Heat capacity effects in protein folding and ligand binding: a re-evaluation of the role of water in biomolecular thermodynamics

Large "anomalous" heat capacity (DeltaC(p)) effects are a common feature of the thermodynamics of biomolecular interactions in aqueous solution and, as a result of the improved facility for direct calorimetric measurements, there is a growing body of experimental data for such effects in protein folding, protein-protein and protein-ligand interactions. Conventionally such heat capacity effects have been ascribed to hydrophobic interactions, and there are some remarkably convincing demonstrations of the usefulness of this concept. Nonetheless, there is also increasing evidence that hydrophobic interactions are not the only possible source of such effects. Here we re-evaluate the possible contributions of other interactions to the heat capacity changes to be expected for cooperative biomolecular folding and binding processes, with particular reference to the role of hydrogen bonding and solvent water interactions. Simple models based on the hydrogen-bonding propensity of water as a function of temperature give quantitative estimates of DeltaC(p) that compare well with experimental observations for both protein folding and ligand binding. The thermodynamic contribution of bound waters in protein complexes is also estimated. The prediction from simple lattice models is that trapping of water in a complex should give more exothermic binding (DeltaDeltaH-6 to -12 kJ mol(-1)) with lower entropy (DeltaDeltaS(0) approximately -11 J mol(-1) K(-1)) and more negative DeltaC(p) (by about -75 J mol(-1) K(-1)) per water molecule. More generally, it is clear that significant DeltaC(p) effects are to be expected for any macromolecular process involving a multiplicity of cooperative weak interactions of whatever kind.     

Evaluation of a fast implicit solvent model for molecular dynamics simulations.

A solvation term based on the solvent accessible surface area (SASA) is combined with the CHARMM polar hydrogen force field for the efficient simulation of peptides and small proteins in aqueous solution. Only two atomic solvation parameters are used: one is negative for favoring the direct solvation of polar groups and the other positive for taking into account the hydrophobic effect on apolar groups. To approximate the water screening effects on the intrasolute electrostatic interactions, a distance-dependent dielectric function is used and ionic side chains are neutralized. The use of an analytical approximation of the SASA renders the model extremely efficient (i.e., only about 50% slower than in vacuo simulations). The limitations and range of applicability of the SASA model are assessed by simulations of proteins and structured peptides. For the latter, the present study and results reported elsewhere show that with the SASA model it is possible to sample a significant amount of folding/unfolding transitions, which permit the study of the thermodynamics and kinetics of folding at an atomic level of detail.     

Maximal stabilities of reversible two-state proteins

The hydrophobic effect is the major force driving protein folding. Around room temperature, small organic solutes and hydrophobic amino acids have low solubilities in water and the hydrophobic effect is the strongest. These facts suggest that globular proteins should be maximally stable around room temperature. While this fundamental paradigm has been expected, it has not actually been shown to hold. Toward this goal, we have collected and analyzed experimental thermodynamic data for 31 proteins that show reversible two-state folding <--> unfolding transitions at or near neutral pH. Twenty-six of these are unique, and 20 of the 26 are maximally stable around room temperature irrespective of their structural properties, the melting temperature, or the living temperatures of their source organisms. Their average temperature of maximal stability is 293 +/- 8 K (20 +/- 8 degrees C). These proteins differ in size, fold, and number of domains, hydrophobic folding units, and oligomeric states. They derive from the cold-loving psychrophiles, from mesophiles, and from thermophiles. Analysis of the single-domain proteins present in this set shows that the variations in their thermodynamic parameters are correlated in a way which may explain the adaptation of the proteins to the living temperatures of the organisms from which they derive. The average energetic contribution of the individual amino acids toward protein stability decreases with an increase in protein size, suggesting that there may be an upper limit for protein maximal thermodynamic stability. For the remaining proteins, deviation of the maximal stability temperatures from room temperature may be due to greater uncertainties in their heat capacity change (DeltaC(p)) values, a weaker hydrophobic effect, and/or a stronger electrostatic contribution.     

