Inevitably, almost all cancer patients develop resistance to targeted therapy. Intratumor heterogeneity (ITH) is a major cause of drug resistance. Mathematical models that explain experiments quantitatively is useful in understanding the origin of ITH, which then could be used to explore scenarios for efficacious therapy. Here, we develop a mathematical model to investigate ITH in breast cancer by exploiting the observation that HER2+ and HER2- cells could divide symmetrically or asymmetrically. Our predictions for the evolution of cell fractions are in quantitative agreement with single-cell experiments. Remarkably, the colony size of HER2+ cells emerging from a single HER2- cell (or vice versa), which occurs in about four cell doublings, agrees perfectly with experimental results, without tweaking any parameter in the model. The theory quantitatively explains experimental data on the responses of breast cancer tumor under different treatment protocols. We then used the model to predict that, not only the order of two drugs, but also the treatment period for each drug and the tumor cell plasticity could be manipulated to improve the treatment efficacy. Mathematical models, when integrated with data on patients, make possible exploration of a broad range of parameters readily, which might provide insights in devising effective therapies.
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