Origins of protein denatured state compactness and hydrophobic clustering in aqueous urea: inferences from nonpolar potentials of mean force

Free energies of pairwise hydrophobic association are simulated in aqueous solutions of urea at concentrations ranging from 0-8 M. Consistent with the expectation that hydrophobic interactions are weakened by urea, the association of relatively large nonpolar solutes is destabilized by urea. However, the association of two small methane-sized nonpolar solutes in water has the opposite tendency of being slightly strengthened by the addition of urea. Such size effects and the dependence of urea-induced stability changes on the configuration of nonpolar solutes are not predicted by solvent accessible surface area approaches based on energetic parameters derived from bulk-phase solubilities of model compounds. Thus, to understand hydrophobic interactions in proteins, it is not sufficient to rely solely on transfer experiment data that effectively characterize a single nonpolar solute in an aqueous environment but not the solvent-mediated interactions among two or more nonpolar solutes. We find that the m-values for the rate of change of two-methane association free energy with respect to urea concentration is a dramatically nonmonotonic function of the spatial separation between the two methanes, with a distance-dependent profile similar to the corresponding two-methane heat capacity of association in pure water. Our results rationalize the persistence of residual hydrophobic contacts in some proteins at high urea concentrations and explain why the heat capacity signature (DeltaC(P)) of a compact denatured state can be similar to DeltaC(P) values calculated by assuming an open random-coil-like unfolded state.     

Amino acid interaction preferences in proteins

Understanding the key factors that influence the interaction preferences of amino acids in the folding of proteins have remained a challenge. Here we present a knowledge‐based approach for determining the effective interactions between amino acids based on amino acid type, their secondary structure, and the contact based environment that they find themselves in the native state structure as measured by their number of neighbors. We find that the optimal information is approximately encoded in a 60 × 60 matrix describing the 20 types of amino acids in three distinct secondary structures (helix, beta strand, and loop). We carry out a clustering scheme to understand the similarity between these interactions and to elucidate a nonredundant set. We demonstrate that the inferred energy parameters can be used for assessing the fit of a given sequence into a putative native state structure.     

Extent of protein-protein interactions and quasi-equivalence in viral capsids

Viral capsids are composed of multiple copies of one or a few gene products that self-assemble on their own or in the presence of the viral genome and/or auxiliary proteins into closed shells (capsids). We have analyzed 75 high-resolution virus capsid structures by calculating the average fraction of the solvent-accessible surface area of the coat protein subunits buried in the viral capsids. This fraction ranges from 0 to 1 and represents a normalized protein-protein interaction (PPI) index and is a measure of the extent of protein-protein interactions. The PPI indices were used to compare the extent of association of subunits among different capsids. We further examined the variation of the PPI indices as a function of the molecular weight of the coat protein subunit and the capsid diameter. Our results suggest that the PPI indices in T=1 and pseudo-T=3 capsids vary linearly with the molecular weight of the subunit and capsid size. This is in contrast to quasi-equivalent capsids with T>or=3, where the extent of protein-protein interactions is relatively independent of the subunit and capsid sizes. The striking outcome of this analysis is the distinctive clustering of the "T=2" capsids, which are distinguished by higher subunit molecular weights and a much lower degree of protein-protein interactions. Furthermore, the calculated residual (R(sym)) of the fraction buried surface areas of the structurally unique subunits in capsids with T>1 was used to calculate the quasi-equivalence of different subunit environments.     

Improving the prediction accuracy of residue solvent accessibility and real-value backbone torsion angles of proteins by guided-learning through a two-layer neural network

This article attempts to increase the prediction accuracy of residue solvent accessibility and real-value backbone torsion angles of proteins through improved learning. Most methods developed for improving the backpropagation algorithm of artificial neural networks are limited to small neural networks. Here, we introduce a guided-learning method suitable for networks of any size. The method employs a part of the weights for guiding and the other part for training and optimization. We demonstrate this technique by predicting residue solvent accessibility and real-value backbone torsion angles of proteins. In this application, the guiding factor is designed to satisfy the intuitive condition that for most residues, the contribution of a residue to the structural properties of another residue is smaller for greater separation in the protein-sequence distance between the two residues. We show that the guided-learning method makes a 2-4% reduction in 10-fold cross-validated mean absolute errors (MAE) for predicting residue solvent accessibility and backbone torsion angles, regardless of the size of database, the number of hidden layers and the size of input windows. This together with introduction of two-layer neural network with a bipolar activation function leads to a new method that has a MAE of 0.11 for residue solvent accessibility, 36 degrees for psi, and 22 degrees for phi. The method is available as a Real-SPINE 3.0 server in http://sparks.informatics.iupui.edu.     

