Date of Award

1-1-2012

Document Type

Campus Access Dissertation

Department

Mathematics

First Advisor

Qi Wang

Abstract

Biofilms form when bacteria adhere to surface in moist environments by excreting a slimy, glue-like substance. In nature, biofilms almost always consist of rich mixtures of many species of bacteria. Biofilms are held together by sugary molecular strands, collectively termed 'extracellular polymeric substances' or 'EPS'. The cells produce EPS and are held together by these stands, allowing them to develop complex, three-dimensional, resilient, attached communities.

In our binary (two components) model, we consider the bacteria and the EPS as one effective EPS network component and the solvent along with nutrient as another effective solvent component. We also extend our model to a quasi-ternary model, in which we model the bacteria and EPS network explicitly as two components along with the effective solvent as the third component. We further modify our model to study the bacteria pattern formation. In nature, bacteria are often found in biofilms or other bacterial colonies, which can grow into spectacular patterns visible under the microscope. Also in the laboratory, bacteria such as E. coli form regular geometric patterns like simple concentric rings and elaborate ordered form. The experimental evidence indicates that the pattern formation may be a consequence of a phase separation which is embedded in our model. By using a double well free energy density function and adding a logistic growth model, we found our model captures the pattern formation experiments very well qualitatively. We also added more features to our model like adhesion energy to simulate more realistic 3-D experiments. We use a finite difference scheme based on a 3-D cube geometry. The numerical scheme is implemented parallelly on graphics processing units (GPUs).

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