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Inevitably, almost all cancer patients develop resistance to targeted therapy. Intratumour heterogeneity is a major cause of drug resistance. Mathematical models that explain experiments quantitatively are useful in understanding the origin of intratumour heterogeneity, which then could be used to explore scenarios for efficacious therapy. Here, we develop a mathematical model to investigate intratumour heterogeneity 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, also agrees with experimental results, without tweaking any parameter in the model. The theory explains experimental data on the responses of breast tumours 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 tumour 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. 

Collective cell movement, characterized by multiple cells that are in contact for substantial periods of time and undergo correlated motion, plays a central role in cancer and embryogenesis. Recent imaging experiments have provided time-dependent traces of individual cells, thus providing an unprecedented picture of tumor spheroid growth. By using simulations of a minimal cell model, we analyze the experimental data that map the movement of cells in a fibrosarcoma tumor spheroid embedded in a collagen matrix. Both simulations and experiments show that cells in the core of the spheroid exhibit subdiffusive glassy dynamics (mean square displacement, Δ( t ) ≈ t α with α < 1), whereas cells in the periphery exhibit superdiffusive motion, Δ( t ) ≈ t α with α > 1. The motion of most of the cells near the periphery is highly persistent and correlated directional motion due to cell doubling and apoptosis rates, thus explaining the observed superdiffusive behavior. The α values for cells in the core and periphery, extracted from simulations and experiments, are in near quantitative agreement with each other, which is surprising given that no parameter in the model was used to fit the measurements. The qualitatively different dynamics of cells in the core and periphery is captured by the fourth order susceptibility, introduced to characterize metastable states in glass forming systems. Analyses of the velocity autocorrelation of individual cells show remarkable spatial heterogeneity with no two cells exhibiting similar behavior. The prediction that α should depend on the location of the cells in the tumor is amenable to experimental testing. The highly heterogeneous dynamics of cells in the tumor spheroid provides a plausible mechanism for the origin of intratumor heterogeneity. 

Heterogeneity is a hallmark of all cancers. Tumor heterogeneity is found at different levels — interpatient, intrapatient, and intratumor heterogeneity. All of them pose challenges for clinical treatments. The latter two scenarios can also increase the risk of developing drug resistance. Although the existence of tumor heterogeneity has been known for two centuries, a clear understanding of its origin is still elusive, especially at the level of intratumor heterogeneity (ITH). The coexistence of different subpopulations within a single tumor has been shown to play crucial roles during all stages of carcinogenesis. Here, using concepts from evolutionary game theory and public goods game, often invoked in the context of the tragedy of commons, we explore how the interactions among subclone populations influence the establishment of ITH. By using an evolutionary model, which unifies several experimental results in distinct cancer types, we develop quantitative theoretical models for explaining data from in vitro experiments involving pancreatic cancer as well as in vivo data in glioblastoma multiforme. Such physical and mathematical models complement experimental studies, and could optimistically provide new ideas for the design of efficacious therapies for cancer patients.