Date of Award


Document Type

Open Access Dissertation



First Advisor

Qi Wang


Cells are fundamental units in all living organisms as all living organisms are made up of cells of different varieties. The study of cells is therefore an essential part of research in life science. Cells can be classified into two basic types: prokaryotic cells and eukaryotic cells. One typical organisms of prokaryotes is bacterium. And eukaryotes mainly consist of animal cells. In this thesis, we focus on developing predictive models mathematically to study bacteria colonies and animal cell mitotic dynamics.

Instead of living alone, bacteria usually survive in a biofilm, which is a microorganism where bacteria stick together by extracellular matrix primarily made up of extracellular polymeric substances (EPS) that the bacteria excrete. By treating the biofilm and solvent as a fluid mixture, we have developed a mathematical modeling framework and computational tool to investigate the mechanisms of biofilm formation and function. The bacteria in biofilms can be categorized into various types either by their persistence to antimicrobial treatments or by their reactions to quorum sensing molecules. We have studied dynamics of 3D heterogeneous biofilm formation under hydrodynamic stress, investigated the pros and cons of quorum sensing mechanism in an aqueous environment subject to hydrodynamic impact, explored the mechanism of antimicrobial persistence, looked into optimal dosing strategies, and examined the impact of cell motility on the development of biofilm morphology. As an integral part of the study, we have also validated our model of biofilm persistence to antimicrobial treatment against the experimental results obtained in our collaborators’ laboratory. Using the validated model, we then have probed the scenario of biofilm relapse after the antimicrobial treatment. These studies have demonstrated that our model and computational package can be an effective tool for analyzing the mechanism of biofilm formation and function.

During an eukaryotic cell cycle, mitosis is a process in which a mother cell divides into two genetically identical daughter cells. In the initial stage of mitosis, the mother cell, spreaded on a substrate, undergoes a dramatic shape change by detaching from the substance and forming a spherical shape. During the late stage of mitosis, a contractile ring forms on the cell division plane, splitting the mother cell into two identical daughter cells. This late stage of mitotic process is also known as cytokinesis for eukaryotic cells. We have developed a modeling framework for simulating the space-time evolution of cell morphology, cell motility and mitotic dynamics of eukaryotic cells by a multiphase field complex fluids approach. In order to solve the complex cellular dynamics models, we have developed a series of efficient, energy law preserving, stable schemes and implemented them on GPU clusters for high-performance computing. The models have shown qualitative agreement with experiments on cell rounding, movement, wrinkling, blebbing, and dividing processes.


© 2015, Jia Zhao

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Mathematics Commons