Flexible docking simulations: Scaled collective variable Monte Carlo minimization approach using Bezier splines,and comparison with a standard Monte Carlo algorithm

An algorithm for docking a flexible ligand onto a flexible or rigid receptor, using the scaled‐collective‐variables Monte Carlo with energy minimization approach, is presented. Energy minimization is shown to be one of the best techniques for distinguishing between native‐ and nonnative‐generated conformations. Incorporation of this technique into a Monte Carlo procedure enables one to distinguish the native conformation directly during the conformational search. It avoids the generation of a large number of ligand conformers for which more sophisticated energy evaluation tools would have had to be applied to identify the nativelike conformations. The efficiency of the Monte Carlo minimization was greatly improved by incorporating a new grid‐based energy evaluation technique using Bezier splines for which the energy function, as well as all of its derivatives, can be deduced from the values at the grid points. Comparison between our ECEPP/3‐based algorithm and the Monte Carlo algorithm presented elsewhere (Hart, T. N.; Read, R. J. Prot Struct Funct Genet 1992, 13, 206–222) has been made for docking NH₂ D Phe Pro Arg COOH, the noncovalent analog of NH₂ D Phe Pro Arg chloromethylketone (PPACK), onto the active site of human α‐thrombin. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 244–252, 1999     

Docking small ligands in flexible binding sites

A novel procedure for docking ligands in a flexible binding site is presented. It relies on conjugate gradient minimization, during which nonbonded interactions are gradually switched on. Short Monte Carlo minimization runs are performed on the most promising candidates. Solvation is implicitly taken into account in the evaluation of structures with a continuum model. It is shown that the method is very accurate and can model induced fit in the ligand and the binding site. The docking procedure has been successfully applied to three systems. The first two are the binding of progesterone and 5β-androstane-3,17-dione to the antigen binding fragment of a steroid binding antibody. A comparison of the crystal structures of the free and the two complexed forms reveals that any attempt to model binding must take protein rearrangements into account. Furthermore, the two ligands bind in two different orientations, posing an additional challenge. The third test case is the docking of N^α-(2-naphthyl-sulfonyl-glycyl)-D -para-amidino-phenyl-alanyl-piperidine (NAPAP) to human α-thrombin. In contrast to steroids, NAPAP is a very flexible ligand, and no information of its conformation in the binding site is used. All docking calculations are started from X-ray conformations of proteins with the uncomplexed binding site. For all three systems the best minima in terms of free energy have a root mean square deviation from the X-ray structure smaller than 1.5 Å for the ligand atoms. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 21–37, 1998     

Computer simulations of ligand–protein binding with ensembles of protein conformations: A Monte Carlo study of HIV‐1 protease binding energy landscapes

We present the results of molecular docking simulations with HIV‐1 protease for the sb203386 and skf107457 inhibitors by Monte Carlo simulated annealing. A simplified piecewise linear energy function, the standard AMBER force field, and the AMBER force field with solvation and a soft‐core smoothing component are employed in simulations with a single‐protein conformation to determine the relationship between docking simulations with a simple energy function and more realistic force fields. The temperature‐dependent binding free energy profiles of the inhibitors interacting with a single protein conformation provide a detailed picture of relative thermodynamic stability and a distribution of ligand binding modes in agreement with experimental crystallographic data. Using the simplified piecewise linear energy function, we also performed Monte Carlo docking simulations with an ensemble of protein conformations employing preferential biased sampling of low‐energy protein conformations, and the results are analyzed in connection with the free energy profiles. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 73–84, 1999     

Exploring hierarchical refinement techniques for induced fit docking with protein and ligand flexibility

