Protein docking and complementarity

Predicting the structures of protein-protein complexes is a difficult problem owing to the topographical and thermodynamic complexity of these structures. Past efforts in this area have focussed on fitting the interacting proteins together using rigid body searches, usually with the conformations of the proteins as they occur in crystal structure complexes. Here we present work which uses a rigid body docking method to generate the structures of three known protein complexes, using both the bound and unbound conformations of the interacting molecules. In all cases we can regenerate the geometry of the crystal complexes to high accuracy. We also are able to find geometries that do not resemble the crystal structure but nevertheless are surprisingly reasonable both mechanistically and by some simple physical criteria. In contrast to previous work in this area, we find that simple methods for evaluating the complementarity at the protein-protein interface cannot distinguish between the configurations that resemble the crystal structure complex and those that do not. Methods that could not distinguish between such similar and dissimilar configurations include surface area burial, solvation free energy, packing and mechanism-based filtering. Evaluations of the total interaction energy and the electrostatic interaction energy of the complexes were somewhat better. Of the techniques that we tried, energy minimization distinguished most clearly between the "true" and "false" positives, though even here the energy differences were surprisingly small. We found the lowest total interaction energy from amongst all of the putative complexes generated by docking was always within 5 A root-mean-square of the crystallographic structure. There were, however, several putative complexes that were very dissimilar to the crystallographic structure but had energies that were close to that of the low energy structure. The magnitude of the error in energy calculations has not been established in macromolecular systems, and thus the reliability of the small differences in energy remains to be determined. The ability of this docking method to regenerate the crystallographic configurations of the interacting proteins using their unbound conformations suggests that it will be a useful tool in predicting the structures of unsolved complexes.     

An evaluation of Poisson-Boltzmann electrostatic free energy calculations through comparison with experimental mutagenesis data

For systems involving highly and oppositely charged proteins, electrostatic forces dominate association and contribute to biomolecular complex stability. Using experimental or theoretical alanine-scanning mutagenesis, it is possible to elucidate the contribution of individual ionizable amino acids to protein association. We evaluated our electrostatic free energy calculations by comparing calculated and experimental data for alanine mutants of five protein complexes. We calculated Poisson-Boltzmann electrostatic free energies based on a thermodynamic cycle, which incorporates association in a reference (Coulombic) and solvated (solution) state, as well as solvation effects. We observe that Coulombic and solvation free energy values correlate with experimental data in highly and oppositely charged systems, but not in systems comprised of similarly charged proteins. We also observe that correlation between solution and experimental free energies is dependent on dielectric coefficient selection for the protein interior. Free energy correlations improve as protein dielectric coefficient increases, suggesting that the protein interior experiences moderate dielectric screening, despite being shielded from solvent. We propose that higher dielectric coefficients may be necessary to more accurately predict protein-protein association. Additionally, our data suggest that Coulombic potential calculations alone may be sufficient to predict relative binding of protein mutants.     

Non-Boltzmann thermodynamic integration (NBTI) for macromolecular systems: relative free energy of binding of trypsin to benzamidine and benzylamine

The relative free energies of binding of trypsin to two amine inhibitors, benzamidine (BZD) and benzylamine (BZA), were calculated using non-Boltzmann thermodynamic integration (NBTI). Comparison of the simulations with the crystal structures of both complexes, trypsin-BZD and trypsin-BZA, shows that NBTI simulations better sample conformational space relative to thermodynamic integration (TI) simulations. The relative binding free energy calculated using NBTI was much closer to the experimentally determined value than that obtained using TI. The error in the TI simulation was found to be primarily due to incorrect sampling of BZA's conformation in the binding pocket. In contrast, NBTI produces a smooth mutation from BZD to BZA using a surrogate potential, resulting in a much closer agreement between the inhibitors' conformations and the omit electron density maps. This superior agreement between experiment and simulation, of both relative binding free energy differences and conformational sampling, demonstrates NBTI's usefulness for free energy calculations in macromolecular simulations.     

