isobolograms

Isobolograms are graphical tools used to analyze interactions between two drugs or other active agents. They plot the combinations of doses that produce a specified level of effect, such as 50 percent of the maximal response (ED50).

The x-axis represents the dose of drug A and the y-axis the dose of drug B. The line of additivity, or Loewe isobole, is drawn by connecting the points where each drug alone achieves the target effect: (ED_Ax, 0) and (0, ED_Bx). Under Loewe additivity, any combination lying on this line is predicted to be additive.

Interpreting experimental data: if an observed combination point falls below the line, it is interpreted as synergistic (the combination achieves the effect at lower total doses); if it falls above, antagonism is indicated. Points on the line indicate pure additivity.

Construction and use: first determine dose–response curves for each drug alone to identify EDx values for the chosen effect level. Then plot the intercepts and draw the additivity line. Plot observed combinations and assess their position relative to the line. Isobolograms can be generated for multiple effect levels and extended to fixed-ratio designs or to more than two agents with careful interpretation.

Limitations: the method assumes comparable maximal effects and similar dose–response shapes; deviations in these assumptions can distort the interpretation. It is most reliable when pharmacodynamics of the agents are well characterized and the data come from appropriately designed experiments.

History: isobolographic analysis was developed in pharmacology by S. Loewe and has become a standard approach to evaluating synergy and antagonism in drug combinations, toxicology, and combination therapies.