Receptor models, variability

This model also can accommodate dose-response curve having Hill coefficients different from unity. This can occur if the stimulus-response coupling mechanism has inherent cooperativity. A general procedure can be used to change any receptor model into a variable slope operational function. This is done by passing the receptor stimulus through a forcing function. 

FIGURE 10.7 Figure illustrating the comparison of concentration-response curves to two full agonists. Equations describe response in terms of the operational model (variable slope version equation see Section 10.6.1). Schematic indicates the interacting species in this case, two full agonists A1 and A2 activating a common receptor R to produce response. Boxes show the relevant measurements (EPMRs) and definitions of the parameters of the model used in the 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. 

From the receptor model viewpoint, the total aerosol mass, M, collected on a filter at a receptor Is the dependent variable and equal to a linear sum of the mass contributed by p Individual sources,... 

While the source-oriented model begins with measurements at the source (i.e., emission rates for the period under study), and estimates ambient concentrations, the receptor-oriented model begins with the actual ambient measurements and estimates the source contributions to them. The receptor model relies on properties of the aerosol which are common to source and receptor and that are unique to specific source types. These properties are composition, size and variability. 

The starting point for the receptor model is the source model. Though the source model may not deliver accurate results under many conditions, its limitations are primarily due to its inability to include every environmentally relevant variable and inadequate measurements for the variables it does include. The general mathematical formulations, however, are representative of the way in which particulate matter travels from source to receptor. 

The mathematical obfuscation of these models must not remove the requirement that every receptor model must be representative of and derivable from physical reality as represented by the source model. A statistical relationship between the variability of one observable and another is Insufficient to define cause and effect unless this physical significance can be established. 

The measurements required for the present receptor models Include particulate matter composition, size and variability for both source and receptor. Obtaining these data requires attention to field study design and data management, source characterization, and analytical methods. 

Particulate emissions data for 21 studies of coal-fired power plants were compiled for use in receptor models. Enrichment factors were calculated (relative to Al) with respect to the earth s crust (EFcrust) and to the input coal (EFcoai). Enrichment factors for input coals relative to crustal material were also calculated. Enrichment factors for some elements that are most useful as tracers of coal emissions (e.g., As, Se) vary by more than ten-fold. The variability can be reduced by considering only the types of plants used in a given area, e.g., plants with electrostatic precipitators (ESPs) burning bituminous coal. For many elements (e.g., S, Se, As, V), EFcrust values are higher for plants with scrubbers than for plants with ESPs. For most lithophiles, EFcrust values are similar for the coarse (>2.5 ym) and fine (<2.5 ym) particle fractions. 

From a modeling point of view, the last equilibrium assumption that can be relaxed, for the processes depicted in Figure 10.1, is H4, between the activated receptors (v variable in the occupancy model) and the response E. Instead of the activated receptors directly producing the response, they interfere with some other process, which in turn produces the response E. This mechanism is usually described mathematically with a transducer function T which is no longer linear (cf. Section 10.4.1). This type of pharmacodynamic model is called indirect response and includes modeling of the response process usually through a linear differential equation of the form... 

One-way analysis of variance, 229-230, 230f—231f Operational model derivation of, 54-55 description of, 45—47, 46f function for variable slope, 55 for inverse agonists, 221 of agonism, 47f orthosteric antagonism, 222 partial agonists with, 124, 220-221 Opium, 147 Orphan receptors, 180 Orthosteric antagonism... 

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