Geometric accuracy of three-dimensional molecular overlays

This study examines the dependence of molecular alignment accuracy on a variety of factors including the choice of molecular template, alignment method, conformational flexibility, and type of protein target. We used eight test systems for which X-ray data on 145 ligand-protein complexes were available. The use of X-ray structures allowed an unambiguous assignment of bioactive overlays for each compound set. The alignment accuracy depended on multiple factors and ranged from 6% for flexible overlays to 73% for X-ray rigid overlays, when the conformation of the template ligand came from X-ray structures. The dependence of the overlay accuracy on the choice of templates and molecules to be aligned was found to be the most significant factor in six and seven of the eight ligand-protein complex data sets, respectively. While finding little preference for the overlay method, we observed that the introduction of molecule flexibility resulted in a decrease of overlay accuracy in 50% of the cases. We derived rules to maximize the accuracy of alignment, leading to a more than 2-fold improvement in accuracy (from 19% to 48%). The rules also allowed the identification of compounds with a low (<5%) chance to be correctly aligned. Last, the accuracy of the alignment derived without any utilization of X-ray conformers varied from <1% for the human immunodeficiency virus data set to 53% for the trypsin data set. We found that the accuracy was directly proportional to the product of the overlay accuracy from the templates in their bioactive conformations and the chance of obtaining the correct bioactive conformation of the templates. This study generates a much needed benchmark for the expectations of molecular alignment accuracy and shows appropriate usages and best practices to maximize hypothesis generation success.     

<Emphasis Type="Italic">Ab initio</Emphasis> prediction of plausible conformers of a flexible N-(3-chloro-4-fluorophenyl)thiourea (CFT) molecule: A validation study

The current aim of the ab initio crystal structure prediction is to find the possible conformers of the flexible N-(3-chloro-4-fluorophenyl)thiourea (CFT) molecule using gas phase optimization with an MP2/6-31G(d,p) basis set, and the lattice energy minimization in the presence of a repulsion-dispersion electrostatic potential. If the molecule deviates from the gas phase conformation, suitable intermolecular interactions are added, and the molecule favours stable packing. The crystal structure is said to be feasible if the intermolecular lattice energy compensates the intermolecular energy penalty associated with the suboptimal gas phase conformers. The idea of the current research is to find the least energy hydrogen bonded crystal structure from a set of rigid conformers in a conformation region, with a significant similarity of packing, which may lead to the prediction of polymorphs associated with the considered CFT molecule.     

16-fold degeneracy of peptide plane orientations from residual dipolar couplings: analytical treatment and implications for protein structure determination

Residual dipolar couplings (RDCs) measured for internally rigid molecular fragments provide important information about the relative orientations of these fragments. Dependent on the symmetry of the alignment tensor and the symmetry of the molecular fragment, however, there generally exist more than one solution for the fragment orientation consistent with the measured RDCs. Analytical solutions are presented that describe the complete set of orientations of internally rigid fragments that are consistent with multiple dipolar couplings measured in a single alignment medium that is rhombic. For the first time, it is shown that, for a planar fragment such as the peptide plane, there generally exist 16 different solutions with their analytical expressions presented explicitly. The presence of these solutions is shown to be highly relevant for standard structure determination protocols using RDCs to refine molecular structures. In particular, when using standard protein structure refinement with RDCs that were measured in a single alignment medium as constraints, it is found that often more than one of the peptide plane solutions is physically viable; i.e., despite being consistent with measured RDCs, the local backbone structure can be incorrect. On the basis of experimental and simulated examples, it is rationalized why protein structures that are refined against RDCs measured in a single medium can have lower resolution (precision) than one would expect on the basis of the experimental accuracy of the RDCs. Conditions are discussed under which the correct solution can be identified.     

RigFit: A new approach to superimposing ligand molecules

If structural knowledge of a receptor under consideration is lacking, drug design approaches focus on similarity or dissimilarity analysis of putative ligands. In this context the mutual ligand superposition is of utmost importance. Methods that are rapid enough to facilitate interactive usage, that allow to process sets of conformers and that enable database screening are of special interest here. The ability to superpose molecular fragments instead of entire molecules has proven to be helpful too. The RigFit approach meets these requirements and has several additional advantages. In three distinct test applications, we evaluated how closely we can approximate the observed relative orientation for a set of known crystal structures, we employed RigFit as a fragment placement procedure, and we performed a fragment-based database screening. The run time of RigFit can be traded off against its accuracy. To be competitive in accuracy with another state-of-the-art alignment tool, with which we compare our method explicitly, computing times of about 6s per superposition on a common day workstation are required. If longer run times can be afforded the accuracy increases significantly. RigFit is part of the flexible superposition software FlexS which can be accessed on the WWW [http://cartan.gmd.de/FlexS].     

