Properties of hydrophobic free energy found by gas-liquid transfer

Quantifying Amide-Aromatic Interactions at Molecular and Atomic Levels: Experimentally Determined Enthalpic and Entropic Contributions to Interactions of Amide sp2O, N, C and sp3C Unified Atoms with Naphthalene sp2C Atoms in Water

In addition to amide hydrogen bonds and the hydrophobic effect, interactions involving π-bonded sp2 atoms of amides, aromatics, and other groups occur in protein self-assembly processes including folding, oligomerization, and condensate formation. These interactions also occur in aqueous solutions of amide and aromatic compounds, where they can be quantified. Previous analysis of thermodynamic coefficients quantifying net-favorable interactions of amide compounds with other amides and aromatics revealed that interactions of amide sp2O with amide sp2N unified atoms (presumably C═O···H-N hydrogen bonds) and amide/aromatic sp2C (lone pair π, n-π*) are particularly favorable. Sp3C-sp3C (hydrophobic), sp3C-sp2C (hydrophobic, CH-π), sp2C-sp2C (hydrophobic, π-π), and sp3C-sp2N interactions are favorable, sp2C-sp2N interactions are neutral, while sp2O-sp2O and sp2N-sp2N self-interactions and sp2O-sp3C interactions are unfavorable. Here, from determinations of favorable effects of 14 amides on naphthalene solubility at 10, 25, and 45 °C, we dissect amide-aromatic interaction free energies into enthalpic and entropic contributions and find these vary systematically with amide composition. Analysis of these results yields enthalpic and entropic contributions to intrinsic strengths of interactions of amide sp2O, sp2N, sp2C, and sp3C unified atoms with aromatic sp2C atoms. For each interaction, enthalpic and entropic contributions have the same sign and are much larger in magnitude than the interaction free energy itself. The amide sp2O-aromatic sp2C interaction is enthalpy-driven and entropically unfavorable, consistent with direct chemical interaction (e.g., lone pair-π), while amide sp3C- and sp2C-aromatic sp2C interactions are entropy-driven and enthalpically unfavorable, consistent with hydrophobic effects. These findings are relevant for interactions involving π-bonded sp2 atoms in protein processes.

Water-mediated interactions destabilize proteins

Proteins are folded to avoid exposure of the nonpolar groups to water because water‐mediated interactions between nonpolar groups are a promising factor in the thermodynamic stabilities of proteins—which is a well‐accepted view as one of the unique effects of hydrophobic interactions. This article poses a critical question for this classical view by conducting an accurate solvation free‐energy calculation for a thermodynamic cycle of a protein folding using a liquid‐state density functional theory. Here, the solvation‐free energy for a leucine zipper formation was examined in the coiled‐coil protein GCN4‐p1, a typical model for hydrophobic interactions, which demonstrated that water‐mediated interactions were unfavorable for the association of nonpolar groups in the native state, while the dispersion forces between them were, instead, responsible for the association. Furthermore, the present analysis well predicted the isolated helical state stabilized by pressure, which was previously observed in an experiment. We reviewed the problems in the classical concept and semiempirical presumption that the energetic cost of the hydration of nonpolar groups is a driving force of folding.

Experimentally determined strengths of favorable and unfavorable interactions of amide atoms involved in protein self-assembly in water

Folding and other protein self-assembly processes are driven by favorable interactions between O, N, and C unified atoms of the polypeptide backbone and side chains. These processes are perturbed by solutes that interact with these atoms differently than water does. Amide NH···O=C hydrogen bonding and various π-system interactions have been better characterized structurally or by simulations than experimentally in water, and unfavorable interactions are relatively uncharacterized. To address this situation, we previously quantified interactions of alkyl ureas with amide and aromatic compounds, relative to interactions with water. Analysis yielded strengths of interaction of each alkylurea with unit areas of different hybridization states of unified O, N, and C atoms of amide and aromatic compounds. Here, by osmometry, we quantify interactions of 10 pairs of amides selected to complete this dataset. An analysis yields intrinsic strengths of six favorable and four unfavorable atom-atom interactions, expressed per unit area of each atom and relative to interactions with water. The most favorable interactions are sp2O-sp2C (lone pair-π, presumably n-π*), sp2C-sp2C (π-π and/or hydrophobic), sp2O-sp2N (hydrogen bonding) and sp3C-sp2C (CH-π and/or hydrophobic). Interactions of sp3C with itself (hydrophobic) and with sp2N are modestly favorable, while sp2N interactions with sp2N and with amide/aromatic sp2C are modestly unfavorable. Amide sp2O-sp2O interactions and sp2O-sp3C interactions are more unfavorable, indicating the preference of amide sp2O to interact with water. These intrinsic interaction strengths are used to predict interactions of amides with proteins and chemical effects of amides (including urea, N-ethylpyrrolidone [NEP], and polyvinylpyrrolidone [PVP]) on protein stability.

