Perspectives in Pharmacology The Role of Time as a Quantifiable Variable of Toxicity and the Experimental Conditions When Haber’s c 3 t Product Can Be Observed: Implications for Therapeutics

One hundred years ago, Warren established for the first time a quantitative link between dose and time while studying the toxicity of sodium chloride in Daphnia magna (Straus). During this century, many toxicologists in different contexts returned to this idea, which has become known as Haber’s Rule of inhalation toxicology. Most attempts to explore this relationship ended in frustration because of the observed deviations from it, which were unfortunately called exceptions. Thus, toxicologists concentrated on the quantitative relationship between dose and effect under mostly isotemporal conditions, while time was assigned such arbitrary, semiquantitative designations as acute, subacute, subchronic, and chronic. Time itself as a quantifiable variable of toxicity was seldom studied and when it was examined, it was often not done under isodosic (steadystate) conditions. A recent analysis of time as a variable of toxicity indicated the existence of at least three independent time scales (toxicokinetic, toxicodynamic, exposure frequency/ duration) in toxicological studies, which interact with dose and effect to yield the enormous complexity known to every toxicologist. Based on prototypical examples when toxicokinetic (dioxins, chloroacetic acid), toxicodynamic (nitrosamines, soman, sarin, tabun), exposure frequency (methylene chloride), or other experimental design-related conditions (HgCl2, CdCl2) represent the critical time scale, the general validity of the c 3 t 5 k concept will be discussed as a starting point for a theory of toxicology. As endpoints of toxicity, (delayed) acute toxicity, blood dyscrasias, and cancer will be used to illustrate the critical conditions needed to demonstrate the validity of this theory. The relevance of this theory to the pharmacologic action of chemicals and its implication for the therapeutic index are also discussed. This year is the centennial of Warren’s (1900) article on the toxicity of sodium chloride in Daphnia magna (Straus), linking, for the first time, dose and time in a quantitative relationship: (c 2 co) 3 t 5 k. Problems with this simple formula were noted soon thereafter, and Ostwald and Dernoscheck (1910) suggested in analogy to an adsorption isotherm that c 3 t 5 k provides a better description of experimental data. Haber (1924) used the simplest form of the dose/time relationship (c 3 t 5 k) to estimate the toxicity of war gases, and Flury and coworkers examined this phenomenon further when studying the toxicity of solvents (e.g., Flury and Wirth, 1934). Entomologists were the ones who confirmed most frequently the simplest c 3 t 5 k relationship, but they also reported departures from it. Bliss (1940) dealt with the deviations mathematically and concluded that departures from c 3 t 5 k can be described either by c 3 t 5 k or c 3 t 5 k. Druckrey et al. (1967) studied the carcinogenicity of a large number of nitrosamines and came to the conclusion that the latency to cancer can be best characterized by c 3 t 5 k, where in some instances x 5 1. The relationship kept reappearing in different experimental contexts (e.g., Gardner et al., 1977, 1979), but each time anomalies showed up and the claim for generalization was given up because of the occurrence of presumed exceptions. Claiming exceptions to an often observed phenomenon is detrimental to the scientific approach since it puts an end to further inquiry. The more appropriate question is why does a particular experiment show departure from the frequently made observation of c 3 t 5 k? This generalized question arose as a result of experience with studying the toxicity of ABBREVIATIONS: HpCDD, 1,2,3,4,6,7,8-heptachlorodibenzo-p-dioxin; TCDD, 2,3,7,8-tetracholorodibenzo-p-dioxin; MCA, monochloroacetic acid; DENA, diethylnitrosamine; OP, organophosphates. 0022-3565/01/2963-663–668$3.00 THE JOURNAL OF PHARMACOLOGY AND EXPERIMENTAL THERAPEUTICS Vol. 296, No. 3 Copyright © 2001 by The American Society for Pharmacology and Experimental Therapeutics 900037/882970 JPET 296:663–668, 2001 Printed in U.S.A. 663 at A PE T Jornals on M arch 1, 2017 jpet.asjournals.org D ow nladed from dioxins. Why was the remarkably consistent c 3 t 5 k of 1,2,3,4,6,7,8-heptachlorodibenzo-p-dioxin (HpCDD) for delayed acute toxicity (Rozman, 1999) not observed with 2,3,7,8-tetracholorodibenzo-p-dioxin (TCDD)? It was entirely implausible that TCDD would be an “exception” from something that applies to HpCDD considering the perfect structure/activity relationships in terms of all other aspects of their effects. Therefore, the challenge was to identify a critical step(s) that was responsible for the manifestation of c 3 t 5 k in the case of HpCDD and the lack thereof in the case of TCDD. Examination of the c 3 t Concept Rozman and Doull (2000) recently suggested a decision tree-type analysis to identify critical steps in the toxicity of chemicals. Use of this analysis revealed that the critical difference between HpCDD and TCDD resided in their differential kinetics. In other instances, the analysis revealed dynamic step(s) as the crucial one(s) in the manifestation of toxicity. In either instance, frequency/duration of exposure needed to be carefully considered as an additional independent time scale. In the following discussion, examples will be used to illustrate under what circumstances Haber’s Product will be obtainable when either kinetics, dynamics, or exposure frequency represents the rate-determining step in the development of toxicity.