Similarity analysis in two and three dimensions using lattice animals and polycubes

The quantification and analysis of molecular similarity are fundamental problems of both theoretical and applied chemistry. The continuum similarity problem of planar domains with Jordan curve boundaries can be discretized and quantified using interior filling animals (square cell configurations). A similar approach is applicable to the continuum similarity problem of formal molecular bodies enclosed by contour surfaces, where interior filling polycubes provide a method for discretization and quantification of molecular similarity in three dimensions. This technique leads to resolution based similarity measures (RBSMs), suitable for automatic, non-visual evaluation of the degree of similarity between shapes of general objects, in particular, of molecular charge distributions, or fused sphere Van der Waals surfaces. Using the framework of the RBSM method, the polycube method of chirality quantification is extended to the quantification of approximate symmetry of molecular electron distributions.     

Semisimilarity of molecular bodies: Scaling–nesting similarity measures

A simple, new technique for the evaluation of the similarity of molecular shapes is presented. The concept of semisimilarity (asymmetric similarity) is applied within the topological–geometrical framework of scaling–nesting similarity measures of molecules. The practical application of these similarity measures is illustrated by the examples of the three-dimensional formal bodies of electronic charge densities of a set of simple molecules. © 1994 John Wiley & Sons, Inc.     

Representation of square-cell configurations in the complex plane: Tools for the characterization of molecular monolayers and cross sections of molecular surfaces

Two numerical codes, a complex face vector F and a real face vector D are developed for the characterization of square-cell configurations (lattice animals), used for representing the shapes of molecular monolayers and cross sections of molecular surfaces. The real face vector D represents all the intrinsic properties, size, and shape of the lattice animal. The complex face vector F contains complete information about the size, the shape, and also the placement of the particular lattice animal with respect to the lattice. Based on the properties of the face vectors, a method is developed for the classification of similar animals into equivalence classes. The face vector method is proposed for an algorithmic, nonvisual computer analysis of similarity of shapes of molecular monolayers and planar domains of cross sections of molecular surfaces, approximated by lattice animals.     

Toward similarity measures for macromolecular bodies: Medla test calculations for substituted benzene systems

A new method is proposed for the evaluation of numerical similarity measures for large molecules, defined in terms of their electron density (ED) distributions. The technique is based on the Molecular Electron Density Lego Assembler (MEDLA) approach, proposed earlier for the generation of ab initio quality electron densities for proteins and other macromolecules. The reliability of the approach is tested using a family of 13 substituted aromatic systems for which both standard ab initio electron density computations and the MEDLA technique are applicable. These tests also provide additional examples for evaluating the accuracy of the MEDLA technique. Electron densities for a series of 13 substituted benzenes were calculated using the standard ab initio method with STO-3G, 3-21G, and 6-31G** basis sets as well as the MEDLA approach with a 6-31G** database of electron density fragments. For each type of calculation, pairwise similarity measures of these compounds were calculated using a point-by-point numerical comparison of the EDs. From these results, 2D similarity maps were constructed, serving as an aid for quick visual comparisons for the entire molecular family. The MEDLA approach is shown to give virtually equivalent numerical similarity measures and similarity maps as the standard ab initio method using a 6-31G** basis set. By contrast, significant differences are found between the standard ab initio 6-31G** results and the standard ab initio results obtained with smaller STO-3G and 3-21G basis sets. These tests indicate that the MEDLA-based similarity measures faithfully mimic the actual, standard ab initio 6-31G** similarity measures, suggesting the MEDLA method as a reliable technique to assess the shape similarities of proteins and other macromolecules. The speed of the MEDLA computations allows rapid, pairwise comparisons of the actual EDs for a series of molecules, requiring no more computer time than other simplified, less detailed representations of molecular shape. The MEDLA method also reduces the need to store large volumes of numerical density data on disk, as these densities can be quickly recomputed when needed. For these reasons, the proposed MEDLA similarity analysis technique is likely to become a useful tool in computational drug design. © 1995 John Wiley & Sons, Inc.     

A complete shape characterization for molecular charge densities represented by Gaussian-type functions

An algorithm for a detailed 3-D characterization of the shapes of molecular charge distributions is implemented, tested and applied for a family of AB₂ molecules. The characterization is performed by computing a number of topological invariants (“shape groups”) associated with a continuum of molecular surfaces: the complete family of all electronic isodensity contours for the given molecules. These shape groups (the homology groups of truncated surfaces derived from isodensity contours) depend continuously on two parameters: a density value defining the density contour, and a reference curvature value, to which the local curvatures of the isodensity contours are compared. The electronic charge distribution is modeled by means of Gaussian-type functions. The method employs an explicit form of the charge density function in order to compute the curvature properties for the molecular surfaces analytically, from which the shape groups are derived by the algorithm. No visual inspection is required for the characterization and comparison of shapes of molecular charge densities, as these are done algorithmically by the computer. However, visual inspection of the results of the shape analysis is a possible option. For a given molecule, in a given nuclear configuration, the technique provides a two-dimensional shape map, displaying the distribution of shape groups as a function of the local curvature and the level set value (the value of the charge density at the contour). The computer program GSHAPE performs the analysis of shape maps automatically. This feature makes it potentially useful in the context of computer-aided drug design, where unbiased, automated shape characterization methods are valuable tools. As examples, several two-dimensional shape maps for simple systems are discussed. The changes induced in these maps by a change in the nuclear geometry, as well as by the changes of the nuclear charge, are also analyzed. The method is applicable to large biomolecules of interest if charge density information is available.     

A proof of the metric properties of the symmetric scaling-nesting dissimilarity measure and related symmetry deficiency measures

The scaling-nesting similarity measures were proposed earlier for an intuitively simple shape comparison of molecular “bodies” enclosed by isodensity surfaces. Similarity measures have extended utility and provide rigorous comparisons which can be treated by well-known mathematical techniques if they fulfill the conditions for a metric. Here, a proof is presented showing that the symmetric scaling-nesting dissimilarity measure is indeed a proper metric. Some additional features, relevant to the newly proven properties of these similarity measures, are discussed. © 1997 John Wiley & Sons, Inc.     

Three properties of relative shape envelopes of molecular electron density contours

Summary The relative shapes of molecular electron density contour surfaces (MIDCO's), and various molecular shape constraints in solvent-solute interactions, in external electromagnetic fields and within enzyme cavities, are representable by electron densityT-hulls, introduced earlier. Three general properties ofT-hulls are proven, serving as the justification of a recently proposed computational scheme of molecular similarity measures.     

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.     

基于支持向量学习机方法的人体小肠吸收药物活性的预测

为了预测分子在人体小肠中的吸收,本文计算了表征分子的电子、拓扑、几何结构、分子形状等特征的102个分子描述符,用遗传算法变量选择方法使描述符减少到47个。体系共包含了230个化合物分子,69个不能被吸收(mA-),161个可以被吸收(HIA )。对建立的SVM模型,用5重交叉验证和独立测试集进行验证,预测正确率分别达到79．1％和77．1％,结果具有较好的一致性。在模型验证中,通过聚类分析方法组合训练集和测试集,保证了模型的稳定性,提高了建模效率。