Complexity and simplicity of ligand-macromolecule interactions: the energy landscape perspective

The energy landscape approach has contributed to recent progress in understanding the complexity and simplicity of ligand-macromolecule interactions. Significant advances in computational structure prediction of ligand-protein complexes have been made using approaches that include the effects of protein flexibility and incorporate a hierarchy of energy functions. The results suggest that the complexity of structure prediction in molecular recognition may be determined by low-resolution properties of the underlying binding energy landscapes and by the nature of the energy funnels near the native structures of the complexes.     

Assessing the energy landscape of CAPRI targets by FunHunt

RosettaDock has repeatedly created high-resolution structures of protein complexes in the CAPRI experiment, thanks to the explicit modeling of conformational changes of the monomers at the side chain level. These models can be selected based on their energy. During the search for the lowest-energy model, RosettaDock samples a deep funnel around the native orientation, but additional funnels may appear in the energy landscape, especially in cases where backbone conformational changes occur upon binding. We have previously developed FunHunt, a Support Vector Machine-based classifier that distinguishes the energy funnels around the native orientation from other funnels in the energy landscape. Here we assess the ability of FunHunt to help in model selection in the CAPRI experiment. For all of 12 recent CAPRI targets, FunHunt clearly identifies a near-native funnel in comparison to the funnel around the lowest energy model identified by the RosettaDock global search protocol. FunHunt is also able to choose a near-native orientation among models submitted by predictor groups, demonstrating its general applicability for model selection. This suggests that FunHunt will be a valuable tool in coming CAPRI rounds for the selection of models, and for the definition of regions that need further refinement with restricted backbone flexibility.     

Realistic protein-protein association rates from a simple diffusional model neglecting long-range interactions, free energy barriers, and landscape ruggedness

We develop a simple but rigorous model of protein-protein association kinetics based on diffusional association on free energy landscapes obtained by sampling configurations within and surrounding the native complex binding funnels. Guided by results obtained on exactly solvable model problems, we transform the problem of diffusion in a potential into free diffusion in the presence of an absorbing zone spanning the entrance to the binding funnel. The free diffusion problem is solved using a recently derived analytic expression for the rate of association of asymmetrically oriented molecules. Despite the required high steric specificity and the absence of long-range attractive interactions, the computed rates are typically on the order of 10(4)-10(6) M(-1) sec(-1), several orders of magnitude higher than rates obtained using a purely probabilistic model in which the association rate for free diffusion of uniformly reactive molecules is multiplied by the probability of a correct alignment of the two partners in a random collision. As the association rates of many protein-protein complexes are also in the 10(5)-10(6) M(-1) sec(-1) range, our results suggest that free energy barriers arising from desolvation and/or side-chain freezing during complex formation or increased ruggedness within the binding funnel, which are completely neglected in our simple diffusional model, do not contribute significantly to the dynamics of protein-protein association. The transparent physical interpretation of our approach that computes association rates directly from the size and geometry of protein-protein binding funnels makes it a useful complement to Brownian dynamics simulations.     

Protein-protein docking with simultaneous optimization of rigid-body displacement and side-chain conformations

Protein-protein docking algorithms provide a means to elucidate structural details for presently unknown complexes. Here, we present and evaluate a new method to predict protein-protein complexes from the coordinates of the unbound monomer components. The method employs a low-resolution, rigid-body, Monte Carlo search followed by simultaneous optimization of backbone displacement and side-chain conformations using Monte Carlo minimization. Up to 10(5) independent simulations are carried out, and the resulting "decoys" are ranked using an energy function dominated by van der Waals interactions, an implicit solvation model, and an orientation-dependent hydrogen bonding potential. Top-ranking decoys are clustered to select the final predictions. Small-perturbation studies reveal the formation of binding funnels in 42 of 54 cases using coordinates derived from the bound complexes and in 32 of 54 cases using independently determined coordinates of one or both monomers. Experimental binding affinities correlate with the calculated score function and explain the predictive success or failure of many targets. Global searches using one or both unbound components predict at least 25% of the native residue-residue contacts in 28 of the 32 cases where binding funnels exist. The results suggest that the method may soon be useful for generating models of biologically important complexes from the structures of the isolated components, but they also highlight the challenges that must be met to achieve consistent and accurate prediction of protein-protein interactions.     

