Reaction diffusion modelling of bacteria colonies : microbial quiescence and chemotaxis

Abstract

The physiological structure of microbial communities in natural environments is typically a response to changes in internal and external conditions. External conditions may include the availability or depletion of growth-limiting nutrients, and presence of inhibiting or toxic substances while internal conditions may include cell to cell interactions. We present and investigate spatio-temporal bacterioplankton-nutrient-chemoattractant-chemorepellent interaction models that take into account the quiescent stage and chemotaxis. We establish conditions under which microbial population oscillations (boom-and-bust) may occur. In the study, we observe that population oscillations occur when the switching of states is dependent on the active microbial density in the environment or cell-to-cell interaction. Furthermore, in the case where dormant cells are neglected or disregarded, oscillations are not observed in the bacterioplankton population dynamics.

It is well known from experiments that colonies of \emph{Escherichia coli} and \emph{Salmonella typhimurium} exhibit various patterns, therefore, we establish the existence of traveling wavefronts for the proposed reaction-diffusion model. Using the theory of monotone wave fronts for cooperative and partially degenerate reaction-diffusion systems, we show that the minimal wave speed coincides with the spreading speed. However, that is for the constant switch rates case. Whereas, for the switch functions dependent on the chemo-attractant concentration we numerically observe that the model admits non-monotonic traveling wave profiles. Moreover, we demonstrate that neglecting dormant cells overestimates the spreading speed of the colony. Numerical results also indicate the importance of the quiescent stage in the speed of spread.

Microbial populations depend on their environment but can also modify it. Instead of breaking down complex nutrients for their growth, microbes can exhibit negative local or global behaviour by engineering the environment in ways that are detrimental to their proliferation. A reaction diffusion model system consisting of active and inactive microbial population in a harsh environment accounting for the directed movement and switch of cells to dormancy at high concentration is studied. Results show an essential mechanism generating oscillating patterns in microbial populations under environmental stress. Bifurcation analysis of the model and the interplay between Turing and Hopf instability is discussed. Theoretical and numerical investigation of the proposed model is presented to provide insight into the conditions that may lead to the extinction of the microbial population -- ecological suicide. A qualitative study of the proposed numerical schemes is presented. Numerical simulations are provided to support our theoretical observations.