Insights into nucleotide recognition by cell division protein FtsZ from a mant-GTP competition assay and molecular dynamics

Essential cell division protein FtsZ forms the bacterial cytokinetic ring and is a target for new antibiotics. FtsZ monomers bind GTP and assemble into filaments. Hydrolysis to GDP at the association interface between monomers leads to filament disassembly. We have developed a homogeneous competition assay, employing the fluorescence anisotropy change of mant-GTP upon binding to nucleotide-free FtsZ, which detects compounds binding to the nucleotide site in FtsZ monomers and measures their affinities within the millimolar to 10 nM range. We have employed this method to determine the apparent contributions of the guanine, ribose, and the α-, β-, and γ-phosphates to the free energy change of nucleotide binding. Similar relative contributions have also been estimated through molecular dynamics and binding free energy calculations, employing the crystal structures of FtsZ-nucleotide complexes. We find an energetically dominant contribution of the β-phosphate, comparable to the whole guanosine moiety. GTP and GDP bind with similar observed affinity to FtsZ monomers. Loss of the regulatory γ-phosphate results in a predicted accommodation of GDP which has not been observed in the crystal structures. The binding affinities of a series of C8-substituted GTP analogues, known to inhibit FtsZ but not eukaryotic tubulin assembly, correlate with their inhibitory capacity on FtsZ polymerization. Our methods permit testing of FtsZ inhibitors targeting its nucleotide site, as well as compounds from virtual screening of large synthetic libraries. Our results give insight into the FtsZ-nucleotide interactions, which could be useful in the rational design of new inhibitors, especially GTP phosphate mimetics.     

No evidence that mRNAs have lower folding free energies than random sequences with the same dinucleotide distribution

This work investigates whether mRNA has a lower estimated folding free energy than random sequences. The free energy estimates are calculated by the mfold program for prediction of RNA secondary structures. For a set of 46 mRNAs it is shown that the predicted free energy is not significantly different from random sequences with the same dinucleotide distribution. For random sequences with the same mononucleotide distribution it has previously been shown that the native mRNA sequences have a lower predicted free energy, which indicates a more stable structure than random sequences. However, dinucleotide content is important when assessing the significance of predicted free energy as the physical stability of RNA secondary structure is known to depend on dinucleotide base stacking energies. Even known RNA secondary structures, like tRNAs, can be shown to have predicted free energies indistinguishable from randomized sequences. This suggests that the predicted free energy is not always a good determinant for RNA folding.     

SCO Trimers as High-energy Materials? A Density Functional Study

Density functional calculations using the hybrid B3LYP functional have been carried out on the fragmentation reaction of cyclic SCO trimers. Analogous calculations for CO₂ and HNCO have also been performed for comparison. The energies of the different trimers relative to those of the isolated monomers as well as the energy barriers to fragmentation have been calculated. For all the calculations, a reaction path in which three bonds are simultaneously broken has been considered. It has been found that the fragmentation of cyclic SCO trimers is a rather facile process. The same statement applies to the cyclic CO₂ trimer but not to the HNCO one. In addition, the latter is much more stable than three free HNCO monomers, which is not the case for SCO and CO₂.     

Analysis of cyclosporin A and a set of analogs as inhibitors of a T. cruzi cyclophilin by docking and molecular dynamics

Cyclophilins (CyPs) are enzymes involved in protein folding. In Trypanosoma cruzi (T. cruzi), the most abundantly expressed CyP is the isoform TcCyP19. It has been shown that TcCyP19 is inhibited by the immunosuppressive drug cyclosporin A (CsA) and analogs, which also proved to have potent trypanosomicidal activity in vitro. In this work, we continue and expand a previous study on the molecular interactions of CsA, and a set of analogs modeled in complexes with TcCyP19. The modeled complexes were used to evaluate binding free energies by molecular dynamics (MD), applying the Linear Interaction Energy (LIE) method. In addition, putative binding sites were identified by molecular docking. In our analysis, the binding free energy calculations did not correlate with experimental data. The heterogeneity of the non-bonded energies and the variation in the pattern of hydrogen bonds suggest that the systems may not be suitable for the application of the LIE method. Further, the docking calculations identified two other putative binding sites with comparable scoring energies to the active site, a fact that may also explain the lack of correlation found. Kinetic experiments are needed to confirm or reject the multiple binding sites hypothesis. In the meantime, MD simulations at the alternative sites, employing other methods to compute binding free energies, might be successful at finding good correlations with the experimental data.     