Electrostatic contributions to protein-protein interactions: fast energetic filters for docking and their physical basis

The methods of continuum electrostatics are used to calculate the binding free energies of a set of protein-protein complexes including experimentally determined structures as well as other orientations generated by a fast docking algorithm. In the native structures, charged groups that are deeply buried were often found to favor complex formation (relative to isosteric nonpolar groups), whereas in nonnative complexes generated by a geometric docking algorithm, they were equally likely to be stabilizing as destabilizing. These observations were used to design a new filter for screening docked conformations that was applied, in conjunction with a number of geometric filters that assess shape complementarity, to 15 antibody-antigen complexes and 14 enzyme-inhibitor complexes. For the bound docking problem, which is the major focus of this paper, native and near-native solutions were ranked first or second in all but two enzyme-inhibitor complexes. Less success was encountered for antibody-antigen complexes, but in all cases studied, the more complete free energy evaluation was able to identify native and near-native structures. A filter based on the enrichment of tyrosines and tryptophans in antibody binding sites was applied to the antibody-antigen complexes and resulted in a native and near-native solution being ranked first and second in all cases. A clear improvement over previously reported results was obtained for the unbound antibody-antigen examples as well. The algorithm and various filters used in this work are quite efficient and are able to reduce the number of plausible docking orientations to a size small enough so that a final more complete free energy evaluation on the reduced set becomes computationally feasible.     

Monte Carlo refinement of rigid-body protein docking structures with backbone displacement and side-chain optimization

Structures of hitherto unknown protein complexes can be predicted by docking the solved protein monomers. Here, we present a method to refine initial docking estimates of protein complex structures by a Monte Carlo approach including rigid-body moves and side-chain optimization. The energy function used is comprised of van der Waals, Coulomb, and atomic contact energy terms. During the simulation, we gradually shift from a novel smoothed van der Waals potential, which prevents trapping in local energy minima, to the standard Lennard-Jones potential. Following the simulation, the conformations are clustered to obtain the final predictions. Using only the first 100 decoys generated by a fast Fourier transform (FFT)-based rigid-body docking method, our refinement procedure is able to generate near-native structures (interface RMSD <2.5 A) as first model in 14 of 59 cases in a benchmark set. In most cases, clear binding funnels around the native structure can be observed. The results show the potential of Monte Carlo refinement methods and emphasize their applicability for protein-protein docking.     

Restricted sidechain plasticity in the structures of native proteins and complexes

Protein-design methodology can now generate models of protein structures and interfaces with computed energies in the range of those of naturally occurring structures. Comparison of the properties of native structures and complexes to isoenergetic design models can provide insight into the properties of the former that reflect selection pressure for factors beyond the energy of the native state. We report here that sidechains in native structures and interfaces are significantly more constrained than designed interfaces and structures with equal computed binding energy or stability, which may reflect selection against potentially deleterious non-native interactions.     

Funnel hunting in a rough terrain: learning and discriminating native energy funnels

Protein folding and binding is commonly depicted as a search for the minimum energy conformation. Modeling of protein complex structures by RosettaDock often results in a set of low-energy conformations near the native structure. Ensembles of low-energy conformations can appear, however, in other regions, especially when backbone movements occur upon binding. What then characterizes the energy landscape near the correct orientation? We applied a machine learning algorithm to distinguish ensembles of low-energy conformations around the native conformation from other low-energy ensembles. The resulting classifier, FunHunt, identifies the native orientation in 50/52 protein complexes in a test set. The features used by FunHunt teach us about the nature of native interfaces. Remarkably, the energy decrease of trajectories toward near-native orientations is significantly larger than for other orientations. This provides a possible explanation for the stability of association in the native orientation.     

