Beyond the rotamer library: genetic algorithm combined with the disturbing mutation process for upbuilding protein side-chains

The disturbing genetic algorithm, incorporating the disturbing mutation process into the genetic algorithm flow, has been developed to extend the searching space of side-chain conformations and to improve the quality of the rotamer library. Moreover, the growing generation amount idea, simulating the real situation of the natural evolution, is introduced to improve the searching speed. In the calculations using the pseudo energy scoring function of the root mean squared deviation, the disturbing genetic algorithm method has been shown to be highly efficient. With the real energy function based on AMBER force field, the program has been applied to rebuilding side-chain conformations of 25 high-quality crystallographic structures of single-protein and protein-protein complexes. The averaged root mean standard deviation of atom coordinates in side-chains and veracities of the torsion angles of chi(1) and chi(1) + chi(2) are 1.165 A, 88.2 and 72.9% for the buried residues, respectively, and 1.493 A, 79.2 and 64.7% for all residues, showing that the method has equal precision to the program SCWRL, whereas it performs better in the prediction of buried residues and protein-protein interfaces. This method has been successfully used in redesigning the interface of the Basnase-Barstar complex, indicating that it will have extensive application in protein design, protein sequence and structure relationship studies, and research on protein-protein interaction.     

On the contribution of water-mediated interactions to protein-complex stability

Protein-water interactions have long been recognized as a major determinant of chain folding, conformational stability, binding specificity and catalysis. However, the detailed effects of water on stabilizing protein-protein interactions remain elusive. A way to test experimentally the contribution of water-mediated interactions is by applying double mutant cycle analysis on pairs of residues that do not form direct interactions, but are bridged by water. Seven such interactions within the interface between TEM1 and BLIP proteins were evaluated. No significant interaction free energy was found between either of them. Water can bridge interactions, but also stabilize the structure of the monomer. To distinguish between these, we performed a bioinformatic analysis using AQUAPROT (http://bioinfo.weizmann.ac.il/aquaprot) to determine the degree of water conservation between the bound and unbound states. 29 structures of twelve complexes and 20 related monomers were analyzed. Of the 262 water molecules located within the interfaces, 145 were conserved between the unbound and bound structures. Strikingly, all 50 buried or partially buried waters in the monomer structures were conserved at the same location in the bound structures. Thus, buried waters have an important role in stabilizing the monomer fold rather than contributing to protein-protein binding, and are not replaced by residues from the incoming protein. Taking together the experimental and bioinformatics evidence suggests that exposed waters within the interface may be good sites for protein engineering, while buried or mostly buried waters should be left unchanged.     

Side-chain entropy effects on protein secondary structure formation

Loss of conformational entropy is one of the primary factors opposing protein folding. Both the backbone and side-chain of each residue in a protein will have their freedom of motion restricted in the final folded structure. The type of secondary structure of which a residue is part will have a significant impact on how much side-chain entropy is lost. Side-chain conformational entropies have previously been determined for folded proteins, simple models of unfolded proteins, alpha-helices, and a dipeptide model for beta-strands, but not for polyproline II (PII) helices. In this work, we present side-chain conformational estimates for the three regular secondary structure types: alpha-helices, beta-strands, and PII helices. Entropies are estimated from Monte Carlo computer simulations. Beta-strands are modeled as two structures, parallel and antiparallel beta-strands. Our data indicate that restraining a residue to the PII helix or antiparallel beta-strand conformations results in side-chain entropies equal to or higher than those obtained by restraining residues to the parallel beta-strand conformation. Side-chains in the alpha-helix conformation have the lowest side-chain entropies. The observation that extended structures retain the most side-chain entropy suggests that such structures would be entropically favored in unfolded proteins under folding conditions. Our data indicate that the PII helix conformation would be somewhat favored over beta-strand conformations, with antiparallel beta-strand favored over parallel. Notably, our data imply that, under some circumstances, residues may gain side-chain entropy upon folding. Implications of our findings for protein folding and unfolded states are discussed.     

