Master´s thesis defense by Xingyu Zhang – Niels Bohr Institute - University of Copenhagen

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Master´s thesis defense by Xingyu Zhang

Title: Pattern formation by quorum sensing run-and-tumble bacteria

Genetically engineered bacteria to increase the tumbling frequency
of run-and-tumble motion for the higher local bacterial density form
visible stripe pattern composed of a successive high and low density
region as they grow and diffuse on an agar plate. Previously pro-
posed continuum models successfully reproduced the stripe patterns,
but the dynamics of the response of the individual cells to the quorum
sensing signal was not considered explicitly. In this thesis, starting
from a simple model of the regulation of the run-and-tumble motion
of a single bacterium, we propose a microscopic model based on the
stochastic differential equations to describe the state of the individual
cells. From this model, we further derive a macroscopic continuum
model that describes the distribution of the bacterial spatial density
and their internal states. Numerical simulation is performed on these
models to reproduce the stripe patterns. Finally we propose a sim-
plified two-state model that allows us to perform an analytical linear
stability analysis. We show that the time delay in the quorum-sensing
based regulation as well as the system size plays essential role in the
formation of the stripe pattern.