Shape complementarity of protein-protein complexes at multiple resolutions

Biological complexes typically exhibit intermolecular interfaces of high shape complementarity. Many computational docking approaches use this surface complementarity as a guide in the search for predicting the structures of protein-protein complexes. Proteins often undergo conformational changes to create a highly complementary interface when associating. These conformational changes are a major cause of failure for automated docking procedures when predicting binding modes between proteins using their unbound conformations. Low resolution surfaces in which high frequency geometric details are omitted have been used to address this problem. These smoothed, or blurred, surfaces are expected to minimize the differences between free and bound structures, especially those that are due to side chain conformations or small backbone deviations. Despite the fact that this approach has been used in many docking protocols, there has yet to be a systematic study of the effects of such surface smoothing on the shape complementarity of the resulting interfaces. Here we investigate this question by computing shape complementarity of a set of 66 protein-protein complexes represented by multiresolution blurred surfaces. Complexed and unbound structures are available for these protein-protein complexes. They are a subset of complexes from a nonredundant docking benchmark selected for rigidity (i.e. the proteins undergo limited conformational changes between their bound and unbound states). In this work, we construct the surfaces by isocontouring a density map obtained by accumulating the densities of Gaussian functions placed at all atom centers of the molecule. The smoothness or resolution is specified by a Gaussian fall-off coefficient, termed "blobbyness." Shape complementarity is quantified using a histogram of the shortest distances between two proteins' surface mesh vertices for both the crystallographic complexes and the complexes built using the protein structures in their unbound conformation. The histograms calculated for the bound complex structures demonstrate that medium resolution smoothing (blobbyness = -0.9) can reproduce about 88% of the shape complementarity of atomic resolution surfaces. Complexes formed from the free component structures show a partial loss of shape complementarity (more overlaps and gaps) with the atomic resolution surfaces. For surfaces smoothed to low resolution (blobbyness = -0.3), we find more consistency of shape complementarity between the complexed and free cases. To further reduce bad contacts without significantly impacting the good contacts we introduce another blurred surface, in which the Gaussian densities of flexible atoms are reduced. From these results we discuss the use of shape complementarity in protein-protein docking.     

Self-complementarity within proteins: bridging the gap between binding and folding

Complementarity, in terms of both shape and electrostatic potential, has been quantitatively estimated at protein-protein interfaces and used extensively to predict the specific geometry of association between interacting proteins. In this work, we attempted to place both binding and folding on a common conceptual platform based on complementarity. To that end, we estimated (for the first time to our knowledge) electrostatic complementarity (Em) for residues buried within proteins. Em measures the correlation of surface electrostatic potential at protein interiors. The results show fairly uniform and significant values for all amino acids. Interestingly, hydrophobic side chains also attain appreciable complementarity primarily due to the trajectory of the main chain. Previous work from our laboratory characterized the surface (or shape) complementarity (Sm) of interior residues, and both of these measures have now been combined to derive two scoring functions to identify the native fold amid a set of decoys. These scoring functions are somewhat similar to functions that discriminate among multiple solutions in a protein-protein docking exercise. The performances of both of these functions on state-of-the-art databases were comparable if not better than most currently available scoring functions. Thus, analogously to interfacial residues of protein chains associated (docked) with specific geometry, amino acids found in the native interior have to satisfy fairly stringent constraints in terms of both Sm and Em. The functions were also found to be useful for correctly identifying the same fold for two sequences with low sequence identity. Finally, inspired by the Ramachandran plot, we developed a plot of Sm versus Em (referred to as the complementarity plot) that identifies residues with suboptimal packing and electrostatics which appear to be correlated to coordinate errors.     

Protein-protein crystal-packing contacts.

Protein-protein contacts in monomeric protein crystal structures have been analyzed and compared to the physiological protein-protein contacts in oligomerization. A number of features differentiate the crystal-packing contacts from the natural contacts occurring in multimeric proteins. The area of the protein surface patches involved in packing contacts is generally smaller and its amino acid composition is indistinguishable from that of the protein surface accessible to the solvent. The fraction of protein surface in crystal contacts is very variable and independent of the number of packing contacts. The thermal motion at the crystal packing interface and that of the protein core, even for large packing interfaces, though the tendency is to be closer to that of the core. These results suggest that protein crystallization depends on random protein-protein interactions, which have little in common with physiological protein-protein recognition processes, and that the possibility of engineering macromolecular crystallization to improve crystal quality could be widened.     

