Past Event: Oden Institute Seminar

Multiscale modeling of tissue growth and morphogenesis: Bridging the cell and tissue scales

John Lowengrub, Professor, Department of Mathematics, UC Irvine

Abstract

The regulation of cell division, cell sizes and cell arrangements is central to tissue growth and morphogenesis. To study these processes, we develop a mechanistic hybrid continuum-discrete mathematical model of cell dynamics that has advantages over previous approaches. 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. The discrete component of the model implements cell division and thus influences cell sizes and shapes that couple to the continuum equations. We present efficient numerical methods for solving the coupled systems of equations and validate the model using recent in vitro studies of epithelial cell colonies using Madin-Darby canine kidney cells. In good agreement with the experiments, we find that mechanical interactions and constraints on the local expansion of cell size cause inhibition of cell motion and reductive cell division. This leads to successively smaller cells and a transition from exponential to quadratic growth of the colony that is associated with the emergence of short-range ordering and a constant-thickness proliferating rim of cells at the cluster edge. We then discuss extensions of the model to account for different cell types, including stem, progenitor and terminally differentiated cells, that are needed to model stratified epithelial tissues. Finally, we demonstrate how the cell-scale continuum model can be coarse-grained to obtain new, tissue-scale governing equations with parameters that can be directly obtained from cell scale measurements. We relate the new system with previously developed models. Bio: John Lowengrub is a Chancellor's Professor at the University of California at Irvine with appointments in the departments of Mathematics and Biomedical Engineering. He is the inaugural director of the interdisciplinary graduate program in Mathematical, Computational and Systems Biology. Prof. Lowengrub is also a co-leader of the Systems, Pathways and Targets program at the Chao Family Comprehensive Cancer Center at UC Irvine. Prof. Lowengrub’s research interests include applied and computational mathematics, mathematical and computational biology, mathematical oncology, complex fluids and materials science. Prof. Lowengrub has published over 150 journal articles, several book chapters, and a book on multiscale modeling of cancer. Among his awards are a Sloan Fellowship, the Francois Frenkiel award by the American Physical Society, the Chancellor's award for excellence in fostering undergraduate research at UCI, and he was recently elected a fellow of the AAAS. Prof. Lowengrub holds a B.A. from Cornell University (1985) and a Ph.D. from the Courant Institute of Mathematical Sciences at New York University (1988).