A Quantitative Numerical Model for TNF-α Mediated Cellular Apoptosis

Experimental evidence indicates that cells under irradiation induce in the neighbour non- irradiated cells the same biological effects affecting the irradiated ones. This is the so called bystander effect. Up to now in the scientific literature this kind of effect does not appear to be fully understood, even if several experiments show evidence of its existence. It would be reasonable that bystander effect takes place by means of paracrine chemical transmission mediators that would be broadcasted by the damaged cells to the surrounding cells. Furthermore a subset of a special class of signaling proteins, namely the cytokines, are probably the very ones involved in such signaling phenomenon. Among them, Tumor Necrosis Factor (TNF) is a particularly relevant protein belonging to the class of cytokines, because it is known to contribute to mediate various relevant cell functions, like apoptosis, the programmed cell death. As a molecule, TNF is quite interesting, because it can issue two opposite signals through different intracellular molecular signaling chains. One signal induces apoptosis, while the other is opposite, inducing the cell resistance to apoptic signals. The crucial point is thus to understand what makes each of such two signals masking the other. Thus a mathematical model related to the TNF signaling pathway is of interest, paying special attention to the study of the TNF reception mechanisms by cells that are not passed through by the radiation beam. In this work we present a new mathematical model of cellular apoptosis - mediated by TNF - and its validation based on data existent in literature. The model that we present will result to be a stable model with respect to large variation of the parameters and simplified with respect to other models already existent.