Amino acid substitutions at protein–protein interfaces that modulate the oligomeric state

Despite similarities in their sequence and structure, there are a number of homologous proteins that adopt various oligomeric states. Comparisons of these homologous protein pairs, in terms of residue substitutions at the protein–protein interfaces, have provided fundamental characteristics that describe how proteins interact with each other. We have prepared a dataset composed of pairs of related proteins with different homo‐oligomeric states. Using the protein complexes, the interface residues were identified, and using structural alignments, the shadow‐interface residues have been defined as the surface residues that align with the interface residues. Subsequently, we investigated residue substitutions between the interfaces and the shadow interfaces. Based on the degree of the contributions to the interactions, the aligned sites of the interfaces and shadow interfaces were divided into primary and secondary sites; the primary sites are the focus of this work. The primary sites were further classified into two groups (i.e. exposed and buried) based on the degree to which the residue is buried within the shadow interfaces. Using these classifications, two simple mechanisms that mediate the oligomeric states were identified. In the primary‐exposed sites, the residues on the shadow interfaces are replaced by more hydrophobic or aromatic residues, which are physicochemically favored at protein–protein interfaces. In the primary‐buried sites, the residues on the shadow interfaces are replaced by larger residues that protrude into other proteins. These simple rules are satisfied in 23 out of 25 Structural Classification of Proteins (SCOP) families with a different‐oligomeric‐state pair, and thus represent a basic strategy for modulating protein associations and dissociations. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Binding interface prediction by combining protein–protein docking results

We developed a method called residue contact frequency (RCF), which uses the complex structures generated by the protein–protein docking algorithm ZDOCK to predict interface residues. Unlike interface prediction algorithms that are based on monomers alone, RCF is binding partner specific. We evaluated the performance of RCF using the area under the precision‐recall (PR) curve (AUC) on a large protein docking Benchmark. RCF (AUC = 0.44) performed as well as meta‐PPISP (AUC = 0.43), which is one of the best monomer‐based interface prediction methods. In addition, we test a support vector machine (SVM) to combine RCF with meta‐PPISP and another monomer‐based interface prediction algorithm Evolutionary Trace to further improve the performance. We found that the SVM that combined RCF and meta‐PPISP achieved the best performance (AUC = 0.47). We used RCF to predict the binding interfaces of proteins that can bind to multiple partners and RCF was able to correctly predict interface residues that are unique for the respective binding partners. Furthermore, we found that residues that contributed greatly to binding affinity (hotspot residues) had significantly higher RCF than other residues. Proteins 2014; 82:57–66. © 2013 Wiley Periodicals, Inc.     

Protein‐spanning water networks and implications for prediction of protein–protein interactions mediated through hydrophobic effects

Hydrophobic effects, often conflated with hydrophobic forces, are implicated as major determinants in biological association and self‐assembly processes. Protein–protein interactions involved in signaling pathways in living systems are a prime example where hydrophobic effects have profound implications. In the context of protein–protein interactions, a priori knowledge of relevant binding interfaces (i.e., clusters of residues involved directly with binding interactions) is difficult. In the case of hydrophobically mediated interactions, use of hydropathy‐based methods relying on single residue hydrophobicity properties are routinely and widely used to predict propensities for such residues to be present in hydrophobic interfaces. However, recent studies suggest that consideration of hydrophobicity for single residues on a protein surface require accounting of the local environment dictated by neighboring residues and local water. In this study, we use a method derived from percolation theory to evaluate spanning water networks in the first hydration shells of a series of small proteins. We use residue‐based water density and single‐linkage clustering methods to predict hydrophobic regions of proteins; these regions are putatively involved in binding interactions. We find that this simple method is able to predict with sufficient accuracy and coverage the binding interface residues of a series of proteins. The approach is competitive with automated servers. The results of this study highlight the importance of accounting of local environment in determining the hydrophobic nature of individual residues on protein surfaces. Proteins 2014; 82:3312–3326. © 2014 Wiley Periodicals, Inc.     

