Hydrophobic folding units at protein-protein interfaces: implications to protein folding and to protein-protein association.

A hydrophobic folding unit cutting algorithm, originally developed for dissecting single-chain proteins, has been applied to a dataset of dissimilar two-chain protein-protein interfaces. Rather than consider each individual chain separately, the two-chain complex has been treated as a single chain. The two-chain parsing results presented in this work show hydrophobicity to be a critical attribute of two-state versus three-state protein-protein complexes. The hydrophobic folding units at the interfaces of two-state complexes suggest that the cooperative nature of the two-chain protein folding is the outcome of the hydrophobic effect, similar to its being the driving force in a single-chain folding. In analogy to the protein-folding process, the two-chain, two-state model complex may correspond to the formation of compact, hydrophobic nuclei. On the other hand, the three-state model complex involves binding of already folded monomers, similar to the association of the hydrophobic folding units within a single chain. The similarity between folding entities in protein cores and in two-state protein-protein interfaces, despite the absence of some chain connectivities in the latter, indicates that chain linkage does not necessarily affect the native conformation. This further substantiates the notion that tertiary, non-local interactions play a critical role in protein folding. These compact, hydrophobic, two-chain folding units, derived from structurally dissimilar protein-protein interfaces, provide a rich set of data useful in investigations of the role played by chain connectivity and by tertiary interactions in studies of binding and of folding. Since they are composed of non-contiguous pieces of protein backbones, they may also aid in defining folding nuclei.     

Structural motifs at protein-protein interfaces: protein cores versus two-state and three-state model complexes.

The general similarity in the forces governing protein folding and protein-protein associations has led us to examine the similarity in the architectural motifs between the interfaces and the monomers. We have carried out extensive, all-against-all structural comparisons between the single-chain protein structural dataset and the interface dataset, derived both from all protein-protein complexes in the structural database and from interfaces generated via an automated crystal symmetry operation. We show that despite the absence of chain connections, the global features of the architectural motifs, present in monomers, recur in the interfaces, a reflection of the limited set of the folding patterns. However, although similarity has been observed, the details of the architectural motifs vary. In particular, the extent of the similarity correlates with the consideration of how the interface has been formed. Interfaces derived from two-state model complexes, where the chains fold cooperatively, display a considerable similarity to architectures in protein cores, as judged by the quality of their geometric superposition. On the other hand, the three-state model interfaces, representing binding of already folded molecules, manifest a larger variability and resemble the monomer architecture only in general outline. The origin of the difference between the monomers and the three-state model interfaces can be understood in terms of the different nature of the folding and the binding that are involved. Whereas in the former all degrees of freedom are available to the backbone to maximize favorable interactions, in rigid body, three-state model binding, only six degrees of freedom are allowed. Hence, residue or atom pair-wise potentials derived from protein-protein associations are expected to be less accurate, substantially increasing the number of computationally acceptable alternate binding modes (Finkelstein et al., 1995).     

An iterative knowledge-based scoring function for protein-protein recognition

Using an efficient iterative method, we have developed a distance-dependent knowledge-based scoring function to predict protein-protein interactions. The function, referred to as ITScore-PP, was derived using the crystal structures of a training set of 851 protein-protein dimeric complexes containing true biological interfaces. The key idea of the iterative method for deriving ITScore-PP is to improve the interatomic pair potentials by iteration, until the pair potentials can distinguish true binding modes from decoy modes for the protein-protein complexes in the training set. The iterative method circumvents the challenging reference state problem in deriving knowledge-based potentials. The derived scoring function was used to evaluate the ligand orientations generated by ZDOCK 2.1 and the native ligand structures on a diverse set of 91 protein-protein complexes. For the bound test cases, ITScore-PP yielded a success rate of 98.9% if the top 10 ranked orientations were considered. For the more realistic unbound test cases, the corresponding success rate was 40.7%. Furthermore, for faster orientational sampling purpose, several residue-level knowledge-based scoring functions were also derived following the similar iterative procedure. Among them, the scoring function that uses the side-chain center of mass (SCM) to represent a residue, referred to as ITScore-PP(SCM), showed the best performance and yielded success rates of 71.4% and 30.8% for the bound and unbound cases, respectively, when the top 10 orientations were considered. ITScore-PP was further tested using two other published protein-protein docking decoy sets, the ZDOCK decoy set and the RosettaDock decoy set. In addition to binding mode prediction, the binding scores predicted by ITScore-PP also correlated well with the experimentally determined binding affinities, yielding a correlation coefficient of R = 0.71 on a test set of 74 protein-protein complexes with known affinities. ITScore-PP is computationally efficient. The average run time for ITScore-PP was about 0.03 second per orientation (including optimization) on a personal computer with 3.2 GHz Pentium IV CPU and 3.0 GB RAM. The computational speed of ITScore-PP(SCM) is about an order of magnitude faster than that of ITScore-PP. ITScore-PP and/or ITScore-PP(SCM) can be combined with efficient protein docking software to study protein-protein recognition.     

