Experimental validation of a critical domain size in reaction–diffusion systems with Escherichia coli populations

Abstract

In a one-variable, finite size reaction–diffusion system, the existence of a minimal domain size required for the existence of a non-zero steady state is predicted, provided that the reaction–diffusion variable has a fixed value of zero at the boundaries of the domain (Dirichlet boundary conditions). This type of reaction diffusion model can be applied in population biology, in which the finite domain of the system represents a refuge where individuals can live normally immersed in a desert, or region where the conditions are so unfavourable that individuals cannot live in it. Building on a suggestion by Kenkre and Kuperman, and using non-chemotactic E. coli populations and a quasi-one-dimensional experimental design, we were able to find a minimal size (approximately 0.8 cm) for a refuge immersed in a region irradiated with intense UV light. The observed minimal size is in reasonable agreement with theory.