Hydration of protein-protein interfaces

We present an analysis of the water molecules immobilized at the protein-protein interfaces of 115 homodimeric proteins and 46 protein-protein complexes, and compare them with 173 large crystal packing interfaces representing nonspecific interactions. With an average of 15 waters per 1000 A2 of interface area, the crystal packing interfaces are more hydrated than the specific interfaces of homodimers and complexes, which have 10-11 waters per 1000 A2, reflecting the more hydrophilic composition of crystal packing interfaces. Very different patterns of hydration are observed: Water molecules may form a ring around interfaces that remain "dry," or they may permeate "wet" interfaces. A majority of the specific interfaces are dry and most of the crystal packing interfaces are wet, but counterexamples exist in both categories. Water molecules at interfaces form hydrogen bonds with protein groups, with a preference for the main-chain carbonyl and the charged side-chains of Glu, Asp, and Arg. These interactions are essentially the same in specific and nonspecific interfaces, and very similar to those observed elsewhere on the protein surface. Water-mediated polar interactions are as abundant at the interfaces as direct protein-protein hydrogen bonds, and they may contribute to the stability of the assembly.     

Occluded molecular surface: Analysis of protein packing

We describe a novel method to calculate the packing interactions in protein structural models. The method calculates the interatomic occluded surface areas for each atom in the protein model. The identification of, and degree of interaction with, neighboring atoms is accomplished by extending surface normal from a dot surface of each atom to the point of intersection with neighboring atoms. The combined occluded and non-occluded surface areas may be normalized for the amino acid composition of the protein providing a single parameter, the normalized protein surface ratio, which is diagnostic for native-like Structures. Individual residues in the model which are in infrequent occluded surface environments may be identified. The method provides a means to explicitly describe packing densities and packing environments of individual atoms in a protein model. Finally, the method allows estimation of the complementarity between any interacting molecules, for example a ligand binding to a receptor.     

Hydrophobic complementarity in protein-protein docking

Formation of hydrophobic contacts across a newly formed interface is energetically favorable. Based on this observation we developed a geometric-hydrophobic docking algorithm that estimates quantitatively the hydrophobic complementarity at protein-protein interfaces. Each molecule to be docked is represented as a grid of complex numbers, storing information regarding the shape of the molecule in the real part and information regarding the hydropathy of the surface in the imaginary part. The grid representations are correlated using fast Fourier transformations. The algorithm is used to compare the extent of hydrophobic complementarity in oligomers (represented by D2 tetramers) and in hetero-dimers of soluble proteins (complexes). We also test the implication of hydrophobic complementarity in distinguishing correct from false docking solutions. We find that hydrophobic complementarity at the interface exists in oligomers and in complexes, and in both groups the extent of such complementarity depends on the size of the interface. Thus, the non-polar portions of large interfaces are more often juxtaposed than non-polar portions of small interfaces. Next we find that hydrophobic complementarity helps to point out correct docking solutions. In oligomers it significantly improves the ranks of nearly correct reassembled and modeled tetramers. Combining geometric, electrostatic and hydrophobic complementarity for complexes gives excellent results, ranking a nearly correct solution < 10 for 5 of 23 tested systems, < 100 for 8 systems and < 1000 for 19 systems.     

Stereochemical metrics of lectin-carbohydrate interactions: comparison with protein-protein interfaces

