Linear notations and molecular graph similarity

Two simple linear notation systems are suggested to encode molecular structure including stereochemical elements. Both systems give rise to a unique numbering of the molecular graph, and thus also lead to a unique linear notation. Both linear notation systems are extremely compact and require only standard chemical symbols. A string comparison technique is developed to measure the similarity of two molecular linear notations. This procedure allows one to define a molecular similarity index with values that range from zero to unity, the zero value characterizing complete dissimilarity and the value of unity denoting identity. The notation and similarity index procedures are applied to several small molecular structures.     

A novel approach to molecular similarity

Summary We review briefly the general problem of assessing the similarity between one molecule and another. We propose a novel approach to the quantitative estimation of the similarity of two electron distributions. The procedure is based on momentum space concepts, and avoids many of the difficulties associated with the usual position space definitions. Results are presented for the model systems CH₃CH₂CH₃, CH₃OCH₃, CH₃SCH₃, H₂O and H₂S.     

Graph theoretical similarity approach to compare molecular electrostatic potentials

In this work we introduce a graph theoretical method to compare MEPs, which is independent of molecular alignment. It is based on the edit distance of weighted rooted trees, which encode the geometrical and topological information of Negative Molecular Isopotential Surfaces. A meaningful chemical classification of a set of 46 molecules with different functional groups was achieved. Structure--activity relationships for the corticosteroid binding affinity (CBG) of 31 steroids by means of hierarchical clustering resulted in a clear partitioning in high, intermediate, and low activity groups, whereas the results from quantitative structure--activity relationships, obtained from a partial least-squares analysis, showed comparable or better cross-validated correlation coefficients than the ones reported for previous methods based solely in the MEP.     

Novel approach to molecular similarity: Second-order similarity indices from geminal expansion of pair densities

The recently introduced second-order similarity index g_AB was generalized by using the geminal and/or spingeminal expansion of pair densities that they are derived from. The comparison with previous related studies confirms that the generalization does increase the information content of new indices, especially in providing the information about the difference in the spin recoupling of pure singlet and triplet states of electron pairs. Analogously, as in previous studies, the approach was applied to the analysis of several selected pericyclic reactions and possible mechanistic implications arising from the increased information content are briefly discussed. © 1994 John Wiley & Sons, Inc.     

LINGO-DL: a text-based approach for molecular similarity searching

Journal of Computer-Aided Molecular Design - The line notations of chemical structures are more compact than those of graphs and connection tables, so they can be useful for storing and...     

A steroids QSAR approach based on approximate similarity measurements

A new QSAR method based on approximate similarity measurements is described in this paper. Approximate similarity is calculated using both the classical similarity based on the graph isomorphism and a distance computation between nonisomorphic subgraphs. The latter is carried out through a parametric function where different topological invariants can be considered. After optimizing the contribution of nonisomorphic distance to the new graph similarity, predictive models built with approximate similarity matrixes show higher predictive ability than those using traditional similarity matrixes. The new method has been applied to the prediction of steroids binding to the corticosteroid globulin receptor. The proposed model allows us to obtain valuable external predictions (r=0.82 and SEP=0.30) after training the model by cross-validation (Q2=0.84 and SECV=0.47). Slope and bias parameters are also given.     

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.     

A pose prediction approach based on ligand 3D shape similarity

Molecular docking predicts the best pose of a ligand in the target protein binding site by sampling and scoring numerous conformations and orientations of the ligand. Failures in pose prediction are often due to either insufficient sampling or scoring function errors. To improve the accuracy of pose prediction by tackling the sampling problem, we have developed a method of pose prediction using shape similarity. It first places a ligand conformation of the highest 3D shape similarity with known crystal structure ligands into protein binding site and then refines the pose by repacking the side-chains and performing energy minimization with a Monte Carlo algorithm. We have assessed our method utilizing CSARdock 2012 and 2014 benchmark exercise datasets consisting of co-crystal structures from eight proteins. Our results revealed that ligand 3D shape similarity could substitute conformational and orientational sampling if at least one suitable co-crystal structure is available. Our method identified poses within 2 Å RMSD as the top-ranking pose for 85.7 % of the test cases. The median RMSD for our pose prediction method was found to be 0.81 Å and was better than methods performing extensive conformational and orientational sampling within target protein binding sites. Furthermore, our method was better than similar methods utilizing ligand 3D shape similarity for pose prediction.     

Extending molecular similarity to energy surfaces: Boltzmann similarity measures and indices

Maxwell-Boltzmann statistics provides the adequate mathematical background allowing to define similarity measures involving molecular energy surfaces and electrostatic potential maps. Boltzmann similarity measures are described and various illustrative examples are used to show the practical viability of the theory. A new molecular similarity index is also presented. Finally, hybrid measures involving Boltzmann and density distributions are defined.     

Estimation of molecular similarity based on 4D-QSAR analysis: formalism and validation

The 4D-QSAR paradigm has been used to develop a formalism to estimate molecular similarity measures as a function of conformation, alignment, and atom type. It is possible to estimate the molecular similarity of pairs of molecules based upon the entire ensemble of conformational states each molecule can adopt at a given temperature, normally room temperature. Molecular similarity can be measured in terms of the types of atoms composing each molecule leading to multiple measures of molecular similarity. Multiple measures of molecular similarity can also arise from using different alignment rules to perform relative molecular similarity, RMS, analysis. An alignment independent method of determining molecular similarity measures, referred to as absolute molecular similarity, AMS, analysis has been developed. Various sets and libraries of compounds, including the amino acids, are analyzed using 4D-QSAR molecular similarity analysis to demonstrate the features of the formalism. Exploration of molecular similarity as a function of chirality, identification of common embedded 3D pharmacophores in compounds, and elucidation of 3D-isosteric compounds from structurally diverse libraries are carried out in the application studies.     

