The radioisotope dilution test for cyclic AMP with binding protein from beef muscle can be described mathematically with the assumption that one molecule of binding protein binds one molecule of cyclic AMP. Formulas for the dose response under saturation and nonsaturation conditions are given. Quasilinear plots are calculated from them even under nonsaturation conditions. Good agreement exists between calculated and measured curves.
Since Sutherland (1) discovered the important role of adenosine 3':5'monophosphate (cyclic AMP) in the regulation of hormone-controIIed enzymes, many tests for this substance have been deveIoped (2-5). Some of them are multistep ~~rocedures, and since every step may po~ntially be affected by substances accompanying cyclic AMP from natural sources, they are susceptible to interferences, From this viewpoint, radioisotope dilution tests with a suit.abIe binding agent are preferable because these tests contain only a small number of steps: cyclic AMP binding, isolation of the cyclic AMP-binding protein complex from unreacted cyclic AMP, and counting of its radioactivity.
The isolation of the complex by adsorption on cellulose ester filters was described by Walton and Garren (6) and by Gilman (7). The latter test was the basis for our experiments.
Many methods have been em~)loyed to evaluate radioisot,ope data based on competitive prot#ein binding (8,9). Berson and Yalow (10) used plotting of t,he ratio of bound:free radioact,ivity versus concentration of unlabelled compound, while Ekins et al. (II) plotted the free: bound ratio of radioactivity versus the concentrat,ion of unlabelled compound. Neither of these methods led to a linear dose-response curve over a wide range. Therefore, many attempts have been made to linearize the doseresponse curves (8). Hales and Randle (12) calculated t,hat with saturated binding protein a linear dose-response curve is obtained if one plots the quotient of radioactivity bound in the absence (c,) and the presence (c~) of unlabelled compo~lnd versus the concentration of unlabeIIed compound. They found experimentally that, even without sat~lration, there 468 Copyright