Global descriptors

Some simple global descriptors are molecular weight, number of atoms present in a molecule (e.g., number of chlorine atoms), number of double bonds, etc. Other descriptors represent the ramification of the molecule. Certain descriptors take into consideration the electronic charge on a certain atom, or its polarity. 

The reduced radius of gyration (rg) is a global descriptor useful to discriminate large globular features (debris or pellets) from filamentous objects (rg = 0.7 for a disc) (Fig. 14). It is based on the moments of the feature ... 

Dubchak, I., Muchnik, I. Kim, S. H. (1997). Protein folding class predictor for SCOP approach based on global descriptors. Ismb S, 104-7. 

A fundamental difference between 3D- and a 2D-QSAR equation is the non-existence of conformational dependent secondary sites in the latter. Hence, a direct transposition of 3D- and 2D-models is not always possible but the global properties of the chemical structures, if relevant to the activity, may show their presence in both of them. Moreover, in a broader perspective, all 2D-QSAR parameters—physicochemical as well as structural—can be considered as one or the other form of global descriptors. In light of this, to bridge the 2D- and 3D-features the following 2D-QSAR equations have been derived for the antifungal activity of 2,3,4-substituted thiazolidines (Table 21). 

Finally, the average value of the surface property of the molecule is assigned to each excited neuron in the comparative map. Two surfaces can be compared with different tolerance depending on the value of the neuron winning distance different MD thresholds result in a series of different maps. The comparative feature maps can be then described by various global descriptors to be used for QSAR modeling. 

A more discriminating approach should consider the distribution and relative location of bonds in space. We deal now with these families of descriptors. They can be classified into two classes local descriptors, which focus on some special bonds, and global descriptors, which use the entire molecular chain. 

Global Descriptors Persistence Length and Characteristic Ratio... 

Two additional families of global descriptors are related to the curvature features of molecular space curves. Since molecular chains are sequences of bonded straight line segments, they are differentiable along the bonds but not at the nuclear positions. Shape descriptors can be derived assuming two... 

The exponent Df is a characteristic of the curve and thus can be used as a global descriptor of molecular shape.This single number, derived from geometry and connectivity, is associated with a single conformation and does not require the evaluation of averages over configuration space. 

A recent contribution to the HSAB principle is the application of concepts of local softness and local hardness (Torrent-Sucarrat et al. 2010). Instead of global hardness (r ) and global softness (S) (see Equations [3.15] and [3.16]), which are called global descriptors because they describe the properties of a molecule as a whole, the local descriptors are used. 

Besides the global descriptors of reactivity, there are a number of local indices that describe the active sites within a molecnle. Among them, of special interest is the Fukui function [48, 53, 57-60]. This index, besides being a local descriptor of reactivity by itself (i.e., regioselectivity), may act as a convenient distribution function for global quantities. The original definition is as follows [59, 61] ... 

First, a coarse-grained description of the polymer melt is invoked through the definition of the conformation tensor, c, which is a global descriptor of the long-length scale conformation of polymer chains. The conformation tensor c is defined as the second moment tensor of the end-to-end distance vector of a polymer chain reduced by one-third of the unperturbed end-to-end distance and averaged over all chains in the system ... 

The mathematical formulation and definition of GRDs provide information about the overall properties of the chemical systems and are also useful for analysing the thermodynamic aspects of chemical reactions. However, the GRDs caimot identify the reactive part or site of the molecule. Most of the chemical reactions are primarily concerned with the atoms, group of atoms or a specific site in a molecule. The important issues relate to the effect of charge or density fluctuations in chemical reactivity and the observed reactivity trends. The chemical reactivity for a system is determined by the sensitivity of electron density to the perturbations. Therefore, an appropriate definition was required in addition to the global descriptors [18]. A basic local descriptor is related to the change of the local electron density to the chemical potential of the system. This is known as local softness. 

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