Similar chemistry, but different bond preferences in inter versus intra-protein interactions

Proteins fold into a well-defined structure as a result of the collapse of the polypeptide chain, while transient protein-complex formation mainly is a result of binding of two folded individual monomers. Therefore, a protein-protein interface does not resemble the core of monomeric proteins, but has a more polar nature. Here, we address the question of whether the physico-chemical characteristics of intraprotein versus interprotein bonds differ, or whether interfaces are different from folded monomers only in the preference for certain types of interactions. To address this question we assembled a high resolution, nonredundant, protein-protein interaction database consisting of 1374 homodimer and 572 heterodimer complexes, and compared the physico-chemical properties of these interactions between protein interfaces and monomers. We performed extensive statistical analysis of geometrical properties of interatomic interactions of different types: hydrogen bonds, electrostatic interactions, and aromatic interactions. Our study clearly shows that there is no significant difference in the chemistry, geometry, or packing density of individual interactions between interfaces and monomeric structures. However, the distribution of different bonds differs. For example, side-chain-side-chain interactions constitute over 62% of all interprotein interactions, while they make up only 36% of the bonds stabilizing a protein structure. As on average, properties of backbone interactions are different from those of side chains, a quantitative difference is observed. Our findings clearly show that the same knowledge-based potential can be used for protein-binding sites as for protein structures. However, one has to keep in mind the different architecture of the interfaces and their unique bond preference.     

Development of unified statistical potentials describing protein-protein interactions

A residue-based and a heavy atom-based statistical pair potential are developed for use in assessing the strength of protein-protein interactions. To ensure the quality of the potentials, a nonredundant, high-quality dimer database is constructed. The protein complexes in this dataset are checked by a literature search to confirm that they form multimers, and the pairwise amino acid preference to interact across a protein-protein interface is analyzed and pair potentials constructed. The performance of the residue-based potentials is evaluated by using four jackknife tests and by assessing the potentials' ability to select true protein-protein interfaces from false ones. Compared to potentials developed for monomeric protein structure prediction, the interdomain potential performs much better at distinguishing protein-protein interactions. The potential developed from homodimer interfaces is almost the same as that developed from heterodimer interfaces with a correlation coefficient of 0.92. The residue-based potential is well suited for genomic scale protein interaction prediction and analysis, such as in a recently developed threading-based algorithm, MULTIPROSPECTOR. However, the more time-consuming atom-based potential performs better in identifying near-native structures from docking generated decoys.     

Comprehensive statistical analysis of residues interaction specificity at protein-protein interfaces

We calculated interchain contacts on the atomic level for nonredundant set of 4602 protein-protein interfaces using an unbiased Voronoi-Delaune tessellation method, and made 20x20 residue contact matrixes both for homodimers and heterocomplexes. The area of contacts and the distance distribution for these contacts were calculated on both the residue and the atomic levels. We analyzed residue area distribution and showed the existence of two types of interresidue contacts: stochastic and specific. We also derived formulas describing the distribution of contact area for stochastic and specific interactions in parametric form. Maximum pairing preference index was found for Cys-Cys contacts and for oppositely charged interactions. A significant difference in residue contacts was observed between homodimers and heterocomplexes. Interfaces in homodimers were enriched with contacts between residues of the same type due to the effects of structure symmetry.     

