Ligand solvation in molecular docking

Solvation plays an important role in ligand‐protein association and has a strong impact on comparisons of binding energies for dissimilar molecules. When databases of such molecules are screened for complementarity to receptors of known structure, as often occurs in structure‐based inhibitor discovery, failure to consider ligand solvation often leads to putative ligands that are too highly charged or too large. To correct for the different charge states and sizes of the ligands, we calculated electrostatic and non‐polar solvation free energies for molecules in a widely used molecular database, the Available Chemicals Directory (ACD). A modified Born equation treatment was used to calculate the electrostatic component of ligand solvation. The non‐polar component of ligand solvation was calculated based on the surface area of the ligand and parameters derived from the hydration energies of apolar ligands. These solvation energies were subtracted from the ligand‐receptor interaction energies. We tested the usefulness of these corrections by screening the ACD for molecules that complemented three proteins of known structure, using a molecular docking program. Correcting for ligand solvation improved the rankings of known ligands and discriminated against molecules with inappropriate charge states and sizes. Proteins 1999;34:4–16. © 1999 Wiley‐Liss, Inc.     

Investigating protein-protein interaction surfaces using a reduced stereochemical and electrostatic model

A method of calculating the electrostatic potential energy between two molecules, using finite difference potential, is presented. A reduced charge set is used so that the interaction energy can be calculated as the two static molecules explore their full six-dimensional configurational space. The energies are contoured over surfaces fixed to each molecule with an interactive computer graphics program. For two crystal structures (trypsin-trypsin inhibitor and anti-lysozyme Fab-lysozyme), it is found that the complex corresponds to highly favourable interacting regions in the contour plots. These matches arise from a small number of protruding basic residues interacting with enhanced negative potential in each case. The redox pair cytochrome c peroxidase-cytochrome c exhibits an extensive favourably interacting surface within which a possible electron transfer complex may be defined by an increased electrostatic complementarity, but a decreased electrostatic energy. A possible substrate transfer configuration for the glycolytic enzyme pair glyceraldehyde phosphate dehydrogenase-phosphoglycerate kinase is presented.     

Side-chain flexibility in protein-ligand binding: the minimal rotation hypothesis

The goal of this work is to learn from nature about the magnitudes of side-chain motions that occur when proteins bind small organic molecules, and model these motions to improve the prediction of protein-ligand complexes. Following analysis of protein side-chain motions upon ligand binding in 63 complexes, we tested the ability of the docking tool SLIDE to model these motions without being restricted to rotameric transitions or deciding which side chains should be considered as flexible. The model tested is that side-chain conformational changes involving more atoms or larger rotations are likely to be more costly and less prevalent than small motions due to energy barriers between rotamers and the potential of large motions to cause new steric clashes. Accordingly, SLIDE adjusts the protein and ligand side groups as little as necessary to achieve steric complementarity. We tested the hypothesis that small motions are sufficient to achieve good dockings using 63 ligands and the apo structures of 20 different proteins and compared SLIDE side-chain rotations to those experimentally observed. None of these proteins undergoes major main-chain conformational change upon ligand binding, ensuring that side-chain flexibility modeling is not required to compensate for main-chain motions. Although more frugal in the number of side-chain rotations performed, this model substantially mimics the experimentally observed motions. Most side chains do not shift to a new rotamer, and small motions are both necessary and sufficient to predict the correct binding orientation and most protein-ligand interactions for the 20 proteins analyzed.     

Effect of local shape modifications of molecular surfaces on rigid-body protein-protein docking

Geometric complementarity is the most dominant term in protein-protein docking and therefore, a good geometric representation of the molecules, which takes into account the flexibility of surface residues, is desirable. We present a modified geometric representation of the molecular surface that down-weighs the contribution of specified parts of the surface to the complementarity score. We apply it to the mobile ends of the most flexible side chains: lysines, glutamines and arginines (trimming). The new representation systematically reduces the complementarity scores of the false-positive solutions, often more than the scores of the correct solutions, thereby improving significantly our ability to identify nearly correct solutions in rigid-body docking of unbound structures. The effect of trimming lysine residues is larger than trimming of glutamine or arginine residues. It appears to be independent of the conformations of the trimmed residues but depends on the relative abundance of such residues at the interface and on the non-interacting surface. Combining the modified geometric representation with electrostatic complementarity further improves the docking results.     