Direct Measurement of Length Scale Dependence of the Hydrophobic Free Energy of a Single Collapsed Polymer Nanosphere

The physics underlying hydrophobicity at macroscopic and microscopic levels is fundamentally distinct. However, experimentally quantifying the length scale dependence of hydrophobicity is challenging. Here we show that the size-dependent hydrophobic free energy of a collapsed polymer nanosphere can be continuously monitored from its single-molecule force-extension curve using a novel theoretical framework. The hydrophobic free energy shows a change from cubic to square dependence of the radius of the polymer nanosphere at a radius of ∼1  nm-this is consistent with Lum-Chandler-Weeks theory and simulations. We can also observe a large variation of the hydrophobic free energy of each polymer nanosphere implying the heterogeneity of the self-assembled structures and/or the fluctuation of the water-polymer interface. We expect that our approach can be used to address many fundamental questions about hydrophobic hydration, which are otherwise inaccessible by ensemble measurements.

A Comparison of QM/MM Simulations with and without the Drude Oscillator Model Based on Hydration Free Energies of Simple Solutes

Maintaining a proper balance between specific intermolecular interactions and non-specific solvent interactions is of critical importance in molecular simulations, especially when predicting binding affinities or reaction rates in the condensed phase. The most rigorous metric for characterizing solvent affinity are solvation free energies, which correspond to a transfer from the gas phase into solution. Due to the drastic change of the electrostatic environment during this process, it is also a stringent test of polarization response in the model. Here, we employ both the CHARMM fixed charge and polarizable force fields to predict hydration free energies of twelve simple solutes. The resulting classical ensembles are then reweighted to obtain QM/MM hydration free energies using a variety of QM methods, including MP2, Hartree⁻Fock, density functional methods (BLYP, B3LYP, M06-2X) and semi-empirical methods (OM2 and AM1 ). Our simulations test the compatibility of quantum-mechanical methods with molecular-mechanical water models and solute Lennard⁻Jones parameters. In all cases, the resulting QM/MM hydration free energies were inferior to purely classical results, with the QM/MM Drude force field predictions being only marginally better than the QM/MM fixed charge results. In addition, the QM/MM results for different quantum methods are highly divergent, with almost inverted trends for polarizable and fixed charge water models. While this does not necessarily imply deficiencies in the QM models themselves, it underscores the need to develop consistent and balanced QM/MM interactions. Both the QM and the MM component of a QM/MM simulation have to match, in order to avoid artifacts due to biased solute⁻solvent interactions. Finally, we discuss strategies to improve the convergence and efficiency of multi-scale free energy simulations by automatically adapting the molecular-mechanics force field to the target quantum method.

1-Butanol as a Solvent for Efficient Extraction of Polar Compounds from Aqueous Medium: Theoretical and Practical Aspects

The extraction of polar molecules from aqueous solution is a challenging task in organic synthesis. 1-Butanol has been used sporadically as an eluent for polar molecules, but it is unclear which molecular features drive its efficiency. Here, we employ free energy simulations to study the partitioning of 15 solutes between water and 1-butanol. The simulations demonstrate that the high affinity of polar molecules to the wet 1-butanol phase is associated with its nanostructure. Small inverse micelles of water are able to accommodate polar solutes and locally mimic an aqueous environment. We verify the simulations based on partition coefficients between water and 1-octanol, and include a blind prediction of the water/1-butanol partition coefficient of cyclohexane-1,2-diol. The calculations are in excellent agreement with experiment, reaching root-mean-square deviations below 0.7 kcal/mol. Actual extractions of cyclohexane-1,2-diol from buffer solutions that mimic cell lysates and suspensions in biocatalytic reactions further exemplify our findings. The yields highlight that extractions with 1-butanol can be significantly more efficient than the conventional protocol based on ethyl acetate.

