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The Dynamical Basis of the Decanalization of Gene Expression in Kr uppel Mutant Embryos

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dc.contributor.advisor Reinitz, John en_US
dc.contributor.author Panok, Lena en_US
dc.contributor.other Department of Applied Mathematics and Statistics. en_US
dc.date.accessioned 2017-09-20T16:49:53Z
dc.date.available 2017-09-20T16:49:53Z
dc.date.issued 2013-12-01 en_US
dc.identifier.uri http://hdl.handle.net/11401/76271 en_US
dc.description 135 pg. en_US
dc.description.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 </italic>D.melanogaster</italic> 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 </italic>Kr<super>-<super></italic> data, correctly captures the wild type averaged data and the lowered gap gene expression in </italic>Kr<super>-<super></italic>. Through a dynamical analysis on a simplified version of this model, we investigate pattern formation in both wild type and </italic>Kr<super>-<super></italic>. The analysis is concentrated on the gap genes </italic>hb</italic>, </italic>Kr</italic>, </italic>gt</italic> and </italic>kni</italic> with outside input from maternal genes </italic>bcd</italic> and </italic>Cad</italic>. Canalization manifests itself in this model by producing a lower variance, in wild type, of posterior </italic>gt</italic> domain, in comparison to Bcd. </italic>Kr<super>-<super></italic> 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 </italic>Kr</italic>), we can smoothly turn down the function of </italic>Kr</italic> 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. en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Applied mathematics en_US
dc.subject.other canalization, dynamical analysis, pattern formation en_US
dc.title The Dynamical Basis of the Decanalization of Gene Expression in Kr uppel Mutant Embryos en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Green, David en_US
dc.contributor.committeemember Deng, Yuefan en_US
dc.contributor.committeemember Martens, Marco. en_US

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