Crystal contacts as nature's docking solutions

The assumption that crystal contacts reflect natural macromolecular interactions makes a basis for many studies in structural biology. However, the crystal state may correspond to a global minimum of free energy where biologically relevant interactions are sacrificed in favor to unspecific contacts. A large‐scale docking experiment was performed to assess the extent of misrepresentation of natural (in‐solvent) protein dimers by crystal packing. As found, the failure rate of docking may be quantitatively interpreted if both calculation errors and misrepresentation effects are taken into account. The failure rate analysis is based on the assumption that crystal structures reflect thermodynamic equilibrium between different dimeric configurations. The analysis gives an estimate of misrepresentation probability, which suggests that weakly bound complexes with K_D ≥ 100 μM (some 20% of all dimers in the PDB) have higher than 50% chances to be misrepresented by crystals. The developed theoretical framework is applicable in other studies, where experimental results may be viewed as snapshots of systems in thermodynamic equilibrium. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Update of the ATTRACT force field for the prediction of protein–protein binding affinity

Determining the protein–protein interactions is still a major challenge for molecular biology. Docking protocols has come of age in predicting the structure of macromolecular complexes. However, they still lack accuracy to estimate the binding affinities, the thermodynamic quantity that drives the formation of a complex. Here, an updated version of the protein–protein ATTRACT force field aiming at predicting experimental binding affinities is reported. It has been designed on a dataset of 218 protein–protein complexes. The correlation between the experimental and predicted affinities reaches 0.6, outperforming most of the available protocols. Focusing on a subset of rigid and flexible complexes, the performance raises to 0.76 and 0.69, respectively. © 2017 Wiley Periodicals, Inc.     

Conformation and Biological Activity of Cyclic Peptides

Cyclic peptides containing biologically active hormone sequences are suitable models for studying conformation-activity relationships. In such models the usual flexibility of peptide chains is reduced by their cyclic arrangement. However, conformational analysis of such systems by experimental means is possible only if a single conformer predominates at equilibrium, and criteria for this are put forward. NMR spectroscopic methods, including many recent advances, are discussed in relation to their ability to contribute to peptide conformational analysis.     

Modeling loop backbone flexibility in receptor‐ligand docking simulations

The relevance of receptor conformational change during ligand binding is well documented for many pharmaceutically relevant receptors, but is still not fully accounted for in in silico docking methods. While there has been significant progress in treatment of receptor side chain flexibility sampling of backbone flexibility remains challenging because the conformational space expands dramatically and the scoring function must balance protein–protein and protein–ligand contributions. Here, we investigate an efficient multistage backbone reconstruction algorithm for large loop regions in the receptor and demonstrate that treatment of backbone receptor flexibility significantly improves binding mode prediction starting from apo structures and in cross docking simulations. For three different kinase receptors in which large flexible loops reconstruct upon ligand binding, we demonstrate that treatment of backbone flexibility results in accurate models of the complexes in simulations starting from the apo structure. At the example of the DFG‐motif in the p38 kinase, we also show how loop reconstruction can be used to model allosteric binding. Our approach thus paves the way to treat the complex process of receptor reconstruction upon ligand binding in docking simulations and may help to design new ligands with high specificity by exploitation of allosteric mechanisms. © 2012 Wiley Periodicals, Inc.     

Simulation of conformational changes occurring when a protein interacts with its receptor

In order to simulate the conformational changes occurring when a protein interacts with its receptor, we firstly evaluated the structural differences between the experimental unbound and bound conformations for selected proteins and created theoretical complexes by replacing, in each experimental complex, the protein-bound with the protein-unbound chain. The theoretical models were then subjected to additional modeling refinements to improve the side chain geometry. Comparing the theoretical and experimental complexes in term of structural and energetic factors is resulted that the refined theoretical complexes became more similar to the experimental ones. We applied the same procedure within an homology modeling experiment, using as templates the experimental structures of human interleukin-1beta (IL-1beta) unbound and bound with its receptor, to build models of the homologous proteins from mouse and trout in unbound and bound conformations and to simulate the interaction with the related receptors. Our results suggest that homology modeling techniques are sensitive to differences between bound and unbound conformations, and that modeling with accuracy the side chains in the complex improves the interaction and molecular recognition. Moreover, our refinement procedure could be used in protein-protein interaction studies and, also, applied in conjunction with rigid-body docking when is not available the protein-bound conformation.     

