases are estimated to be approx. $40 and -260 cal/A2, respectively, from an analysis of the morphology of succinic acid crystals. These solvation energies predict values for contact angles in reasonable agreement with measurements determined from macroscopic monolayer surfaces. Transfer free energies between vapor and water phases for a series of carboxylic acids are also predicted reasonably well by these solvation energies, provided the surface exposure of different groups is quantitated with the molecular surface area rather than the more traditional accessible surface area. In general, molecular surfaces and molecular surface areas are seen to have important advantages for characterizing the structure and energetics of macromolecular surfaces. Crystal faces of succinic acid with the lowest surface energies in aqueous solution are characteristically smooth. Increasing surface roughness and apolarity are associated with higher surface energies, which suggests an approach for modifying the surface properties of proteins and other macromolecules.     

The effect of vicinal polar and charged groups on hydrophobic hydration.

The use of a linear relationship between free energy of hydrophobic hydration and solvent-accessible apolar surface area has been helpful in interpreting the thermodynamics of biological macromolecules. However, a recent study (Y.-K. Cheng, P. J. Rossky, Nature 1998, Vol. 392, pp. 696-699) has established a substantial enthalpic dependence on biomolecular surface topography, originating from solvent hydrogen-bonding loss in a restrictive geometry. In this study, we use molecular dynamics simulations of 2-Zn insulin in water solvent to explore the further effect of vicinal polar or charged groups on hydrophobic hydration at a biomolecular surface. In contrast to the case for solvent more isolated from such polar solute influences, the binding energies of the water that is proximal to the hydrophobic dimeric interface of insulin and vicinal to polar and charged groups are comparable to the bulk solvent value, a result of compensating interaction primarily with the solute counterions. The results suggest a special importance for such polar/charged groups in biological processes involving hydrophobic surface regions of restricted geometry and also suggest a general route for tuning the hydrophobicity of interfaces.     

Ligand solvation in molecular docking

Solvation plays an important role in ligand‐protein association and has a strong impact on comparisons of binding energies for dissimilar molecules. When databases of such molecules are screened for complementarity to receptors of known structure, as often occurs in structure‐based inhibitor discovery, failure to consider ligand solvation often leads to putative ligands that are too highly charged or too large. To correct for the different charge states and sizes of the ligands, we calculated electrostatic and non‐polar solvation free energies for molecules in a widely used molecular database, the Available Chemicals Directory (ACD). A modified Born equation treatment was used to calculate the electrostatic component of ligand solvation. The non‐polar component of ligand solvation was calculated based on the surface area of the ligand and parameters derived from the hydration energies of apolar ligands. These solvation energies were subtracted from the ligand‐receptor interaction energies. We tested the usefulness of these corrections by screening the ACD for molecules that complemented three proteins of known structure, using a molecular docking program. Correcting for ligand solvation improved the rankings of known ligands and discriminated against molecules with inappropriate charge states and sizes. Proteins 1999;34:4–16. © 1999 Wiley‐Liss, Inc.     

A structural model of the acetylcholine receptor channel based on partition energy and helix packing calculations.

A structural model of the transmembrane portion of the acetylcholine receptor was developed from sequences of all its subunits by using transfer energy calculations to locate transmembrane alpha-helices and to calculate which helical side chains should be in contact with water inside the channel, with portions of other transmembrane helices, or with lipid hydrocarbon chains. "Knobs-into-holes" side chain packing calculations were used with other factors to stack the transmembrane alpha-helices together. In the model each subunit has the following structures in order along the sequence from the NH2 terminus: a large extracellular domain of undetermined structure, a short apolar alpha-helix that lies on the extracellular lipid surface of the membrane; three apolar transmembrane alpha-helices (I, II, and III), a cytoplasmic domain of undetermined structure, an amphipathic transmembrane alpha-helix (L) that forms the channel lining, a short extracellular alpha-helix, another apolar transmembrane alpha-helix (IV), and a small cytoplasmic domain formed by the COOH-terminal end of the chain. Three concentric layers form the pore. A bundle of five amphipathic L helices forms the channel lining. This bundle is surrounded by a bundle of 10 alternating II and III helices. Helices I and IV cover portions of the outer surface of the bundle formed by helices II and III. Positions of disulfide bridges are predicted and a mechanism for opening and closing conformational changes is proposed that requires tilting transmembrane helices and possibly a thiol-disulfide interchange reaction.     