Empirical lipid propensities of amino acid residues in multispan alpha helical membrane proteins

Characterizing the interactions between amino acid residues and lipid molecules is important for understanding the assembly of transmembrane helices and for studying membrane protein folding. In this study we develop TMLIP (TransMembrane helix-LIPid), an empirically derived propensity of individual residue types to face lipid membrane based on statistical analysis of high-resolution structures of membrane proteins. Lipid accessibilities of amino acid residues within the transmembrane (TM) region of 29 structures of helical membrane proteins are studied with a spherical probe of radius of 1.9 A. Our results show that there are characteristic preferences for residues to face the headgroup region and the hydrocarbon core region of lipid membrane. Amino acid residues Lys, Arg, Trp, Phe, and Leu are often found exposed at the headgroup regions of the membrane, where they have high propensity to face phospholipid headgroups and glycerol backbones. In the hydrocarbon core region, the strongest preference for interacting with lipids is observed for Ile, Leu, Phe and Val. Small and polar amino acid residues are usually buried inside helical bundles and are strongly lipophobic. There is a strong correlation between various hydrophobicity scales and the propensity of a given residue to face the lipids in the hydrocarbon region of the bilayer. Our data suggest a possibly significant contribution of the lipophobic effect to the folding of membrane proteins. This study shows that membrane proteins have exceedingly apolar exteriors rather than highly polar interiors. Prediction of lipid-facing surfaces of boundary helices using TMLIP1 results in a 54% accuracy, which is significantly better than random (25% accuracy). We also compare performance of TMLIP with another lipid propensity scale, kPROT, and with several hydrophobicity scales using hydrophobic moment analysis.     

Water and urea interactions with the native and unfolded forms of a beta-barrel protein

A fundamental understanding of protein stability and the mechanism of denaturant action must ultimately rest on detailed knowledge about the structure, solvation, and energetics of the denatured state. Here, we use (17)O and (2)H magnetic relaxation dispersion (MRD) to study urea-induced denaturation of intestinal fatty acid-binding protein (I-FABP). MRD is among the few methods that can provide molecular-level information about protein solvation in native as well as denatured states, and it is used here to simultaneously monitor the interactions of urea and water with the unfolding protein. Whereas CD shows an apparently two-state transition, MRD reveals a more complex process involving at least two intermediates. At least one water molecule binds persistently (with residence time >10 nsec) to the protein even in 7.5 M urea, where the large internal binding cavity is disrupted and CD indicates a fully denatured protein. This may be the water molecule buried near the small hydrophobic folding core at the D-E turn in the native protein. The MRD data also provide insights about transient (residence time <1 nsec) interactions of urea and water with the native and denatured protein. In the denatured state, both water and urea rotation is much more retarded than for a fully solvated polypeptide. The MRD results support a picture of the denatured state where solvent penetrates relatively compact clusters of polypeptide segments.     

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.     

An empirical relationship between rotational correlation time and solvent accessible surface area

Structure–dynamics interrelationships are important in understanding protein function. We have explored the empirical relationship between rotational correlation times (_c and the solvent accessible surface areas (SASA) of 75 proteins with known structures. The theoretical correlation between SASA and _c through the equation SASA = K_rc ^(2/3) is also considered. SASA was determined from the structure, _c ^calc was determined from diffusion tensor calculations, and _c ^expt was determined from NMR backbone¹³ C or ¹⁵N relaxation rate measurements. The theoretical and experimental values of _c correlate with SASA with regression analyses values of K_r as 1696 and 1896 m²s^-(2/3), respectively, and with corresponding correlation coefficients of 0.92 and 0.70.     

