Use of the proportionality equations for analyses of dose–response curves

Abstract

A proportionality-oriented theory was applied to analyze dose–response curves commonly generated in pharmacology. The principle of the proportionality theory is to express changes of two associated variables in reference to their asymptotes. Thus, a linear relationship between the two associated variables can be obtained if proper dimensions and scales are used. Based on this proportionality approach, we have developed equations which are used to analyze dose–response curves (1) generated by simulation data based on the Michaelis–Menten equation and the Hill equation and (2) obtained from the contractile effect of acetylcholine (ACh) in isolated guinea pig ileum and the contractile effect of neurokinin NK 1 agonists (NK 1) in guinea pig trachea muscle strips. Graphic methods are provided for plotting the graphs and for simultaneous determination of asymptote, slope parameter, and position constant. The slope parameter and position constant relate the concentration of an agonist to its response. Apparent equilibrium dissociation constant ( K A), which is the product of position constant and asymptote in this approach, can be determined directly from the analysis of agonist dose–response curves. It is demonstrated that the proportionality theory and equations are useful for analyzing dose–response curves and for interpreting drug–receptor interactions.