We present a series of molecular‐mechanics‐based protein refinement methods, including two novel ones, applied as part of an induced fit docking procedure. The methods used include minimization; protein and ligand sidechain prediction; a hierarchical ligand placement procedure similar to a‐priori protein loop predictions; and a minimized Monte Carlo approach using normal mode analysis as a move step. The results clearly indicate the importance of a proper opening of the active site backbone, which might not be accomplished when the ligand degrees of freedom are prioritized. The most accurate method consisted of the minimized Monte Carlo procedure designed to open the active site followed by a hierarchical optimization of the sidechain packing around a mobile flexible ligand. The methods have been used on a series of 88 protein‐ligand complexes including both cross‐docking and apo‐docking members resulting in complex conformations determined to within 2.0 Å heavy‐atom RMSD in 75% of cases where the protein backbone rearrangement upon binding is less than 1.0 Å α‐carbon RMSD. We also demonstrate that physics‐based all‐atom potentials can be more accurate than docking‐style potentials when complexes are sufficiently refined. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

FDS: flexible ligand and receptor docking with a continuum solvent model and soft-core energy function

The docking of flexible small molecule ligands to large flexible protein targets is addressed in this article using a two-stage simulation-based method. The methodology presented is a hybrid approach where the first component is a dock of the ligand to the protein binding site, based on deriving sets of simultaneously satisfied intermolecular hydrogen bonds using graph theory and a recursive distance geometry algorithm. The output structures are reduced in number by cluster analysis based on distance similarities. These structures are submitted to a modified Monte Carlo algorithm using the AMBER-AA molecular mechanics force field with the Generalized Born/Surface Area (GB/SA) continuum model. This solvent model is not only less expensive than an explicit representation, but also yields increased sampling. Sampling is also increased using a rotamer library to direct some of the protein side-chain movements along with large dihedral moves. Finally, a softening function for the nonbonded force field terms is used, enabling the potential energy function to be slowly turned on throughout the course of the simulation. The docking procedure is optimized, and the results are presented for a single complex of the arabinose binding protein. It was found that for a rigid receptor model, the X-ray binding geometry was reproduced and uniquely identified based on the associated potential energy. However, when side-chain flexibility was included, although the X-ray structure was identified, it was one of three possible binding geometries that were energetically indistinguishable. These results suggest that on relaxing the constraint on receptor flexibility, the docking energy hypersurface changes from being funnel-like to rugged. A further 14 complexes were then examined using the optimized protocol. For each complex the docking methodology was tested for a fully flexible ligand, both with and without protein side-chain flexibility. For the rigid protein docking, 13 out of the 15 test cases were able to find the experimental binding mode; this number was reduced to 11 for the flexible protein docking. However, of these 11, in the majority of cases the experimental binding mode was not uniquely identified, but was present in a cluster of low energy structures that were energetically indistinguishable. These results not only support the presence of a rugged docking energy hypersurface, but also suggest that it may be necessary to consider the possibility of more than one binding conformation during ligand optimization.     

Low-mode conformational search elucidated: Application to C39H80 and flexible docking of 9-deazaguanine inhibitors into PNP

We previously described a new conformational search method, termed low-mode search (LMOD), and discussed its utility for conformational searches performed on cycloalkanes and a cyclic penta-peptide. 1 In this report, we discuss a rigorous implementation of mode following (c-LMOD) for conformational searching, and we demonstrate that for a conformational search involving cycloheptadecane, this rigorous implementation is capable of finding all of the previously known structures. To the best of our knowledge, this is the first computational proof that mode following can be used for conformational searches conducted on a complex molecular system. We show, however, that, as expected, it is generally inefficient to perform a conformational search in this manner. Nonetheless, c-LMOD has been shown to be an excellent method for conducting conformational analyses involving conformational interconversions, where the location of saddle points is important. We also describe refinement to our original LMOD procedure (l-LMOD) and discuss its utility for a difficult conformational search problem, namely locating the global minimum energy conformation of C₃₉H₈₀. For this search, l-LMOD combined with limited torsional Monte Carlo movement was able to locate the lowest energy structures yet reported, and significantly outperformed a pure torsional Monte Carlo and a genetic algorithm-based search. Furthermore, we also demonstrate the utility of l-LMOD combined with random translation/rotation of a ligand for the extremely difficult problem of docking flexible ligands into flexible protein binding sites on a system that includes 9-deaza-guanine-based inhibitors docked into the flexible biding site of PNP. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1671–1684, 1999     