Cation-pi interactions in protein-protein interfaces

Arginine is an abundant residue in protein-protein interfaces. The importance of this residue relates to the versatility of its side chain in intermolecular interactions. Different classes of protein-protein interfaces were surveyed for cation-pi interactions. Approximately half of the protein complexes and one-third of the homodimers analyzed were found to contain at least one intermolecular cation-pi pair. Interactions between arginine and tyrosine were found to be the most abundant. The electrostatic interaction energy was calculated to be approximately 3 kcal/mol, on average. A distance-based search of guanidinium:aromatic interactions was also performed using the Macromolecular Structure Database (MSD). This search revealed that half of the guanidinium:aromatic pairs pack in a coplanar manner. Furthermore, it was found that the cationic group of the cation-pi pair is frequently involved in intermolecular hydrogen bonds. In this manner the arginine side chain can participate in multiple interactions, providing a mechanism for inter-protein specificity. Thus, the cation-pi interaction is established as an important contributor to protein-protein interfaces.     

MULTIPROSPECTOR: an algorithm for the prediction of protein-protein interactions by multimeric threading

In this postgenomic era, the ability to identify protein-protein interactions on a genomic scale is very important to assist in the assignment of physiological function. Because of the increasing number of solved structures involving protein complexes, the time is ripe to extend threading to the prediction of quaternary structure. In this spirit, a multimeric threading approach has been developed. The approach is comprised of two phases. In the first phase, traditional threading on a single chain is applied to generate a set of potential structures for the query sequences. In particular, we use our recently developed threading algorithm, PROSPECTOR. Then, for those proteins whose template structures are part of a known complex, we rethread on both partners in the complex and now include a protein-protein interfacial energy. To perform this analysis, a database of multimeric protein structures has been constructed, the necessary interfacial pairwise potentials have been derived, and a set of empirical indicators to identify true multimers based on the threading Z-score and the magnitude of the interfacial energy have been established. The algorithm has been tested on a benchmark set comprised of 40 homodimers, 15 heterodimers, and 69 monomers that were scanned against a protein library of 2478 structures that comprise a representative set of structures in the Protein Data Bank. Of these, the method correctly recognized and assigned 36 homodimers, 15 heterodimers, and 65 monomers. This protocol was applied to identify partners and assign quaternary structures of proteins found in the yeast database of interacting proteins. Our multimeric threading algorithm correctly predicts 144 interacting proteins, compared to the 56 (26) cases assigned by PSI-BLAST using a (less) permissive E-value of 1 (0.01). Next, all possible pairs of yeast proteins have been examined. Predictions (n = 2865) of protein-protein interactions are made; 1138 of these 2865 interactions have counterparts in the Database of Interacting Proteins. In contrast, PSI-BLAST made 1781 predictions, and 1215 have counterparts in DIP. An estimation of the false-negative rate for yeast-predicted interactions has also been provided. Thus, a promising approach to help assist in the assignment of protein-protein interactions on a genomic scale has been developed.     

A knowledge-based forcefield for protein-protein interface design

A distance-dependent knowledge-based potential for protein-protein interactions is derived and tested for application in protein design. Information on residue type specific C(alpha) and C(beta) pair distances is extracted from complex crystal structures in the Protein Data Bank and used in the form of radial distribution functions. The use of only backbone and C(beta) position information allows generation of relative protein-protein orientation poses with minimal sidechain information. Further coarse-graining can be done simply in the same theoretical framework to give potentials for residues of known type interacting with unknown type, as in a one-sided interface design problem. Both interface design via pose generation followed by sidechain repacking and localized protein-protein docking tests are performed on 39 nonredundant antibody-antigen complexes for which crystal structures are available. As reference, Lennard-Jones potentials, unspecific for residue type and biasing toward varying degrees of residue pair separation are used as controls. For interface design, the knowledge-based potentials give the best combination of consistently designable poses, low RMSD to the known structure, and more tightly bound interfaces with no added computational cost. 77% of the poses could be designed to give complexes with negative free energies of binding. Generally, larger interface separation promotes designability, but weakens the binding of the resulting designs. A localized docking test shows that the knowledge-based nature of the potentials improves performance and compares respectably with more sophisticated all-atoms potentials.     

