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Mathematical Models in Cell Cycle Biology and Pulmonary Immunity

Buckalew, Richard L.
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1395242276

Abstract Details

2014, Doctor of Philosophy (PhD), Ohio University, Mathematics (Arts and Sciences).
Mathematical models are used to study two biological systems: pulmonary innate immunity and autonomous oscillation in yeast. In order to better understand the dynamics of an early infection of the lungs, we construct a predator-prey ODE model of pulmonary innate immunity which describes several observed properties of the pulmonary innate immune system. Under reasonable biological assumptions, the model predicts a single nontrivial equilibrium point with a stable and unstable manifold. Trajectories to one side of the stable manifold are asymptotic to the disease-free equilibrium and on the other side are unbounded in the size of the infection. The model also reproduces a phenomenon observed by Ben-David et al whereby the innate response to an infectious challenge reduces the ability of further infections to take hold. The model may be useful in analyzing and understanding time series data obtained by new methods in pathogen detection in ventilated patients. We also examine several models of autonomous oscillation in yeast (YAO), called the Immediate, Gap, and Mediated models. These models are based on a new concept of Response / Signaling (RS) coupled oscillator models, where feedback signaling and response are phase-dependent. In all three models, clustering of the type seen in YAO is a robust and generic phenomenon. The Gap and Mediated models add a dynamical delay, the latter by modeling a signaling agent present in the culture. For dense populations the Mediated model approximates the Immediate model, but the Mediated model includes dynamical quorum sensing where clustered solutions become stable through density-dependent bifurcations. A partial differential equations model is also examined, and we demonstrate existence and uniqueness of solutions for most parameter values.
Todd Young (Advisor)
Winfried Just (Committee Member)
Alexander Neiman (Committee Member)
Tatiana Savin (Committee Member)
82 p.
Applied Mathematics; Cellular Biology; Immunology
mathematical biology; cell cycle; pulmonary innate immunity; immunity; ODE model; PDE model; couples oscillators; VAP; ventilator associated pneumonia; autonomous oscillation; S cerevisiae; quorum sensing; cell cycle clustering; dynamical systems

Recommended Citations

Citations

  • Buckalew, R. L. (2014). Mathematical Models in Cell Cycle Biology and Pulmonary Immunity [Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1395242276

    APA Style (7th edition)

  • Buckalew, Richard. Mathematical Models in Cell Cycle Biology and Pulmonary Immunity. 2014. Ohio University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1395242276.

    MLA Style (8th edition)

  • Buckalew, Richard. "Mathematical Models in Cell Cycle Biology and Pulmonary Immunity." Doctoral dissertation, Ohio University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1395242276

    Chicago Manual of Style (17th edition)

ohiou1395242276
692
© 2014, some rights reserved.Creative Commons License Mathematical Models in Cell Cycle Biology and Pulmonary Immunity by Richard L. Buckalew is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Ohio University and OhioLINK.