Aggregation behavior of sodium 3-(octyloxy)-4-nitrobenzoate in aqueous solution

3-(Octyloxy)-4-nitrobenzoate, a PLA₂ inhibitor, is a better surfactant than other octyl derivatives and can be used as a model for 3-(octanoyloxy)-4-nitrobenzoic acid.

Experimental Atom-by-Atom Dissection of Amide-Amide and Amide-Hydrocarbon Interactions in H2O

Quantitative information about amide interactions in water is needed to understand their contributions to protein folding and amide effects on aqueous processes and to compare with computer simulations. Here we quantify interactions of urea, alkylated ureas, and other amides by osmometry and amide-aromatic hydrocarbon interactions by solubility. Analysis of these data yields strengths of interaction of ureas and naphthalene with amide sp2O, amide sp2N, aliphatic sp3C, and amide and aromatic sp2C unified atoms in water. Interactions of amide sp2O with urea and naphthalene are favorable, while amide sp2O-alkylurea interactions are unfavorable, becoming more unfavorable with increasing alkylation. Hence, amide sp2O-amide sp2N interactions (proposed n-σ* hydrogen bond) and amide sp2O-aromatic sp2C (proposed n-π*) interactions are favorable in water, while amide sp2O-sp3C interactions are unfavorable. Interactions of all ureas with sp3C and amide sp2N are favorable and increase in strength with increasing alkylation, indicating favorable sp3C-amide sp2N and sp3C-sp3C interactions. Naphthalene results show that aromatic sp2C-amide sp2N interactions in water are unfavorable while sp2C-sp3C interactions are favorable. These results allow interactions of amide and hydrocarbon moieties and effects of urea and alkylureas on aqueous processes to be predicted or interpreted in terms of structural information. We predict strengths of favorable urea-benzene and N-methylacetamide interactions from experimental information to compare with simulations and indicate how amounts of hydrocarbon and amide surfaces buried in protein folding and other biopolymer processes and transition states can be determined from analysis of urea and diethylurea effects on equilibrium and rate constants.

Molecular determinant of the effects of hydrostatic pressure on protein folding stability

Hydrostatic pressure is an important environmental variable that plays an essential role in biological adaptation for many extremophilic organisms (for example, piezophiles). Increase in hydrostatic pressure, much like increase in temperature, perturbs the thermodynamic equilibrium between native and unfolded states of proteins. Experimentally, it has been observed that increase in hydrostatic pressure can both increase and decrease protein stability. These observations suggest that volume changes upon protein unfolding can be both positive and negative. The molecular details of this difference in sign of volume changes have been puzzling the field for the past 50 years. Here we present a comprehensive thermodynamic model that provides in-depth analysis of the contribution of various molecular determinants to the volume changes upon protein unfolding. Comparison with experimental data shows that the model allows quantitative predictions of volume changes upon protein unfolding, thus paving the way to proteome-wide computational comparison of proteins from different extremophilic organisms.

Proteins can be both stabilized and destabilized by pressure. Here the authors analyse the factors contributing to both negative and positive protein volume change upon denaturation, and shed light on the molecular determinants allowing proteins to be stable at high pressures.

Designing Fluorinated Proteins

As methods to incorporate noncanonical amino acid residues into proteins have become more powerful, interest in their use to modify the physical and biological properties of proteins and enzymes has increased. This chapter discusses the use of highly fluorinated analogs of hydrophobic amino acids, for example, hexafluoroleucine, in protein design. In particular, fluorinated residues have proven to be generally effective in increasing the thermodynamic stability of proteins. The chapter provides an overview of the different fluorinated amino acids that have been used in protein design and the various methods available for producing fluorinated proteins. It discusses model proteins systems into which highly fluorinated amino acids have been introduced and the reasons why fluorinated residues are generally stabilizing, with particular reference to thermodynamic and structural studies from our laboratory. Lastly, details of the methodology we have developed to measure the thermodynamic stability of oligomeric fluorinated proteins are presented, as this may be generally applicable to many proteins.