A dissection of specific and non-specific protein-protein interfaces

We compare the geometric and physical-chemical properties of interfaces involved in specific and non-specific protein-protein interactions in crystal structures reported in the Protein Data Bank. Specific interactions are illustrated by 70 protein-protein complexes and by subunit contacts in 122 homodimeric proteins; non-specific interactions are illustrated by 188 pairs of monomeric proteins making crystal-packing contacts selected to bury more than 800 A2 of protein surface. A majority of these pairs have 2-fold symmetry and form "crystal dimers" that cannot be distinguished from real dimers on the basis of the interface size or symmetry. The chemical and amino acid compositions of the large crystal-packing interfaces resemble the protein solvent-accessible surface. These interfaces are less hydrophobic than in homodimers and contain much fewer fully buried atoms. We develop a residue propensity score and a hydrophobic interaction score to assess preferences seen in the chemical and amino acid compositions of the different types of interfaces, and we derive indexes to evaluate the atomic packing, which we find to be less compact at non-specific than at specific interfaces. We test the capacity of these parameters to identify homodimeric proteins in crystal structures, and show that a simple combination of the non-polar interface area and the fraction of buried interface atoms assigns the quaternary structure of 88% of the homodimers and 77% of the monomers in our data set correctly. These success rates increase to 93-95% when the residue propensity score of the interfaces is taken into consideration.     

Studies of protein-protein interfaces: a statistical analysis of the hydrophobic effect.

Data sets of 362 structurally nonredundant protein-protein interfaces and of 57 symmetry-related oligomeric interfaces have been used to explore whether the hydrophobic effect that guides protein folding is also the main driving force for protein-protein associations. The buried nonpolar surface area has been used to measure the hydrophobic effect. Our analysis indicates that, although the hydrophobic effect plays a dominant role in protein-protein binding, it is not as strong as that observed in the interior of protein monomers. Comparison of interiors of the monomers with those of the interfaces reveals that, in general, the hydrophobic amino acids are more frequent in the interior of the monomers than in the interior of the protein-protein interfaces. On the other hand, a higher proportion of charged and polar residues are buried at the interfaces, suggesting that hydrogen bonds and ion pairs contribute more to the stability of protein binding than to that of protein folding. Moreover, comparison of the interior of the interfaces to protein surfaces indicates that the interfaces are poorer in polar/charged than the surfaces and are richer in hydrophobic residues. The interior of the interfaces appears to constitute a compromise between the stabilization contributed by the hydrophobic effect on the one hand and avoiding patches on the protein surfaces that are too hydrophobic on the other. Such patches would be unfavorable for the unassociated monomers in solution. We conclude that, although the types of interactions are similar between protein-protein interfaces and single-chain proteins overall, the contribution of the hydrophobic effect to protein-protein associations is not as strong as to protein folding. This implies that packing patterns and interatom, or interresidue, pairwise potential functions, derived from monomers, are not ideally suited to predicting and assessing ligand associations or design. These would perform adequately only in cases where the hydrophobic effect at the binding site is substantial.     

FRET microscopy in the living cell: different approaches, strengths and weaknesses

New imaging methodologies in quantitative fluorescence microscopy, such as F?rster resonance energy transfer (FRET), have been developed in the last few years and are beginning to be extensively applied to biological problems. FRET is employed for the detection and quantification of protein interactions, and of biochemical activities. Herein, we review the different methods to measure FRET in microscopy, and more importantly, their strengths and weaknesses. In our opinion, fluorescence lifetime imaging microscopy (FLIM) is advantageous for detecting inter-molecular interactions quantitatively, the intensity ratio approach representing a valid and straightforward option for detecting intra-molecular FRET. Promising approaches in single molecule techniques and data analysis for quantitative and fast spatio-temporal protein-protein interaction studies open new avenues for FRET in biological research.     

Potential of mean force for protein-protein interaction studies.

Calculating protein-protein interaction energies is crucial for understanding protein-protein associations. On the basis of the methodology of mean-field potential, we have developed an empirical approach to estimate binding free energy for protein-protein interactions. This knowledge-based approach has been used to derive distance-dependent free energies of protein complexes from a nonredundant training set in the Protein Data Bank (PDB), with a careful treatment of homology. We calculate atom pair potentials for 16 pair interactions, which can reflect the importance of hydrophobic interactions and specific hydrogen-bonding interactions. The derived potentials for hydrogen-bonding interactions show a valley of favorable interactions at a distance of approximately 3 A, corresponding to that of an established hydrogen bond. For the test set of 28 protein complexes, the calculated energies have a correlation coefficient of 0.75 compared with experimental binding free energies. The performance of the method in ranking the binding energies of different protein-protein complexes shows that the energy estimation can be applied to value binding free energies for protein-protein associations.     

