Mathematical models of pattern formation in baterium Proteus mirabilis colonies

Chuan Xue
Mathematical Biosciences Institute (MBI), The Ohio State University

(October 28, 2008 10:30 AM - 11:30 AM)

Mathematical models of pattern formation in baterium Proteus mirabilis colonies

Abstract

The bacterium Proteus mirabilis is known for its ability to swarm over hard surfaces and form spectacular concentric ring patterns. During pattern formation, the colony front is observed to move outward from the inoculation site either continuously or periodically, due to collective movement of elongated, hyper-flagellated swarmer cells at the leading edge. The formation of the rings was thought to arise from periodic colony expansion. However, recent experimental results show that swimmer cells stream inward toward the inoculation site, and form a number of complex patterns, including radial and spiral streams, rings and traveling trains. To understand the underlying mechanism of these complicated patterns, we developed a hybrid cell-based model which incorporates a simplified single cell signal transduction model with both the adaptation and excitation components. By assuming that swimmer cells respond to a chemoattractant that they produce, we are able to predict the formation of radial streams as a result of the modulation of the local attractant concentration by the cells. We further predict the spiral streams by incorporating a swimming bias of the cells near the surface of the medium. The hybrid cell-based model becomes computationally expensive because of the large number of cells due to cell division, therefore a higer level description is needed. We also present a moment-closure method for deriving macroscopic evolution equations from the hybrid cell-based model using perturbation analysis, and compare the solutions of the cell-based model and the derived continuum model.