Hydrophobic regions on protein surfaces. Derivation of the solvation energy from their area distribution in crystallographic protein structures.

For the first time, a direct approach for the derivation of an atomic solvation parameter from macromolecular structural data alone is presented. The specific free energy of solvation for hydrophobic surface regions of proteins is delineated from the area distribution of hydrophobic surface patches. The resulting value is 18 cal/(mol.A2), with a statistical uncertainty of +/-2 cal/mol.A2) at the 5% significance level. It compares favorably with the parameters for carbon obtained by other authors who use the the crystal geometry of succinic acid or energies of transfer from hydrophobic solvent to water for small organic compounds. Thus, the transferability of atomic solvation parameters for hydrophobic atoms to macromolecules has been directly demonstrated. A careful statistical analysis demonstrates that surface energy parameters derived from thermodynamic data of protein mutation experiments are clearly less confident.     

Adsorption properties of polar/apolar inducers at a charged interface and their relevance to leukemia cell differentiation.

The interfacial adsorption properties of polar/apolar inducers of cell differentiation (PAIs) were studied on a mercury electrode. This study, on a clean and reproducible charged surface, unraveled the purely physical interactions among these compounds and the surface, apart from the complexity of the biological membrane. The interfacial behavior of two classical inducers, hexamethylenebisacetamide (HMBA) and dimethylsulfoxide, was compared with that of a typical apolar aliphatic compound, 1-octanol, that has a similar hydrophobic moiety as HMBA but a much smaller dipolar moment. Both HMBA and Octanol adsorb flat in contact with the surface because of hydrophobic forces, with a very similar free energy of adsorption. However, the ratio of polar to apolar moieties in PAIs turned out to be crucial to drive the adsorption maximum toward physiological values of surface charge density, where octanol is desorbed. The electrostatic effects in the interfacial region reflected the adsorption properties: the changes in the potential drop across the interfacial region as a function of the surface charge density, in the physiological range, were opposite in PAIs as compared with apolar aliphatic compounds, as exemplified by octanol. This peculiar electrostatic effect of PAIs has far-reaching relevance for the design of inducers with an adequate therapeutic index to be used in clinical trials.     

Description of hydration free energy density as a function of molecular physical properties

A method to calculate the solvation free energy density (SFED) at any point in the cavity surface or solvent volume surrounding a solute is proposed. In the special case in which the solvent is water, the SFED is referred to as the hydration free energy density (HFED). The HFED is described as a function of some physical properties of the molecules. These properties are represented by simple basis functions. The hydration free energy of a solute was obtained by integrating the HFED over the solvent volume surrounding the solute, using a grid model. Of 34 basis functions that were introduced to describe the HFED, only six contribute significantly to the HFED. These functions are representations of the surface area and volume of the solute, of the polarization and dispersion of the solute, and of two types of electrostatic interactions between the solute and its environment. The HFED is described as a linear combination of these basis functions, evaluated by summing the interaction energy between each atom of the solute with a grid point in the solvent, where each grid point is a representation of a finite volume of the solvent. The linear combination coefficients were determined by minimizing the error between the calculated and experimental hydration free energies of 81 neutral organic molecules that have a variety of functional groups. The calculated hydration free energies agree well with the experimental results. The hydration free energy of any other solute molecule can then be calculated by summing the product of the linear combination coefficients and the basis functions for the solute.