Determination of the preferred conformation of the bicyclic Galerucella pheromone using density functional theory optimization and calculations of chemical shifts

A pheromone from the beetle, Galerucella calmariensis, was recently isolated and identified (Bartelt, R. J. et al. J. Chem. Ecol. 2006, 32, 693-712) as a 14-carbon, bicyclic dimethylfuran lactone, with the systematic name 12,13-dimethyl-5,14-dioxabicyclo[9.2.1]tetradeca-1(13),11-dien-4-one. The main 12-membered lactone ring is very flexible; as a result, there exist multiple possible conformations. The preferred conformation cannot be deduced solely from room-temperature NMR measurements. Using density functional (DFT) studies, 26 unique conformers with energies within 10.0 kcal/mol of the global minimum-energy structure were found. A mirror-image plane exists so that each conformer has an "inverse" structure with the same energy, for which the dihedral angles around the flexible ring have opposite sign. The isotropic 1H and 13C NMR chemical shifts of the DFT-optimized structures were calculated using the gauge-including atomic orbital (GIAO) method. By considering the relative energies of the conformers and the calculated and observed NMR spectra, we concluded that the molecule exists primarily as a mixture of two distinct conformers at room temperature, each being present with its mirror-image inverse. Structural interconversions among these likely occur on a time scale that is fast compared to the NMR experiments. Using mode-following and dihedral-driving techniques, several potential pathways were found for the conversion of the lowest-energy conformer to its mirror-image structure. Ab initio molecular dynamics (AIMD) using the 4-31G basis set was carried out for 50 ps to test the availability of various low-energy minima and the transition states found from the searches noted above.     

3D QSAR studies on protein tyrosine phosphatase 1B inhibitors: comparison of the quality and predictivity among 3D QSAR models obtained from different conformer-based alignments

A set of 65 flexible peptidomimetic competitive inhibitors (52 in the training set and 13 in the test set) of protein tyrosine phosphatase 1B (PTP1B) has been used to compare the quality and predictive power of 3D quantitative structure-activity relationship (QSAR) comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) models for the three most commonly used conformer-based alignments, namely, cocrystallized conformer-based alignment (CCBA), docked conformer-based alignment (DCBA), and global minima energy conformer-based alignment (GMCBA). These three conformers of 5-[(2S)-2-({(2S)-2-[(tert-butoxycarbonyl)amino]-3-phenylpropanoyl}amino)3-oxo-3-pentylamino)propyl]-2-(carboxymethoxy)benzoic acid (compound number 66) were obtained from the X-ray structure of its cocrystallized complex with PTP1B (PDB ID: 1JF7), its docking studies, and its global minima by simulated annealing. Among the 3D QSAR models developed using the above three alignments, the CCBA provided the optimal predictive CoMFA model for the training set with cross-validated r2 (q2)=0.708, non-cross-validated r2=0.902, standard error of estimate (s)=0.165, and F=202.553 and the optimal CoMSIA model with q2=0.440, r2=0.799, s=0.192, and F=117.782. These models also showed the best test set prediction for the 13 compounds with predictive r2 values of 0.706 and 0.683, respectively. Though the QSAR models derived using the other two alignments also produced statistically acceptable models in the order DCBA>GMCBA in terms of the values of q2, r2, and predictive r2, they were inferior to the corresponding models derived using CCBA. Thus, the order of preference for the alignment selection for 3D QSAR model development may be CCBA>DCBA>GMCBA, and the information obtained from the CoMFA and CoMSIA contour maps may be useful in designing specific PTP1B inhibitors.     

