Isobolographic Analysis for Combinations of a Full and Partial Agonist: Curved Isoboles

Abstract

Combinations of drugs are frequently used therapeutically to achieve an enhanced effect without using an excess quantity of either agent. If the drugs exert overtly similar action, e.g., two analgesics, the effect of the combination may be tested for additivity, i.e., an effect level that is achieved based on the individual drug potencies. But combinations of agonists will sometimes display either superadditive (synergistic) or subadditive responses. Whether the two agonists are both drugs, or a combination of a drug and an endogenous chemical, there is interest in characterizing the interaction to determine whether it departs from additivity because quantitative information of this kind, aside from its therapeutic importance, may also illuminate mechanism. A common method for this characterization uses the isobologram. This is a plot in rectangular coordinates of dose combinations (a,b) that produce the same effect level (often taken to be 50% of the maximum). In its usual form, this plot is constructed as a straight line (of additivity) connecting intercepts that represent the individually effective doses, e.g., ED 50 values of each. This line is the reference for distinguishing additive from nonadditive interactions accordingly as the tested combination is on or off this line. Discussed here are the assumptions that underlie this linear plot. Specifically we show that a combination of drugs with a variable potency ratio, exemplified by a full and a partial agonist, lead to curvilinear isoboles of additivity that may erroneously be attributed to either synergism or subadditivity.When two drugs produce overtly similar effects, e.g., two analgesics or two antihypertensives, their presence together may produce an effect whose magnitude is different from that predicted by the individual drug potencies. Combinations that achieve predictable effects based on individual potencies are said to be additive. Determining the additive effect for a drug combination is the first step in detecting synergism. That determination is straightforward when the drugs act through different receptors and have a constant relative potency R, i.e., when equally effective doses have the same ratio over the range of effects being studied. The constancy of R is implicit in most studies of combinations that use isobolographic analysis. In such studies the dose-response curves of the individual agents allow a determination of each drug's dose that gives a specified effect such as the half-maximal effect. That dose, the D 50 (or ED 50 if the dose-response data are quantal), for each drug is plotted as an intercept on a Cartesian coordinate system in which the axes represent the individual drug doses, and the two intercepts define a straight line called the line of additivity. All points (a,b) on this line are dose pairs, called additive isoboles, that give the half-maximal effect if the joint action is in accord with their individual potencies. Although an effect level ϭ 50% E max is the most common, any other effect level up to the ma...

Synergistic antinociceptive effects of anandamide, an endocannabinoid, and nonsteroidal anti-inflammatory drugs in peripheral tissue: A role for endogenous fatty-acid ethanolamides?

“…The dose-response curves for anandamide, rofecoxib and their combination were determined by simultaneous analysis using ALLFIT software (De Léan et al, 1978). Interactions between anandamide and rofecoxib were performed using isobolographic analysis as described by Tallarida et al (1997) and Grabovsky and Tallarida (2004). The theoretical additive ED 50 was calculated for the combination of drugs based on the individual ED 50 and the fixed dose ratio (1:11).…”

Interactions between drugs and occupied receptors

“…In this situation the isobole of additivity is no longer a straight line but is curved (Grabovsky & Tallarida, 2004) as shown in Fig. 4.…”

“…A numerical example that applies equation (3) follows. An actual example, describing the combined action of a cannabinoid and an NMDA antagonist on body temperature , is discussed by Grabovsky and Tallarida (2004).…”

“…A numerical example that applies equation (3) follows. An actual example, describing the combined action of a cannabinoid and an NMDA antagonist on body temperature , is discussed by Grabovsky and Tallarida (2004).Example. In order to illustrate the application of equation (3) The two isoboles from this example are shown graphically in figure 4.…”

Nonlinear isobologram and superadditive withdrawal from cocaine:cannabinoid combinations in planarians

“…The isobole of additivity for the 50% effect is the set of combination dose pairs (a,b) of the partial and full agonist, respectively, and given by the equation below (Grabovsky and Tallarida, 2004 The dose-response curves for cocaine alone and for WIN 55212-2 alone are shown in Fig 1A. It is seen that cocaine was effective over an extended dose range and achieved the 100% effect, while WIN 55212-2 produced a lesser maximum and was effective over a narrower dose range (the figure legend gives the fitted equations). Because these agents have a variable potency ratio, the isobole of additivity is curved (Grabovsky and Tallarida, 2004;Tallarida, 2006) as shown in Fig 1B. For each of five fixed-ratio combinations complete dose-effect data were also collected from which the 50% effect level yielded the dose pairs denoted by the points shown as A-E in Fig 1B. Two combinations (points A and B) were found to be significantly below the additive values (P < 0.01) and indicate superadditivity. Point A, representing a fixedratio combination containing 23.5% WIN 55212-2 and 76.5% cocaine, has the ordinate value (cocaine component) = 0.00032 ± 0.00018, and point B, containing 12.4% WIN 55212-2 and 87.6% cocaine has the ordinate 0.00166 ± 0.00067.…”