title: Fronts under arrest: Nonlocal boundary dynamics in biology.
abstract: We introduce a minimal geometric partial differential equation framework to understand pattern formation from interacting, counterpropagating fronts. Our approach concentrates on the interfaces between different states in a system, and relies on both nonlocal interactions and mean-curvature flow to track their evolution. As an illustration, we use this approach to describe a phenomenon in bacterial colony formation wherein sibling colonies can arrest each other's growth. This arrested motion leads to static separations between healthy, growing colonies. As our minimal model faithfully recovers the geometry of these competing colonies, it captures and elucidates the key leading-order mechanisms responsible for such patterned growth.
authors.affiliation: Department of Mathematical Sciences, MSU, Bozeman, Montana 59717, USA and Department of Mathematics and Statistics, CSULB, Long Beach, California 90840, USA.
authors.forename: Scott G
authors.initials: SG
authors.lastname: McCalla
authors.affiliation: Department of Mathematical Sciences, MSU, Bozeman, Montana 59717, USA and Department of Mathematics and Statistics, CSULB, Long Beach, California 90840, USA.
authors.forename: James H
authors.initials: JH
authors.lastname: von Brecht
mesh_terms: D000898:Antibiosis; D001419:Bacteria / Q000254:growth & development; D018407:Bacterial Physiological Phenomena; D008954:Models, Biological