Great interactions: How binding incorrect partners can teach us about protein recognition and function

Protein–protein interactions play a key part in most biological processes and understanding their mechanism is a fundamental problem leading to numerous practical applications. The prediction of protein binding sites in particular is of paramount importance since proteins now represent a major class of therapeutic targets. Amongst others methods, docking simulations between two proteins known to interact can be a useful tool for the prediction of likely binding patches on a protein surface. From the analysis of the protein interfaces generated by a massive cross‐docking experiment using the 168 proteins of the Docking Benchmark 2.0, where all possible protein pairs, and not only experimental ones, have been docked together, we show that it is also possible to predict a protein's binding residues without having any prior knowledge regarding its potential interaction partners. Evaluating the performance of cross‐docking predictions using the area under the specificity‐sensitivity ROC curve (AUC) leads to an AUC value of 0.77 for the complete benchmark (compared to the 0.5 AUC value obtained for random predictions). Furthermore, a new clustering analysis performed on the binding patches that are scattered on the protein surface show that their distribution and growth will depend on the protein's functional group. Finally, in several cases, the binding‐site predictions resulting from the cross‐docking simulations will lead to the identification of an alternate interface, which corresponds to the interaction with a biomolecular partner that is not included in the original benchmark. Proteins 2016; 84:1408–1421. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.     

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.     

Local and global anatomy of antibody‐protein antigen recognition

Deciphering antibody‐protein antigen recognition is of fundamental and practical significance. We constructed an antibody structural dataset, partitioned it into human and murine subgroups, and compared it with nonantibody protein‐protein complexes. We investigated the physicochemical properties of regions on and away from the antibody‐antigen interfaces, including net charge, overall antibody charge distributions, and their potential role in antigen interaction. We observed that amino acid preference in antibody‐protein antigen recognition is entropy driven, with residues having low side‐chain entropy appearing to compensate for the high backbone entropy in interaction with protein antigens. Antibodies prefer charged and polar antigen residues and bridging water molecules. They also prefer positive net charge, presumably to promote interaction with negatively charged protein antigens, which are common in proteomes. Antibody‐antigen interfaces have large percentages of Tyr, Ser, and Asp, but little Lys. Electrostatic and hydrophobic interactions in the Ag binding sites might be coupled with Fab domains through organized charge and residue distributions away from the binding interfaces. Here we describe some features of antibody‐antigen interfaces and of Fab domains as compared with nonantibody protein‐protein interactions. The distributions of interface residues in human and murine antibodies do not differ significantly. Overall, our results provide not only a local but also a global anatomy of antibody structures.     

Hidden partners: Using cross‐docking calculations to predict binding sites for proteins with multiple interactions

Protein‐protein interactions control a large range of biological processes and their identification is essential to understand the underlying biological mechanisms. To complement experimental approaches, in silico methods are available to investigate protein‐protein interactions. Cross‐docking methods, in particular, can be used to predict protein binding sites. However, proteins can interact with numerous partners and can present multiple binding sites on their surface, which may alter the binding site prediction quality. We evaluate the binding site predictions obtained using complete cross‐docking simulations of 358 proteins with 2 different scoring schemes accounting for multiple binding sites. Despite overall good binding site prediction performances, 68 cases were still associated with very low prediction quality, presenting individual area under the specificity‐sensitivity ROC curve (AUC) values below the random AUC threshold of 0.5, since cross‐docking calculations can lead to the identification of alternate protein binding sites (that are different from the reference experimental sites). For the large majority of these proteins, we show that the predicted alternate binding sites correspond to interaction sites with hidden partners, that is, partners not included in the original cross‐docking dataset. Among those new partners, we find proteins, but also nucleic acid molecules. Finally, for proteins with multiple binding sites on their surface, we investigated the structural determinants associated with the binding sites the most targeted by the docking partners.     

