Isobolographic analysis of interactions: an update on applications and utility.

Isobolographic analysis provides a fundamental basis for assessing whether biological responses induced by mixtures of agents are greater, equal or smaller than would have been expected on the basis of the individual activities of the component agents and the concept of dose additivity. Limited in its direct application to binary mixtures, isobolographic analysis provides a conceptual framework and an unambiguous terminology, as well as an algebraic paradigm for the analysis of the interaction of ternary and higher order mixtures. A library of examples generously illustrated graphically is provided to facilitate the understanding of the methodology and serve as a guide for investigators who are unfamiliar with the approach. Also discussed are the theoretical derivation of the isobologram, the representation of various dosage combinations, the derivation of the principle of dose additivity, supra-additivity, infra-additivity, antagonism, the methods for probit analysis of mixture potency, effect addition and the consequences of peak effect coincidence in time or lack thereof, and the role of isobolographic analysis in the various aspects of dose-response surface methodology.