In this work, we propose a framework to develop testable hypotheses for the effects of changes in the experimental conditions on the dynamics of a biological system using mathematical models. We discuss the uncertainties present in this process and show how information from different experiment regimes can be used to identify a region in the parameter space over which subsequent mathematical analysis can be conducted. To determine the significance of variation in the parameters due to varying experimental conditions, we propose using sensitivity analysis. Using our framework, we hypothesize that the experimentally observed decrease in the survivability of bacterial populations of Xylella fastidiosa (causal agent of Pierce’s Disease) upon addition of zinc, might be because of starvation of the bacteria in the biofilm due to an inhibition of the diffusion of the nutrients through the extracellular matrix of the biofilm. We also show how sensitivity is related to uncertainty and identifiability; and how it can be used to drive analysis of dynamical systems, illustrating it by analyzing a model which simulates bursting oscillations in pancreatic β-cells. For sensitivity analysis, we use Sobol’ indices for which we provide algorithmic improvements towards computational efficiency. We also provide insights into the interpretation of Sobol’ indices, and consequently, define a notion of the importance of parameters in the context of inherently flexible biological systems. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2019. / April 16, 2019. / Bacterial growth, Dynamical systems, Mathematical modeling, Sensitivity analysis, Sobol Indices, Xylella fastidiosa / Includes bibliographical references. / Nick Cogan, Professor Co-Directing Thesis; M.Y. Hussaini, Professor Co-Directing Thesis; Eric Chicken, University Representative; Harsh Jain, Committee Member; Richard Bertram, Committee Member; Washington Mio, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_709711 |
| Contributors | Aggarwal, Manu (author), Cogan, Nicholas G. (Professor Co-Directing Thesis), Hussaini, M. Yousuff (Professor Co-Directing Thesis), Chicken, Eric (University Representative), Jain, Harsh Vardhan (Committee Member), Bertram, R. (Richard) (Committee Member), Mio, Washington (Committee Member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Mathematics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (126 pages), computer, application/pdf |
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