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Mathematical modelling of epithelial dynamics: from cells to tissues

Dr Alexander Fletcher ( Mathematical Institute, University of Oxford )

The movement and organisation of epithelial tissues plays a central role during development, growth, disease and wound healing. These processes occur as a result of cell adhesion, migration, division, differentiation and death, and involve multiple processes acting at the cellular and molecular level. Alongside experimental approaches, mathematical modelling can help us understand what factors are involved in regulating cell and tissue level behaviour, and how this can go wrong. In this talk I describe work done to understand epithelial dynamics in two settings: intestinal tissue self-renewal and embryonic tissue size control.

 A particularly important adult epithelium is that of the colon, which is folded to form invaginations called crypts. Using mouse models of colorectal cancer for parameterization, I describe a model of a colonic crypt that couples a stochastic description of cell proliferation with an individual-based model of cell movement. Taking account of the crypt’s curved geometry, I simulate the process of monoclonal conversion, where the progeny of one cell takes over the entire crypt, facilitating the spread of mutations. Comparison with a classical Moran model highlights the significant effect of the crypt’s spatial structure on monoclonal conversion times. Extensions to the model reveal a strong dependence of monoclonal conversion on dysregulation of cell adhesion and provide evidence that the 'wiggles' in the width of a clonal ribbon represents a temporal record of that clone's stem cell population dynamics.

 Developing embryos must carefully orchestrate growth, division, and death to control tissue size and repair patterning defects. However, the fundamental size control mechanisms acting at a cellular level remain poorly understood. In the embryonic epidermis of Drosophila, a model organism, epidermal growth factor receptor (EGFR) signalling plays an important role in regulating cell growth and survival. I describe ongoing work to combine measurements of apical cell geometry and EGFR signalling from immunohistochemical stainings and live-imaging with an in silico model of epidermal segment growth and patterning in order to elucidate the mechanisms underlying cellular decision making and morphogen signal interpretation.

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