Quantitative structure-activity linear models

In this chapter we provide a historical perspective of the development of the field of computational toxicology. Beginning from the similarity-based grouping of elements into the periodic table, the chapter presents a chronology of developments from the simple observations of qualitative relations between structure and toxicity through LFER (linear free energy related) and QSAR (quantitative structure activity relationship) models, to the current... 

Konemann (1981) demonstrated that the 7 to 14-day LC50 acute lethality of nonreactive nonelectrolyte industrial organic chemicals to the guppy (Poec/7/a reticulata), produced an excellent fit to a linear quantitative structure-activity (QSAR) model (equation 1), where P is the... 

The fundamental assumption of SAR and QSAR (Structure-Activity Relationships and Quantitative Structure-Activity Relationships) is that the activity of a compound is related to its structural and/or physicochemical properties. In a classic article Corwin Hansch formulated Eq. (15) as a linear frcc-cncrgy related model for the biological activity (e.g.. toxicity) of a group of congeneric chemicals [37, in which the inverse of C, the concentration effect of the toxicant, is related to a hy-drophobidty term, FI, an electronic term, a (the Hammett substituent constant). Stcric terms can be added to this equation (typically Taft s steric parameter, E,). 

More recently (2006) we performed and reported quantitative structure-activity relationship (QSAR) modeling of the same compounds based on their atomic linear indices, for finding fimctions that discriminate between the tyrosinase inhibitor compounds and inactive ones [50]. Discriminant models have been applied and globally good classifications of 93.51 and 92.46% were observed for nonstochastic and stochastic hnear indices best models, respectively, in the training set. The external prediction sets had accuracies of 91.67 and 89.44% [50]. In addition to this, these fitted models have also been employed in the screening of new cycloartane compounds isolated from herbal plants. Good behavior was observed between the theoretical and experimental results. These results provide a tool that can be used in the identification of new tyrosinase inhibitor compounds [50]. 

There are several properties of a chemical that are related to exposure potential or overall reactivity for which structure-based predictive models are available. The relevant properties discussed here are bioaccumulation, oral, dermal, and inhalation bioavailability and reactivity. These prediction methods are based on a combination of in vitro assays and quantitative structure-activity relationships (QSARs) [3]. QSARs are simple, usually linear, mathematical models that use chemical structure descriptors to predict first-order physicochemical properties, such as water solubility. Other, similar models can then be constructed that use the first-order physicochemical properties to predict more complex properties, including those of interest here. Chemical descriptors are properties that can be calculated directly from a chemical structure graph and can include abstract quantities, such as connectivity indices, or more intuitive properties, such as dipole moment or total surface area. QSAR models are parameterized using training data from sets of chemicals for which both structure and chemical properties are known, and are validated against other (independent) sets of chemicals. 

Kubinyi, H., Quantitative structure-activity relationships. IV. Non-linear dependence of biological activity on hydrophobic character a new model, Arzneimittel-Forschung - Drug Res., 26, 1991-1997, 1976. 

Another area of molecular modeling involves development of quantitative structure-activity or structure-property relationships (QSAR and QSPR). These studies use a range of statistical methods (linear and nonlinear... 

In addition, traditional quantitative structure-activity relationship (QSAR) models were reported. Gozalbes et al. attempted to predict the blood-brain barrier permeabilities of four arylacetamides using linear discriminant analysis [65], while Medina-Franco et al. discriminated between active and inactive BCG compounds using two-dimensional (2D) and three-dimensional (3D) structural-similarity methods [66]. 

Recently (2006), the quantitative structure-activity relationship (QSAR) modeling of the same compounds based on their atomic linear indices, for finding fimctions that discriminate between the tyrosinase inhibitor compounds and inactive ones, has been reported by the same group [50]. 

Quantitative Structure - Activity Relationships (QSARs) are estimation methods developed and used to predict certain effects or properties of chemical substances, which are primarily based on the structure of the chemicals. The development of QSARs often relies on the application of statistical methods such as multiple linear regression (MLR) or partial least squares regression (PLS). However, since toxicity data often include uncertainties and measurements errors, when the aim is to point out the more toxic and thus hazardous chemicals and to set priorities, order models can be used as alternative to statistical methods such as multiple linear regression. 

At the time that the basic formulation and testing of the mathematical models of quantitative structure-activity correlations were being made, another type of approach, the linear free-energy related model, was introduced (2). Using the basic Hammett equation (22, 36) for the chemical reactions of benzoic acid derivatives (Equation 12), several investigators attempted quantitative correlations between physicochemical properties... 

All developments of quantitative structure activity relationships (QSARs)/ quantitative structure-property relationships (QSPRs)/QSDRs go through similar steps (1) collection of a database of measured values for model development and validation/evaluation, (2) selection of chemical descriptors (can include connection indices, atom, bond, or functional groups, molecular orbital calculations), (3) development of the model (develop a correlation between the chemical descriptors and the activity/property/degradation values) using a variety of statistical approaches (linear and non-linear regression, neural networks, partial least squares (PLS), etc. [9]), and (4) validate/evaluate the model for predictability (usually try to use a separate set of chemicals other than the ones used to train the model external validation) [10]. 

Due to the relationships between Hansch analysis and the Free Wilson model, indicator variables (chapter 3.8) have relatively early been included in Hansch analyses (e.g. [21, 427, 428]). Both models can be combined to a mixed approach, in a linear (eq. 78) and a nonlinear form (eq. 79), which offers the advantages of both, Hansch analysis and Free Wilson analysis, and widens their applicability in quantitative structure-activity relationships [22]. 

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