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.     

Linear solvation energy relationship modeling and kinetic studies on reactive extraction of succinic acid by tridodecylamine dissolved in MIBK

Equilibrium and kinetic studies for the extraction of succinic acid from aqueous solution with tridodecylamine diluted in MIBK are reported. All measurements were carried out at 298.15 K. The extent to which the organic phase may be loaded with succinic acid is expressed as a loading ratio, Z. The equilibrium data were also interpreted by a proposed mechanism of three reactions of complexation by which (1:1) and (2:1) acid-amine complexes are formed. Kinetics of extraction of succinic acid by tridodecylamine in MIBK has also been determined. Kinetic studies for the extraction of succinic acid from aqueous solution with tridodecylamine diluted in MIBK were carried out using a stirred cell for kinetic studies. The results of the liquid-liquid equilibrium measurements were correlated by a linear solvation energy relationship (LSER) model, which takes into account physical interactions. From the regression coefficients, information on the solvent-solute interaction is obtained and solvation models are proposed.     

Solvent free vapor phase photografting of maleic anhydride onto poly(ethylene terephthalate) and surface coupling of fluorinated probes, PEG, and an RGD-peptide

Poly(ethylene terephthalate) (PET) was photografted in a solvent free vapor of maleic anhydride and benzophenone. After hydrolysis of the initially grafted succinic anhydride groups, the carboxylic PET surfaces were modified by coupling reactions in organic and aqueous solutions. 2,2,2-Trifluoroethylamine and diamino PEGs of molecular weight 3400 and 2000 were reacted with acid chloride groups obtained by treating the PET-COOH surface with PCl(5). Furthermore, fluoro substituted thiols and a cystein terminated RGD containing peptide were bound to PET-COOH surfaces via a disulfide link by a three step coupling sequence. Coupling yields and surface concentrations of the fluoro substituted ligands were calculated from ESCA data. The RGD-peptide surfaces were evaluated by cultivation with rat smooth muscle cells.     

Amino acid side-chain partition energies and distribution of residues in soluble proteins

Energies required to transfer amino acid side chains from water to less polar environments were calculated from results of several studies and compared with several statistical analyses of residue distributions in soluble proteins. An analysis that divides proteins into layers parallel with their surfaces is more informative than those that simply classify residues as exposed or buried. Most residues appear to be distributed as a function of the distance from the protein-water interface in a manner consistent with partition energies calculated from partitioning of amino acids between water and octanol phases and from solubilities of amino acids in water, ethanol, and methanol. Lys, Arg, Tyr, and Trp residues tend to concentrate near the water-protein interface where their apolar side-chain components are more buried than their polar side-chain components. Residue distributions calculated in this manner do not correlate well with side-chain solvation energies calculated from vapor pressures of side-chain analogs over a water phase. Results of statistical studies that classify residues as exposed to solvent or buried inside the protein interior appear to depend on the method used to classify residues. Data from some of these studies correlate better with solvation energies, but other data correlate better with partition energies. Most other statistical methods that have been used to evaluate effects of water on residue distributions yield results that correlate better with partition energies than with solvation energies.     

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.     

Atomistic Simulation of Mineral Surfaces

Abstract

Atomistic simulation techniques are now able to model the structure of mineral surfaces at the atomic level. In this paper we begin to address the question of whether surface reactivity can be studied reliably by modelling the surface reactivity of calcite, fluorite and forsterite under aqueous conditions. We first used energy minimisation techniques to investigate the interaction between the minerals calcite and fluorite with water and methanoic acid. The relative adsorption energies suggest that methanoic acid preferentially adsorbs onto fluorite surfaces, while water adsorbs preferentially onto calcite as inferred from experiments on mineral separation. Molecular Dynamics simulations were also used to model the effect of temperature on the adsorption of water on the calcite {1014} and fluorite {111} surfaces. Furthermore we used these techniques to model point defect formation at surfaces. We are also interested in modelling the competition between associative and dissociative adsorption on mineral surfaces. Simulations of adsorption of water on the low-index forsterite surfaces have predicted the adsorption energies and equilibrium morphology. The calculated equilibrium morphology adequately reproduces the experimental morphology of forsterite suggesting that the relative stabilities of the surfaces, both unhydrated and hydroxylated, are calculated correctly.     

Interaction of indole derivatives and tryptophan peptides with interfaces of sodium dodecyl sulfate micelles.

