Searching for oxygen: the dynamic phenotype of Bacillus subtilis' aerotaxis system

Aerotaxis is the directed migration of cells along oxygen gradients, and allows many microorganisms to locate favourable conditions. How the organisms respond to the concentration profiles they are exposed to, dictates how widespread and competitive the species can be at colonising different habitats. The way in which the bacteria sense and respond to a stimulus, like an oxygen gradient, over time is known as its Dynamic Phenotype. Fold Change Detection (FCD), is one type of Dynamic Phenotype, where the entire response time profile of a system (output) is the same given a fold change on the background concentration (input). This response rescaling helps the system stay sensitive over large ranges of ligand concentrations, as the adaptation mechanisms shift the sensitivity range to account for the background concentration. The aim of this doctoral project is to assess the dynamic phenotype of the aerotactic response of Bacillus subtilis, and recapture the population level behaviour in a mathematical model. In this thesis, I have exposed Bacillus subtilis cells to a variety of relative linear gradients of oxygen (∇C/C), or fold changes, using the controlled environments that microfluidics offers. To quantify the movement of the population over time, I exposed the cells to a variety of different fold changes, to elucidate the dynamic response of the population of cells. I found that there was no clear trend associated with the accumulation over time (output) for Bacillus subtilis, given different fold changes (input). Additionally, I have utilised another mathematical model of a different organism (Escherichia coli) which has been shown to display FCD. This model was used to recreate the in vivo experiments in silico, and I use this model to show the expected trend associated with a system which does employ FCD. I present hypotheses as to the reason for the difference between the two trends, and discuss experimental procedures to test the theories in the future. To achieve the goal of recapturing the cells’ movement as a population in a mathematical model, it was necessary to assess the Effective Diffusion of the cells as a function of the oxygen concentration. I have quantified single cell trajectories at constant oxygen concentrations, to extract the swimming speed and the rate at which they change direction (tumble), over a variety of static oxygen concentrations. This has quantified the heterogeneity that a clonal population of Bacillus subtilis cells exhibits. I find that the tumble rate does not change as a function of oxygen, but the swimming speed does, which alters the Effective Diffusion of the cells over the oxygen concentrations explored. Finally, I fit the Sensitivity Coefficient, χ, within an Advection Diffusion model, as a function of the concentration and the fold change. I use the output of the in vivo B. subtilis experiments, as well as the output of the in silico model from E. coli, to compare trends for χ associated with the concentration and the fold change. I find that B. subtilis has a negative linear trend between χ and the concentration, and no dependence on the fold change, where the in silico model has no trend associated with the concentration, but a weak positive trend associated with the gradient. I proposed a possible explanation for this difference, and discuss potential extensions of this work to tighten the fitting of the dynamics of the experiments