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.     

Solid model compounds and the thermodynamics of protein unfolding.

Analysis of thermodynamic data on the dissolution of solid cyclic dipeptides into water in terms of group additivity provides a rationale for the enthalpy and entropy convergence temperatures observed for small globular protein denaturation and the dissolution of model compounds into water. Convergence temperatures are temperatures at which the extrapolated enthalpy or entropy changes for a series of related compounds take on a common value. At these temperatures (TH* and TS*) the apolar contributions to the corresponding thermodynamic values (delta H degrees and delta S degrees) are shown to be zero. Other contributions such as hydrogen bonding and configurational effects can then be evaluated and their quantitative effects on the stability of globular proteins assessed. It is shown that the denaturational heat capacity is composed of a large positive contribution from the exposure of apolar groups and a significant negative contribution from the exposure of polar groups in agreement with previous results. The large apolar contribution suggests that a liquid hydrocarbon model of the hydrophobic effect does not accurately represent the apolar contribution to delta H degrees of denaturation. Rather, significant enthalpic stabilizing contributions are found to arise from peptide groups (hydrogen bonding). Combining the average structural features of globular proteins (i.e. number of residues, fraction of buried apolar groups and fraction of hydrogen bonds) with their specific group contributions permits a first-order prediction of the thermodynamic properties of proteins. The predicted values compare well with literature values for cytochrome c, myoglobin, ribonuclease A and lysozyme. The major thermodynamic features are described by the number of peptide and apolar groups in a given protein.     

Thermodynamic model of secondary structure for α-helical peptides and proteins

A thermodynamic model describing formation of α-helices by peptides and proteins in the absence of specific tertiary interactions has been developed. The model combines free energy terms defining α-helix stability in aqueous solution and terms describing immersion of every helix or fragment of coil into a micelle or a nonpolar droplet created by the rest of protein to calculate averaged or lowest energy partitioning of the peptide chain into helical and coil fragments. The α-helix energy in water was calculated with parameters derived from peptide substitution and protein engineering data and using estimates of nonpolar contact areas between side chains. The energy of nonspecific hydrophobic interactions was estimated considering each α-helix or fragment of coil as freely floating in the spherical micelle or droplet, and using water/cyclohexane (for micelles) or adjustable (for proteins) side-chain transfer energies. The model was verified for 96 and 36 peptides studied by ¹H-nmr spectroscopy in aqueous solution and in the presence of micelles, respectively ([set I] and [set 2]) and for 30 mostly α-helical globular proteins ([set 3]). For peptides, the experimental helix locations were identified from the published medium-range nuclear Overhauser effects detected by ¹H-nmr spectroscopy. For sets 1, 2, and 3, respectively, 93, 100, and 97% of helices were identified with average errors in calculation of helix boundaries of 1.3, 2.0, and 4.1 residues per helix and an average percentage of correctly calculated helix—coil states of 93, 89, and 81%, respectively. Analysis of adjustable parameters of the model (the entropy and enthalpy of the helix—coil transition, the transfer energy of the helix backbone, and parameters of the bound coil), determined by minimization of the average helix boundary deviation for each set of peptides or proteins, demonstrates that, unlike micelles, the interior of the effective protein droplet has solubility characteristics different from that for cyclohexane, does not bind fragments of coil, and lacks interfacial area. © 1997 John Wiley & Sons, Inc. Biopoly 42: 239–269, 1997     

Stability of globular proteins in H2O and D2O

In several experimental techniques D2O rather then H2O is often used as a solvent for proteins. Concerning the influence of the solvent on the stability of the proteins, contradicting results have been reported in literature. In this paper the influence of H2O-D2O solvent substitution on the stability of globular protein structure is determined in a systematic way. The differential scanning calorimetry technique is applied to allow for a thermodynamic analysis of two types of globular proteins: hen's egg lysozyme (LSZ) with relatively strong internal cohesion ("hard" globular protein) and bovine serum albumin (BSA), which is known for its conformational adaptability ("soft" globular protein). Both proteins tend to be more stable in D2O compared to H2O. We explain the increase of protein stability in D2O by the observation that D2O is a poorer solvent for nonpolar amino acids than H2O, implying that the hydrophobic effect is larger in D2O. In case of BSA the transitions between different isomeric forms, at low pH values the Nm and F forms, and at higher pH values Nm and B, were observed by the presence of a supplementary peak in the DSC thermogram. It appears that the pH-range for which the Nm form is the preferred one is wider in D2O than in H2O.     

