Matlab Code File 2: Differential Equations from Mathematical modelling of breast cancer cells in response to endocrine therapy and Cdk4/6 inhibition

Estrogen receptor (ER) positive breast cancer is responsive to a number of targeted therapies used clinically. Unfortunately, the continuous application of any targeted therapy often results in resistance to the therapy. Our ultimate goal is to use mathematical modelling to optimize alternating therapies that not only decrease proliferation but also stave off resistance. Toward this end, we measured levels of key proteins and proliferation over a 7-day time course in ER+ MCF-7 breast cancer cells. Treatments included endocrine therapy, either estrogen deprivation, which mimics the effects of an aromatase inhibitor, or fulvestrant, an ER degrader. These data were used to calibrate a mathematical model based on key interactions between ER signalling and the cell cycle. We show that the calibrated model is capable of predicting the combination treatment of fulvestrant and estrogen deprivation. Further, we show that we can add a new drug, palbociclib, to the model by measuring only two key proteins, cMyc and hyperphosphorylated RB1, and adjusting only parameters associated with the drug. The model is then able to predict the combination treatment of estrogen deprivation and palbociclib. We illustrate the model's potential to explore protocols that limit proliferation and hold off resistance by not depending on any one therapy.

雌激素受体（Estrogen Receptor, ER）阳性乳腺癌对多种临床应用的靶向治疗方案具有响应性。然而，持续使用任意一种靶向治疗方案往往会导致肿瘤对该疗法产生耐药性。我们的最终目标是通过数学建模优化交替治疗方案，该方案既能抑制肿瘤增殖，又能延缓耐药性的产生。为此，我们在为期7天的时间进程中，检测了ER阳性MCF-7乳腺癌细胞中关键蛋白的表达水平与细胞增殖情况。本次实验采用的内分泌治疗方案包括两种：一是模拟芳香化酶抑制剂（aromatase inhibitor）作用的雌激素剥夺疗法，二是ER降解剂氟维司群（Fulvestrant）。我们利用这些实验数据对基于ER信号通路与细胞周期关键相互作用的数学模型进行了校准。研究表明，经校准后的模型能够预测氟维司群与雌激素剥夺联合治疗的效果。此外，我们发现仅通过检测cMyc与高磷酸化RB1（hyperphosphorylated RB1）两种关键蛋白的表达水平，并调整与该药物相关的模型参数，即可将新药帕博西尼（Palbociclib）纳入该模型。校准后的模型便可预测雌激素剥夺疗法与帕博西尼联合治疗的效果。我们进一步验证了该模型的应用潜力：通过不依赖单一疗法的方案设计，可探索既能抑制肿瘤增殖、又能延缓耐药性的治疗策略。