A global census of stereochemical metrics including interface size, hydropathy, amino acid propensities, packing and hydrogen bonding was carried out on 32 x-ray-elucidated structures of lectin-carbohydrate complexes covering eight different lectin families. It is shown that the interactions at primary binding subsites are more efficient than at other subsites. Another salient behavior found for primary subsites was a marked negative correlation between the interface size and the polar surface content. It is noteworthy that this demographic rule is delineated by lectins with unrelated phylogenetic origin, indicating that independent interface architectures have evolved through common optimization paths. The structural properties of lectin-carbohydrate interfaces were compared with those characterizing a set of 32 protein homodimers. Overall, the analysis shows that the stereochemical bases of lectin-carbohydrate and protein-protein interfaces differ drastically from each other. In comparison with protein-protein complexes, lectin-carbohydrate interfaces have superior packing efficiency, better hydrogen bonding stereochemistry, and higher interaction cooperativity. A similar conclusion holds in the comparison with protein-protein heterocomplexes. We propose that the energetic consequence of this better interaction geometry is a larger decrease in free energy per unit of area buried, feature that enables lectins and carbohydrates to form stable complexes with relatively small interface areas. These observations lend support to the emerging notion that systems differing from each other in their stereochemical metrics may rely on different energetic bases.     

Protein-protein interactions; coupling of structurally conserved residues and of hot spots across interfaces. Implications for docking

Hot spot residues contribute dominantly to protein-protein interactions. Statistically, conserved residues correlate with hot spots, and their occurrence can distinguish between binding sites and the remainder of the protein surface. The hot spot and conservation analyses have been carried out on one side of the interface. Here, we show that both experimental hot spots and conserved residues tend to couple across two-chain interfaces. Intriguingly, the local packing density around both hot spots and conserved residues is higher than expected. We further observe a correlation between local packing density and experimental deltadeltaG. Favorable conserved pairs include Gly coupled with aromatics, charged and polar residues, as well as aromatic residue coupling. Remarkably, charged residue couples are underrepresented. Overall, protein-protein interactions appear to consist of regions of high and low packing density, with the hot spots organized in the former. The high local packing density in binding interfaces is reminiscent of protein cores.     

Structural Model for the Interaction of a Designed Ankyrin Repeat Protein with the Human Epidermal Growth Factor Receptor 2

Designed Ankyrin Repeat Proteins are a class of novel binding proteins that can be selected and evolved to bind to targets with high affinity and specificity. We are interested in the DARPin H10-2-G3, which has been evolved to bind with very high affinity to the human epidermal growth factor receptor 2 (HER2). HER2 is found to be over-expressed in 30% of breast cancers, and is the target for the FDA-approved therapeutic monoclonal antibodies trastuzumab and pertuzumab and small molecule tyrosine kinase inhibitors. Here, we use computational macromolecular docking, coupled with several interface metrics such as shape complementarity, interaction energy, and electrostatic complementarity, to model the structure of the complex between the DARPin H10-2-G3 and HER2. We analyzed the interface between the two proteins and then validated the structural model by showing that selected HER2 point mutations at the putative interface with H10-2-G3 reduce the affinity of binding up to 100-fold without affecting the binding of trastuzumab. Comparisons made with a subsequently solved X-ray crystal structure of the complex yielded a backbone atom root mean square deviation of 0.84–1.14 Ångstroms. The study presented here demonstrates the capability of the computational techniques of structural bioinformatics in generating useful structural models of protein-protein interactions.     

Computational design of a new hydrogen bond network and at least a 300-fold specificity switch at a protein-protein interface

The redesign of protein-protein interactions is a stringent test of our understanding of molecular recognition and specificity. Previously we engineered a modest specificity switch into the colicin E7 DNase-Im7 immunity protein complex by identifying mutations that are disruptive in the native complex, but can be compensated by mutations on the interacting partner. Here we extend the approach by systematically sampling alternate rigid body orientations to optimize the interactions in a binding mode specific manner. Using this protocol we designed a de novo hydrogen bond network at the DNase-immunity protein interface and confirmed the design with X-ray crystallographic analysis. Subsequent design of the second shell of interactions guided by insights from the crystal structure on tightly bound water molecules, conformational strain, and packing defects yielded new binding partners that exhibited specificities of at least 300-fold between the cognate and the non-cognate complexes. This multi-step approach should be applicable to the design of polar protein-protein interactions and contribute to the re-engineering of regulatory networks mediated by protein-protein interactions.     

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.     

