Empirical descriptors

The primary supposition of any toxicological QSAR is that the potency of a compound is dependent upon its molecular structure, which is typically quantified by chemical properties (Schultz et al., 2002). Chemical descriptors include a variety of types, including atom, substituent, and molecular parameters. The most transparent of these are the molecular-based empirical and quantum chemical descriptors. Empirical descriptors are measured descriptors and include physicochemical properties such as hydrophobicity (Dearden, 1990). Quantum chemical properties are theoretical descriptors and include charge and energy values (Karelson et al., 1996). Physicochemical and quantum chemical descriptors are for the most part easily interpretable with regard to how that property may be related to toxicity. The classic example of this, the partitioning of a toxicant between aqueous and lipid phases, has been used as a measure of hydrophobicity for over a century (Livingstone, 2000). 

Abstract In this chapter we give an overview on QSAR models for treating the mutagenicity of cyclic amines. An extensive discussion is focused on the topological. E-state, quantum chemical, and empirical descriptors (log ) that are often used in corresponding models. Two case studies are presented in more detail. The conclusion addresses the OECD principles for validation of models that are used for regulatory purposes. 

The class of the empirical descriptors is a fuzzy, not well-defined class. In principle, empirical descriptors are those not defined on the basis of a general theory such as, for example, quantum chemistry or graph theory. Rather they are defined by practical rules derived from chemical experience, e.g. considering specific or local structural factors present in the molecules, often sets of congeneric compounds. As a consequence, in most cases, empirical descriptors represent limited subsets of compounds and cannot be extended to classes of compounds different from those for which they were defined. Empirical descriptors have not to be confused with experimentally derived descriptors even if it is well known that several of them are empirically derived. 

Empirical descriptors can be a few user-defined values for discriminating among special molecular fragments or counting local specific atom/fragment occurrences within a molecule. 

Examples of empirical descriptors can be considered to be the -+ Taillander index (restricted to substituted benzenes), - second-grade structural parameters (restricted to alkenes), - polar hydrogen factor (restricted to halogenated hydrocarbons), - hydrophobic fragmental constants, - six-position number, Idoux steric constant, -> hydrophilicity index, - adsorbability index, -> bond flexibility index, and -+ atomic solvation parameter. 

Kaliszan, R., Osmialowski, K., Tomellini, S.A., Hsu, S.-H., Fazio, S.D. and Hartwick, R.A. (1985). Non-Empirical Descriptors of Sub-Molecular Polarity and Dispersive Interactions in Reversed-Phase HPLC Chromatographia, 20,705-708. 

An example of useless empirical descriptor is the Sadhana index (or Sadhna index) [Khadikar, Agrawal et al, 2002 Khadikar, Joshi et al, 2004] defined for polyacene molecules as Sd = 2 h X (5h + 1), where h is the number ofbenzene units. This index is almost perfectly correlated to the PI index, to the square count ofbenzene units, and any quadratic combination of the coefficients of h and h, such as 5h + h or 20h + 4h. 

Descriptors are atomic or molecular parameters or even molecular properties that contain information about the energy of each type of intermolecular interaction. They can be classified into two broad categories empirical and theoretical. Empirical descriptors depend on experimental measurements thus, they are available for a limited number of solutes (16). Theoretical descriptors are derived from the solute structure they are usually based on ab initio or semiempirical quantum chemistry calculations or on the connectivity of atoms in the molecule. With the proper use of dedicated software, the number of structural descriptors that can be assigned to a given solute is practically unlimited. Comprehensive compilations of the literature (17,18) register over 2000 known theoretical descriptors. 

The best Kp pp-odd) fs greedy descriptor can be seen in Tables 7.7 and 7.8 and the best full combinatorial Kp(pp-odd) /fg ° descriptor is shown in Tables 7.9 and 7.10 (here only ij/E and Z are S - or configiuation-dependent). The fuU combinatorial method, achieves to find also a good five-index semi-empirical descriptor,... 

The 1-octanol/water system provides empirical descriptors of the lipophilicity of compounds that work in QSAR analyses (Table 1.1), even though the principal nature of the underlying processes is not yet thoroughly understood. 

Thinking along these lines demonstrates that one has lost track of what is a true concept and what is an empirical descriptor. That nonbonded repulsion and attraction are descriptions of two possible modes of operation of nonbonded atoms, with neither being the rule or the exception, is vividly demonstrated by compilations of data pertaining to the relative stability of 1,2 disubstituted ethenes. Depending on whim, one can easily pronounce either nonbonded repulsion or... 

---