A Mathematical Modelling for Estradiol Influence on DNA Damage Response and G1/S Transition Phase Regulations in Early Stage of Breast Cancer

Breast cancer is a malignant disease that triggers the anomalies of the cells proliferation in breast tissue. There are some known factors that have ability to increase someone risk to suffer this disease, i.e., hormone, genetics, lifestyle, etc. One of the important hormone for the growth of breast tissue is estrogen, but it also contributes to breast cancer via DNA damage induced by producing the oxidative metabolites. Also, estrogen can provoke excessive proliferation that triggers the tumorigenesis process, where the key effectors are C-Myc and Cyclin D1 (CycD1). In this paper, we introduce a new mathematical model of the DNA damage as the response of the estrogen involving the G1/S transition phase in cell cycle. The model is a 15-dimensional system of the first order of ODE that shows the chemical reactions between proteins and hormones that play important roles in cell cycle regulations. The model could be a foundation to understand the initial behavior of the breast cancer. We use numerical simulations by using fourth order Runge Kutta method to study the molecular behavior of the normal cells and the anomalies on the abnormal cells that initially lead breast cancer.