Geometric cooperativity and anticooperativity of three-body interactions in native proteins

Characterizing multibody interactions of hydrophobic, polar, and ionizable residues in protein is important for understanding the stability of protein structures. We introduce a geometric model for quantifying 3-body interactions in native proteins. With this model, empirical propensity values for many types of 3-body interactions can be reliably estimated from a database of native protein structures, despite the overwhelming presence of pairwise contacts. In addition, we define a nonadditive coefficient that characterizes cooperativity and anticooperativity of residue interactions in native proteins by measuring the deviation of 3-body interactions from 3 independent pairwise interactions. It compares the 3-body propensity value from what would be expected if only pairwise interactions were considered, and highlights the distinction of propensity and cooperativity of 3-body interaction. Based on the geometric model, and what can be inferred from statistical analysis of such a model, we find that hydrophobic interactions and hydrogen-bonding interactions make nonadditive contributions to protein stability, but the nonadditive nature depends on whether such interactions are located in the protein interior or on the protein surface. When located in the interior, many hydrophobic interactions such as those involving alkyl residues are anticooperative. Salt-bridge and regular hydrogen-bonding interactions, such as those involving ionizable residues and polar residues, are cooperative. When located on the protein surface, these salt-bridge and regular hydrogen-bonding interactions are anticooperative, and hydrophobic interactions involving alkyl residues become cooperative. We show with examples that incorporating 3-body interactions improves discrimination of protein native structures against decoy conformations. In addition, analysis of cooperative 3-body interaction may reveal spatial motifs that can suggest specific protein functions.     

Polar residues in the protein core of Escherichia coli thioredoxin are important for fold specificity

Most globular proteins contain a core of hydrophobic residues that are inaccessible to solvent in the folded state. In general, polar residues in the core are thermodynamically unfavorable except when they are able to form intramolecular hydrogen bonds. Compared to hydrophobic interactions, polar interactions are more directional in character and may aid in fold specificity. In a survey of 263 globular protein structures, we found a strong positive correlation between the number of polar residues at core positions and protein size. To probe the importance of buried polar residues, we experimentally tested the effects of hydrophobic mutations at the five polar core residues in Escherichia coli thioredoxin. Proteins with single hydrophobic mutations (D26I, C32A, C35A, T66L, and T77V) all have cooperative unfolding transitions like the wild type (wt), as determined by chemical denaturation. Relative to wt, D26I is more stable while the other point mutants are less stable. The combined 5-fold mutant protein (IAALV) is less stable than wt and has an unfolding transition that is substantially less cooperative than that of wt. NMR spectra as well as amide deuterium exchange indicate that IAALV is likely sampling a number of low-energy structures in the folded state, suggesting that polar residues in the core are important for specifying a well-folded native structure.     

Heat capacity of hydrogen-bonded networks: an alternative view of protein folding thermodynamics

Large changes in heat capacity (deltaCp) have long been regarded as the characteristic thermodynamic signature of hydrophobic interactions. However, similar effects arise quite generally in order-disorder transitions in homogeneous systems, particularly those comprising hydrogen-bonded networks, and this may have significance for our understanding of protein folding and other biomolecular processes. The positive deltaCp associated with unfolding of globular proteins in water, thought to be due to hydrophobic interactions, is also typical of the values found for the melting of crystalline solids, where the effect is greatest for the melting of polar compounds, including pure water. This suggests an alternative model of protein folding based on the thermodynamics of phase transitions in hydrogen-bonded networks. Folded proteins may be viewed as islands of cooperatively-ordered hydrogen-bonded structure, floating in an aqueous network of less-well-ordered H-bonds in which the degree of hydrogen bonding decreases with increasing temperature. The enthalpy of melting of the protein consequently increases with temperature. A simple algebraic model, based on the overall number of protein and solvent hydrogen bonds in folded and unfolded states, shows how deltaCp from this source could match the hydrophobic contribution. This confirms the growing view that the thermodynamics of protein folding, and other interactions in aqueous systems, are best described in terms of a mixture of polar and non-polar effects in which no one contribution is necessarily dominant.     