Validation of an automated procedure for the prediction of relative free energies of binding on a set of aldose reductase inhibitors

Among the available methods for predicting free energies of binding of ligands to a protein, the molecular mechanics Poisson–Boltzmann surface area (MM-PBSA) and molecular mechanics generalized Born surface area (MM-GBSA) approaches have been validated for a relatively limited number of targets and compounds in the training set. Here, we report the results of an extensive study on a series of 28 inhibitors of aldose reductase with experimentally determined crystal structures and inhibitory activities, in which we evaluate the ability of MM-PBSA and MM-GBSA methods in predicting binding free energies using a number of different simulation conditions. While none of the methods proved able to predict absolute free energies of binding in quantitative agreement with the experimental values, calculated and experimental free energies of binding were significantly correlated. Comparing the predicted and experimental ΔG of binding, MM-PBSA proved to perform better than MM-GBSA, and within the MM-PBSA methods, the PBSA of Amber performed similarly to Delphi. In particular, significant relationships between experimental and computed free energies of binding were obtained using Amber PBSA and structures minimized with a distance-dependent dielectric function. Importantly, while free energy predictions are usually made on large collections of equilibrated structures sampled during molecular dynamics in water, we have found that a single minimized structure is a reasonable approximation if relative free energies of binding are to be calculated. This finding is particularly relevant, considering that the generation of equilibrated MD ensembles and the subsequent free energy analysis on multiple snapshots is computationally intensive, while the generation and analysis of a single minimized structure of a protein–ligand complex is relatively fast, and therefore suited for high-throughput virtual screening studies. At this aim, we have developed an automated workflow that integrates all the necessary steps required to generate structures and calculate free energies of binding. The procedure is relatively fast and able to screen automatically and iteratively molecules contained in databases and libraries of compounds. Taken altogether, our results suggest that the workflow can be a valuable tool for ligand identification and optimization, being able to automatically and efficiently refine docking poses, which sometimes may not be accurate, and rank the compounds based on more accurate scoring functions.     

Quantum mechanical electronic structure calculation reveals orientation dependence of hydrogen bond energy in proteins

Hydrogen bond plays a unique role in governing macromolecular interactions with exquisite specificity. These interactions govern the fundamental biological processes like protein folding, enzymatic catalysis, molecular recognition. Despite extensive research work, till date there is no proper report available about the hydrogen bond's energy surface with respect to its geometric parameters, directly derived from proteins. Herein, we have deciphered the potential energy landscape of hydrogen bond directly from the macromolecular coordinates obtained from Protein Data Bank using quantum mechanical electronic structure calculations. The findings unravel the hydrogen bonding energies of proteins in parametric space. These data can be used to understand the energies of such directional interactions involved in biological molecules. Quantitative characterization has also been performed using Shannon entropic calculations for atoms participating in hydrogen bond. Collectively, our results constitute an improved way of understanding hydrogen bond energies in case of proteins and complement the knowledge‐based potential. Proteins 2017; 85:1046–1055. © 2017 Wiley Periodicals, Inc.     

Protein-protein recognition: exploring the energy funnels near the binding sites

We present a rapidly executable minimal binding energy model for molecular docking and use it to explore the energy landscape in the vicinity of the binding sites of four different enzyme inhibitor complexes. The structures of the complexes are calculated starting with the crystal structures of the free monomers, using DOCK 4.0 to generate a large number of potential configurations, and screening with the binding energy target function. In order to investigate possible correlations between energy and variation from the native structure, we introduce a new measure of similarity, which removes many of the difficulties associated with root mean square deviation. The analysis uncovers energy gradients, or funnels, near the binding site, with decreasing energy as the degree of similarity between the native and docked structures increases. Such energy funnels can increase the number of random collisions that may evolve into productive stable complex, and indicate that short-range interactions in the precomplexes can contribute to the association rate. The finding could provide an explanation for the relatively rapid association rates that are observed even in the absence of long-range electrostatic steering.     