The free energies of transfer for indole and tryptophan derivatives and pentapeptides having single tryptophan residues from aqueous to sodium dodecyl sulfate (SDS) micellar phases have been systematically studied using the conventional method of ultraviolet absorption spectrophotometry. The free energies for the position isomers of methyl indoles varied depending on the substitution positions. Thus, the contribution of the methyl group to the binding affinity of the 4-methyl indole to the micelle was about twice that of the 2- and 7-methyl indoles. The free energy changes with the introduction of halogen groups to the indole rings were correlated to the nonpolar water-accessible surface area (DeltaA(np)) of the halogen moieties, which were regarded as hydrophobic. The relationships followed straight lines passing through the origins. Position dependence having tendencies similar to the methyl indoles was observed among the magnitudes of the slopes of the straight lines. These results strongly suggest that the indole rings of the derivatives residing in the micellar interface regions direct their imino moieties --NH-- toward the micellar surfaces. Experiments using model tryptophan pentapeptides showed that the magnitude of free energy change per methylene unit of an alkyl amino acid residue in the pentapeptide increased with elongation of the alkyl moiety and was not a constant value as reported for various alkyl compounds. When the peptides distribute to the SDS micelles, the peptide backbones are anchored in aqueous phases and the amino acid side chains in the interfaces extend their alkyl groups toward the micellar centers. Thus, the free energy changes can be connected to the positions of the alkyl groups of the amino acid residues in the micelles.     

Evaluation of the conformational free energies of loops in proteins

In this paper we discuss the problem of including solvation free energies in evaluating the relative stabilities of loops in proteins. A conformational search based on a gas-phase potential function is used to generate a large number of trial conformations. As has been found previously, the energy minimization step in this process tends to pack charged and polar side chains against the protein surface, resulting in conformations which are unstable in the aqueous phase. Various solvation models can easily identify such structures. In order to provide a more severe test of solvation models, gas phase conformations were generated in which side chains were kept extended so as to maximize their interaction with the solvent. The free energies of these conformations were compared to that calculated for the crystal structure in three loops of the protein E. coli RNase H, with lengths of 7, 8, and 9 residues. Free energies were evaluated with a finite difference Poisson-Boltzmann (FDPB) calculation for electrostatics and a surface area-based term for nonpolar contributions. These were added to a gas-phase potential function. A free energy function based on atomic solvation parameters was also tested. Both functions were quite successful in selecting, based on a free energy criterion, conformations quite close to the crystal structure for two of the three loops. For one loop, which is involved in crystal contacts, conformations that are quite different from the crystal structure were also selected. A method to avoid precision problems associated with using the FDPB method to evaluate conformational free energies in proteins is described. © 1994 John Wiley & Sons, Inc.     

An extended aqueous solvation model based on atom-weighted solvent accessible surface areas: SAWSA v2.0 model

A new method is proposed for calculating aqueous solvation free energy based on atom-weighted solvent accessible surface areas. The method, SAWSA v2.0, gives the aqueous solvation free energy by summing the contributions of component atoms and a correction factor. We applied two different sets of atom typing rules and fitting processes for small organic molecules and proteins, respectively. For small organic molecules, the model classified the atoms in organic molecules into 65 basic types and additionally. For small organic molecules we proposed a correction factor of hydrophobic carbon to account for the aggregation of hydrocarbons and compounds with long hydrophobic aliphatic chains. The contributions for each atom type and correction factor were derived by multivariate regression analysis of 379 neutral molecules and 39 ions with known experimental aqueous solvation free energies. Based on the new atom typing rules, the correlation coefficient (r) for fitting the whole neutral organic molecules is 0.984, and the absolute mean error is 0.40 kcal mol^–1, which is much better than those of the model proposed by Wang et al. and the SAWSA model previously proposed by us. Furthermore, the SAWSA v2.0 model was compared with the simple atom-additive model based on the number of atom types (NA). The calculated results show that for small organic molecules, the predictions from the SAWSA v2.0 model are slightly better than those from the atom-additive model based on NA. However, for macromolecules such as proteins, due to the connection between their molecular conformation and their molecular surface area, the atom-additive model based on the number of atom types has little predictive power. In order to investigate the predictive power of our model, a systematic comparison was performed on seven solvation models including SAWSA v2.0, GB/SA_1, GB/SA_2, PB/SA_1, PB/SA_2, AM1/SM5.2R and SM5.0R. The results showed that for organic molecules the SAWSA v2.0 model is better than the other six solvation models. For proteins, the model classified the atoms into 20 basic types and the predicted aqueous free energies of solvation by PB/SA were used for fitting. The solvation model based on the new parameters was employed to predict the solvation free energies of 38 proteins. The predicted values from our model were in good agreement with those from the PB/SA model and were much better than those given by the other four models developed for proteins.Figure The definition of hydrophobic carbons. Here CA, CB and CD are three carbon atoms; X represents a heteroatom. According to our definition, CB is a hydrophobic carbon, CA is not a hydrophobic carbon because a heteroatom is within four atoms and CD is not a hydrophobic carbon because CD is sp²- hydridized and in a six-member ring.Electronic Supplementary Material Supplementary material is available for this article at     