Aromatic-aromatic interactions in the zinc finger motif. Analysis of the two-dimensional nuclear magnetic resonance structure of a mutant domain.

The folding and stability of globular proteins are determined by a variety of chemical mechanisms, including hydrogen bonds, salt bridges and the hydrophobic effect. Of particular interest are weakly polar interactions involving aromatic rings, which are proposed to regulate the geometry of closely packed protein interiors. Such interactions reflect the electrostatic contribution of pi-electrons and, unlike van der Waals' interactions and the hydrophobic effect, may, in principle, introduce a directional force in a protein's hydrophobic core. Although the weakly polar hypothesis is supported by a statistical analysis of protein structures, the general importance of such contributions to protein folding and stability is unclear. Here, we show the presence of alternative aromatic-aromatic interactions in the two-dimensional nuclear magnetic resonance structure of a mutant Zn finger. Changes in aromatic packing lead in turn to local and non-local differences between the structures of a wild-type and mutant domain. The results provide insight into the evolution of Zn finger sequences and have implications for understanding how geometric relationships may be chemically encoded in a simple sequence template.     

Studies on protein folding, unfolding and fluctuations by computer simulation. IV. Hydrophobic interactions.

The theoretical model of proteins on the two-dimensional square lattice, introduced previously, is extended to include the hydrophobic interactions. Two proteins, whose native conformations have different folded patterns, are studied. Units in the protein chains are classified into polar units and nonpolar units. If there is a vacant lattice point next to a nonpolar unit, it is interpreted as being occupied by solvent water and the entropy of the system is assumed to decrease by a certain amount. Besides these hydrophobic free energies, the specific long-range interactions studied in previous papers are assumed to be operative in a protein chain. Equilibrium properties of the folding and unfolding transitions of the two proteins are found to be similar, even though one of them was predicted, based on the one globule model of the transitions, to unfold through a significant intermediate state (or at least to show a tendency toward such a behavior), when the hydrophobic interactions are strongly weighted. The failure of this prediction led to the development of a more refined model of transitions; a non-interacting local structure model. The hydrophobic interactions assumed here have a character of non-specific long-range interactions. Because of this character the hydrophobic interactions have the effect of decelerating the folding kinetics. The deceleration effect is less pronounced in one of the two proteins, whose native conformation is stabilized by many pairs of medium-range interactions. It is therefore inferred that the medium-range interactions have the power to cope with the decelerating effect of the non-specific hydrophobic interactions.     

Forces stabilizing proteins

The goal of this article is to summarize what has been learned about the major forces stabilizing proteins since the late 1980s when site-directed mutagenesis became possible. The following conclusions are derived from experimental studies of hydrophobic and hydrogen bonding variants. (1) Based on studies of 138 hydrophobic interaction variants in 11 proteins, burying a –CH₂− group on folding contributes 1.1 ± 0.5 kcal/mol to protein stability. (2) The burial of non-polar side chains contributes to protein stability in two ways: first, a term that depends on the removal of the side chains from water and, more importantly, the enhanced London dispersion forces that result from the tight packing in the protein interior. (3) Based on studies of 151 hydrogen bonding variants in 15 proteins, forming a hydrogen bond on folding contributes 1.1 ± 0.8 kcal/mol to protein stability. (4) The contribution of hydrogen bonds to protein stability is strongly context dependent. (5) Hydrogen bonds by side chains and peptide groups make similar contributions to protein stability. (6) Polar group burial can make a favorable contribution to protein stability even if the polar group is not hydrogen bonded. (7) Hydrophobic interactions and hydrogen bonds both make large contributions to protein stability.     

Thermodynamic differences among homologous thermophilic and mesophilic proteins.