The chicken-egg scenario of protein folding revisited

What is the first step in protein folding - hydrophobic collapse (compaction) or secondary structure formation? It is still not clear if the major driving force in protein folding is hydrogen bonding or hydrophobic interactions or both. We analyzed data on the conformational characteristics of 41 globular proteins in native and partially folded conformational states. Our analysis shows that a good correlation exists between relative decrease in hydrodynamic volume and increase in secondary structure content. No compact equilibrium intermediates lacking secondary structure, or highly ordered non-compact species, were found. This correlation provides experimental support for the hypothesis that hydrophobic collapse occurs simultaneously with formation of secondary structure in the early stages of the protein folding.     

Sequential unfolding of the hemolysin two‐partner secretion domain from Proteus mirabilis

Protein secretion is a major contributor to Gram‐negative bacterial virulence. Type Vb or two‐partner secretion (TPS) pathways utilize a membrane bound β‐barrel B component (TpsB) to translocate large and predominantly virulent exoproteins (TpsA) through a nucleotide independent mechanism. We focused our studies on a truncated TpsA member termed hemolysin A (HpmA265), a structurally and functionally characterized TPS domain from Proteus mirabilis. Contrary to the expectation that the TPS domain of HpmA265 would denature in a single cooperative transition, we found that the unfolding follows a sequential model with three distinct transitions linking four states. The solvent inaccessible core of HpmA265 can be divided into two different regions. The C‐proximal region contains nonpolar residues and forms a prototypical hydrophobic core as found in globular proteins. The N‐proximal region of the solvent inaccessible core, however, contains polar residues. To understand the contributions of the hydrophobic and polar interiors to overall TPS domain stability, we conducted unfolding studies on HpmA265 and site‐specific mutants of HpmA265. By correlating the effect of individual site‐specific mutations with the sequential unfolding results we were able to divide the HpmA265 TPS domain into polar core, nonpolar core, and C‐terminal subdomains. Moreover, the unfolding studies provide quantitative evidence that the folding free energy for the polar core subdomain is more favorable than for the nonpolar core and C‐terminal subdomains. This study implicates the hydrogen bonds shared among these conserved internal residues as a primary means for stabilizing the N‐proximal polar core subdomain.     

Structure-derived hydrophobic potential. Hydrophobic potential derived from X-ray structures of globular proteins is able to identify native folds.

We present a model for the hydrophobic interaction in globular proteins that is based entirely on an analysis of known X-ray structures. This structure-derived hydrophobic force is identified as the strongest among the non-covalent interactions that stabilize native folds. The functional form of the hydrophobic interaction is found to be linear, corresponding to a constant force along the observable distance range (5 to 70 A). The parameters of the hydrophobic amino acid pair potentials yield a structure-derived hydrophobicity scale that correlates strongly with scales derived by a variety of complementary approaches. We demonstrate that the structure-derived hydrophobic interaction alone is able to distinguish a substantial number of native conformations from a large pool of misfolded structures.     

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.     

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.     

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.     

On the Importance of Polar Interactions for Complexes Containing Intrinsically Disordered Proteins

There is a growing recognition for the importance of proteins with large intrinsically disordered (ID) segments in cell signaling and regulation. ID segments in these proteins often harbor regions that mediate molecular recognition. Coupled folding and binding of the recognition regions has been proposed to confer high specificity to interactions involving ID segments. However, researchers recently questioned the origin of the interaction specificity of ID proteins because of the overrepresentation of hydrophobic residues in their interaction interfaces. Here, we focused on the role of polar and charged residues in interactions mediated by ID segments. Making use of the extended nature of most ID segments when in complex with globular proteins, we first identified large numbers of complexes between globular proteins and ID segments by using radius-of-gyration-based selection criteria. Consistent with previous studies, we found the interfaces of these complexes to be enriched in hydrophobic residues, and that these residues contribute significantly to the stability of the interaction interface. However, our analyses also show that polar interactions play a larger role in these complexes than in structured protein complexes. Computational alanine scanning and salt-bridge analysis indicate that interfaces in ID complexes are highly complementary with respect to electrostatics, more so than interfaces of globular proteins. Follow-up calculations of the electrostatic contributions to the free energy of binding uncovered significantly stronger Coulombic interactions in complexes harbouring ID segments than in structured protein complexes. However, they are counter-balanced by even higher polar-desolvation penalties. We propose that polar interactions are a key contributing factor to the observed high specificity of ID segment-mediated interactions.     

Matrix proteins from insect pliable cuticles: are they flexible and easily deformed?