Efficient inclusion of receptor flexibility in grid-based protein-ligand docking

Accounting for receptor flexibility is an essential component of successful protein-ligand docking but still marks a major computational challenge. For many target molecules of pharmaceutical relevance, global backbone conformational changes are relevant during the ligand binding process. However, popular methods that represent the protein receptor molecule as a potential grid typically assume a rigid receptor structure during ligand-receptor docking. A new approach has been developed that combines inclusion of global receptor flexibility with the efficient potential grid representation of the receptor molecule. This is achieved using interpolation between grid representations of the receptor protein deformed in selected collective degrees of freedom. The method was tested on the docking of three ligands to apo protein kinase A (PKA), an enzyme that undergoes global structural changes upon inhibitor binding. Structural variants of PKA were generated along the softest normal mode of an elastic network representation of apo PKA. Inclusion of receptor deformability during docking resulted in a significantly improved docking performance compared with rigid PKA docking, thus allowing for systematic virtual screening applications at small additional computational cost.     

DOX: A new computational protocol for accurate prediction of the protein–ligand binding structures

Molecular docking techniques have now been widely used to predict the protein–ligand binding modes, especially when the structures of crystal complexes are not available. Most docking algorithms are able to effectively generate and rank a large number of probable binding poses. However, it is hard for them to accurately evaluate these poses and identify the most accurate binding structure. In this study, we first examined the performance of some docking programs, based on a testing set made of 15 crystal complexes with drug statins for the human 3‐hydroxy‐3‐methylglutaryl coenzyme A reductase (HMGR). We found that most of the top ranking HMGR–statin binding poses, predicted by the docking programs, were energetically unstable as revealed by the high theoretical‐level calculations, which were usually accompanied by the large deviations from the geometric parameters of the corresponding crystal binding structures. Subsequently, we proposed a new computational protocol, DOX, based on the joint use of molecular Docking, ONIOM, and eXtended ONIOM (XO) methods to predict the accurate binding structures for the protein–ligand complexes of interest. Our testing results demonstrate that the DOX protocol can efficiently predict accurate geometries for all 15 HMGR‐statin crystal complexes without exception. This study suggests a promising computational route, as an effective alternative to the experimental one, toward predicting the accurate binding structures, which is the prerequisite for all the deep understandings of the properties, functions, and mechanisms of the protein–ligand complexes. © 2015 Wiley Periodicals, Inc.     

Fully automated molecular mechanics based induced fit protein-ligand docking method

We describe a method for docking a ligand into a protein receptor while allowing flexibility of the protein binding site. The method employs a multistep procedure that begins with the generation of protein and ligand conformations. An initial placement of the ligand is then performed by computing binding site hotspots. This initial placement is followed by a protein side-chain refinement stage that models protein flexibility. The final step of the process is an energy minimization of the ligand pose in the presence of the rigid receptor. Thus the algorithm models flexibility of the protein at two stages, before and after ligand placement. We validated this method by performing docking and cross docking studies of eight protein systems for which crystal structures were available for at least two bound ligands. The resulting rmsd values of the 21 docked protein-ligand complexes showed values of 2 A or less for all but one of the systems examined. The method has two critical benefits for high throughput virtual screening studies. First, no user intervention is required in the docking once the initial binding site selection has been made in the protein. Second, the initial protein conformation generation needs to be performed only once for a given binding region. Also, the method may be customized in various ways depending on the particular scenario in which dockings are being performed. Each of the individual steps of the method is fully independent making it straightforward to explore different variants of the high level workflow to further improve accuracy and performance.     