A mini-protein designed by removing a module from barnase: molecular modeling and NMR measurements of the conformation.

A globular domain can be decomposed into compact modules consisting of contiguous 10-30 amino acid residues. The correlation between modules and exons observed in different proteins suggests that each module was encoded by an ancestral exon and that modules were combined into globular domains by exon fusion. Barnase is a single domain RNase consisting of 110 amino acid residues and was decomposed into six modules. We designed a mini-protein by removing the second module, M2, from barnase in order to gain an insight into the structural and functional roles of the module. In the molecular modeling of the mini-protein, we evaluated thermodynamic stability and aqueous solubility together with mechanical stability of the model. We chemically synthesized a mini-barnase with (15)N-labeling at 10 residues, whose corresponding residues in barnase are all found in the region around the hydrophobic core. Circular dichroism and NMR measurements revealed that mini-barnase takes a non-random specific conformation that has a similar hydrophobic core structure to that of barnase. This result, that a module could be deleted without altering the structure of core region of barnase, supports the view that modules act as the building blocks of protein design.     

Novel approach for alpha-helical topology prediction in globular proteins: generation of interhelical restraints

The protein folding problem represents one of the most challenging problems in computational biology. Distance constraints and topology predictions can be highly useful for the folding problem in reducing the conformational space that must be searched by deterministic algorithms to find a protein structure of minimum conformational energy. We present a novel optimization framework for predicting topological contacts and generating interhelical distance restraints between hydrophobic residues in alpha-helical globular proteins. It should be emphasized that since the model does not make assumptions about the form of the helices, it is applicable to all alpha-helical proteins, including helices with kinks and irregular helices. This model aims at enhancing the ASTRO-FOLD protein folding approach of Klepeis and Floudas (Journal of Computational Chemistry 2003;24:191-208), which finds the structure of global minimum conformational energy via a constrained nonlinear optimization problem. The proposed topology prediction model was evaluated on 26 alpha-helical proteins ranging from 2 to 8 helices and 35 to 159 residues, and the best identified average interhelical distances corresponding to the predicted contacts fell below 11 A in all 26 of these systems. Given the positive results of applying the model to several protein systems, the importance of interhelical hydrophobic-to-hydrophobic contacts in determining the folding of alpha-helical globular proteins is highlighted.     

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.     

Coarse-grained strategy for modeling protein stability in concentrated solutions

We present a coarse-grained approach for modeling the thermodynamic stability of single-domain globular proteins in concentrated aqueous solutions. Our treatment derives effective protein-protein interactions from basic structural and energetic characteristics of the native and denatured states. These characteristics, along with the intrinsic (i.e., infinite dilution) thermodynamics of folding, are calculated from elementary sequence information using a heteropolymer collapse theory. We integrate this information into Reactive Canonical Monte Carlo simulations to investigate the connections between protein sequence hydrophobicity, protein-protein interactions, protein concentration, and the thermodynamic stability of the native state. The model predicts that sequence hydrophobicity can affect how protein concentration impacts native-state stability in solution. In particular, low hydrophobicity proteins are primarily stabilized by increases in protein concentration, whereas high hydrophobicity proteins exhibit richer nonmonotonic behavior. These trends appear qualitatively consistent with the available experimental data. Although factors such as pH, salt concentration, and protein charge are also important for protein stability, our analysis suggests that some of the nontrivial experimental trends may be driven by a competition between destabilizing hydrophobic protein-protein attractions and entropic crowding effects.     

The problem of the stability of globular proteins

Summary The article gives a survey on protein stability. Starting out from approaches for stability measurement which are based on the determination of Gibbs energy change in protein unfolding by denaturants, protonation, heat, scanning calorimetry, and hydrogen exchange, their implications such as reversibility, completeness of unfolding and the two-state assumption are dealt with.A data compilation of Gibbs energy change in unfolding of different proteins is given. The data, which for the most part range between 25 and 60 kJ mol^–1, are discussed in terms of protein functioning, turnover, and structural properties. Phase diagrams are proposed in order to realize a more comprehensive thermodynamic treatment of proteins.Factors which contribute to protein stability are summarized. The paper includes the thermodynamic principles of protein stability as well as special studies on proteolytic fragments, amino acid replacements, cross links, prosthetic groups, and ions which contribute to protein stability.     

