My work in this thesis is conducted in areas of developing mathematical models to study the swarming phenomenon of bacteria Pseudomonas aeruginosa and Myxococcus xanthus. I have developed mathematical models coupling continuum PDEs and stochastic models and used high-order accurate numerical methods for direct numerical simulations involving hydrodynamic flow.
Many bacteria including Pseudomonas aeruginosa use motility described as swarming to colonize surfaces and form biofilm. In experiments, we observed the development and propagation of cell waves (bright ring pattern) and formation of branched tendril patterns controlled by bacterial population and self-production of rhamnolipid. Biologically justified cell-based multiscale model simulations suggest a mechanism of wave propagation as well as a branched tendril formation at the edge of the population that depends upon competition between the changing viscosity of the bacterial liquid suspension and the liquid film boundary expansion caused by Marangoni forces. Therefore, cells uses surfactant rhamnolipid for controlling physical forces needed by swarm to efficiently expand over surfaces as a thin liquid film. Additionally, simulation results generated a hypothesis regarding how the cell wave forms. We hypothesize that the cell wave formation is due to increased cell division rate and rhamnolipid production rate and cell alignment. The model predictions of wave speed and swarm expansion rate as well as cell alignment in tendrils were confirmed experimentally.
Myxococcus xanthus undergoes multicellular aggregation and differentiation under starvation. Sporulation within the nascent fruiting body requires signaling between moving cells, in order that the rod-shaped cells differentiate at the appropriate time. The discrete stochastic off-lattice model is used to simulate the cell movement and cell-cell signaling pathway based on biological rules of Myxobacteria. The movement algorithms are justified by the biology of Myxobacteria which uses two motility engines known as Adventurous and Social motility as well as directional reversals. We also model C-signaling and sporulation by giving each cell a counter for C-signal and a state of being either a motile or non-motile spore. Simulations suggest that the fruiting bodies have a heterogeneous structure consisting of interconnected pockets of relative high and low density regions, which is in agreement with the pockets of spore clusters observed experimentally.