Looking at structure, stability, and evolution of proteins through the principal eigenvector of contact matrices and hydrophobicity profiles

We review and further develop an analytical model that describes how thermodynamic constraints on the stability of the native state influence protein evolution in a site-specific manner. To this end, we represent both protein sequences and protein structures as vectors: structures are represented by the principal eigenvector (PE) of the protein contact matrix, a quantity that resembles closely the effective connectivity of each site; sequences are represented through the "interactivity" of each amino acid type, using novel parameters that are correlated with hydropathy scales. These interactivity parameters are more strongly correlated than the other hydropathy scales that we examine with: (1) the change upon mutations of the unfolding free energy of proteins with two-states thermodynamics; (2) genomic properties as the genome-size and the genome-wide GC content; (3) the main eigenvectors of the substitution matrices. The evolutionary average of the interactivity vector correlates very strongly with the PE of a protein structure. Using this result, we derive an analytic expression for site-specific distributions of amino acids across protein families in the form of Boltzmann distributions whose "inverse temperature" is a function of the PE component. We show that our predictions are in agreement with site-specific amino acid distributions obtained from the Protein Data Bank, and we determine the mutational model that best fits the observed site-specific amino acid distributions. Interestingly, the optimal model almost minimizes the rate at which deleterious mutations are eliminated by natural selection.     

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.     

Identifying folding nucleus based on residue contact networks of proteins

In the native structure of a protein, all the residues are tightly parked together in a specific order following its folding and every residue contacts with some spatially neighbor residues. A residue contact network can be constructed by defining the residues as nodes and the native contacts as edges. During the folding of small single-domain proteins, there is a set of contacts (or bonds), defined as the folding nucleus (FN), which is formed around the transition state, i.e., a rate-limiting barrier located at about the middle between the unfolded states and the native state on the free energy landscape. Such a FN plays an essential role in the folding dynamics and the residues, which form the related contacts called as folding nucleus residues (FNRs). In this work, the FNRs in proteins are identified by using quantities which characterize the topology of residue contact networks of proteins. By comparing the specificities of residues with the network quantities K(R), L(R), and D(R), up to 90% FNRs of six typical proteins found experimentally are identified. It is found that the FNRs behave the full-closeness centrals rather than degree or closeness centers in the residue contact network, implying that they are important to the folding cooperativity of proteins. Our study shows that the FNRs can be identified solely from the native structures of proteins based on the analysis of residue contact network without any knowledge of the transition state ensemble.     

Prediction of probable pathways of folding in globular proteins

A method is described for the prediction of probable folding pathways of globular proteins, based on the analysis of distance maps. It is applicable to proteins of unknown spatial structure but known amino acid sequence as well as to proteins of known structure. It is based on an objective procedure for the determination of the boundary of compact regions that contain high densities of interresidue contacts on the distance map of a globular protein. The procedure can be used both with contact maps derived from a known three-dimensional protein structure and with predicted contact maps computed by means of a statistical procedure from the amino acid sequence alone. The computed contact map can also be used to predict the location of compact short-range structures, viz. -helices and -turns, thereby complementing other statistical predictive procedures. The method provides an objective basis for the derivation of a theoretically predicted pathway of protein folding, proposed by us earlier [Tanaka and Scheraga (1977) Macromolecules10, 291–304; Némethy and Scheraga (1979) Proc. Natl. Acad. Sci., U.S.A.76, 6050–6054].     

Distinct character in hydrophobicity of amino acid compositions of mitochondrial proteins

A compact mitochondrial gene contains all essential information about the synthesis of mitochondrial proteins which play their roles in a small compartment of the mitochondrium. Almost no noncoding regions have been found through the gene, but a necessary set of tRNAs for the 20 amino acids is provided for biosynthesis, some of them coding different amino acids from those in a usual cell. Since the gene is so compact that the produced proteins would have some characteristic aspects for the mitochondrium, amino acid compositions of mitochondrial proteins (mt-proteins) were examined in the 20-dimensional composition space. The results show that compositions of proteins translated from the mitochondrial genes have a distinct character having more hydrophobic content than others, which is illustrated by a clustered distribution in the multidimensional composition space. The cluster is located at the tail edge of the global distribution pattern of a Gaussian shape for other various kinds of proteins in the space. The mt-proteins are rich in hydrophobic amino acids as is a membrane protein, but are different from other membrane proteins in a lesser content of Val. A good correlation found between the base and amino acid compositions for the mitochondria was examined in comparison to those of organisms such as thermophilic bacterium having an extreme G-C-rich base composition.     