A physical reference state unifies the structure-derived potential of mean force for protein folding and binding

Extracting knowledge-based statistical potential from known structures of proteins is proved to be a simple, effective method to obtain an approximate free-energy function. However, the different compositions of amino acid residues at the core, the surface, and the binding interface of proteins prohibited the establishment of a unified statistical potential for folding and binding despite the fact that the physical basis of the interaction (water-mediated interaction between amino acids) is the same. Recently, a physical state of ideal gas, rather than a statistically averaged state, has been used as the reference state for extracting the net interaction energy between amino acid residues of monomeric proteins. Here, we find that this monomer-based potential is more accurate than an existing all-atom knowledge-based potential trained with interfacial structures of dimers in distinguishing native complex structures from docking decoys (100% success rate vs. 52% in 21 dimer/trimer decoy sets). It is also more accurate than a recently developed semiphysical empirical free-energy functional enhanced by an orientation-dependent hydrogen-bonding potential in distinguishing native state from Rosetta docking decoys (94% success rate vs. 74% in 31 antibody-antigen and other complexes based on Z score). In addition, the monomer potential achieved a 93% success rate in distinguishing true dimeric interfaces from artificial crystal interfaces. More importantly, without additional parameters, the potential provides an accurate prediction of binding free energy of protein-peptide and protein-protein complexes (a correlation coefficient of 0.87 and a root-mean-square deviation of 1.76 kcal/mol with 69 experimental data points). This work marks a significant step toward a unified knowledge-based potential that quantitatively captures the common physical principle underlying folding and binding. A Web server for academic users, established for the prediction of binding free energy and the energy evaluation of the protein-protein complexes, may be found at http://theory.med.buffalo.edu.     

Cofactor effects on the protein folding reaction: acceleration of alpha-lactalbumin refolding by metal ions

About 30% of proteins require cofactors for their proper folding. The effects of cofactors on the folding reaction have been investigated with alpha-lactalbumin as a model protein and metal ions as cofactors. Metal ions accelerate the refolding of alpha-lactalbumin by lessening the energy barrier between the molten globule state and the transition state, mainly by decreasing the difference of entropy between the two states. These effects are linked to metal ion binding to the protein in the native state. Hence, relationships between the metal affinities for the intermediate states and those for the native state are observed. Some residual specificity for the calcium ion is still observed in the molten globule state, this specificity getting closer in the transition state to that of the native state. The comparison between kinetic and steady-state data in association with the Phi value method indicates the binding of the metal ions on the unfolded state of alpha-lactalbumin. Altogether, these results provide insight into cofactor effects on protein folding. They also suggest new possibilities to investigate the presence of residual native structures in the unfolded state of protein and the effects of such structures on the protein folding reaction and on protein stability.     

Association of protein-DNA recognition complexes: electrostatic and nonelectrostatic effects

In this study the electrostatic and nonelectrostatic contributions to the binding free energy of a number of different protein-DNA recognition complexes are investigated. To determine the electrostatic effects in the protein-DNA association the Poisson-Boltzmann approach was applied. Overall the salt-dependent electrostatic free energy opposed binding in all protein-DNA complexes except one, and the salt-independent electrostatic contribution favored binding in more than half of the complexes. Further the salt-dependent electrostatic free energy increased with higher ionic concentrations and therefore complex association is stronger opposed at higher ionic concentrations. The hydrophobic effect in the protein-DNA complexes was determined from the buried accessible surface area and the surface tension. A majority of the complexes showed more polar than nonpolar buried accessible surface area. Interestingly the buried DNA-accessible surface area was preferentially hydrophilic, only in one complex a slightly more hydrophobic buried accessible surface area was observed. A quite sophisticated balance between several different free energy components seems to be responsible for determining the free energy of binding in protein-DNA systems.     

