Nature of Dose-Effect Curves and Drug Interactions | ||||
---|---|---|---|---|
Mutually exclusive (similar mode of action)^{a} | Mutually nonexclusive (independent mode of action)^{b} | |||
First order^{c} | Higher order^{d} | First order^{c} | Higher order^{d} | |
Webb's fractional product method^{e} | No | No | Yes | No |
Loewe's isobologram method^{f} | Yes | Yes | No | No |
Multiple drug effect equation^{g} | Yes | Yes | Yes | Yes |
↵ a Mutually exclusive drugs in mixture give a parallel median-effect plot with respect to each drug alone
↵ b Mutually nonexclusive drugs in mixture give a upwardly concave dose-effect curve with respect to each drug alone
↵ c Hyperbolic dose-effect curve
↵ d Sigmoidal dose-effect curve
↵ e i_{1,2} = 1 – [(1 – i_{1})(1 – i_{2})] or (f_{u})_{1,2} = (f_{u})_{1} (f_{u})_{2} (see Webb, 1963)
↵ f See Loewe (1957)
↵ g see Eq. 16, which is the classic isobologram for mutually exclusive drugs. The conservative isobologram is for mutually nonexclusive drugs (Chou and Talalay, 1984). Since the early 1990s Chou has proposed using the mutually exclusive assumption as the universal standard for synergism and antagonism analysis, and, therefore, integrated the nonexclusive condition as an intrinsic contribution to the synergistic effect in the overall synergism and antagonism analysis. Thus, the isobologram and the F_{a}-CI plot become two sides of the same coin (see section II.C.6 or Chou, 1991, 1994, 1998): the F_{a}-CI plot is `effect-oriented', whereas the isobologram is `dose-oriented'