As a population wave expands, organisms at the tip typically experience plentiful nutrients while those behind the front become nutrient-depleted. If the environment also contains a gradient of some inhibitor (e.g. a toxic drug), a tradeoff exists: the nutrient-rich tip is more exposed to the inhibitor, while the nutrient-starved region behind the front is less exposed. Here we show that this can lead to complex dynamics when the organism's response to the inhibitory substance is coupled to nutrient availability. We model a bacterial population which expands in a spatial gradient of antibiotic, under conditions where either fast-growing bacteria at the wave's tip, or slow-growing, resource-limited bacteria behind the front are more susceptible to the antibiotic. We find that growth-rate dependent susceptibility can have strong effects on the dynamics of the expanding population. If slow-growing bacteria are more susceptible, the population wave advances far into the inhibitory zone, leaving a trail of dead bacteria in its wake. In contrast, if fast-growing bacteria are more susceptible, the wave is blocked at a much lower concentration of antibiotic, but a large population of live bacteria remains behind the front. Our results may contribute to understanding the efficacy of different antimicrobials for spatially structured microbial populations such as biofilms, as well as the dynamics of ecological population expansions more generally. PAPEROriginal content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.

Surface-attached bacterial biofilms cause disease and industrial biofouling, as well as being widespread in the natural environment. Density-dependent quorum sensing is one of the mechanisms implicated in biofilm initiation. Here we present and analyse a model for quorum-sensing triggered biofilm initiation. In our model, individual, planktonic bacteria adhere to a surface, proliferate and undergo a collective transition to a biofilm phenotype. This model predicts a stochastic transition between a loosely attached, finite, layer of bacteria near the surface, and a growing biofilm. The transition is governed by two key parameters: the collective transition density relative to the carrying capacity, and the immigration rate relative to the detachment rate. Biofilm initiation is complex, but our model suggests that stochastic nucleation phenomena may be relevant.

Surface-attached bacterial biofilms cause disease and industrial biofouling, as well as being widespread in the natural environment. Density-dependent quorum sensing is one of the mechanisms implicated in biofilm initiation. Here we present and analyse a model for quorum-sensing triggered biofilm initiation. In our model, individual, planktonic bacteria adhere to a surface, proliferate and undergo a collective transition to a biofilm phenotype. This model predicts a stochastic transition between a loosely attached, finite, layer of bacteria near the surface, and a growing biofilm. The transition is governed by two key parameters: the collective transition density relative to the carrying capacity, and the immigration rate relative to the detachment rate. Biofilm initiation is complex, but our model suggests that stochastic nucleation phenomena may be relevant.

Biofouling of marine surfaces such as ship hulls is a major industrial problem. Antifouling (AF) paints delay the onset of biofouling by releasing biocidal chemicals. We present a computational model for microbial colonization of a biocide-releasing AF surface. Our model accounts for random arrival from the ocean of microorganisms with different biocide resistance levels, biocide-dependent proliferation or killing, and a transition to a biofilm state. Our computer simulations support a picture in which biocide-resistant microorganisms initially form a loosely attached layer that eventually transitions to a growing biofilm. Once the growing biofilm is established, immigrating microorganisms are shielded from the biocide, allowing more biocide-susceptible strains to proliferate. In our model, colonization of the AF surface is highly stochastic. The waiting time before the biofilm establishes is exponentially distributed, suggesting a Poisson process. The waiting time depends exponentially on both the concentration of biocide at the surface and the rate of arrival of resistant microorganisms from the ocean. Taken together our results suggest that biofouling of AF surfaces may be intrinsically stochastic and hence unpredictable, but immigration of more biocide-resistant species, as well as the biological transition to biofilm physiology, may be important factors controlling the time to biofilm establishment.