Docking of ATP to Ca-ATPase: considering protein domain motions

Most standard molecular docking algorithms take into account only ligand flexibility, while numerous studies demonstrate that receptor flexibility may be also important. While some efficient methods have been proposed to take into account local flexibility of protein side chains, the influence of large-scale domain motions on the docking results still represents a challenge for computational methods. In this work we compared the results of ATP docking to different models of Ca-ATPase: crystallographic apo- and holo-forms of the enzyme as well as "flexible" target models generated via molecular dynamics (MD) simulations in water. MD simulations were performed for two different apo-forms and one holo-form of Ca2+-ATPase and reveal large-scale domain motions of type "closure", which is consistent with experimental structures. Docking to a set of MD-conformers yielded correct solutions with ATP bound in both domains regardless of the starting Ca2+-ATPase structure. Also, special attention was paid to proper ranking of docking solutions and some particular features of different scoring functions and their applicability for the model of "flexible" receptor. Particularly, the results of docking ATP were ranked by a scoring criterion specially designed to estimate ATP-protein interactions. This criterion includes stacking and hydrophobic interactions characteristic of ATP-protein complexes. The performance of this ligand-specific scoring function was considerably better than that of a standard scoring function used in the docking algorithm.     

Flexible docking of ligands into synthetic receptors using a two-sided incremental construction algorithm

We present a new algorithm for the fast and reliable structure prediction of synthetic receptor-ligand complexes. Our method is based on the protein-ligand docking program FlexX and extends our recently introduced docking technique for synthetic receptors, which has been implemented in the program FlexR. To handle the flexibility of the relevant molecules, we apply a novel docking strategy that uses an adaptive two-sided incremental construction algorithm which incorporates the structural flexibility of both the ligand and synthetic receptor. We follow an adaptive strategy, in which one molecule is expanded by attaching its next fragment in all possible torsion angles, whereas the other (partially assembled) molecule serves as a rigid binding partner. Then the roles of the molecules are exchanged. Geometric filters are used to discard partial conformations that cannot realize a targeted interaction pattern derived in a graph-based precomputation phase. The process is repeated until the entire complex is built up. Our algorithm produces promising results on a test data set comprising 10 complexes of synthetic receptors and ligands. The method generated near-native solutions compared to crystal structures in all but one case. It is able to generate solutions within a couple of minutes and has the potential of being used as a virtual screening tool for searching for suitable guest molecules for a given synthetic receptor in large databases of guests and vice versa.     

Ranking protein–protein docking results using steered molecular dynamics and potential of mean force calculations

Crystallization of protein–protein complexes can often be problematic and therefore computational structural models are often relied on. Such models are often generated using protein–protein docking algorithms, where one of the main challenges is selecting which of several thousand potential predictions represents the most near‐native complex. We have developed a novel technique that involves the use of steered molecular dynamics (sMD) and umbrella sampling to identify near‐native complexes among protein–protein docking predictions. Using this technique, we have found a strong correlation between our predictions and the interface RMSD (iRMSD) in ten diverse test systems. On two of the systems, we investigated if the prediction results could be further improved using potential of mean force calculations. We demonstrated that a near‐native (<2.0 Å iRMSD) structure could be identified in the top‐1 ranked position for both systems. © 2016 Wiley Periodicals, Inc.     

A fast algorithm for the interactive docking maneuver with flexible macromolecules and probes

A new algorithm for the interactive docking maneuver is presented. Full attention is given to the flexibility of both substrate and macromolecule, i.e., all the fragments are allowed to move. It is assumed that any numerical quantity which depends only on the isolated macromolecule at energy minimum is disposable when approximate expressions are derived. The central idea is the concept of relevant docking coordinates which reflect the essential features of the macromolecular deformations during the docking maneuver and which substantially diminish the number of considered degrees of freedom (DF). The conformational energy is divided into two parts. The first part, represented by condensed potential functions, needs no approximations. For the second part, termed E_rest, a quadratic approximation in the subspace spanned by the relevant docking coordinates is used. All the pairwise interactions between the atoms of the macromolecule are eliminated. A simple computational example using the ECEPP force field is given. Atomic coordinate computations are simplified by the introduction of virtual rotation axes for the backbone. In connection with drug design the concept of pressure pattern is defined and related to quantities appearing in the energy gradient. Extensions to substrate induced allosteric transitions are discussed.     