Here, we analyze the thermodynamic parameters and their correlations in families containing homologous thermophilic and mesophilic proteins which show reversible two-state folding <--> unfolding transitions between the native and the denatured states. For the proteins in these families, the melting temperatures correlate with the maximal protein stability change (between the native and the denatured states) as well as with the enthalpic and entropic changes at the melting temperature. In contrast, the heat capacity change is uncorrelated with the melting temperature. These and additional results illustrate that higher melting temperatures are largely obtained via an upshift and broadening of the protein stability curves. Both thermophilic and mesophilic proteins are maximally stable around room temperature. However, the maximal stabilities of thermophilic proteins are considerably greater than those of their mesophilic homologues. At the living temperatures of their respective source organisms, homologous thermophilic and mesophilic proteins have similar stabilities. The protein stability at the living temperature of the source organism does not correlate with the living temperature of the protein. We tie thermodynamic observations to microscopics via the hydrophobic effect and a two-state model of the water structure. We conclude that, to achieve higher stability and greater resistance to high and low temperatures, specific interactions, particularly electrostatic, should be engineered into the protein. The effect of these specific interactions is largely reflected in an increased enthalpy change at the melting temperature.     

Hydrophobicity scale for proteins based on inverse temperature transitions.

In general, proteins fold with hydrophobic residues buried, away from water. Reversible protein folding due to hydrophobic interactions results from inverse temperature transitions where folding occurs on raising the temperature. Because homoiothermic animals constitute an infinite heat reservoir, it is the transition temperature, Tt, not the endothermic heat of the transition, that determines the hydrophobically folded state of polypeptides at body temperature. Reported here is a new hydrophobicity scale based on the values of Tt for each amino acid residue as a guest in a natural repeating peptide sequence, the high polymers of which exhibit reversible inverse temperature transitions. Significantly, a number of ways have been demonstrated for changing Tt such that reversibly lowering Tt from above to below physiological temperature becomes a means of isothermally and reversibly driving hydrophobic folding. Accordingly, controlling Tt becomes a mechanism whereby proteins can be induced to carry out isothermal free energy transduction.     

Inversion of the balance between hydrophobic and hydrogen bonding interactions in protein folding and aggregation

Identifying the forces that drive proteins to misfold and aggregate, rather than to fold into their functional states, is fundamental to our understanding of living systems and to our ability to combat protein deposition disorders such as Alzheimer's disease and the spongiform encephalopathies. We report here the finding that the balance between hydrophobic and hydrogen bonding interactions is different for proteins in the processes of folding to their native states and misfolding to the alternative amyloid structures. We find that the minima of the protein free energy landscape for folding and misfolding tend to be respectively dominated by hydrophobic and by hydrogen bonding interactions. These results characterise the nature of the interactions that determine the competition between folding and misfolding of proteins by revealing that the stability of native proteins is primarily determined by hydrophobic interactions between side-chains, while the stability of amyloid fibrils depends more on backbone intermolecular hydrogen bonding interactions.     

Ab initio folding of proteins with all-atom discrete molecular dynamics

Discrete molecular dynamics (DMD) is a rapid sampling method used in protein folding and aggregation studies. Until now, DMD was used to perform simulations of simplified protein models in conjunction with structure-based force fields. Here, we develop an all-atom protein model and a transferable force field featuring packing, solvation, and environment-dependent hydrogen bond interactions. We performed folding simulations of six small proteins (20-60 residues) with distinct native structures by the replica exchange method. In all cases, native or near-native states were reached in simulations. For three small proteins, multiple folding transitions are observed, and the computationally characterized thermodynamics are in qualitative agreement with experiments. The predictive power of all-atom DMD highlights the importance of environment-dependent hydrogen bond interactions in modeling protein folding. The developed approach can be used for accurate and rapid sampling of conformational spaces of proteins and protein-protein complexes and applied to protein engineering and design of protein-protein interactions.     

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.     

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.     

