A True Threshold Dose in Chemical Carcinogenesis Cannot be Defined for a Population, Irrespective of the Mode of Action: Commentary

Werner K. Lutz, Ph.D.

Department of Toxicology, University of Wuerzburg,

9 Versbacher St, Wuerzburg D-97078, Germany

Tel: +49-931-2015402

Fax: +49-931-2013446

E-mail: lutz@toxi.uni-wuerzburg.de


Strongly sigmoidal (S-shaped) dose-cancer incidence relationships are often observed in animal bioassays for carcinogenicity. If a genotoxic contribution is not plausible, an epigenetic mode of carcinogen action is proposed and a thresholded low-dose response suggested. In a strict sense, a threshold implies a no-yes situation, i.e., no effect up to the threshold dose and an effect above the threshold dose. A convincing explanation of the discontinuity of the gradient of the dose-response curve at the threshold dose is not available to me. However, the existence of a threshold is accepted for an individual. The threshold dose is the dose required for the manifestation of the tumor in an individual exactly at the end of a defined period of observation (for instance, 2 years in an animal bioassay, 75 years in humans). Because of genetic and life style-dependent susceptibility differences, each animal or human has its individual threshold dose. For a group, no single threshold dose can be defined, irrespective of the mode of carcinogen action. Furthermore, in view of the stochastic elements in the process of carcinogenesis, the exact threshold dose can only be defined after tumor incidence and cannot be predicted.


In my response to Dr. Klaunig's article, I would like to focus on one single aspect, namely the discussion of putative "thresholds" in the dose-response relationship for epigenetic carcinogens. Strongly sigmoidal (S-shaped) dose-response curves in a bioassay for carcinogenicity are often interpreted as indicative of a thresholded low dose-response relationship. For cancer risk assessment and extrapolation, a safety factor approach starting from a no-observed-effect level is then proposed instead of a linear extrapolation. Parts of the debate between threshold proponents and threshold opponents result from different definitions, others reflect a different understanding of the process of chemical carcinogenesis. Let me present my view and refer to a number of recent publications which pertain.

In a strict mathematical sense, a thresholded dose-response relationship is defined by a dose, the threshold dose, below which there is no response and above which there is a response. In terms of the slope of the dose-response curve, this means that the gradient is zero up to the threshold dose, and >zero above (Figure 1). The central question for me is: what happens mechanistically when the threshold dose is exceded by a minute increment? In other words, what effect can 1,000,000,000,001 molecules have that 1,000,000,000,000 cannot. So far, nobody had a convincing answer to this question of a discontinuity of the dose response implicated by a threshold assumption.

Figure 1. Schematic dose-response relationship defining the shape at the low dose end as either sublinear (initial gradient of slope >0) or thresholded (gradient of slope = 0 up to the threshold dose)

Genotoxic vs. epigenetic modes of action

For DNA-damaging carcinogens, the additional DNA damage can be considered an increment to a background DNA damage that contributes to what is called spontaneous cancer incidence1,2. Therefore, linearity at low dose is widely accepted. For carcinogens which act by "epigenetic" modes, e.g., by affecting cell differentiation, toxicity, and cell turnover, thresholded dose response relationships are more often postulated3. Here, the assumption is that there is a homeostatic control of "normality" which has to be overcome before an adverse effect is produced. This idea is also put forward to postulate a thresholded dose response for inducers of oxidative stress. Reactive oxygen species (ROS) are responsible for a considerable part of the background DNA damage. Any small increase results in an incremental DNA damage before homeostatic control upregulates the level of detoxification processes. Therefore, a true threshold is not expected.

The "hockey stick" model is Not a Toxicokinetic Model

Many proponents of the threshold concept cite the article published by Jerome Cornfield, professor of statistics, in 1977 in Science4. It is often assumed to be derived from a toxicokinetic model of a metabolic toxication/detoxication process. One must carefully read the paper to realize that some of the assumptions are not biochemically plausible. In particular, Cornfield assumes that activated molecules react with a "deactivator" at infinite rate. Therefore, as long as any free deactivator is available, not one single activated molecule can escape the deactivator and react, for instance, with DNA.

This opinion cannot be shared in terms of the kinetics of diffusion and chemical reactions. The rate of competing processes is expected to be proportional to the concentration of the reaction partners. In terms of the ROS-example introduced above, every single superoxide anion radical molecule formed has a non-zero chance of resulting in a DNA base hydroxylation.

In fact, Cornfield himself was much more careful than many of those who advocate his model. Firstly, he calls his model a simple kinetic model (not a pharmaco- or toxicokinetic model); secondly, he states in the summary that "the striking (bottom) part of the hockey stick will turn out to be flat or nearly flat until the dose administered saturates the deactivation system". He actually allows for a shallow gradient of the slope also below his "threshold" dose, as shown also in Figure 1. I think this is the case for most observations of a sublinear low dose-response relationship. Cornfield's paper should not be overinterpreted.

Additivity to Background Also for Epigenetic Modes of Action

Epigenetic modes of carcinogen action are considered to be ineffective as long as homeostatic regulation operates. I agree that overwhelming of the regulation at some dose can result in a strongly sublinear (convex, up-bent) shape of the dose-response relationship. I do not agree that this generally results in a true threshold. As expressed already ten years ago5, the question is whether there is an endogenous process that is accelerated by the exogenous carcinogen. If yes, the linear-incremental theory holds also for epigenetic modes of action.