A new, structurally nonredundant, diverse data set of protein-protein interfaces and its implications

Here, we present a diverse, structurally nonredundant data set of two-chain protein-protein interfaces derived from the PDB. Using a sequence order-independent structural comparison algorithm and hierarchical clustering, 3799 interface clusters are obtained. These yield 103 clusters with at least five nonhomologous members. We divide the clusters into three types. In Type I clusters, the global structures of the chains from which the interfaces are derived are also similar. This cluster type is expected because, in general, related proteins associate in similar ways. In Type II, the interfaces are similar; however, remarkably, the overall structures and functions of the chains are different. The functional spectrum is broad, from enzymes/inhibitors to immunoglobulins and toxins. The fact that structurally different monomers associate in similar ways, suggests "good" binding architectures. This observation extends a paradigm in protein science: It has been well known that proteins with similar structures may have different functions. Here, we show that it extends to interfaces. In Type III clusters, only one side of the interface is similar across the cluster. This structurally nonredundant data set provides rich data for studies of protein-protein interactions and recognition, cellular networks and drug design. In particular, it may be useful in addressing the difficult question of what are the favorable ways for proteins to interact. (The data set is available at http://protein3d.ncifcrf.gov/~keskino/ and http://home.ku.edu.tr/~okeskin/INTERFACE/INTERFACES.html.)     

A combinatorial score to distinguish biological and nonbiological protein-protein interfaces

With the large amount of protein-protein complex structural data available, to understand the key features governing the specificity of protein-protein recognition and to define a suitable scoring function for protein-protein interaction predictions, we have analyzed the protein interfaces from geometric and energetic points of view. Atom-based potential of mean force (PMFScore), packing density, contact size, and geometric complementarity are calculated for crystal contacts in 74 homodimers and 91 monomers, which include real biological interactions in dimers and nonbiological contacts in monomers and dimers. Simple cutoffs were developed for single and combinatorial parameters to distinguish biological and nonbiological contacts. The results show that PMFScore is a better discriminator between biological and nonbiological interfaces comparable in size. The combination of PMFScore and contact size is the most powerful pairwise discriminator. A combinatorial score (CFPScore) based on the four parameters was developed, which gives the success rate of the homodimer discrimination of 96.6% and error rate of the monomer discrimination of 6.0% and 19.8% according to Valdar's and our definition, respectively. Compared with other statistical learning models, the cutoffs for the four parameters and their combinations are directly based on physical models, simple, and can be easily applied to protein-protein interface analysis and docking studies.     

Charged residues at protein interaction interfaces: unexpected conservation and orchestrated divergence

Protein-protein interactions play an essential role in the functioning of cell. The importance of charged residues and their diverse role in protein-protein interactions have been well studied using experimental and computational methods. Often, charged residues located in protein interaction interfaces are conserved across the families of homologous proteins and protein complexes. However, on a large scale, it has been recently shown that charged residues are significantly less conserved than other residue types in protein interaction interfaces. The goal of this work is to understand the role of charged residues in the protein interaction interfaces through their conservation patterns. Here, we propose a simple approach where the structural conservation of the charged residue pairs is analyzed among the pairs of homologous binary complexes. Specifically, we determine a large set of homologous interactions using an interaction interface similarity measure and catalog the basic types of conservation patterns among the charged residue pairs. We find an unexpected conservation pattern, which we call the correlated reappearance, occurring among the pairs of homologous interfaces more frequently than the fully conserved pairs of charged residues. Furthermore, the analysis of the conservation patterns across different superkingdoms as well as structural classes of proteins has revealed that the correlated reappearance of charged residues is by far the most prevalent conservation pattern, often occurring more frequently than the unconserved charged residues. We discuss a possible role that the new conservation pattern may play in the long-range electrostatic steering effect.     