Protein-protein interactions: hot spots and structurally conserved residues often locate in complemented pockets that pre-organized in the unbound states: implications for docking

Energetic hot spots account for a significant portion of the total binding free energy and correlate with structurally conserved interface residues. Here, we map experimentally determined hot spots and structurally conserved residues to investigate their geometrical organization. Unfilled pockets are pockets that remain unfilled after protein-protein complexation, while complemented pockets are pockets that disappear upon binding, representing tightly fit regions. We find that structurally conserved residues and energetic hot spots are strongly favored to be located in complemented pockets, and are disfavored in unfilled pockets. For the three available protein-protein complexes with complemented pockets where both members of the complex were alanine-scanned, 62% of all hot spots (DeltaDeltaG>2kcal/mol) are within these pockets, and 60% of the residues in the complemented pockets are hot spots. 93% of all red-hot residues (DeltaDeltaG>/=4kcal/mol) either protrude into or are located in complemented pockets. The occurrence of hot spots and conserved residues in complemented pockets highlights the role of local tight packing in protein associations, and rationalizes their energetic contribution and conservation. Complemented pockets and their corresponding protruding residues emerge among the most important geometric features in protein-protein interactions. By screening the solvent, this organization shields backbone hydrogen bonds and charge-charge interactions. Complemented pockets often pre-exist binding. For 18 protein-protein complexes with complemented pockets whose unbound structures are available, in 16 the pockets are identified to pre-exist in the unbound structures. The root-mean-squared deviations of the atoms lining the pockets between the bound and unbound states is as small as 0.9A, suggesting that such pockets constitute features of the populated native state that may be used in docking.     

Protein-protein binding is often associated with changes in protonation state

pK(a) values of ionizable residues have been calculated using the PROPKA method and structures of 75 protein-protein complexes and their corresponding free forms. These pK(a) values were used to compute changes in protonation state of individual residues, net changes in protonation state of the complex relative to the uncomplexed proteins, and the correction to a binding energy calculated assuming standard protonation states at pH 7. For each complex, two different structures for the uncomplexed form of the proteins were used: the X-ray structures determined for the proteins in the absence of the other protein and the individual protein structures taken from the structure of the complex (referred to as unbound and bound structures, respectively). In 28 and 77% of the cases considered here, protein-protein binding is accompanied by a complete (>95%) or significant (>50%) change in protonation state of at least one residue using unbound structures. Furthermore, in 36 and 61% of the cases, protein-protein binding is accompanied by a complete or significant net change in protonation state of the complex relative to the separated monomers. Using bound structures, the corresponding values are 12, 51, 20, and 48%. Comparison to experimental data suggest that using unbound and bound structures lead to over- and underestimation of binding-induced protonation state changes, respectively. Thus, we conclude that protein-protein binding is often associated with changes in protonation state of amino acid residues and with changes in the net protonation state of the proteins. The pH-dependent correction to the binding energy contributes at least one order of magnitude to the binding constant in 45 and 23%, using unbound and bound structures, respectively.     

Dissecting subunit interfaces in homodimeric proteins

The subunit interfaces of 122 homodimers of known three-dimensional structure are analyzed and dissected into sets of surface patches by clustering atoms at the interface; 70 interfaces are single-patch, the others have up to six patches, often contributed by different structural domains. The average interface buries 1,940 A2 of the surface of each monomer, contains one or two patches burying 600-1,600 A2, is 65% nonpolar and includes 18 hydrogen bonds. However, the range of size and of hydrophobicity is wide among the 122 interfaces. Each interface has a core made of residues with atoms buried in the dimer, surrounded by a rim of residues with atoms that remain accessible to solvent. The core, which constitutes 77% of the interface on average, has an amino acid composition that resembles the protein interior except for the presence of arginine residues, whereas the rim is more like the protein surface. These properties of the interfaces in homodimers, which are permanent assemblies, are compared to those of protein-protein complexes where the components associate after they have independently folded. On average, subunit interfaces in homodimers are twice larger than in complexes, and much less polar due to the large fraction belonging to the core, although the amino acid compositions of the cores are similar in the two types of interfaces.     

Comparison of protein-protein interactions in serine protease-inhibitor and antibody-antigen complexes: implications for the protein docking problem

The protein-protein interaction energy of 12 nonhomologous serine protease-inhibitor and 15 antibody-antigen complexes is calculated using a molecular mechanics formalism and dissected in terms of the main-chain vs. side-chain contribution, nonrotameric side-chain contributions, and amino acid residue type involvement in the interface interaction. There are major differences in the interactions of the two types of protein-protein complex. Protease-inhibitor complexes interact predominantly through a main-chain-main-chain mechanism while antibody-antigen complexes interact predominantly through a side-chain-side-chain or a side-chain-main-chain mechanism. However, there is no simple correlation between the main-chain-main-chain interaction energy and the percentage of main-chain surface area buried on binding. The interaction energy is equally effected by the presence of nonrotameric side-chain conformations, which constitute approximately 20% of the interaction energy. The ability to reproduce the interface interaction energy of the crystal structure if original side-chain conformations are removed from the calculation is much greater in the protease-inhibitor complexes than the antibody-antigen complexes. The success of a rotameric model for protein-protein docking appears dependent on the extent of the main-chain-main-chain contribution to binding. Analysis of (1) residue type and (2) residue pair interactions at the interface show that antibody-antigen interactions are very restricted with over 70% of the antibody energy attributable to just six residue types (Tyr > Asp > Asn > Ser > Glu > Trp) in agreement with previous studies on residue propensity. However, it is found here that 50% of the antigen energy is attributable to just four residue types (Arg = Lys > Asn > Asp). On average just 12 residue pair interactions (6%) contribute over 40% of the favorable interaction energy in the antibody-antigen complexes, with charge-charge and charge/polar-tyrosine interactions being prominent. In contrast protease inhibitors use a diverse set of residue types and residue pair interactions.     

