Quantitative analysis for complex biological models using qualitative data: Applications in developmental biology
Abstract
Better understanding the many complex processes governing living organisms relies on the combination of efficient experimentation and careful consideration in a theoretical framework. Informed by experimental data, mathematical modeling offers many tools to aid comprehension of complex systems, providing critical support throughout biological sciences. However, the technical challenges to performing precise experiments and making many molecular measurements, all in fragile living systems, limit the ability to quantify data. Much biological data is instead qualitative, especially in fields such as developmental biology, which emphasizes imaging molecular distributions across many cells or whole tissues. In contrast with quantitative measurements, there is an absence of tools to incorporate information from these qualitative data into the mathematical models used to understand complex interactions, compare and distinguish hypotheses, predict behavior, and plan experiments. The work presented in this dissertation develops strategies to address the technical limitations to quantitative modeling with qualitative data, applied in the context of developmental biology. Two parallel objectives are discussed. The theoretical objective is the development of a parameter estimation procedure for complex models that accommodates qualitative information, based on existing qualitative and quantitative techniques. The biological objective is the elucidation of stem cell regulatory mechanisms through study of the Drosophila germarium, a stem cell niche in the ovary. Mathematical representations of the germarium system are formulated based on experimental evidence, and employed to evaluate the viability and potential effects of several proposed mechanisms. Through the newly developed parameter estimation procedure, multiple hypothetical mechanisms are compared based on a compilation of published qualitative data from wild type flies and genetic mutants. The extent to which these experiments can distinguish hypotheses is shown, and the quantitatively tuned models are used to estimate the utility of feasible future experiments to refine models and better discriminate among them. The framework and procedure developed herein offer benefits to many applications of mathematical modeling in biology, biotechnology and other fields where qualitative data are prevalent.
Degree
Ph.D.
Advisors
Umulis, Purdue University.
Subject Area
Biomedical engineering
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