Free energy decomposition of protein-protein interactions.

A free energy decomposition scheme has been developed and tested on antibody-antigen and protease-inhibitor binding for which accurate experimental structures were available for both free and bound proteins. Using the x-ray coordinates of the free and bound proteins, the absolute binding free energy was computed assuming additivity of three well-defined, physical processes: desolvation of the x-ray structures, isomerization of the x-ray conformation to a nearby local minimum in the gas-phase, and subsequent noncovalent complex formation in the gas phase. This free energy scheme, together with the Generalized Born model for computing the electrostatic solvation free energy, yielded binding free energies in remarkable agreement with experimental data. Two assumptions commonly used in theoretical treatments; viz., the rigid-binding approximation (which assumes no conformational change upon complexation) and the neglect of vdW interactions, were found to yield large errors in the binding free energy. Protein-protein vdW and electrostatic interactions between complementary surfaces over a relatively large area (1400--1700 A(2)) were found to drive antibody-antigen and protease-inhibitor binding.     

Docking study and binding free energy calculation of poly (ADP-ribose) polymerase inhibitors

Recently, the massively parallel computation of absolute binding free energy with a well-equilibrated system (MP-CAFEE) has been developed. The present study aimed to determine whether the MP-CAFEE method is useful for drug discovery research. In the drug discovery process, it is important for computational chemists to predict the binding affinity accurately without detailed structural information for protein / ligand complex. We investigated the absolute binding free energies for Poly (ADP-ribose) polymerase-1 (PARP-1) / inhibitor complexes, using the MP-CAFEE method. Although each docking model was used as an input structure, it was found that the absolute binding free energies calculated by MP-CAFEE are well consistent with the experimental ones. The accuracy of this method is much higher than that using molecular mechanics Poisson-Boltzmann / surface area (MM / PBSA). Although the simulation time is quite extensive, the reliable predictor of binding free energies would be a useful tool for drug discovery projects.     

Small-world network approach to identify key residues in protein-protein interaction

We show that protein complexes can be represented as small-world networks, exhibiting a relatively small number of highly central amino-acid residues occurring frequently at protein-protein interfaces. We further base our analysis on a set of different biological examples of protein-protein interactions with experimentally validated hot spots, and show that 83% of these predicted highly central residues, which are conserved in sequence alignments and nonexposed to the solvent in the protein complex, correspond to or are in direct contact with an experimentally annotated hot spot. The remaining 17% show a general tendency to be close to an annotated hot spot. On the other hand, although there is no available experimental information on their contribution to the binding free energy, detailed analysis of their properties shows that they are good candidates for being hot spots. Thus, highly central residues have a clear tendency to be located in regions that include hot spots. We also show that some of the central residues in the protein complex interfaces are central in the monomeric structures before dimerization and that possible information relating to hot spots of binding free energy could be obtained from the unbound structures.     

Exploring PHD Fingers and H3K4me0 Interactions with Molecular Dynamics Simulations and Binding Free Energy Calculations: AIRE-PHD1, a Comparative Study

PHD fingers represent one of the largest families of epigenetic readers capable of decoding post-translationally modified or unmodified histone H3 tails. Because of their direct involvement in human pathologies they are increasingly considered as a potential therapeutic target. Several PHD/histone-peptide structures have been determined, however relatively little information is available on their dynamics. Studies aiming to characterize the dynamic and energetic determinants driving histone peptide recognition by epigenetic readers would strongly benefit from computational studies. Herein we focus on the dynamic and energetic characterization of the PHD finger subclass specialized in the recognition of histone H3 peptides unmodified in position K4 (H3K4me0). As a case study we focused on the first PHD finger of autoimmune regulator protein (AIRE-PHD1) in complex with H3K4me0. PCA analysis of the covariance matrix of free AIRE-PHD1 highlights the presence of a “flapping” movement, which is blocked in an open conformation upon binding to H3K4me0. Moreover, binding free energy calculations obtained through Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) methodology are in good qualitative agreement with experiments and allow dissection of the energetic terms associated with native and alanine mutants of AIRE-PHD1/H3K4me0 complexes. MM/PBSA calculations have also been applied to the energetic analysis of other PHD fingers recognizing H3K4me0. In this case we observe excellent correlation between computed and experimental binding free energies. Overall calculations show that H3K4me0 recognition by PHD fingers relies on compensation of the electrostatic and polar solvation energy terms and is stabilized by non-polar interactions.     

