Threshold dose response for tumor induction by genotoxic carcinogens modeled via cell-cycle delay

Dose-response relationships for tumor induction in animal bioassays for carcinogenicity are often postulated to include thresholds, particularly for nongenotoxic chemicals that increase the rate of cell proliferation at high doses. In this report, thresholds are postulated also for genotoxic carcinogens. The hypothesis is based on the idea of a delay of the cell cycle induced by low-level DNA damage and an acceleration at cytotoxic dose levels, thus resulting in a J-shaped (or U-shaped) dose response for cell turnover. Calculations were based on the 2-stage clonal expansion model of carcinogenesis. The background values chosen for the model parameters resulted in a 10.5% "spontaneous" 2-year cumulative tumor incidence. Using this as a starting point, a decrease by 3, 10, and 30% in the rates of cell turnover resulted in a decrease in the spontaneous tumor incidence to 9.4, 7.1 and 3.0%, respectively. Dose-responses with J-shaped curves for the rates of cell birth and death were modeled by shifted quadratic functions reaching the minimum at dose 1. Combinations with linearly increasing mutation rates also generated, under certain conditions, J-shaped dose-response curves for tumor incidence. As an example, for a 30% increase in mutation rates and a 10% decrease in cell turnover rates (both at dose 1), the dose-response curve showed an initial decrease of tumor incidence below the spontaneous rate, a reversion to the background value at 0.8 dose units, and an increase thereafter. The 0.8 dose could be considered to represent the "threshold dose." The approach presented might reconcile opposing views on thresholds on a biologically plausible mechanistic basis, and show a way for the quantitative estimation of threshold doses.