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].     

Fast 3D molecular superposition and similarity search in databases of flexible molecules

We present a new method (fFLASH) for the virtual screening of compound databases that is based on explicit three-dimensional molecular superpositions. fFLASH takes the torsional flexibility of the database molecules fully into account, and can deal with an arbitrary number of conformation-dependent molecular features. The method utilizes a fragmentation-reassembly approach which allows for an efficient sampling of the conformational space. A fast clique-based pattern matching algorithm generates alignments of pairs of adjacent molecular fragments on the rigid query molecule that are subsequently reassembled to complete database molecules. Using conventional molecular features (hydrogen bond donors and acceptors, charges, and hydrophobic groups) we show that fFLASH is able to rapidly produce accurate alignments of medium-sized drug-like molecules. Experiments with a test database containing a diverse set of 1780 drug-like molecules (including all conformers) have shown that average query processing times of the order of 0.1 seconds per molecule can be achieved on a PC.     

Calculating the knowledge-based similarity of functional groups using crystallographic data

A knowledge-based method for calculating the similarity of functional groups is described and validated. The method is based on experimental information derived from small molecule crystal structures. These data are used in the form of scatterplots that show the likelihood of a non-bonded interaction being formed between functional group A (the `central group') and functional group B (the `contact group' or `probe'). The scatterplots are converted into three-dimensional maps that show the propensity of the probe at different positions around the central group. Here we describe how to calculate the similarity of a pair of central groups based on these maps. The similarity method is validated using bioisosteric functional group pairs identified in the Bioster database and Relibase. The Bioster database is a critical compilation of thousands of bioisosteric molecule pairs, including drugs, enzyme inhibitors and agrochemicals. Relibase is an object-oriented database containing structural data about protein-ligand interactions. The distributions of the similarities of the bioisosteric functional group pairs are compared with similarities for all the possible pairs in IsoStar, and are found to be significantly different. Enrichment factors are also calculated showing the similarity method is statistically significantly better than random in predicting bioisosteric functional group pairs.     

Morphological similarity: A 3D molecular similarity method correlated with protein-ligand recognition

Recognition of small molecules by proteins depends on three-dimensional molecular surface complementarity. However, the dominant techniques for analyzing the similarity of small molecules are based on two-dimensional chemical structure, with such techniques often outperforming three-dimensional techniques in side-by-side comparisons of correlation to biological activity. This paper introduces a new molecular similarity method, termed morphological similarity (MS), that addresses the apparent paradox. Two sets of molecule pairs are identified from a set of ligands whose protein-bound states are known crystallographically. Pairs that bind the same protein sites form the first set, and pairs that bind different sites form the second. MS is shown to separate the two sets significantly better than a benchmark 2D similarity technique. Further, MS agrees with crystallographic observation of bound ligand states, independent of information about bound states. MS is efficient to compute and can be practically applied to large libraries of compounds.     

Upperbound procedures for the identification of similar three-dimensional chemical structures

Summary This paper describes techniques for calculating the degree of similarity between an input query molecule and each of the molecules in a database of 3-D chemical structures. The inter-molecular similarity measure used is the number of atoms in the 3-D common substructure (CS) between the two molecules which are being compared. The identification of 3-D CSs is very demanding of computational resources, even when an efficient clique detection algorithm is used for this purpose. Two types of upperbound calculation are described which allow reductions in the number of exact CS searches which need to be carried out to identify those molecules from a database which are similar to a 3-D target molecule.     

Linear scaling approaches to quantum macromolecular similarity: evaluating the similarity function

The evaluation of the electron density based similarity function scales quadratically with respect to the size of the molecules for simplified, atomic shell densities. Due to the exponential decay of the function's atom-atom terms most interatomic contributions are numerically negligible on large systems. An improved algorithm for the evaluation of the Quantum Molecular Similarity function is presented. This procedure identifies all non-negligible terms without computing unnecessary interatomic squared distances, thus effectively turning to linear scaling the similarity evaluation. Presented also is a minimalist dynamic electron density model. Approximate, single shell densities together with the proposed algorithm facilitate fast electron density based alignments on macromolecules.     

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.     