PSI-DOCK: towards highly efficient and accurate flexible ligand docking

We have developed a new docking method, Pose-Sensitive Inclined (PSI)-DOCK, for flexible ligand docking. An improved SCORE function has been developed and used in PSI-DOCK for binding free energy evaluation. The improved SCORE function was able to reproduce the absolute binding free energies of a training set of 200 protein-ligand complexes with a correlation coefficient of 0.788 and a standard error of 8.13 kJ/mol. For ligand binding pose exploration, a unique searching strategy was designed in PSI-DOCK. In the first step, a tabu-enhanced genetic algorithm with a rapid shape-complementary scoring function is used to roughly explore and store potential binding poses of the ligand. Then, these predicted binding poses are optimized and compete against each other by using a genetic algorithm with the accurate SCORE function to determine the binding pose with the lowest docking energy. The PSI-DOCK 1.0 program is highly efficient in identifying the experimental binding pose. For a test dataset of 194 complexes, PSI-DOCK 1.0 achieved a 67% success rate (RMSD < 2.0 A) for only one run and a 74% success rate for 10 runs. PSI-DOCK can also predict the docking binding free energy with high accuracy. For a test set of 64 complexes, the correlation between the experimentally observed binding free energies and the docking binding free energies for 64 complexes is r = 0.777 with a standard deviation of 7.96 kJ/mol. Moreover, compared with other docking methods, PSI-DOCK 1.0 is extremely easy to use and requires minimum docking preparations. There is no requirement for the users to add hydrogen atoms to proteins because all protein hydrogen atoms and the flexibility of the terminal protein atoms are intrinsically taken into account in PSI-DOCK. There is also no requirement for the users to calculate partial atomic charges because PSI-DOCK does not calculate an electrostatic energy term. These features are not only convenient for the users but also help to avoid the influence of different preparation methods.     

Computational analysis of binding of P1 variants to trypsin

The binding of P1 variants of bovine pancreatic trypsin inhibitor (BPTI) to trypsin has been investigated by means of molecular dynamics simulations. The specific interaction formed between the amino acid at the primary binding (P1) position of the binding loop of BPTI and the specificity pocket of trypsin was estimated by use of the linear interaction energy (LIE) method. Calculations for 13 of the naturally occurring amino acids at the P1 position were carried out, and the results obtained were found to correlate well with the experimental binding free energies. The LIE calculations rank the majority of the 13 variants correctly according to the experimental association energies and the mean error between calculated and experimental binding free energies is only 0.38 kcal/mole, excluding the Glu and Asp variants, which are associated with some uncertainties regarding protonation and the possible presence of counter-ions. The three-dimensional structures of the complex with three of the P1 variants (Asn, Tyr, and Ser) included in this study have not at present been solved by any experimental techniques and, therefore, were modeled on the basis of experimental data from P1 variants of similar size. Average structures were calculated from the MD simulations, from which specific interactions explaining the broad variation in association energies were identified. The present study also shows that explicit treatment of the complex water-mediated hydrogen bonding network at the protein-protein interface is of crucial importance for obtaining reliable binding free energies. The successful reproduction of relative binding energies shows that this type of methodology can be very useful as an aid in rational design and redesign of biologically active macromolecules.     

