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Item Two central limit theorems and their application to the estimation of both parameters in the binomial distribution(Montana State University - Bozeman, College of Letters & Science, 1964) Alberda, Willis JohnItem Gene regulation in the lac operon(Montana State University - Bozeman, College of Letters & Science, 2009) Patterson, Kathryn Grace; Chairperson, Graduate Committee: Tomas GedeonThe lac operon, a jointly controlled series of genes in the bacteria E. coli, has been studied extensively since the 1940's. The lac operon genes are transcribed and then translated into proteins necessary for transport and digestion of lactose. The operon is activated in the presence of lactose after glucose, the preferred carbon source, has been expended. In this thesis, we introduce a biophysical model using the Shea-Ackers framework for modeling promoter dynamics. The model spans two scales: the inputs are biophysical parameters of molecular interactions and the result is a level of gene expression - a macroscopic behavior of the cell. We include all experimentally suggested control mechanisms into the model, even though the experimental evidence is stronger for some of these mechanisms than others. We compare our model to experimental data and explore the individual contribution of the proposed mechanisms by removing them one by one and testing the reduced model's fit to the data. Finally, we find a minimal model which faithfully represents the available data, yet includes only the minimal number of control mechanisms.