UBC Mathematical Biology Seminar: John Lowengrub

The form and function of tissues and organs emerge out of cell-to-cell interactions. Cell interaction dynamics take place on a variety of temporal and spatial scales, and reflect processes—diffusion, migration, force production/sensing, growth, and proliferation. In this talk, we develop a multiscale framework where directly measurable quantities at the discrete cell-scale inform the model parameters at the continuum tissue scale through upscaling. In principle, this enables the model to be truly predictive because the data used for calibration (e.g., at the cell scale) is distinct from that used for validation (e.g., at the tissue scale). This model borrows ideas from statistical physics, materials science and applied mathematics and follows the framework of dynamic density functional theory. This approach provides a strategy for coarse-graining systems of stochastically interacting particles. By appropriately accounting for cell size and shape variability, we obtain a system of continuum equations that are able to capture plastic, viscoelastic and elastic deformations in the clusters while providing single-cell resolution. We validate this approach by comparisons with recent in vitro studies of epithelial cell colonies using Madin-Darby canine kidney cells. We then use this framework to develop a new continuum elastic model for tissues that contains microscale information, including cell-cell correlations. The governing equations are obtained by using a 1-mode approximation and coarse-graining. We simulate the system numerically and analyze the system using matched asymptotic expansions to relate the new model with previously developed approaches.