Molecular similarity 452 Subject

Molecular similarity analysis has developed substantially over the years, especially as digital computers became faster, more compact, and widely available to scientists. Handling large sets of molecules is generally not a problem. The main problem confronting MSA is the problem of the lack of topological invariance of the chemistry spaces induced by the various similarity measures. Unfortunately, this problem may be fundamentally related to the inherent subjectivity of similarity and thus cannot be addressed in any simple manner. 

It is possible at present to identify two main levels at which molecular similarity is of importance in proteins. First, detection of large-scale similarities between different protein structures, i.e. similarities in the way that the linear polypeptide sequence is folded up to form a three-dimensional structure. This is the subject of the remainder of Sect. 4. Second, comparative analysis of local aspects of protein structure, for example the examination of specific binding sites, or of the environments of particular sidechains. These methods are described in Sect. 5. 

The main difficulty for commonly used 3D descriptors results from the treatment of conformational flexibility. Considering that only a single conformation is inadequate for most classes of pharmaceutically relevant molecules, averaging over conformational space provides only a very rough view as to what is intended to be described, namely the possible arrangement of pharmacophoric groups in Cartesian space. In this section a more detailed view on three subjectively selected approaches to describe molecular similarity will be presented. The approaches have in common the fact that similarity is quantified to a less dependable degree from only the 2D structure or specific 3D conformations. 

These trends were first observed for commercial surfactants (8-10). In most respects pure and complex surfactants are similar. Both types show alkane scans with pronounced minima. In both cases n. is increased by increasing surfactant molecular weiffe (subject to structural modifications, e.g. ref. 11), by increasing NaCl concentration or by decreasing temperature (12). Addition of alcohol cosurfactants produces similar n changes in both cases... 

The next section, entitled Basic Aspects of Molecular Similarity, gives a general overview of molecular similarity and the usual vocabulary used by chemists in this field. In the section entitled The Electron Density as Molecular Descriptor, some elements of quantum chemistry will be presented. These sections should not be expected by the reader to offer a rigorous discussion of all aspects of such broad fields, and therefore, only the most important definitions and concepts will be introduced. The following sections will then address extensively the subject of molecular quantum similarity in both theoretical and practical aspects. An ample references list will help the interested reader to look up the more specialized literature. 

The functioning of the brain is dependent on its composition and structure that is, on the molecular environment of the mind. The presence in the brain of molecules of lV,N-diethyl-D-lysergamide, mescaline, or some other schizophrenogenic substance is associated with profound psychic effects (3). Gherkin has recently pointed out (4) that in 1799 Humphry Davy described similar subjective reactions to the inhalation of nitrous oxide. The phenomenon of general anesthesia also illustrates the dependence of the mind (consciousness, ephemeral memory) on its molecular environment (5). 

Molecular similarity seemed to be ideally suited for the task, except for one important thing. Unlike the certainty of substructure searches that identified compounds that either did or did not contain the query substructure, similarity is a subjective notion and thus is more difficult to exploit since there is no right answer. For example, in similarity-based searching, knowing a compound s structure is not sufficient the key concern is what molecular features do the two molecules have in common. This begs a number of questions. What molecular features should be considered How is their relative importance assessed How is this information... 

A key element in computing molecular similarity is the choice of a representation that captures the chemical information appropriate to the desired application. Because similarity is a subjective concept this is not an easy task, the choices made can have a profound effect on the results obtained. For example, consider the set of bulk phys-icochanical properties of the two aromatic ring compounds, benzene and thiophene, shown in Figure 15.1. It is clear from the figure that both molecules share property... 

Because of its fundamentally subjective nature, molecular similarity methods provide more powerful means for accessing a broad spectrum of structure and property-based information than more objective approaches such as substructure searching. This power, however, comes at a cost because its very subjectivity makes the development and testing of molecular similarity methods problematic at best. In addition, as noted in the quote at the beginning of this chapter, Similarity like pornography is difficult to define, but you know it when you see it, but even this phrase does not capture all of the subtleties of similarity be they molecular or otherwise. 

What does this all mean One interpretation suggests that new similarity measures more compatible with human perception might be helpful, but how are we to develop them Since similarity methods provide comparative measures of similarity that are inherently subjective, is it even possible to design new methods that are materially better than those in use today Regardless of the answers to these and related questions, and despite the fact that the results provided by MS As are highly subjective in character, it is clear that the concept of molecular similarity will continue to play an important role in many aspects of chemical, biological, and pharmaceutical researches as the material in the following chapters of this book clearly demonstrate. 

Because of this, most apphcations of molecular similarity over large sets of compounds generally employ 2-D similarity methods. It should be emphasized, however, that procedures for comparing 2-D versus 3-D similarity methods are imperfect by their very nature since, as noted earlier, similarity is a subjective concept that does not admit to absolute comparisons of aity type. 

Over the past decade, a number of books have provided a good overview of many aspects of the field of chemical informatics [26-30], and a number of reviews and papers on molecular similarity [31-34] and CS [35-40] have also been published. These sources should be consulted for additional details on aity of the subjects discussed in this work. 

The computational methods described above provide algorithms for computing molecular similarities, albeit imperfect ones, due to the inherently subjective nature of similarity. This, however, begs the question as to how these similarity measures accord with the perceptions of chemists, an issue that has been discussed in more detail in several recent publications [10, 34]. An important question in this regard is whether similarity scales used intuitively by chemists agree with those obtained computationally. The answer, as we shall see, is that they do not. 

As noted earlier, since similarity measmes are not invariant to the representation or similarity coefficient employed, small differences with respect to one measure may not be comparably small with respect to another measme. In such cases, activity cliffs themselves will not be invariant to similarity measttre [10, 34, 41], an uneasy state of affairs that raises the question of whether activity cliffs actually exist [134]. Alternative representations based on matched molecular pairs (MMPs) have sought to address this question using the 2-D structural representation favored by chemists, but entirely quantitative results have yet to be obtained [135, 136]. Because of its inherent subjectivity, it is unlikely that invariant values (absolute values) of molecular similarity can ever be obtained. Nevertheless, while it may be difficult to quantitate the magnitudes of activity cliffs, there is no donbt that they exist since many examples of small structural changes, as perceived by medicinal chemists, have resulted in relatively large activity differences [134]. 

The system is particular in that the turkey ovomucoid inhibitor, TOMl (PDB access code IPPF), is an elastase inhibitor consisting of 56 residues (814 atoms), that is, characterized by a size drastically larger than the diflu-oroketone inhibitor, DFKi (PDB access code 4EST), with 70 atoms (Online Resource 1). Due to that particularity, it has been the subject of several studies [26-29] regarding their alignment using molecular similarity-based techniques. 

This section attempts a brief review of several areas of research on the significance of phases, mainly for quantum phenomena in molecular systems. Evidently, due to limitation of space, one cannot do justice to the breadth of the subject and numerous important works will go unmentioned. It is hoped that the several cited papers (some of which have been chosen from quite recent publications) will lead the reader to other, related and earlier, publications. It is essential to state at the outset that the overall phase of the wave function is arbitrary and only the relative phases of its components are observable in any meaningful sense. Throughout, we concentrate on the relative phases of the components. (In a coordinate representation of the state function, the phases of the components are none other than the coordinate-dependent parts of the phase, so it is also true that this part is susceptible to measurement. Similar statements can be made in momentum, energy, etc., representations.)... 

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