A contribution to the theory of biological staining based on the principles for structural organization of biological macromolecules

Biological staining is to a large degree explainable based on the principles governing folding and aggregation of macromolecules in aqueous solution. Most macromolecules are polyions, which, except for heteropolysaccharides, have a large proportion of nonpolar or only slightly polar residues. Because they are amphiphilic, they react in water by a complex set of hydrophobic interactions involving charged residues, nonpolar residues and water molecules. The hydrophobic interactions lead to complex folding systems or micelle-like structures. Dyes are amphiphilic molecules with a tendency to form micelles, but with limitations due to geometric constraints and charge repulsion. Macromolecules and dyes react with each other in aqueous solution following the same principles as for the structural organization of macromolecules, as in protein folding for example. Dye binding requires near contact between nonpolar groups in both the dye and macromolecule, and this is accomplished by choosing a pH at which the dye and macromolecule have opposite net charges. Charge attraction is insufficient for binding in most cases, but it is directive because it determines which macromolecules a given dye ion is able to contact. These considerations apply to the staining of globular (cytoplasmic) proteins and to nucleic acid staining. The staining mechanism is by hydrophobic interactions. Above approximately pH 3.5, DNA may also bind dyes by hydrophobic intercalation between the bases of the double helix; at lower pH the double helix opens and dye binding is as for RNA and globular proteins. Heteroglycans (mucins) have virtually no nonpolar groups, so nonpolar interactions are restricted to the dye molecules. Metachromatic staining of heteroglycans is due to hydrophobic bonding or micelle formation between the monovalent planar dye molecules aided by charge neutralization by the negatively charged heteroglycans. Alternatively, as the charge attraction increases with the number of closely placed charges, acidic heteroglycans may be stained by a polycation such as alcian blue or colloidal iron. For elastic fiber and collagen staining, actual hydrophobic interactions are less important and hydrogen bonding and simple nonpolar interactions play a major role. These macromolecules may therefore be stained using a nonaqueous alcoholic solution.     

A contribution to the theory of biological staining based on the principles for structural organization of biological macromolecules

Biological staining is to a large degree explainable based on the principles governing folding and aggregation of macromolecules in aqueous solution. Most macromolecules are polyions, which, except for heteropolysaccharides, have a large proportion of nonpolar or only slightly polar residues. Because they are amphiphilic, they react in water by a complex set of hydrophobic interactions involving charged residues, nonpolar residues and water molecules. The hydrophobic interactions lead to complex folding systems or micelle-like structures. Dyes are amphiphilic molecules with a tendency to form micelles, but with limitations due to geometric constraints and charge repulsion. Macromolecules and dyes react with each other in aqueous solution following the same principles as for the structural organization of macromolecules, as in protein folding for example. Dye binding requires near contact between nonpolar groups in both the dye and macromolecule, and this is accomplished by choosing a pH at which the dye and macromolecule have opposite net charges. Charge attraction is insufficient for binding in most cases, but it is directive because it determines which macromolecules a given dye ion is able to contact. These considerations apply to the staining of globular (cytoplasmic) proteins and to nucleic acid staining. The staining mechanism is by hydrophobic interactions. Above approximately pH 3.5, DNA may also bind dyes by hydrophobic intercalation between the bases of the double helix; at lower pH the double helix opens and dye binding is as for RNA and globular proteins. Heteroglycans (mucins) have virtually no nonpolar groups, so nonpolar interactions are restricted to the dye molecules. Metachromatic staining of heteroglycans is due to hydrophobic bonding or micelle formation between the monovalent planar dye molecules aided by charge neutralization by the negatively charged heteroglycans. Alternatively, as the charge attraction increases with the number of closely placed charges, acidic heteroglycans may be stained by a polycation such as alcian blue or colloidal iron. For elastic fiber and collagen staining, actual hydrophobic interactions are less important and hydrogen bonding and simple nonpolar interactions play a major role. These macromolecules may therefore be stained using a nonaqueous alcoholic solution.     

