Statistical Models 1 Receptor Modeling Methods

De Lean, A., Hancock, A. A. and Lefkowitz, R. J. (1982). Validation and statistical analysis of a computer modeling method for quantitative analysis of radioligand binding data for mixtures of pharmacological receptor subtypes, Mol. Pharmacol., 21, 5-16. 

There are statistical methods to determine the verisimilitude of experimental data to models. One major procedure to do this is nonlinear curve fitting to dose-response curves predicted by receptor models. 

The two mostly used statistical methods for calculating receptor models are CMB and TTFA. 

A couple of years ago a workshop was organized to compare the performance of the various statistical methods applied for receptor model (12). To create an objective basis for the comparison of the different analyses, a synthetic data set was generated according to the following equation ... 

In this paper the PLS method was introduced as a new tool in calculating statistical receptor models. It was compared with the two most popular methods currently applied to aerosol data Chemical Mass Balance Model and Target Transformation Factor Analysis. The characteristics of the PLS solution were discussed and its advantages over the other methods were pointed out. PLS is especially useful, when both the predictor and response variables are measured with noise and there is high correlation in both blocks. It has been proved in several other chemical applications, that its performance is equal to or better than multiple, stepwise, principal component and ridge regression. Our goal was to create a basis for its environmental chemical application. 

Among the multivariate statistical techniques that have been used as source-receptor models, factor analysis is the most widely employed. The basic objective of factor analysis is to allow the variation within a set of data to determine the number of independent causalities, i.e. sources of particles. It also permits the combination of the measured variables into new axes for the system that can be related to specific particle sources. The principles of factor analysis are reviewed and the principal components method is illustrated by the reanalysis of aerosol composition results from Charleston, West Virginia. An alternative approach to factor analysis. Target Transformation Factor Analysis, is introduced and its application to a subset of particle composition data from the Regional Air Pollution Study (RAPS) of St. Louis, Missouri is presented. 

The problem mentioned before has led to the development of statistical receptor models (Fig. 3) which nowadays are the most widely used tools for PM source apportionment. They can be applied even to a single site and need a time series of PM mass concentrations and corresponding chemical composition data. Depending on the method, these analyses are based only on the receptor data or additionally use information on the chemical composition from the relevant emission sources (emission profiles). 

In addition to the biochemistry introduced in this chapter, a great deal of emphasis is placed on the determination of the activity of a compound by an analysis of its structure. Quantitative structure-activity relationships (QSAR), used judiciously, have the ability to help set testing priorities and identify potentially toxic materials in mixtures. Heavily reliant upon the quality of the toxicity data discussed in Chapter 4, these methods use sophisticated statistical techniques or analysis of interaction of a toxicant with the receptor to estimate toxicity. A method that uses structure-activity relationships coupled with availability and an assumed additive model for toxicity is presented to estimate the risk due to polyaromatic hydrocarbons (PAHs). 

If the nature of the major sources influencing a particular receptor is unknown, statistical factor analysis methods can be combined with ambient measurements to estimate the source composition. Assuming that for a particular location several ambient particulate samples are collected and analyzed for several elements, the resulting data will probably include information about the fingerprints of the sources affecting the location. Principal-component analysis (PCA) is one of the factor analysis methods used to unravel the hidden source information from a rich ambient measurement data set. Factor analysis models are mathematically complex, and their results are often difficult to interpret. 

Ligand- and structure-based approaches are valuable tools for the identification and optimization of lead compounds. Each strategy needs special prerequisites and has strengths and weaknesses. In some cases only the strengths of both methods may be combined for a joint approach, called structure-based pharmacophore alignment. Here, the receptor site serves as a complement to build the pharmacophore model and sophisticated statistical methods from 3D-QSAR (PCA and PLS) are applied for the prediction of activity [19, 20]. 

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