The power issue: determination of KB or Ki from IC 50: A closer look at the Cheng–Prusoff equation, the Schild plot and related power equations

Abstract

Introduction: The Cheng–Prusoff equation (1973) is often applied to the determination of equilibrium dissociation constant ( K B) of a competitive antagonist when the IC 50 value is available. The purpose of this study is to illustrate that the slope function ( K) of an agonist concentration–response curve is critical to the determination of K B values. Methods: The article describes new equations, which incorporate the slope function, consequently yielding more accurate estimation of K B values for antagonists, and tests them using simulated data. The value of K B was calculated according to the following new power equation: K B=IC 50/(1+ A K / K P)=IC 50/[1+( A/EC 50) K ], where IC 50 is the concentration of the antagonist producing 50% inhibition, A is the concentration of the agonist against which the IC 50 is being determined and K P is the apparent equilibrium dissociation constant of the agonist. Results: The new equation is the same as the Cheng–Prusoff equation when the slope function K is exactly unity. Application of the equation avoids errors inherent in the use of the Cheng–Prusoff equation when the slope function of the agonist concentration–response curve deviates from unity. The new equation was applicable to slope functions less than, equal to or greater than unity. All inhibition curves have a negative slope function of 1, indicating that there is only one single receptor population even though different slope functions of agonist concentration–response curves are involved. The importance of the power function in the Schild plot is illustrated by using the equation: log ( x K −1)=log B−log K B, where x is the concentration ratio and B is the concentration of the antagonist. Discussion: This investigation illustrates the application of six power equations for accurate estimation of K B values covering situations with different slope functions of the agonist concentration–response curves.