Automated docking of peptides and proteins by using a genetic algorithm combined with a tabu search.

A genetic algorithm (GA) combined with a tabu search (TA) has been applied as a minimization method to rake the appropriate associated sites for some biomolecular systems. In our docking procedure, surface complementarity and energetic complementarity of a ligand with its receptor have been considered separately in a two-stage docking method. The first stage was to find a set of potential associated sites mainly based on surface complementarity using a genetic algorithm combined with a tabu search. This step corresponds with the process of finding the potential binding sites where pharmacophores will bind. In the second stage, several hundreds of GA minimization steps were performed for each associated site derived from the first stage mainly based on the energetic complementarity. After calculations for both of the two stages, we can offer several solutions of associated sites for every complex. In this paper, seven biomolecular systems, including five bound complexes and two unbound complexes, were chosen from the Protein Data Bank (PDB) to test our method. The calculated results were very encouraging-the hybrid minimization algorithm successfully reaches the correct solutions near the best binded modes for these protein complexes. The docking results not only predict the bound complexes very well, but also get a relatively accurate complexed conformation for unbound systems. For the five bound complexes, the results show that surface complementarity is enough to find the precise binding modes, the top solution from the tabu list generally corresponds to the correct binding mode. For the two unbound complexes, due to the conformational changes upon binding, it seems more difficult to get their correct binding conformations. The predicted results show that the correct binding mode also corresponds to a relatively large surface complementarity score. In these two test cases, the correct solution can be found in the top several solutions from the tabu list. For unbound complexes, the interaction energy from energetic complementarity is very important, it can be used to filter these solutions from the surface complementarity. After the evaluation of the energetic complementarity, the conformations and orientations close to the crystallographically determined structures are resolved. In most cases, the smallest root mean square distance (r.m.s.d.) from the GA combined with TA solutions is in a relatively small region. Our program of automatic docking is really a universal one among the procedures used for the theoretical study of molecular recognition.     

Computer design of bioactive molecules: a method for receptor-based de novo ligand design.

The design of molecules to bind specifically to protein receptors has long been a goal of computer-assisted molecular design. Given detailed structural knowledge of the target receptor, it should be possible to construct a model of a potential ligand, by algorithmic connection of small molecular fragments, that will exhibit the desired structural and electrostatic complementarity with the receptor. However, progress in this area of receptor-based, de novo ligand design has been hampered by the complexity of the construction process, in which potentially huge numbers of structures must be considered. By limiting the scope of the structure-space examined to one particular class of ligands--namely, peptides and peptide-like compounds--the problem complexity has been reduced to the point that successful, de novo design is now possible. The methodology presented employs a large template set of amino acid conformations which are iteratively pieced together in a model of the target receptor. Each stage of ligand growth is evaluated according to a molecular mechanics-based energy function, which considers van der Waals and coulombic interactions, internal strain energy of the lengthening ligand, and desolvation of both ligand and receptor. The search space is managed by use of a data tree which is kept under control by pruning according to the energy evaluation. Ligands grown by this procedure are subjected to follow-up evaluation in which an approximate binding enthalpy is determined. This methodology has proven useful as a precise model-builder and has also shown the ability to design bioactive ligands.     

Electrostatic lock-and-key model for the study of biological isosterism: role of structural water in the binding of basic pancreatic trypsin inhibitor to beta-trypsin

We propose the electrostatic lock-and-key model for the analysis of the interaction between beta-trypsin and basic pancreatic trypsin inhibitor (BPTI). Prerequisite for the proper recognition of the ligand by the protein is that, beside a steric complementarity, matching of electrostatic patterns is attained. It is found that the complementarity is imperfect in the vicinity of BPTI backbone carbonyl oxygen atoms and this imperfection is diminished by the presence of structural water molecules bound to the contact surface. Some novel types of biological isosteres are proposed. It is expected that the Gibbs free energy of binding increases upon changing the moieties greater than C = O ... H-OH and greater than C = O to greater than CHCH2 CH2OH and greater than CHOH groups, respectively.     

Examination of shape complementarity in docking of unbound proteins.