Distance-constraint approach to higher-order structures of globular proteins with empirically determined distances between amino acid residues

An analysis of higher-order structures of globular proteins by means of a distance-constraint approach is presented. Conformations are generated for each of 21 test proteins of small and medium sizes by optimizing an objective functionf=w _ij(d _ij–d _ij)², whered _ij is a distance between residuesi andj in a calculated conformation, d _ij is an assigned distance to the (ij) pair of residues which is determined based on the statistics of known three-dimensional structures of 14 proteins in the earlier study, andw _ij is a weighting factor. d _ij involves information about hydrophobicity and hydrophilicity of each amino acid residue and about connectivity of a polypeptide chain. In these calculations, only the amino acid sequence is used as input data specific to a calculated protein. With respect to higher-order structures regenerated in the optimized conformations, the following properties are analyzed: (a) N14 of a residue, defined as the number of residues surrounding the residue located within a sphere of radius of 14 Å; (b) root-mean-square differences of the global and local conformations from the corresponding X-ray conformations; (c) distance profiles in the short and medium ranges; and (d) distance maps. The effects of supplementary information about locations of secondary structures and disulfide bonds are also examined to discuss the potential ability of this methodology to predict the three-dimensional structures of globular proteins.     

Dissecting contact potentials for proteins: relative contributions of individual amino acids

Mimotopes mimic the three-dimensional topology of an antigen epitope, and are frequently recognized by antibodies with affinities comparable to those obtained for the original antibody-antigen interaction. Peptides and anti-idiotypic antibodies are two classes of protein mimotopes that mimic the topology (but not necessarily the sequence) of the parental antigen. In this study, we combine these two classes by selecting mimotopes based on single domain IgNAR antibodies, which display exceptionally long CDR3 loop regions (analogous to a constrained peptide library) presented in the context of an immunoglobulin framework with adjacent and supporting CDR1 loops. By screening an in vitro phage-display library of IgNAR variable domains (V(NAR)s) against the target antigen monoclonal antibody MAb5G8, we obtained four potential mimotopes. MAb5G8 targets a linear tripeptide epitope (AYP) in the flexible signal sequence of the Plasmodium falciparum Apical Membrane Antigen-1 (AMA1), and this or similar motifs were detected in the CDR loops of all four V(NAR)s. The V(NAR)s, 1-A-2, -7, -11, and -14, were demonstrated to bind specifically to this paratope by competition studies with an artificial peptide and all showed enhanced affinities (3-46 nM) compared to the parental antigen (175 nM). Crystallographic studies of recombinant proteins 1-A-7 and 1-A-11 showed that the SYP motifs on these V(NAR)s presented at the tip of the exposed CDR3 loops, ideally positioned within bulge-like structures to make contact with the MAb5G8 antibody. These loops, in particular in 1-A-11, were further stabilized by inter- and intra- loop disulphide bridges, hydrogen bonds, electrostatic interactions, and aromatic residue packing. We rationalize the higher affinity of the V(NAR)s compared to the parental antigen by suggesting that adjacent CDR1 and framework residues contribute to binding affinity, through interactions with other CDR regions on the antibody, though of course definitive support of this hypothesis will rely on co-crystallographic studies. Alternatively, the selection of mimotopes from a large (<4 x 10(8)) constrained library may have allowed selection of variants with even more favorable epitope topologies than present in the original antigenic structure, illustrating the power of in vivo selection of mimotopes from phage-displayed molecular libraries.     

How to guarantee optimal stability for most representative structures in the Protein Data Bank

We proposed recently an optimization method to derive energy parameters for simplified models of protein folding. The method is based on the maximization of the thermodynamic average of the overlap between protein native structures and a Boltzmann ensemble of alternative structures. Such a condition enforces protein models whose ground states are most similar to the corresponding native states. We present here an extensive testing of the method for a simple residue-residue contact energy function and for alternative structures generated by threading. The optimized energy function guarantees high stability and a well-correlated energy landscape to most representative structures in the PDB database. Failures in the recognition of the native structure can be attributed to the neglect of interactions between different chains in oligomeric proteins or with cofactors. When these are taken into account, only very few X-ray structures are not recognized. Most of them are short inhibitors or fragments and one is a structure that presents serious inconsistencies. Finally, we discuss the reasons that make NMR structures more difficult to recognizeCopyright 2001 Wiley-Liss, Inc.     

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.     

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.     

Modern and prebiotic amino acids support distinct structural profiles in proteins

The earliest proteins had to rely on amino acids available on early Earth before the biosynthetic pathways for more complex amino acids evolved. In extant proteins, a significant fraction of the ‘late’ amino acids (such as Arg, Lys, His, Cys, Trp and Tyr) belong to essential catalytic and structure-stabilizing residues. How (or if) early proteins could sustain an early biosphere has been a major puzzle. Here, we analysed two combinatorial protein libraries representing proxies of the available sequence space at two different evolutionary stages. The first is composed of the entire alphabet of 20 amino acids while the second one consists of only 10 residues (ASDGLIPTEV) representing a consensus view of plausibly available amino acids through prebiotic chemistry. We show that compact conformations resistant to proteolysis are surprisingly similarly abundant in both libraries. In addition, the early alphabet proteins are inherently more soluble and refoldable, independent of the general Hsp70 chaperone activity. By contrast, chaperones significantly increase the otherwise poor solubility of the modern alphabet proteins suggesting their coevolution with the amino acid repertoire. Our work indicates that while both early and modern amino acids are predisposed to supporting protein structure, they do so with different biophysical properties and via different mechanisms.     