Docking flexible ligands in proteins with a solvent exposure- and distance-dependent dielectric function

Physics-based force fields for ligand–protein docking usually determine electrostatic energy with distance-dependent dielectric (DDD) functions, which do not fully account for the dielectric permittivity variance between ~2 in the protein core and ~80 in bulk water. Here we propose an atom–atom solvent exposure- and distance-dependent dielectric (SEDDD) function, which accounts for both electrostatic and dehydration energy components. Docking was performed using the ZMM program, the AMBER force field, and precomputed libraries of ligand conformers. At the seeding stage, hundreds of thousands of positions and orientations of conformers from the libraries were sampled within the rigid protein. At the refinement stage, the ten lowest-energy structures from the seeding stage were Monte Carlo-minimized with the flexible ligand and flexible protein. A search was considered a success if the root mean square deviation (RMSD) of the ligand atoms in the apparent global minimum from the x-ray structure was <2 Å. Calculations on an examining set of 60 ligand–protein complexes with different DDD functions and solvent-exclusion energy revealed outliers in most of which the ligand-binding site was located at the protein surface. Using a training set of 16 ligand–protein complexes, which did not overlap with the examining set, we parameterized the SEDDD function to minimize the RMSD of the apparent global minima from the x-ray structures. Recalculation of the examining set with the SEDDD function demonstrated a 20% increase in the success rate versus the best-performing DDD function.     

Comparison of two implementations of the incremental construction algorithm in flexible docking of thrombin inhibitors

A set of 32 known thrombin inhibitors representing different chemical classes has been used to evaluate the performance of two implementations of incremental construction algorithms for flexible molecular docking: DOCK 4.0 and FlexX 1.5. Both docking tools are able to dock 10–35% of our test set within 2 Å of their known, bound conformations using default sampling and scoring parameters. Although flexible docking with DOCK or FlexX is not able to reconstruct all native complexes, it does offer a significant improvement over rigid body docking of single, rule-based conformations, which is still often used for docking of large databases. Docking of sets of multiple conformers of each inhibitor, obtained with a novel protocol for diverse conformer generation and selection, yielded results comparable to those obtained by flexible docking. Chemical scoring, which is an empirically modified force field scoring method implemented in DOCK 4.0, outperforms both interaction energy scoring by DOCK and the Böhm scoring function used by FlexX in rigid and flexible docking of thrombin inhibitors. Our results indicate that for reliable docking of flexible ligands the selection of anchor fragments, conformational sampling and currently available scoring methods still require improvement.     

FLAME: a program to flexibly align molecules

Herein, we describe a method to flexibly align molecules (FLAME = FLexibly Align MolEcules). FLAME aligns two molecules by first finding maximum common pharmacophores between them using a genetic algorithm. The resulting alignments are then subjected to simultaneous optimizations of their internal energies and an alignment score. The utility of the method in pairwise alignment, multiple molecule flexible alignment, and database searching was examined. For pairwise alignment, two carboxypeptidase ligands (Protein Data Bank codes and ), two estrogen receptor ligands ( and ), and two thrombin ligands ( and ) were used as test sets. Alignments generated by FLAME starting from CONCORD structures compared very well to the X-ray structures (average root-mean-square deviation = 0.36 A) even without further minimization in the presence of the protein. For multiple flexible alignments, five structurally diverse D3 receptor ligands were used as a test set. The FLAME alignment automatically identified three common pharmacophores: a base, a hydrogen-bond acceptor, and a hydrophobe/aromatic ring. The best alignment was then used to search the MDDR database. The search results were compared to the results using atom pair and Daylight fingerprint similarity. A similar database search comparison was also performed using estrogen receptor modulators. In both cases, hits identified by FLAME were structurally more diverse compared to those from the atom pair and Daylight fingerprint methods.     

Similarity recognition of molecular structures by optimal atomic matching and rotational superposition

An algorithm for similarity recognition of molecules and molecular clusters is presented which also establishes the optimum matching among atoms of different structures. In the first step of the algorithm, a set of molecules are coarsely superimposed by transforming them into a common reference coordinate system. The optimum atomic matching among structures is then found with the help of the Hungarian algorithm. For this, pairs of structures are represented as complete bipartite graphs with a weight function that uses intermolecular atomic distances. In the final step, a rotational superposition method is applied using the optimum atomic matching found. This yields the minimum root mean square deviation of intermolecular atomic distances with respect to arbitrary rotation and translation of the molecules. Combined with an effective similarity prescreening method, our algorithm shows robustness and an effective quadratic scaling of computational time with the number of atoms.     

