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Erschienen in:
Buchtitelbild

2014 | OriginalPaper | Buchkapitel

1. Introduction to Molecular Similarity and Chemical Space

verfasst von : Gerald M. Maggiora

Erschienen in: Foodinformatics

Verlag: Springer International Publishing

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Abstract

The size of the chemical universe of small organic molecules is estimated to be around 200 billion, and its true size may be even larger. Because the size of “representative” subsets of that universe can still be substantial, computer-based methods are required to capture, manage, and search the massive amount of available chemical information associated with these molecules. This has given rise to the field of chemical informatics. Three concepts play major roles in this field, two of which, molecular similarity and chemical space (CS), are dealt with in this chapter. Of the two, molecular similarity is the more fundamental since it plays a crucial role in the definition of CS itself. The third concept, activity and property landscapes, while important, will not be considered here. Though the potentially relevant subset of molecules that is applicable in food science applications is considerably smaller than the universe of small organic molecules, it nonetheless is large enough to benefit from concepts of molecular similarity and CS that have proved useful in medicinal chemistry and related fields of chemistry. The present chapter provides a relatively detailed and somewhat didactic description of the two concepts, how they are implemented, and how they can be applied in typical chemical applications.

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Nächstes Kapitel The Chemical Space of Flavours
Fußnoten
1
The term database (DB) will generally be used to describe large collection of compounds whether or not material exists for screening the compounds.
 
2
Interestingly, since FP-based similarity coefficients are ratios of two integers, they represent a limited subset of rational numbers. Hence, they can by their very nature only yield restricted set of values on the unit interval of the real line.
 
3
In that case, the set of features in MQ are a subset of those in MR.
 
4
Strictly speaking, these vectors should be called geometric vectors since they do not, in all cases, satisfy the properties of algebraic vectors (e.g., algebraic vectors satisfy the axioms of a linear vector space, namely, the addition of two vectors or the multiplication of a vector by a scalar should result in another vector that also lies in the space). Nevertheless, the terminology “vector,” which is common in chemical informatics, will be used here to include both classes of vectors.
 
5
An interesting relationship between the FP- and vector-based similarity coefficients occurs when both have binary component values, e.g. m l = (1,0,0,0,1,1,0,1,0,1) and x row(l) = (1,0,0,0,1,1,0,1,0,1). In such cases, but only in such cases, the similarity coefficients based on binary FPs or binary vectors yield exactly the same similarity value for all of the similarity coefficients described above. However, this limitation has not been consistently adhered to and similarity values computed using continuous vectors or weighted FPs based on Eqs. (1.27)–(1.29) yield values that may differ significantly from their corresponding FP-based similarity coefficients.
 
6
The RRF rule works best with rank values since similarities can in certain cases have zero values leading to undefined values for the reciprocals, a situation that can be overcome by the addition of a small positive constant to the denominator of each term.
 
7
It should be noted that similarity cliffs are more general than scaffold hops since all scaffold hops do not result in compounds that are highly dissimilar, as may be the case when the scaffolds associated with scaffold hops are approximate bioisosteres or compounds with dissimilar scaffold nonetheless have similar overall structures.
 
8
Even though the overall percentage of active compounds in large DBs is usually quite small, since most compounds are inactive in a given assay, the fraction of those actives where both compounds of a compound pair are approximately of equal activity can be significant.
 
9
Supervised machine learning methods typically try to model the relationship of a set of predictor (independent) variables to a set of known values (e.g., biological activities and/or solubilities) associated with one or more dependent variables. Unsupervised methods only require information associated with predictor (independent) variables (e.g., physicochemical descriptors).
 
10
Since CSs are inherently discrete, the concept of discontinuity, which applies to continuous systems, is only approximate. Thus, “discontinuities” in these spaces, such as those arising from the presence of activity cliffs, are denoted as quasi-discontinuities.
 
11
In mathematics these are generally called Gram matrices and in statistics are usually called association matrices.
 
12
Note that the coefficient (n − 1)−1 would, if ignored, merely scale the eigenvalues by n − 1; the eigenvectors are unaffected.
 
13
In function notation, the mapping in Eq. (1.54) is given by \(\Phi \left( {{{\bf{x}}_i}} \right) = {{\rm{C}}_k},\,\,i = 1,2,...,n;\,\,\,\,k = 1,2,...,{N_{{\rm{cells}}}}\).
 
14
Note that there are a number of “correction factors,” such as the well-known Laplace correction, that can be applied to the cells of a contingency table to correct for empty cells.
 
15
A similar situation exists in the case of threshold graphs obtained from labeled graphs when the edge values exceed some threshold value. Details of this are described in Sect. 1.3.7 on graph-based CSs.
 
16
Self-similarity is the similarity of the molecule with itself, and thus, its value is always unity. Graphs without self-loops and multiple edges between vertices are also called simple graphs.
 
17
Although it is not addressed here, the vertex degree of directed graphs/networks can be handled by assessing the “in-degree” and “out-degree” of a vertex that corresponds, respectively, to the number of edges directed towards the vertex and the number directed away from the vertex.
 
18
Note that the summations are over all unique pairs of vertices (i.e., molecules) and that the coefficient cancels out of the numerator and denominator of Eq. (1.64).
 
19
Note that this can also be interpreted as the fraction of vertices of degree k.
 
20
This argument is, of course, oversimplified since it depends on the width (standard deviation) of the probability distribution.
 
21
There are, of course, other docking processes that are of importance in biology including protein–protein, ligand–nucleic acid, nucleic acid–nucleic acid docking to name a few. Ligand–protein docking is highlighted in this work because of its importance in drug discovery and its widespread application in that field.
 
22
See Sect. 1.2.3 for related discussion.
 
23
In order to simplify discussion, the terminology “target class specific” will be used in the remainder of this section.
 
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Metadaten
Titel
Introduction to Molecular Similarity and Chemical Space
verfasst von
Gerald M. Maggiora
Copyright-Jahr
2014
Buch
Foodinformatics

Print ISBN: 978-3-319-10225-2

Electronic ISBN: 978-3-319-10226-9

Copyright-Jahr: 2014

DOI
https://doi.org/10.1007/978-3-319-10226-9_1