Here we carry out an examination of shape complementarity as a criterion in protein-protein docking and binding. Specifically, we examine the quality of shape complementarity as a critical determinant not only in the docking of 26 protein-protein "bound" complexed cases, but in particular, of 19 "unbound" protein-protein cases, where the structures have been determined separately. In all cases, entire molecular surfaces are utilized in the docking, with no consideration of the location of the active site, or of particular residues/atoms in either the receptor or the ligand that participate in the binding. To evaluate the goodness of the strictly geometry-based shape complementarity in the docking process as compared to the main favorable and unfavorable energy components, we study systematically a potential correlation between each of these components and the root mean square deviation (RMSD) of the "unbound" protein-protein cases. Specifically, we examine the non-polar buried surface area, polar buried surface area, buried surface area relating to groups bearing unsatisfied buried charges, and the number of hydrogen bonds in all docked protein-protein interfaces. For these cases, where the two proteins have been crystallized separately, and where entire molecular surfaces are considered without a predefinition of the binding site, no correlation is observed. None of these parameters appears to consistently improve on shape complementarity in the docking of unbound molecules. These findings argue that simplicity in the docking process, utilizing geometrical shape criteria may capture many of the essential features in protein-protein docking. In particular, they further reinforce the long held notion of the importance of molecular surface shape complementarity in the binding, and hence in docking. This is particularly interesting in light of the fact that the structures of the docked pairs have been determined separately, allowing side chains on the surface of the proteins to move relatively freely. This study has been enabled by our efficient, computer vision-based docking algorithms. The fast CPU matching times, on the order of minutes on a PC, allow such large-scale docking experiments of large molecules, which may not be feasible by other techniques. Proteins 1999;36:307-317.     

How organic molecules can control electronic devices.

This article examines a somewhat counter-intuitive approach to molecular-based electronic devices. Control over the electronic energy levels at the surfaces of conventional semiconductors and metals is achieved by assembling on the solid surfaces, poorly organized, partial monolayers (MLs) of molecules instead of the more commonly used ideal ones. Once those surfaces become interfaces, these layers exert electrostatic rather than electrodynamic control over the resulting devices, based on both electrical monopole and dipole effects of the molecules. Thus electronic transport devices, incorporating molecules, can be constructed without current flow through the molecules. This is illustrated for a gallium arsenide (GaAs) sensor as well as for gold-silicon (Au-Si) and Au-GaAs diodes. Incorporating molecules into solid interfaces becomes possible, using a 'soft' electrical contacting procedure, so as not to damage the molecules. Because there are only a few molecular restrictions, this approach opens up possibilities for the use of more complex (including biologically active) molecules as it circumvents requirements for ideal MLs and for molecules that can tolerate actual electron transport through them.     

BiGGER: a new (soft) docking algorithm for predicting protein interactions

A new computationally efficient and automated "soft docking" algorithm is described to assist the prediction of the mode of binding between two proteins, using the three-dimensional structures of the unbound molecules. The method is implemented in a software package called BiGGER (Bimolecular Complex Generation with Global Evaluation and Ranking) and works in two sequential steps: first, the complete 6-dimensional binding spaces of both molecules is systematically searched. A population of candidate protein-protein docked geometries is thus generated and selected on the basis of the geometric complementarity and amino acid pairwise affinities between the two molecular surfaces. Most of the conformational changes observed during protein association are treated in an implicit way and test results are equally satisfactory, regardless of starting from the bound or the unbound forms of known structures of the interacting proteins. In contrast to other methods, the entire molecular surfaces are searched during the simulation, using absolutely no additional information regarding the binding sites. In a second step, an interaction scoring function is used to rank the putative docked structures. The function incorporates interaction terms that are thought to be relevant to the stabilization of protein complexes. These include: geometric complementarity of the surfaces, explicit electrostatic interactions, desolvation energy, and pairwise propensities of the amino acid side chains to contact across the molecular interface. The relative functional contribution of each of these interaction terms to the global scoring function has been empirically adjusted through a neural network optimizer using a learning set of 25 protein-protein complexes of known crystallographic structures. In 22 out of 25 protein-protein complexes tested, near-native docked geometries were found with C(alpha) RMS deviations < or =4.0 A from the experimental structures, of which 14 were found within the 20 top ranking solutions. The program works on widely available personal computers and takes 2 to 8 hours of CPU time to run any of the docking tests herein presented. Finally, the value and limitations of the method for the study of macromolecular interactions, not yet revealed by experimental techniques, are discussed.     