A critical evaluation of several global optimization algorithms for the purpose of molecular docking

Several global optimization algorithms were applied to the problem of molecular docking: random walk and Metropolis Monte Carlo Simulated Annealing as references, and Stochastic Approximation with Smoothing (SAS), and Terminal Repeller Unconstrained Subenergy Tunneling (TRUST) as new methodologies. Of particular interest is whether any of these algorithms could be used to dock a database of typical small molecules in a reasonable amount of time. To address this question, each algorithm was used to dock four small molecules presenting a wide range of sizes, degrees of flexibility, and types of interactions. Of the algorithms tested, only stochastic approximation with smoothing appeared to be sufficiently fast and reliable to be useful for database searches. This algorithm can reliably dock relatively small and fairly rigid molecules in a few seconds, and larger and more flexible molecules in a few minutes. The remaining algorithms tested were able to reliably dock the small and fairly rigid molecules, but showed little or no reliability when docking large or flexible molecules. In addition, to decrease the error in the typical grid-based energy evaluations a new form of interpolation, logarithmic interpolation, is proposed. This interpolation scheme is shown to both quantitatively reduce the numerical error and practically to improve the docking results. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1740–1751, 1999     

A QXP-based multistep docking procedure for accurate prediction of protein-ligand complexes

The two great challenges of the docking process are the prediction of ligand poses in a protein binding site and the scoring of the docked poses. Ligands that are composed of extended chains in their molecular structure display the most difficulties, predominantly because of the torsional flexibility. On the basis of the molecular docking program QXP-Flo+0802, we have developed a procedure particularly for ligands with a high degree of rotational freedom that allows the accurate prediction of the orientation and conformation of ligands in protein binding sites. Starting from an initial full Monte Carlo docking experiment, this was achieved by performing a series of successive multistep docking runs using a local Monte Carlo search with a restricted rotational angle, by which the conformational search space is limited. The method was established by using a highly flexible acetylcholinesterase inhibitor and has been applied to a number of challenging protein-ligand complexes known from the literature.     

An efficient molecular docking using conformational space annealing

Molecular docking falls into the general category of global optimization problems because its main purpose is to find the most stable complex consisting of a receptor and its ligand. Conformational space annealing (CSA), a powerful global optimization method, is incorporated with the Tinker molecular modeling package to perform molecular docking simulations of six receptor-ligand complexes (3PTB, 1ULB, 2CPP, 1STP, 3CPA, and 1PPH) from the Protein Data Bank. In parallel, Monte Carlo with the minimization (MCM) method is also incorporated into the Tinker package for comparison. The energy function, consisting of electrostatic interactions, van der Waals interactions, and torsional energy terms, is calculated using the AMBER94 all-atom empirical force field. Rigid docking simulations for all six complexes and flexible docking simulations for three complexes (1STP, 3CPA, and 1PPH) are carried out using the CSA and the MCM methods. The simulation results show that the docking procedures using the CSA method generally find the most stable complexes as well as the native-like complexes more efficiently and accurately than those using the MCM, demonstrating that CSA is a promising search method for molecular docking problems.     

Conformation‐Family Monte Carlo (CFMC): An Efficient Computational Method for Identifying the Low‐Energy States of a Macromolecule

A highly efficient method, Conformation‐Family Monte Carlo (CFMC), has been developed for searching the conformational space of a macromolecule and identifying its low‐energy conformations. This method maintains a database of low‐energy conformations that are clustered into families. The conformations in this database are improved iteratively by a Metropolis‐type Monte Carlo procedure, together with energy minimization, in which the search is biased towards investigating the regions of the lowest‐energy families. The CFMC method has the advantages of our earlier potential‐smoothing methods (in that it `coarse‐grains' the conformational space and exploits information about nearby low‐energy states), but avoids their disadvantages (such as the displacement of the global minimum at large smoothings). The CFMC method is applied to a test protein, domain B of Staphylococcal protein A. Independent CFMC runs yielded the same low‐energy families of conformations from random starts, indicating that the thermodynamically relevant conformational space of this protein has been explored thoroughly. The CFMC method is highly efficient, performing as well as or better than competing methods, such as Monte Carlo with minimization, conformational‐space annealing, and the self‐consistent basin‐to‐deformed‐basin method.     

