Population Dynamics and Evolution of Cancer Cells

Abstract

Abstract While the core of cancer research is concerned with molecular cell biology, principles from the fields of population dynamics and evolutionary biology can provide important, complementary insights that can improve our understanding of disease development and therapy outcomes. Cell division and death processes, mutations, and selection are central to carcinogenesis, the response to treatment, and the evolution of drug resistance. Mathematical models have become an increasingly important tool to study these dynamical interactions and evolutionary processes, allowing us to capture a set of biological assumptions and to follow them to their logical conclusions. This review discusses different ways in which mathematical models can be useful in cancer research: mathematical models can lead to the formulation of new concepts; application of mathematical models to clinical data can allow us to estimate central kinetic parameters; and parameterized mathematical models can be used to make predictions about disease and therapy outcomes. Examples of these approaches will be discussed in the context of case studies from our own research and brought into context with the broader oncology literature. The first half of the review is concerned with dynamical and evolutionary processes that contribute to the development of cancer, while the second part concentrates on the dynamics and evolution of cells during therapeutic and preventative interventions. We will explore, how mathematical models and clinical data can be combined to make patient-specific predictions about treatment outcomes.