Back to Departmental Colloquium: Spring 2013
Departmental Colloquium
Date: Thursday, Feb 14, 2013
Time: 4:15PM
Location: JWB 335
Jun Allard
University of California, Davis
Title |
Traveling waves in crawling cells |
Abstract |
Crawling cells, including the white blood cells that patrol your body in search of infections, display several distinct dynamical patterns driven by both biochemistry (diffusion and reactions between chemical species) and mechanics (physical forces between the components inside cells). Our understanding of these spatiotemporal patterns has been aided by mathematical modeling using techniques including partial differential equations (PDEs). Recently, traveling waves have been observed in the protein actin, which powers certain cells’ ability to crawl. Following experimental observation of one type of crawling cell, the fish epithelial keratocyte, we hypothesized that traveling waves are excitable waves arising from interactions of three components: actin, adhesion sites that attach the cell to its environment, and VASP, a protein that regulates actin. We developed a mathematical model formulated as a system of PDEs with a nonlocal integral term and noise. Numerical solutions lead to a number of predictions, including that VASP also exhibits a traveling wave out of phase with the actin wave, later discovered in further experiments. Our model also reveals a role for tension in the membrane that surrounds the cell, which would otherwise be difficult to observe directly by experiment. |
Dynamical Systems
Mathematical Biology
Differential Equations