Date: Wednesday, November 20, 2002
Time: 4:30 PM
Location: 117, Hayes-Healy Hall, Notre Dame

Speaker: Dr. Frithjof Lutscher

From: Center for Mathematical Biology, Department of Mathematical and Statistical Sciences
University of Alberta, Edmonton, AB T6G 2G1, Canada

Host: Mark S. Alber (Mathematics)

Title: Individual Behavior and Population Patterns in Myxobacteria

Abstract:
It is well known that certain cell types and bacteria use long range signaling to induce coordinated movement behavior, e.g., chemotaxis. A major question is whether or not also short range signaling or local interaction can be the cause of coordinated movement behavior and morphogenetic processes. There is strong experimental evidence that the rippling behavior observed in Myxobacteria is caused by nearest neighbor interaction only. Several mathematical models have been developed which all confirm that rippling patterns can emerge from purely local interaction.

As a model problem for these patterns, we derive and study a one-dimensional hyperbolic system of Goldstein-Kac type with density dependent coefficients. Linear analysis and construction of invariant domains give qualitative conditions on the coefficient functions under which the system exhibits traveling wavetrain solutions which look much like rippling. The system is also able to produce aggregation. Simulations of individual paths show markedly different behavior of cells in the different emerging population patterns.