Transport Models for Collective Dynamics in Biological Systems

Multiscale Analysis in Biology - Successes and Open Problems

Hans Othmer

University of Minnesota
[SLIDES]

New techniques in cell and molecular biology have produced huge advances in our understanding of signal transduction and cellular response in many systems, and this has led to better cell-level models for problems ranging from biofilm formation to embryonic development. However, many problems involve very large numbers of cells, and detailed cell-based descriptions are computationally prohibitive at present. Thus rational techniques for incorporating cell-level knowledge into macroscopic equations are needed for these problems. In this talk we discuss several examples that arise in the context of cell motility and pattern formation, where one begins with a transport equation and attempts to derive a Patlak-Keller-Segel type of chemotaxis equation. We will discuss systems in which the micro-to-macro transition can be made more or less completely, and also describe other systems that will require new insights and techniques.