Achieving 80% ten-fold cross-validated accuracy for secondary structure prediction by large-scale training

An integrated system of neural networks, called SPINE, is established and optimized for predicting structural properties of proteins. SPINE is applied to three-state secondary-structure and residue-solvent-accessibility (RSA) prediction in this paper. The integrated neural networks are carefully trained with a large dataset of 2640 chains, sequence profiles generated from multiple sequence alignment, representative amino acid properties, a slow learning rate, overfitting protection, and an optimized sliding-widow size. More than 200,000 weights in SPINE are optimized by maximizing the accuracy measured by Q(3) (the percentage of correctly classified residues). SPINE yields a 10-fold cross-validated accuracy of 79.5% (80.0% for chains of length between 50 and 300) in secondary-structure prediction after one-month (CPU time) training on 22 processors. An accuracy of 87.5% is achieved for exposed residues (RSA >95%). The latter approaches the theoretical upper limit of 88-90% accuracy in assigning secondary structures. An accuracy of 73% for three-state solvent-accessibility prediction (25%/75% cutoff) and 79.3% for two-state prediction (25% cutoff) is also obtained.     

Thermodynamics of the Trp‐cage miniprotein unfolding in urea

The thermodynamic properties of unfolding of the Trp‐cage mini protein in the presence of various concentrations of urea have been characterized using temperature‐induced unfolding monitored by far‐UV circular dichroism spectroscopy. Analysis of the data using a two‐state model allowed the calculation of the Gibbs energy of unfolding at 25°C as a function of urea concentration. This in turn was analyzed by the linear extrapolation model that yielded the dependence of Gibbs energy on urea concentration, i.e. the m‐value for Trp‐cage unfolding. The m‐value obtained from the experimental data, as well as the experimental heat capacity change upon unfolding, were correlated with the structural parameters derived from the three dimensional structure of Trp‐cage. It is shown that the m‐value can be predicted well using a transfer model, while the heat capacity changes are in very good agreement with the empirical models based on model compounds studies. These results provide direct evidence that Trp‐cage, despite its small size, is an excellent model for studies of protein unfolding and provide thermodynamic data that can be used to compare with atomistic computer simulations. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Reversible and irreversible modifications ofβ-lactoglobulin upon exposure to heat

Modifications in the exposure to the solvent of hydrophobic residues, changes in their organization into surface hydrophobic patches, and alterations in the dimerization equilibrium of-lactoglobulin upon thermal treatment at neutralpH were studied. Exposure of tryptophan residues was temperature dependent and was essentially completed on the time scale of seconds. Reorganization of generic hydrophobic protein patches on the protein surface was monitored through binding of 1,8-anilinonaphthalenesulfonate, and was much slower than changes in tryptophan exposure. Different phases in surface hydrophobicity changes were related to the swelling and the subsequent collapse of the protein, which formed a metastable swollen intermediate. Heat treatment of-lactoglobulin also resulted in the formation of soluble oligomeric aggregates. The aggregation process was studied as a function of temperature, demonstrating that (i) dimer dissociation was a necessary step in a sequential polymerization mechanism and (ii) cohesion of hydrophobic patches was the major driving force for aggregation.     

Modeling the effects of mutations on the denatured states of proteins.

We develop a model for the reversible denaturation of proteins and for the effects of single-site mutations on the denatured states. The model is based on short chains of sequences of H (hydrophobic) and P (other) monomers configured as self-avoiding walks on the two-dimensional square lattice. The N (native) state is defined as the unique conformation of lowest contact energy, whereas the D (denatured) state is defined as the collection of all other conformations. With this model we are able to determine the exact partition function, and thus the exact native-denatured equilibrium for various solvent conditions, using the computer to exhaustively enumerate every possible configuration. Previous studies confirm that this model shows many aspects of protein-like behavior. The present study attempts to model how the denatured state (1) depends on the amino acid sequence, and (2) is changed by single-site mutations. The model accounts for two puzzling experimental results: (1) the replacement of a polar residue by a hydrophobic amino acid on the surface of a protein can destabilize a native protein, and (2) the "denaturant slope," m = partial delta G/partial c (where c is the concentration of denaturant--urea, guanidine hydrochloride), can sometimes change by as much as 30% due to a single mutation. The principal conclusion of the present study is that, under strong folding conditions, the denatured conformations that are in equilibrium with the native state are not open random configurations. Instead, they are an ensemble of highly compact conformations with a distribution that depends on the residue sequence and that can be substantially altered by single mutations. Most importantly, we conclude that mutations can exert their dominant effects on protein stability by changing the entropy of folding.     