Fast docking using the CHARMM force field with EADock DSS

The prediction of binding modes (BMs) occurring between a small molecule and a target protein of biological interest has become of great importance for drug development. The overwhelming diversity of needs leaves room for docking approaches addressing specific problems. Nowadays, the universe of docking software ranges from fast and user friendly programs to algorithmically flexible and accurate approaches. EADock2 is an example of the latter. Its multiobjective scoring function was designed around the CHARMM22 force field and the FACTS solvation model. However, the major drawback of such a software design lies in its computational cost. EADock dihedral space sampling (DSS) is built on the most efficient features of EADock2, namely its hybrid sampling engine and multiobjective scoring function. Its performance is equivalent to that of EADock2 for drug‐like ligands, while the CPU time required has been reduced by several orders of magnitude. This huge improvement was achieved through a combination of several innovative features including an automatic bias of the sampling toward putative binding sites, and a very efficient tree‐based DSS algorithm. When the top‐scoring prediction is considered, 57% of BMs of a test set of 251 complexes were reproduced within 2 Å RMSD to the crystal structure. Up to 70% were reproduced when considering the five top scoring predictions. The success rate is lower in cross‐docking assays but remains comparable with that of the latest version of AutoDock that accounts for the protein flexibility. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Harmonic modes as variables to approximately account for receptor flexibility in ligand–receptor docking simulations: Application to DNA minor groove ligand complex

An approach to approximately account for receptor flexibility in ligand–receptor docking simulations is described and applied to a DNA/Hoechst 33258 analogue complex. Harmonic modes corresponding to eigenvectors with small eigenvalues of the Hessian matrix of the potential energy function were used as independent variables to describe receptor flexibility. For the DNA minor groove ligand case most of the conformational difference between an energy minimized free DNA and ligand-bound structure could be assigned to 5–40 harmonic receptor modes with small eigenvalues. During docking, deformations of the DNA receptor structure in the subset of harmonic modes were limited using a simple penalty function that avoided the summation over all intrareceptor atom pairs. Significant improvement of the sterical fit between ligand and receptor was found upon relaxation of the DNA in the subset of harmonic modes after docking of the ligand at the position found in the known crystal structure. In addition, the harmonic mode relaxation resulted in DNA structures that were more similar to the energy minimized ligand-bound form. Although harmonic mode relaxation also leads to improved sterical fit for other ligand placements, the placement as observed in the crystal structure could still be identified as the site with the most favorable sterical interactions. Because relaxation in the harmonic modes is orders of magnitude faster than conventional energy minimization using all atom coordinates as independent variables, the approach might be useful as a preselection tool to recognize ligand binding sites accessible only upon small conformational changes of the receptor. The harmonic mode relaxed structures can only be considered as approximate structures because deformation of the receptor in the harmonic modes can lead to small perturbations of the stereochemical geometry of the molecule. Energy minimization of preselected ligand–DNA docking candidates in all atom coordinates is required to reduce these deviations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 287–300, 1999     

Gaussian mapping of chemical fragments in ligand binding sites

We present a new approach to automatically define a quasi-optimal minimal set of pharmacophoric points mapping the interaction properties of a user-defined ligand binding site. The method is based on a fitting algorithm where a grid of sampled interaction energies of the target protein with small chemical fragments in the binding site is approximated by a linear expansion of Gaussian functions. A heuristic approximation selects from this expansion the smallest possible set of Gaussians required to describe the interaction properties of the binding site within a prespecified accuracy. We have evaluated the performance of the approach by comparing the computed Gaussians with the positions of aromatic sites found in experimental protein-ligand complexes. For a set of 53 complexes, good correspondence is found in general. At a 95% significance level, approximately 65% of the predicted interaction points have an aromatic binding site within 1.5 A. We then studied the utility of these points in docking using the program DOCK. Short docking times, with an average of approximately 0.18 s per conformer, are obtained, while retaining, both for rigid and flexible docking, the ability to sample native-like binding modes for the ligand. An average 4-5-fold speed-up in docking times and a similar success rate is estimated with respect to the standard DOCK protocol.     