How well can we predict native contacts in proteins based on decoy structures and their energies?

One strategy for ab initio protein structure prediction is to generate a large number of possible structures (decoys) and select the most fitting ones based on a scoring or free energy function. The conformational space of a protein is huge, and chances are rare that any heuristically generated structure will directly fall in the neighborhood of the native structure. It is desirable that, instead of being thrown away, the unfitting decoy structures can provide insights into native structures so prediction can be made progressively. First, we demonstrate that a recently parameterized physics-based effective free energy function based on the GROMOS96 force field and a generalized Born/surface area solvent model is, as several other physics-based and knowledge-based models, capable of distinguishing native structures from decoy structures for a number of widely used decoy databases. Second, we observe a substantial increase in correlations of the effective free energies with the degree of similarity between the decoys and the native structure, if the similarity is measured by the content of native inter-residue contacts in a decoy structure rather than its root-mean-square deviation from the native structure. Finally, we investigate the possibility of predicting native contacts based on the frequency of occurrence of contacts in decoy structures. For most proteins contained in the decoy databases, a meaningful amount of native contacts can be predicted based on plain frequencies of occurrence at a relatively high level of accuracy. Relative to using plain frequencies, overwhelming improvements in sensitivity of the predictions are observed for the 4_state_reduced decoy sets by applying energy-dependent weighting of decoy structures in determining the frequency. There, approximately 80% native contacts can be predicted at an accuracy of approximately 80% using energy-weighted frequencies. The sensitivity of the plain frequency approach is much lower (20% to 40%). Such improvements are, however, not observed for the other decoy databases. The rationalization and implications of the results are discussed.     

Water molecules participate in proteinase-inhibitor interactions: crystal structures of Leu18, Ala18, and Gly18 variants of turkey ovomucoid inhibitor third domain complexed with Streptomyces griseus proteinase B.

Crystal structures of the complexes of Streptomyces griseus proteinase B (SGPB) with three P1 variants of turkey ovomucoid inhibitor third domain (OMTKY3), Leu18, Ala18, and Gly18, have been determined and refined to high resolution. Comparisons among these structures and of each with native, uncomplexed SGPB reveal that each complex features a unique solvent structure in the S1 binding pocket. The number and relative positions of water molecules bound in the S1 binding pocket vary according to the size of the side chain of the P1 residue. Water molecules in the S1 binding pocket of SGPB are redistributed in response to the complex formation, probably to optimize hydrogen bonds between the enzyme and the inhibitor. There are extensive water-mediated hydrogen bonds in the interfaces of the complexes. In all complexes, Asn 36 of OMTKY3 participates in forming hydrogen bonds, via water molecules, with residues lining the S1 binding pocket of SGPB. For a homologous series of aliphatic straight side chains, Gly18, Ala18, Abu18, Ape18, and Ahp18 variants, the binding free energy is a linear function of the hydrophobic surface area buried in the interface of the corresponding complexes. The resulting constant of proportionality is 34.1 cal mol-1 A-2. These structures confirm that the binding of OMTKY3 to the preformed S1 pocket in SGPB involves no substantial structural disturbances that commonly occur in the site-directed mutagenesis studies of interior residues in other proteins, thus providing one of the most reliable assessments of the contribution of the hydrophobic effect to protein-complex stability.     

Consensus scoring for enriching near-native structures from protein-protein docking decoys

The identification of near native protein-protein complexes among a set of decoys remains highly challenging. A strategy for improving the success rate of near native detection is to enrich near native docking decoys in a small number of top ranked decoys. Recently, we found that a combination of three scoring functions (energy, conservation, and interface propensity) can predict the location of binding interface regions with reasonable accuracy. Here, these three scoring functions are modified and combined into a consensus scoring function called ENDES for enriching near native docking decoys. We found that all individual scores result in enrichment for the majority of 28 targets in ZDOCK2.3 decoy set and the 22 targets in Benchmark 2.0. Among the three scores, the interface propensity score yields the highest enrichment in both sets of protein complexes. When these scores are combined into the ENDES consensus score, a significant increase in enrichment of near-native structures is found. For example, when 2000 dock decoys are reduced to 200 decoys by ENDES, the fraction of near-native structures in docking decoys increases by a factor of about six in average. ENDES was implemented into a computer program that is available for download at http://sparks.informatics.iupui.edu.     

