Bulletin of Mathematical Biology (2006) : 837–861 DOI 10.1007/s11538-005-9031-2 ORIGINAL ARTICLE Two Continuum Models for the Spreading of Myxobacteria Swarms Angela Gallegos a , Barbara Mazzag b , Alex Mogilner a,∗ a Department of Mathematics, University of California, Davis, CA 95616, USA b Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA Received: 11 March 2004 / Accepted: 23 March 2005 / Published online: 8 April 2006 C  Society for Mathematical Biology 2006 Abstract We analyze the phenomenon of spreading of a Myxococcus xanthus bacterial colony on plates coated with nutrient. The bacteria spread by gliding on the surface. In the first few hours, cell growth is irrelevant to colony spread. In this case, bacteria spread through peninsular protrusions from the edge of the initial colony. We analyze the diffusion through the narrowing reticulum of cells on the surface mathematically and derive formulae for the spreading rates. On the time scale of tens of hours, effective diffusion of the bacteria, combined with cell division and growth, causes a constant linear increase in the colony’s radius. Mathematical analysis and numerical solution of reaction-diffusion equa- tions describing the bacterial and nutrient dynamics demonstrate that, in this regime, the spreading rate is proportional to the square root of both the ef- fective diffusion coefficient and the nutrient concentration. The model predic- tions agree with the data on spreading rate dependence on the type of gliding motility. Keywords Myxobacteria swarms · Gliding motility · Continuum model · Traveling wave · Colony spreading 1. Introduction Historically, bacteria were considered solely as single-cell organisms. In recent decades, however, multicellular activities necessary for cell response to environ- mental changes were accepted to be common among bacteria (Shapiro, 1998). Ex- amples of such multicellular behavior include “quorum-sensing,” auto-aggregation of chemotactic bacteria, and self-organization in bacterial colonies (Shapiro, 1998). Coordinated movements in bacterial colonies create beautiful spatio-temporal pat- terns that are very useful as assays for intra- and inter-cellular signaling. A good ∗ Corresponding author. E-mail address: mogilner@math.ucdavis.edu (Alex Mogilner).