Accounting for protein-solvent contacts facilitates design of nonaggregating lattice proteins

The folding specificity of proteins can be simulated using simplified structural models and knowledge-based pair-potentials. However, when the same models are used to simulate systems that contain many proteins, large aggregates tend to form. In other words, these models cannot account for the fact that folded, globular proteins are soluble. Here we show that knowledge-based pair-potentials, which include explicitly calculated energy terms between the solvent and each amino acid, enable the simulation of proteins that are much less aggregation-prone in the folded state. Our analysis clarifies why including a solvent term improves the foldability. The aggregation for potentials without water is due to the unrealistically attractive interactions between polar residues, causing artificial clustering. When a water-based potential is used instead, polar residues prefer to interact with water; this leads to designed protein surfaces rich in polar residues and well-defined hydrophobic cores, as observed in real protein structures. We developed a simple knowledge-based method to calculate interactions between the solvent and amino acids. The method provides a starting point for modeling the folding and aggregation of soluble proteins. Analysis of our simple model suggests that inclusion of these solvent terms may also improve off-lattice potentials for protein simulation, design, and structure prediction.     

Secondary structure of prothymosin alpha evidenced for conformational transitions induced by changes in temperature and concentration of n-dodecyltrimethylammonium bromide

Conformational changes of prothymosin alpha (ProTalpha) induced by changes in temperature and concentration of the denaturant n-dodecyltrimethylammonium bromide (C12TAB) were studied by difference spectroscopy. The conformational transition of ProTalpha by C12TAB was followed as a function of denaturant concentration by absorbance measurements at 230 nm and the data were analyzed to obtain the Gibbs energy of the transition in water (deltaG0(w)) and in a hydrophobic environment (deltaG0(hc)) for saturated protein-surfactant complexes. The value of deltaG0(w) was 6.38 kJ mol(-1) and that for deltaG0(hc), which is not affected by temperature, was -18.62 kJ mol(-1). Changes of absorbance at 230 nm of ProTalpha with temperature can be assumed to resemble a transition in the secondary structure. The parameters characterizing the thermodynamics of unfolding, melting temperature (Tm), enthalpy (deltaHm), entropy (deltaSm) and heat capacity (deltaCp) were determined. The values obtained for Tm, deltaHm, and deltaSm are smaller that those found for other globular proteins; deltaCp was found to be much smaller. These results suggest that ProTalpha exhibits some type of secondary structure under these conditions (10 mM glycine buffer, pH 2.4).     

The nucleation of monomeric parallel beta-sheet-like structures and their self-assembly in aqueous solution

The aromatic diacid residue 4,6-dibenzofuranbispropionic acid (1) was designed to nucleate a parallel beta-sheet-like structure in small peptides in aqueous solution via a hydrogen-bonded hydrophobic cluster. Even though a 14-membered ring hydrogen bond necessary for parallel beta-sheet formation is favored in simple amides composed of 1, this hydrogen bonding interaction does not appear to be sufficient to nucleate parallel beta-sheet formation in the absence of hydrophobic clustering between the dibenzofuran portion of 1 and the hydrophobic side chains of the flanking alpha-amino acids. The subsequence --hydrophobic residue-1-hydrophobic residue-- is required for folding in the context of a nucleated two-stranded parallel beta-sheet structure. In all cases where the peptidomimetics can fold into two diastereomeric parallel beta-sheet structures having different hydrogen bonding networks, these conformations appear to exchange rapidly. The majority of the parallel beta-sheet structures evaluated herein undergo linked intramolecular folding and self-assembly, affording a fibrillar beta-sheet quaternary structure. To unlink folding and assembly, asymmetric parallel beta-sheet structures incorporating N-methylated alpha-amino acid residues have been synthesized using a new solid phase approach. Residue 1 facilitates the folding of several peptides described within affording a monomeric parallel beta-sheet-like structure in aqueous solution, as ascertained by a variety of spectroscopic and biophysical methods, increasing our understanding of parallel beta-sheet structure.     

