Linking spatial drug heterogeneity to microbial growth dynamics in theory and experiment
Authors: Hu Zhijian , Wu Yuzhen , Freire Tomas , Gjini Erida , Wood Kevin 
Published: November 2024

Diffusion and migration play pivotal roles in microbial communities - shaping, for example, colonization in new environments and the maintenance of spatial structures of biodiversity. While previous research has extensively studied free diffusion, such as range expansion, there remains a gap in understanding the effects of biologically or physically deleterious confined environments. In this study, we examine the interplay between migration and spatial drug heterogeneity within an experimental meta-community ofE. faecalis, a Gram-positive opportunistic pathogen. When the community is confined to spatially-extended habitats (‘islands’) bordered by deleterious conditions, we find that the population level response depends on the trade-off between the growth rate within the island and the rate of transfer into regions with harsher conditions, a phenomenon we explore by modulating antibiotic concentration within the island. In heterogeneous islands, composed of spatially patterned patches that support varying levels of growth, the population’s fate depends critically on the specific spatial arrangement of these patches - the same spatially averaged growth rate leads to diverging responses. These results are qualitatively captured by simple simulations, and analytical expressions which we derive using first-order perturbation approximations to reaction-diffusion models with explicit spatial dependence. Among all possible spatial arrangements, our theoretical and experimental findings reveal that the arrangement with the highest growth rates at the center most effectively mitigates population decline, while the arrangement with the lowest growth rates at the center is the least effective. Extending this approach to more complex experimental communities with varied spatial structures, such as a ring-structured community, further validates the impact of spatial drug arrangement. Our findings suggest new approaches to interpreting diverging clinical outcomes when applying identical drug doses and inform the possible optimization of spatially-explicit dosing strategies.

Author summary

In this study, we develop an automated platform to experimentally investigate short-term population growth and migration dynamics under spatial drug heterogeneity. Our findings reveal that the collective spatial response of the population can vary significantly, even with the same migration rate and averaged drug dose, due to different spatial drug arrangements. By constructing a simple reaction-diffusion model, we observed that simulated short-term spatial growth rate closely matches the experimental data. Furthermore, this short-term spatial growth rate aligns well with the long-term spatial growth rate, defined by the largest eigenvalue, as the spatial system quickly enters the equilibrium growth state. Using concepts from perturbation theory, we derived an analytical relationship between the boundary diffusion effect, homogeneous growth effect, and heterogeneous effect. Our results highlight that in spatially-extended habitats, the spatial growth response is an emergent property. The bacterial population quickly enters equilibrium growth, suggesting that the spatial growth rate measured at an ecological scale may be used to predict resistance evolutionary behavior.