Proteins from pliable cuticle of locusts, Schistocerca gregaria, and silk moth larvae, Hyalophora cecropia, were studied in solution by means of a fluorescent probe, 8-anilinonaphthalene-1-sulphonic acid (ANS), which is much more fluorescent in non-polar media than in polar media. An intense ANS-fluorescence was observed in the presence of the cuticular proteins at pH-values close to their acidic isoelectric points, and the fluorescence decreased markedly when pH was increased to neutrality or when small amounts of denaturants were added. Aggregation and eventual precipitation of both H. cecropia and locust proteins were obtained by addition of neutral salts, and the aggregation was accompanied by an increased ANS-fluorescence intensity. A decreased ANS-fluorescence was observed at salt concentrations too low to cause visible aggregation of the H. cecropia proteins, probably due to weakened electrostatic interactions between chain segments, but such a decrease was not observed for the locust proteins. The changes in intensity of ANS-fluorescence induced by addition of small amounts of denaturants or salts to solutions of the proteins indicate that more hydrophobic residues are exposed to the solvent, when either hydrophobic interactions or electrostatic attractions between chain segments are weakened. The result is a less compact protein structure, where fewer and smaller hydrophobic clusters are available for protecting ANS-molecules from the quenching effects of water. The effects of denaturants on ANS-fluorescence in the presence of the cuticular proteins are different from those observed for globular proteins, such as hen egg albumen, and the differences can be explained by the suggestion that the cuticular proteins do not have a precisely folded and densely packed hydrophobic core comparable to that present in native globular proteins, and that accordingly they do not undergo a process of denaturation corresponding to that of globular proteins. The behaviour of the cuticular proteins resembles that described for unordered, randomly coiled, thermally agitated polymer chains, whose hydrodynamic volumes depend upon the composition of the medium. It is proposed that the major part of the peptide chains of the cuticular proteins are in an unordered, random structure both when the proteins are in solution and when present in the intact cuticle; probably only the chain regions involved in binding the proteins to chitin will have a well-defined spatial organisation.     

The heat capacity of proteins

The heat capacity plays a major role in the determination of the energetics of protein folding and molecular recognition. As such, a better understanding of this thermodynamic parameter and its structural origin will provide new insights for the development of better molecular design strategies. In this paper we have analyzed the absolute heat capacity of proteins in different conformations. The results of these studies indicate that three major terms account for the absolute heat capacity of a protein: (1) one term that depends only on the primary or covalent structure of a protein and contains contributions from vibrational frequencies arising from the stretching and bending modes of each valence bond and internal rotations; (2) a term that contains the contributions of noncovalent interactions arising from secondary and tertiary structure; and (3) a term that contains the contributions of hydration. For a typical globular protein in solution the bulk of the heat capacity at 25°C is given by the covalent structure term (close to 85% of the total). The hydration term contributes about 15 and 40% to the total heat capacity of the native and unfolded states, respectively. The contribution of non-covalent structure to the total heat capacity of the native state is positive but very small and does not amount to more than 3% at 25°C. The change in heat capacity upon unfolding is primarily given by the increase in the hydration term (about 95%) and to a much lesser extent by the loss of noncovalent interactions (up to ～5%). It is demonstrated that a single universal mathematical function can be used to represent the partial molar heat capacity of the native and unfolded states of proteins in solution. This function can be experimentally written in terms of the molecular weight, the polar and apolar solvent accessible surface areas, and the total area buried from the solvent. This unique function accurately predicts the different magnitude and temperature dependences of the heat capacity of both the native and unfolded states, and therefore of the heat capacity changes associated with folding/unfolding transitions. © 1995 Wiley-Liss, Inc.     

Inter-residue interactions in protein folding and stability

During the process of protein folding, the amino acid residues along the polypeptide chain interact with each other in a cooperative manner to form the stable native structure. The knowledge about inter-residue interactions in protein structures is very helpful to understand the mechanism of protein folding and stability. In this review, we introduce the classification of inter-residue interactions into short, medium and long range based on a simple geometric approach. The features of these interactions in different structural classes of globular and membrane proteins, and in various folds have been delineated. The development of contact potentials and the application of inter-residue contacts for predicting the structural class and secondary structures of globular proteins, solvent accessibility, fold recognition and ab initio tertiary structure prediction have been evaluated. Further, the relationship between inter-residue contacts and protein-folding rates has been highlighted. Moreover, the importance of inter-residue interactions in protein-folding kinetics and for understanding the stability of proteins has been discussed. In essence, the information gained from the studies on inter-residue interactions provides valuable insights for understanding protein folding and de novo protein design.     