Analysis of interactive packing of secondary structural elements in alpha/beta units in proteins

An alpha-helix and a beta-strand are said to be interactively packed if at least one residue in each of the secondary structural elements loses 10% of its solvent accessible contact area on association with the other secondary structural element. An analysis of all such 5,975 nonidentical alpha/beta units in protein structures, defined at < or = 2.5 A resolution, shows that the interaxial distance between the alpha-helix and the beta-strand is linearly correlated with the residue-dependent function, log[(V/nda)/n-int], where V is the volume of amino acid residues in the packing interface, nda is the normalized difference in solvent accessible contact area of the residues in packed and unpacked secondary structural elements, and n-int is the number of residues in the packing interface. The beta-sheet unit (beta u), defined as a pair of adjacent parallel or antiparallel hydrogen-bonded beta-strands, packing with an alpha-helix shows a better correlation between the interaxial distance and log(V/nda) for the residues in the packing interface. This packing relationship is shown to be useful in the prediction of interaxial distances in alpha/beta units using the interacting residue information of equivalent alpha/beta units of homologous proteins. It is, therefore, of value in comparative modeling of protein structures.     

Protein-protein docking with a reduced protein model accounting for side-chain flexibility

A protein-protein docking approach has been developed based on a reduced protein representation with up to three pseudo atoms per amino acid residue. Docking is performed by energy minimization in rotational and translational degrees of freedom. The reduced protein representation allows an efficient search for docking minima on the protein surfaces within. During docking, an effective energy function between pseudo atoms has been used based on amino acid size and physico-chemical character. Energy minimization of protein test complexes in the reduced representation results in geometries close to experiment with backbone root mean square deviations (RMSDs) of approximately 1 to 3 A for the mobile protein partner from the experimental geometry. For most test cases, the energy-minimized experimental structure scores among the top five energy minima in systematic docking studies when using both partners in their bound conformations. To account for side-chain conformational changes in case of using unbound protein conformations, a multicopy approach has been used to select the most favorable side-chain conformation during the docking process. The multicopy approach significantly improves the docking performance, using unbound (apo) binding partners without a significant increase in computer time. For most docking test systems using unbound partners, and without accounting for any information about the known binding geometry, a solution within approximately 2 to 3.5 A RMSD of the full mobile partner from the experimental geometry was found among the 40 top-scoring complexes. The approach could be extended to include protein loop flexibility, and might also be useful for docking of modeled protein structures.     

Effective scoring function for protein sequence design

We have developed an effective scoring function for protein design. The atomic solvation parameters, together with the weights of energy terms, were optimized so that residues corresponding to the native sequence were predicted with low energy in the training set of 28 protein structures. The solvation energy of non-hydrogen-bonded hydrophilic atoms was considered separately and expressed in a nonlinear way. As a result, our scoring function predicted native residues as the most favorable in 59% of the total positions in 28 proteins. We then tested the scoring function by comparing the predicted stability changes for 103 T4 lysozyme mutants with the experimental values. The correlation coefficients were 0.77 for surface mutations and 0.71 for all mutations. Finally, the scoring function combined with Monte Carlo simulation was used to predict favorable sequences on a fixed backbone. The designed sequences were similar to the natural sequences of the family to which the template structure belonged. The profile of the designed sequences was helpful for identification of remote homologues of the native sequence.     

