A new method for estimation of agonist dissociation constants (KA): directly fitting the postinactivation concentration-response curve to a nested hyperbolic equation.

The common method for estimating agonist dissociation constants (KA) is the method proposed separately by Furchgott and Mackay. Concentrations of the given agonist producing the same response before ([A]) and after ([A']) irreversible inactivation of a fraction of the receptors (1-q) are described by the equation: 1/[A] = 1/(q*[A']) + (1-q)/(q*KA) and plotted on axes of 1/[A] vs. 1/[A']. The double reciprocal method suffers from the disadvantage that undue weight may be placed on values generated from the smallest observed responses. Our new method of estimating KA and q uses hyperbolic functions to directly fit both concentration-response curves. The control curve is fit to the logistic equation: response = (M* [A]n)/(kn + [A]n); where M is the maximal tissue response, n is the apparent kinetic order of the response at low [A] and k is [A] required for a half-maximal response. The postinactivation concentration-response curve is simultaneously fit to the following equation: response' = M/(((k/(q*KA*[A']))*(KA + [A']* (1-q)))n + 1). This new method was shown to determine KA and q more accurately and precisely than other methods when applied to an artificial data set. In experiments with the rat anococcygeus muscle, the nested hyperbolic method gave estimates of KA with less variance and less range than the double reciprocal method. The nested hyperbolic method was shown to be a valid method of estimating KA and q that has advantages over the other methods.