A Mathematical Model for the Hydrogenotrophic Metabolism of Sulphate-Reducing Bacteria

Sulphate-reducing bacteria (SRB) are studied across a range of scientific fields due to their characteristic ability to metabolise sulphate and produce hydrogen sulphide, which can lead to significant consequences for human activities. Importantly, they are members of the human gastrointestinal microbial population, contributing to the metabolism of dietary and host secreted molecules found in this environment. The role of the microbiota in host digestion is well studied, but the full role of SRB in this process has not been established. Moreover, from a human health perspective, SRB have been implicated in a number of functional gastrointestinal disorders such as Irritable Bowel Syndrome and the development of colorectal cancer. To assist with the study of SRB, we present a mathematical model for the growth and metabolism of the well-studied SRB, Desulfovibrio vulgaris in a closed system. Previous attempts to model SRB have resulted in complex or highly specific models that are not easily adapted to the study of SRB in different environments, such as the gastrointestinal tract. We propose a simpler, Monod-based model that allows for easy alteration of both key parameter values and the governing equations to enable model adaptation. To prevent any incorrect assumptions about the nature of SRB metabolic pathways, we structure the model to consider only the concentrations of initial and final metabolites in a pathway, which circumvents the current uncertainty around hydrogen cycling by SRB. We parameterise our model using experiments with varied initial substrate conditions, obtaining parameter values that compare well with experimental estimates in the literature. We then validate our model against four independent experiments involving D. vulgaris with further variations to substrate availability. Further use of the model will be possible in a number of settings, notably as part of larger models studying the metabolic interactions between SRB and other hydrogenotrophic microbes in the human gastrointestinal tract and how this relates to functional disorders.