Aromaticity in linear polyacenes: generalized population analysis and molecular quantum similarity approach

The relative aromaticity of benzenoid rings in the linear polyacenes is investigated using two novel aromaticity approaches. According to the first, the aromaticity of individual benzene rings was gauged by the values of six-center bond indices (SCI) calculated within the so-called Generalized Population Analysis (GPA). In the second approach, the same goal is addressed using the theory of Molecular Quantum Similarity (MQS). Both independent approaches are found to correlate very well, and both point toward decreasing aromaticity in any linear polyacenes upon going from the outer to inner rings.     

eSHAFTS: Integrated and graphical drug design software based on 3D molecular similarity

With the development of computer technology, computer-aided drug design (CADD) has become an important means for drug research and development, and its representative method is virtual screening. Various virtual screening platforms have emerged in an endless stream and play great roles in the field of drug discovery. With the increasing number of compound molecules, virtual screening platforms face two challenges: low fluency and low visibility of software operations. In this article, we present an integrated and graphical drug design software eSHAFTS based on three-dimensional (3D) molecular similarity to overcome these shortcomings. Compared with other software, eSHAFTS has four main advantages, which are integrated molecular editing and drawing, interactive loading and analysis of proteins, multithread and multimode 3D molecular similarity calculation, and multidimensional information visualization. Experiments have verified its convenience, usability, and reliability. By using eSHAFTS, various tasks can be submitted and visualized in one desktop software without locally installing any dependent plug-ins or software. The software installation package can be downloaded for free at http://lilab.ecust.edu.cn/home/resource.html . © 2019 Wiley Periodicals, Inc.     

A graph theoretical approach to structure-property and structure-activity correlations

The structure similarity and dissimilarity implied in many structure-property and structure-activity relationships has been examined from the graph theoretical point of view. The approach outlined is fundamentally different from generally used schemes in that, rather than seeking a new parametrization which will quantitatively fit observed data and trends,similarities among the skeletal forms and connectivities of the compounds of interest are studied quantitatively. The basis of the method is the assumption that skeletal forms of apparent similarity will yield similar enumerations for a number of graph theoretical invariants. In particular, allpaths within molecular skeletons are enumerated and sequences of path numbers (i.e., the number of paths of different length) are compared. The degree of similarity between molecules is proportional to the distance between points in the corresponding structure space obtained by interpreting the entries in molecular path sequences as coordinates inn-dimensional space. As anexample of the use of the concept of structural similarity, structure-activity data relating cerebral dopamine agonist properties for a series of N-substituted 2-aminotetralins are considered. The analysis suggests that the method may find wide application in the field of structure-activity correlations and structure-property studies. The data could be mass spectra, the fingerprint regions of infrared spectra, optical rotation and circular dichroism measurements, or any of many not fullyunderstood complex experimental findings suspected of having an inherent structural basis.On leave from Ames Laboratory - DOE, Iowa State University, Ames, Iowa 50011     

Using molecular similarity to construct accurate semiempirical electronic structure theories

Ab initio electronic structure methods give accurate results for small systems, but do not scale well to large systems. Chemical insight tells us that molecular functional groups will behave approximately the same way in all molecules, large or small. This molecular similarity is exploited in semiempirical methods, which couple simple electronic structure theories with parameters for the transferable characteristics of functional groups. We propose that high-level calculations on small molecules provide a rich source of parametrization data. In principle, we can select a functional group, generate a large amount of ab initio data on the group in various small-molecule environments, and "mine" this data to build a sophisticated model for the group's behavior in large environments. This work details such a model for electron correlation: a semiempirical, subsystem-based correlation functional that predicts a subsystem's two-electron density matrix as a functional of its one-electron density matrix. This model is demonstrated on two small systems: chains of linear, minimal-basis (H-H)(5), treated as a sum of four overlapping (H-H)(2) subsystems; and the aldehyde group of a set of HOC-R molecules. The results provide an initial demonstration of the feasibility of the approach.     

Applications of the molecular orbital graph theory: A topological method to calculate aN–K based on aN

A formula of the coefficient a_N–K of the eigenpolynomials connected with the zero-order term's coefficient of the eigenpolynomials corresponding the k-order-induced subgraph's molecular fragments has been induced. From this formula, a_N–K can be calculated and the contributions of the induced subgraph's molecular fragments to the stability and reactivity of the molecules are revealed. © 1994 John Wiley & Sons, Inc.     

Modified molecular charge similarity indices for choosing molecular analogues

Toward the goal of defining a molecular charge similarity idex that best quantifies the concept of molecular similarity as it relates to biological activity, we have evaluated a variety of definitions of the molecular charge distribution function, ρ, for use in the charge similarity index formalism. Spatially distributed nuclear charges are incorporated into electron distribution functions to approximately account for the screening of core electronic charge and to model the net effect of the total charge distribution in a manner that better reflects the inherent relation to the molecular electrostatic potential. The resulting charge similarity indices are evaluated based on their sensitivity to relative molecule displacement and their ability to meaningfully group or order a simple set of molecular structures: CH₃CH₂CH₃, CH₃OCH₃, and CH₃SCH₃.