X-ray snapshots of the maturation of an antibody response to a protein antigen

The process whereby the immune system generates antibodies of higher affinities during a response to antigen (affinity maturation) is a prototypical example of molecular evolution. Earlier studies have been confined to antibodies specific for small molecules (haptens) rather than for proteins. We compare the structures of four antibodies bound to the same site on hen egg white lysozyme (HEL) at different stages of affinity maturation. These X-ray snapshots reveal that binding is enhanced, not through the formation of additional hydrogen bonds or van der Waals contacts or by an increase in total buried surface, but by burial of increasing amounts of apolar surface at the expense of polar surface, accompanied by improved shape complementarity. The increase in hydrophobic interactions results from highly correlated rearrangements in antibody residues at the interface periphery, adjacent to the central energetic hot spot. This first visualization of the maturation of antibodies to protein provides insights into the evolution of high affinity in other protein-protein interfaces.     

Assessing methods for identifying pair-wise atomic contacts across binding interfaces

An essential step in understanding the molecular basis of protein-protein interactions is the accurate identification of inter-protein contacts. We evaluate a number of common methods used in analyzing protein-protein interfaces: a Voronoi polyhedra-based approach, changes in solvent accessible surface area (DeltaSASA) and various radial cutoffs (closest atom, Cbeta, and centroid). First, we compared the Voronoi polyhedra-based analysis to the DeltaSASA and show that using Voronoi polyhedra finds knob-in-hole contacts. To assess the accuracy between the Voronoi polyhedra-based approach and the various radial cutoff methods, two sets of data were used: a small set of 75 experimental mutants and a larger one of 592 structures of protein-protein interfaces. In an assessment using the small set, the Voronoi polyhedra-based methods, a solvent accessible surface area method, and the closest atom radial method identified 100% of the direct contacts defined by mutagenesis data, but only the Voronoi polyhedra-based method found no false positives. The other radial methods were not able to find all of the direct contacts even using a cutoff of 9A. With the larger set of structures, we compared the overall number contacts using the Voronoi polyhedra-based method as a standard. All the radial methods using a 6-A cutoff identified more interactions, but these putative contacts included many false positives as well as missed many false negatives. While radial cutoffs are quicker to calculate as well as to implement, this result highlights why radial cutoff methods do not have the proper resolution to detail the non-homogeneous packing within protein interfaces, and suggests an inappropriate bias in pair-wise contact potentials. Of the radial cutoff methods, using the closest atom approach exhibits the best approximation to the more intensive Voronoi calculation. Our version of the Voronoi polyhedra-based method QContacts is available at .     

Examination of shape complementarity in docking of unbound proteins.

Here we carry out an examination of shape complementarity as a criterion in protein-protein docking and binding. Specifically, we examine the quality of shape complementarity as a critical determinant not only in the docking of 26 protein-protein "bound" complexed cases, but in particular, of 19 "unbound" protein-protein cases, where the structures have been determined separately. In all cases, entire molecular surfaces are utilized in the docking, with no consideration of the location of the active site, or of particular residues/atoms in either the receptor or the ligand that participate in the binding. To evaluate the goodness of the strictly geometry-based shape complementarity in the docking process as compared to the main favorable and unfavorable energy components, we study systematically a potential correlation between each of these components and the root mean square deviation (RMSD) of the "unbound" protein-protein cases. Specifically, we examine the non-polar buried surface area, polar buried surface area, buried surface area relating to groups bearing unsatisfied buried charges, and the number of hydrogen bonds in all docked protein-protein interfaces. For these cases, where the two proteins have been crystallized separately, and where entire molecular surfaces are considered without a predefinition of the binding site, no correlation is observed. None of these parameters appears to consistently improve on shape complementarity in the docking of unbound molecules. These findings argue that simplicity in the docking process, utilizing geometrical shape criteria may capture many of the essential features in protein-protein docking. In particular, they further reinforce the long held notion of the importance of molecular surface shape complementarity in the binding, and hence in docking. This is particularly interesting in light of the fact that the structures of the docked pairs have been determined separately, allowing side chains on the surface of the proteins to move relatively freely. This study has been enabled by our efficient, computer vision-based docking algorithms. The fast CPU matching times, on the order of minutes on a PC, allow such large-scale docking experiments of large molecules, which may not be feasible by other techniques. Proteins 1999;36:307-317.     