Structural mining: self-consistent design on flexible protein-peptide docking and transferable binding affinity potential

A flexible protein-peptide docking method has been designed to consider not only ligand flexibility but also the flexibility of the protein. The method is based on a Monte Carlo annealing process. Simulations with a distance root-mean-square (dRMS) virtual energy function revealed that the flexibility of protein side chains was as important as ligand flexibility for successful protein-peptide docking. On the basis of mean field theory, a transferable potential was designed to evaluate distance-dependent protein-ligand interactions and atomic solvation energies. The potential parameters were developed using a self-consistent process based on only 10 known complex structures. The effectiveness of each intermediate potential was judged on the basis of a Z score, approximating the gap between the energy of the native complex and the average energy of a decoy set. The Z score was determined using experimentally determined native structures and decoys generated by docking with the intermediate potentials. Using 6600 generated decoys and the Z score optimization criterion proposed in this work, the developed potential yielded an acceptable correlation of R(2) = 0.77, with binding free energies determined for known MHC I complexes (Class I Major Histocompatibility protein HLA-A(*)0201) which were not present in the training set. Test docking on 25 complexes further revealed a significant correlation between energy and dRMS, important for identifying native-like conformations. The near-native structures always belonged to one of the conformational classes with lower predicted binding energy. The lowest energy docked conformations are generally associated with near-native conformations, less than 3.0 Angstrom dRMS (and in many cases less than 1.0 Angstrom) from the experimentally determined structures.     

Do Intrinsically Disordered Proteins Possess High Specificity in Protein–Protein Interactions?

Specific protein–protein interactions are critical to cellular function. Structural flexibility and disorder‐to‐order transitions upon binding enable intrinsically disordered proteins (IDPs) to overcome steric restrictions and form complementary binding interfaces, and thus, IDPs are widely considered to have high specificity and low affinity for molecular recognition. However, flexibility may also enable IDPs to form complementary binding interfaces with misbinding partners, resulting in a great number of nonspecific interactions. Consequently, it is questionable whether IDPs really possess high specificity. In this work, we investigated this question from a thermodynamic viewpoint. We collected mutant thermodynamic data for 35 ordered protein complexes and 43 disordered protein complexes. We found that the enthalpy–entropy compensation for disordered protein complexes was more complete than that for ordered protein complexes. We further simulated the binding processes of ordered and disordered protein complexes under mutations. Simulation data confirmed the observation of experimental data analyses and further revealed that disordered protein complexes possessed smaller changes in binding free energy than ordered protein complexes under the same mutation perturbations. Therefore, interactions of IDPs are more malleable than those of ordered proteins due to their structural flexibility in the complex. Our results provide new clues for exploring the relationship between protein flexibility, adaptability, and specificity.     

Assessing search strategies for flexible docking

We assess the efficiency of molecular dynamics (MD), Monte Carlo (MC), and genetic algorithms (GA) for docking five representative ligand–receptor complexes. All three algorithms employ a modified CHARMM-based energy function. The algorithms are also compared with an established docking algorithm, AutoDock. The receptors are kept rigid while flexibility of ligands is permitted. To test the efficiency of the algorithms, two search spaces are used: an 11-Å-radius sphere and a 2.5-Å-radius sphere, both centered on the active site. We find MD is most efficient in the case of the large search space, and GA outperforms the other methods in the small search space. We also find that MD provides structures that are, on average, lower in energy and closer to the crystallographic conformation. The GA obtains good solutions over the course of the fewest energy evaluations. However, due to the nature of the nonbonded interaction calculations, the GA requires the longest time for a single energy evaluation, which results in a decreased efficiency. The GA and MC search algorithms are implemented in the CHARMM macromolecular package. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1623–1631, 1998