Type
Text
Type
Dissertation
Advisor
Green, David | Reinitz, John | Deng, Yuefan | Martens, Marco.
Date
2013-12-01
Keywords
Applied mathematics | canalization, dynamical analysis, pattern formation
Department
Department of Applied Mathematics and Statistics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76271
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
Canalization is the ability of an organism's phenotype to remain stable under a perturbation in their genotype or the environment. It has been noted that there is no canalization or canalization is to a much smaller degree in mutants than in wild type. Waddington's idea was to understand canalization through studying gene interactions. We investigate the mechanisms of canalization of gap gene patterns in D.melanogaster through dynamical analysis of the gene circuit. To carry out this investigation we construct a dynamical model of the evolution of the concentration of protein products of the gap genes in time. Our model, which is fitted to both wild type and Kr- data, correctly captures the wild type averaged data and the lowered gap gene expression in Kr-. Through a dynamical analysis on a simplified version of this model, we investigate pattern formation in both wild type and Kr-. The analysis is concentrated on the gap genes hb, Kr, gt and kni with outside input from maternal genes bcd and Cad. Canalization manifests itself in this model by producing a lower variance, in wild type, of posterior gt domain, in comparison to Bcd. Kr- mutants do not canalize Bcd perturbation. We find the geometric structure that ensures the canalization in wild type. This structure is an unstable manifold that patterns the posterior of the wild type embryos while remaining invariant with respect to changes in Bcd. By continuously changing one parameter in our model (maximum synthesis rate of Kr), we can smoothly turn down the function of Kr in such a way as to model an allelic series running from homozygous wild type levels to heterozygous, and then to hypomorphic and finally to functional null. We discovered that that there is an abrupt onset of the mutant phenotype and loss of canalization triggered by the loss of the canalizing unstable manifold. | 135 pages
Recommended Citation
Panok, Lena, "The Dynamical Basis of the Decanalization of Gene Expression in Kr uppel Mutant Embryos" (2013). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2199.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2199