Hydrophobic potential of mean force as a solvation function for protein structure prediction

We have developed a solvation function that combines a Generalized Born model for polarization of protein charge by the high dielectric solvent, with a hydrophobic potential of mean force (HPMF) as a model for hydrophobic interaction, to aid in the discrimination of native structures from other misfolded states in protein structure prediction. We find that our energy function outperforms other reported scoring functions in terms of correct native ranking for 91% of proteins and low Z scores for a variety of decoy sets, including the challenging Rosetta decoys. This work shows that the stabilizing effect of hydrophobic exposure to aqueous solvent that defines the HPMF hydration physics is an apparent improvement over solvent-accessible surface area models that penalize hydrophobic exposure. Decoys generated by thermal sampling around the native-state basin reveal a potentially important role for side-chain entropy in the future development of even more accurate free energy surfaces.     

Distance dependent centroid to centroid force fields using high resolution decoys

Simplified force fields play an important role in protein structure prediction and de novo protein design by requiring less computational effort than detailed atomistic potentials. A side chain centroid based, distance dependent pairwise interaction potential has been developed. A linear programming based formulation was used in which non-native "decoy" conformers are forced to take a higher energy compared with the corresponding native structure. This model was trained on an enhanced and diverse protein set. High quality decoy structures were generated for approximately 1400 nonhomologous proteins using torsion angle dynamics along with restricted variations of the hydrophobic cores of the native structure. The resulting decoy set was used to train the model yielding two different side chain centroid based force fields that differ in the way distance dependence has been used to calculate energy parameters. These force fields were tested on an independent set of 148 test proteins with 500 decoy structures for each protein. The side chain centroid force fields were successful in correctly identifying approximately 86% native structures. The Z-scores produced by the proposed centroid-centroid distance dependent force fields improved compared with other distance dependent C(alpha)-C(alpha) or side chain based force fields.     

Solvent accessibility, protein surfaces, and protein folding.

Studies of the native structures of proteins, together with measurements of the thermodynamic properties of the transition between unfolded and native states, have defined the major components of the forces that stabilize native protein structures. However, the nature of the intermediates in the folding process remains largely hypothetical. It is a fairly widespread and not implausible assumption that the intermediates in the folding of a monomeric protein contain the same kinds of secondary and tertiary structures that appear in the native conformation, and that, although unstable, their lifetimes are prolonged by forces similar to those that stabilize the native structure. We wished to examine what happens if, during the folding of a monomeric protein, regions of secondary structure come together to form an intermediate of reduced instability. We applied calculations of accessible surface area (a measure of hydrophobic stabilization) and parameterized nonbonded energy calculations (measuring the strengths of van der Waals forces) to identify the kinds of stabilizing interactions that might be available to such an intermediate. First, we analyzed the total buried surface area of two types of proteins into contributions from formation of secondary structure alone, interaction of pairs of secondary-structural elements, the formation of the structure alone, interaction of pairs of secondary-structural elements, the formation of the complete secondary structure without the turns, and the complete native structure. The formation of secondary structure alone, without tertiary-structural interactions, buries roughly half the surface that the complete structure does. We then analyzed in more detail the approach of two alpha-helices to form a complex, as an illustrative example of the nature of the interaction between compact structural units which remain fairly rigid during their interaction. Many features of the results are not limited to the interaction of alpha-helices. (The results therefore neither confirm nor refute the hypothesis that alpha-helices are intermediates in the folding proteins). We find that the first forces to be felt upon approach arise from solvent conditions on the relative position and orientation of the two helices as does the close packing which optimizes the van der Waals interactions at shorter distances apart. Therefore there appears to be a range of distances in which hydrophobic interactions could create a nonspecific complex between two helices in which the side chains might have sufficient time to seek the proper interdigitation observed in the native structure, where the two helices are in intimate contact. Indeed, we find that only in the final stages of approach is the native geometry the most stable; in the region in which solvent-exclusion forces predominate, the conformation with helix axes parallel is more stable than the native conformation, in the cases we examined...     

