Answer:
The most common method for the quantitative assessment of unusual interaction between agonist drugs is the method of isoboles. This is a graphical procedure, introduced and developed by Loewe,8-10 that uses the dose-effect relation of each drug (alone) in order to derive the set of dose combinations that are expected to give a specified effect level. Most often the selected effect level is 50% of the maximum effect, and the doses of each full agonist drug that individually give this effect are therefore their ED50 doses. In its simplest form this procedure uses the ED50 doses of the individual drugs and uses these as intercept values on a Cartesian coordinate system in which doses are represented on the x- and y-axes. The straight line connecting these intercepts represents the set of points (dose pairs) that give the specified effect (50% of Emax) when there is no interaction between the drugs. This line, called an isobole, conveys numerical information that shows the reduction in the required dose of one drug that accompanies the presence of a dose of the second drug. Understandably this line has a negative slope since the increase in quantity of Drug A means that a lesser quantity of Drug B is needed to achieve the specified effect level. If we denote the intercepts by A for the ED50 of Drug A and by B for the ED50 of Drug B, then the isobole is expressed by the simple linear equation:
aA+bB=1,
where a is the dose of Drug A and b is the dose of Drug B when the 2 are present together (Fig. 1). If an effect level other than 50% of the maximum is used, then this equation still applies and denotes the dose pair (a,b) that gives that particular effect level where the A and B are now the respective individual doses for that effect level. The isobole expressed in Equation 1 allows the assessment of superadditive and subadditive interactions when actual combination doses are tested. If testing shows that the specified effect of a combination is achieved by a dose pair that plots as a point below the isobole, this means that the effect was attained with doses less than those on the line, a situation that denotes superadditivity or synergism. In contrast, an experiment may show that greater combination doses are needed to produce the specified effect and therefore this dose pair plots as a point above the isobole line. Dose pairs that experimentally lie on the line (or not significantly off the line) are termed additive, a situation that means no interaction between the 2 drugs. These cases are illustrated in Fig. 1. Other forms of Equation 1 have been used; for example, one may use an expression for the total dose (a + b) for any fixed ratio combination of doses. These forms are contained in the author’s monograph.4 The reason that a point on the line is termed additive is explained subsequently. But first we ask, why is Equation 1 the basis for defining a zero interaction, and, further, how is this equation derived? The answer to these questions is contained in the section below, which discusses the concept of dose equivalence.