Mathematical modeling of skin papilloma data in SENCAR mice

Published data from SENCAR mice were analyzed to elucidate mechanisms underlying the formation of chemically induced skin papillomas. The experimental data followed a two-step protocol using 7,12-dimethylbenz[a]anthracene (DMBA) for initiation and 12-O-tetradecanoylphorbol-13-acetate (TPA) for promotion. The two-mutation model of Ellwein and Cohen was used to simulate the data. In this model, probabilities of stem cell birth and death along with initiation and increased cell division are allowed to vary in time. We incorporated a pulse dose with exponential decay to represent the effect of DMBA on the probability of initiation over time, and a summation of pulse doses to represent the repeated topical applications of TPA and its effect on cell division and cell death. We fitted the model to the papilloma and carcinoma data sequentially, and indirectly determined the dependence of model parameters on the administered dose of DMBA and TPA. The occurrence of chemically induced epidermal hyperplasia is a fundamental assumption in our fits of the papilloma data. We found a delay in the onset of normal and initiated cell death relative to the enhancement of cell division rates. In addition, the model parameters display a nonlinear dependence on the dose of DMBA or TPA administered.