General Response Curve

Interaction of a chemical species (X) with sensor (S) can be described by the equilibrium  

The rates of the forward ( f) and reverse (kT) reactions together with the mass transport parameters of the species involved in the transduction mechanism are important for the response of the sensor. Introducing reaction rates into the definition of the equilibrium constant introduces the notion of time. Thus, for the same value of K we can have fast and slow, forward and reverse reactions, and therefore fast or slow equilibrium. The equilibrium constant (K) is expressed in terms of activities. 

Here asx is the activity of the bound species and ax and as are the activities of the species in the sample and of the binding site in the sensor, respectively. For the purpose of this discussion, the binding site can be thought of as a defined but separate component of the selective layer, such as in heterogeneous selective layers, or it may be a specific part of the uniform matrix, as in homogeneous selective layers. (More on the origins of selectivity are discussed later.) The free energy of interaction for reaction depicted in (1.1) is 

It follows from (1.4) that upon the change of sample activity, the interaction of the species with the sensor will take place if the change of the standard free energy AG° is negative. If the binding equilibrium constant is too high (K 104 AG° -23 kJ mole-1), the reaction will be, from a practical point of view, nearly irreversible, and the device will respond in a nonequilibrium manner, as a dosimeter. 

The measurement or reading of a sensor is generated by the change in some physical parameter, as a result of some chemical stimulation. This is called the sensor s response. Of course, the exact type of physical change depends on both the sensor and the sensing environment. For the purposes of the following discussion, we describe response as a general phenomenon. 

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In this equation, K[ = Ki/Kx is the selectivity coefficient. It applies to each interfer-ant individually. The smaller the value of K[, the more selective the layer is to the analyte (X) than to the interferant species ( ). Equation (1.9) defines three operating regions on the general response curve. 

Every accelerometer has a response curve of the type shown schematically in Figure 4-222. Instead of having an ideal linear response, a nonlinear response is generally obtained with a skewed acceleration for zero current, a scale factor error and a nonlinearity error. In addition, the skew and the errors vary with temperature. If the skew and all the errors are small or compensated in the accelerometer s electronic circuits, the signal read is an ideal response and can be used directly to calculate the borehole inclination. If not, modeling must be resorted to, i.e., making a correction with a computer, generally placed at the surface, to find the ideal response. This correction takes account of the skew,... 

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. 

The operational model allows simulation of cellular response from receptor activation. In some cases, there may be cooperative effects in the stimulus-response cascades translating activation of receptor to tissue response. This can cause the resulting concentration-response curve to have a Hill coefficient different from unity. In general, there is a standard method for doing this namely, reexpressing the receptor occupancy and/or activation expression (defined by the particular molecular model of receptor function) in terms of the operational model with Hill coefficient not equal to unity. The operational model utilizes the concentration of response-producing receptor as the substrate for a Michaelis-Menten type of reaction, given as... 

There are statistical procedures available to determine whether the data can be fit to a model of dose-response curves that are parallel with respect to slope and all share a common maximal response (see Chapter 11). In general, dose-response data can be fit to a three-parameter logistic equation of the form... 

General Procedure Full dose-response curves to a full and partial agonist are obtained in the same receptor preparation. It is essential that the same preparation be used as there can be no differences in the receptor density and/or stimulus-response coupling behavior for the receptors for all agonist curves. From these dose-response curves, concentrations are calculated that produce the same response (equiactive concentrations). These are used in linear transformations to yield estimates of the affinity of the partial agonist. 

General Procedure A set of close-response curves to an agonist are obtained, one in the absence of and the others in the presence of a range of concentrations of the antagonist. The magnitude of the displacement of the curves along the concentration axis is used to determine the potency of the antagonist. 

General Procedure Dose-response curves to a full agonist are obtained in the absence and presence of the noncompetitive antagonist. From these curves, equiactive concentrations of full agonist are compared in a linear regression (see Section 12.2.1). The slope of this regression is used to estimate the KB for the noncompetitive antagonist. 

General Procedure Dose-response curves are obtained for an agonist in the absence and presence of a range of concentrations of the antagonist. The dextral displacement of these curves (ECSo values) are fit to a hyperbolic equation to yield the potency of the antagonist and the maximal value for the cooperativity constant (a) for the antagonist. 

General Procedure A dose-response curve to an agonist is obtained and a concentration of agonist that produces... 

Thus as shown previously in Sec. 2.1.1.1, if the step response curve has the general shape of an exponential, the response can be fitted to the above first-order lag model by determining x at the 63% point. The response can now be used as part of a dynamical model, either in the time domain or in Laplace transfer form. 

The results of the studies reviewed here show that the neurotoxic effects of MDMA generalize to the primate. Further, they indicate that monkeys are considerably more sensitive than rats to the serotonin-depleting effects of MDMA, and that the dose-response curve of MDMA in the monkey is much steeper than in the rat. Perhaps as a consequence of this, the toxic effects of MDMA in the monkey involve serotonergic nerve fibers as well as cell bodies, whereas in the rat, only nerve fibers are affected. The present studies also show that the toxic dose of MDMA in the monkey... 

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