X-ray structures of small ligand-FKBP complexes provide an estimate for hydrophobic interaction energies

A new crystal form of native FK506 binding protein (FKBP) has been obtained which has proved useful in ligand binding studies. Three different small molecule ligand complexes and the native enzyme have been determined at higher resolution than 2.0 A. Dissociation constants of the related small molecule ligands vary from 20 mM for dimethylsulphoxide to 200 microM for tetrahydrothiophene 1-oxide. Comparison of the four available crystal structures shows that the protein structures are identical to within experimental error, but there are differences in the water structure in the active site. Analysis of the calculated buried surface areas of these related ligands provides an estimated van der Waals contribution to the binding energy of -0.5 kJ/A(2) for non-polar interactions between ligand and protein.     

Folding funnels and conformational transitions via hinge-bending motions

In this article we focus on presenting a broad range of examples illustrating low-energy transitions via hinge-bending motions. The examples are divided according to the type of hinge-bending involved; namely, motions involving fragments of the protein chains, hinge-bending motions involving protein domains, and hinge-bending motions between the covalently unconnected subunits. We further make a distinction between allosterically and nonallosterically regulated proteins. These transitions are discussed within the general framework of folding and binding funnels. We propose that the conformers manifesting such swiveling motions are not the outcome of “induced fit” binding mechanism; instead, molecules exist in an ensemble of conformations that are in equilibrium in solution. These ensembles, which populate the bottoms of the funnels,a priori contain both the “open” and the “closed” conformational isomers. Furthermore, we argue that there are no fundamental differences among the physical principles behind the folding and binding funnels. Hence, there is no basic difference between funnels depicting ensembles of conformers of single molecules with fragment, or domain motions, as compared to subunits in multimeric quaternary structures, also showing such conformational transitions. The difference relates only to the size and complexity of the system. The larger the system, the more complex its corresponding fused funnel(s). In particular, funnels associated with allosterically regulated proteins are expected to be more complicated, because allostery is frequently involved with movements between subunits, and consequently is often observed in multichain and multimolecular complexes. This review centers on the critical role played by flexibility and conformational fluctuations in enzyme activity. Internal motions that extend over different time scales and with different amplitudes are known to be essential for the catalytic cycle. The conformational change observed in enzyme-substrate complexes as compared to the unbound enzyme state, and in particular the hinge-bending motions observed in enzymes with two domains, have a substantial effect on the enzymatic catalytic activity. The examples we review span the lipolytic enzymes that are particularly interesting, owing to their activation at the water-oil interface; an allosterically controlled dehydrogenase (lactate dehydrogenase); a DNA methyltransferase, with a covalently-bound intermediate; large-scale flexible loop motions in a glycolytic enzyme (TIM); domain motion in PGK, an enzyme which is essential in most cells, both for ATP generation in aerobes and for fermentation in anaerobes; adenylate kinase, showing large conformational changes, owing to their need to shield their catalytic centers from water; a calcium-binding protein (calmodulin), involved in a wide range of cellular calcium-dependent signaling; diphtheria toxin, whose large domain motion has been shown to yield “domain swapping” the hexameric glutamate dehydrogenase, which has been studied both in a thermophile and in a mesophile; an allosteric enzyme, showing subunit motion between the R and the T states (aspartate transcarbamoylase), and the historically well-studied lac represoor. Nonallosteric subunit transitions are also addressed with some examples (aspartate receptor andBamHI endonuclease). Hence, using this enzyme-catalysis-centered discussion, we address energy funnel landscapes of large-scale conformational transitions, rather than the faster, quasi-harmonic, thermal fluctuations.     

