Pattern recognition strategies for molecular surfaces. I. Pattern generation using fuzzy set theory

A new method for the characterization of molecules based on the model approach of molecular surfaces is presented. We use the topographical properties of the surface as well as the electrostatic potential, the local lipophilicity/hydrophilicity, and the hydrogen bond density on the surface for characterization. The definition and the calculation method for these properties are reviewed shortly. The surface is segmented into overlapping patches with similar molecular properties. These patches can be used to represent the characteristic local features of the molecule in a way that is beyond the atomistic resolution but can nevertheless be applied for the analysis of partial similarities of different molecules as well as for the identification of molecular complementarity in a very general sense. The patch representation can be used for different applications, which will be demonstrated in subsequent articles.     

Pattern recognition strategies for molecular surfaces. II. Surface complementarity

Fuzzy logic based algorithms for the quantitative treatment of complementarity of molecular surfaces are presented. Therein, the overlapping surface patches defined in article I1 of this series are used. The identification of complementary surface patches can be considered as a first step for the solution of molecular docking problems. Standard technologies can then be used for further optimization of the resulting complex structures. The algorithms are applied to 33 biomolecular complexes. After the optimization with a downhill simplex method, for all these complexes one structure was found, which is in very good agreement with the experimental results.     

Molecular surface-volume and property matching to superpose flexible dissimilar molecules

Summary Steric complementarity is a prerequisite for ligand-receptor recognition; this implies that drugs with a common receptor binding site should possess sterically similar binding surfaces. This principle is used as the basis for an automatic and unbiased method that superposes molecules. One molecule is rotated and translated to maximize the overlap between the two molecular surface volumes. A fast grid-based method is used to determine the extent of this overlap, and this is optimized using simulated annealing. Matches with high steric similarity scores are then sorted on the basis of both hydrogen-bond and electrostatic similarity between the matched molecules. Flexible molecules are treated as a set of rigid representative conformers. The algorithm has correctly predicted superpositions between a number of pairs of molecules, according to crystallographic data from ligands that have been co-crystallized at common enzyme binding sites.     

Algorithm for determination of the local similarity of molecules

An algorithm for seeking common structural fragments in compounds of different classes is developed. The algorithm allows for the molecular geometry and atomic characteristics, It may be used for recognition of compounds with properties associated with the local similarity of molecules such as ligand complementarity to a receptor. An example of seeking common structural elements for nondrug analgesics (para-acetamidophenol, acetylsalicylic acid, and amidopyrine) is given. I. I. Polzunov Altai State Technical University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 6, pp. 1083–1087, November–December, 1995. Translated by L. Smolina     

Molecular Simulations using Spherical Harmonics

Computer-aided drug design is to develop a chemical that binds to a target macromolecule known to play a key role in a disease state. In recognition of ligands by their protein receptors, molecular surfaces are often used because they represent the in-teracting part of molecules and they should reflex the comple-mentarity between ligand and receptor. However, assessing the surface complementarity by searching all relative position of two surfaces is often computationally expensive. The comple-mentarity of lobe-hole is very important in protein-ligand inter-actions. Spherical harmonic models based on expansions of spherical harmonic functions were used as a f‘mgerprint to ap-proximate the binding cavity and the ligand, respectively. This defines a new way to identify the complementarity between lobes and holes. The advantage of this method is that two spherical harmonic surfaces to be compared can be defined sep-arately. This method can be used as a filter to eliminate candi-dates among a large number of conformations, and it will speed up the docking procedure. Therefore, it is possible to select complementary ligands or complementary conformations of a ligand and the macromolecules, by comparing their fingerprints previously stored in a database.     

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.     

