isobologrammi

Isobologrammi, or isobolograms, are graphical tools used to analyze interactions between two pharmacological agents that produce a common endpoint. They are widely employed in pharmacology, toxicology, and drug development to assess whether combinations are additive, synergistic, or antagonistic relative to the effects expected from each drug alone.

Construction and interpretation

To build an isobogram for a fixed effect level (for example, the ED50, the dose that yields 50% of the maximal response), one first determines the single-agent doses that achieve that effect: EDx1 for Drug A and EDx2 for Drug B. The isobole (the line or curve on the plot) represents all dose pairs (D1, D2) that produce the same effect under a null hypothesis of additivity, commonly described by the Loewe additivity model. For two drugs with additive interaction, the relationship satisfies D1/EDx1 + D2/EDx2 = 1 (for the EDx level). On a graph with Drug A dose on the x-axis and Drug B dose on the y-axis, the line of additivity passes through (EDx1, 0) and (0, EDx2).

If an observed combination point lies on the line, the interaction is considered additive; if it lies inside (toward the origin), the combination is synergistic; if it lies outside, the interaction is antagonistic. Isobolograms can be constructed for different effect levels (e.g., ED25, ED75) and are used to visualize dose–response relationships for combinations.

Applications and limitations

Isobolograms are used to optimize combination therapies in cancer, infectious disease, and toxicology, as well as to study potential drug–drug or drug–chemical interactions. Limitations include assumptions of similar maximal effects and mechanisms, potential non-parallel dose–response curves, and sensitivity to experimental variability. Extensions include the Chou–Talalay combination index method, which provides a quantitative index of synergy or antagonism.