Microbial communities are an important component of biogeochemical cycles in ecosystems across our planet. Photosynthetic phytoplankton perform carbon fixation, converting carbon dioxide into organic molecules. Some of these organic molecules are released by the phytoplankton and can be subsequently metabolised by heterotrophic bacteria, therefore heterotrophic bacteria play an important role in determining the fate of fixed carbon. In order to understand how carbon is transported within ecosystems it is important to study the metabolic processes, like photosynthesis, respiration and inter-species nutrient exchange, which underpin the microbial contribution to the carbon cycle. The multitude of species and interactions that exist within a natural microbial community makes studying specific inter-species nutrient dynamics challenging. The approach of this thesis is to use a two species co-culture in order to reduce complexity and increase control over experimental parameters. As a result, it becomes possible to study the carbon exchange between algae and bacteria in detail.

This thesis considers the co-culture between a vitamin B12-dependent alga, the metE7 mutant of Chlamydomonas reinhardtii, and a B12-producing, heterotrophic bacterium, Mesorhizobium loti. The interaction between these two species is a type of mutualism, because both species benefit from the presence of the other. The bacteria provide B12 to the algae and in exchange the bacteria are able to metabolise some of the organic carbon molecules produced by the algae. The carbon dynamics were studied experimentally using stable isotope labelling and Secondary Ion Mass Spectrometry (SIMS), providing temporal measurements at the single cell level of the carbon assimilation by the algae and its transfer to bacteria.

In the mathematical ecology of interacting species, competition and predator-prey dynamics have been studied more extensively than cooperation. Models that are used to describe interacting species are typically at the population level and only relatively recently have nutrient dynamics been included more explicitly. Creating models that encode our current understanding of metabolic processes means that it is possible to test how well these processes are able to account for experimental observations. Extending a model that was previously developed to describe a mutualism at a distance, the carbon dynamics in the algal-bacterial co-culture were described mathematically by considering algal photosynthesis, organic carbon exchange, bacterial respiration and bacterial inorganic carbon metabolism. The model was used to fit carbon isotope labelling dynamics measured experimentally using SIMS, and thus to test our understanding of the carbon dynamics in an algal-bacterial co-culture. Additionally, the model was used to predict potential origins of the temporal evolution of the single-cell distributions observed in the SIMS measurements. The predictive power of the model is illustrated by examining the effect of changing an initial condition or model parameter, providing examples of possible experiments that could further test the model.