Novel self-associative and multiphasic nanostructured soft carriers based on amphiphilic hyaluronic acid derivatives

The purpose of the present study was to investigate the physicochemical properties in aqueous media of amphiphilic hyaluronic acid (HA) derivatives obtained by reaction of HA's hydroxyl groups with octenyl succinic anhydride (OSA). The self-associative properties of the resulting octenyl succinic anhydride-modified hyaluronic acid (OSA-HA) derivatives were studied by fluorescence spectroscopy using Nile Red as fluorophore. The morphology, size and surface charge of the OSA-HA assemblies were determined by transmission electron microscopy, dynamic light scattering and by measuring their electrophoretic mobility, respectively. OSA-HA was shown to spontaneously self-associate in aqueous media into negatively charged spherical and multiphasic nanostructures with a hydrodynamic diameter between 170 and 230 nm and to solubilize hydrophobic compounds such as Nile Red. This was a good indication that OSA-HA could be used as building block for the formulation of soft nanocarriers towards the encapsulation and controlled delivery of hydrophobic active ingredients or drugs.     

Prediction of the aqueous solvation free energy of organic compounds by using autocorrelation of molecular electrostatic potential surface properties combined with response surface analysis

Several quantitative structure-property relationship (QSPR) approaches have been explored for the prediction of aqueous solubility or aqueous solvation free energies, DeltaG(sol), as crucial parameter affecting the pharmacokinetic profile and toxicity of chemical compounds. It is mostly accepted that aqueous solvation free energies can be expressed quantitatively in terms of properties of the molecular surface electrostatic potentials of the solutes. In the present study we have introduced autocorrelation molecular electrostatic potential (autoMEP) vectors in combination with nonlinear response surface analysis (RSA) as alternative 3D-QSPR strategy to evaluate the aqueous solvation free energy of organic compounds. A robust QSPR model (r(cv)=0.93) has been obtained by using a collection of 248 organic chemicals. An external test set based on 23 molecules confirmed the good predictivity of the autoMEP/RSA model suggesting its further applicability in the in silico prediction of water solubility of large organic compound libraries.     

A CFF 91-based Continuum Solvation Model: Solvation Free Energies of Small Organic Molecules and Conformations of the Alanine Dipeptide in Solution

Abstract

For molecular mechanics simulations of solvated molecules, it is important to use a consistent approach for calculating both the force field energy and the solvation free energy. A continuum solvation model based upon the atomic charges provided with the CFF91 force field is derived. The electrostatic component of the solvation free energy is described by the Poisson-Bolzmann equation while the nonpolar comonent of the solvation energy is assumed to be proportional to the solvent accessible surface area of the solute. Solute atomic radii used to describe the interface between the solute and solvent are fitted to reproduce the energies of small organic molecules. Data for 140 compounds are presented and compared to experiment and to the results from the well-characterized quantum mechanical solvation model AM1-SM2. In particular, accurate results are obtained for amino acid neutral analogues (mean unsigned error of 0.3 kcal/mol). The conformational energetics of the solvated alanine dipeptide is discussed.     

Fast accurate evaluation of protein solvent exposure

Protein solvation energies are often taken to be proportional to solvent-accessible surface areas. Computation of these areas is numerically demanding and may become a bottleneck for folding and design applications. Fast graph-based methods, such as dead-end elimination (DEE), become possible if all energies, including solvation energies, are expressed as single-residue and pair-residue terms. To this end, Street and Mayo originated a pair-residue approximation for solvent-accessible surface areas (Street AG, Mayo SL. Pairwise calculation of protein solvent accessible surface areas. Fold Des 1998;3:253-258). The dominant source of error in this method is the overlapping burial of side-chain surfaces in the protein core. Here we report a new pair-residue approximation, which greatly reduces this overlap error by the use of optimized generic side-chains. We have tested the generic-side-chain method for the ten proteins studied by Street and Mayo and for 377 single-domain proteins from the CATH database (Orengo CA, Michie AD, Jones S, Jones DT, Swindells MB, Thornton JM. CATH-A hierarchic classification of protein domain structures. Structure 1997;5:1093-1108). With little additional cost in computation, the new method consistently reduces error for total areas and residue-by-residue areas by more than a factor of two. For example, the residue-by-residue error (for buried area) is reduced from 7.42 A(2) to 3.70 A(2). This difference translates into a solvation energy difference of approximately 0.2 kcal/mol per residue, amounting to a reduction in root-mean-square energy error of 2 kcal/mol for a 100 residue chain, a potentially critical difference for both protein folding and design applications.     