Thermodynamic databases for proteins and protein-nucleic acid interactions

Thermodynamic data regarding proteins and their interactions are important for understanding the mechanisms of protein folding, protein stability, and molecular recognition. Although there are several structural databases available for proteins and their complexes with other molecules, databases for experimental thermodynamic data on protein stability and interactions are rather scarce. Thus, we have developed two electronically accessible thermodynamic databases. ProTherm, Thermodynamic Database for Proteins and Mutants, contains numerical data of several thermodynamic parameters of protein stability, experimental methods and conditions, along with structural, functional, and literature information. ProNIT, Thermodynamic Database for Protein-Nucleic Acid Interactions, contains thermodynamic data for protein-nucleic acid binding, experimental conditions, structural information of proteins, nucleic acids and the complex, and literature information. These data have been incorporated into 3DinSight, an integrated database for structure, function, and properties of biomolecules. A WWW interface allows users to search for data based on various conditions, with different display and sorting options, and to visualize molecular structures and their interactions. These thermodynamic databases, together with structural databases, help researchers gain insight into the relationship among structure, function, and thermodynamics of proteins and their interactions, and will become useful resources for studying proteins in the postgenomic era.     

Hydrophobicity of transmembrane proteins: spatially profiling the distribution

A hallmark of soluble globular protein tertiary structure is a hydrophobic core and a protein exterior populated predominantly by hydrophilic residues. Recent hydrophobic moment profiling of the spatial distribution of 30 globular proteins of diverse size and structure had revealed features of this distribution that were comparable. Analogous profiling of the hydrophobicity distribution of the alpha-helical buried bundles of several transmembrane proteins, as the lipid/protein interface is approached from within the bilayer, reveals spatial hydrophobicity profiles that contrast with those obtained for the soluble proteins. The calculations, which enable relative changes of hydrophobicity to be simply identified over the entire spatial extent of the multimer within the lipid bilayer, show the accumulated zero-order moments of the bundles to be mainly inverted with respect to that found for the soluble proteins. This indicates a statistical increase in the average residue hydrophobic content as the lipid bilayer is approached. This result differs from that of a relatively recent calculation and qualitatively agrees with earlier calculations involving lipid exposed and buried residues of the alpha-helices of transmembrane proteins. Spatial profiling, over the entire spatial extent of the multimer with scaled values of residue hydrophobicity, provides information that is not available from calculations using lipid exposure alone.     

Unifying temperature effects on the growth rate of bacteria and the stability of globular proteins

The specific growth rate constant for bacterial growth does not obey the Arrhenius-type kinetics displayed by simple chemical reactions. Instead, for bacteria, steep convex curves are observed on an Arrhenius plot at the low- and high-temperature ends of the biokinetic range, with a region towards the middle of the growth range loosely approximating linearity. This central region has been considered by microbiologists to be the "normal physiological range" for bacterial growth, a concept whose meaningfulness we now question. We employ a kinetic model incorporating thermodynamic terms for temperature-induced enzyme denaturation, central to which is a term to account for the large positive heat capacity change during unfolding of the proteins within the bacteria. It is now widely believed by biophysicists that denaturation of complex proteins and/or other macromolecules is due to hydrophobic hydration of non-polar compounds. Denaturation is seen as the process by which enthalpic and entropic forces becomes imbalanced both at high and at low temperatures resulting in conformational changes in the enzyme structure that expose hydrophobic amino acid groups to the surrounding water molecules. The "thermodynamic" rate model, incorporating the heat capacity change and its effect on the enthalpy and entropy of the system, fitted 35 sets of data for psychrophilic, psychrotrophic, mesophilic and thermophilic bacteria well, resulting in biologically meaningful estimates for the important thermodynamic parameters. As these results mirror those obtained by biophysicists for globular proteins, it appears that the same or a similar mechanism applies to bacteria as applies to proteins.     

Local and nonlocal interactions in globular proteins and mechanisms of alcohol denaturation.