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.     

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.     

Context-dependent effects of proline residues on the stability and folding pathway of ubiquitin.

Substitution of trans-proline at three positions in ubiquitin (residues 19, 37 and 38) produces significant context-dependent effects on protein stability (both stabilizing and destabilizing) that reflect changes to a combination of parameters including backbone flexibility, hydrophobic interactions, solvent accessibility to polar groups and intrinsic backbone conformational preferences. Kinetic analysis of the wild-type yeast protein reveals a predominant fast-folding phase which conforms to an apparent two-state folding model. Temperature-dependent studies of the refolding rate reveal thermodynamic details of the nature of the transition state for folding consistent with hydrophobic collapse providing the overall driving force. Br?nsted analysis of the refolding and unfolding rates of a family of mutants with a variety of side chain substitutions for P37 and P38 reveals that the two prolines, which are located in a surface loop adjacent to the C terminus of the main alpha-helix (residues 24-33), are not significantly structured in the transition state for folding and appear to be consolidated into the native structure only late in the folding process. We draw a similar conclusion regarding position 19 in the loop connecting the N-terminal beta-hairpin to the main alpha-helix. The proline residues of ubiquitin are passive spectators in the folding process, but influence protein stability in a variety of ways.     

Folding of beta-sheets in membranes: specificity and promiscuity in peptide model systems

The interactions that drive the folding of beta-barrel membrane proteins have not been well studied because there have been few available model systems for membrane beta-sheets. In this work, we expand on a recently described model system to explore the contributions of interstrand hydrogen bonds, side-chain/side-chain interactions and side-chain/membrane interactions to beta-sheet formation in membranes. These experiments are based on the observation that the hydrophobic hexapeptide acetyl-Trp-Leu-Leu-Leu-Leu-Leu-OH (AcWLLLLL) folds, cooperatively and reversibly, into oligomeric, antiparallel beta-sheets in phosphatidylcholine membranes. To systematically characterize the important interactions that drive beta-sheet formation in membranes, we have used circular dichroism spectroscopy to determine the membrane secondary structure of each member of a complete host-guest family of related peptides of the form AcWLL-X-LL, where X is one of the natural amino acids. Peptides with hydrophobic X-residues of any size or character (X=Ala, Val, Ile, Leu, Cys, Met, Phe and Trp) form similar beta-sheets in membranes, while peptides with any polar X-residue or Gly or Pro at the X-position are random-coils, even when bound to membranes at high concentrations. The observed membrane sheet preferences correlate poorly with intrinsic sheet propensity scales measured in soluble proteins, but they correlate well with several membrane hydrophobicity scales. These results support the idea that the predominant interactions of the side-chains in membrane-bound beta-sheets are with the membrane lipids, and that backbone hydrogen bonding is the major driving force for the stabilization of beta-sheets in membranes.     

Critical Examination of the Colloidal Particle Model of Globular Proteins

Recent studies of globular protein solutions have uniformly adopted a colloidal view of proteins as particles, a perspective that neglects the polymeric primary structure of these biological macromolecules, their intrinsic flexibility, and their ability to sample a large configurational space. While the colloidal perspective often serves as a useful idealization in many cases, the macromolecular identity of proteins must reveal itself under thermodynamic conditions in which the native state is no longer stable, such as denaturing solvents and high protein concentrations where macromolecules tend to have screened excluded volume, charge, and hydrodynamic interactions. Under extreme pH conditions, charge repulsion interactions within the protein chain can overcome the attractive hydrogen-bonding interactions, holding it in its native globular state. Conformational changes can therefore be expected to have great significance on the shear viscosity and other rheological properties of protein solutions. These changes are not envisioned in conventional colloidal protein models and we have initiated an investigation of the scattering and rheological properties of model proteins. We initiate this effort by considering bovine serum albumin because it is a globular protein whose solution properties have also been extensively investigated as a function of pH, temperature, ionic strength, and concentration. As we anticipated, near-ultraviolet circular dichroism measurements and intrinsic viscosity measurements clearly indicate that the bovine serum albumin tertiary structure changes as protein concentration and pH are varied. Our findings point to limited validity of the colloidal protein model and to the need for further consideration and quantification of the effects of conformational changes on protein solution viscosity, protein association, and the phase behavior. Small-angle Neutron Scattering measurements have allowed us to assess how these conformational changes influence protein size, shape, and interprotein interaction strength.