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.     

Protein structures in SDS micelle-protein complexes.

Sodium dodecyl sulfate (SDS) is used more often than any other detergent as an excellent denaturing or "unfolding" detergent. However, formation of ordered structure (alpha-helix or beta-sheet) in certain peptides is known to be induced by interaction with SDS micelles. The SDS-induced structures formed by these peptides are amphiphilic, having both a hydrophobic and a hydrophilic face. Previous work in this area has revealed that SDS induces helical folding in a wide variety of non-helical proteins. Here, we describe the interaction of several structurally unrelated proteins with SDS micelles and the correlation of these structures to helical amphiphilic regions present in the primary sequence. It is likely that the ability of native nonordered protein structures to form induced amphiphilic ordered structures is rather common.     

Free energy determinants of tertiary structure and the evaluation of protein models

We develop a protocol for estimating the free energy difference between different conformations of the same polypeptide chain. The conformational free energy evaluation combines the CHARMM force field with a continuum treatment of the solvent. In almost all cases studied, experimentally determined structures are predicted to be more stable than misfolded "decoys." This is due in part to the fact that the Coulomb energy of the native protein is consistently lower than that of the decoys. The solvation free energy generally favors the decoys, although the total electrostatic free energy (sum of Coulomb and solvation terms) favors the native structure. The behavior of the solvation free energy is somewhat counterintuitive and, surprisingly, is not correlated with differences in the burial of polar area between native structures and decoys. Rather. the effect is due to a more favorable charge distribution in the native protein, which, as is discussed, will tend to decrease its interaction with the solvent. Our results thus suggest, in keeping with a number of recent studies, that electrostatic interactions may play an important role in determining the native topology of a folded protein. On this basis, a simplified scoring function is derived that combines a Coulomb term with a hydrophobic contact term. This function performs as well as the more complete free energy evaluation in distinguishing the native structure from misfolded decoys. Its computational efficiency suggests that it can be used in protein structure prediction applications, and that it provides a physically well-defined alternative to statistically derived scoring functions.     

Stereochemical theory of the 3-dimensional structure of globular proteins. I. Highly helical intermediate structures

The authors analyze the physical prerequisites on which the proposed stereochemical theory of the three-dimensional structure of globular proteins is based. The theory represents a stereochemical modelling of the mechanism of protein self-organization suggested earlier by one of the authors. According to this mechanism, a highly helical intermediate structure(s) is formed at first and then it passes into the native one. In the highly-helical intermediate structure the arrangement of the polypeptide chain in space is the same as in the native structure. These two structures differ mainly by the secondary structure of the chain. The transition into the native structure proceeds under the effect of long-range interactions which transform the excess alpha-helices into beta-structural and irregular conformations. The so-called s-helices are considered (the alpha-helix, whose hydrophobic groups form a separate cluster on its surface). s-Helices can be obtained on the greater part of the polypeptide chain of any globular protein. In the unfolded protein chain they are the most stable and rapidly formed structures. It has been shown that namely s-helices are the initial blocks for the formation of the highly-helical intermediate structure. Stereochemical principles of the s-helix packing that permit to predict the three-dimensional structure of highly helical proteins have been found. According to these principles the highly helical structure represents the packing of hydrophobic surfaces and s-helices. In their turn, hydrophobic surfaces are formed as a result of complementary interaction of borders of hydrophobic clusters of two s-helices according to the "knob-hole" principle.     

Folding Lennard-Jones proteins by a contact potential

We studied the possibility to approximate a Lennard-Jones interaction by a pairwise contact potential. First we used a Lennard-Jones potential to design off-lattice, protein-like heteropolymer sequences, whose lowest energy (native) conformations were then identified by molecular dynamics. Then we turned to investigate whether one can find a pairwise contact potential, whose ground states are the contact maps associated with these native conformations. We show that such a requirement cannot be satisfied exactly, i.e., no such contact parameters exist. Nevertheless, we found that one can find contact energy parameters for which an energy minimization procedure, acting in the space of contact maps, yields maps whose corresponding structures are close to the native ones. Finally, we show that when these structures are used as the initial point of a molecular dynamics energy minimization process, the correct native folds are recovered with high probability.     