Time-efficient flexible superposition of medium-sized molecules

We present an efficient algorithm for the structural alignment of medium-sized organic molecules. The algorithm has been developed for applications in 3D QSAR and in receptor modeling. The method assumes one of the molecules, the reference ligand, to be presented in the conformation that it adopts inside the receptor pocket. The second molecule, the test ligand, is considered to be flexible, and is assumed to be given in an arbitrary low-energy conformation. Ligand flexibility is modeled by decomposing the test ligand into molecular fragments, such that ring systems are completely contained in a single fragment. Conformations of fragments and torsional angles of single bonds are taken from a small finite set, which depends on the fragment and bond, respectively. The algorithm superimposes a distinguished base fragment of the test ligand onto a suitable region of the reference ligand and then attaches the remaining fragments of the test ligand in a step-by-step fashion. During this process, a scoring function is optimized that encompasses bonding terms and terms accounting for steric overlap as well as for similarity of chemical properties of both ligands. The algorithm has been implemented in the FLEXS system. To validate the quality of the produced results, we have selected a number of examples for which the mutual superposition of two ligands is experimentally given by the comparison of the binding geometries known from the crystal structures of their corresponding protein–ligand complexes. On more than two-thirds of the test examples the algorithm produces rms deviations of the predicted versus the observed conformation of the test ligand below 1.5 Å. The run time of the algorithm on a single problem instance is a few minutes on a common-day workstation. The overall goal of this research is to drastically reduce run times, while limiting the inaccuracies of the model and the computation to a tolerable level.     

Ultrafast shape recognition to search compound databases for similar molecular shapes

Finding a set of molecules, which closely resemble a given lead molecule, from a database containing potentially billions of chemical structures is an important but daunting problem. Similar molecular shapes are particularly important, given that in biology small organic molecules frequently act by binding into a defined and complex site on a macromolecule. Here, we present a new method for molecular shape comparison, named ultrafast shape recognition (USR), capable of screening billions of compounds for similar shapes using a single computer and without the need of aligning the molecules before testing for similarity. Despite its extremely fast comparison rate, USR will be shown to be highly accurate at describing, and hence comparing, molecular shapes.     

Alignment of molecules by the Monte Carlo optimization of molecular similarity indices

3D-QSAR uses statistical techniques to correlate calculated structural properties with target properties like biological activity. The comparison of calculated structural properties is dependent upon the relative orientations of molecules in a given data set. Typically molecules are aligned by performing an overlap of common structural units. This “alignment rule” is adequate for a data set, that is closely related structurally, but is far more difficult to apply to either a diverse data set or on the basis of some structural property other than shape, even for sterically similar molecules. In this work we describe a new algorithm for molecular alignment based upon optimization of molecular similarity indices. We show that this Monte Carlo based algorithm is more effective and robust than other optimizers applied previously to the similarity based alignment problem. We show that QSARs derived using the alignments generated by our algorithm are superior to QSARs derived using the more common alignment of fitting of common structural units. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18 : 1344–1353, 1997     

ELECT++: Faster conformational search method for docking flexible molecules using molecular similarity

We have developed a program, ELECT++ (Effective LEssening of Conformations by Template molecules in C++), to speed up the conformational search for small flexible molecules using the similar property principle. We apply this principle to molecular shape and, importantly, to molecular flexibility. After molecules in a database are clustered according to flexibility and shape (FCLUST++), additional reagents are generated to screen the conformational space of molecules in each cluster (TEMPLATE++). We call these representative reagents of each cluster template reagents. Template reagents and clustered reagents produce, after reaction, template molecules and clustered molecules, respectively (tREACT++). The conformations of a template molecule are searched in the context of a macromolecular target. Acceptable conformational choices are then applied to all molecules in its cluster, thus effectively biasing conformational space to speed up conformational searches (tSEARCH++). In our incremental search method, it is necessary to calculate the root-mean-square deviations (RMSD) matrix of distances between different conformations of the same molecule to reduce the number of conformations. Instead of calculating the RMSD matrix for all molecules in a cluster, the RMSD matrix of a template molecule is chosen as a reference and applied to all the molecules in its cluster. We demonstrate that FCLUST++ clusters the primary amine reagents from the Available Chemicals Directory (ACD) successfully. The program tSEARCH++ was applied to dihydrofolate reductase with virtual molecules generated by tREACT++ using clustered primary amine reagents. The conformational search by the program tSEARCH++ was about 4.8 times faster than by SEARCH++, with an acceptable range of errors. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1834–1852, 1998