Singular value decomposition of torsional angles of analogs of the dopamine reuptake inhibitor GBR 12909

Analysis of large, flexible molecules, such as the dopamine reuptake inhibitor GBR 12909 (1), is complicated by the fact that they can take on a wide range of closely related conformations. The first step in the analysis is to classify the conformers into groups. Here, Singular Value Decomposition (SVD) was used to group conformations of GBR 12909 analogs by the similarity of their nonring torsional angles. The significance of the present work, the first application of SVD to the analysis of very flexible molecules, lies in the development of a novel scaling technique for circular data and in the grouping of molecular conformations using a technique that is independent of molecular alignment. Over 700 conformers each of a piperazine (2) and piperidine (3) analog of 1 were studied. Analysis of the score and loading plots showed that the conformers of 2 separate into three large groups due to torsional angles on the naphthalene side of the molecule, whereas those of 3 separate into nine groups due to torsional angles on the bisphenyl side of the molecule. These differences are due to nitrogen inversion at the unprotonated piperazinyl nitrogen of 2, which results in a different ensemble of conformers than those of 3, where no inversion is possible at the corresponding piperidinyl carbon.     

Different approaches toward an automatic structural alignment of drug molecules: Applications to sterol mimics,thrombin and thermolysin inhibitors

Summary A relative comparison of the binding properties of different drug molecules requires their mutual superposition with respect to various alignment criteria. In order to validate the results of different alignment methods, the crystallographically observed binding geometries of ligands in the pocket of a common protein receptor have been used. The alignment function in the program SEAL that calculates the mutual superposition of molecules has been optimized with respect to these references. Across the reference data set, alignments could be produced that show mean rms deviations of approximately 1 Å compared to the experimental situation. For structures with obvious skeletal similarities a multiple-flexible fit, linking common pharmacophoric groups by virtual springs, has been incorporated into the molecular mechanics program MOMO. In order to combine conformational searching with comparative alignments, the optimized SEAL approach has been applied to sets of conformers generated by MIMUMBA, a program for conformational analysis. Multiple-flexible fits have been calculated for inhibitors of ergosterol biosynthesis. Sets of different thrombin and thermolysin inhibitors have been conformationally analyzed and subsequently aligned by a combined MIMUMBA/SEAL approach. Since for these examples crystallographic data on their mutual alignment are available, an objective assessment of the computed results could be performed. Among the generated conformers, one geometry could be selected for the thrombin and thermolysin inhibitors that approached reasonably well the experimentally observed alignment.     

Simulation of the lanthanide induced shifts : Description of a computer method and its applications to conformational equilibria of simple systems

A computer method to simulate the observed Lanthanide Induced Shifts (LIS) is described and its applications to the study of the conformational equilibria in solution for simple systems are reported. Starting from structurally rigid systems, it is shown that the LIS simulation process allows mistaken assignment to be corrected by systematic permutation of signals with uncertain assignments.Some examples of structurally flexible systems with an internal rotation angle are studied (2-carbonyl derivatives of furan and thiophene, N-vinylpyrrolidone, cyclopropanecarboxyamides), and the results allow the structures actually present in the conformational equilibrium to be determined.It has been also found that it is possible to estimate the population ratio between s-cis and s-trans conformers in a number of α,β-unsaturated systems.     

Molecular properties from conformational ensembles. 1. Dipole moments of molecules with multiple internal rotations

We present a novel method for constructing the stable conformational space of small molecules with many rotatable bonds that uses our iterative stochastic elimination (ISE) algorithm, a robust stochastic search method capable of finding ensembles of best solutions for large combinatorial problems. To validate the method, we show that ISE reproduces the best conformers found in a fully exhaustive search, as well as compare computed dipole moments to experimental values, based on molecular ensembles and their Boltzmann distributions. Results were also compared to the alternative molecular dynamics and simulated annealing methods. Our results clarify that many low energy conformations may be required to reproduce molecular properties, while single low energy conformers or ensembles of low energy conformers cannot account for the experimental properties of flexible molecules. Whereas ISE well reproduces conformations that are not separated by very large energy barriers, it has not been successful in reproducing conformations of strained molecules.