Concepts for Describing the Interaction of Two Agents

Abstract

Combinations for which this relationship might be expected are those where the individual quanta of each agent obey simple probability laws in acting independently. Such agents have simple exponential survival curves. So far, so good, but Zaider goes on to make the assumption that independent action is the same as lack of interaction, which forces him to conclude that only when both agents in a have exponential survival curves can the show no interaction. In all other cases, any will show interaction. The problem with this reasoning is that simple exponential survival curves are the result of a particular mechanism of action, familiar from target theory, in which survivors have escaped inactivation in discrete, crucial targets by discrete, randomly acting quanta of agent. Agents of this type are largely, although not exclusively, confined to those that damage DNA, especially ionizing radiations and alkylating agents. However, the great majority of biologically active agents have nonexponential types of dose-response curves (sigmoid, log-linear, log-log, etc.), because their mechanisms of action are different from those described by target theory. Now, combinations of agents with nonexponential doseresponse curves may also satisfy Eq. (1). For example, this may be the case with mutually nonexclusive enzyme inhibitors (2-5), good examples of which were provided by Woolfolk and Stadtman (6). These combinations showed independent action because they satisfied Eq. (1) but, as the dose-response curves of such agents are sigmoid, not exponential, they must, according to Zaider, show interaction also. Here, both independent action and nonexponential curves result from the manner of binding of the agents to their target molecules, so these features are inseparable. Thus Zaider's analysis leads inevitably to contradictions. Such dilemmas may be avoided only by approaches that do ot depend on particular forms of dose-response curves or modes of action, but are based solely on quantitative considerations, i.e., the observed effects of the combinations and their constituent agents. Lack of interaction is then defined as existing where the quantitative effect of the is that expected from the dose-response curves of the agents. This expectation is obtained by considering the sort of agent which always has the expected effect, i.e., the sham combination of various doses dl,d2 of one and the same agent. Here, because we are dealing with one agent only, E(d ,d2) necessarily equals E(d, + d2), whatever the relationship between dose and effect. The effects of d ,d2 and (d ,d2) are obtained directly from the dose-response curve and, in an isobologram, the isoeffect curve (isobole) is a straight line. It has been shown rigorously (7, 8) that noninteractive combinations of different agents well behave similarly, and satisfy Eq. (2), which is the equation for a straight isobole.