Concentration/response

Dmg distribution into tissue reservoirs depends on the physicochemical properties of the dmg. Tissue reservoirs include fat, bone, and the principal body organs. Access of dmgs to these reservoirs depends on partition coefficient, charge or degree of ionization at physiological pH, and extent of protein binding. Thus, lipophilic molecules accumulate in fat reservoirs and this accumulation can alter considerably both the duration and the concentration—response curves of dmg action. Some dmgs may accumulate selectively in defined tissues, for example, the tetracycline antibiotics in bone (see Antibiotics,tetracyclines). 

Fig. 6. Cumulative log concentration-response curves for the homologous-A/-aLkylcatecholamines,...

FIGURE 3.11 Constitutive activity in melanophores expressing hCTR2 receptor, (a) Basal melanophore activity, (b) Effect of transfection with human cDNA for human calcitonin receptors (16 j-ig/ml). (c) Concentration response curve for cDNA for human calcitonin receptors (abscissae as log scale) and constitutive activity. Data redrawn from [27]. 

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... 

FIGURE 5.4 Microphysiometry responses of HEK 293 cells transfected with human calcitonin receptor, (a) Use of microphysiometry to detect receptor expression. Before transfection with human calcitonin receptor cDNA, HEK cells do not respond to human calcitonin. After transfection, calcitonin produces a metabolic response, thereby indicating successful membrane expression of receptors, (b) Cumulative concentration-response curve to human calcitonin shown in real time. Calcitonin added at the arrows in concentrations of 0.01, 0.1, 1.10, and lOOnM. Dose-response curve for the effects seen in panel B. 

The receptor occupancy curve can be converted to concentration-response curves by processing occupancy through the operational model for agonism (see Section 3.6). Under these circumstances, Equation 6.6 becomes... 

FIGURE 6.17 Fitting of data to models, (a) Concentration response curves obtained to an agonist in the absence (circles) and presence of an antagonist at concentrations 3 jiM (triangles) and 30 j.lM (diamonds), (b) Data fit to model for insurmountable orthosteric antagonism (Equation 6.31) with Emax = 1, Ka = 1 pM, t = 30 and KB = 1 pM. 

In cases where there is a substantial receptor reserve such that there is a measurable dextral displacement of the concentration response curves, then another reliable method for determining the affinity of the noncompetitive antagonist is to measure the pA2 (—log of the molar concentration that produces a twofold shift to the right of the agonist concentration-response curve). It can be shown that for purely noncompetitive antagonists the pA2 is related to the pKB with the relation (see Section 6.8.10)... 

A characteristic of hemi-equilibria is the observation of a depressed plateau of maximal responses. Thus, while a truly insurmountable antagonist will eventually depress the concentration-response curves to basal levels hemi-equilibrium conditions can produce partial but not complete inhibition of the agonist maximal response. This is shown in Figure 6.21. 

It can be seen that when there is no effect on the affinity of the receptor for the agonist (a=l) Equation 7.6 is identical to the describing orthosteric noncompetitive antagonism derived by Gaddum and colleagues [31] (see Equation 6.10). However, while the equation is identical and the pattern of concentration-response curves is the same as that for an orthos teric antagonist it should be... 

If there is no receptor reserve for the system, then an insurmountable antagonist, whether allosteric or orthosteric, will produce immediate depression of the agonist concentration-response curve with no concomitant shift to the right. Under these circumstances,... 

FIGURE 7.14 Effect of an allosteric modulator that increases the efficacy of the agonist but has no effect on affinity in two different systems, (a) For full agonists, increases in efficacy produce parallel shifts to the left of the concentration-response curves. Responses modeled with Equation 7.3 with a= 1, , = 5, t = 20, and Ka = 3j.lM. Curves shown for [B]/Kb = 0, 0.3, 1, 3, 10, and 30. (b) In systems with lower receptor density and/or poorer receptor coupling where the agonists does not produce the full system maximal response, an allosteric modulator increases the maximal response and shifts the curves to the left. Responses modeled with Equation 7.3 for the same agonist and same allosteric modulator but in a different tissue (parameters as for A except t= 1). 

As with insurmountable orthosteric antagonists, the shift to the right of concentration-response curves produced by allosteric insurmountable antagonists can be used to calculate a pA2 value, and in turn this can be related to the pKB of the antagonist. A concentration of antagonist equal to the pA2 (i.e., concentration = 10-pA2) causes a dose ratio of 2, leading to the following equality ... 

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. 

Alter the location parameter of the concentration-response curve... 

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