Two Models in Math Biology

Laurent MacKay, UBC Mathematics
December 4, 2023 3:00 pm LSK 306

I will talk about two very different projects in the realm of math biology. First, I discuss work related to viscoelastic effects during tubulogenesis in the drosophila salivary gland. This salivary gland is a simple model for flat tissues that deform themselves into tubes through concentrically organized squeezing forces. We incorporate stress-relaxation, an intrinsic property of the structural elements of this tissue, into a vertex-based model of a cell sheet by using viscoelastic elements and observe significant increases in tissue deformation. The relative contribution of stretching and compression of cell-cell interfaces is investigated and quantified. We also investigate how stress-relaxation influences topological transitions in the network of interfaces.

I will also describe a model of reptilian tooth replacement that seeks to reproduce species-specific waves of tooth replacement. A previously developed ODE model is thoroughly investigated using continuation methods to enumerate all possible solution behaviours. We then extend the model to a PDE that explicitly accounts for the diffusion of inhibitory signals between teeth, yielding some novel solution types. Again using continuation methods, we delineate parameter regimes with solutions that closely resemble experimental observations in leopard geckos.

Refreshments will be served preceding the talk, starting at 2:45.