A novel method for protein-protein interaction site prediction using phylogenetic substitution models

Protein-protein binding events mediate many critical biological functions in the cell. Typically, functionally important sites in proteins can be well identified by considering sequence conservation. However, protein-protein interaction sites exhibit higher sequence variation than other functional regions, such as catalytic sites of enzymes. Consequently, the mutational behavior leading to weak sequence conservation poses significant challenges to the protein-protein interaction site prediction. Here, we present a phylogenetic framework to capture critical sequence variations that favor the selection of residues essential for protein-protein binding. Through the comprehensive analysis of diverse protein families, we show that protein binding interfaces exhibit distinct amino acid substitution as compared with other surface residues. On the basis of this analysis, we have developed a novel method, BindML, which utilizes the substitution models to predict protein-protein binding sites of protein with unknown interacting partners. BindML estimates the likelihood that a phylogenetic tree of a local surface region in a query protein structure follows the substitution patterns of protein binding interface and nonbinding surfaces. BindML is shown to perform well compared to alternative methods for protein binding interface prediction. The methodology developed in this study is very versatile in the sense that it can be generally applied for predicting other types of functional sites, such as DNA, RNA, and membrane binding sites in proteins.     

Identification of protein interaction partners and protein-protein interaction sites

Rigid-body docking has become quite successful in predicting the correct conformations of binary protein complexes, at least when the constituent proteins do not undergo large conformational changes upon binding. However, determining whether two given proteins interact is a more difficult problem. Successful docking procedures often give equally good scores for proteins that do not interact experimentally. This is the case for the multiple minimization approach we use here. An analysis of the results where all proteins within a set are docked with all other proteins (complete cross-docking) shows that the predictions can be greatly improved if the location of the correct binding interface on each protein is known, since the experimental complexes are much more likely to bring these two interfaces into contact, at the same time as yielding good interaction energy scores. While various methods exist for identifying binding interfaces, it is shown that simply studying the interaction of all potential protein pairs within a data set can itself help to identify the correct interfaces.     

Three distinct molecular surfaces in ephrin-A5 are essential for a functional interaction with EphA3

Eph receptor tyrosine kinases (Ephs) function as molecular relays that interact with cell surface-bound ephrin ligands to direct the position of migrating cells. Structural studies revealed that, through two distinct contact surfaces on opposite sites of each protein, Eph and ephrin binding domains assemble into symmetric, circular heterotetramers. However, Eph signal initiation requires the assembly of higher order oligomers, suggesting additional points of contact. By screening a random library of EphA3 binding-compromised ephrin-A5 mutants, we have now determined ephrin-A5 residues that are essential for the assembly of high affinity EphA3 signaling complexes. In addition to the two interfaces predicted from the crystal structure of the homologous EphB2.ephrin-B2 complex, we identified a cluster of 10 residues on the ephrin-A5 E alpha-helix, the E-F loop, the underlying H beta-strand, as well as the nearby B-C loop, which define a distinct third surface required for oligomerization and activation of EphA3 signaling. Together with a corresponding third surface region identified recently outside of the minimal ephrin binding domain of EphA3, our findings provide experimental evidence for the essential contribution of three distinct protein-interaction interfaces to assemble functional EphA3 signaling complexes.     

Conformation of pseudoazurin in the 152 kDa electron transfer complex with nitrite reductase determined by paramagnetic NMR

Copper-containing nitrite reductase is able to catalyze the reduction of nitrite with a turnover rate of several hundreds per second. Electrons for the reaction are donated by the electron transfer protein pseudoazurin. The process of protein complex formation, electron transfer and dissociation must occur on the millisecond timescale to enable the fast turnover of the enzyme. The structure of this transient protein complex has been studied using paramagnetic NMR spectroscopy. Gadolinium complexes were attached specifically through two engineered Cys residues on three sites on the surface of nitrite reductase, causing strong distance-dependent relaxation effects on the residues of pseudoazurin. Docking of the two proteins based on these NMR-derived distance restraints and the chemical shift perturbation data shows convergence to a cluster of structures with an average root-mean-square deviation of 1.5 Å. The binding interface consists of polar and non-polar residues surrounded by charges. The interprotein distance between the two type-1 copper sites is 15.5(± 0.5) Å, enabling fast interprotein electron transfer. The NMR-based lower limit estimate of 600 s⁻¹ for the dissociation rate constant and the fast electron transfer are consistent with the transient nature of the complex.     

