Date of Award

Spring 2014

Document Type


Degree Name

Doctor of Philosophy (PhD)


Computer Science

Committee Director

Stephan Olariu

Committee Member

Irwin Levinstein

Committee Member

Ravi Mukkamala

Committee Member

Michele C. Weigle

Committee Member

Holly Gaff


Because of the stochastic nature of biological systems, mathematical and computational modeling approaches have become more acceptable to experimentalists and clinicians in recent years as contributing to new understandings of complicated cell mechanisms and tissue physiology. Indeed, even single cell or small tissue samples are complex dynamic systems that adapt to environmental challenges in space and time which is poorly understood. Mathematical models and computer simulations can explain and uncover unknown aspects of cell behavior and tissue functions. Models based on key biological mechanisms can give interesting insights and formulate predictions that cannot be derived from physical experiments or statistical data alone. Therefore; novel research approaches should incorporate interdisciplinary dialogues between Biology, Mathematics and Computational Sciences to validate experimental data and non-intuitive scenarios such as the stem cell hypothesis. The tissue of a higher organism such as a human being can be described as a set of a large number of cells with certain functions and morphology. However, most of the mature cells are deprived of the potential to replenish themselves. Such imperfection of mature cells is compensated by the presence of a population of stem cells which possesses the capability to self renew and to differentiate into various cell lineages. This process of continual cell replacement, is called homeostasis, is critical for the maintenance of adult tissues, and is maintained through the presence of different control mechanisms. The homeostatic replacement: of cells varies substantially among different. tissues. Unquestionably, the most important ability of a stern cell is to maintain the homeostasis by continuously supplying specialized cells. The decision for an individual stem cell to either renew or differentiate can be described as a stochastic process. Several research programs supported by hospitals and health institutes are trying to understand the underlying mechanism of how stem cells proliferate, differentiate, and maintain equilibrium with or without feedback. At this stage researchers are not able to answer key questions, for example the rate of proliferation, stem cell homeostasis and feedback that plays a. crucial role in tissue equilibrium. This dissertation work is within the realm of Bioinformatics where computer scientists have to face more algorithmic challenges because of the huge amount of data with exception, numerous rules and conditions. This thesis attempts to present stochastic models which can predict stem cell growth, understand stem cell homeostasis characteristics, and formalize mathematical relationships of tissue lineage homeostasis.


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