Mathematical Modeling of Proliferation and Apoptosis Pathways in Mammary Epithelial Cells during the Menstrual Cycles

The development and regression of mammary epithelial tissue during the menstrual cycles driven by progesterone and estrogen over a woman's lifetime have been associated with the risk of breast cancer. The present work develops an ODE-based model to investigate the impact of periodic hormone fluctuations on the intracellular signaling of mammary epithelial cells. The main question is to understand at the molecular level how progesterone and estrogen promote cell proliferation and apoptosis. The ~28-day cycles of the hormones were modeled by periodic functions, while the complexity of molecular processes with kinetic equations. Model simulations can capture the change in molecular processes and biological phenomena that agree with experimental data. The rise in progesterone promotes the proliferation of epithelial cells, starting from day 11 and reaching its maximum on day 24 in the luteal phase. Meanwhile, estrogen induces apoptosis via caspase activation, reaching a high level on day 28. The model can be extended by considering other conditions (irregular menstrual cycles, irregular protein activities, etc.) that may lead to an imbalance between mammary epithelial cell proliferation and apoptosis.