Vital significance of addition of “shape similarity” between solutes to shape complementarity for more precise molecular recognition in aqueous binary solvents

Precise and specific molecular recognition is vital to living systems. Discrimination has mainly been studied by using particular host molecules (e.g., crown ethers, cyclodextrin and urea derivatives). Several studies in various fields have pointed out that the famous “lock‐and‐key theory” (the concept of shape complementarity) is, at present, insufficient for understanding precise discrimination. This seems to come from the fact that various types of intermolecular interactions are decisive in such discrimination. This Review intends to describe the novel concept that “shape similarity” between interacting solutes should be added to “shape complementarity” for more precise discrimination to be achieved. Further, the role of shape similarity between solvent and solute molecules is also described. In relation to precise molecular recognition, weak interactions, which depend on the three‐dimensional shape of substituents (shape‐specific weak interactions), are described. Possibility of alterations in solvent structures is discussed in aqueous binary solvents. DOI 10.1002/tcr.201100001     

Mathematical correction for fingerprint similarity measures to improve chemical retrieval

In many modern chemoinformatics systems, molecules are represented by long binary fingerprint vectors recording the presence or absence of particular features or substructures, such as labeled paths or trees, in the molecular graphs. These long fingerprints are often compressed to much shorter fingerprints using a simple modulo operation. As the length of the fingerprints decreases, their typical density and overlap tend to increase, and so does any similarity measure based on overlap, such as the widely used Tanimoto similarity. Here we show that this correlation between shorter fingerprints and higher similarity can be thought of as a systematic error introduced by the fingerprint folding algorithm and that this systematic error can be corrected mathematically. More precisely, given two molecules and their compressed fingerprints of a given length, we show how a better estimate of their uncompressed overlap, hence of their similarity, can be derived to correct for this bias. We show how the correction can be implemented not only for the Tanimoto measure but also for all other commonly used measures. Experiments on various data sets and fingerprint sizes demonstrate how, with a negligible computational overhead, the correction noticeably improves the sensitivity and specificity of chemical retrieval.     

Similarity metrics for ligands reflecting the similarity of the target proteins

In this study we evaluate how far the scope of similarity searching can be extended to identify not only ligands binding to the same target as the reference ligand(s) but also ligands of other homologous targets without initially known ligands. This "homology-based similarity searching" requires molecular representations reflecting the ability of a molecule to interact with target proteins. The Similog keys, which are introduced here as a new molecular representation, were designed to fulfill such requirements. They are based only on the molecular constitution and are counts of atom triplets. Each triplet is characterized by the graph distances and the types of its atoms. The atom-typing scheme classifies each atom by its function as H-bond donor or acceptor and by its electronegativity and bulkiness. In this study the Similog keys are investigated in retrospective in silico screening experiments and compared with other conformation independent molecular representations. Studied were molecules of the MDDR database for which the activity data was augmented by standardized target classification information from public protein classification databases. The MDDR molecule set was split randomly into two halves. The first half formed the candidate set. Ligands of four targets (dopamine D2 receptor, opioid delta-receptor, factor Xa serine protease, and progesterone receptor) were taken from the second half to form the respective reference sets. Different similarity calculation methods are used to rank the molecules of the candidate set by their similarity to each of the four reference sets. The accumulated counts of molecules binding to the reference target and groups of targets with decreasing homology to it were examined as a function of the similarity rank for each reference set and similarity method. In summary, similarity searching based on Unity 2D-fingerprints or Similog keys are found to be equally effective in the identification of molecules binding to the same target as the reference set. However, the application of the Similog keys is more effective in comparison with the other investigated methods in the identification of ligands binding to any target belonging to the same family as the reference target. We attribute this superiority to the fact that the Similog keys provide a generalization of the chemical elements and that the keys are counted instead of merely noting their presence or absence in a binary form. The second most effective molecular representation are the occurrence counts of the public ISIS key fragments, which like the Similog method, incorporates key counting as well as a generalization of the chemical elements. The results obtained suggest that ligands for a new target can be identified by the following three-step procedure: 1. Select at least one target with known ligands which is homologous to the new target. 2. Combine the known ligands of the selected target(s) to a reference set. 3. Search candidate ligands for the new targets by their similarity to the reference set using the Similog method. This clearly enlarges the scope of similarity searching from the classical application for a single target to the identification of candidate ligands for whole target families and is expected to be of key utility for further systematic chemogenomics exploration of previously well explored target families.     

