Theoretical study for combined effect of X-ray and N-ethyl-N-nitrosourea on lymphomagenesis in mice.

Under the circumstances of modern lifestyle with multiple carcinogens, cancer cause could be ascribed to exposure to not single carcinogen but combinations of multiple ones. They interact with each other, and dose-effect relationship of combined exposures is not necessarily additive, but sometimes more than additive (synergistic) or less than additive (antagonistic). We developed theoretical two-stage model, which takes account of the order of carcinogen exposure. We applied our model to experimental data of joint effect of ethylnitrosourea (ENU) and X-rays on lymphomagenesis in mice. It was found that X-ray at the doses above threshold followed by ENU appeared to produce more than additive effect on the induction of thymic lymphomas, whereas the reverse sequence resulted in a nearly additive effect. Based on the estimation by our mathematical analysis using the maximum likelihood method, we concluded that the X-ray mainly acts at the first step and ENU acts at the second step.The Joint Annual Meetings of the Society for Mathematical Biology and the Japanese Society for Mathematical Biolog