Motility-induced patterning in quorum sensing bacteria

Thesis

Populations of bacteria regulate motility through chemical signalling to control emergent self-organisation. We investigate emergent behaviour in a population of bacteria whose motility is controlled through a type of chemical signalling called quorum sensing (QS). We develop a cell-level mathematical model that accounts for both QS and genetic regulation of motility. By systematically upscaling our model with the Fokker–Planck equation, we derive two multi-scale continuum models that describe the system at the population level. Our first model uses chemical structuring to capture genetic regulation of motility. We derive our second model by effectively averaging out the chemical structure, leading to a simpler reaction-diffusion system. Through analysis and simulation of both models, we characterise different types of emergent behaviour for various broad classes of gene-regulatory networks. Examples of emergent behaviour include motility-induced phase separation, spatio-temporal oscillations, and oscillator synchronisation. We investigate qualitative and quantitative differences between the two models in order to characterise situations where chemical structure is important. This comparison provides insight on the reliability of reaction-diffusion models for motile signalling bacteria, which should benefit future modelling efforts.

Authors: Ridgway, WJM

• DOI: 10.5287/ora-bd065k72z
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: emergent behaviour; self-organization; asymptotic analysis; motility-induced phase separation; quorum sensing
• Subjects: Applied mathematics