Distribution and complementarity of hydropathy in multisubunit proteins

A survey of 40 multisubunit proteins and 2 protein-protein complexes was performed to assay quantitatively the distribution of hydropathy among the exterior surface, interior, contact surface, and noncontact exterior surface of the isolated subunits. We suggest a useful way to present this distribution by using a "hydropathy level diagram." Additionally, we have devised a function called "hydropathy complementarity" to quantitate the degree to which interacting surfaces have matching hydropathy distributions. Our survey revealed the following patterns: (1) The difference in hydropathy between the interior and exterior of subunits is a fairly invariant quantity. (2) On average, the hydropathy of the contact surface is higher than that of the exterior surface, but is not greater than that of the protein as a whole. There was variation, however, among the proteins. In some instances, the contact surface was more hydrophilic than the noncontact exterior, and in a few cases the contact surface was as hydrophobic as the protein interior. (3) The average interface manifests significant hydropathy complementarity, signifying that proteins interact by placing hydrophobic centers of one surface against hydrophobic centers of the other surface, and by similarly matching hydrophilic centers. As a measure of recognition and specificity, hydropathy complementarity could be a useful tool for predicting correct docking of interacting proteins. We suggest that high hydropathy complementarity is associated with static inflexible interactions. (4) We have found that some subunits that bind predominantly through hydrophilic forces, such as hydrogen bonds, ionic pairs, and water and metal bridges, are involved in dynamic quaternary organization and allostery.     

A "solvated rotamer" approach to modeling water-mediated hydrogen bonds at protein-protein interfaces

Water-mediated hydrogen bonds play critical roles at protein-protein and protein-nucleic acid interfaces, and the interactions formed by discrete water molecules cannot be captured using continuum solvent models. We describe a simple model for the energetics of water-mediated hydrogen bonds, and show that, together with knowledge of the positions of buried water molecules observed in X-ray crystal structures, the model improves the prediction of free-energy changes upon mutation at protein-protein interfaces, and the recovery of native amino acid sequences in protein interface design calculations. We then describe a "solvated rotamer" approach to efficiently predict the positions of water molecules, at protein-protein interfaces and in monomeric proteins, that is compatible with widely used rotamer-based side-chain packing and protein design algorithms. Finally, we examine the extent to which the predicted water molecules can be used to improve prediction of amino acid identities and protein-protein interface stability, and discuss avenues for overcoming current limitations of the approach.     

The jigsaw puzzle model: search for conformational specificity in protein interiors

The jigsaw puzzle model postulates that the predominant factor relating primary sequence to three-dimensional fold lies in the stereospecific packing of interdigitating side-chains within densely packed protein interiors. An attempt has been made to check the validity of the model by means of a surface complementarity function. Out of a database of 100 highly resolved protein structures the contacts between buried hydrophobic residues (Leu, Ile, Val, Phe) and their neighbours have been categorized in terms of the extent of side-chain surface area involved in a contact (overlap) and their steric fit (Sm). The results show that the majority of contacts between a buried residue and its immediate neighbours (side-chains) are of high steric fit and in the case of extended overlap at least one of the angular parameters characterizing interresidue geometry to have pronounced deviation from a random distribution, estimated by chi(2). The calculations thus tend to support the "jigsaw puzzle" model in that 75-85% of the contacts involving hydrophobic residues are of high surface complementarity, which, coupled to high overlap, exercise fairly stringent constraints over the possible geometrical orientations between interacting residues. These constraints manifest in simple patterns in the distributions of orientational angles. Approximately 60-80% of the buried side-chain surface packs against neighbouring side-chains, the rest interacting with main-chain atoms. The latter partition of the surface maintains an equally high steric fit (relative to side-chain contacts) emphasizing a non-trivial though secondary role played by main-chain atoms in interior packing. The majority of this class of contacts, though of high complementarity, is of reduced overlap. All residues whether hydrophobic or polar/charged show similar surface complementarity measures upon burial, indicating comparable competence of all amino acids in packing effectively with their atomic environments. The specificity thus appears to be distributed over the entire network of contacts within proteins. The study concludes with a proposal to classify contacts as specific and non-specific (based on overlap and fit), with the former perhaps contributing more to the specificity between sequence and fold than the latter.