An anchor-dependent molecular docking process for docking small flexible molecules into rigid protein receptors

A molecular docking method designated as ADDock, anchor- dependent molecular docking process for docking small flexible molecules into rigid protein receptors, is presented in this article. ADDock makes the bond connection lists for atoms based on anchors chosen for building molecular structures for docking small flexible molecules or ligands into rigid active sites of protein receptors. ADDock employs an extended version of piecewise linear potential for scoring the docked structures. Since no translational motion for small molecules is implemented during the docking process, ADDock searches the best docking result by systematically changing the anchors chosen, which are usually the single-edge connected nodes or terminal hydrogen atoms of ligands. ADDock takes intact ligand structures generated during the docking process for computing the docked scores; therefore, no energy minimization is required in the evaluation phase of docking. The docking accuracy by ADDock for 92 receptor-ligand complexes docked is 91.3%. All these complexes have been docked by other groups using other docking methods. The receptor-ligand steric interaction energies computed by ADDock for some sets of active and inactive compounds selected and docked into the same receptor active sites are apparently separated. These results show that based on the steric interaction energies computed between the docked structures and receptor active sites, ADDock is able to separate active from inactive compounds for both being docked into the same receptor.     

Docking macromolecules with flexible segments

We address a major obstacle to macromolecular docking algorithms by presenting a new method that takes into account the induced conformational adjustment of flexible loops situated at a protein/macromolecule interface. The method, MC2, is based on a multiple copy representation of the loops, coupled with a Monte Carlo conformational search of the relative position of the macromolecules and their side chain conformations. The selection of optimal loop conformations takes place during Monte Carlo cycling by the iterative adjustment of the weight of each copy. We describe here the parameterization of the method and trials on a protein-DNA complex of known 3-D structure, involving the Drosophila prd paired domain protein and its target oligonucleotide Wenqing, X. et al., Cell 1995, 80, 639. We demonstrate that our algorithm can correctly configure and position this protein, despite its relatively complex interactions with both grooves of DNA.     

Identification of ligands for RNA targets via structure-based virtual screening: HIV-1 TAR

Binding of the Tat protein to TAR RNA is necessary for viral replication of HIV-1. We screened the Available Chemicals Directory (ACD) to identify ligands to bind to a TAR RNA structure using a four-step docking procedure: rigid docking first, followed by three steps of flexible docking using a pseudobrownian Monte Carlo minimization in torsion angle space with progressively more detailed conformational sampling on a progressively smaller list of top-ranking compounds. To validate the procedure, we successfully docked ligands for five RNA complexes of known structure. For ranking ligands according to binding avidity, an empirical binding free energy function was developed which accounts, in particular, for solvation, isomerization free energy, and changes in conformational entropy. System-specific parameters for the function were derived on a training set of RNA/ligand complexes with known structure and affinity. To validate the free energy function, we screened the entire ACD for ligands for an RNA aptamer which binds l-arginine tightly. The native ligand ranked 17 out of ca. 153,000 compounds screened, i.e., the procedure is able to filter out >99.98% of the database and still retain the native ligand. Screening of the ACD for TAR ligands yielded a high rank for all known TAR ligands contained in the ACD and suggested several other potential TAR ligands. Eight of the highest ranking compounds not previously known to be ligands were assayed for inhibition of the Tat-TAR interaction, and two exhibited a CD₅₀ of ca. 1 M.     