How important are helical propensities in determining the conformations of globular proteins? Using the two-dimensional lattice model and two monomer types, H (hydrophobic) and P (polar), we explore both nonlocal interactions, through an HH contact energy, as developed in earlier work, and local interactions, through a helix energy, σ. By computer enumeration, the partition functions for short chains are obtained without approximation for the full range of both types of energy. When nonlocal interactions dominate, some sequences undergo coil-globule collapse to a unique native structure. When local interactions dominate, all sequences undergo helix–coil transitions. For two different conformational properties, the closest correspondence between the lattice model and proteins in the Protein Data Bank is obtained if the model local interactions are made small compared to the HH contact interaction, suggesting that helical propensities may be only weak determinants of globular protein structures in water. For some HP sequences, varying σ/ leads to additional sharp transitions (sometimes several) and to “conformational switching” between unique conformations. This behavior resembles the transitions of globular proteins in water to helical states in alcohols. In particular, comparison with experiments shows that whereas urea as a denaturant is best modeled as weakening both local and nonlocal interactions, trifluoroethanol is best modeled as mainly weakening HH interactions and slightly enhancing local helical interactions.     

Detection of secondary structure elements in proteins by hydrophobic cluster analysis.

Hydrophobic cluster analysis (HCA) is a protein sequence comparison method based on alpha-helical representations of the sequences where the size, shape and orientation of the clusters of hydrophobic residues are primarily compared. The effectiveness of HCA has been suggested to originate from its potential ability to focus on the residues forming the hydrophobic core of globular proteins. We have addressed the robustness of the bidimensional representation used for HCA in its ability to detect the regular secondary structure elements of proteins. Various parameters have been studied such as those governing cluster size and limits, the hydrophobic residues constituting the clusters as well as the potential shift of the cluster positions with respect to the position of the regular secondary structure elements. The following results have been found to support the alpha-helical bidimensional representation used in HCA: (i) there is a positive correlation (clearly above background noise) between the hydrophobic clusters and the regular secondary structure elements in proteins; (ii) the hydrophobic clusters are centred on the regular secondary structure elements; (iii) the pitch of the helical representation which gives the best correspondence is that of an alpha-helix. The correspondence between hydrophobic clusters and regular secondary structure elements suggests a way to implement variable gap penalties during the automatic alignment of protein sequences.     

Estimation of the maximum change in stability of globular proteins upon mutation of a hydrophobic residue to another of smaller size.

Although the hydrophobic effect is generally considered to be one of the most important forces in stabilizing the folded structure of a globular protein molecule, there is a lack of consensus on the precise magnitude of this effect. The magnitude of the hydrophobic effect is most directly measured by observing the change in stability of a protein molecule when an internal hydrophobic residue is mutated to another of smaller size. Results of such measurements have, however, been confusing because they vary greatly and are generally considerably larger than expected from the transfer free energies of corresponding small molecules. In this article, a thermodynamic argument is presented to show (1) that the variation is mainly due to that in the flexibility of the protein molecule at the site of mutation, (2) that the maximum destabilization occurs when the protein at the site of mutation is rigid, in which case the value of the destabilization is approximately given by the work of cavity formation in water, and (3) that the transfer free energy approximately gives the minimum of the range of variations. The best numerical agreements between the small molecule and the protein systems are obtained when the data from the small molecule system are expressed as the molarity-based standard free energies without other corrections.     

Sequence periodicity and secondary structure propensity in model proteins

We explore the question of whether local effects (originating from the amino acids intrinsic secondary structure propensities) or nonlocal effects (reflecting the sequence of amino acids as a whole) play a larger role in determining the fold of globular proteins. Earlier circular dichroism studies have shown that the pattern of polar, non polar amino acids (nonlocal effect) dominates over the amino acid intrinsic propensity (local effect) in determining the secondary structure of oligomeric peptides. In this article, we present a coarse grained computational model that allows us to quantitatively estimate the role of local and nonlocal factors in determining both the secondary and tertiary structure of small, globular proteins. The amino acid intrinsic secondary structure propensity is modeled by a dihedral potential term. This dihedral potential is parametrized to match with experimental measurements of secondary structure propensity. Similarly, the magnitude of the attraction between hydrophobic residues is parametrized to match the experimental transfer free energies of hydrophobic amino acids. Under these parametrization conditions, we systematically explore the degree of frustration a given polar, non polar pattern can tolerate when the secondary structure intrinsic propensities are in opposition to it. When the parameters are in the biophysically relevant range, we observe that the fold of small, globular proteins is determined by the pattern of polar, non polar amino acids regardless of their instrinsic secondary structure propensities. Our simulations shed new light on previous observations that tertiary interactions are more influential in determining protein structure than secondary structure propensity. The fact that this can be inferred using a simple polymer model that lacks most of the biochemical details points to the fundamental importance of binary patterning in governing folding.     