Exploring the primary electron acceptor (QA)-site of the bacterial reaction center from Rhodobacter sphaeroides. Binding mode of vitamin K derivatives.

The functional replacement of the primary ubiquinone (QA) in the photosynthetic reaction center (RC) from Rhodobacter sphaeroides with synthetic vitamin K derivatives has provided a powerful tool to investigate the electron transfer mechanism. To investigate the binding mode of these quinones to the QA binding site we have determined the binding free energy and charge recombination rate from QA(-) to D+ (kAD) of 29 different 1,4-naphthoquinone derivatives with systematically altered structures. The most striking result was that none of the eight tested compounds carrying methyl groups in both positions 5 and 8 of the aromatic ring exhibited functional binding. To understand the binding properties of these quinones on a molecular level, the structures of the reaction center-naphthoquinone complexes were predicted with ligand docking calculations. All protein--ligand structures show hydrogen bonds between the carbonyl oxygens of the quinone and AlaM260 and HisM219 as found for the native ubiquinone-10 in the X-ray structure. The center-to-center distance between the naphthoquinones at QA and the native ubiquinone-10 at QB (the secondary electron acceptor) is essentially the same, compared to the native structure. A detailed analysis of the docking calculations reveals that 5,8-disubstitution prohibits binding due to steric clashes of the 5-methyl group with the backbone atoms of AlaM260 and AlaM249. The experimentally determined binding free energies were reproduced with an rmsd of approximately 4 kJ x mol(-1) in most cases providing a valuable tool for the design of new artificial electron acceptors and inhibitors.     

How common is the funnel‐like energy landscape in protein‐protein interactions?

The goal of this study is to verify the concept of the funnel-like intermolecular energy landscape in protein-protein interactions by use of a series of computational experiments. Our preliminary analysis revealed the existence of the funnel in many protein-protein interactions. However, because of the uncertainties in the modeling of these interactions and the ambiguity of the analysis procedures, the detection of the funnels requires detailed quantitative approaches to the energy landscape analysis. A number of such approaches are presented in this study. We show that the funnel detection problem is equivalent to a problem of distinguishing between distributions of low-energy intermolecular matches in the funnel and in the low-frequency landscape fluctuations. If the fluctuations are random, the decision about whether the minimum is the funnel is equivalent to determining whether this minimum is significantly different from a would-be random one. A database of 475 nonredundant cocrystallized protein-protein complexes was used to re-dock the proteins by use of smoothed potentials. To detect the funnel, we developed a set of sophisticated models of random matches. The funnel was considered detected if the binding area was more populated by the low-energy docking predictions than by the matches generated in the random models. The number of funnels detected by use of different random models varied significantly. However, the results confirmed that the funnel may be the general feature in protein-protein association.     

ClusPro: an automated docking and discrimination method for the prediction of protein complexes

MOTIVATION: Predicting protein interactions is one of the most challenging problems in functional genomics. Given two proteins known to interact, current docking methods evaluate billions of docked conformations by simple scoring functions, and in addition to near-native structures yield many false positives, i.e. structures with good surface complementarity but far from the native. RESULTS: We have developed a fast algorithm for filtering docked conformations with good surface complementarity, and ranking them based on their clustering properties. The free energy filters select complexes with lowest desolvation and electrostatic energies. Clustering is then used to smooth the local minima and to select the ones with the broadest energy wells-a property associated with the free energy at the binding site. The robustness of the method was tested on sets of 2000 docked conformations generated for 48 pairs of interacting proteins. In 31 of these cases, the top 10 predictions include at least one near-native complex, with an average RMSD of 5 A from the native structure. The docking and discrimination method also provides good results for a number of complexes that were used as targets in the Critical Assessment of PRedictions of Interactions experiment. AVAILABILITY: The fully automated docking and discrimination server ClusPro can be found at http://structure.bu.edu