An improved pair potential to recognize native protein folds

We present a novel method to improve a simple pair potential of mean force, derived from experimentally determined protein structures, in such a way that it recognizes native protein folds with high reliability. This improvement is based on the use of mutation data matrices to overcome difficulties arising from the poor statistics of small sample sizes. A set of 167 protein chains taken from the Brookhaven Protein Structure Data Base, selected from high-resolution structures and avoiding homologous proteins, is used for generation of the potential set. The potential describes interresidue pair energies depending on distance and sequential separation, and is calculated using the Boltzmann equation. Its performance is evaluated by jackknife tests that try to identify the native fold for a given sequence among a large number of possible threadings on all structures in the set without allowing for gaps. Up to 94% of the protein chains are correctly assigned to their native folds, so that all proper single-chain domains are recognized. © 1994 John Wiley & Sons, Inc.     

Distance-scaled,finite ideal-gas reference state improves structure-derived potentials of mean force for structure selection and stability prediction

The distance-dependent structure-derived potentials developed so far all employed a reference state that can be characterized as a residue (atom)-averaged state. Here, we establish a new reference state called the distance-scaled, finite ideal-gas reference (DFIRE) state. The reference state is used to construct a residue-specific all-atom potential of mean force from a database of 1011 nonhomologous (less than 30% homology) protein structures with resolution less than 2 A. The new all-atom potential recognizes more native proteins from 32 multiple decoy sets, and raises an average Z-score by 1.4 units more than two previously developed, residue-specific, all-atom knowledge-based potentials. When only backbone and C(beta) atoms are used in scoring, the performance of the DFIRE-based potential, although is worse than that of the all-atom version, is comparable to those of the previously developed potentials on the all-atom level. In addition, the DFIRE-based all-atom potential provides the most accurate prediction of the stabilities of 895 mutants among three knowledge-based all-atom potentials. Comparison with several physical-based potentials is made.     

Interaction of DnaK with native proteins and membrane proteins correlates with their accessible hydrophobicity

Molecular chaperones are involved in protein folding, protein targeting to membranes, and protein renaturation after stress. They interact specifically with hydrophobic sequences that are exposed in unfolded proteins, and buried in native proteins. We have studied the interaction of DnaK with native water-soluble proteins and membrane proteins. DnaK–native protein interactions are characterized by dissociation constants between 1 and 50 μM (compared with 0.01–1 μM for unfolded proteins). This affinity is within the range of most intracellular protein concentrations, suggesting that DnaK interacts with a greater number of native proteins than previously suspected. We found a correlation between the affinity of native proteins for DnaK and their affinity for hydrophobic-interaction chromatography adsorbents, suggesting that DnaK interacts with exposed hydrophobic groups in native proteins. The interaction between DnaK and membrane proteins is characterized by DnaK's high affinity for detergent-solubilized membrane proteins, and its lower affinity for membrane proteins inserted in lipid bilayers, suggesting that the chaperone can interact with the hydrophobic sequences of the former, while it cannot penetrate the hydrophobic core of lipid bilayers. Thus, the specificity of DnaK for hydrophobic sequences is involved in its interaction with not only unfolded proteins, but also native water-soluble proteins and membrane proteins. All proteins interact with DnaK according to their exposed hydrophobicity.     

Effective interactions between chaotropic agents and proteins

Chaotropic agents are cosolutes that can disrupt the hydrogen bonding network between water molecules and reduce the stability of the native state of proteins by weakening the hydrophobic effect. In this work, we represent the chaotropic agent as a factor that reduces the amount of order in the structures formed by water molecules, both in the bulk and the hydration shells around hydrophobic amino acids. In this framework we show that low chaotrope concentrations lead to a destabilization of the native state of proteins, and that high concentrations induce complete denaturation. We also find that the reduction of the number of bulk ordered states of water molecules can give origin to an effective interaction between chaotropic molecules and proteins.     