Origins of globular structure in proteins

Thermodynamic incompatibility of polymers in a common solvent is possibly a driving force for formation and evolution of globular protein structures. Folding of polypeptide chains leads to a decrease in both excluded volume of molecules and chemical differences between surfaces of globular molecules with chemical information hidden in the hydrophobic interior. Folding of polypeptide chains results in 'molecular or thermodynamic mimicry' of globular proteins and in at least more than 10-fold higher phase separation threshold values of mixed protein solutions compared to those of classical polymers. Unusually high co-solubility might be necessary for efficient biological functioning of proteins, e.g. enzymes, enzyme inhibitors, etc.     

A procedure for detection and quantitation of cavity volumes proteins. Application to measure the strength of the hydrophobic driving force in protein folding

Accurate identification of cavities is important in the study of protein structure, stability, design, and ligand binding. Identification and quantitation of cavities is a nontrivial problem because most cavities are connected to the protein exterior. We describe a computational procedure for quantitating cavity volumes and apply this to derive an estimate of the hydrophobic driving force in protein folding. A grid-based Monte Carlo procedure is used to position water molecules on the surface of a protein. A Voronoi procedure is used to identify and quantitate empty space within the solvated protein. Additional cavities not detected by other existing procedures can be identified. Most of these are close to surface concavities. Residue volumes for both the interior and the surface residues as well as cavity volumes are in good agreement with volumes calculated from fully hydrated protein structures obtained from molecular dynamic simulations. We show that the loss of stability because of cavity-creating mutations correlates better with cavity volumes determined by this procedure than with cavity volumes determined by other methods. Available structural and thermodynamic data for a number of cavity-containing mutants were analyzed to obtain estimates of 26.1 cal x mol(-1) x A(-3) and 18.5 cal x mol(-1) x A(-2) for the relative contributions of cavity formation and the hydrophobic effect to the observed stability changes. The present estimate for the hydrophobic driving force is at the lower end of estimates derived from model compound studies and considerably lower than previous estimates of approximately 50 cal x mol(-1) x A(-2) derived from protein mutational data. In the absence of structural rearrangement, on average, deletion of a single methylene group is expected to result in losses in stability of 0.41 and 0.70 kcal x mol(-1) resulting from decrease in hydrophobicity and packing, respectively.     

Shedding light on the extra thermal stability of thermophilic proteins

An entropic stabilization mechanism has recently gained attention and credibility as the physical ground for the extra thermal stability of globular proteins from thermophilic microorganisms. An empirical result, obtained from the analysis of thermodynamic data for a large set of proteins, strengthens the general reliability of the theoretical approach originally devised to rationalize the occurrence of cold denaturation [Graziano, PCCP 2014, 16, 21755–21767]. It is shown that this theoretical approach can readily account for the entropic stabilization mechanism. On decreasing the conformational entropy gain associated with denaturation, the thermal stability of a model globular protein increases markedly.     

Correlations between internal mobility and stability of globular proteins.

The recent work is surveyed which leads to the suggestions that the conformation of globular proteins in solution corresponds to a dynamic ensemble of rapidly interconverting spatial structures, that clusters of hydrophobic amino acid side chains have an important role in the architecture of protein molecules, and that mechanistic aspects of protein denaturation can be correlated with internal mobility seen in the native conformation. These conclusions resulted originally from high resolution 1H nuclear magnetic resonance (NMR) studies of aromatic ring mobility, exchange of interior amide protons and thermal denaturation of the basic pancreatic trypsin inhibitor and a group of related proteins. Various new approaches to further characterize proteins in solution have now been taken and preliminary data are presented. These include computer graphics to outline hydrophobic clusters in globular protein structures, high resolution 1H-NMR experiments at variable hydrostatic pressure and 13C-NMR relaxation measurements. At the present early stage of these new investigations it appears that the hydrophobic cluster model for globular proteins is compatible with the data obtained.