dc.contributor.author	Conrad, Emery David	en
dc.contributor.committeechair	Rogers, Robert C.	en
dc.contributor.committeecochair	Tyson, John J.	en
dc.contributor.committeemember	Renardy, Michael J.	en
dc.contributor.committeemember	Phillips, John B.	en
dc.contributor.committeemember	Laubenbacher, Reinhard C.	en
dc.contributor.department	Mathematics	en
dc.date.accessioned	2014-03-14T20:11:06Z	en
dc.date.adate	2006-05-10	en
dc.date.available	2014-03-14T20:11:06Z	en
dc.date.issued	2006-04-14	en
dc.date.rdate	2006-05-10	en
dc.date.sdate	2006-04-27	en
dc.description.abstract	Circadian rhythms are the endogenous, roughly 24-hour rhythms that coordinate an organism's interaction with its cycling environment. The molecular mechanism underlying this physiological process is a cell-autonomous oscillator comprised of a complex regulatory network of interacting DNA, RNA and proteins that is surprisingly conserved across many different species. It is not a trivial task to understand how the positive and negative feedback loops interact to generate an oscillator capable of a) maintaining a 24-hour rhythm in constant conditions; b) entraining to external light and temperature signals; c) responding to pulses of light in a rather particular, predictable manner; and d) compensating itself so that the period is relatively constant over a large range of temperatures, even for mutations that affect the basal period of oscillation. Mathematical modeling is a useful tool for dealing with such complexity, because it gives us an object that can be quickly probed and tested in lieu of the experiment or actual biological system. If we do a good job designing the model, it will help us to understand the biology better by predicting the outcome of future experiments. The difficulty lies in properly designing a model, a task that is made even more difficult by an acute lack of quantitative data. Thankfully, our qualitative understanding of a particular phenomenon, i.e. the observed physiology of the cell, can often be directly related to certain mathematical structures. Bifurcation analysis gives us a glimpse of these structures, and we can use these glimpses to build our models with greater confidence. In this dissertation, I will discuss the particular problem of the circadian clock and describe a number of new methods and tools related to bifurcation analysis. These tools can effectively be applied during the modeling process to build detailed models of biological regulatory with greater ease.	en
dc.description.degree	Ph. D.	en
dc.identifier.other	etd-04272006-110409	en
dc.identifier.sourceurl	http://scholar.lib.vt.edu/theses/available/etd-04272006-110409/	en
dc.identifier.uri	http://hdl.handle.net/10919/27378	en
dc.publisher	Virginia Tech	en
dc.relation.haspart	Fig_1_1_b_and_Fig_1_2_permissions.pdf	en
dc.relation.haspart	Fig_1_1_a_permissions.pdf	en
dc.relation.haspart	Fig_1_6_permissions_need_fax_too.pdf	en
dc.relation.haspart	Fig_1_5_permissions.pdf	en
dc.relation.haspart	phd_20060510.pdf	en
dc.rights	In Copyright	en
dc.rights.uri	http://rightsstatements.org/vocab/InC/1.0/	en
dc.subject	circadian rhythms	en
dc.subject	parameter optimization	en
dc.subject	bifurcation analysis	en
dc.title	Bifurcation Analysis and Qualitative Optimization of Models in Molecular Cell Biology with Applications to the Circadian Clock	en
dc.type	Dissertation	en
thesis.degree.discipline	Mathematics	en
thesis.degree.grantor	Virginia Polytechnic Institute and State University	en
thesis.degree.level	doctoral	en
thesis.degree.name	Ph. D.	en

Bifurcation Analysis and Qualitative Optimization of Models in Molecular Cell Biology with Applications to the Circadian Clock

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