Mathematical Modeling of the Phoenix Rising Pathway

Apoptosis is a tightly controlled process in mammalian cells. It is important for embryogenesis, tissue homoeostasis, and cancer treatment. Apoptosis not only induces cell death, but also leads to the release of signals that promote rapid proliferation of surrounding cells through the Phoenix Rising (PR) pathway. To quantitatively understand the kinetics of interactions of different molecules in this pathway, we developed a mathematical model to simulate the effects of various changes in the PR pathway on the secretion of prostaglandin E2 (PGE2), a key factor for promoting cell proliferation. These changes include activation of caspase 3 (C3), caspase 7 (C7), and nuclear factor κB (NFκB). In addition, we simulated the effects of cyclooxygenase-2 (COX2) inhibition and C3 knockout on the level of secreted PGE2. The model predictions on PGE2 in MEF and 4T1 cells at 48 hours after 10-Gray radiation were quantitatively consistent with the experimental data in the literature. Compared to C7, the model predicted that C3 activation was more critical for PGE2 production. The model also predicted that PGE2 production could be significantly reduced when COX2 expression was blocked via either NFκB inactivation or treatment of cells with exogenous COX2 inhibitors, which led to a decrease in the rate of conversion from arachidonic acid to prostaglandin H2 in the PR pathway. In conclusion, the mathematical model developed in this study yielded new insights into the process of tissue regrowth stimulated by signals from apoptotic cells. In future studies, the model can be used for experimental data analysis and assisting development of novel strategies/drugs for improving cancer treatment or normal tissue regeneration.Author Summary: Apoptosis, or programmed cell death, is known to be important for embryogenesis, tissue homoeostasis, and cancer treatment. Furthermore, researchers have recently observed that apoptosis may promote wound healing and tissue regeneration, and accelerate undesired solid tumor regrowth after chemotherapy/radiation therapy. Mechanisms of apoptosis-induced tissue regrowth are related to a molecular network discovered recently in our lab. To quantitatively understand the kinetics of interactions of different molecules in this network, we developed a mathematical model and validated it by comparing the simulation results to experimental data reported in previous studies. To gain new insights into the process of tissue regrowth after inducing apoptosis, we used the model to simulate the effects of radiation on the production of a key growth stimulating factor, PGE2, in apoptotic cells. Additionally, we simulated how PGE2 production could be altered when cells were treated with different inhibitors. We expect that the new mathematical model can be used in future studies to facilitate design of better approaches to cancer treatment or normal tissue regeneration.