A distance-dependent atomic knowledge-based potential for improved protein structure selection.

A heavy atom distance-dependent knowledge-based pairwise potential has been developed. This statistical potential is first evaluated and optimized with the native structure z-scores from gapless threading. The potential is then used to recognize the native and near-native structures from both published decoy test sets, as well as decoys obtained from our group's protein structure prediction program. In the gapless threading test, there is an average z-score improvement of 4 units in the optimized atomic potential over the residue-based quasichemical potential. Examination of the z-scores for individual pairwise distance shells indicates that the specificity for the native protein structure is greatest at pairwise distances of 3.5-6.5 A, i.e., in the first solvation shell. On applying the current atomic potential to test sets obtained from the web, composed of native protein and decoy structures, the current generation of the potential performs better than residue-based potentials as well as the other published atomic potentials in the task of selecting native and near-native structures. This newly developed potential is also applied to structures of varying quality generated by our group's protein structure prediction program. The current atomic potential tends to pick lower RMSD structures than do residue-based contact potentials. In particular, this atomic pairwise interaction potential has better selectivity especially for near-native structures. As such, it can be used to select near-native folds generated by structure prediction algorithms as well as for protein structure refinement.     

An empirical energy potential with a reference state for protein fold and sequence recognition.

We consider modifications of an empirical energy potential for fold and sequence recognition to represent approximately the stabilities of proteins in various environments. A potential used here includes a secondary structure potential representing short-range interactions for secondary structures of proteins, and a tertiary structure potential consisting of a long-range, pairwise contact potential and a repulsive packing potential. This potential is devised to evaluate together the total conformational energy of a protein at the coarse grained residue level. It was previously estimated from the observed frequencies of secondary structures, from contact frequencies between residues, and from the distributions of the number of residues in contact in known protein structures by regarding those distributions as the equilibrium distributions with the Boltzmann factor of these interaction energies. The stability of native structures is assumed as a primary requirement for proteins to fold into their native structures. A collapse energy is subtracted from the contact energies to remove the protein size dependence and to represent protein stabilities for monomeric and multimeric states. The free energy of the whole ensemble of protein conformations that is subtracted from the conformational energy to represent protein stability is approximated as the average energy expected for a typical native structure with the same amino acid composition. This term may be constant in fold recognition but essentially varies in sequence recognition. A simple test of threading sequences into structures without gaps is employed to demonstrate the importance of the present modifications that permit the same potential to be utilized for both fold and sequence recognition. Proteins 1999;36:357-369. Published 1999 Wiley-Liss, Inc.     

Extracting contact energies from protein structures: A study using a simplified model

In this study, we exploited an elementary 2-dimensional square lattice model of HP polymers to test the premise of extracting contact energies from protein structures. Given a set of prespecified energies for H–H, H–P, and P–P contacts, all possible sequences of various lengths were exhaustively enumerated to find sequences that have unique lowest-energy conformations. The lowest-energy structures (or native structures) of such (native) sequences were used to extract contact energies using the Miyazawa-Jernigan procedure and here-defined reference state. The relative magnitudes of the original energies were restored reasonably well, but the extracted contact energies were independent of the absolute magnitudes of the initial energies. We turned to a more detailed characterization of the energy landscapes of the native sequences in light of a new theoretical framework on protein folding. Foldability of such sequences imposes two limits on the absolute value of the prespecified energies: a lower bound entailed by the minimum requirement for thermodynamic stability and an upper bound associated with the entrapment of the chain to local minima. We found that these two limits confine the prespecified energy values to a rather narrow range which, surprisingly, also contains the extracted energies in all the cases examined. These results indicate that the quasi-chemical approximation can be used to connect quantitatively the occurrence of various residue–residue contacts in an ensemble of native structures with the energies of the contacts. More importantly, they suggest that the extracted contact energies do contain information on structural stability and can be used to estimate actual structural energetics. This study also encourages the use of structure-derived contact energies in threading. The finding that there is a rather narrow range of energies that are optimal for folding a sequence also cautions the use of arbitrary energy Hamiltonion in minimal folding models. Proteins 31:299–308, 1998. © 1998 Wiley-Liss, Inc.     

