Modeling Tissue Division Patterns and Loss of Cell Polarity in Cancer

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Cancer represents one of the biggest problems for modern societies. In 2015, there were 1.6 million new cancer cases and 590,000 cancer-related deaths in the US. Mathematical and computational models enable critical examination of mechanisms that may be involved in the initiation and development of tumors. Due to ongoing renewal of tissue, some individual human cells divide as many as 5000 times during a lifetime, accumulating deleterious mutations that may result in a cell becoming cancerous. The principal investigator will test how the probability of tissues accumulating mutations depends on the spatial organization of cells, and the developmental stage of the cell where the initial cancer-causing mutation occurs. Determining which cellular division patterns slow down mutation accumulation and delay the onset of cancer will advance our understanding of mechanisms driving tumorigenesis and provide quantitative predictions that can be validated experimentally. The project will train undergraduate and graduate students through research involvement in an interdisciplinary field. The mathematical models developed in this research project will be incorporated into a summer course on Cancer Dynamics in the q-bio Summer School that introduces students from diverse disciplines such as mathematics, physics, and computer science to modeling in biology. Dynamical models will be used to study the effects of cellular differentiation hierarchy on the estimated time to cancer development and treatment outcomes in various cancer types. Trade-offs between symmetric cell division and the production of more differentiated cells via asymmetric division will be explored in a stochastic model of different cell types and their spatial locations. On an intracellular level, a model for unequal distribution of cellular components (cellular polarity) that regulates asymmetric divisions will be developed. Computational tests will examine the effects of mutations of different key proteins in the polarity biochemical network and relate them to macroscopic behavior in a population level model of tissue. This project will aid in understanding how disruption of asymmetric division mechanisms can act as a cancer promoting mechanism.