Effects of the stabilization of the molten globule state on the folding mechanism of alpha-lactalbumin: a study of a chimera of bovine and human alpha-lactalbumin

The N-terminal half of the alpha-domain (residues 1 to 34) is more important for the stability of the acid-induced molten globule state of alpha-lactalbumin than the C-terminal half (residues 86 to 123). The refolding and unfolding kinetics of a chimera, in which the amino acid sequence of residues 1 to 34 was from human alpha-lactalbumin and the remainder of the sequence from bovine alpha-lactalbumin, were studied by stopped-flow tryptophan fluorescence spectroscopy. The chimeric protein refolded and unfolded substantially faster than bovine alpha-lactalbumin. The stability of the molten globule state formed by the chimera was greater than that of bovine alpha-lactalbumin, and the hydrophobic surface area buried inside of the molecule in the molten globule state was increased by the substitution of residues 1 to 34. Peptide fragments corresponding to the A- and B-helix of the chimera showed higher helix propensity than those of the bovine protein, indicating the contribution of local interactions to the high stability of the molten globule state of the chimera. Moreover, the substitution of residues 1-34 decreased the free energy level of the transition state and increased hydrophobic surface area buried inside of the molecule in the transition state. Our results indicate that local interactions as well as hydrophobic interactions formed in the molten globule state are important in guiding the subsequent structural formation of alpha-lactalbumin.     

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.     

Analysis of hydrophobicity in the alpha and beta chemokine families and its relevance to dimerization.

The chemokine family of chemotactic cytokines plays a key role in orchestrating the immune response. The family has been divided into 2 subfamilies, alpha and beta, based on the spacing of the first 2 cysteine residues, function, and chromosomal location. Members within each subfamily have 25-70% sequence identity, whereas the amino acid identity between members of the 2 subfamilies ranges from 20 to 40%. A quantitative analysis of the hydrophobic properties of 11 alpha and 9 beta chemokine sequences, based on the coordinates of the prototypic alpha and beta chemokines, interleukin-8 (IL-8), and human macrophage inflammatory protein-1 beta (hMIP-1 beta), respectively, is presented. The monomers of the alpha and beta chemokines have their strongest core hydrophobic cluster at equivalent positions, consistent with their similar tertiary structures. In contrast, the pattern of monomer surface hydrophobicity between the alpha and beta chemokines differs in a manner that is fully consistent with the observed differences in quaternary structure. The most hydrophobic surface clusters on the monomer subunits are located in very different regions of the alpha and beta chemokines and comprise in each case the amino acids that are buried at the interface of their respective dimers. The theoretical analysis of hydrophobicity strongly supports the hypothesis that the distinct dimers observed for IL-8 and hMIP-1 beta are preserved for all the alpha and beta chemokines, respectively. This provides a rational explanation for the lack of receptor crossbinding and reactivity between the alpha and beta chemokine subfamilies.     

Properties of integral membrane protein structures: derivation of an implicit membrane potential

Distributions of each amino acid in the trans-membrane domain were calculated as a function of the membrane normal using all currently available alpha-helical membrane protein structures with resolutions better than 4 A. The results were compared with previous sequence- and structure-based analyses. Calculation of the average hydrophobicity along the membrane normal demonstrated that the protein surface in the membrane domain is in fact much more hydrophobic than the protein core. While hydrophobic residues dominate the membrane domain, the interfacial regions of membrane proteins were found to be abundant in the small residues glycine, alanine, and serine, consistent with previous studies on membrane protein packing. Charged residues displayed nonsymmetric distributions with a preference for the intracellular interface. This effect was more prominent for Arg and Lys resulting in a direct confirmation of the positive inside rule. Potentials of mean force along the membrane normal were derived for each amino acid by fitting Gaussian functions to the residue distributions. The individual potentials agree well with experimental and theoretical considerations. The resulting implicit membrane potential was tested on various membrane proteins as well as single trans-membrane alpha-helices. All membrane proteins were found to be at an energy minimum when correctly inserted into the membrane. For alpha-helices both interfacial (i.e. surface bound) and inserted configurations were found to correspond to energy minima. The results demonstrate that the use of trans-membrane amino acid distributions to derive an implicit membrane representation yields meaningful residue potentials.     

Dissecting protein-protein recognition sites

The recognition sites in 70 pairwise protein-protein complexes of known three-dimensional structure are dissected in a set of surface patches by clustering atoms at the interface. When the interface buries <2000 A2 of protein surface, the recognition sites usually form a single patch on the surface of each component protein. In contrast, larger interfaces are generally multipatch, with at least one pair of patches that are equivalent in size to a single-patch interface. Each recognition site, or patch within a site, contains a core made of buried interface atoms, surrounded by a rim of atoms that remain accessible to solvent in the complex. A simple geometric model reproduces the number and distribution of atoms within a patch. The rim is similar in composition to the rest of the protein surface, but the core has a distinctive amino acid composition, which may help in identifying potential protein recognition sites on single proteins of known structures.     

Are protein–protein interfaces more conserved in sequence than the rest of the protein surface?