Selective staining of proteins with hydrophobic surface sites on a native electrophoretic gel

Chemical proteomics aims to characterize all of the proteins in the proteome with respect to their function, which is associated with their interaction with other molecules. We propose the identification of a subproteomic library of expressed proteins whose native structures are typified by the presence of hydrophobic surface sites, which are often involved in interactions with small molecules, membrane lipids, and other proteins, pertaining to their functions. We demonstrate that soluble globular proteins with hydrophobic surface sites can be detected selectively by staining on an electrophoretic gel run under nondenaturing conditions. The application of these staining techniques may help elucidate new catalytic, transport, and regulatory functionalities in complex proteomic screenings.     

Hydrophobic forces between protein molecules in aqueous solutions of concentrated electrolyte

Protein-protein interactions have been measured for a mutant (D101F) lysozyme and for native lysozyme in concentrated solutions of ammonium sulfate at pH 7 and sodium chloride at pH 4.5. In the mutant lysozyme, a surface aspartate residue has been replaced with a hydrophobic phenylalanine residue. The protein-protein interactions of D101F lysozyme are more attractive than those of native lysozyme for all conditions studied. The salt-induced attraction is correlated with a solvation potential of mean force given by the work required to desolvate the part of the protein surfaces that is buried by the protein-protein interaction. This work is proportional to the aqueous surface-tension increment of the salt and the fractional non-polar surface coverage of the protein. Experimental measurements of osmotic second virial coefficients validate a proposed potential of mean force that ascribes the salt-induced attraction between protein molecules to an enhancement of the hydrophobic attraction. This model provides a first approximation for predicting the protein-protein potential of mean force in concentrated aqueous electrolyte solutions; this potential is useful for determining solution conditions favorable for protein crystallization.     

Mapping electrostatic interactions in macromolecular associations.

In the association of electron transfer proteins, electrostatics has been proposed to play a role in maintaining the stability and specificity of the biomolecular complexes formed. An excellent model system is the interaction between mammalian cytochrome b5 and cytochrome c, in which the X-ray structures of the individual components reveal a complementary asymmetry of charges surrounding their respective redox centers. Determining the exact extent of the electrostatic interactions and identifying the specific residues involved in the formation of the electron transfer complex has proved more elusive. We report herein the utilization of high-pressure techniques, together with site-directed mutagenesis, to provide a map of the interaction domains in biomolecular complex formation. The application of high pressure disrupts macromolecular associations since dissociation of the complex results in a decreased volume of the system due to the solvation of charges that had been previously sequestered in the interface region and force solvation of hydrophobic surfaces. Site-directed mutagenesis of a totally synthetic gene for rat liver cytochrome b5, which expresses this mammalian protein in Escherichia coli as a hemecontaining soluble component, was used to selectively alter negatively charged residues of cytochrome b5 to neutral amide side-chains. We have demonstrated that the interaction domain of cytochrome b5 with cytochrome c can be mapped from a comparison of dissociation volumes of these modified cytochrome b5-cytochrome c complexes with the native complex. Using these techniques we can specifically investigate the role of particular residues in the equilibrium association of these two electron transfer proteins. Single-point mutations in the interaction domain give nearly identical effects on the measured dissociation volumes, yet removal of acidic residues outside the recognition surface yield volumes similar to wild-type protein. Multiple mutations in the proposed protein-protein interaction site are found to allow greater solvent-accessibility of the interface as reflected in a diminution in the volume changes on subsequent charge removal. This is indicative that the interprotein salt-bridges in this complex provide a mechanism for a greater exclusion of solvent from the interfacial domain of the complex, resulting in a more stable association.