Hydrophobic complementarity in protein-protein docking

Formation of hydrophobic contacts across a newly formed interface is energetically favorable. Based on this observation we developed a geometric-hydrophobic docking algorithm that estimates quantitatively the hydrophobic complementarity at protein-protein interfaces. Each molecule to be docked is represented as a grid of complex numbers, storing information regarding the shape of the molecule in the real part and information regarding the hydropathy of the surface in the imaginary part. The grid representations are correlated using fast Fourier transformations. The algorithm is used to compare the extent of hydrophobic complementarity in oligomers (represented by D2 tetramers) and in hetero-dimers of soluble proteins (complexes). We also test the implication of hydrophobic complementarity in distinguishing correct from false docking solutions. We find that hydrophobic complementarity at the interface exists in oligomers and in complexes, and in both groups the extent of such complementarity depends on the size of the interface. Thus, the non-polar portions of large interfaces are more often juxtaposed than non-polar portions of small interfaces. Next we find that hydrophobic complementarity helps to point out correct docking solutions. In oligomers it significantly improves the ranks of nearly correct reassembled and modeled tetramers. Combining geometric, electrostatic and hydrophobic complementarity for complexes gives excellent results, ranking a nearly correct solution < 10 for 5 of 23 tested systems, < 100 for 8 systems and < 1000 for 19 systems.     

Molecular docking using surface complementarity

A method is described to dock a ligand into a binding site in a protein on the basis of the complementarity of the inter-molecular atomic contacts. Docking is performed by maximization of a complementarity function that is dependent on atomic contact surface area and the chemical properties of the contacting atoms. The generality and simplicity of the complementarity function ensure that a wide range of chemical structures can be handled. The ligand and the protein are treated as rigid bodies, but displacement of a small number of residues lining the ligand binding site can be taken into account. The method can assist in the design of improved ligands by indicating what changes in complementarity may occur as a result of the substitution of an atom in the ligand. The capabilities of the method are demonstrated by application to 14 protein–ligand complexes of known crystal structure. © 1996 Wiley Liss, Inc.     

Preorientation of protein and RNA just before contacting

Protein and RNA molecules interact and form complexes in many biological processes. However, it is still unclear how they can find the correct docking direction before forming complex. In this paper, we study preorientation of RNA and protein separated at a distance of 5–7?Å just before they form contacts and interact with each other only through pure electrostatic interaction when neglecting the influence of other molecules and complicated environment. Since geometric complementary has no meaning at such a distance, this is not a docking problem and so the conventional docking methods, like FTDock, are inapplicable. However, like the usual docking problem, we need to sample all the positions and orientations of RNA surrounding the protein to find the lowest energy orientations between RNA and protein. Therefore, we propose a long-range electrostatic docking-like method using Fast Fourier Transform-based sampling, LEDock, to study this problem. Our results show that the electrostatically induced orientations between RNA and protein at a distance of 5–7?Å are very different from the random ones and are much closer to those in their native complexes. Meanwhile, electrostatic funnels are found around the RNA-binding sites of the proteins in 62 out of 78 bound protein–RNA complexes. We also tried to use LEDock to find RNA-binding residues and it seems to perform slightly better than BindN Server for 23 unbound protein–RNA complexes.     

Protein-protein docking with multiple residue conformations and residue substitutions

The protein docking problem has two major aspects: sampling conformations and orientations, and scoring them for fit. To investigate the extent to which the protein docking problem may be attributed to the sampling of ligand side‐chain conformations, multiple conformations of multiple residues were calculated for the uncomplexed (unbound) structures of protein ligands. These ligand conformations were docked into both the complexed (bound) and unbound conformations of the cognate receptors, and their energies were evaluated using an atomistic potential function. The following questions were considered: (1) does the ensemble of precalculated ligand conformations contain a structure similar to the bound form of the ligand? (2) Can the large number of conformations that are calculated be efficiently docked into the receptors? (3) Can near‐native complexes be distinguished from non‐native complexes? Results from seven test systems suggest that the precalculated ensembles do include side‐chain conformations similar to those adopted in the experimental complexes. By assuming additivity among the side chains, the ensemble can be docked in less than 12 h on a desktop computer. These multiconformer dockings produce near‐native complexes and also non‐native complexes. When docked against the bound conformations of the receptors, the near‐native complexes of the unbound ligand were always distinguishable from the non‐native complexes. When docked against the unbound conformations of the receptors, the near‐native dockings could usually, but not always, be distinguished from the non‐native complexes. In every case, docking the unbound ligands with flexible side chains led to better energies and a better distinction between near‐native and non‐native fits. An extension of this algorithm allowed for docking multiple residue substitutions (mutants) in addition to multiple conformations. The rankings of the docked mutant proteins correlated with experimental binding affinities. These results suggest that sampling multiple residue conformations and residue substitutions of the unbound ligand contributes to, but does not fully provide, a solution to the protein docking problem. Conformational sampling allows a classical atomistic scoring function to be used; such a function may contribute to better selectivity between near‐native and non‐native complexes. Allowing for receptor flexibility may further extend these results.     