Protein interfaces are thought to be distinguishable from the rest of the protein surface by their greater degree of residue conservation. We test the validity of this approach on an expanded set of 64 protein-protein interfaces using conservation scores derived from two multiple sequence alignment types, one of close homologs/orthologs and one of diverse homologs/paralogs. Overall, we find that the interface is slightly more conserved than the rest of the protein surface when using either alignment type, with alignments of diverse homologs showing marginally better discrimination. However, using a novel surface-patch definition, we find that the interface is rarely significantly more conserved than other surface patches when using either alignment type. When an interface is among the most conserved surface patches, it tends to be part of an enzyme active site. The most conserved surface patch overlaps with 39% (+/- 28%) and 36% (+/- 28%) of the actual interface for diverse and close homologs, respectively. Contrary to results obtained from smaller data sets, this work indicates that residue conservation is rarely sufficient for complete and accurate prediction of protein interfaces. Finally, we find that obligate interfaces differ from transient interfaces in that the former have significantly fewer alignment gaps at the interface than the rest of the protein surface, as well as having buried interface residues that are more conserved than partially buried interface residues.     

The impact of protein flexibility on protein-protein docking

Accounting for protein flexibility in protein-protein docking algorithms is challenging, and most algorithms therefore treat proteins as rigid bodies or permit side-chain motion only. While the consequences are obvious when there are large conformational changes upon binding, the situation is less clear for the modest conformational changes that occur upon formation of most protein-protein complexes. We have therefore studied the impact of local protein flexibility on protein-protein association by means of rigid body and torsion angle dynamics simulation. The binding of barnase and barstar was chosen as a model system for this study, because the complexation of these 2 proteins is well-characterized experimentally, and the conformational changes accompanying binding are modest. On the side-chain level, we show that the orientation of particular residues at the interface (so-called hotspot residues) have a crucial influence on the way contacts are established during docking from short protein separations of approximately 5 A. However, side-chain torsion angle dynamics simulations did not result in satisfactory docking of the proteins when using the unbound protein structures. This can be explained by our observations that, on the backbone level, even small (2 A) local loop deformations affect the dynamics of contact formation upon docking. Complementary shape-based docking calculations confirm this result, which indicates that both side-chain and backbone levels of flexibility influence short-range protein-protein association and should be treated simultaneously for atomic-detail computational docking of proteins.     

Improved side-chain modeling for protein-protein docking

Success in high-resolution protein-protein docking requires accurate modeling of side-chain conformations at the interface. Most current methods either leave side chains fixed in the conformations observed in the unbound protein structures or allow the side chains to sample a set of discrete rotamer conformations. Here we describe a rapid and efficient method for sampling off-rotamer side-chain conformations by torsion space minimization during protein-protein docking starting from discrete rotamer libraries supplemented with side-chain conformations taken from the unbound structures, and show that the new method improves side-chain modeling and increases the energetic discrimination between good and bad models. Analysis of the distribution of side-chain interaction energies within and between the two protein partners shows that the new method leads to more native-like distributions of interaction energies and that the neglect of side-chain entropy produces a small but measurable increase in the number of residues whose interaction energy cannot compensate for the entropic cost of side-chain freezing at the interface. The power of the method is highlighted by a number of predictions of unprecedented accuracy in the recent CAPRI (Critical Assessment of PRedicted Interactions) blind test of protein-protein docking methods.     

SymmRef: a flexible refinement method for symmetric multimers

Symmetric protein complexes are abundant in the living cell. Predicting their atomic structure can shed light on the mechanism of many important biological processes. Symmetric docking methods aim to predict the structure of these complexes given the unbound structure of a single monomer, or its model. Symmetry constraints reduce the search-space of these methods and make the prediction easier compared to asymmetric protein-protein docking. However, the challenge of modeling the conformational changes that the monomer might undergo is a major obstacle. In this article, we present SymmRef, a novel method for refinement and reranking of symmetric docking solutions. The method models backbone and side-chain movements and optimizes the rigid-body orientations of the monomers. The backbone movements are modeled by normal modes minimization and the conformations of the side-chains are modeled by selecting optimal rotamers. Since solved structures of symmetric multimers show asymmetric side-chain conformations, we do not use symmetry constraints in the side-chain optimization procedure. The refined models are re-ranked according to an energy score. We tested the method on a benchmark of unbound docking challenges. The results show that the method significantly improves the accuracy and the ranking of symmetric rigid docking solutions. SymmRef is available for download at http:// bioinfo3d.cs.tau.ac.il/SymmRef/download.html.