Use of liquid hydrocarbon and amide transfer data to estimate contributions to thermodynamic functions of protein folding from the removal of nonpolar and polar surface from water.

This extension of the liquid hydrocarbon model seeks to quantify the thermodynamic contributions to protein stability from the removal of nonpolar and polar surface from water. Thermodynamic data for the transfer of hydrocarbons and organic amides from water to the pure liquid phase are analyzed to obtain contributions to the thermodynamics of folding from the reduction in water-accessible surface area. Although the removal of nonpolar surface makes the dominant contribution to the standard heat capacity change of folding (delta C0fold), here we show that inclusion of the contribution from removal of polar surface allows a quantitative prediction of delta C0fold within the uncertainty of the calorimetrically determined value. Moreover, analysis of the contribution of polar surface area to the enthalpy of transfer of liquid amides provides a means of estimating the contributions from changes in nonpolar and polar surface area as well as other factors to the enthalpy of folding (delta H0fold). In addition to estimates of delta H0fold, this extension of the liquid hydrocarbon model provides a thermodynamic explanation for the observation [Privalov, P. L., & Khechinashvili, N. N. (1974) J. Mol. Biol. 86, 665-684] that the specific enthalpy of folding (cal g-1) of a number of globular proteins converges to a common value at approximately 383 K. Because amounts of nonpolar and polar surface area buried by these proteins upon folding are found to be linear functions of molar mass, estimates of both delta C0fold and delta H0fold may be obtained given only the molar mass of the protein of interest.(ABSTRACT TRUNCATED AT 250 WORDS)     

Solvent effects on the conformational transition of a model polyalanine peptide

We have investigated the folding of polyalanine by combining discontinuous molecular dynamics simulation with our newly developed off-lattice intermediate-resolution protein model. The thermodynamics of a system containing a single Ac-KA(14)K-NH(2) molecule has been explored by using the replica exchange simulation method to map out the conformational transitions as a function of temperature. We have also explored the influence of solvent type on the folding process by varying the relative strength of the side-chain's hydrophobic interactions and backbone hydrogen bonding interactions. The peptide in our simulations tends to mimic real polyalanine in that it can exist in three distinct structural states: alpha-helix, beta-structures (including beta-hairpin and beta-sheet-like structures), and random coil, depending upon the solvent conditions. At low values of the hydrophobic interaction strength between nonpolar side-chains, the polyalanine peptide undergoes a relatively sharp transition between an alpha-helical conformation at low temperatures and a random-coil conformation at high temperatures. As the hydrophobic interaction strength increases, this transition shifts to higher temperatures. Increasing the hydrophobic interaction strength even further induces a second transition to a beta-hairpin, resulting in an alpha-helical conformation at low temperatures, a beta-hairpin at intermediate temperatures, and a random coil at high temperatures. At very high values of the hydrophobic interaction strength, polyalanines become beta-hairpins and beta-sheet-like structures at low temperatures and random coils at high temperatures. This study of the folding of a single polyalanine-based peptide sets the stage for a study of polyalanine aggregation in a forthcoming paper.     

Energy of hydrogen bonds probed by the adhesion of functionalized lipid layers

It is now well admitted that hydrophobic interactions and hydrogen bonds are the main forces driving protein folding and stability. However, because of the complex structure of a protein, it is still difficult to separate the different energetic contributions and have a reliable estimate of the hydrogen bond part. This energy can be quantified on simpler systems such as surfaces bearing hydrogen-bonding groups. Using the surface force apparatus, we have directly measured the interaction energy between monolayers of lipids whose headgroups can establish hydrogen bonds in water: nitrilotriacetate, adenosine, thymidine, and methylated thymidine lipids. From the adhesion energy between the surfaces, we have deduced the energy of a single hydrogen bond in water. We found in each case an energy of 0.5 kcal/mol. This result is in good agreement with recent experimental and theoretical studies made on protein systems showing that intramolecular hydrogen bonds make a positive contribution to protein stabilization.