Experimental Binding Energies in Supramolecular Complexes

On the basis of many literature measurements, a critical overview is given on essential noncovalent interactions in synthetic supramolecular complexes, accompanied by analyses with selected proteins. The methods, which can be applied to derive binding increments for single noncovalent interactions, start with the evaluation of consistency and additivity with a sufficiently large number of different host-guest complexes by applying linear free energy relations. Other strategies involve the use of double mutant cycles, of molecular balances, of dynamic combinatorial libraries, and of crystal structures. Promises and limitations of these strategies are discussed. Most of the analyses stem from solution studies, but a few also from gas phase. The empirically derived interactions are then presented on the basis of selected complexes with respect to ion pairing, hydrogen bonding, electrostatic contributions, halogen bonding, π-π-stacking, dispersive forces, cation-π and anion-π interactions, and contributions from the hydrophobic effect. Cooperativity in host-guest complexes as well as in self-assembly, and entropy factors are briefly highlighted. Tables with typical values for single noncovalent free energies and polarity parameters are in the Supporting Information.

Thermodynamic and Structural Evidence for Reduced Hydrogen Bonding among Water Molecules near Small Hydrophobic Solutes

The structure of water molecules near a hydrophobic solute remains elusive despite a long history of scrutiny. Here, we re-examine the subtle issue by a combination of thermodynamic analysis for Henry's constants of several nonpolar gases over a broad range of temperatures and molecular dynamic simulations for the water structure in the hydration shell using several popular semiempirical models of liquid water. Both the structural and thermodynamic data indicate that hydrophobic hydration reduces the degree of the hydrogen bonding among water molecules, and the effect becomes more prominent at high temperatures. Hydrogen-bond formation is slightly hindered near a hydrophobic solute due to the restriction of the degree of freedom for water molecules in the solvation shell, and the confinement effect becomes more significant as temperature increases. Reduction in the extent of hydrogen bonding is fully consistent with a positive contribution of a small hydrophobic solute to the solution heat capacity. As predicted by the scaled-particle theory, both Henry's constants and simulation results suggest that the hydration entropy is determined primarily by cavity formation in liquid water, with its magnitude rising with the solute size but declining with temperature.

Peptide backbone effect on hydration free energies of amino acid side chains

We have studied the hydrophobicity of amino acid side chains by computing conditional solvation free energies that account for effects of the peptide backbone on the side chains' solvent environment. The free energies reported herein correspond to a gas-liquid transfer process, which mimics solvation of the side chain under the condition that the backbone has been solvated already, and have been obtained on the basis of free energy calculations with empirical force field models. We find that the peptide backbone strongly impacts the solvation of nonpolar side chains, while its effect on the polar side chains is less pronounced. The results indicate that, in the presence of the short peptide backbone, nonpolar amino acid side chains are less hydrophobic than what is expected based on small molecule (analogue) solvation data.

Dynamic hydration shell restores Kauzmann's 1959 explanation of how the hydrophobic factor drives protein folding

Kauzmann's explanation of how the hydrophobic factor drives protein folding is reexamined. His explanation said that hydrocarbon hydration shells are formed, possibly of clathrate water, and they explain why hydrocarbons have uniquely low solubilities in water. His explanation was not universally accepted because of skepticism about the clathrate hydration shell. A revised version is given here in which a dynamic hydration shell is formed by van der Waals (vdw) attraction, as proposed in 1985 by Jorgensen et al. [Jorgensen WL, Gao J, Ravimohan C (1985) J Phys Chem 89:3470-3473]. The vdw hydration shell is implicit in theories of hydrophobicity that contain the vdw interaction between hydrocarbon C and water O atoms. To test the vdw shell model against the known hydration energetics of alkanes, the energetics should be based on the Ben-Naim standard state (solute transfer between fixed positions in the gas and liquid phases). Then the energetics are proportional to n, the number of water molecules correlated with an alkane by vdw attraction, given by the simulations of Jorgensen et al. The energetics show that the decrease in entropy upon hydration is the root cause of hydrophobicity; it probably results from extensive ordering of water molecules in the vdw shell. The puzzle of how hydrophobic free energy can be proportional to nonpolar surface area when the free energy is unfavorable and the only known interaction (the vdw attraction) is favorable, is resolved by finding that the unfavorable free energy is produced by the vdw shell.

