  The exchange of diffusive metabolites is known to control the spatial
patterns formed by microbial populations, as revealed by recent studies in the
laboratory. However, the matrices used, such as agarose pads, lack the
structured geometry of many natural microbial habitats, including in the soil
or on the surfaces of plants or animals. Here we address the important question
of how such geometry may control diffusive exchanges and microbial interaction.
We model mathematically mutualistic interactions within a minimal unit of
structure: two growing reservoirs linked by a diffusive channel through which
metabolites are exchanged. The model is applied to study a synthetic mutualism,
experimentally parameterised on a model algal-bacterial co-culture. Analytical
and numerical solutions of the model predict conditions for the successful
establishment of remote mutualisms, and how this depends, often
counterintutively, on diffusion geometry. We connect our findings to
understanding complex behaviour in synthetic and naturally occurring microbial
communities.