An efficient technique for the prediction of solvent-dependent morphology: the COSMIC method

We have developed a method of calculating the solvation energy of a surface based on an implicit solvent model. This new model called COSMIC, is an extension of the established COSMO solvation approach and allows the technique to be applied to systems of any periodicity from finite molecules, through polymers and surfaces, to cavities of water within a bulk unit cell. As well as extending the scope of the COSMO technique, it also improves the numerical stability through removal of a number of discontinuities in the potential energy surface. The COSMIC model has been applied to barium sulfate, where it was found to produce similar surface energies and configurations to the much more computationally expensive explicit molecular dynamics simulations. The calculated solvated morphology of barium sulfate was found to differ significantly to that calculated in vacuum with a reduced number of faces present.     

Interaction of the peptide bond with solvent water: a vapor phase analysis

A dynamic technique, using radioactivity as a means of detection, makes it possible to measure the partial pressures of highly polar compounds in dilute aqueous solution. The results can be expressed in terms of the dimensionless distribution coefficient for transfer of a compound from dilute aqueous solution to the vapor phase. For acetic acid this coefficient is 1.1 X 10(-5), for acetamide 7.6 X 10(-8), for N-methylacetamide 4.1 X 10(-8), and for N,N-dimethylacetamide 5.4 X 10(-7). Thus acetamide is much more strongly solvated than the uncharged acetic acid molecule. The results suggest: (1) that the peptide bond represents an extreme among uncharged functional groups in the degree to which it is stabilized by solvent water; (2) that the very great hydrophilic character of the peptide bond may be associated mainly with hydrogen bonding of the solvent to the carbonyl oxygen atom (rather than the N-H group); and (3) that the observed equilibria of biosynthesis and hydrolysis of peptide bonds in aqueous solution are largely determined by differences between reactants and products in their free energies of solvation. It is anticipated that where "bound" water is found in proteins, it will often be found to be associated with peptide bonds, and will tend to be associated with the C-O group rather than with the N-H group.     

Correlation between knowledge-based and detailed atomic potentials: application to the unfolding of the GCN4 leucine zipper.

The relationship between the unfolding pseudo free energies of reduced and detailed atomic models of the GCN4 leucine zipper is examined. Starting from the native crystal structure, a large number of conformations ranging from folded to unfolded were generated by all-atom molecular dynamics unfolding simulations in an aqueous environment at elevated temperatures. For the detailed atomic model, the pseudo free energies are obtained by combining the CHARMM all-atom potential with a solvation component from the generalized Born, surface accessibility, GB/SA, model. Reduced model energies were evaluated using a knowledge-based potential. Both energies are highly correlated. In addition, both show a good correlation with the root mean square deviation, RMSD, of the backbone from native. These results suggest that knowledge-based potentials are capable of describing at least some of the properties of the folded as well as the unfolded states of proteins, even though they are derived from a database of native protein structures. Since only conformations generated from an unfolding simulation are used, we cannot assess whether these potentials can discriminate the native conformation from the manifold of alternative, low-energy misfolded states. Nevertheless, these results also have significant implications for the development of a methodology for multiscale modeling of proteins that combines reduced and detailed atomic models.     

A novel method reveals that solvent water favors polyproline II over beta-strand conformation in peptides and unfolded proteins: conditional hydrophobic accessible surface area (CHASA)

In aqueous solution, the ensemble of conformations sampled by peptides and unfolded proteins is largely determined by their interaction with water. It has been a long-standing goal to capture these solute-water energetics accurately and efficiently in calculations. Historically, accessible surface area (ASA) has been used to estimate these energies, but this method breaks down when applied to amphipathic peptides and proteins. Here we introduce a novel method in which hydrophobic ASA is determined after first positioning water oxygens in hydrogen-bonded orientations proximate to all accessible peptide/protein backbone N and O atoms. This conditional hydrophobic accessible surface area is termed CHASA. The CHASA method was validated by predicting the polyproline-II (P(II)) and beta-strand conformational preferences of non-proline residues in the coil library (i.e., non-alpha-helix, non-beta-strand, non-beta-turn library derived from X-ray elucidated structures). Further, the method successfully rationalizes the previously unexplained solvation energies in polyalanyl peptides and compares favorably with published experimentally determined P(II) residue propensities. We dedicate this paper to Frederic M. Richards.     

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.     

Energy functions for protein design I: efficient and accurate continuum electrostatics and solvation

Electrostatics and solvation energies are important for defining protein stability, structural specificity, and molecular recognition. Because these energies are difficult to compute quickly and accurately, they are often ignored or modeled very crudely in computational protein design. To address this problem, we have developed a simple, fast, and accurate approximation for calculating Born radii in the context of protein design calculations. When these approximate Born radii are used with the generalized Born continuum dielectric model, energies calculated by the 10(6)-fold slower finite difference Poisson-Boltzmann model are faithfully reproduced. A similar approach can be used for estimating solvent-accessible surface areas (SASAs). As an independent test, we show that these approximations can be used to accurately predict the experimentally determined pK(a)s of >200 ionizable groups from 15 proteins.