Folding of beta/alpha-unit scrambled forms of S. cerevisiae triosephosphate isomerase: Evidence for autonomy of substructure formation and plasticity of hydrophobic and hydrogen bonding interactions in core of (beta/alpha)8-barrel

We show that residues at the interfaces of protein-protein complexes have higher side-chain energy than other surface residues. Eight different sets of protein complexes were analyzed. For each protein pair, the complex structure was used to identify the interface residues in the unbound monomer structures. Side-chain energy was calculated for each surface residue in the unbound monomer using our previously developed scoring function.1 The mean energy was calculated for the interface residues and the other surface residues. In 15 of the 16 monomers, the mean energy of the interface residues was higher than that of other surface residues. By decomposing the scoring function, we found that the energy term of the buried surface area of non-hydrogen-bonded hydrophilic atoms is the most important factor contributing to the high energy of the interface regions. In spite of lacking hydrophilic residues, the interface regions were found to be rich in buried non-hydrogen-bonded hydrophilic atoms. Although the calculation results could be affected by the inaccuracy of the scoring function, patch analysis of side-chain energy on the surface of an isolated protein may be helpful in identifying the possible protein-protein interface. A patch was defined as 20 residues surrounding the central residue on the protein surface, and patch energy was calculated as the mean value of the side-chain energy of all residues in the patch. In 12 of the studied monomers, the patch with the highest energy overlaps with the observed interface. The results are more remarkable when only three residues with the highest energy in a patch are averaged to derive the patch energy. All three highest-energy residues of the top energy patch belong to interfacial residues in four of the eight small protomers. We also found that the residue with the highest energy score on the surface of a small protomer is very possibly the key interaction residue.     

A method for computing the inter-residue interaction potentials for reduced amino acid alphabet

Inter-residue potentials are extensively used in the design and evaluation of protein structures. However,dealing with all (20 x 20) interactions becomes computationally difficult in extensive investigations. Hence, it is desirable to reduce the alphabet of 20 amino acids to a smaller number. Currently, several methods of reducing the residue types exist; however a critical assessment of these methods is not available. Towards this goal,here we review and evaluate different methods by comparing with the complete (20 x 20) matrix of Miyazawa-Jernigan potential, including a method of grouping adopted by us, based on multi dimensional scaling (MDS). The second goal of this paper is the computation of inter-residue interaction energies for the reduced amino acid alphabet, which has not been explicitly addressed in the literature until now. By using a least squares technique, we present a systematic method of obtaining the interaction energy values for any type of grouping scheme that reduces the amino acid alphabet. This can be valuable in designing the protein structures.     

An algorithm for predicting protein-protein interaction sites: Abnormally exposed amino acid residues and secondary structure elements

Multiprotein systems mediate most regulatory processes in living organisms. Although the structures of the individual proteins are often defined, less is known of the structures of multiprotein systems. Computational methods for predicting interfaces, using evolutionary conservation and/or physicochemical data, have been developed. Here we consider the use of solvent accessibility, residue propensity, and hydrophobicity, in conjunction with secondary structure data, as prediction parameters. We analyze the influence of residue type and secondary structure on solvent accessibility and define a measure of "relative exposedness." Clustering abnormally high scoring residues provides a basis for predicting interaction sites. The analysis is extended to investigate abnormally exposed secondary structure elements, particularly beta-sheet strands. We show that surface-exposed beta-strands lacking protective features are more likely to be found at protein-protein interfaces, allowing us to create an algorithm with approximately 68% and approximately 75% accuracy in differentiating between interacting and edge strands in isolated beta-strands and beta-sheet strands, respectively. These methods of identifying abnormally exposed surface regions are combined in an algorithm, which, on a data set of 77 unbound and disjoint (single chain extracted from complex) structures, predicts 79% of the protein-protein interfaces correctly. If enzyme-inhibitor complexes, where the inhibitor mimics a nonprotein substrate, are excluded, the accuracy increases to 85%.     

Inter-residue interactions in protein structures exhibit power-law behavior

Inter-residue interactions play an essential role in driving protein folding, and analysis of these interactions increases our understanding of protein folding and stability and facilitates the development of tools for protein structure and function prediction. In this work, we systematically characterized the change of inter-residue interactions at various sequence separation cutoffs using two protein datasets. The first set included 100 diverse, nonredundant and high-resolution soluble protein structures, covering all four major structural classes, all-alpha, alpha/beta, alpha+beta, and all-beta; and the second set included 20 diverse, nonredundant and high-resolution membrane protein structures, representing 19 unique superfamilies. It was shown that the average number of inter-residue interactions in structures of both datasets displays the power-law behavior. Fitting parameters of the power-law function are directly related to the structural classes analyzed. These findings provided further insight into the distribution of short-, medium-, and long-range inter-residue interactions in both soluble and membrane proteins and could be used for protein structure prediction.