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.

Nonlinearity in bacterial population dynamics: Proposal for experiments for the observation of abrupt transitions in patches

“…Although this could have also been done in the one-mask scenario of ref. 9, we explain the idea here in the two-mask case. Additional confirmation of the theoretical picture of the dynamics of the bacteria might be provided by observing how the critical L-d values change with the intensity of the ultraviolet light.…”

“…Need for the experimental proposal that we present here arises because the stationary single-mask experiment (8,9) uses for its interpretation a number of inputs that suffer from a certain degree of uncertainty. Some of these uncertainties are about the values of D and a (11), and others are about the extent to which other phenomena, such as signaling (9), that occur in bacterial movement might affect the outcome of the experiment.…”

“…Some of these uncertainties are about the values of D and a (11), and others are about the extent to which other phenomena, such as signaling (9), that occur in bacterial movement might affect the outcome of the experiment. Because absolute values of critical lengths may be difficult to obtain with an acceptable degree of accuracy, we propose here stationary mask observations that focus, instead, on the interdependence of two critical lengths.…”

“…1. The previously investigated case with a single mask (8,9) corresponds, obviously, to infinite d. To test the idea behind the new proposal, we carried out numerical studies of the full nonlinear Fisher Eq. 1 with given values of D, a, a 1 , and b (10, 0.1, −0.9 and 1 in appropriate units).…”

“…A quite different experiment using stationary masks of varying sizes, and employing bacterial extinction as the key phenomenon, was then proposed (8). That proposal was carried out experimentally (9) and the predictions of ref. 8 were verified.…”