Correlation between sequence hydrophobicity and surface-exposure pattern of database proteins

Hydrophobicity is thought to be one of the primary forces driving the folding of proteins. On average, hydrophobic residues occur preferentially in the core, whereas polar residues tend to occur at the surface of a folded protein. By analyzing the known protein structures, we quantify the degree to which the hydrophobicity sequence of a protein correlates with its pattern of surface exposure. We have assessed the statistical significance of this correlation for several hydrophobicity scales in the literature, and find that the computed correlations are significant but far from optimal. We show that this less than optimal correlation arises primarily from the large degree of mutations that naturally occurring proteins can tolerate. Lesser effects are due in part to forces other than hydrophobicity, and we quantify this by analyzing the surface-exposure distributions of all amino acids. Lastly, we show that our database findings are consistent with those found from an off-lattice hydrophobic-polar model of protein folding.     

Denaturant m values and heat capacity changes: relation to changes in accessible surface areas of protein unfolding.

Denaturant m values, the dependence of the free energy of unfolding on denaturant concentration, have been collected for a large set of proteins. The m value correlates very strongly with the amount of protein surface exposed to solvent upon unfolding, with linear correlation coefficients of R = 0.84 for urea and R = 0.87 for guanidine hydrochloride. These correlations improve to R = 0.90 when the effect of disulfide bonds on the accessible area of the unfolded protein is included. A similar dependence on accessible surface area has been found previously for the heat capacity change (delta Cp), which is confirmed here for our set of proteins. Denaturant m values and heat capacity changes also correlate well with each other. For proteins that undergo a simple two-state unfolding mechanism, the amount of surface exposed to solvent upon unfolding is a main structural determinant for both m values and delta Cp.     

Hydrophobicity of amino acid subgroups in proteins

Protein folding studies often utilize areas and volumes to assess the hydrophobic contribution to conformational free energy (Richards, F.M. Annu. Rev. Biophys. Bioeng. 6:151-176, 1977). We have calculated the mean area buried upon folding for every chemical group in each residue within a set of X-ray elucidated proteins. These measurements, together with a standard state cavity size for each group, are documented in a table. It is observed that, on average, each type of group buries a constant fraction of its standard state area. The mean area buried by most, though not all, groups can be closely approximated by summing contributions from three characteristic parameters corresponding to three atom types: (1) carbon or sulfur, which turn out to be 86% buried, on average; (2) neutral oxygen or nitrogen, which are 40% buried, on average; and (3) charged oxygen or nitrogen, which are 32% buried, on average.     

Electrostatic interactions play a critical role in Mycobacterium tuberculosis Hsp16.3 binding of substrate proteins

Mycobacterium tuberculosis Hsp16.3, a member of a small heat shock protein family, has chaperone-like activity in vitro and suppresses thermally or chemically induced aggregation of proteins. The nature of the interactions between Hsp16.3 and the denatured substrate proteins was investigated. A dramatic enhancement of chaperone-like activity of Hsp16.3 upon increasing temperature was accompanied by decreased ANS-detectable surface hydrophobicity. Hsp16.3 exhibited significantly enhanced chaperone-like activity after preincubation at 100°C with almost unchanged surface hydrophobicity. The interaction between Hsp16.3 and dithiothreitol-treated insulin B chains was markedly weakened in the presence of NaCl but greatly enhanced by the addition of a low-polarity alcohol, accompanied by significantly increased and decreased surface hydrophobicity, respectively. A working model for Hsp16.3 binding to its substrate proteins is proposed.     

How well can we predict native contacts in proteins based on decoy structures and their energies?