Kinetic evidence for a two-stage mechanism of protein denaturation by guanidinium chloride

Dry molten globular (DMG) intermediates, an expanded form of the native protein with a dry core, have been observed during denaturant-induced unfolding of many proteins. These observations are counterintuitive because traditional models of chemical denaturation rely on changes in solvent-accessible surface area, and there is no notable change in solvent-accessible surface area during the formation of the DMG. Here we show, using multisite fluorescence resonance energy transfer, far-UV CD, and kinetic thiol-labeling experiments, that the guanidinium chloride (GdmCl)-induced unfolding of RNase H also begins with the formation of the DMG. Population of the DMG occurs within the 5-ms dead time of our measurements. We observe that the size and/or population of the DMG is linearly dependent on [GdmCl], although not as strongly as the second and major step of unfolding, which is accompanied by core solvation and global unfolding. This rapid GdmCl-dependent population of the DMG indicates that GdmCl can interact with the protein before disrupting the hydrophobic core. These results imply that the effect of chemical denaturants cannot be interpreted solely as a disruption of the hydrophobic effect and strongly support recent computational studies, which hypothesize that chemical denaturants first interact directly with the protein surface before completely unfolding the protein in the second step (direct interaction mechanism).

Design, synthesis, and study of fluorinated proteins

Highly fluorinated analogs of hydrophobic amino acids have proven to be generally effective in increasing the thermodynamic stability of proteins. These non-proteogenic amino acids can be incorporated into both α-helix and β-sheet structural motifs and generally enhance protein stability towards unfolding by heat and chemical denaturants, and retard their degradation by proteases. Recent detailed structural and thermodynamic studies have demonstrated that the increase in buried hydrophobic surface area that accompanies fluorination is primarily responsible for the stabilizing properties of fluorinated side chains. Fluorination appears to be a particularly useful strategy for increasing protein stability because fluorinated amino acids closely retain the shape of the side chain, and are thus minimally perturbing to protein structure and function. The first part of this chapter discusses some examples of highly fluorinated model proteins designed by our laboratory and protocols for their synthesis. In the second part, methods for determining their thermodynamic stability, along with conditions that have proven to be useful for crystallizing these proteins, are presented.

Molecular-scale hydrophobic interactions between hard-sphere reference solutes are attractive and endothermic

The osmotic second virial coefficients, B2, for atomic-sized hard spheres in water are attractive (B2 < 0) and become more attractive with increasing temperature (ΔB2/ΔT < 0) in the temperature range 300 K ≤ T ≤ 360 K. Thus, these hydrophobic interactions are attractive and endothermic at moderate temperatures. Hydrophobic interactions between atomic-sized hard spheres in water are more attractive than predicted by the available statistical mechanical theory. These results constitute an initial step toward detailed molecular theory of additional intermolecular interaction features, specifically, attractive interactions associated with hydrophobic solutes.

Computational and theoretical methods for protein folding

A computational approach is essential whenever the complexity of the process under study is such that direct theoretical or experimental approaches are not viable. This is the case for protein folding, for which a significant amount of data are being collected. This paper reports on the essential role of in silico methods and the unprecedented interplay of computational and theoretical approaches, which is a defining point of the interdisciplinary investigations of the protein folding process. Besides giving an overview of the available computational methods and tools, we argue that computation plays not merely an ancillary role but has a more constructive function in that computational work may precede theory and experiments. More precisely, computation can provide the primary conceptual clues to inspire subsequent theoretical and experimental work even in a case where no preexisting evidence or theoretical frameworks are available. This is cogently manifested in the application of machine learning methods to come to grips with the folding dynamics. These close relationships suggested complementing the review of computational methods within the appropriate theoretical context to provide a self-contained outlook of the basic concepts that have converged into a unified description of folding and have grown in a synergic relationship with their computational counterpart. Finally, the advantages and limitations of current computational methodologies are discussed to show how the smart analysis of large amounts of data and the development of more effective algorithms can improve our understanding of protein folding.