Mathematical Modeling of Bacterial Crosstalk in a Dual Chamber Reactor

Abstract

Bacteria have the ability to communicate with each other or communicate with themselves. Crosstalk is the process in which multiple species of bacteria or strains of the same species use different signalling pathways to share a common signal or signals. The main focus of this thesis is on how bacterial crosstalk can be implemented into a working mathematical model to conduct research into its effects on a population, with a set of six ordinary differential equations. These equations describe an experimental device consisting of two chambers separated by a thin, porous membrane. Each chamber contains a distinct bacterial species, both of which utilize the same nutrient substrate and communicate via the same signal. Standard linearization techniques and stability theory illustrate the behaviours of three sub-models in correlation to the full model. Both Python and XPPAUT are used for phase-plane and sensitivity analysis to gather which model parameters have the greatest effect on the desired outcome. With focus on signal transport and a desired spatial effect, it is shown that the system can stably achieve mixed steady states (existence of down- and up-regulation co-currently) and coexistence of both bacteria is achieved.