Topological shape

Mezey, P.G. (1995) Methods of molecular shape-similarity analysis and topological shape design. 

A normalized centric index C was also introduced in order to reflect the topological shape of alkanes. By definition, C = 0 for n-alkanes (chain-graph) ... 

Comparison of topological, shape, and docking methods in virtual screening. J Chem Inf Model 47(4)4504-1519... 

Apparently, the concept of similarity plays an important role in the chemistry of functional groups. Motivated by the recent revival of interest in molecular similarity [7-39], we shall present a systematic approach towards a quantum chemical description of functional groups. There are two main components of the approach described in this report. The first component is shape-similarity, based on the topological shape groups and topological similarity measures of molecular electron densities[2,19-34], whereas the second component is the Density Domain approach to chemical bonding [4]. The topological Density Domain is a natural basis for a quantum... 

Mezey, P.G.,"Methods of Molecular Shape-Similarity Analysis and Topological Shape Design". In Dean, P.M., ed., Molecular Similarity in Drug Design (Chapman Hall - Blackie Publishers, Glasgow, U.K., 1995). 

The three-dimensional shape of this fuzzy body of the electronic distribution has many important features not revealed by the simple, skeletal ball and stick model. One of the most important tasks of topological shape analysis of molecules is the precise analysis and concise description of the three-dimensional electronic charge distributions, such as that illustrated by the selected MIDCO s of allyl alcohol in Figure 1.2. Various methods and computational techniques of such topological shape analyses are discussed in detail in this book. 

Molecular topology [155-158,190-199] presents a systematic framework for general shape analysis methods applicable, in principle, to all molecules. The same framework is also the basis for special shape analysis methods designed to exploit the typical features of some special, distinguished molecular families, such as the folding properties of polypeptides, proteins, and other chain biomolecules. Molecular topology and the associated topological shape analysis approaches form the basis of the present book. 

The stereochemical shape concept covers a wide range of possible resolutions, from the details of electron density distributions between pairs of nuclei in relatively small molecules to the structural organization of the tertiary structure of proteins [201-203], the architecture of supramolecular assemblies [204-230], the problems of shape selectivity in reactions of large molecules [231-233], and the intriguing shape features of self-replicating chemical systems [234-239]. In the following chapters we shall discuss various topological shape analysis techniques, suitable for the relevant level of resolution. 

In this book we shall be concerned only with a very limited. selection of the elements of topology, relevant to the basics of topological shape analysis of molecules. All the tools we shall use will be described in sufficient detail in the book. However, for readers interested in more details of the fundamentals, some introductory and advanced texts are listed among the references [113-122]. 

Convexity and curvature properties. In the above discussion and examples we have already used the concepts of convexity and locally convex domains in an intuitive manner. Whereas our goal is to provide a topological shape characterization for molecules, we shall often use geometrical tools at intermediate steps toward a topological description. These steps often involve the concepts of convexity, curvature, and a characterization of critical points of functions. 

TOPOLOGICAL SHAPE GROUPS, SHAPE CODES, SHAPE GRAPHS, SHAPE MATRICES, AND SHAPE... 

We have seen that a simple list of Betti numbers of the shape groups can serve as a numerical shape code for a partitioned molecular surface. Some of the alternative topological shape de.scriptors of molecular surfaces, such as the shape matrices s(a,b) and shape graphs g(a,b), can also serve as 3D topological shape codes 143,109,110,158,199]. In Chapter 6, several examples of shape codes are described and used as numerical shape similarity measures. 

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