Predicting absolute ligand binding free energies to a simple model site

A central challenge in structure-based ligand design is the accurate prediction of binding free energies. Here we apply alchemical free energy calculations in explicit solvent to predict ligand binding in a model cavity in T4 lysozyme. Even in this simple site, there are challenges. We made systematic improvements, beginning with single poses from docking, then including multiple poses, additional protein conformational changes, and using an improved charge model. Computed absolute binding free energies had an RMS error of 1.9 kcal/mol relative to previously determined experimental values. In blind prospective tests, the methods correctly discriminated between several true ligands and decoys in a set of putative binders identified by docking. In these prospective tests, the RMS error in predicted binding free energies relative to those subsequently determined experimentally was only 0.6 kcal/mol. X-ray crystal structures of the new ligands bound in the cavity corresponded closely to predictions from the free energy calculations, but sometimes differed from those predicted by docking. Finally, we examined the impact of holding the protein rigid, as in docking, with a view to learning how approximations made in docking affect accuracy and how they may be improved.     

Insights into protein-protein binding by binding free energy calculation and free energy decomposition for the Ras-Raf and Ras-RalGDS complexes

Absolute binding free energy calculations and free energy decompositions are presented for the protein-protein complexes H-Ras/C-Raf1 and H-Ras/RalGDS. Ras is a central switch in the regulation of cell proliferation and differentiation. In our study, we investigate the capability of the molecular mechanics (MM)-generalized Born surface area (GBSA) approach to estimate absolute binding free energies for the protein-protein complexes. Averaging gas-phase energies, solvation free energies, and entropic contributions over snapshots extracted from trajectories of the unbound proteins and the complexes, calculated binding free energies (Ras-Raf: -15.0(+/-6.3)kcal mol(-1); Ras-RalGDS: -19.5(+/-5.9)kcal mol(-1)) are in fair agreement with experimentally determined values (-9.6 kcal mol(-1); -8.4 kcal mol(-1)), if appropriate ionic strength is taken into account. Structural determinants of the binding affinity of Ras-Raf and Ras-RalGDS are identified by means of free energy decomposition. For the first time, computationally inexpensive generalized Born (GB) calculations are applied in this context to partition solvation free energies along with gas-phase energies between residues of both binding partners. For selected residues, in addition, entropic contributions are estimated by classical statistical mechanics. Comparison of the decomposition results with experimentally determined binding free energy differences for alanine mutants of interface residues yielded correlations with r(2)=0.55 and 0.46 for Ras-Raf and Ras-RalGDS, respectively. Extension of the decomposition reveals residues as far apart as 25A from the binding epitope that can contribute significantly to binding free energy. These "hotspots" are found to show large atomic fluctuations in the unbound proteins, indicating that they reside in structurally less stable regions. Furthermore, hotspot residues experience a significantly larger-than-average decrease in local fluctuations upon complex formation. Finally, by calculating a pair-wise decomposition of interactions, interaction pathways originating in the binding epitope of Raf are found that protrude through the protein structure towards the loop L1. This explains the finding of a conformational change in this region upon complex formation with Ras, and it may trigger a larger structural change in Raf, which is considered to be necessary for activation of the effector by Ras.     

A comprehensive examination of the contributions to the binding entropy of protein–ligand complexes

One of the most important requirements in computer‐aided drug design is the ability to reliably evaluate the binding free energies. However, the process of ligand binding is very complex because of the intricacy of the interrelated processes that are difficult to predict and quantify. In fact, the deeper understanding of the origin of the observed binding free energies requires the ability to decompose these free energies to their contributions from different interactions. Furthermore, it is important to evaluate the relative entropic and enthalpic contributions to the overall free energy. Such an evaluation is useful for assessing temperature effects and exploring specialized options in enzyme design. Unfortunately, calculations of binding entropies have been much more challenging than calculations of binding free energies. This work is probably the first to present microscopic evaluation of all of the relevant components to the binding entropy, namely configurational, polar solvation, and hydrophobic entropies. All of these contributions are evaluated by the restraint release approach. The calculated results shed an interesting light on major compensation effects in both the solvation and hydrophobic effect and, despite some overestimate, can provide very useful insight. This study also helps in analyzing some problems with the widely used molecular mechanics/Poisson‐Boltzmann surface area approach. Proteins 2010. © 2010 Wiley‐Liss, Inc.