Torsional flexing: Conformational searching of cyclic molecules in biased internal coordinate space

A new stochastic (Monte Carlo) procedure, termed torsional flexing, has been devised for searching the conformational space of cyclic molecules. Torsional flexing causes a local, torsion angle-biased, distortion of a ring bond in a cyclic molecule. Because torsional flexing does not cause large atomic movements, even when it is applied to several bonds simultaneously, subsequent energy minimization generally proceeds rapidly. Nevertheless, the torsional flexing method is prone to generate structures that cross energy barriers so that the structure resulting after energy minimization is frequently a different conformer of the cyclic molecule. Conformational searches on cycloheptadecane, oxobrefeldin A, cyclopenta-L -alanine, and rifamycin SV based upon torsional flexing indicated that torsional flexing is among the best methods yet devised for searching the conformational space of flexible cyclic molecules. © 1993 John Wiley & Sons, Inc.     

Implementation of the ECEPP algorithm,the Monte Carlo minimization method,and the electrostatically driven Monte Carlo method on the Kendall square research KSR1 computer

In this article the adaptation of the Empirical Conformational Energy Program for Peptides (ECEPP/3) and two conformational search methods [viz., the Monte Carlo minimization (MCM) method and the electrostatically driven Monte Carlo (EDMC) method] to the Kendall Square Research KSR1 computer is described. The MCM and EDMC methods were developed to surmount the multiple-minima problem in protein folding. Parallelization of these codes led to substantial speedups (expressed as the ratio between the mean time per energy evaluation in one processor and the mean time per energy evaluation in a set of processors) over the serial versions of these codes. A comparison of the performance of these algorithms on the KSR1 and on the IBM ES9000 computers is presented. © 1995 by John Wiley & Sons, Inc.     

Conformational search using a molecular dynamics–minimization procedure: Applications to clusters of coulombic charges,Lennard–Jones particles,and waters

A new conformational search method, molecular dynamics–minimization (MDM), is proposed, which combines a molecular dynamics sampling strategy with energy minimizations in the search for low-energy molecular structures. This new method is applied to the search for low energy configurations of clusters of coulombic charges on a unit sphere, Lennard–Jones clusters, and water clusters. The MDM method is shown to be efficient in finding the lowest energy configurations of these clusters. A closer comparison of MDM with alternative conformational search methods on Lennard–Jones clusters shows that, although MDM is not as efficient as the Monte Carlo–minimization method in locating the global energy minima, it is more efficient than the diffusion equation method and the method of minimization from randomly generated structures. Given the versatility of the molecular dynamics sampling strategy in comparison to Monte Carlo in treating molecular complexes or molecules in explicit solution, one anticipates that the MDM method could be profitably applied to conformational search problems where the number of degrees of freedom is much greater. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 60–70, 1998     

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.     

Efficiency of monte carlo minimization procedures and their use in analysis of NMR data obtained from flexible peptides

The Monte Carlo minimization (MCM) method of Li and Scheraga is an efficient tool for generating low energy minimized structures of peptides, in particular the global energy minimum (GEM). In a recent article we proposed an enhancement to MCM, called the free energy Monte Carlo minimization (FMCM) procedure. With FMCM the conformational search is carried out with respect to the harmonic free energy, which approximates the free energy of the potential energy wells around the energy minimized structures (these wells are called localized microstates). In this work we apply both methods to the pentapeptide Leu-enkephalin described by the potential energy function ECEPP, and study their efficiency in identifying the GEM structure as well as the global harmonic free energy (GFM) structure. We also investigate the efficiency of these methods to generate localized microstates, which pertain to different energy and harmonic free energy intervals above the GEM and GFM, respectively. Such microstates constitute an important ingredient of our statistical mechanical methodology for analyzing nuclear magnetic resonance data of flexible peptides. Aspects of this methodology related to the stability properties of the localized microstates are examined. © 1997 by John Wiley & Sons, Inc.