One strategy for ab initio protein structure prediction is to generate a large number of possible structures (decoys) and select the most fitting ones based on a scoring or free energy function. The conformational space of a protein is huge, and chances are rare that any heuristically generated structure will directly fall in the neighborhood of the native structure. It is desirable that, instead of being thrown away, the unfitting decoy structures can provide insights into native structures so prediction can be made progressively. First, we demonstrate that a recently parameterized physics-based effective free energy function based on the GROMOS96 force field and a generalized Born/surface area solvent model is, as several other physics-based and knowledge-based models, capable of distinguishing native structures from decoy structures for a number of widely used decoy databases. Second, we observe a substantial increase in correlations of the effective free energies with the degree of similarity between the decoys and the native structure, if the similarity is measured by the content of native inter-residue contacts in a decoy structure rather than its root-mean-square deviation from the native structure. Finally, we investigate the possibility of predicting native contacts based on the frequency of occurrence of contacts in decoy structures. For most proteins contained in the decoy databases, a meaningful amount of native contacts can be predicted based on plain frequencies of occurrence at a relatively high level of accuracy. Relative to using plain frequencies, overwhelming improvements in sensitivity of the predictions are observed for the 4_state_reduced decoy sets by applying energy-dependent weighting of decoy structures in determining the frequency. There, approximately 80% native contacts can be predicted at an accuracy of approximately 80% using energy-weighted frequencies. The sensitivity of the plain frequency approach is much lower (20% to 40%). Such improvements are, however, not observed for the other decoy databases. The rationalization and implications of the results are discussed.     

Protein folding simulation with genetic algorithm and supersecondary structure constraints

We describe an algorithm to compute native structures of proteins from their primary sequences. The novel aspects of this method are: 1) The hydrophobic potential was set to be proportional to the nonpolar solvent accessible surface. To make computation feasible, we developed a new algorithm to compute the solvent accessible surface areas rapidly. 2) The supersecondary structures of each protein were predicted and used as restraints during the conformation searching processes. This algorithm was applied to five proteins. The overall fold of these proteins can be computed from their sequences, with deviations from crystal structures of 1.48–4.48 Å for C_α atoms. Proteins 31:247–257, 1998. © 1998 Wiley-Liss, Inc.     

KFC2: a knowledge-based hot spot prediction method based on interface solvation, atomic density, and plasticity features

Hot spots constitute a small fraction of protein-protein interface residues, yet they account for a large fraction of the binding affinity. Based on our previous method (KFC), we present two new methods (KFC2a and KFC2b) that outperform other methods at hot spot prediction. A number of improvements were made in developing these new methods. First, we created a training data set that contained a similar number of hot spot and non-hot spot residues. In addition, we generated 47 different features, and different numbers of features were used to train the models to avoid over-fitting. Finally, two feature combinations were selected: One (used in KFC2a) is composed of eight features that are mainly related to solvent accessible surface area and local plasticity; the other (KFC2b) is composed of seven features, only two of which are identical to those used in KFC2a. The two models were built using support vector machines (SVM). The two KFC2 models were then tested on a mixed independent test set, and compared with other methods such as Robetta, FOLDEF, HotPoint, MINERVA, and KFC. KFC2a showed the highest predictive accuracy for hot spot residues (True Positive Rate: TPR = 0.85); however, the false positive rate was somewhat higher than for other models. KFC2b showed the best predictive accuracy for hot spot residues (True Positive Rate: TPR = 0.62) among all methods other than KFC2a, and the False Positive Rate (FPR = 0.15) was comparable with other highly predictive methods.     

A Simple Definition of Structural Regions in Proteins and Its Use in Analyzing Interface Evolution

Analysis of proteins commonly requires the partition of their structure into regions such as the surface, interior, or interface. Despite the frequent use of such categorization, no consensus definition seems to exist. This study thus aims at providing a definition that is general, is simple to implement, and yields new biological insights. This analysis relies on 397, 196, and 701 protein structures from Escherichia coli, Saccharomyces cerevisiae, and Homo sapiens, respectively, and the conclusions are consistent across all three species. A threshold of 25% relative accessible surface area best segregates amino acids at the interior and at the surface. This value is further used to extend the core-rim model of protein-protein interfaces and to introduce a third region called support. Interface core, rim, and support regions contain similar numbers of residues on average, but core residues contribute over two-thirds of the contact surface. The amino acid composition of each region remains similar across different organisms and interface types. The interface core composition is intermediate between the surface and the interior, but the compositions of the support and the rim are virtually identical with those of the interior and the surface, respectively. The support and rim could thus “preexist” in proteins, and evolving a new interaction could require mutations to form an interface core only. Using the interface regions defined, it is shown through simulations that only two substitutions are necessary to shift the average composition of a  1000-Ų surface patch involving ∼ 28 residues to that of an equivalent interface. This analysis and conclusions will help understand the notion of promiscuity in protein-protein interaction networks.