The ASPP interaction network: electrostatic differentiation between pro‐ and anti‐apoptotic proteins

The ASPP proteins are apoptosis regulators: ASPP1 and ASPP2 promote, while iASPP inhibits, apoptosis. The mechanism by which these different outcomes are achieved is still unknown. The C‐terminal ankyrin repeats and SH3 domain (ANK‐SH3) mediate the interactions of the ASPP proteins with major apoptosis regulators such as p53, Bcl‐2, and NFκB. The structure of the complex between ASPP2_ANK‐SH3 and the core domain of p53 (p53CD) was previously determined. We have recently characterized the individual interactions of ASPP2_ANK‐SH3 with Bcl‐2 and NFκB, as well as a regulatory intramolecular interaction with the proline rich domain of ASPP2. Here we compared the ASPP interactions at two levels: ASPP2_ANK‐SH3 with different proteins, and different ASPP family members with each protein partner. We found that the binding sites of ASPP2 to p53CD, Bcl‐2, and NFκB are different, yet lie on the same face of ASPP2_ANK‐SH3. The intramolecular binding site to the proline rich domain overlaps the three intermolecular binding sites. To reveal the basis of functional diversity in the ASPP family, we compared their protein‐binding domains. A subset of surface‐exposed residues differentiates ASPP1 and ASPP2 from iASPP: ASPP1/2 are more negatively charged in specific residues that contact positively charged residues of p53CD, Bcl‐2, and NFκB. We also found a gain of positive charge at the non‐protein binding face of ASPP1/2, suggesting a role in electrostatic direction towards the negatively charged protein binding face. The electrostatic differences in binding interfaces between the ASPP proteins may be one of the causes for their different function. Copyright © 2010 John Wiley & Sons, Ltd.     

Interactions in native binding sites cause a large change in protein dynamics

Cellular functions are regulated by molecules that interact with proteins and alter their activities. To enable such control, protein activity, and therefore protein conformational distributions, must be susceptible to alteration by molecular interactions at functional sites. Here we investigate whether interactions at functional sites cause a large change in the protein conformational distribution. We apply a computational method, called dynamics perturbation analysis (DPA), to identify sites at which interactions have a large allosteric potential D(x), which is the Kullback-Leibler divergence between protein conformational distributions with and without an interaction. In DPA, a protein is decorated with surface points that interact with neighboring protein atoms, and D(x) is calculated for each of the points in a coarse-grained model of protein vibrations. We use DPA to examine hundreds of protein structures from a standard small-molecule docking test set, and find that ligand-binding sites have elevated values of D(x): for 95% of proteins, the probability of randomly obtaining values as high as those in the binding site is 10(-3) or smaller. We then use DPA to develop a computational method to predict functional sites in proteins, and find that the method accurately predicts ligand-binding-site residues for proteins in the test set. The performance of this method compares favorably with that of a cleft analysis method. The results confirm that interactions at small-molecule binding sites cause a large change in the protein conformational distribution, and motivate using DPA for large-scale prediction of functional sites in proteins. They also suggest that natural selection favors proteins whose activities are capable of being regulated by molecular interactions.     

Predicting permanent and transient protein–protein interfaces

Protein–protein interactions (PPIs) are involved in diverse functions in a cell. To optimize functional roles of interactions, proteins interact with a spectrum of binding affinities. Interactions are conventionally classified into permanent and transient, where the former denotes tight binding between proteins that result in strong complexes, whereas the latter compose of relatively weak interactions that can dissociate after binding to regulate functional activity at specific time point. Knowing the type of interactions has significant implications for understanding the nature and function of PPIs. In this study, we constructed amino acid substitution models that capture mutation patterns at permanent and transient type of protein interfaces, which were found to be different with statistical significance. Using the substitution models, we developed a novel computational method that predicts permanent and transient protein binding interfaces (PBIs) in protein surfaces. Without knowledge of the interacting partner, the method uses a single query protein structure and a multiple sequence alignment of the sequence family. Using a large dataset of permanent and transient proteins, we show that our method, BindML+, performs very well in protein interface classification. A very high area under the curve (AUC) value of 0.957 was observed when predicted protein binding sites were classified. Remarkably, near prefect accuracy was achieved with an AUC of 0.991 when actual binding sites were classified. The developed method will be also useful for protein design of permanent and transient PBIs. © Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Analysis and network representation of hotspots in protein interfaces using minimum cut trees