Let me illustrate this on the basis of mitogenesis. Accelerated cell division is considered a risk factor in mutagenesis and carcinogenesis, because DNA replication can result in the "fixation" of a primary DNA damage in the form of a heritable mutation and in the loss of heterozygosity for tumor suppressor genes by mitotic recombination, to name only two of a number of possible mechanisms. If we now assume that the division of a given cell is triggered by the occupation of 1,000 but not 999 growth factor receptor molecules, one molecule of an agonistic exogenous mitogen could trigger cell division. The dose response can therefore have a non-zero gradient starting at dose 0, and a true threshold dose cannot be defined.

For an individual, a threshold dose could be defined retrospectively, irrespective of the mode of carcinogen action

What does the y-axis in a dose-cancer incidence curve actually represent? It shows the fraction (a percentage) of a group that was diagnosed with cancer within a specified period of observation. The contribution of an individual to the count of tumor-bearing animals or humans can only be zero or one, depending on whether the count is made before or after tumor manifestation. Therefore, on a time axis, each individual that turns up with a tumor will increase the cumulative cancer incidence stepwise. An example of groups of ten is shown in Figure 2.

Figure 2. Schematic time-incidence relationships in groups of ten individuals treated with a carcinogen at various dose levels. Individual susceptibility to both the spontaneous and carcinogen-accelerated process of tumor induction results in a stepwise time-to-tumor. The star indicates the individual for which dose 2 could in retrospect be defined as the threshold dose.

In the absence of any added carcinogen, the individual background rate of the process of carcinogenesis determines the course of the stepwise increase6. Additional exposure to a carcinogen results in a reduction of the time-to-tumor7 and more individuals manifest cancer within the period of observation. In this representation, one could theoretically define a threshold dose for each individual as the dose that resulted in tumor manifestation at exactly the end of the period of observation. In Figure 2, for instance, dose 2 was the threshold dose for the individual that was 7th in the time ranking shown.

For the group as a whole, there cannot be one single threshold dose, in view of the individual differences in genetic and life style-dependent susceptibility8. Furthermore, in view of the stochastic elements of the process of carcinogenesis, the threshold dose can only be defined after tumor incidence and cannot be predicted.

Apparent Thresholds Could in Fact be J-Shaped Dose-Response Relationships

There is increasing evidence that DNA damage induced by a genotoxic carcinogen does not simply add to the background DNA damage. In a number of bioassays, spontaneous tumor incidence decreased at low dose and increased only at high dose9. The anticarcinogenic effect is rarely significant but is hotly debated as a phenomenon. If it turns out to be real, what looks like a threshold could in fact be a J-shaped (or: u-shaped) dose response. If this is the case, there is no longer a need to explain an unexplainable discontinuity of the dose-response curve.

In the last few years, the investigation of the role of tumor suppressor genes in the regulation of DNA repair and the cell cycle shed more light on a putative mechanism underlying a J-shaped dose response. At low dose, DNA damage can result in a delay of the cell cycle and an increase in DNA repair. At high dose, the damage can become too extensive, and cell death is the result. For the sake of survival of the organism, a neighbouring cell divides prematurely. On the basis of the understanding that DNA replication is a risk factor in mutagenesis and carcinogenesis (see above), a J-shaped dose response relationship follows for tumor incidence.

We recently calculated a few examples of J-shaped dose-response curves on the basis of the two-stage clonal expansion model10. We showed that the reduction of the rate of cell turnover required for a substantial decrease in the number of spontaneous and induced tumors is well within an experimentally observable range11. The J-shape approach might reconcile opposing views on "thresholds" on a biologically plausible mechanistic basis. Nevertheless, it does not result in one single "practical" threshold dose for a population but will still be individually dispersed.


1 Krewski D, Gaylor DW, Lutz WK. Additivity to background and linear extrapolation. in Low-Dose Extrapolation of Cancer Risks: Issues and Perspectives (eds. Olin, S. et al.), 1995; ILSI/International Life Sciences Institute Washington, DC, 105-121.

2 Gupta RC, Lutz WK. Background DNA damage from endogenous and unavoidable exogenous carcinogens: a basis for spontaneous cancer incidence? Mutat Res 1999; 424: 1-8.

3 Purchase IFH, Auton TR. Thresholds in chemical carcinogenesis. Regul Toxicol Pharmacol 1995; 22: 199-205.

4 Cornfield J. Carcinogenic risk assessment. Science 1977; 198: 693-699.

5 Lutz WK. Dose-response relationships in chemical carcinogenesis: From DNA adducts to tumor incidence. Adv Exp Med Biol 1990; 283: 151-156.

6 Lutz WK. Dose-response relationships in chemical carcinogenesis reflect differences in individual susceptibility. Consequences for cancer risk assessment, extrapolation, and prevention. Hum exp Toxicol 1999; 18: 707-712.

7 Lutz WK, Gaylor D. Significance of DNA adducts at low dose: shortening the time to spontaneous tumor occurrence. Regul Toxicol Pharmacol 1996; 23: 29-34.

8 Lutz WK. Carcinogens in the diet vs. overnutrition. Individual dietary habits, malnutrition, and genetic susceptibility modify carcinogenic potency and cancer risk. Mutat Res 1999; 443: 251-258.

9 Lutz WK. Dose-response relationships in chemical carcinogenesis: superposition of different mechanisms of action, resulting in linear-sublinear curves, practical thresholds, J-shapes. Mutat Res 1998; 405: 117-124.

10 Lutz WK, Kopp-Schneider A. Threshold dose response for tumor induction by genotoxic carcinogens modeled via cell-cycle delay. Toxicol Sci 1999; 49: 110-115.

11 Lutz U, Lugli S, Bitsch A, Schlatter J et al. Dose response for the stimulation of cell division by caffeic acid in forestomach and kidney of the male F344 rat. Fund Appl Toxicol 1997; 39: 131-137.