Flexible docking allowing induced fit in proteins: Insights from an open to closed conformational isomers

Here we dock a ligand onto a receptor surface allowing hinge-bending domain/substructural movements. Our approach mimics and manifests induced fit in molecular recognition. All angular rotations are allowed on the one hand, while a conformational space search is avoided on the other. Rather than dock each of the molecular parts separately with subsequent reconstruction of the consistently docked molecules, all parts are docked simultaneously while still utilizing the position of the hinge from the start. Like pliers closing on a screw, the receptor automatically closes on its ligand in the best surface-matching way. Movements are allowed either in the ligand or in the larger receptor, hence reproducing induced molecular fit. Hinge bending movements are frequently observed when molecules associate. There are numerous examples of open versus closed conformations taking place upon binding. Such movements are observed when the substrate binds to its respective enzyme. In particular, such movements are of interest in allosteric enzymes. The movements can involve entire domains, subdomains, loops, (other) secondary structure elements, or between any groups of atoms connected by flexible joints. We have implemented the hinges at points and at bonds. By allowing 3-dimensional (3-D) rotation at the hinge, several rotations about (consecutive or nearby) bonds are implicitly taken into account. Alternatively, if required, the point rotation can be restricted to bond rotation. Here we illustrate this hinge-bending docking approach and the insight into flexibility it provides on a complex of the calmodulin with its M13 ligand, positioning the hinges either in the ligand or in the larger receptor. This automated and efficient method is adapted from computer vision and robotics. It enables utilizing entire molecular surfaces rather than focusing a priori on active sites. Hence, allows attaining the overall optimally matching surfaces, the extent and type of motions which are involved. Here we do not treat the conformational flexibility of side-chains or of very small pieces of the molecules. Therefore, currently available methods addressing these issues and the method presented here, are complementary to each other, expanding the repertoire of computational docking tools foreseen to aid in studies of recognition, conformational flexibility and drug design. Proteins 32:159–174, 1998. © 1998 Wiley-Liss, Inc.     

A model for the non-specific binding of catabolite gene activator protein to DNA

The binding of E. coli catabolite gene activator protein (CAP) to non-specific sequences of DNA has been modelled as an electrostatic interaction between four basic side chains of the CAP dimer and the charged phosphates of DNA. Calculation of the electrostatic contribution to the binding free energy at various separations of the two molecules shows that complex formation is favored when CAP and DNA are separated by as much as 12 A. Thus, the long range electrostatic interactions may provide the initial energy for complex formation and also the correct relative orientation of CAP and DNA. The non-specific complex does not involve the penetration of amino acid side chains into the major grooves of DNA and permits 'sliding' of the protein along DNA, which would enhance the rate of association of CAP with the specific site as has been proposed previously for lac repressor. We propose that, as it 'slides', CAP is moving in and out of the major grooves in order to sample the DNA sequence. Recognition of the specific DNA site is achieved by a complementarity in structure and hydrogen bonding between amino acids and the edges of base pairs exposed in the major grooves of DNA.     

A protein-protein docking algorithm dependent on the type of complexes

An efficient 'soft docking' algorithm is described to assist the prediction of protein-protein association using three-dimensional structures of molecules. The basic tools are the 'simplified protein' model and the docking algorithm of Wodak and Janin. The side chain flexibility of Arg, Lys, Asp, Glu and Met residues at the protein surface is taken into account. The complex type-dependent filtering technique on the basis of the geometric matching, hydrophobicity and electrostatic complementarity is used to select candidate binding modes. Subsequently, we calculate a scoring function which includes electrostatic and desolvation energy terms. In the 44 complexes tested including enzyme-inhibitor, antibody-antigen and other complexes, native-like structures were all found, of which 30 were ranked in the top 20. Thus, our soft docking algorithm has the potential to predict protein-protein recognition.