Predicting protein folding rates from geometric contact and amino acid sequence

Protein folding speeds are known to vary over more than eight orders of magnitude. Plaxco, Simons, and Baker (see References) first showed a correlation of folding speed with the topology of the native protein. That and subsequent studies showed, if the native structure of a protein is known, its folding speed can be predicted reasonably well through a correlation with the "localness" of the contacts in the protein. In the present work, we develop a related measure, the geometric contact number, N (alpha), which is the number of nonlocal contacts that are well-packed, by a Voronoi criterion. We find, first, that in 80 proteins, the largest such database of proteins yet studied, N (alpha) is a consistently excellent predictor of folding speeds of both two-state fast folders and more complex multistate folders. Second, we show that folding rates can also be predicted from amino acid sequences directly, without the need to know the native topology or other structural properties.     

Correlated mutations and residue contacts in proteins

The maintenance of protein function and structure constrains the evolution of amino acid sequences. This fact can be exploited to interpret correlated mutations observed in a sequence family as an indication of probable physical contact in three dimensions. Here we present a simple and general method to analyze correlations in mutational behavior between different positions in a multiple sequence alignment. We then use these correlations to predict contact maps for each of 11 protein families and compare the result with the contacts determined by crystallography. For the most strongly correlated residue pairs predicted to be in contact, the prediction accuracy ranges from 37 to 68% and the improvement ratio relative to a random prediction from 1.4 to 5.1. Predicted contact maps can be used as input for the calculation of protein tertiary structure, either from sequence information alone or in combination with experimental information. © 1994 John Wiley & Sons, Inc.     

Sequence determinants of protein folding rates: positive correlation between contact energy and contact range indicates selection for fast folding

In comparison with intense investigation of the structural determinants of protein folding rates, the sequence features favoring fast folding have received little attention. Here, we investigate this subject using simple models of protein folding and a statistical analysis of the Protein Data Bank (PDB). The mean-field model by Plotkin and coworkers predicts that the folding rate is accelerated by stronger-than-average interactions at short distance along the sequence. We confirmed this prediction using the Finkelstein model of protein folding, which accounts for realistic features of polymer entropy. We then tested this prediction on the PDB. We found that native interactions are strongest at contact range l = 8. However, since short range contacts tend to be exposed and they are frequently formed in misfolded structures, selection for folding stability tends to make them less attractive, that is, stability and kinetics may have contrasting requirements. Using a recently proposed model, we predicted the relationship between contact range and contact energy based on buriedness and contact frequency. Deviations from this prediction induce a positive correlation between contact range and contact energy, that is, short range contacts are stronger than expected, for 2/3 of the proteins. This correlation increases with the absolute contact order (ACO), as expected if proteins that tend to fold slowly due to large ACO are subject to stronger selection for sequence features favoring fast folding. Our results suggest that the selective pressure for fast folding is detectable only for one third of the proteins in the PDB, in particular those with large contact order.     

Importance of hydrophobic cluster formation through long-range contacts in the folding transition state of two-state proteins

Understanding the folding pathways of proteins is a challenging task. The Phi value approach provides a detailed understanding of transition-state structures of folded proteins. In this work, we have computed the hydrophobicity associated with each residue in the folded state of 16 two-state proteins and compared the Phi values of each mutant residue. We found that most of the residues with high Phi value coincide with local maximum in surrounding hydrophobicity, or have nearby residues that show such maximum in hydrophobicity, indicating the importance of hydrophobic interactions in the transition state. We have tested our approach to different structural classes of proteins, such as alpha-helical, SH3 domains of all-beta proteins, beta-sandwich, and alpha/beta proteins, and we observed a good agreement with experimental results. Further, we have proposed a hydrophobic contact network pattern to relate the Phi values with long-range contacts, which will be helpful to understand the transition-state structures of folded proteins. The present approach could be used to identify potential hydrophobic clusters that may form through long-range contacts during the transition state.     

Towards accurate residue-residue hydrophobic contact prediction for alpha helical proteins via integer linear optimization

A new optimization-based method is presented to predict the hydrophobic residue contacts in alpha-helical proteins. The proposed approach uses a high resolution distance dependent force field to calculate the interaction energy between different residues of a protein. The formulation predicts the hydrophobic contacts by minimizing the sum of these contact energies. These residue contacts are highly useful in narrowing down the conformational space searched by protein structure prediction algorithms. The proposed algorithm also offers the algorithmic advantage of producing a rank ordered list of the best contact sets. This model was tested on four independent alpha-helical protein test sets and was found to perform very well. The average accuracy of the predictions (separated by at least six residues) obtained using the presented method was approximately 66% for single domain proteins. The average true positive and false positive distances were also calculated for each protein test set and they are 8.87 and 14.67 A, respectively.