We propose a novel approach to analyze and visualize residue contact networks of protein interfaces by graph‐based algorithms using a minimum cut tree (mincut tree). Edges in the network are weighted according to an energy function derived from knowledge‐based potentials. The mincut tree, which is constructed from the weighted residue network, simplifies and summarizes the complex structure of the contact network by an efficient and informative representation. This representation offers a comprehensible view of critical residues and facilitates the inspection of their organization. We observed, on a nonredundant data set of 38 protein complexes with experimental hotspots that the highest degree node in the mincut tree usually corresponds to an experimental hotspot. Further, hotspots are found in a few paths in the mincut tree. In addition, we examine the organization of hotspots (hot regions) using an iterative clustering algorithm on two different case studies. We find that distinct hot regions are located on specific sites of the mincut tree and some critical residues hold these clusters together. Clustering of the interface residues provides information about the relation of hot regions with each other. Our new approach is useful at the molecular level for both identification of critical paths in the protein interfaces and extraction of hot regions by clustering of the interface residues. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Beauty Is in the Eye of the Beholder: Proteins Can Recognize Binding Sites of Homologous Proteins in More than One Way

Understanding the mechanisms of protein–protein interaction is a fundamental problem with many practical applications. The fact that different proteins can bind similar partners suggests that convergently evolved binding interfaces are reused in different complexes. A set of protein complexes composed of non-homologous domains interacting with homologous partners at equivalent binding sites was collected in 2006, offering an opportunity to investigate this point. We considered 433 pairs of protein–protein complexes from the ABAC database (AB and AC binary protein complexes sharing a homologous partner A) and analyzed the extent of physico-chemical similarity at the atomic and residue level at the protein–protein interface. Homologous partners of the complexes were superimposed using Multiprot, and similar atoms at the interface were quantified using a five class grouping scheme and a distance cut-off. We found that the number of interfacial atoms with similar properties is systematically lower in the non-homologous proteins than in the homologous ones. We assessed the significance of the similarity by bootstrapping the atomic properties at the interfaces. We found that the similarity of binding sites is very significant between homologous proteins, as expected, but generally insignificant between the non-homologous proteins that bind to homologous partners. Furthermore, evolutionarily conserved residues are not colocalized within the binding sites of non-homologous proteins. We could only identify a limited number of cases of structural mimicry at the interface, suggesting that this property is less generic than previously thought. Our results support the hypothesis that different proteins can interact with similar partners using alternate strategies, but do not support convergent evolution.     

Structural Determinants of Yeast Protein-Protein Interaction Interface Evolution at the Residue Level

Interfaces of contact between proteins play important roles in determining the proper structure and function of protein–protein interactions (PPIs). Therefore, to fully understand PPIs, we need to better understand the evolutionary design principles of PPI interfaces. Previous studies have uncovered that interfacial sites are more evolutionarily conserved than other surface protein sites. Yet, little is known about the nature and relative importance of evolutionary constraints in PPI interfaces. Here, we explore constraints imposed by the structure of the microenvironment surrounding interfacial residues on residue evolutionary rate using a large dataset of over 700 structural models of baker’s yeast PPIs. We find that interfacial residues are, on average, systematically more conserved than all other residues with a similar degree of total burial as measured by relative solvent accessibility (RSA). Besides, we find that RSA of the residue when the PPI is formed is a better predictor of interfacial residue evolutionary rate than RSA in the monomer state. Furthermore, we investigate four structure-based measures of residue interfacial involvement, including change in RSA upon binding (ΔRSA), number of residue-residue contacts across the interface, and distance from the center or the periphery of the interface. Integrated modeling for evolutionary rate prediction in interfaces shows that ΔRSA plays a dominant role among the four measures of interfacial involvement, with minor, but independent contributions from other measures. These results yield insight into the evolutionary design of interfaces, improving our understanding of the role that structure plays in the molecular evolution of PPIs at the residue level.     

