Gaddum equation

One shortcoming of Schild analysis is an overemphasized use of the control dose-response curve (i.e., the accuracy of every DR value depends on the accuracy of the control EC o value). An alternative method utilizes nonlinear regression of the Gaddum equation (with visualization of the data with a Clark plot [10], named for A. J. Clark). This method, unlike Schild analysis, does not emphasize control pECS0, thereby giving a more balanced estimate of antagonist affinity. This method, first described by Lew and Angus [11], is robust and theoretically more sound than Schild analysis. On the other hand, it is not as visual. Schild analysis is rapid and intuitive, and can be used to detect nonequilibrium steady states in the system that can corrupt... 

Converting to equilibrium dissociation constants (Ka = 1 /Ka) leads to the Gaddum equation [4] ... 

In the presence of a competitive antagonist, the response producing species ([AR]/[Rtot] = p ) is given by the Gaddum equation as... 

Aim This procedure measures the affinity and cooperativ-ity constant of an allosteric antagonist. It is used for known allosteric antagonists or molecules that produce a saturable antagonism that does not appear to follow the Gaddum equation for simple competitive antagonism. 

Gaddum equation for, 122, 125 nonsurmountable, 99 operational classifications of, 127 operational definition of, 99 orthos teric... 

Cheng-Prasoff relationship, 65-66, 214 Cholecystokinin receptor antagonists, 80 Cimetidine, 9-10 Clark, Alfred J., 3, 3f, 12, 41 Clark plot, 114 Clearance, 165—166 Clinical pharmacokinetics, 165 Cocaine, 149, 150f Competitive antagonism description of, 114 Gaddum equation for, 101-102, 113,... 

Here, KA and KB are the dissociation equilibrium constants for the binding of agonist and antagonist, respectively. This is the Gaddum equation, named after J. H. Gaddum, who was the first to derive it in the context of competitive antagonism. Note that if [B] is set to zero, we have the Hill-Langmuir equation (Section 1.2.1). 

We assume here that the del Castillo-Katz model applies. Using the Gaddum equation, based on the simpler scheme explored by Hill and by Clark, leads to exactly the same conclusion, as the reader can easily show by following the same steps but starting with Eq. (1.48). 

This relationship has often been used to obtain evidence that two antagonists act at the same site. It can also be derived by taking the Gaddum equation as the starting point rather than expressions based on the del Castillo-Katz mechanism. 

Gaddum equation (competitive antagonism) the pivotal simple equation (see Chapter 6, Sections 6.2 and 6.8.1) describing the competition between two ligands for a single receptor site. It forms the basis for Schild analysis. 

Gaddum equation (noncompetitive antagonism) this technique measures the affinity of a noncompetitive antagonist based on a double reciprocal plot of equiactive agonist concentrations in the absence and presence of the noncompetitive antagonist. The antagonist must depress the maximal response to the agonist for the method to be effective see Chapter 6, Section 6.4. 

---