Build-up algorithm for atomic correspondence between chemical structures

Determining a one-to-one atom correspondence between two chemical compounds is important to measure molecular similarities and to find compounds with similar biological activities. This calculation can be formalized as the maximum common substructure (MCS) problem, which is well-studied and has been shown to be NP-complete. Although many rigorous and heuristic algorithms have been developed, none of these algorithms is sufficiently fast and accurate. We developed a new program, called "kcombu" using a build-up algorithm, which is a type of the greedy heuristic algorithms. The program can search connected and disconnected MCSs as well as topologically constrained disconnected MCS (TD-MCS), which is introduced in this study. To evaluate the performance of our program, we prepared two correct standards: the exact correspondences generated by the maximum clique algorithms and the 3D correspondences obtained from superimposed 3D structure of the molecules in a complex 3D structure with the same protein. For the five sets of molecules taken from the protein structure database, the agreement value between the build-up and the exact correspondences for the connected MCS is sufficiently high, but the computation time of the build-up algorithm is much smaller than that of the exact algorithm. The comparison between the build-up and the 3D correspondences shows that the TD-MCS has the best agreement value among the other types of MCS. Additionally, we observed a strong correlation between the molecular similarity and the agreement with the correct and 3D correspondences; more similar molecule pairs are more correctly matched. Molecular pairs with more than 40% Tanimoto similarities can be correctly matched for more than half of the atoms with the 3D correspondences.     

Heuristics for similarity searching of chemical graphs using a maximum common edge subgraph algorithm

Recently a method (RASCAL) for determining graph similarity using a maximum common edge subgraph algorithm has been proposed which has proven to be very efficient when used to calculate the relative similarity of chemical structures represented as graphs. This paper describes heuristics which simplify a RASCAL similarity calculation by taking advantage of certain properties specific to chemical graph representations of molecular structure. These heuristics are shown experimentally to increase the efficiency of the algorithm, especially at more distant values of chemical graph similarity.     

Pattern recognition strategies for molecular surfaces: III. Binding site prediction with a neural network

An algorithm for the identification of possible binding sites of biomolecules, which are represented as regions of the molecular surface, is introduced. The algorithm is based on the segmentation of the molecular surface into overlapping patches as described in the first article of this series.1 The properties of these patches (calculated on the basis of physical and chemical properties) are used for the analysis of the molecular surfaces of 7821 proteins and protein complexes. Special attention is drawn to known protein binding sites. A binding site identification algorithm is realized on the basis of the calculated data using a neural network strategy. The neural network is able to classify surface patches as protein-protein, protein-DNA, protein-ligand, or nonbinding sites. To show the capability of the algorithm, results of the surface analysis and the predictions are presented and discussed with representative examples.     

Quantum similarity superposition algorithm (QSSA): a consistent scheme for molecular alignment and molecular similarity based on quantum chemistry

The use of the molecular quantum similarity overlap measure for molecular alignment is investigated. A new algorithm is presented, the quantum similarity superposition algorithm (QSSA), expressing the relative positions of two molecules in terms of mutual translation in three Cartesian directions and three Euler angles. The quantum similarity overlap is then used to optimize the mutual positions of the molecules. A comparison is made with TGSA, a topogeometrical approach, and the influence of differences on molecular clustering is discussed.     

SHAFTS: a hybrid approach for 3D molecular similarity calculation. 1. Method and assessment of virtual screening

We developed a novel approach called SHAFTS (SHApe-FeaTure Similarity) for 3D molecular similarity calculation and ligand-based virtual screening. SHAFTS adopts a hybrid similarity metric combined with molecular shape and colored (labeled) chemistry groups annotated by pharmacophore features for 3D similarity calculation and ranking, which is designed to integrate the strength of pharmacophore matching and volumetric overlay approaches. A feature triplet hashing method is used for fast molecular alignment poses enumeration, and the optimal superposition between the target and the query molecules can be prioritized by calculating corresponding "hybrid similarities". SHAFTS is suitable for large-scale virtual screening with single or multiple bioactive compounds as the query "templates" regardless of whether corresponding experimentally determined conformations are available. Two public test sets (DUD and Jain's sets) including active and decoy molecules from a panel of useful drug targets were adopted to evaluate the virtual screening performance. SHAFTS outperformed several other widely used virtual screening methods in terms of enrichment of known active compounds as well as novel chemotypes, thereby indicating its robustness in hit compounds identification and potential of scaffold hopping in virtual screening.