Predicting where Small Molecules Bind at Protein-Protein Interfaces

Small molecules that bind at protein-protein interfaces may either block or stabilize protein-protein interactions in cells. Thus, some of these binding interfaces may turn into prospective targets for drug design. Here, we collected 175 pairs of protein-protein (PP) complexes and protein-ligand (PL) complexes with known three-dimensional structures for which (1) one protein from the PP complex shares at least 40% sequence identity with the protein from the PL complex, and (2) the interface regions of these proteins overlap at least partially with each other. We found that those residues of the interfaces that may bind the other protein as well as the small molecule are evolutionary more conserved on average, have a higher tendency of being located in pockets and expose a smaller fraction of their surface area to the solvent than the remaining protein-protein interface region. Based on these findings we derived a statistical classifier that predicts patches at binding interfaces that have a higher tendency to bind small molecules. We applied this new prediction method to more than 10 000 interfaces from the protein data bank. For several complexes related to apoptosis the predicted binding patches were in direct contact to co-crystallized small molecules.     

Molecular principles of the interactions of disordered proteins

Thorough knowledge of the molecular principles of protein-protein recognition is essential to our understanding of protein function at the cellular level. Whereas interactions of ordered proteins have been analyzed in great detail, complexes of intrinsically unstructured/disordered proteins (IUPs) have hardly been addressed so far. Here, we have collected a database of 39 complexes of experimentally verified IUPs, and compared their interfaces with those of 72 complexes of ordered, globular proteins. The characteristic differences found between the two types of complexes suggest that IUPs represent a distinct molecular implementation of the principles of protein-protein recognition. The interfaces do not differ in size, but those of IUPs cover a much larger part of the surface of the protein than for their ordered counterparts. Moreover, IUP interfaces are significantly more hydrophobic relative to their overall amino acid composition, but also in absolute terms. They rely more on hydrophobic-hydrophobic than on polar-polar interactions. Their amino acids in the interface realize more intermolecular contacts, which suggests a better fit with the partner due to induced folding upon binding that results in a better adaptation to the partner. The two modes of interaction also differ in that IUPs usually use only a single continuous segment for partner binding, whereas the binding sites of ordered proteins are more segmented. Probably, all these features contribute to the increased evolutionary conservation of IUP interface residues. These noted molecular differences are also manifested in the interaction energies of IUPs. Our approximation of these by low-resolution force-fields shows that IUPs gain much more stabilization energy from intermolecular contacts, than from folding, i.e. they use their binding energy for folding. Overall, our findings provide a structural rationale to the prior suggestions that many IUPs are specialized for functions realized by protein-protein interactions.     

Exploiting sequence and structure homologs to identify protein-protein binding sites

A rapid increase in the number of experimentally derived three-dimensional structures provides an opportunity to better understand and subsequently predict protein-protein interactions. In this study, structurally conserved residues were derived from multiple structure alignments of the individual components of known complexes and the assigned conservation score was weighted based on the crystallographic B factor to account for the structural flexibility that will result in a poor alignment. Sequence profile and accessible surface area information was then combined with the conservation score to predict protein-protein binding sites using a Support Vector Machine (SVM). The incorporation of the conservation score significantly improved the performance of the SVM. About 52% of the binding sites were precisely predicted (greater than 70% of the residues in the site were identified); 77% of the binding sites were correctly predicted (greater than 50% of the residues in the site were identified), and 21% of the binding sites were partially covered by the predicted residues (some residues were identified). The results support the hypothesis that in many cases protein interfaces require some residues to provide rigidity to minimize the entropic cost upon complex formation.