Dose and time as variables of toxicity.

Recognizing that if there is no exposure, there is no toxicity leads us to the conclusion that if there is exposure, toxicity can ensue when exposure exceeds a certain dose and/or time and that it will be dependent on toxicokinetics and toxicodynamics. Analysis of the fundamental description of toxicity (dT/dE=dT/dDxdD/dKxdK/dE, where T stands for toxicity, D for toxicodynamics, K for toxicokinetics and E for exposure) yields the recognition of three independent time scales, the first being an intrinsic property of a given compound (what does the chemical do to the organism), which is the dynamic time scale. The second time scale is an intrinsic property of a the organism (what does the organism do to the chemical), which represents the kinetic time scale. The frequency of exposure denotes the third time scale, which is independent of the dynamic and kinetic time scales. Frequency of exposure depends on the experimental design or on nature, but not on the organism or substance. A liminal condition occurs when the frequency becomes so high that it is indistinguishable from continuous exposure. Continuous exposure forces the two other time scales to become synchronized thereby reducing complexity to three variables: dose, effect and one time scale. Keeping one of those variables constant allows for the study of the other two variables reproducibly under isoeffective or isodosic or isotemporal conditions. However, any departure from continuous exposure will introduce the full complexity of four independent variables (dose and kinetic, dynamic and frequency time scales) impacting on the effect (dependent variable) at the same time. The examples discussed in this paper demonstrate how nature in the form of long half-lives provides liminal conditions when either kinetic or dynamic half lives force synchronization of all three time scales. However, for compounds having very short dynamic or kinetic half-lives, only continuous exposure will provide a synchronized time scale. A decision tree-type approach is being used to illustrate how to reduce the enormous complexity generated by five variables (dose, effect and up to three time scales) in toxicology to manageable proportions by identifying and modeling the rate-determining (-limiting) step(s) in the manifestation of toxicity.